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The Publishers and the Authors will be grateful to 
any of the readers of this volume who will kindly call 
their attention to any errors of omission or of commis- 
sion that they may find therein. It is intended to make 
our publications standard works of study and reference, 
and, to that end, the greatest accuracy is sought. It 
rarely happens that the early editions of works of any 
size are frqe from errors; but it is the endeavor of the 
Publishers to have them removed immediately upon bemg 
discovered, and it is therefore desired that the Authors 
may be aided in their task of revision, from time to time, 
by the kindly criticism of their readers. 

JOHN WILEY & SONS, Inc. 
432 4th Avenue. 



WORKS OF WILLIAM KENT 



PUBLISHED BY 



JOHN WILEY & SONS. 



The Mechanical Engineers' Pocket-Book. 

A Reference Book of Rules, Tables, Data, and 
Formulae, for the Use of Engineers, Mechanics, 
and Students. Ninth edition. Thoroughly 
revised with the assistance of Robert T. Kent. 
xlv + 1526 pages, 4 by 6 %. Leather, $5.00 net. 

S team-Boiler Economy. 

A treatise on the Theory and Practice of Fuel 
Economy in the Operation of S team-Boilers. 
Second edition, 1915. xvii + 717 pages, 6 by 9, 
287 figures, cloth, $4.50 net. 



Investigating an Industry. 

A Scientific Diagnosis of the Diseases of Man- 
agement. With an introduction by Henry L. 
Gantt, author of " Work, Wages and Profits." 
xi + 126 pages, 5 by 7^4, cloth, $1.00 net. 



THE 



MECHANICAL ENGINEERS' 
POCKET-BOOK. - 



A REFERENCE'BOOK OF RULES, TABLES, 
DATA, AND FORMULAE. 



WILLIAM KENT, M. E., Sc.D., 

Consulting Engineer. 
Member Arii£r. Soc'y Mechl. Engrs. and Amer. Inst, Mining Engrs, 



NINTH EDITION, THOROUGHLY REVISED 

WITH THE ASSISTANCE OF 

ROBERT THURSTON KENT, M. E., 

Consulting Engineer. 
Junior American Society of Mechanical Engineers, 



TOTAL ISSUE, ONE HUNDRED AND EIGHT THOUSAND* 



NEW YORK 

JOHN WILEY & SONS, Inc. 

London: CHAPMAN & HALL, Limited 

1916 



-<-\^'' 

"xV k 



i::- 



xV 



s^'^%> 



Copyright, 1895, 1902, 1910, 1915, 

' BY 

WILLIAM KENT. 



Eighth Edition entered at Stationers' Hall. 



)CI,A4180'4G ^ 



Composition and Electrotyping by the StanhopB Press, Boston, Mass., and 

the Publishers Printing Company, New York. 

Printing and Binding by Braunworth & Company, Brooklyn, N. Y. 



QEC 14 1915 



, PREFACE TO THE NINTH EDITION. 

r NOVEMBER, 1915. 

Since the eighth edition was published, five years ago, there have 
been notable advances in many branches of engineering, rendering 
jobsolete portions of the book which at that time were in accord with 
^practice. In addition, many engineering standards have been changed 
^during the five-year period, necessitating a thorough revision of many 
sections of the work. The absolutely necessary revisions to bring the 
'book up to date have involved changes in over 400 pages of the eighth 
' edition, and the addition of over 150 pages of new matter. The 
treatment of many subjects in the earUer edition has been condensed 
into smaller space to enable the insertion of the new matter without 
increasing the size of the book to unwieldy proportions. Extensive 
revisions have been made in the subjects' of materials, mechanics, 
fans and blowers, heating and ventilation, fuel, steam-boilers and 
engines, and steam-turbines. The chapter on machine-shop practice 
has been rewritten and doubled in size, and now covers many subjects 
which were omitted in earlier editions. The new matter includes 
many data on planing, milhng, drilUng and grinding, together with 
an elaborate treatment of the subject of macliine-tool driving. The 
subject of electrical engineering has been completely rewritten and 
brought into agreement with present practice. Of the new tables 
added the following are considered of special importance. Square 
roots of fifth powers; Four-place logarithms; Standard sizes of welded 
steel pipe; Standard pipe flanges; Properties of wire rope; Fire brick 
and other refractories; Properties of structural sections and columns; 
Chemical standards for iron castings; Flow of air, water and steam; 
Analyses and heating values of coals; Rankine efficiency; CooUng 
towers; Properties of ammonia; Power required for driving machine 
tools of all types, both singly and in groups; Electric resistance and 
conductivity of wires; Street railway installation; Electric lamp char- 
acteristics; Illuminating data. 



ui 



IV PREFACE. 



ABSTRACT FROM PREFACE TO THE 
FIRST EDITION, 1895. 

More than twenty years ago the author began to follow the advice 
given by Nystrom: " Every engineer should make his own pocket-book, 
as he proceeds in study and practice, to suit his particular business." 
The manuscript pocket-book thus begun, however, soon gave place to 
more modern means for disposing of the accumulation of engineering 
facts and figures, viz., the index rerum, the scrap-book, the collection of 
indexed envelopes, portfolios and boxes, the card catalogue, etc. Four 
years ago, at the request of the publishers, the labor was begun of selecting 
from this accum.ulated mass such matter as pertained to mechanical 
engineering, and of condensing, digesting, and arranging it in form for 
publication. In addition to this, a careful examination was made of the 
transactions of engineering societies, and of the most important recent 
works on mechanical engineering, in order to fill gaps that might be left 
in the original collection, and insure that no important facts had been 
overlooked. 

Some ideas have been kept in mind during the preparation of the 
Pocket-book that will, it is believed, cause it to differ from other works 
of its class. In the first place it was considered that the field of mechani- 
cal engineering was so great, and the literature of the subject so vast, that 
as little space as possible should be given to subjects which especially 
belong to civil engineering. While the mechanical engineer must con- 
tinuklly deal with problems which belong properly to civil engineering, 
this latter branch is so well covered by Traut wine's " Civil Engineer's 
Pocket-book " that any attempt, to treat it exhaustively would not only 
fill no " long-felt want," but would occupy space which should be given 
to mechanical engineering. 

Another idea prominently kept in view by the author has been that he 
would not assume the position of an " authority " in giving rules and 
formulae for designing, but only that of compiler, giving not only the 
name of the originator of the rule, where it was known, but also the volume 
and page from which it was taken, so that its derivation may be traced 
when desired. When different formulae for the same problem have been 
found they have been given in contrast, and in many cases examples 
have been calculated by each to show the difference between them. In 
some cases these differences are quite remarkable, as will be seen under 
Safety-valves and Crank-pins. Occasionally the study of these differences 
has led to the author's devising a new formula, in which case the deriva- 
tion of the formula is given. 

Much attention has been paid to the abstracting of data of experiments 
from recent periodical literature, and numerous references to other data 
are given. In this respect the present work will be found to differ from 
other Pocket-books. 

The author desires to express liis obligation to the many persons who 
have assisted him in the preparation of the work, to manufacturers who 



PREFACE. V 

have furnished their catalogues and given permission for the use of their 
tables, and to many engineers who have contributed original data and 
tables. The names of these persons are mentioned in their proper places 
in the text, and in all cases it has been endeavored to give credit to whom 

credit is due. 

WiLLL^^ Kent. 



PREFACE TO THE EIGHTH EDITION. 

SEPTEMBER, 1910. 

During the first ten years following the issue of the first edition of this 
book, in 1895, the attempt was made to keep it up to date by the method 
of cutting out pages and paragraphs, inserting new ones in their places, by 
inserting new pages lettered a, b, c, etc., and by putting some new matter 
in an appendix. In this way the book passed to its 7th edition in October, 
1904. After 50,000 copies had been printed it was found that the electro- 
typed plates were beginning to wear out, so that extensive resetting of type 
would soon be necessary. The advances in engineering practice also had 
been so great that it was evident that many chapters required to be entirely 
rewritten. It was therefore determined to make a thorough revision of the 
book, and to reset the type throughout. This has now been accomplished 
after four years of hard labor. The size of the book has increased over 300 
pages, in spite of all efforts to save space by condensation and elision of 
much of the old matter and by resetting many of the tables and formulae 
in shorter form. A new style of type for the tables has been designed for 
the book, which is believed to be much more easily read than the old. 

The thanks of the author are due to many manufacturers who have fur- 
nished new tables of materials and machines, and to many engineers who 
have made valuable contributions and helpful suggestions. He is especially 
indebted to his son, Robert Thurston Kent, M.E., who has done the work 
of revising manufacturers' tables of materials and has done practically all 
of the revising of the subjects of Compressed Air, Fans and Blowers, Hoist- 
ing and Conveying, and Machine Shop. 



CONTENTS. 

(For Alphabetical Index see page 1479.) 



MATHEMATICS. 

Arithmetic. 



PAGE 



Arithmetical and Algebraical Signs 1 

Greatest Common Divisor 2 

Least Common Multiple 2 

Fractions 3 

tIw?''^ Decimal EqiiiValents of Fractions oVOnW Inch'. '. ". :'...: | 

Table Products of Fractions expressed m Decimals 4 

Compound or Denominate Numbers _ 

Reduction Descending and Ascending . ^ 

Decimals of a Foot Equivalent to Fractions of an Inch | 

Ratio and Proportion ..-..•• 7 

Involution, or Powers of Numbers .. . . .... . . ... •••••• 7 

Table First Nine Powers of the First Nine Numbers 7 

Table. First Forty Powers of 2 g 

Evolution. Square Root g 

Cube Root 9 

Alligation 10 

Permutation ^0 

Combination 1q 

Arithmetical Progression .^ 

Geometrical Progression ..-.. •. . 2 

Percentage, Profit and Loss, Efficiency J| 

Interest 13 

Discount 13 

Compound Interest •.••••••;•••••,• w •• ' • ' ; 14 

Compound Interest Table, 3, 4, 5, and 6 per cent 1| 

Equation of Payments 14 

Partial Payments ','.'..[ 15 

T^bles^ of Amount,' Present Values,' etc.'. 'of 'Annuities 15 

Weights and Measures. 

Long Measure 17 

Old Land Measure j7 

Nautical Measure Ig 

Square Measure Ig 

SoUd or Cubic Measure Ig 

Liquid Measure Ig 

The Miners' Inch Ig 

Apothecaries' Fluid Measure ^^ 

Dry Measure 19 

Shipping Measure 19 

Avoirdupois Weight 19 

Troy Weight 20 

Apothecaries' Weight / W i " U' 20 

To Weigh Correctly on an Incorrect Balance ^^ 

Circular Measure 20 

Measure of Time 

vii 



Till CONTENTS. 



Board and Timber IVIeasure 

Table. Contents in Feet of Joists, Scantlings, and Timber. . . . 

French or Metric Measures 

British and French Equivalents 

Metric Conversion Tables 

Compound Units 

of Pressure and Weight 

of Water, Weight and Bulk 

of Air, Weight and A'olume 

of Work, Power, and Duty 

of Velocity 

Wire and Sheet Metal Gages 

Circular-mil AVire Gage 29, 30 

U. S. Standard Wire and Sheet Gage (1893) 29, 32 

Twist-drill and Steel-wire Gages 31 

Decimal Gage 32 

Algebra. 

Addition, Multiplication, etc 

Powers of Numbers 

Parentheses, Division 

Simple Equations and Problems 

Equations containing two or more Unknown Quantities 

Elimination 

Quadratic Equations 

Theory of Exponents 

Binominal Theorem 

Oeometrical Problems of Construction 

of Straight Lines 

of Angles 

of Circles 

of Triangles 

of Squares and Polygons 

of the Ellipse 

of the Parabola 

of the Hyperbola 

of the Cycloid ^ 

of the Tractrix or Schiele Anti-friction Curve 

of the Spiral ' 

of Rings inside a Circle 

of Arc of a Large Circle 

of the Catenary 

of the Involute 

of plotting Angles 

Geometrical Propositions 

Degree of a Railway Curve 

Mensuration, Plane Surfaces. 

Quadrilateral, Parallelogram, etc 

Trapezium and Trapezoid 

Triangles 

Polygons. Table of Polygons 

Irregular Figures 

Properties of the Circle 

Values of it and its Multiples, etc 

Relations of arc, chord, etc 

Relations of circle to inscribed square, etc 

Formulae for a Circular Curve 

Sectors and Segments 

Circular Ring 

The Ellipse 

The Helix 

The Spiral 

Surfaces and Volumes of Similar Solids 



CONTENTS. IX 

Mensuration, Solid Bodies. page 

Prism . 62 

Pyramid 62 

Wedge : . . . 62 

Kectangular Prismoid 62 

Cylinder 62 

Cone 62 

Sphere 62 

Spherical Triangle • 63 

Spherical Polygon 63 

The Prismoid 63 

The Prismoidal Formula 63 

Polyedron 63 

Spherical Zone 64 

Spherical Segment 64 

Spheroid or ElHpsoid 64 

Cylindrical Ring 64 

Solids of Revolution 64 

Spindles 64 

Frustum of a Spheroid 64 

Parabolic Conoid 65 

Volume of a Cask 65 

Irregular Solids 65 

Plane Trigonometry. 

Solution of Plane Triangles 66 

Sine, Tangent, Secant, etc 66 

Signs of the Trigonometric Functions 67 

Trigonometrical Formulae 68 

Solution of Plane Right-angled Triangles 69 

Solution of Oblique-angled Triangles 69 

Analytical Geometry. 

Ordinates and Abscissas ; 70 

Equations of a Straight Line, Intersections, etc 70 

Equations of the Circle ' 71 

Equations of the Ellipse 71 

Equations of the Parabola 72 

Equations of the Hyperbola 72 

Logarithmic Curves 73 

Differential Calculus. 

Definitions 73 

Differentials of Algebraic Functions 74 

Formulae for Differentiating 74 

Partial Differentials 75 

Integrals 75 

Formulae for Integration 75 

Integration between Limits 76 

Quadrature of a Plane Surface 76 

Quadrature of Surfaces of Revolution 77 

Cubature of Volumes of Revolution 77 

Second, Third, etc., Differentials 77 

IVIaclaurin's and Taylor's Theorems 78 

INIaxima and Minima 78 

Differential of an Exponential Function 79 

Logarithms 79 

Differential Forms which have Known Integrals 80 

Exponential Functions 80 

Circular Functions 81 

The Cycloid 81 

Integral Calculus 82 



X CONTENTS. 

The Slide Rule. 

PAGE 

Examples solved by the SUde Rule 82 

Logarithmic Ruled Paper. 

Plotting on Logarithmic Paper 2 84 

Mathematical Tables. 

Formula for Interpolation 86 

Reciprocals of Numbers 1 to 2000 87 

Squares, Cubes, Square Roots and Cube Roots from 0.1 to 1600 93 

Squares and Cubes of Decimals 108 

Fifth Roots and Fifth Powers 109 

Square Roots of Fifth Powers of Pipe Sizes 110 

Circumferences and Areas of Circles Ill 

Circumferences of Circles in Feet and Inches from 1 inch to 32 

feet 1 1 inches in diameter 120 

Areas of the Segments of a Circle 121 

Lengths of Circular Arcs, Degrees Given 122 

Lengths of Circular Arcs, Height of Arc Given 124 

Circles and Squares of Equal Area 125 

Number of Circles Inscribed within a Large Circle 125 

Spheres 126 

Square Feet in Plates 3 to 32 feet long and 1 inch wide 128 

Gallons in a Number of Cubic Feet 130 

Cubic Feet in a Number of Gallons 130 

Contents of Pipes and Cylinders, Cubic Feet and Gallons 131 

Cylindrical Vessels, Tanks, Cisterns, etc 132 

Capacities of Rectangular Tanks in Gallons 133 

Number of Barrels in Cylindrical Cisterns and Tanks 134 

Logarithms 135 

Table of Logarithms 137 

Hyperbolic Logarithms 164 

Four-place Logarithms of Numbers from 1 to 1000 167 

Natural Trigonometric Fimctions 169 

Logarithmic Trigonometric Functions 172 

Materials. 

Chemical Elements 173 

Specific Gravity and Weight of ]Materials 173 

The Hydrometer 175 

Metals, Properties of 177 

Aluminum 177 

Antimony 177 

Bismuth 178 

Cadmium 178 

Copper 178 

Gold 178 

Iridium 178 

Iron 178 

Lead 178 

Magnesium 179 

Manganese 179 

Mercury 179 

Nickel 179 

Platinum 179 

Silver 179 

Tin 179 

Zinc 179 

Miscellaneous Materials. 

Order of Malleability, etc., of Aletals 180 

Measures and Weights of Various Materials 180 



CONTENTS. XI 

PAGE 

Pormulae and Table for Weight of Rods, Plates, etc 181 

Commercial Sizes of Iron and Steel Bars 182 

Weights of Iron and Steel Sheets 183 

of Iron Bars 184 

of Roimd Steel Bars ^ 185 

of Fillets 185 

of Romid, Square, and Hexagon Steel 186 

of Plate Iron 187 

of Flat Rolled Iron 188 

of Steel Blooms 190 

of Roofing Materials 191-196 

Snow and Wind Loads on Roofs 191 

Roof Construction 191 

Specifications for Tin and Terne Plates 194 

Corrugated Sheets 194 

Weights and Thickness of Cast-iron Pipe 196-199 

Weights of Cast-iron Pipe Columns 200 

Weight of Open-end Cast-iron Cylinders 200 

Standard Sizes of Welded Pipe 201-205 

Weight and Bursting Strength of Welded Pipe 205 

Tubular Electric Line Poles 206 

Protective Coatings for Pipes 206 

Valves and Fittings 206-217 

Standard Pipe Flanges 208-212 

Forged Steel Flanges 211 

Standard Hose Couplings 218 

Wooden Stave Pipe 218 

Riveted Hydraulic Pipe 219 

Riveted Iron Pipes 220 

Spiral Riveted Pipe 220 

Weight of Steel for Riveted Pipe 221 

Bent and Coiled Pipes 221 

Flexibility of Pipe Bends 221 

Shelby Cold-drawn Steel Tubing 222 

Seamless Brass and Copper Tubes 224, 225 

Aluminum Tubing 226 

Lead and Tin-lined Lead Pipe 226 

Iron Pipe Lined with Tin, Lead, Brass, and Copper 227 

Weight of Sheet and Bar Brass 228 

of Sheet Zinc 228 

of Copper and Brass Wire and Plates 229 

of Aluminum Sheets, Bars, and Plates 230 

of Copper Rods 230 

Screw-threads, U. S. Standard 231 

Whitworth Screw-threads 232 

Limit-gages for Screw-threads 232 

Automobile Screws and Nuts 233 

International Screw-thread 233 

Acme Screw-thread 234 

Machine Screws, A. S. M. E. Standard 234 

Standard Taps 235 

Wood Screws 236 

Machine Screw Heads 237 

Set Screws and Cap Screws 238 

Weights of Rivets 238, 239 

Shearing Value of Rivets. Bearing Value of Riveted Plates 240 

Length of Rivets for Various Grips 241 

Lag Screws 241 

Weight of Bolts with Square Heads and Nuts 242 

Washers 242, 243 

Hanger Bolts 243 

Tumbuckles 243 

Track Bolts 244 

Cut Nails 244 

Material Required per Mile of Railroad Track 245 

Wire Nails 246 

Spikes , , , , 248 



Xll CONTENTS. 

PAGE 

Wires of Different Metals 248 

Steel Wire, Size, Strength, etc 249 

Piano Wire 250 

Telegraph Wire 250-252 

Plow-steel Wire 250, 258 

Galvanized Iron Wire 250 

Copper Wire, Bare and Insulated 251, 252 

Notes on Wire Rope 253 

Wire Rope Tables 255-262 

Varieties and Uses of Wire Rope 256 

Splicing of Wire Ropes 263 

Chains and Chain Cables 264 

Sizes of Fire Brick 266 

Refractoriness of American Fire-brick 268 

Slag Bricks and Slag Blocks 268 

Magnesia Bricks 269 

Fire Clay Analysis 269 

Zirconia 270 

Asbestos V 270 

Standard Cross-sections of Materials, for Draftsmen 271 

Strength of Materials. 

Stress and Strain 272 

Elastic Limit 273 

Yield Point 273 

Modulus of Elasticity 274 

Resilience 274 

Elastic Limit and Ultimate Stress 275 

Repeated Stresses 275 

Repeated Shocks 276 

Stresses due to Sudden Shocks • 278 

Tensile Strength 278 

Measurement of Elongation 279 

Shapes of Test Specimens 280 

Increasing Tensile Strength of Bars by Twisting 280 

Compressive Strength 281 

Columns. Pillars, or Struts 283 

Hodgkinson's Formula. Euler's Formula 283 

Gordon's Formula. Rankine's Formula 284 

Wrought-iron Columns 285 

Built Columns 285-286 

The Straight-line Formula 285 

Comparison of Column Formulae 286 

Tests of Large Built Steel Columns 287 

Working Strains in Bridge ]M embers 287 

Strength of Cast-iron Columns 289 

Safe Load on Cast-iron Columns 291 

Strength of Brackets on Cast-iron Columns 292 

Moment of Inertia 293 

Radius of Gyration 293 

Elements of Usual Sections 294 

Eccentric Loading of Columns 296 

Transverse Strength 297 

Formulae for Flexure of Beams 297 

Safe Loads on Steel Beams 298, 309 

Beams of Uniform Strength 301 

Dimensions and Weights of Structural Steel Sections 302 

Allowable Tension in Steel Bars 305 

Properties of Rolled Structural Shapes 305 

" Steel I-Beams 307 

** Steel Wrought Plates 308 

" Corrugated Plates 310 

Spacing of Steel I-Beams 311 

Properties of Steel Channels 312 

" T Shapes 313 



CONTENTS. XIU 

PAGE 

Properties of Angles 316 

" Z-bars 317 

Rivet Spacing for Structural Work 321 

Dimensions and Safe Load on Built Steel Columns 323-330 

Bethlehem Girder and I-beams and H-columns 331 

,. Torsional Strength 334 

Elastic Resistance to Torsion 334 

Combined Stresses 335 

Stress due to Temperature 335 

Strength of Plat Plates 336 

Thickness of Flat Cast-iron Plates 336 

Strength of Unstayed Flat Siu-faces 337 

Unbraced Heads of Boilers 337 

Strength of Stayed Surfaces 338 

Stresses in Steel Plating under Water Pressure 338 

Spherical Shells and Domed Heads 339 

Thick Hollow Cylinders under Tension 339 

,i, Thin Cylinders under Tension 340 

Carrying Capacity of Steel Rollers and Balls 340 

Resistance of Hollow Cylinders to Collapse 341, 343 

Formula for Corrugated Furnaces 342 

Hollow Copper Balls 345 

Holding Power of Nails, Spikes, Bolts, and Screws 346 

Cut versus W^ire Nails 347 

Strength of Bolts 347 

Initial Strain on Bolts 347 

Strength of Chains 348 

Stand Pipes and their Design 349 

Riveted Steel Water-pipes ^51 

Kirkaldy's Tests of Materials 352-358 

^ Cast Iron 352 

Iron Castings 352 

Iron Bars, Forgings, etc 352 

Steel Rails and Tires 353 

Spring Steel, Steel Axles, Shafts 354 

Riveted Joints, Welds 355 

Copper, Brass, Bronze, etc 356 

Wire-rope 356 

Wire 357 

Ropes, Hemp, and Cotton 357 

Belting, Canvas 357 

Stones 357 

Brick, Cement, W^ood 358 

Tensile Strength of Wire 358 

Watertown Testing-machine Tests 359 

'' Riveted Joints 359 

Wrought-iron Bars, Compression Tests 359 

I Steel Eye-bars * 360 

Wrought-iron Columns 360 

Cold Drawn Steel 361 

j Tests of Steel Angles 362 

I Shearing Strength 362 

I Relation of Shearing to Tensile Strength 362 

; Strength of Iron and Steel Pipe 363 

Threading Tests of Pipe ^ 363 

1 Old Tubes used as Columns 363 

Methods of Testing Hardness of Metals 364 

Holding Power of Boiler-tubes 364 

i Strength of Glass 365 

Strength of Ice 366 

Strength of Timber 366 

Expansion of Timber 367, 369 

Tests of American Woods 367 

Shearing Strength of Woods 367 

Copper at High Temperatures 368 

Drying of Wood 368 

Preservation of Timber 368 



XIV CONTENTS. 

PAGE 

Copper Castings of High Conductivity 368 

Tensile Strength of Rolled Zinc Plates 369 

Strength of Brick, Stone, etc ..." 369 

" Lime and Cement Mortar 372 

" Flagging 373 

Tests of Portland Cement 373 ' 

ModuU of Elasticity of Various Materials 374 

Factors of Safety 374 

Properties of Cork 377 

Vulcanized India-Rubber 378 

Specifications for Air Hose 379 

Nickel 379 

Aluminum, Properties and Uses 380 

Alloys. 

Alloys of Copper and Tin, Bronze 384 

Alloys of Copper and Zinc, Brass 386 

Variation in Strength of Bronze 386 

Copper-tin-zinc Alloys 387 

Liquation or Separation of Metals 388 

Alloys used in Brass Foundries = 390 

Tobin Bronze 392 

Qualities of Miscellaneous Alloys 392 

Copper-zinc-iron Alloys 393 

' Alloys of Copper, Tin, and Lead 394 

Phosphor Bronze 394 

Alloys for Casting under Pressure 395 

Aluminum Alloys 396 

Caution as to Strength of Alloys 398 

Alloys of Aluminum, SiUcon, and Iron 398 

Tungsten-aluminum Alloys 399 

The Thermit Process 400 

Aluminum-tin Alloys 400 

Manganese Alloys 401 

JManganese Bronze 401 

German Silver 402 

IMonel Metal 403 

Copper-nickel Alloys • 403 

Alloys of Bismuth 404 

Fusible Alloys 404 

Bearing Metal Alloys 405 

Bearing Metal Practice, 1907 407 

White iNIetal for Engine Bearings 407 

Alloys containing Antimony '. 407 , 

White-metal Alloys 407 

Babbitt Metals 407, 408 

Type-metal 408 

Solders 409 

Ropes and Cables. 

Strength of Hemp, Iron, and Steel Ropes 410 

Rope for Hoisting or Transmission 411 

Cordage, Technical Terms of 411 

Splicing of Ropes 412 

Cargo Hoisting 414 

Working Loads for Manila Rope 414 

Knots 415 

Life of Hoisting and Transmission Rope 415; 

Efficiency of Rope Tackles 4ir 

Springs. 

Laminated Steel Springs 417 

HeUcal Steel Springs 418 



CONTENTS. XV 

PAGE 

Carrying Capacity of Springs 419 

Elliptical Springs 423 

Springs to Resist Torsional Force 423 

Phosphor-bronze Springs 424 

Chromium-Vanadium Spring Steel 424 

Test of a Vanadium Steel Spring 424 

Riveted Joints. 

Fairbaim's Experiments 424 

Loss of Strength by Punching 424 

Strength of Perforated Plates 424 

Hand versus Hydraulic Riveting 424 

Formulae for Pitch of Rivets 427, 434 

Proportions of Joints 427 

Efficiencies of Joints 428 

Diameter of Rivets 429 

Shearing Resistance of Rivet Iron and Steel 430 

Strength of Riveted Joints 431 

Riveting Pressures 435 

Tests of Soft Steel Rivets 435 

Iron and Steel. 

Classification of Iron and Steel 436 

Grading of Pig Iron 437 

Manufacture of Cast Iron 437 

Influence of Silicon Sulphur, Phos. and Mn on Cast Iron 438 

Microscopic Constituents 439 

Analyses of Cast Iron 439 

Specifications for Pig Iron and Castings 441, 443 

Specifications for Cast-iron Pipe 441 

Chemical Standards for Castings 441 

Strength of Cast Iron 444, 451 

Strength in Relation to Cross-section 446, 447 

"Semi-steel" 446, 453 

Shrinkage of Cast Iron 447 

White Iron Converted into Gray 448 

Mobility of Molecules of Cast Iron 449 

Expansion of Iron by Heat 449, 465 

Permanent Expansion of Cast Iron by Heating 449 

Castings from Blast Furnace Metal 450 

Effect of Cupola Melting 450 

Additions of Titanium, etc., to Cast Iron 450, 451 

Mixture of Cast Iron with Steel 453 

Bessemerized Cast Iron 453 

Bad Cast Iron 453 

Malleable Cast Iron 454 

Design of Malleable Castings 457 

Specifications of Malleable Iron 457 

Strength of Malleable Cast Iron 458 

Wrought Iron 459 

Chemistry of Wrought Iron 460 

Electrolytic Iron 460 

Infiuence of Rolling on Wrought Iron 460 

Specifications for Wrought Iron 461 

Stay-bolt Iron 462 

Tenacity of Iron at High Temperatures 463 

Effect of Cold on Strength of Iron 464 

Durability of Cast Iron 465 

Corrosion of Iron and Steel 466 

Corrosion of Iron and Steel Pipes 467 

Electrolytic Theory, and Prevention of Corrosion 468 

^Chrome Paints, Anti-corrosive 469 

Corrosion Caused by Stray Electric Currents 470 

Electrolytic Corrosion due to Overstrain 470 



XVI CONTENTS. 

PAGE 

Preservative Coatings, Paints, etc ^ 471 

Inoxydation Processes, Bower-Barfl, etc 472 

Aluminum Coatings 473 

Galvanizing 473 

Sherardizing, Galvanizing by Cementation 474 

Lead Coatings 474 

Steel. 

Manufacture of Steel 475 

Crucible, Bessemer, and Open Hearth Steel 475 

Relation between Chemical and Physical Properties 476 

Electric Conductivity 477 

*' Armco Ingot Iron " 477 

Variation in Strength 477, 478 

Bending Tests of Steel 478 t 

Effect of Heat Treatment and of Work 478 1 

Hardening Soft Steel 479 F 

Effect of Cold Rolling 479 L 

Comparison of Full-sized and SmaU Pieces 480 

Recalescence of Steel 480 

Critical Point 480 

Metallography 480 

Burning, Overheating, and Restoring Steel 481 

Working Steel at a Blue Heat 482 

Oil Tempering and Anneahng 482 

Brittleness due to Long-continued Heating 483 

Influence of Annealing upon Magnetic Capacity 483 

Treatment of Structural Steel 483 

May Carbon be Burned out of Steel? 485 

Effect of Nicking a Bar 485 ' 

Dangerous Low Carbon Steel 486 . 

Specific Gravity 486 *^ 

Occasional Failures 486 

Segregation in Ingots and Plates 487 

Endurance of Steel under Repeated Stresses 487 

Yielding of Steel 488 

The Thermit Welding Process 488 

Oxy-acetylene Welding and Cutting of Metals 488 

Hydraulic Forging ' 488 

Fluid-compressed Steel 488 < 

Steel Castings 489 1} 

Crucible Steel 490 i 

Effect of Heat on Grain 491 ' 

Heating and Forging 491 ; 

Tempering Steel 493 t* 

Kinds of Steel used for Different Purposes 494 * 

High-speed Tool Steel 494 

Manganese Steel 494 

Chrome Steel 496 , 

Aluminum Steel 496 

Tungsten Steel 496 

Nickel Steel 497 \ 

Copper Steel 499 f 

Nickel-Vanadium Steel 499 * 

Static and Dynamic Properties of Steel » . 500 

Strength and Fatigue Resistance of Steels 501 

Chromium- Vanadium Steel 502 

Heat Treatment of Alloy Steels 502, 503 

Specifications for Steel 504-511 

High-strength Steel for Shipbuilding 507 

Fire-box Steel 508 

Steel Rails 508 



MECHANICS. 

Matter, Weight, Mass 511 

Force, Unit of Force 512 



5 



CONTENTS. XVll 

PAGE 

Local Weight 512 

Inertia 513 

Newton's Laws of Motion 513 

Resolution of Forces 513 

Parallelogram of Forces 513 

Moment of a Force 514 

Statical Moment, Stability 515 

Stability of a Dam 515 

Parallel Forces 515 

Couples . . . , 515 

Equilibrium of Forces 516 

Center of Gravity 516 

Moment of Inertia 517 

Centers of Oscillation and Percussion 518 

Center and Radius of Gyration 518 

The Pendulum 520 

Conical Pendulum 520 

Centrifugal Force 521 

Velocity, Acceleration. Falling Bodies 521 

Value of er 522 

Angular Velocity 522 

Height due to Velocity . 523 

Parallelogram of Velocities 523 

Velocity due to Falling a Given Height 524 

Fundamental Equations in Dynamics 525 

Force of Acceleration 526 

Formulae for Accelerated Motion 527 

Motion on Inchned Planes 527 

Momentum 527 

Work, Energy, Power 528 

Work of Acceleration 529 

Work of Accelerated Rotation 529 

Force of a Blow 529 

Impact of Bodies 530 

Energy of Recoil of Guns 531 

Conservation of Energy 531 

Sources of Energy 531 

Perpetual Motion 532 

EflSciency of a Machine 532 

Animal-power, Man-power 532 

Man-wheel, Tread Mills 533 

Work of a Horse 533 

Horse-gin 534 

Resistance of Vehicles 534 



Elements of Mechanics. 

The Lever 535 

The Bent Lever 536 

The Moving Strut 536 

The Toggle-joint 536 

The Inclined Plane 537 

The Wedge 537 

The Screw 537 

The Cam 537 

Efficiency of a Screw 538 

Efficiency of Screw Bolts 538 

Pulleys or Blocks 539 

Differential Pulley 539 

Wheel and Axle 539 

Toothed- wheel Gearing 539 

Endless Screw, Worm Gear 540 

Differential Windlass 540 

Differential Screw. 540 

Efficiency of a Differential Screw 541 



XVm CONTENTS. 

Stresses In Framed Structures. 

PAGE 

Cranes and Derricks 541 

Shear Poles and Guys 542 

King Post Truss or Bridge 543 

Queen Post Truss 543 

Burr Truss 544 

Pratt or Whipple Truss 544 

Method of Moments 545 

Howe Truss 546 

Warren Girder 546 

Roof Truss 547 

The Economical Angle 548 

HEAT. 

Thermometers and Pyrometers 549 

Centigrade and Fahrenheit degrees compared 550 

Temperature Conversion Table 552 

Copper-ball Pyrometer 553 

Thermo-electric Pyrometer 554 

Temperatures in Furnaces 554 

Seger's Fire-clay Pyrometer 555 

Wiborgh Air Pyrometer 555 

Mesure and Nouel's Pyrometer 556 

Uehling and Steinbart Pyrometer 557 

Air-thermometer 557 

High Temperatures Judged by Color 558 

Boiling-points of Substances 559 

Melting-points 559 

Unit of Heat 560 

Mechanical Equivalent of Heat 560 

Heat of Combustion 560 

Heat Absorbed by Decomposition 561 

Specific Heat 562 

Thermal Capacity of Gases 564 

Expansion by Heat 565 

Absolute Temperature, Absolute Zero 567 

Latent Heat of Fusion 568 

Latent Heat of Evaporation 568 

Total Heat of Evaporation 569 

Evaporation and Drying 569 

Evaporation from Reservoirs 569 

Evaporation by the Multiple System 570 

Resistance to Boiling 570 

Manufacture of Salt 570 

Solubihty of Salt 571 

Salt Contents of Brines 571 

Concentration of Sugar Solutions 572 

Evaporating by Exhaust Steam 572 

Drying in Vacuum 573 

Driers and Drying 574 

Design of Drying Apparatus 576 

Humidity Table 577 

Radiation of Heat 578 

Black-body Radiation 579 

Conduction and Convection of Heat 579 

Rate of External Conduction 580 

Heat Conduction of Insulating Materials 581 

Heat Resistance, Reciprocal of Heat Conductivity 582 

Steam-pipe Coverings 584 

Transmission through Plates 587 ^ 

Transmission in Condenser Tubes 588 

Transmission of Heat in Feed-water Heaters 590 

Transmission through Cast-iron Plates 591 

Heating Water by Steam Coils 591 

Transmission from Air or Gases to Water 592 



CONTENTS. XIX 

PAGE 

Transmission from Flame to Water 593 

Cooling of Air 594 

Transmission from Steam or Hot Water to Air 595 

Thermodynamics 597 

Entropy 599 

Reversed Carnot Cycle, Refrigeration 600 

Principal Equations of a Perfect Gas 600 

Construction of the Curve PV^ = C 602 

Temperature-Entropy Diagram of Water and Steam 602 

PHYSICAL PROPERTIES OF GASES. 

Expansion of Gases 603 

Boyle and Marriotte's Law 603 

Law of Charles, Avogadro's Law 604 

Saturation Point of Vapors 604 

Law of Gaseous Pressure 604 

Flow of Gases 605 

Absorption by Liquids 605 

Liquefaction of Gases, Liquid Air 605 

AIR. 

Properties of Air 606 

Barometric Pressures 606 

Air-manometer 607 

Conversion Table for Air Pressures 607 

Pressure at Different Altitudes 607, 609 

Leveling by the Barometer and by Boiling Water 607 

To find Difference in Altitude 608 

Weight of Air at Different Pressures and Temperatures 609 

Moisture in Atmosphere 609, 611 

Humidity Table 610 

Weight of Air and Mixtures of Air and Vapor 610, 613 

Specific Heat of Air .„ 614 

Flow of Air. 

Flow of Air through Orifices 615 

Flow of Air in Pipes 617 

Tables of Flow of Air B22, 623 

Effects of Bends in Pipe 624 

Anemometer Measurements 624 

Equahzation of Pipes 625 

Wind. 

Force of the Wind ^ 626 

Wind Pressure in Storms 627 

Windmills 627 

Capacity of Windmills 629 

Economy of Windmills 630 

Electric Power from Windmills 632 

Compressed Air. 

Heating of Air by Compression 632 

Loss of Energy in Compressed Air 632 

Loss due to Heating 633 

Work of Adiabatic Compression of Air 634 

Compound Air-compression 635 



XX CONTENTS. 

PAGE 

Mean Effective Pressures 635, 636 

Horse-power Required for Compression 637 

Compressed-air Engines 638 

Mean and Terminal Pressures 638 

Air-compression at Altitudes 639 

Popp Compressed-air System 639 

Small Compressed-air Motors 640 

EflQciency of Air-heating Stoves 640 

Efiaciency of Compressed-air Transmission 640 

Eflaciency of Compressed-air Engines 640 

Air-compressors 641 

Tests of Air compressors 643 

Steam Required to Compress 100 Cu. Ft. of Air 644 

Requirements of Rock-drills 645 

Compressed Air for Pumping Plants 645 

Compressed Air for Hoisting Engines 646 

Practical Results with Air Transmission 647 

Effect of Intake Temperature 647 

Compressed-air Motors with Retiun Circuit 648 

Intercoolers for Air-compressors 648 

Centrifugal Air-compressors 648 

High-pressure Centrifugal Fans 649 

Test of a Hydraulic Air-compressor 650 

Mekarski Compressed-air Tramways 652 

Compressed Air Working Pimips in Mines 652 

Compressed Air for Street Railways 652 

Fans and Blowers. 

Centrifugal Fans 653 

Best Proportions of Fans 653 

Pressure due to Velocity 653 

Blast Area or Capacity Area . . . . » 655 

Pressure Characteristics of Fans 655 

Quantity of Air Delivered 655 

EflQciency of Fans and Positive Blowers 657 

Tables of Centrifugal Fans 658-666 

Effect of Resistance on Capacity of Fans 664 

Sirocco or INIultivane Fans 664 

Methods of Testing Fans 667 

Horse-power of a Fan 668 

Pitot Tube INIeasurements 669 

Thomas Electric Air and Gas Meter 669 

Flow of Air through an Orifice 670 

Diameter of Blast-pipes 670 

Centrifugal Ventilators for INIines 672 

Experiments on Mine Ventilators 673 

Disk Fans 675 

EflQciency of Disk Fans 676 

Positive Rotary Blowers 677 

Steam-jet Blowers and Exhausters 679 

Blowing Engines 680 

HEATING AND VENTILATION. 

Ventilation 681 

Quantity of Air Discharged through a Ventilating Duct 683 

Heating and Ventilating of Large Buildings 684 

Comfortable Temperatures and Humidities 685 

Carbon Dioxide Allowable in Factories 685 

Standards of Ventilation 686 

Air Washing 687 

Contamination of Air 687 

Standards for Calculating Heating Problems 687 



CONTENTS. XXI 

PAGE 

Heating Value of Coal 687 

Heat Transmission through Walls, etc 688 

Allowance for Exposure and Leakage 689 

Heating by Hot-air Furnaces 690 

Carrying Capacity of Air-pipes 691 

Voliune of Air at Different Temperatures 692 

Sizes of Pipes Used in Furnace Heating 692 

Furnace Heating with Forced Air Supply 693 

Rated Capacity of Boilers for House Heating 693 

Capacity of Grate-surface 694 

Steam Heating, Rating of Boilers 694 

Testing Cast-iron Heating Boilers 696 

Proportioning House Heating Boilers 696 

Coefficient of Transmission in Direct Radiation 697 

Heat Transmitted in Indirect Radiation 698 

Short Rules for Computing Radiating Surface 698 

Carrying Capacity of Steam Pipes in Low Pressure Heating 698 

Proportioning Pipes to Radiating Surface 700 

Sizes of Pipes in Steam Heating Plants 701 

Resistance of Fittings 701 

Removal of Air, Vacuum Systems 702 

Overhead Steam-pipes 702 

Steam-consumption in Car-heating 702 

Heating a Greenhouse by Steam 702 

Heating a Greenhouse by Hot Water 703 

Hot- water Heating 703 

Velocity of Flow in Hot-water Heating 703 

Sizes of Pipe for Hot- water HeatiQg 704 

Sizes of Flow and Return Pipes 705 

Heating by Hot- water, with Forced Circulation 707 

Corrosion of Pipe in Hot-water Heating 708 

Blower System of Heating and Ventilating 708 

Advantages and Disadvantages of the Plemun System 708 

Heat Radiated from Coils in the Blower System 708 

Test of Cast-iron Heaters for Hot-blast Work 709 

Factory Heating by the Fan System 710 

Artificial Cooling of Air 710 

Capacities of Fans for Hot-blast Heating 711 

Relative Efficiency of Fans and Heated Chimneys 712 

Heating a Building to 70° F 712 

Heating by Electricity 713 

Mine- ventilation 714 

Friction of Air in Underground Passages 714 

Equivalent Orifices • 715 

WATER. 

Expansion of Water 716 

Weight of Water at Different Temperatures 716, 717 

Pressure of Water due to its Weight 718, 719 

Head Corresponding to Pressures 718 

Buoyancy 719 

Boiling-point 719 

Freezing-point 719 

Sea-water 719 

Ice and Snow 720 

Specific Heat of Water 720 

Compressibility of Water 720 

Impurities of Water 720 

Causes of Incrustation 721 

Means for Preventing Incrustation 721 

Analyses of Boiler-scale 722 

Hardness of Water 723 

Purifying Feed-water 723 

Softening Hard Water 724 



XXll CONTENTS. 

Hydraulics. Flow of Water. page 

Formulae for Discharge through Orifices and Weirs 726 

Flow of Water from Orifices 727 

Flow in Open and Closed Channels 728 

General Formulae for Flow 728 

Chezy's Formula 728 

Values of the Coefficient c 728, 732 

Table, Fall in Feet per mile, etc 729 

Values of V7~for Circular Pipes 730 

Kutter's Formula 730 

D'Arcy's Fornuila 732 

Values of a \/r for Chezy's Formula 733 

Values of the Coefficient of Friction 734 

Loss of Head 735 

Resistance at the Inlet of a pipe 735 

Exponential Formuli3e, WilUams' and Hazen's Tables 736 

Short Formulae 737 

Flow of Vv^ater in a 20-inch Pipe 737 

Coefficients for Reducing H. and W. to Chezy's Formula 737 

Tables of Flow of Water in Circular Pipes 738-743 

Flow of Water in Riveted Pipes 743 

Long Pipe Lines 743 

Flow of Water in House-service Pipes 744 

Friction Loss in Clean Cast-iron Pipe 745 

Approximate Hydraulic Formulae 746 

Compoimd Pipes, and Pipes with Branches 746 

Rifled Pipes for Conveying Oils 746 

Effect of Bend and Curves 747 

Loss of Pressure Caused by Valves, etc 747, 748 

Hydraulic Grade-fine 748 

Air-bound Pipes 748 

Water Hammer 749 

Vertical Jets 749 

Water Delivered through Meters 749 

Price Charged for Water in Cities 749 

Fire Streams 749 

Hydrant Pressures Required with Different Lengths and Sizes of 

Hose 750 

Pump Inspection Table 751 

Pipe Sizes for Ordinary Fire Streams 752 

Friction Losses in Hose 752 

Rated Capacity of Steam Fire-engines 752 

Flow of Water through Nozzles 753 

The Siphon 754 

Velocity of Water in Open Channels 755 

Mean Surface and Bottom Velocities 755 

Safe Bottom and Mean Velocities 755 

Resistance of Soil to Erosion 755 

Abrading and Transporting Power of Water 755 

Frictional Resistance of Surfaces Moved in Water 756 

Grade of Sewers 757 

Measurement of Flowing Water 757 

Piezometer 757 

Pitot Tube Gauge 757 

Maximum and Mean Velocities in Pipes 758 

The Venturi Meter 758 

Measurement of Discharge by Means of Nozzles 759 

The Lea V-notch Recording Meter 759 

Flow through Rectangular Orifices 760 

Measurement of an Open Stream 760 

Miners' Inch Measurements 761 

Flow of Water over Weirs 762 

Francis's Formula for Weirs 762 

Weir Table 763 

Bazin's Experiments 763 

The Cippoleti, or Trapezoidal Weir 764 

The Triangular Weir 764 



CONTENTS. XXIU 
WATEB-POWEE. 

PAGE 

Power of a Fall of Water 765 

Horse-power of a Running Stream 765 

Current Motors 765 

Bemouilli's Theorem 765 

Maximum EflSciency of a Long Conduit 766 

Mill-power 766 

Value of Water-power 766 

Water Wheels. Turbine Wheels. 

Water Wheels 768 

Proportions of Turbines 768 

Tests of Turbines 773 

Dimensions of Turbines 774 

Rating and Efficiency of Turbines 774 

Rating Table for Turbines 777 

Turbines of 13,500 H. P. each 778 

TJhe Fall-increaser for Turbines 778 

Tangential or Impulse Water Wheel 779 

The Pelton Water Wheel 779 

Considerations in the Choict^ of a Tangential Wheel 780 

Control of Tangential Water Wheels 781 

Tangential Water-wheel Table 782 

Amount of Water Required to Develop a Given Horse-Power . 784 

Efficiency of the Doble Nozzle 785 

Water Plants Operating under High Pressure 785 

Formulae for Calculating the Power of Jet Water Wheels 785 

The Power of Ocean Waves. 

Energy of Deep Sea Waves 786 

UtiUzation of Tidal Power 787 

PUMPS AND PUMPING ENGINES. 

Theoretical Capacity of a Pump 788 

Depth of Suction 788 

The Deane Pump 789 

Sizes of Direct-acting Pumps 789, 791 

Amoimt of Water Raised by a Single-acting Lift-pump 790 

Proportioning the Steam-cylinder of a Direct-acting Pump 790 

Speed of Water through Pipes and Pump-passages 790 

Efficiency of Small Pumps 790 

The Worthington Duplex Pump 791 

Speed of Piston 791-792 

Speed of W^ater through Valves 792 

Underwriters' Pumps, Standard Sizes 792 

Boiler-feed Pumps 792 

Pump Valves 793 

The Worthington High-duty Pumping Engine 793 

The d'Auria Pumping Engine 793 

A 72,000, 000-Gallon Pumping Engine 793 

The Screw Pumping Engine 794 

Finance of Pumping Engine Economy 794 

Cost of Pumping 1000 Gallons per Minute 795 

Centrifugal Pumps 796 

Design of a Four-stage Turbine Pump 797 

Relation of Peripheral Speed to Head 797 

Tests of De Laval Centrifugal Pump 798 

A High-duty Centrifugal Pump 801 

Rotary Pumps 801 

Tests of Centrifugal and Rotary Pumps 802 

Duty Trials of Pumping Engines 802 



XXIV . CONTENTS. 

PAGE 

Leakage Tests of Pximps 803 

Notable High-duty Pump Records 805 

Vacuum Pumps 806 

The Pulsometer 806 

The Jet Pmnp 807 

The Injector 807 

Pumping by Compressed Air 808 

Gas-engine Pmnps; The Humphrey Gas Pump 808 

Air-hft Pump 808 

Air-hfts for Deep Oil-wells 809 

The HydrauUc Ram 810 

Quantity of Water Delivered -by the Hydraulic Ram 810 

Hydraulic Pressure Transmission. 

Energy of Water under Pressure 812 

Eflaciency of Apparatus 812 

HydrauUc Presses 813 

Hydraulic Power in London 814 

Hydraulic Riveting Machines 814 

Hydraulic Forging 814 

Hydrauhc Engine 815 



FUEL. 

Theory of Combustion 816 

Analyses of the Gases of Combustion 817 

Temperature of the Fire 818 

Classification of Solid Fuels 818 

Classification of Coals 819 

Analyses of Coals 820 

Caking and Non-Caking Coals 820 

Cannel Coals 821 

Rhode Island Graphitic Anthracite 821 

Analysis and Heating Value of Coals 821-828 

Approximate Heating Values . . : 822 

Lord and Haas's Tests 823 

Sizes of Anthracite Coal 823 

Space occupied by Anthracite 823 

Bemice Basin. Pa., Coal 824 

Connellsville Coal and Coke 824 

Bituminous Coals of the Western States 824 

Analysis of Foreign Coals 825 

Sampling Coal for Analyses 825 

Relative Value of Steam Coals 826 

Calorimetric Tests of Coals 826 

Classified Lists of Coals 828-830 

Purchase of Coal Under Specifications 830 

Weathering of Coal 830 

Pressed Fuel 831 

Spontaneous Combustion of Coal 832 

Coke 832 

Experiments in Coking 833 

Coal Washing 833 

Recovery of By-products in Coke Manufacture 833 

Generation of Steam from the Waste Heat and Gases from Coke- 
ovens 834 

Products of the Distillation of Coal 834 

Wood as Fuel 835 

Heating Value of Wood 835 

Composition of Wood 835 

Charcoal 836 

Yield of Charcoal from a Cord of Wood 836 

Consumption of Charcoal in Blast Furnaces 837 



CONTENTS. XXV 

PAGE 

Absorption of Water and of Gases by Charcoal 837 

Miscellaneous Solid Fuels • 837 

Dust-fuel — rDust Explosions 837 

Peat or Turf 838 

Sawdust as Fuel 838 

Wet Tan-bark as Fuel 838 

Straw as Fuel 839 

Bagasse as Fuel in Sugar Manufactiire 839 

Liquid Fuel. 

Products of Distillation of Petroleum 840 

Lima Petroleum 840 

Value of Petroleum as Fuel 840 

Fuel Oil Burners 842 

Specifications for Purchase of Fuel Oil 843 

Alcohol as Fuel 843 

Specific Gravity of Ethyl Alcohol 844 

Vapor Pressures of Saturation of Alcohol and other Liquids .... 844 

Fuel Gas. 

Carbon Gas 845 

Anthracite Gas 845 

Bituminous Gas 846 

Water Gas 846 

Natural Gas in Ohio and Indiana 847 

Natural Gas as a Fuel for Boilers 847 

Producer-gas from One Ton of Coal 848 

Combustion of Producer-gas 849 

Proportions of Gas Producers and Scrubbers 849 

Gas Producer Practice 851 

Capacity of Producers 851 

High Temperature Required for Production of CO 852 

The Mond Gas Producer 852 

Relative EflSciency of Different Coals in Gas-engine Tests . . . . ,^ 853 

Use of Steam in Producers and Boiler Furnaces .' 854 

Gas Analyses by Volume and by Weight 854 

Gas Fuel for Small Furnaces 854 

Blast-furnace Gas 855 

Acetylene and Calcium Carbide. 

Acetylene 855 

Calcium Carbide 856 

Acetylene Generators and Burners 857 

The Acetylene Blowpipe 857 

Ignition Temperature of Gases 858 

Illuminating _Gas. 

Coal-gas 858 

Water-gas 858 

Analyses of Water-gas and Coal-gas 860 

Calorific Equivalents of Constituents 860 

Efficiency of a Water-gas Plant 861 

Space Required for a Water-gas Plant 862 

Fuel- value of Illuminating Gas 863 

Flow of Gas in Pipes 864-866 

Services for Lamps 864 

Factors for Reducing Volumes of Gas 865 

STEAM. 

Temperature and Pressure 867 

Total Heat 867 

Latent Heat of Steam 867 



XXVI CONTENTS. 

PAGE 

Specific Heat of Saturated Steam 867 

The Mechanical Equivalent of Heat 868 

Pressure of Saturated Steam 868 

Volume of Saturated Steam 868 

Specific Heat of Superheated Steam 869 

Specific Density of Gaseous Steam 870 

Table of the Properties of Saturated Steam 871-874 

Table of the Properties of Superheated Steam 874, 875 

Flow of Steam. 

Flow of Steam through a Nozzle 876 

Napier's Approximate Rule 876 

Flow of Steam in Pipes 877 

Flow of Steam in Long Pipes, Ledoux's Formula 877 

Table of Flow of Steam in Pipes 878 

Carrying Capacity of Extra Heavy Steam Pipes 879 

Resistance to Flow by Bends, Valves, etc 879 

Sizes of Steam-pipes for Stationary Engines 879 

Sizes of Steam-pipes for Marine Engines 880 

Proportioning Pipes for Minimum Loss by Radiation and Friction 880 

Available Maximum Efficiency of Expanded Steam 881 

Steam-pipes. 

Bursting-tests of Copper Steam-pipes 882 

Failure of a Copper Steam-pipe 882 

Wire-wound Steam-pipes 882 

Materials for Pipes and Valves for Superheated Steam 882 

Riveted Steel Steam-pipes 883 

Valves in Steam-pipes 883 

The Steam Loop 883 

Loss from an Uncovered Steam-pipe 884 

Condensation in an Underground Pipe Line 884 

Steam Receivers in Pipe Lines 884 

Equation of Pipes 884 

Identification of Power House Piping by Colors 885 

THE STEAM-BOILER. 

The Horse-power of a Steam-boiler 885 

Measures for Comparing the Duty of Boilers 886 

Unit of Evaporation 886 

Steam-boiler Proportions 887 

Heating-surface 887 

Horse-power, Builders' Rating 888 

Grate-surface 888 

Areas of Flues 889 

Air-passages Through Grate-bars 889 

Performance of Boilers 889 

Conditions which Secure Economy 890 

Air Leakage in Boiler Settings 891 

Efficiency of a Boiler 891 

Autographic CO2 Recorders 891 

Relation of Efficiency to Rate of Driving, Air Supply, etc 893 

Effect of Quahty of Coal upon Efficiency 895 

Effect of Imperfect Combustions and Excess Air Supply 896 

Theoretical Efficiency with Pittsburgh Coal 896 

The Straight Line Formula for Efficiency 896 

High Rates of Evaporation 898 

Boilers Using Waste Gases 898 

Maximum Efficiencies at Different Rates of Driving 898 

Rules for Conducting Boiler Tests 899 

Heat Balance in Boiler Tests 907 

Factors of Evaporation 908 



CONTENTS. XXVU 

Strength of Steam-boilers. page 

Rules for Construction 908 

Shell-plate Formulae 913 

Efficiency of Riveted Joints '. . . 914 

Loads Allowed on Stays 916 

Holding Power of Boiler Tubes 916 

Safe-working Pressures 918 

Boiler Attachments, Furnaces, etc. 

Fusible Plugs 918 

Steam Domes 918 

Mechanical Stokers 918 

The Hawley Down-draught Furnace 919 

Under-feed Stokers 919 

Smoke Prevention 920 

Burning Illinois Coal without Smoke 921 

Conditions of Smoke Prevention 922 

Forced Combustion 923 

Fuel Economizers 924 

Thermal Storage 927 

Incrustation and Corrosion 927 

Boiler-scale Compounds 929 

Removal of Hard Scale 930 

Corrosion in Marine Boilers 930 

Use of Zinc 931 

Effect of Deposit on Flues 931 

Dangerous Boilers 932 

Safety-valves. 

Rules for Area of Safety-valves 932 

Spring-loaded Safety-valves 933 

Safety Valves for Locomotives 935 

The Injector. 

Equation of the Injector 936 

Performance of Injectors 937 

Boiler-feeding Pumps 937 

Feed-water Heaters. 

Percentage of Saving Due to Use of Heaters 938 

Strains Caused by Cold Feed-water 939 

Calculation of Surface of Heaters and Condensers 939 

Open vs. Closed Feed-water Heaters 940 

Steam Separators. 

Eflaciency of Steam Separators 941 

Determination of Moisture in Steam. 

Steam Calorimeters 942 

Coil Calorimeter 942 

Throttling Calorimeters 943 

Separating Calorimeters 943 

Identification of Dry Steam • 944 

Usual Amount of Moisture in Steam 944 

Chimneys. 

Chimney Draught Theory 944 

Force of Intensity of Draught 945 

Rate of Combustion Due to Height of Chimney 947 



XXVlll CONTENTS. 

PAGE 

High Chimneys not Necessary 948 

Height of Chimneys Required for Different Fuels 948 

Protection of Chimney from Lightning 949 

Table of Size of Chimneys 950 

Velocity of Gas in Chimneys 951 

Size of Chimneys for Oil Fuel 951 

Chimneys with Forced Draught ■ 952 

Largest Chimney in the World 952 

Some Tall Brick Chimneys 953, 954 

Stabihty of Chimneys 954 

Steel Chimneys 956 

Reinforced Concrete Chimneys 958 

Sheet-iron Chimneys 958 

THE STEAM ENGINE. 

Expansion of Steam 959 

Mean and Terminal Absolute Pressures 960 

Calculation of Mean Effective Pressure 961 

Mechanical Energy of Steam Expanded Adiabatically 963 

Measures for Comparing the Duty of Engines 963 

Efficiency, Thermal Units per Minute 964 

Real Ratio of Expansion 965 

Effect of Compression 965 ^ 

Clearance in Low- and High-speed Engines 966 

Cylinder-condensation 966 

Water-consumption of Automatic Cut-off Engines 967 

Experiments on Cylinder-condensatipn . 967 

Indicator Diagrams 968 

Errors of Indicators 969 

Pendulum Indicator Rig 969 

The Manograph 969 

The Lea Continuous Recorder 970 

Indicated Horse-power 970 

Rules for Estimating Horse-power 970 

Horse-power Constants 971 

Table of Engine Constants 972 

To Draw Clearance on Indicator-diagram 974 

To Draw Hyperbola Curve on Indicator-diagram 974 

Theoretical Water Consumption 975 

Leakage of Steam 976 

Compound Engines. 

Advantages of Compounding 976 

Woolf and Receiver Types of Engines 977 

Combined Diagrams 979 

Proportions of Cylinders in Compound Engines 980 

Receiver Space 980 

Formula for Calculating Work of Steam 981 

Calculation of Diameters of Cylinders 982 

Triple-expansion Engines 983 

Proportions of Cylinders 983 

Formulae for Proportioning Cylinders 983 

Types of Three-stage Expansion Engines 985 

Sequence of Cranks 986 

Velocity of Steam through Passages 986 

A Double-tandem Triple-expansion Engine 986 

Quadruple-expansion Engines . .' 986 

Steam-engine Economy. 

Economic Performance of Steam-engines 987 

Feed-water Consumption of Different Types 987 

Sizes and Calculated Performances of Vertical High-speed Engine 988 



CONTENTS. XXIX 

PAGE 

The Willans Law, Steam Consumption at Different Loads 991 

Relative Economy of Engines mider Variable Loads 992 

Steam Consumption of Various Sizes 992 

Steam Consumption in Small Engines 993 

Steam Consumption at Various Speeds 993 

Capacity and Economy of Steam Fire Engines 993 

Economy Tests of High-speed Engines 994 

Limitation of Engine Speed 995 

British High-speed Engines 995 

Advantage of High Initial and Low-back Pressure 996 

Comparison of Compound and Single-cylinder Engines 997 

Two-cyhnder and Three-cylinder Engines 997 

Steam Consumption of Engines with Superheated Steam 998 

Steam Consumption of Different Types of Engine 999 

The Lentz Compound Engine 999 

Efficiency of Non-condensing Compound Engines 1000 

Economy of Engines under Varying Loads 1000 

Effect of Water in Steam on Efficiency 1001 

Influence of Vacuum and Superheat on Steam Consumption. ... 1001 

Practical Application of Superheated Steam • 1002 

Performance of a Quadruple Engine 1003 

Influence of the Steam-jacket 1004 

Best Economy of the Piston Steam Engine 1005 

Highest Economy of Pumpuig-engines 1006 

Sulphur-dioxide Addendum to Steam-engine 1007 

Standard Dimensions of Direct-connected Generator Sets 1007 

Dimensions of Parts of Large Engines 1007 

Large Rolhng-mill Engines 1008 

Coimterbalancing Engines 1008 

Preventing Vibrations of Engines 1008 

Foundations Embedded in Air 1009 

Most Economical Point of Cut-off 1009 

Type of Engine used when Exhaust-steam is used for Heating. . 1009 

Cost of Steam-power 1009 

Cost of Coal for Steam-power 1010 

Power-plant Economics 1011 

Analysis of Operating Costs of Power-plants 1013 

Economy of Combination of Gas Engines and Turbines 1014 

Storing Steam Heat in Hot Water 1014 

Utilizing the Sun's Heat as a Source of Power 1015 

Rules for Conducting Steam-engine Tests 1015 

Dimensions of Parts of Engines. 

Cylinder 1021 

Clearance of Piston 1021 

Thickness of Cylinder 1021 

Cylinder Heads 1022 

Cyhnder-head Bolts 1022 

The Piston 1023 

Piston Packing-rings 1023 

Fit of Piston-rod 1024 

Diameter of Piston-rods 1024 

Piston-rod Guides 1024 

The Connecting-rod 1025 

Connecting-rod Ends 1026 

Tapered Connecting-rods 1026 

The Crank-pin 1027 

Crosshead-pin or Wrist-pin 1029 

The Crank-arm 1029 

The Shaft, Twisting Resistance 1030 

Resistance to Bending 1032 

Equivalent Twisting Moment 1032 

Fly-wheel Shafts 1033 

Length of Shaft-bearings 1034 

Crank-shafts with Center-crank and Double-crank Arms 1036 



XXX CONTENTS. 

PAGE 

Crank-shaft with two Cranks Coupled at 90° 1037 

Crank-shaft with three Cranks at 120° 1038 

Valve-stem or Valve-rod 1038 

The Eccentric 1039 

The Eccentric-rod 1039 

Reversing-gear 1039 

Current Practice in Engine Proportions, 1897 1039 

Current Practice in Steam-engine Design, 1909 1040 

Shafts and Bearings of Engines 1042 

Calculating the Dimensions of Bearings 1042 

Engine-frames or Bed-plates 1044 

Fly-wheels. 

Weight of Fly-wheels 1044 

Weight of Fly-wheels for Alternating-current Units 1047 

Centrifugal Force in Fly-wheels 1047 

Diameters for Various Speeds 1048 

Strains in the Rims 1049 

Arms of Fly-wheels and Pulleys 1050 

Thickness of Rims 1050 

A Wooden Rim Fly-wheel 1051 

Wire- wound Fly-wheels 1052 

The SUde-Valve. 

Definitions, Lap, Lead, etc 1052 

Sweet's Valve-diagram 1054 

The Zeuner Valve-diagram 1054 

Port Opening, Lead, and Inside Lead 1057 

Crank Angles for Connecting-rods of Different Lengths 1058 

Ratio of Lap and of Port-opening to Valve- travel 1058 

Relative Motions of Crosshead and Crank 1060 

Periods of Admission or Cut-off for Various Laps and Travels . . 1060 

Piston- valves 1061 

Setting the Valves of an Engine 1061 

To put an Engine on its Center 1061 

Link-motion 1062 

The Walschaerts Valve-gear 1064 

Governors. 

Pendulum or Fly-ball Governors 1065 

To Change the Speed of an Engine 1066 

Fly-wheel or Shaft Governors 1066 

The Rites Inertia Governor 1066 

Calculation of Springs for Shaft-governors 1066 

Condensers, Au*-pumps, Circulating-pumps, etc. 

The Jet Condenser 1068 

Quantity of Coohng Water 1068 

Ejector Condensers 1069 

The Barometric Condensers 1069 

The Surface Condenser 1069 

Coefficient of Heat Transference in Condensers 1070 

The Power Used for Condensing Apparatus 1071 

Vacuum, Inches of Mercury and Absolute Pressure 1071 

Temperatures, Pressm-es and Volumes of Saturated Air 1072 

Condenser Tubes 1072 

Tube-plates 1073 

Spacing of Tubes 1073 

Air-pump 1073 

Area through Valve-seats 1073 

Work done by an Air-pump 1074 



CONTENTS. XXXI 

PAGE 

Most Economical Vacuum for Turbines 1075 

Circulating-pimip 1075 

The Lcblanc Condenser 1076 

Feed-pumps for Marine Engines 1076 

An Evaporative Surface Condenser 1076 

Continuous Use of Condensing Water 1076 

Increase of Power by Condensers 1077 

Advantage of High Vacuum in Reciprocating Engines 1078 

The Choice of a Condenser 1078 

CooUng Towers 1079 

Calculation of Air Supply for Cooling Towers 1080 

Tests of a Cooling Tower and Condenser 1080 

Water Evaporated in a Cooling Tower 1080 

Weight of Water Vapor mixed with One Pound of Air 1081 

Evaporators and Distillers 1082 

Rotary Steam Engines — Steam Turbines. 

Rotary Steam Engines 1082 

Impulse and Reaction Turbines 1082 

The DeLaval Turbine 1082 

The Zollev or Rateau Turbine 1083 

The Parsons Turbine 1083 

The Westinghouse Double-flow Tm-bino 1083 

Mechanical Theory of the Steam Tm-bine 1084 

Heat Theory of the Steam Turbine 1084 

Velocity of Steam in Nozzles 1085 

Speed of the Blades 1086 

Comparison of Impulse and Reaction Turbines 1087 

Loss due to Windage 1087 

Efficiency of the Machine 1087 

Steam Consumption of Turbines 1088 

Effect of Vacumn on Steam Turbines 1088 

Tests of Tm-bines 1088 

Efficiency of the Rankine Cycle 1089 

Factors for Reduction to Equivalent Efficiency 1090 

Effect of Pressure, Vacuum and Superheat 1090 

Steam and Heat Consumption of the Ideal Engine 1091 

Westinghouse Turbines at 74th St. Station, New York 1092 

A Steam Turbine Guarantee 1092 

Efficiency of a 5000-K.W. Steam Turbine Generator 1092 

Comparison of Large Turbines and Reciprocating Engines 1092 

Steam Consumption of Small Steam Turbines 1093 

Low-pressure Steam Turbines 1093 

Tests of a 15.000-K.W. Steam-engine Turbine Unit. 1095 

Reduction Gear for Steam Turbines 1095 

Hot-air Engines. 

Hot-air or Caloric Engines 1095 

Test of a Hot-air Engine 1095 

Internal Combustion Engines. 

Four-cycle and Two-cycle Gas-engines 1096 

Temperatures and Pressures Developed 1096 

Calculation of the Power Of Cras-engnies 1097 

Pressures and Temperatures at End of Compression. 1098 

Pressiu-es and Temperature at Release 1099 

after Combustion 1099 

Mean Effective Pressures 1099 

Sizes of Large Gas-engines 1 100 

Engine Constants for Gas-engines 1101 

Rated Capacity of Automobile Engines 1101 

Estimate of the Horse-power of a Gas-engine 1101 



XXXU CONTENTS. 

PAGE 

Oil and Gasoline Engines 1101 

The Diesel Oil Engine 1102 

The De La Vergne Oil Engine 1102 

Alcohol Engines 1 102 

Ignition 1102 

Timing 1103 

Governing 1103 

Gas and Oil Engine Troubles 1103 

Conditions of Maximiun Efficiency 1103 

Heat Losses in the Gas-engine 1104 

Economical Performance of Gas-engines 1104 

Utilization of Waste Heat from Gas-engines 1105 

Rules for Conducting Tests of Gas and Oil Engines 1105 

LOCOMOTIVES. 

Beslstance of Trains 1108 

Resistance of Electric Railway Cars and Trains 1110 

Efficiency of the Mechanism of a Locomotive 1111 

Adhesion 1111 

Tractive Force 1111 

Size of Locomotive Cylinders 1112 

Horse-power of a Locomotive 1113 

Size of Locomotive Boilers 1113 

Wootten's Locomotive 1114 

Grate-surface. Smokestacks, and Exhaust-nozzles 1115 

Fire-brick Arches 1115 

Economy of High Pressures 1116 

Leading American Types 1116 

Classification of Locomotives 1116 

Steam Distribution for High Speed 1117 

Formulae for Curves 1117 

Speed of Railway Trains 1118 

Performance of a High-speed Locomotive 1118 

Fuel Efficiency of American Locomotives. 1119 

Locomotive Link-motion 1119 

Dimensions of Some American Locomotives 1120 

The Mallet Compound Locomotive 1120 

Indicated Water Consumption 1122 

Indicator Tests of a Locomotive at High-speed 1122 

Locomotive Testing Apparatus 1123 

Weights and Prices of Locomotives 1124 

Waste of Fuel in Locomotives 1125 

Advantages of Compounding 1125 

Depreciation of Locomotives 1125 

Average Train Loads 1125 

Tractive Force of Locomotives, 1893 and 1905 1125 

Superheating in Locomotives 1126 

Coimterbalancing Locomotives 1126 

Narrow-gauge Railways 1127 

Petroleum-burning Locomotives 1127 

Fireless Locomotives 1127 

Self-propelled Railway Cars 1127 

Compressed-air Locomotives 1128 

Air Locomotives with Compound Cylinders 1129 

SHAFTING. 

Diameters to Resist Torsional Strain 1130 

Deflection of Shafting 1131 

Horse-power Transmitted by Shafting 1132 

Flange Couplings 1133 

Effect of Cold Rolling 1133 

Hollow Shafts 1133 

Sizes of Collars for Shafting 1133 

Table for Laying Out Shafting 1134 



CONTENTS. XXXlll 

PULLEYS. p^^E 

Proportions of Pulleys 1135 

Convexity of Pulleys 1 136 

Cone or Step Pulleys 1 136 

Method of Determining Diameters of Cone Pulleys 1136 

Speeds of Shafts with Cone Pulleys 1137 

Speeds in Geometrical Progression , 1138 

BELTING. 

Theory of Belts and Bands 1138 

Centrifugal Tension 1139 

Belting Practice, Formulae for Belting 1139 

Horse-power of a Belt one inch wide 1140 

A. F. Nagle's Formula 1141 

Width of Belt for Given Horse-power 1141 

Belt Factors 1142 

Taylor's Rules for Belting 1143 

Barth's Studies on Belting 1146 

Notes on Belting 1146 

Lacing of Belts 1147 

Setting a Belt on Quarter-twist 1147 

To Find the Length of Belt 1148 

To Find the Angle of the Arc of Contact 1148 

To Find the Length of Belt when Closely Rolled 1148 

To Find the Approximate Weight of Belts 1148 

Relations of the Size and Speeds of Driving and Driven Pulleys. 1148 

Evils of Tight Belts 1149 

Sag of Belts 1149 

Arrangement of Belts and Pulleys 1149 

Care of Belts 1150 

Strength of Belting 1150 

Adhesion, Independent of Diameter 1151 

Endless Belts 1151 

Belt Data 1151 

U. S. Navy Specifications for Leather Belting 1151 

Belt Dressings 1 151 

Cement for Cloth or Leather 1152 

Rubber Belting 1152 

Steel Belts -, 1152 

Chain Drives. 

Roller Chain and Sprocket Drives 1153 

Belting versus Chain Drives 1155 

Data used in Design of Chain Drives 1156 

Comparison of Rope and Chain Drives 1157 

GEAREVG. 

Pitch, Pitch-circle, etc 1 157 

Diametral and Circular Pitch 1 158 

Diameter of Pitch-Une of Wheels from 10 to 100 Teeth 1159 

Chordal Pitch - 1159 

Proportions of Teeth 1159 

Gears with Short Teeth 1160 

Formulae for Dimensions of Teeth 1160 

Width of Teeth 1161 

Proportions of Gear-wheels 1161 

Rules for Calculating the Speed of Gears and Pulleys 1162 

Milling Cutters for Interchangeable Gears 1162 

Forms of the Teeth. 

The Cycloidal Tooth 1162 

The Involute Tooth 1165 



XXXiv CONTENTS. 

PAGE 

Approxima4:ion by Circular Arcs 1166 

Stub Gear Teeth for Automobiles 1167 

Stepped Gears 1168 

Twisted Teeth 1168 

Spiral Gears 1168 

Worm Gearing 1168 

The Hindley Worm 1169 

Teeth of Bevel-wheels 1169 

Annular and Differential Gearing 1169 

Efficiency of Gearing 1170 

Efficiency of Worm Gearing 1171 

Efficiency of Automobile Gears 1172 

Strength of Gear Teeth. 

Various Formulae for Strength 1172 

Comparison of Formulae 1 171 

Raw-hide Pinions 1177 

Maximum Speed of Gearing 1177 

A Heavy Machine-cut Spur-gear 1 178 

Frictional Gearing 1178 

Frictional Grooved Gearing 1178 

Power Transmitted by Friction Drives 1178 

Friction Clutches 1179 

Coil Friction Clutches 1180 

HOISTING AND CONVEYING. 

Working Strength of Blocks 1181 

Chain-blocks 1181 

Efficiency of Hoisting Tackle 1182 

Proportions of Hooks 1182 

Heavy Crane Hooks 1183 

Strength of Hooks and Shackles 1184 

Power of Hoisting Engines 1184 

Effect of Slack Rope on Strain In Hoisting 1186 

Limit of Depth for Hoisting 1186 

Large Hoisting Records 1186 

Safe Loads for Ropes and Chains 1187 

Pneumatic Hoisting 1187 

Coimterbalancing of Winding-engines 1188 

Cranes. 

Classification of Cranes 1189 

Position of the Inclined Brace in a Jib Crane 1190 

Electric Overhead TraveUng Cranes 1190 

Power Required to Drive Cranes 1191 

Dimensions, Loads and Speeds of Electric Cranes 1191 

Notable Crane Installations 1192 

A 150-ton Pillar Crane 1192 

Compressed-air Traveling Cranes 1192 

Electric versus Hydraulic Cranes 1193 

Power Required for Traveling Cranes and Hoists 1193 

Lifting Magnets 1193 

Telplierage 1196 

Coal-handling Machinery. 

Weight of Overhead Bins 1196 

Supply-pipes from Bins 1196 

Types of Coal Elevators 1196 

Combined Elevators and Conveyors 1197 

Coal Conveyors 1197 

Horse-power of Conveyors 1198 



CONTENTS. XXXV 

PAGE 

Bucket, Screw, and Belt Conveyors 1198 

Weight of Chain and of FUghts 1199 

Capacity of Belt Conveyors 1199 

Belt Conveyor Construction 1200 

Horse-power to Drive Belt Conveyors 1200 

Relative Wearing Power of Conveyor Belts 1200 

Pneumatic Conveying 1201 

Pneumatic Postal Transmission 1201 

Wire-rope Haulage. 

Self-acting Inclined Plane 1202 

Simple Engine Plane 1203 

Tail-rope System 1203 

Endless Rope System 1203 

Wire-rope Tramways 1204 

Stress in Hoisting-ropes on Inclined Planes 1204 

An Aerial Tramway 21 miles long 1205 

Suspension Cableways and Cable Hoists 1205 

Tension Required to Prevent Wire Slipping on Drums 1206 

Formulae for Deflection of a Wire Cable 1207 

Taper Ropes of Uniform Tensile Strength 1208 

WIRE-ROPE TRANSMISSION. 

Working Tension of Wire Ropes 1208 

Sheaves for Wire-rope Transmission 1208 

Breaking Strength of Wire Ropes 1209 

Bending Stresses of Wire Ropes 1209 

Horse-power Transmitted 1210 

Diameters of Minimum Sheaves 1211 

Deflection of the Rope 1211 

Limits of Span 1212 

Long-distance Transmission 1212 

Inclined Transmissions 1212 

Bending Curvature of Wire Ropes 1213 

EOPE-DRIVING. 

Formulae for Rope-driving 1214 

Horse-power of Transmission at Various Speeds 1215 

Sag of the Rope between Pulleys 1216 

Tension on the Slack Part of the Rope 12-16 

Miscellaneous Notes on Rope-driving 1217 

Data of Manila Transmission Rope 1218 

Cotton Ropes 1218 

FRICTION AND LUBRICATION. 

Coeflacient of Friction 1219 

Rolling Friction 1219 

Friction of Solids 1219 

Friction of Rest 1219 

Laws of Unlubricated Friction 1219 

Friction of Tires SHding on Rails 1219 

CoeflQcient of Rolling Friction 1220 

Laws of Fluid Friction 1220 

Angles of Repose of Building Materials 1220 

Coefficient of Friction of Journals 1220 

Friction of Motion 1221 

Experiments on Friction of a Journal 1221 

Coefficients of Friction of Journal with Oil Bath 1221, 1223 

Coefficients of Friction of Motion and of Rest 1222 

Value of Anti-friction Metals 1223 

Cast-iron for Bearings 1223 



XXXVi CONTENTS. 

PAGE 

Friction of Metal under Steam-pressure 1223 

Morin's Laws of Friction 1223 

Laws of Friction of Well-lubricated Journals 1225 

Allowable Pressures on Bearing-surfaces 1226 

Oil-pressure in a Bearing 1228 

Friction of Car-journal Brasses 1228 

Experiments on Overheating of Bearings 1228 

Moment of Friction and Work of Friction 1229 

Tests of Large Shaft Bearings 1230 

Clearance between Journal and Bearing 1230 

Allowable Pressures on Bearings 1230 

Bearing Pressm-es for Heavy Intermittent Loads 1231 

Bearings for Very High Rotative Speed 1231 

Bearing Pressures in Shafts of Parsons Turbine 1232 

Thrust Bearings in Marine Practice 1232 

Bearings for Locomotives 1232 

Bearings of Corhss Engines 1232 

Temperature of Engine Bearings 1232 

Pivot Bearings 1232 

The Schiele Curve 1232 

Friction of a Flat Pivot-bearing 1233 

Mercury-bath Pivot 1233 

Ball Bearings, Roller Bearings, etc 1233 

Friction Rollers 1233 

Conical Roller Thrust Bearings 1234 

The Hyatt Roller Bearing 1235 

Notes on Ball Bearings 1235 

Saving of Power by Use of Ball Bearings 1237 

Knife-edge Bearings 1238 

Friction of Steam-engines 1238 

. Distribution of the Friction of Engines 1238 

Friction Brakes and Friction Clutches. 

Friction Brakes 1239 

Friction Clutches 1239 

Magnetic and Electric Brakes 1240 

Design of Band Brakes 1240 

Friction of Hydaullc Plunger Paclcing 1241 

Lubrication. 

Durability of Lubricants 1241 

Qualifications of Lubricants 1242 

Examination of Oils 1242 

Specifications for Petroleum Lubricants 1243 

Penna. R. R. Specifications 1244 

Grease Lubricants 1244 

Testing Oil for Steam Turbines 1244 

Quantity of Oil to Run an Engine 1245 

Cylinder Lubrication 1245 

Soda Mixture for Machine Tools 1246 

Water as a Lubricant 1246 

Acheson's Deflocculated Graphite 1246 

Solid Lubricants 1246 

Graphite, Soapstone, Metahne : 1246 

THE FOUNDEY. 

Cupola Practice 1247 

Melting Capacity of Different Cupolas 1248 

Charging a Cupola 1248 

Improvement of Cupola Practice 1249 

Charges in Stove Foundries 1250 

Foundry Blower Practice 1250 



CONTENTS. XXXVU 

PAGE 

Results of Incroased Driving 1252 

Power Required for a Cupola Fan 1253 

Utilization of Cupola Gases 1253 

Loss of Iron in Melting 1253 

Use of Softeners 1253 

Weakness of Large Castings 1-253 

Sfirinkage of Castings 1254 

Growth of Cast Iron by Heating 1254 

Hard Iron due to Excessive Silicon 1254 

Ferro Alloys for Foundry Use 1255 

Dangerous Ferro-silicon 1255 

Quality of Foundry Coke 1255 

Castings made in Permanent Cast-iron Molds 1255 

Weight of Castings from Weight of Pattern 1256 

Molding Sand 1256 

Foundry Ladles 1257 

THE MACHEVE-SHOP. 

Speed of Cutting Tools 1258 

Table of Cutting Speeds 1258 

Spindle Speeds of Lathes 1259 

Rule for Gearing Lathes 1259 

Change-gears for Lathes 1260 

Quick Change Gears 1260 

Metric Screw-threads 1261 

Cold Chisels , 1261 

Setting the Taper in a Lathe 1261 

Lubricants for Lathe Centers 1261 

Taylor's Experiments on Tool Steel 1261 

Proper Shape of Lathe Tool ' 1261 

Forging and Grinding Tools 1263 

Best Grmding W^heel for Tools 1263 

Chatter 1264 

Use of Water on Tool 1264 

Interval between Grindings 1264 

Effect of Feed and Depth of Cut on Speed 1264 

Best High Speed Tool Steel — Heat Treatment 1265 

Table, Cutting Speeds of Taylor- Wliite Tools 1266 

Best Method of Treating Tools in Small Shops 1268 

Quahty of Different Tool Steels 1268 

Parting and Thread Tools 1268 

Durabihty of Cutting Tools 1268 

Economical Cutting Speeds 1268 

New High Speed Steels, 1909 1269 

SteUite 1269 

Planer Work 1270-1275 

Cutting and Return Speeds of Planers 1270 

Power Required for Planing 1270 

Time Required for Planing 1271 

Standard Planer Tools 1271-1275 

Milhng Machine Practice 1275-1284 

Forms of Milling Cutters 1275 

Niunber of Teeth in INlimng Cutters 1276 

Keyways in MiUing Cutters 1277 

Power Required for MiUing 1278 

Modern Milling Practice, 1914 1279 

Milhng wioh or against the Feed 1280 

Lubricant for Milhng Cutters 1281 

Typical Milling Jobs, Speeds, Feeds 1281 

High-speed Milling 1282 

Limiting Factors of MiUing Practice 1283 

Speeds and Feeds for Gear Cuttmg 1284 

Drills and DriUing 1285-1290 

Forms of Drills 1285 

DriUing Compounds 1286 



XXXVlll CONTENTS. 

PAGE 

Twist Drill and Steel Wire Gages 1286 

Power Required to Drive Drills 1286, 1287 

Feeds and Speeds of Drills 1288 

Extreme Results with Drills 1289 

Experiments on Twist Drills 1289 

Cutting Speeds for Tapping and Threading 1290 

Sawing Metals 1291 

Case-hardening, Cementation, Harveyizing 1291 

Change of Shape due to Hardening and Tempering 1291 

Power Required for Machine Tools. 

Resistance Overcome in Cutting Metal 1292 

Power Required to Run Lathes 1292-1295 

Sizes of Motors for Machine Tools 1294-1298 

Horse-power Constants for Cutting Metals 1299 

Pulley Diameters for Motors 1300 

Geared Connections for Motors, Table 1301 

Motor Requirements for Planers 1302 

Tests on a Motor-driven Planer 1303 

Power Required for Wood-working Machinery 1303 

Power Required to Drive Shafting 1305 

Power Required to Drive Machines in Groups 1305 

Machine Tool Drives, Speeds and Feeds. . . . , 1307 

Geometrical Progression of Speeds and Feeds 1307 

Methods of Driving Machine Tools 1307 

Abrasive Processes. 

The Cold Saw 1309 

Reese's Fusing-disk 1309 

Cutting Stone with Wire 1309 

The Sand-blast 1309 

Pohshing and Buffing 1310 

Laps and Lapping 1310 

Emery-wheels 1311-1317 

Artificial Abrasives 1313 

Movmting Grinding Wheels, Safety Devices 1314 

Grinding as a Substitute for Finish Turning 1317 

Grindstones '. 1317 

Various Tools and Processes. 

Taper Bolts, Pins, Reamers, etc 1318 

Morse Tapers 1319 

Jarno Taper 1319 

Tap Drills 1320 

Taper Pins 1321 

T-slots, T-bolts and T-nuts 1321 

Punches and Dies, Presses, etc 1321 

Punch and Die Clearances 1321 

Kennedy's Spiral Punch 1322 

Sizes of Blanks Used in the Drawing Press 1322 

Pressure Obtained by the Drop Press 1322 

Flow of Metals 1323 

Fly-wheels for Presses, Punches, Shears, etc 1323 

Forcing, Shrinking, and Running Fits 1324 

Pressures for Mounting Wheels and Crank Pins 1324 

Fits for Machine Parts 1325 

Running Fits 1325 

Shop Allowances for Electrical Machinery 1326 

Pressure Required for Press Fits 1326 

Stresses due to Force and Shrink Fits 1326 

Force Required to Start Force and Shrink Fits 1327 

Formulae for Flat and Square Keys 1328 



CONTENTS. XXXIX 

PAGE 

Keys of Various Forms 1328-1331 

Depth of Key Seats 1329 

Gib Keys 1332 

Holding Power of Keys and Set Screws 1332 

DYNAMOMETERS. 

Traction Dynamometers 1333 

The Prony Brake 1333 

The Alden Dynamometer 1334 

Capacity of Friction-brakes 1334 

Transmission Dynamometers 1335 

ICE MAKING OR REFRIGERATING-MACHEVES. 

Operations of a Refrigerating-Machine 1336 

Pressures, etc., of Available Liquids 1337 

Properties of Sulphur Dioxide Gas 1338 

Properties of Ammonia 1339, 1340 

SolubiUty of Ammonia 1341 

Properties of Saturated Vapors 1341 

Heat Generated by Absorption of Ammonia 1341 

Coohng Effect, Compressor Volume and Power Required, with 

Different Coohng Agents 1341 

Ratios of Condenser, Mean Effective, and Vaporizer Pressures . . 1342 

Properties of Brine used to absorb Refrigerating Effect 1343 

Chloride-of-calcium Solution 1343 

Ice-melting Effect 1344 

Ether-machines 1344 

Air-machines 1344 

Carbon Dioxide Machines 1344 

Methyl Chloride Machines 1345 

Sulphur-dioxide Machines 1345 

Machines Using Vapor of Water 1345 

Ammonia Compression-machines 1345 

Dry, Wet and Flooded Systems 1345 

Ammonia Absorption-machines 1346 

Relative Performance of Compression and Absorption Machines 1346 

Efficiency of a Refrigerating-machine 1347 

Diagrams of Ammonia Machine Operation 1348 

Cylinder-heating 1349 

Volumetric Efficiency 1349 

Poimds of Ammonia per Ton of Refrigeration 1350, 1351 

Mean Effective Pressure, and Horse-power '. . 1350 

The Voorhees Multiple Effect Compressor 1350 

Size and Capacities of Ammonia Machines 1352 

Piston Speeds and Revolutions per Minute 1353 

Condensers for Refrigerating-machines 1353 

Coohng Tower Practice in Refrigerating Plants 1354 

Test Trials of Refrigerating-machines 1355 

Comparison of Actual and Theoretical Capacity 1355 

Performance of Ammonia Compression-machines 1356 

Economy of Ammonia Compression-machines 1357 

Form of Report of Test 1358 

Temperature Range 1359 

Metering the Ammonia 1359 

Performance of Ice-making Machines 1359 

Performance of a 75-ton Refrigerating-machine 1361-1363 

Ammonia Compression-machine, Results of Tests 1364 

Performance of a Single-acting Ammonia Compressor 1364 

Performance of Ammonia Absorption-machine 1364 

Means for Applying the Cold 1365 

Artificial Ice-manufacture 1366 

Test of the New York Hygeia Ice-making Plant 1367 

An Absorption Evaporator Ice-making System 1367 

Ice-making with Exhaust Steam 1367 



Xl CONTENTS. 

PAGE 

Tons of Ice per Ton of Coal 1367 

Standard Ice Cans or Molds 1368 

Cubic Feet of Insulated Space per Ton Refrigeration 1368 

MARINE ENGINEERING. 

Rules for Measuring and Obtaining Tonnage of Vessels 1368 

The Displacement of a Vessel 1369 

Coefficient of Fineness 1369 

Coefficient of Water-line 1369 

Resistance of Ships 1369 

Coefficient of Performance of Vessels 1370 

Defects of the Common Formula for Resistance 1370 

Rankine's Formula 1370 

Empirical Equations for Wetted Surface 1371 

E. R. Mumford's Method 1371 

Dr. Kirk's Method 1372 

To find the I.H.P. from the Wetted Surface 1372 

Relative Horse-power required for Different Speeds of Vessels . . 1373 

Resistance per Horse-power for Different Speeds 1373 

Estimated Displacement, Horse-power, etc., of Steam- vessels. . . 1374 

Speed of Boats with Internal Combustion Engines 1374 

Data of Ships of Various Types 1376 

Relation of Horse-power to Speed 1376 

The Screw-propeller. 

Pitch and Size of Screw 1377 

Propeller Coefficients 1378 

Efficiency of the Propeller 1379 

Pitch-ratio and Slip for Screws of Standard Form 1379 

Table for Calculating Dimensions of Screws 1380 

Marine Practice. 

Comparison of Marine Engines, 1872, 1881, 1891, 1901 1380 

Turbines and Boilers of the " Lusitania" 1381 

Performance of the "Lusitania," 1908 1381 

Dimensions and Performance of Notable Atlantic Steamers .... 1382 

Relative Economy of Turbines and Reciprocating Engines 1382 

Reciprocating Engines with a Low-pressure Turbine 1383 

The Paddle-wheel. 

Paddle-wheels with Radial Floats 1383 

Feathering Paddle-wheels 1383 

Efficiency of Paddle-wheels 1384 

Jet Propulsion. 

Reaction of a Jet 1384 

CONSTRUCTION OF BUILDINGS. 

Foundations. 

Bearing Power of Soils 1385 

Bearing Power of Piles 1386 

Safe Strength of Brick Piers 1386 

Thickness of Foundation Walls 1386 

Masonry. 

Allowable Pressures on Masonry 1386 

Crushing Strength of Concrete 1386 

Reinforced Concrete 1386 



CONTENTS. Xli 

Beams and Girders. page 

Safe Loads on Beams 1387 

Safe Loads on Wooden Beams 1387 

Maximum Permissible Stresses in Structm-al Materials 1388 

Walls. 

Thickness of Walls of Buildings 1388 

Walls of Warehouses, Stores, Factories, and Stables 1388 

Floors, Columns and Posts. 

Strength of Floors, Roofs, and Supports 1389 

Columns and Posts ' 1389 

Fireproof Buildings 1389 

Iron and Steel Columns 1389 

Lintels, Bearings, and Supports 1390 

Strains on Girders and Rivets . 1390 

Maximum Load on Floors ' 1390 

Strength of Floors 1391 

Maximum Spans for 1, 2 and 3 inch Plank 1392 

Mill Columns 1393 

Safe Distributed Loads on Southern-pine Beams 1393 

Approximate Cost of Mill Buildings 1394 

ELECTRICAL ENGINEERING. 

C. G. S. System of Physical Measurement 1396 

Practical Units used in Electrical Calculations 1396 

Relations of Various Units 1397 

Units of the Magnetic Circuit 1398 

Equivalent Electrical and Mechanical Units 1399 

Permeabihty 1400 

Analogies between Flow of Water and Electricity 1400 

Electrical Resistance. 

Laws of Electrical Resistance 1400 

Electrical Conductivity of Different IVIetals and Alloys 1401 

Conductors and Insulators 1402 

Resistance Varies with Temperature 1402 

Annealing 1402 

Standard of Resistance of Copper Wire 1402 

Wire Table, Standard Annealed Copper 1404 

Direct Electric Currents. 

Ohm's Law 1406 

Series and Parallel or Multiple Circuits 1406 

Resistance of Conductors in Series and Parallel 1407 

Internal Resistance 1408 

Power of the Circuit 1408 

Electrical. Indicated, and Brake Horse-power 1408 

Heat Generated by a Current 1408 

Heating of Conductors 1409 

Heating of Coils 1409 

Fusion of Wires 1409 

Allowable Carrying Capacity of Copper Wires 1410 

Underwriters' Insulation 1410 

Electric Transmission, Direct-Currents. 

Drop of Voltage in Wires Carrying Allowed Cm-rents 1410 

Section of Wire Required for a Given Current 1410 

Weight of Copper for a Given Power 1411 



Xlii CONTENTS. 

PAGE 

Short-circuiting 1411 

Economy of Electric Transmission 1411 

Efficiency of Electric Systems 1412 

Wire Table for 110, 220, 500, 1000, and 2000 volt Circuits 1413 

Resistances of Pure Aluminum Wire 1414 

Electric Railways. 

Schedule Speeds, Miles per Hour 1414 

Train Resistance 1415 

Rates of Acceleration 1415 

Safe Maximum Speed on Curves 1416 

Electric Resistance of Rails and Bonds 1416 

Electric Locomotives 1416 

Efficiencies of Distributing Systems 1417 

Steam Railroad Electrifications 1418 

Electric Welding. 

Arc Welding 1419 

Data of Electric Welding in Railway Shops 1419 

Resistance Welding 1419 

Cost of Welding 1420 

Electric Heaters. 

Elementary Form of Heater 1420 

Relative Efficiency of Electric and Steam Heating 1421 

Heat Required to Warm and Ventilate a Room 1421 

Domestic Heating 1421 

Electric Furnaces. 

Arc Furnaces and Resistance Furnaces 1422 

Uses of Electric Furnaces 1423 

Electric Smelting of Pig-iron 1424 

Ferro-alloys 1424 

Non-ferrous Metals 1424 

Electric Batteries. 

Primary Batteries . 1425 

Description of Storage-batteries or Accumulators 1425 

Rules for Care of Storage-batteries 1426 

Efficiency of a Storage Cell 1427 

Uses of Storage-batteries 1427 

Edison Alkaline Battery 1428 

Electrolysis 1428 

Electro-chemical Equivalents 1429 

The Magnetic Circuit. 

Lines and Loops of Force 1430 

Values of B and H 1431 

Tractive or Lifting Force of a Magnet 1431 

Determining the Polarity of Electro-magnets 1432 

Determining the Dii'ection of a Current 1432 

Dynamo-electric Machines. 

Rating of Generators and Motors 1432 

Temperature Limitations of Capacity 1433 

Methods of Determining Temperatures 1434 

Temperature Limits of Hottest Spot 1434 

Moving Force of a Dynamo-electric Machine 1435 



CONTENTS. xliii 

PAGE 

Torque of an Armature 1435 

Torque, Horse-power and Revolutions 1436 

Electro-motive Force of the Armature Circuit 1436 

Strength of the Magnetic Field 1436 

Direct-Current Generators. 

Series-, Shunt- and Compound-woUnd 1437 

Commutating Pole Machines 1438 

Parallel Operation 1439 

Three- Wire System 1439 

Alternating Currents. 

Maximum, Average and Effective Values 1440 

Frequency 1440 

Inductance ,1440 

Capacity 1440 

Power Factor 1440 

Reactance, Impedance, Admittance 1441 

Skin Effect 1442 

Ohm's Law Applied to Alternating Current Circuits 1442 

Impedance Polygons 1442 

Self-inductance of Lines and Circuits 1446 

Capacity of Conductors 1446 

Single-phase and Polyphase Currents 1446 

Measurement of Power in Polyphase Circuits 1447 

Alternating Current Generators. 

Synchronous Generators 1448 

Ratmg 1448 

Efficiency 1448 

Regulation 1449 

Rating of a Generator Unit 1449 

Windings 1449 

Voltages •. 1450 

Parallel Operation 1450 

Exciters 1450 

Transformers. 

Primary and Secondary 1451 

Voltage Ratio 1451 

Rating 1451 

Efficiency 1451 

Connections 1452 

Auto Transformers 1453 

Constant-Current Transformers 1453 

Synchronous Cqi^verters. 

Description 1453 

Effective E.M.F. between Collector Rings 1454 

Voltage Regulation 1455 

Starting Synchronous Converters 1455 

Motor-Generators. 

I 

Balancers 1456 

Boosters 1456 

Dynamotors 1457 

Frequency Changers 1457 

Mercury Arc Rectifier 1457 



xliv CONTENTS. 

AlternatingCurrent Circuits. 

PAGE 

Calculation of Alternating Current Circuits 1457 

Relative Weight of Copper Required in Different Systems 1459 

Rule for Size of Wires for Three-phase Transmission Lines 1459 

Notes on High-tension Transmission 1459 

Voltages Advisable for Various Line Lengths 1460 

Line Spacing 1460 

Size of Line Conductors 1460 

A 135, 000- volt Three-phase Transmission System 1461 

Electric Motors. 

Classification of Motors 1461 

Characteristics of Motors 1461 

Series Motor. 1461 

Speed Control of Motors 1462 

Shunt Motor 1462 

Compound Motor 1462 

Induction Motor; Squirrel-cage Motor 1463 

Multi-speed Induction Ivlotors 1463 

Synchronous Motors 1463 

Single-phase Series Motor 1464 

Repulsion Induction Motor 1464 

Reversible Repulsion Motor 1464 

Variable-speed Repulsion Motor 1464 

Motor Applications. 

Pumps 1464 

Fans 1465 

Air Compressors 1465 

Hoists 1465 

Machine Tools 1466 

Motors for Machine Tools 1467 

Illumination — ElectriclandlGaslLighting. 

Illumination v 1468 

Terms, Units, Definitions 1468 

Relative Color Values of lUuminants 1469 

Relation of Illumination to Vision 1469 

Types of Electric Lamps 1470 

Street Lighting 1470 

Illumination by Arc Lamps at Different Distances 1471 

Data of Some Arc Lamps 1471 

Relative Efficiency of Illuminants 1472 

Characteristics of Tungsten Lamps 1473 

Interior Illumination 1473 

Quantity of Electricity or Gas Required for Illuminating 1474 

Standard Units ; Mazda and Welsbach 1475 

Cost of Electric Lighting 1475 

Recent Street Lighting Installations 1476 

Symbols Used in Electric Diagrvns 1477 



NAMES AND ABBREVIATIONS OF PERIODICALS AND 
TEXT -BOOKS FREQUENTLY REFERRED TO IN 
THIS WORK. 



Am. Mach. American Machinist. 

App. Cyl. Mech. Appleton's Cyclopaedia of Mechanics, Vols. I and II. 

Bull. I. & S. A. Bulletin of the American Iron and Steel Association. 

Burr's Elasticity and Resistance of Materials. 

Clark, R. T. D. D. K. Clark's Rules, Tables, and Data for Mechanical 
Engineers. 

Clark, S. E. D. K. Clark's Treatise on the Steam-Engine. 

Col. Coll. Qly. Columbia College Quarterly. 

El. Rev. Electrical Review. 

El. World. Electrical World and Engineer. 

Engg. Engineering (London). 

Eng. News. Engineering News. 

Eng. Rec. Engineering Record. 

Engr. The Engineer (London). 

Fairbairn's Useful Information for Engineers. 

Flynn's Irrigation Canals and Flow of Water. 

Indust. Eng. Industrial Engineering. 

Jour. A. C. I. W. Jom-nal of American Charcoal Iron Workers* 
Association. 

Jour. Ass. Eng. Soc. Joiu-nal of the Association of Engineering 
Societies. 

Jour. F. I. Journal of the Franklin Institute. 

Lanza's Applied Mechanics. 

Machy. Machinery. 

Merriman's Strength of Materials. 

Modem Mechanism. Supplementary volume of Appleton's Cyclo- 
paedia of Mechanics. 

Peabody's Thermodynamics. 

Proc. A. S. H. V. E. Proceedings. Am. Soc'y of Heating and Ventilat- 
ing Engineers. 

Proc. A. S. T. M. Proceedings Amer. Soc'y for Testing Materials. 

Proc. Inst. C. E. Proceedings Institution of Civil Engineers (London). 

Proc. Inst. M. E. Proceedings Institution of Mechanical Engineers 
(London) . 

Proceedings Engineers' Club of Philadelphia. 

Rankine, S. E. Rankine's The Steam Engine and other Prime Movers. 

Rankine's Machinery and Millwork. 

Rankine, R. T. D. Rankine's Rules, Tables, and Data. 

Reports of U. S. Iron and Steel Test Board. 

Reports of U. S. Testing Machine at Watertown, Massachusetts. 

Rontgen's Thermodynamics. 

Seaton's Manual of Marine Engineering. 

Hamilton Smith, Jr.'s Hydraulics. 

Stevens Indicator. 

Thompson's Dynamo-electric Machinery. 

Thurston's Manual of the Steam Engine. 

Thurston's Materials of Engineering. 

Trans. A. I. E. E. Transactions American Institute of Electrical 
Engineers. 

Trans. A. I. M. E. Transactions American Institute of Mining 
Engineers. 

Trans. A. S. C. E. Transactions American Society of Civil Engineers. 

Trans. A. S. M. E. Transactions American Society of Mechanical 
Engineers. 

Trautwine's Civil Engineer's Pocket Book. 

The Locomotive (Hartford, Connecticut). 

Unwiu's Elements of Machine Design. 

Weisbach's Mechanics of Engineering. 

Wood's Resistance of Materials. 

Wood's Thermodynamics. 



MATHEMATICS. 







Greek Letters. 






H 


f) 


Eta 


N V Nu 


T 


T Tan 





u 


Theta 


H ^ Xi 


Y 


u Upsilon 


I 


I 


Iota 


o Omicron 


^ 


</> Phi 


K 


K 


Kappa 


n TT Pi 


X 


X Chi 


A 


A 


Lambda 


P p Kho 


>!' 


»// Psi 


M 


A* 


Mu 


2 0-9 Sigma 


12 


(o Omega 



A a Alpha 

B /3 Beta 

r Y Gamma 

A 6 Delta 

E e Epsiloii 

Z ^ Zeta 

Arithmetical and Algebraical Signs and Abbreviations* 



4- plus (addition). 
+ positive. 

- minus (subtraction). 

— negative. 

± plus or minus. 
T minus or plus. 
= equals. 
X multiplied by. 
ah or a.b ^ a X b, 
-5- divided by. 
/ divided by. 

£ = a/& = a -^ 6. 15-16 = ^• 

9 ' o lO 

02 = j^;0.002 = ;^^. 

V square root. 

^ cube root. 

>/ 4th root. 

: IS to, :: so is, : to (proportion). 

2 : 4 :: 3 : 6, 2 is to 4 as 3 is to 6. 

: ratio; divided by. 

2 : 4, ratio of 2 to 4 = 2/4. 

.'. therefore. 

> greater than. 

< less than. 

D square. 

O round. 

° degrees, arc or thermometer. 

'minutes or feet. 

" seconds or inches. 

' " "' accents to distinguish letters, 
as a' , a", a"' . 

fli, «2, fls, flft, etc, read a sub 1, a sub 
6, etc. 

() [ 1 J \ parenthesis, brackets, 

braces, vinculum; denoting 
that the numbers enclosed are 
to be taken toget her; as, 
(a + &)c = 4 + 3 X 5 = 35. 

a2, a3, a squared, a cubed. 

a^, a raised to the nth power, 

a§ = ^a2, ai = Vas. 

a a2 

109 = 10 to the 9th power = 

1,000,000,000. 
sin a = the sine of a. 
sin~i a = the arc whose sine is a. 

sin a— 1 = 

sm a 
log = logarithm. 

loge or hyp log = hyperbolic loga- 
rithm. 
% per cent. 
A angle. 



L right angle. 
J- perpendicular to. 
sin, sine. 
cos, cosine, 
tan, tangent, 
sec, secant, 
versin, versed sine, 
cot, cotangent, 
cosec, cosecant, 
covers, co-versed sine. 

In Algebra, the first letters of 
the alphabet, a, 6, c, cf, etc., are 
generally used to denote known 
quantities, and the last letters, 
w, X, y, z, etc., unknown quantities. 

Abbreviations and Symbols com- 
monly used, 
d, differential (in calculus). 



/: 



, integral (in calculus). 



integral between limits a and b. 



A, delta, difference. 

2, Sigma, sign of summation. 

TT, pi, ratio of circumference of 

circle to diameter = 3.14159. 
g, acceleration due to gravity = 

32.16 ft. per second per second. 

Abbreviations frequently used in 

this Book. 
L., 1., length in feet and inches. 
B., b., breadth in feet and inches. 
D., d., depth or diameter. 
H., h., height, feet and inches. 
T., t., thickness or temperature. 
v., v., velocity. 
F., force, or factor of safety, 
f., coefficient of friction. 
E., coefficient of elasticity. 
R., r., radius. 
W., w., weight. 
P., p., pressure or load. 
H.P., horse-power. 
I.H.P., indicated horse-power. 
B.H.P., brake horse-power, 
h. p., high pressure, 
i. p., intermediate pressure. 
1. p., low pressure. 
A.W.G., American Wire Gauge 

(Brown & Sharpe). 
B.W.G., Birmingham Wire Gauge, 
r. p. m., or revs, per min., revolu- 
tions per minute. 
Q. = quantity, or volume. 



2 ARITHMETia 



ARITHMETIC. 

The user of this book is supposed to have had a training in arithmetic as 
well as in elementary algebra. Only those rules are given here which are 
apt to be easily forgotten. 

GREATEST COMMON MEASURE, OR GREATEST 
C03I3ION DIVISOR OF TWO NUMBERS. 

Rule. — Divide the greater number by the less ; then divide the divisor 
by the remainder, and so on, dividing always the last divisor by the last 
remainder, until there is no remainder, and the last divisor is the greatest 
common measure required. 



LEAST C030ION 3rULTrPLE OF TWO OR MORE 
NU3IBERS. 

Rule. — Divide the given numbers by any number that will divide the 
greatest number of them without a remainder, and set the quotients with 
the undivided numbers in a line beneath. 

Divide the second line as before, and so on, until there are no two num- 
bers that can be divided; then the continued product of the divisors, last 
quotients, and undivided numbers will give the multiple required. 

FRACTIONS. 

To reduce a common fraction to its lowest terms. — Divide both 

terms by their greatest common divisor: 39/52 = ^U. 

To change an improper fraction to a mixed number. — Divide the 
numerator by the denominator; the quotient is the whole number, and 
the remainder placed over the denominator is the fraction: 39/4 = 93/4. 

To change a mixed number to an improper fraction. — Multiply 
the whole number by the denominator of the fraction; to the product add 
the numerator; place the sum over the denominator: 17/8 = i5/g. 

To express a whole number in the form of a fraction with a given 
denominator. — Multiply the whole number by the given denominator, 
and place the product over that denominator: 13 = 39/3. 

To reduce a compound to a simple fraction, also to multiply 
fractions. — Multiply the numerators together for a new numerator ana 
the denominators together for a new denominator: 

2 ^ 4 8 , 2 ,, 4 8 
-of- = -. also 3X3 = 5- 

To reduce a complex to a simple fraction. — The numerator and 
denominator must each first be given the form of a simple fraction; then 
multiply the numerator of the upper fraction by the denominator of the 
lower for the new numerator, and the denominator of the upper by the 
numerator of the lower for the new denominator: 

7/8 _^ 7/8 ^ 28 ^ 1 
13/4 7/4 56 2* 

To divide fractions. — Reduce both to the form of simple fractions, 
invert the divisor, and proceed as in multiplication: 

4 '* 44 4^5 20 5 

Cancellation of fractions. — In compound or multiplied fractions, 
divide any numerator and any denominator by any number which will 
divide them both without remainder, striking out the numbers thus 
divided and setting down the quotients in their stead. 

To reduce fractions to a common denominator. — Reduce each 
fraction to the form of a simple fraction; then multiply each numerator 



DECIMALS. 



3 



'by all the denominators except its own for the new numerator, and all 
the denominators together for the common denominator: 



21 . 

42' 



14^ 

42' 



18 
42' 



To add fractions. — Reduce them to a common denominator, then 
add the numerators and place their sum over the common denominator: 



+ ;; = 



21 + 14 + 18 
42 



= i=ixi/«. 



To subtract fractions. — Reduce them to a common denominator, 
subtract the numerators and place the difference over the common denom- 
inator: 

1 _ 3 7-6 _ 1_ 

2 7 "" 14 14 



DECIMALS. 

To add decimals. — Set down the figures so that the decimal points 
•are one above the other, then proceed as in simple addition: 18.75' +■ 0.012 
= 18.762. 

To subtract decimals. — Set down the figures so that the decimal 
points are one above the other, then proceed as in simple subtraction: 
18.75 - 0.012 = 18.738. 

To multiply decimals. — Multiply as in multipUcation of whole num- 
bers, then point off as many decimal places as there are in multiplier and 
multiplicand taken together: 1.5 X 0.02 = .030 = 0.03. 

To divide decimals. — Divide as in whole numbers, and point off in 
the quotient as many decimal places as those in the dividend exceed those 
in the divisor. Ciphers must be added to the dividend to make its decimal 
places at least equal those in the divisor, and as many more as it is desired 
to have in the quotient: 1.5 -j- 0.25 = 6. 0.1 -f- 0.3 = 0.10000 -^ 0.3 
= 0.3333 +. 

Decimal Equivalents of Fractions of One Inch. 



1-64 


.015625 


17-64 


.265625 


33-64 


.515625 


49-64 


.765625 


1-32 


.03125 


9-32 


.28125 


17-32 


.53125 


25-32 


.78125 


3-64 


.046875 


19-64 


.296875 


35-64 


.546875 


51-64 


.796875 


1-16 


.0625 


5-16 


.3125 


9-16 


.5625 


13-16 


.8125 


5-64 


.078125 


21-64 


.328125 


37-64 


.578125 


53-64 


.828125 


3-32 


.09375 


11-32 


.34375 


19-32 


.59375 


27-32 


.84375 


7-64 


.109375 


23-64 


.359375 


39-64 


.609375 


55-64 


.859375 


1-8 


.125 


3-8 


.375 


5-8 


.625 


7-8 


.875 


9-64 


.140625 


25-64 


.390625 


41-64 


.640625 


57-64 


.890625 


5-32 


.15625 


13-32 


.40625 


21-32 


.65625 


29-32 


.90625 


11-64 


.171875 


27-64 


.421875 


43-64 


.671875 


59-64 


.921875 


3-16 


.1875 


7-16 


.4375 


11-16 


.6875 


15-16 


.9375 


13-64 


.203125 


29-64 


.453125 


45-64 


.703125 


61-64 


.953125 


7-32 


.21875 


15-32 


.46875 


23-32 


.71875 


31-32 


.96875 


15-64 


.234375 


31-64 


.484375 


47-64 


.734375 


63-64 


.984375 


1-4 


.25 


1-3 


.50 


3-4 


.75 


1 


1. 



To convert a common fraction into a decimal. — Divide the nume- 
rator by the denominator, adding to the numerator as many ciphers 
prefixed by a decimal point as are necessary to give the number of decimal 
places desired in the result: 1/3 = 1.0000 ^ 3 = 0.3333 +. 

To convert a decimal into a common fraction. — Set down the 
decimal as a numerator, and place as the denominator 1 with as many 
ciphers annexed as there are decimal places in the numerator; erase the 



ARITHMETIC. 






o 



f-l 
















1 




GO O^ 


t-loo 


sO c<^ o 
mom 
>0 eg t>. 
rN 00 00 


-4h 


— c^ r>. u-> 

S 2 5 :j 

>q t>. !>. oq 


ecl^ 


m Tt en — o 
(s o nO c<^ o 
nO O m o m 
m^ nO vO l>. t>j 




t>, vo ^o vO in in 
<N m GO — -^ t>» 
r>. — m o "* 00 
■^^ m m vo vO vO 


»cloo 














^. 


t^ 00 CO C> On O 

On GO t>. no in m 
<N vO O "^ 00 csj 
"^. "^. "^. "^. "^ ^ 


Cl^ 
^i-^ 














nO 

in 

CO 


i>i On o eg en m 
vO — t>. eg r>. eg 

00 rg m On rg no 
en '^^ -"T "^^ m^ in 


^CX 










§ 

m 




m 

CO 


CO O en m GO O 
m m nO r>^ 00 O 
'^ r>. o en nO O 
en en -^^ '^^ ■^^ m 


-^ 








Si 


00 

00 
?4 




CO 


GO — m 00 <N m 
O 00 m cs| o r>. 
O <N m 00 — en 
en en en en ""r 'i; 


ccloo 






•1 


1 


in 

2 


I 


c<^ 


00 en r^ >— nO O 
hN — ^ oo — m 
m 00 O <S in t>. 
rg CNi en en en en 


•^^ 








en 


3 

m 


00 
m 


en 
in 


GO '<»■ On T O m 

^ ^ en en en e^l 
*- en m r>. o^ — 
«s rg <s eg eg en 


H^ 




m 

i. 


00 r<^ 

B S 


2 


o 
m 


i 


vO 

m 


ON m — r>. -^ O 
— r> en 00 T O 
r^ 00 O — en m 

'". '". ^. ^. ^. *^ 


"^ 


m 
O 


q 


S S 

m hN 
q q 


O 
CM 


00 


m 
in 
o 


B 


On no en — GO m 
oo O eg TT m rN 
eg rr m no r^ 00 


Hoo 


m c<^ 
q q 


en 
q 


s s 


m 
q 


m 

i. 


en 

q 


oo 

s 


On oo nO -^ e^ O 
in en •— On i^ m 
00 ON o o — eg 
q q — , — , — , — . 




Ov 00 1^ 

r<^ r^ »- 
o o — 
q q q 


NO 

m 
q 


m "-r 

5. o 




CO 

q 


q 


On 

3 


O On 00 t>» nO in 

en nO O "^ 00 eg 
rr -T m m m nO 
q q q q q q 


1—1 


mom 
<si m r>. 

vO <S 00 


s 

m 


m o 
(S m 
— r-x 


m 

en 


i. 


in 

vO 

m 


o 

m 

3. 


m O in o m 
r>. O eg m r>. o 

GO m — r>. en O 

nO r> 00 00 On O 


° 


-tS-l-c.^ 


^I^xC^CC^X 


^^'^c-^'^ii^c-i^r^^T''-' 



COMPOUND NUMBERS. 



decimal point in the numerator, and reduce the fraction thus formed to Its 
lowest terms: 

°-25 = lfo=i'0-^333=^^ = i. nearly. 

To reduce a recurring decimal to a common fraction. — Subtract 
the decimal figures that do not recur from the whole decimal including 
one set of recurring figures; set down the remainder as the numerator of 
the fraction, and as many nines as there are recurring figures, followed by 
as many ciphers as there are non-recurring figures, in the denominator. 
Thus: 

0.79054054, the recurring figures being 054. 
Subtract 79 

78975 . , ^ ^ .. 1 w s 117 

QQQOn ^ (reduced to its lowest terms) — ^* 



C03IPOIIND OR DEN03IINATE NU3IBERS. 

Reduction descending. — To reduce a compound number to a lower 
denomination. Multiply the number by as many units of the lower 
denomination as makes one of the higher. 

3 yards to inches: 3 X 36 = 108 inches. 

0.04 square feet to square inches: .04 X 144 = 5.76 sq. in. 

If the given number is in more than one denomination proceed in steps 
from the highest denomination to the next lower, and so on to the lowest, 
adding in the units of each denomination as the operation proceeds. 

3 yds. 1 ft. 7 in. to inches: 3X3 = 9, +1 = 10, 10 X 12 = 120, +7 = 127 in. 

Reduction ascending. — To express a number of a lower denomina- 
tion in terms of a higher, divide the number by the number of units of 
the lower denomination contained in one of the next higher; the quotient 
is in the higher denomination, and the remainder, if any, in the lower. 
127 inches to higher denomination. 
127 -7- 12 = 10 feet + 7 inches; 10 feet -J- 3 = 3 yards + 1 foot. 

Ans. 3 yds. 1 ft. 7 in. 

To express the result in decimals of the higher denomination, divide the 
given number by the number of units of the given denomination contained 
in one of the required denomination, carrying the result to as many places 
of decimals as may be desired. 

127 inches to yards: 127 -f- 36 = 319/36 = 3.5277 + yards. 



Decimals of a Foot Equivalent to Inches and Fractions 
of an Inch. 



Inches 





Vs 


H 


Vs 


H 


Vs 


H 


Vs 








.01042 


.02083 


.03125 


.04167 


.05208 


.06250 


.07292 


1 


.0833 


.0938 


.1042 


.1146 


.1250 


.1354 


.1458 


.1563 


2 


.1667 


.1771 


.1875 


.1979 


.2083 


.2188 


.2292 


.2396 


3 


.2500 


.2604 


.2708 


.2813 


.2917 


.3021 


.3125 


.3229 


4 


.3333 


.3438 


.3542 


.3646 


.3750 


.3854 


.3958 


.4063 


5 


.4167 


.4271 


.4375 


.4479 


.4583 


.4688 


.4792 


.4896 


6 


.5000 


.5104 


.5208 


.5313 


.5417 


.5521 


.5625 


.5729 


7 


.5833 


.5938 


.6042 


.6146 


.6250 


.6354 


.6458 


.6563 


8 


.6667 


.6771 


.6875 


.6979 


.7083 


.7188 


.7292 


.7396 


9 


.7500 


.7604 


.7708 


.7813 


.7917 


.8021 


.8125 


.8229 


10 


.8333 


.8438 


.8542 


.8646 


.8750 


.8854 


.8958 


.9063 


11 


.9167 


.9271 


.9375 


.9479 


.9583 


.9688 


.9792 


.9896 



ARITHMETIC. 



RATIO AND PROPORTION. 

Ratio Is the relation of one number to another, as obtained by dividing 
the first number by the second. Synonymous with quotient. 

Ratio of 2 to 4, or 2 : 4 = 2/4= 1/2. 
Ratio of 4 to 2, or 4 : 2 = 2. 

Proportion is the equality of two ratios. Ratio of 2 to 4 equals ratio 
of 3 to 6, 2/4=3/6; expressed thus, 2 : 4 :: 3 : 6; read, 2 is to 4 as 3 is to 6. 

The first and fourth terms are called the extremes or outer terms, the 
second and third the means or inner terms. 

The product of the means equals the product of the extremes: 

2 : 4 : ; 3 : 6; 2 X 6 = 12; 3 X 4 = 12. 

Hence, given the first three terms to find the fourth, multiply the 
second and third terms together and divide by the first. 

2 : 4 : : 3 : what number? Ans. ^~-^ = 6. 

o c 
Algebraic expression of proportion. — a : b : : c : d] r = -^; ac? »= 6c; 

* 1,. v, be . be , ad ad 

from which a = ~r ; d=' — ;o= — ; c = -r- • 
a a c b 

From the above equations may also be derived the following: 

b : a: :d : c a + b : a : :c + d : c a + b : a — b : : c + d ; c -^ d 

a : c::b I d a + b i b : :c -h d : d a^ : b^ : : c^ : d'^ 

aib^cid a - b :b::c - did ^: ^: :y/c ^d 

a — b : a: :c — d : c 

Mean proportional between two given numbers, 1st and 2d, is such 
a number that the ratio which the first bears to it equals the ratio which it 
bears to the second. Thus, 2:4::4:8;4isa mean proportional between 

2 and 8. To find the mean proportional between two numbers, extract 
the square root of their product. ' 

Mean proportional of 2 and 8 = ^/2 x 8 = 4. 

Single Rule of Three; or, finding the fourth term of a proportion 
when three terms are given. — Rule, as above, when the terms are stated 
in their proper order, multiply the second by the third and divide by the 
first. The difficulty is to state the terms in their proper order. The 
term which is of the same kind as the required or fourth term is made the 
third; the first and second must be like each other in kind and denomina- 
tion. To determine which is to be made second and which first requires 
a little reasoning. If an inspection of the problem shows that the answer 
should be greater than the third term, then the greater of the other two 
given terms should be made the second term — otherwise the first. Thus, 

3 men remove 54 cubic feet of rock in a day; how many men will remove 
in the same time 10 cubic yards? The answer is to be men — make men 
third term; the answer is to be more than three men, therefore make the 
greater quantity, 10 cubic yards, the second term; but as it is not the same 
denomination as the other term it must be reduced, = 270 cubic feet. 
The proportion is then stated: 

3 X 270 
54 : 270 : : Z :x (the required number); x = — ^7 — = 15 men. 

The problem is more complicated if we increase the number of given 
terms. Thus, in the above question, substitute for the words "in the 
same time" the words "in 3 days." First solve it as above, as if the work 
were to be done in the same time; then make another proportion, stating 
it thus: If 15 men do it in the same time, it will take fewer men to do it in 
3 days; make 1 day the second term and 3 days the first term. 3:1:: 
15 men : 5 men. 



POWERS OF NUMBERS. 



Compound Proportion, or Double Rule of Three. — By this rule 
are solved questions like the one just given, in which two or more statings 
are required by the single rule of three. In it, as in the single rule, there 
is one third term, which is of the same kind and denomination as the 
fourth or required term, but there may be two or more first and second 
terms. Set down the third term, take each pair of terms of the same kind 
separately, and arrange them as first and second by the same reasoning as 
is adopted in the single rule of three, making the^greater of the pair the 
second if this pair considered alone should require the answer to be greater. 

Set down all the first terms one under the other, and likewise all the 
second terms. Multiply all the first terms together and ail the second 
terms together. Multiply the product of all the second terms by the third 
term, and divide this product by the product of all the first terms. 
Example: If 3 men remove 4 cubic yards in one day, working 12 hours a 
day, how many men working 10 hours a day will remove 20 cubic yards 
in 3 days? 

Yards 4 : 20 



Days 
Hours 



3 ; 

10 ; 



3 men : x men . 



Products 120 : 240 : : 3 : 6 men. Ans. 

To abbreviate by cancellation, any one of the first terms may cancel 
either the third or any of the second terms; thus, 3 in first cancels 3 in 
third, making it 1, 10 cancels into 20 making the latter 2, which into 4 
makes it 2, which into 12 makes it 6, and the figures remaining are only 
1 : 6 : : 1 : 6. 



INVOLUTION, OR POWERS OF NUMBERS. 

Involution is the continued multiplication of a number by itself a given 
number of times. The number is called the root, or first power, and the 
products are called powers. The second power is called the square and 
the third power the cube. The operation may be indicated without being 
performed by writing a small figure called the index or exponent to the 
right of and a little above the root; thus, 3^ = cube of 3, = 27. 

To multiply two or more powers of the same number, add their expo- 
nents; thus, 22 X 23 = 25, or 4 X 8 = 32 = 2^. 

To divide two powers of the same number, subtract their exponents; 

thus, 23 ^ 22 = 21 = 2; 22 -j- 2< = 2*2 = i^ = 4 ' '^^* exponent may 
thus be negative. 2^ -^ 2^ = 2^ = 1, whence the zero power of any 
number = 1. The first power of a number is the number itself. The 
exponent may be fractional, as 2^, 2^, which means that the root is to be 
raised to a power whose exponent is the numerator of the fraction, and 
the root whose sign is the denominator is to be extracted (see Evolution). 
The exponent may be a decimal, as 2^'^, 2^'^; read, two to the five-tenths 
power, two to the one and five-tenths power. These powers are solved by 
means of Logarithms (which see). 

First Nine Powers of the First Nine Numbers. 





^ o 


^ o 


4th 


5th 


6th 


7th 


8th 


9th 


Power. 


Power. 


Power. 


Power. 


Power. 


Power. 


PW 


p^ 


& 














1 

2 


1 

4 


] 
8 


1 
16 


1 
32 


1 
64 


1 

128 


1 

256 


I 
512 


3 


9 


27 


81 


243 


729 


2187 


6561 


19683 


4 


16 


64 


256 


1024 


4096 


16384 


65536 


262144 


5 


25 


125 


625 


3125 


15625 


78125 


390625 


1953125 


6 


36 


216 


1296 


7776 


46656 


279936 


1679616 


10077696 


7 


49 


343 


2401 


16807 


1 1 7649 


823543 


5764801 


40353607 


8 


64 


512 


4096 


32768 


262144 


2097152 


16777216 


134217728 


9 


81 


729 


6561 


59049 


531441, 


4782969 


43046721 


387420489 



8 



ARITHMETIC 



The First Forty Powers of 2, 





<6 

1 




i 


C 

1 




is 


i 




1 





1 


9 


512 


18 


262144 


27 


134217728 


36 


68719476736 


1 


2 


10 


1024 


19 


524288 


28 


268435456 


37 


137438953472 


2 


4 


11 


2048 


20 


1048576 


29 


536870912 


38 


274877906944 


3 


8 


12 


4096 


21 


2097152 


30 


1073741824 


39 


549755813888 


4 


16 


13 


8192 


22 


4194304 


31 


2147483648 


40 


1099511627776 


5 


32 


14 


16384 


23 


8388608 


32 


4294967296 






6 


64 


15 


32768 


24 


16777216 


33 


8589934592 






7 


128 


16 


65536 


25 


33554432 


34 


17179869184 






8 


256 


17 


131072 


26 


67108864 


35 


34359738368 







EVOLUTION. 

Evolution is the finding of the root (or extracting the root) of any 
number the power of which is given. ^ 

The sign \/ indicates that the square root is to be extracted: "^ V Vi 
the cube root, 4th root, nth root. 

A fractional exponent with 1 for the numerator of the fraction is also 
used to indicate that the operation of extracting the root is to be per- 
formed; thus, 2^, 2* = ^J2, ^2. 

When the power of a number is indicated, the involution not being per- 
formed, the extraction of any root of that power may also be indicated by 
dividing the index of the power by the index of the root, indicating the 
division by a fraction. Thus, extract the square root of the 6th power 
of 2: _ 

V'26 = 2t = 2x = 23 = 8. 

The 6th power of 2, as in the table above, is 64; ^^ = 8. 

Difficult problems in evolution are performed by logarithms, but the 
square root and the cube root may be extracted directly according to the 
rules given below. The 4th root is the square root of the square root. 
The 6th root is the cube root of the square root, or the square root of the 
cube root; the 9th root is the cube root of the cube root; etc. 

To Extract the Square Root. — Point off the given number into 
periods of two places each, beginning with units. If there are decimals, 
point these off likewise, beginning at the decimal point, and supplying 
as many ciphers as may be needed. Find the greatest number whose 
square is less than the first left-hand period, and place it as the first 
figure in the quotient. Subtract its square from the left-hand period, 
and to the remainder annex the two figures of the second period for 
a dividend. Double the first figure of the quotient for a partial divisor; 
find how many times the latter is contained in the dividend exclusive 
of the right-hand figure, and set the figure representing that number of 
times as the second figure in the quotient, and annex it to the right of 
the partial divisor, forming the complete divisor. Multiply this divisor 
by the second figure in the quotient and subtract the product from the 
dividend. To the remainder bring down the next period and proceed as 
before, in each case doubling the figures in the root already found to obtain 
the trial divisor. Should the product of the second figure in the root by 
the completed divisor be greater than the dividend, erase the second 
figure both from the quotient and from the divisor, and substitute the 
next smaller figure, or one small enough to make the product of the second 
figure by the divisor less than or equal to the dividend. 



SQUARE ROOT. 

3.1415926536 LL77245 + 
1 

27|214 




35444 



:UBE ROOT. 




9 


CUBE ROOT. 




i.S8i.365.963.625l 12345 
1 


300 X 12 
30 X 1 


= 300 
X2 = 60 

22= 4 

364 

= 43200 

: 3 = 1080 

32 = 9 


881 
728 


300 X 122 
30X12 X 


153365 




44289 

= 4538700 
= 14760 
= 16 


132867 


300 X 1232 
30 X 123 X 4 

42 


20498963 




4553476 


18213904 



300 X 1 2342 = 456826800 

30X1234X5= 185100 

52= 25 



457011925 



2285059625 



2285059625 



To extract the square root of a fraction, extract the root of a numerator 

V/4 2 
and denominator separately. i/;q = o' or first convert the fraction into 
2 T y o 

I = V.4444 + = 0.6666 +. 

To Extract the Cube Root. — Point off the number into periods of 3 
figures each, beginning at the right hand, or unit's place. Point off 
decimals in periods of 3 figures from the decimal point. Find the greatest 
cube that does not exceed the left-hand period; write its root as the first 
figure in the required root. Subtract the cube from the left-hand period, 
and to the remainder bring down the next period for a dividend. 

Square the first figure of the root; multiply by 300, and divide the 
product into the dividend for a trial divisor; write the quotient after 
the first figure of the root as a trial second figure. 

Complete the divisor by adding to 300 times the square of the first 
figure, 30 times the product of the first by the second figure, and the 
square of the second figure. Multiply this divisor by the second figure; 
subtract the product from the remainder. (Should the product be greater 
than the remainder, the last figure of the root and the complete divisor 
are too large; substitute for the last figure the next smaller number, and 
correct the trial divisor accordingly.) 

To the remainder bring down the next period, and proceed as before to 
find the third figure of the root — that is, square the two figures of thd" 
root already found; multiply by 300 for a trial divisor, etc. 

If at any time the trial divisor is greater than the dividend, bring down 
another period of 3 figures, and place in the root and proceed. 

The cube root of a number will contain as many figures as there are 
periods of 3 in the number. 

To Extract a Higher Root than the Cube. — The fourth root is the 
square root of the square root; the sixth root is the cube root of the square 
root or the square root of the cube root. Other roots are most conve- 
niently found by the use of logarithms. 



ALLIGATION. 

shows the value of a mixture of different ingredients when the quantity 
and value of each are known. 

Let the ingredients be a, b, c, d, etc., and their respective values per 
unit w, X, Pt z^ etc, 



10 ARITHMETIC. 

A «= the sum of the quantities = a+b-hc-^d, etc 
P = mean value or price per unit of A, 
AP = aw + hx + cy -\- dz, etc. 
p _ <iw + bx 4- cy 4- dz 
A 

PERl^rUTATION 

shows in how many positions any number of things may be arranged in a 
row; thus, the letters a, b, c may be arranged in six positions, viz. abc, acb, 
cab, cba, bac, bca. 

Rule. — Multiply together all the numbers used in counting the things; 
thus, permutations of 1, 2, and 3 = 1X2X3 = 6. In how many 
positions can 9 things in a row be placed? 

1X2X3X4X5X6X7X8X9 = 362880. 

COMBINATION 

shows how many arrangements of a few things may be made out of a 
greater number. Rule: Set down that figure which indicates the greater 
number, and after it a series of figures diminishing by 1, until as many are 
set down as the number of the few things to be taken in each combination. 
Then beginning under the last one, set down said number of few things; 
then going backward set down a series diminishing by 1 until arriving 
under the first of the upper numbers. Multiply together all the upper 
numbers to form one product, and all the lower numbers to form another; 
divide the upper product by the lower one. 

How many combinations of 9 things can be made, taking 3 in each com- 

^^^^^^°^' 9X8X7 504 ,, 

1X2X3 6 

ABITHMETICAL, PROGRESSION, 

in a series of numbers, is a progressive increase or decrease in each succes- 
sive number by the addition or subtraction of the same amount at each 
step, as 1, 2, 3, 4, 5, etc., or 15, 12, 9, 6, etc. The num^bers are called terms, 
and the equal increase or decrease the difference. Examples in arithmeti- 
cal progression may be solved by the following formulae: 

Let a = first term, I = last term, d = common difference, n = number 
of terms, s = sum of the terms: 

I = a + {n - l)d, 

2s 
= — — a, 
n 

5 = -n[2a+ (n - l)d], 
a = Z - (n - 1)(/, 



ld±^{l+ldy-2ds. 



d = 



/ 


— a 




n 


- 1 

^2 - 


a2 


2s 


- I 


- a 


l_ 


— a 

rl 


+ 1. 



2s 

I +a* 2d 



= -\d± ^2ds + (a - 


w- 


s (n - l)d 




"= - + ■ ?; • 




n 2 




I -h a , P - a^ 




"2 ' 2d ■• 




^ln[2l - (n -l)d]. 




5 (n - l)d 




2 • 




n 






2(s - an) 




n(7i - 1) ' 




2(nl - s) 




n(n - 1) 




d - 2a ± V(2a - dy 


+ Sds 


"" 2d 




2Z + d ± ^(21 + d)2 - 


- Sds 



GEOMETRICAL PROGRESSION. 



11 



GE03IETRICAL PROGRESSION. 

in a series of numbers, is a progressive increase or decrease in each suc- 
cessive number by the same multipher or divisor at each step, as 1, 2, 4, 8, 
16, etc., or 243, 81, 27, 9, etc. The common multipher is caUed the ratio. 
Let a = first terra, I = last term, r = ratio or constant multiplier, n = 
number of terms, m = any term, as 1st, 2d, etc., s = sum of the terms: 



log I = log a + (n 
m = ar^~^ 

airn - l) 

I 

n-ii 



a -h (r — l)s 



(r-l)srn-i 



1) log r, lis - l)^-^ - ais - ap-i = 0. 

log m = log a + (m — 1) log r. 

n— 1 , 



rl — a 
r - 1 ' 



"-^F- 



-^^ 



(r - 1)5 



log a = log Z 



Ir^ - I 



(n — 1) logr. 






s - I 



fU . 



-r + 



■ 0. 



+ 1, 



a ' a 
log Z - log g 
logr 

log I — log g 

log {s - a) - log (s - I) 




+ 1, = 



log r 
log [Ir — (r — l)s] 



log I 



log r 



= 0. 



+ I. 



Population of the United States. 

(A problem in geometrical progression.) 



Year.* 


Population. 


1860 


31,443,321 


1870 


39,818,449* 


1880 


50,155,783 


1890 


62,622,250 


1900 


76,295,220 


1910 


91,972.267 


1920 


Est. 110,367,000 



Increase in 10 Annual Increases 
Years, per cent. per cent. 



Est, 



26.63 

25.96 

24.86 

21.834 

20.53 

20.0 



Est, 



2.39 

2.33 

2.25 

1.994 

1.886 

1.840 



Estimated Population in Each Year from 1880 to 1919. 
(Based on the above rates of increase, in even thousands.) 



1880 


50.156 


1890.... 


62.622 


1900.... 


76.295 


1910.. .. 


91.972 


1881 


51.281 


1891.... 


63.871 


1901 .. .. 


77.734 


1911 .. .. 


93,665 


1882 


52.433 


1892.... 


65.145 


1902.... 


79,201 


1912.. .. 


95,388 


1883 


53.610 


1893.. .. 


66 444 


1903.... 


80.695 


1913.. .. 


97.143 


1884 


54.813 


1894.... 


67.770 


1904.. .. 


82.217 


1914.. .. 


98.930 


1885 


56.043 


1895.... 


69.122 


1905.. .. 


83.768 


1915.. .. 


100.750 


1886 


57.301 


1896.. .. 


70.500 


1906.. .. 


85.348 


1916.. .. 


102.604 


1887 


58.588 


1897.. .. 


71.906 


1907.. .. 


86.958 


1917.. .. 


104.492 


1888 


59.903 


1898.. .. 


73,34J 


1908.. .. 


88.598 


1918.. .. 


106.414 


1889 


61.247 


1899.... 


74.803 


1909.. .. 


90.269 


1919.. .. 


108.373 



* Corrected by addition of 1,260,078, estimated error of the census of 
1870, Census Bulletin No. 16, Dec. 12, 1890. 



12 ARITHMETIC. 

The preceding table has been calculated by logarithms as follows: 
log r = log ; - log a -^ (71 - 1), log m = log a + (w - 1) log r 

Pop. 1900. . .76,295,220 log = 7.8824988 = log/ 

" 1890. . .62,622,250 log = 7.7967285 = log a 

diff. = .0857703 
n •= 11, n - 1 = 10; diff. h- 10 = .00857703 = logr, 

add log for 1890 7.7967285 = log a 



log for 1891 = 7.80530553 No. = 63,871 , 
add again .00857703 



log for 1892 7.81388256 No. = 65,145 . . . 
Compound interest is a form of geometrical progression; the ratio 
being 1 plus the percentage. 



PERCENTAGE: PROFIT AND LOSS: PER CENT 
OF EFFICIENCY. 

Per cent means "by the hundred." A profit of 10 per cent means a 
gain of SIO on every SlOO expended. If a thing is bought for SI and sold 
for $2 the profit is 100 per cent; but if it is bought for $2 and sold for $1 
the loss is not 100 per cent, but only 50 per cent. 

Rule for percentage: Per cent gain or loss is the gain or loss divided by 
the original cost, and the quotient multipUed by 100. 

Eflaciency is defined in engineering as the quotient "output divided by 
input," that is, the energy utilized divided by the energy expended. The 
difference between the input and the output is the loss or waste of energy. 
Expressed as a fraction, efficiency is nearly always less than unity. Ex- 
pressed as a per cent, it is this fraction multiplied by 100. Thus we may 
say that a motor has an efficiency of 0.9 or of 90 per cent. 

The efficiency of a boiler is the ratio of the heat units absorbed by the 
boiler in heating Vv^ater and making steam to the heating value of the coal 
burned. The saving in fuel due to increasing the efliciencv of a boiler 
from 60 to 75% is not 25%, but only 20%. The rule is: Divide the gain 
in efficiency (15) by the greater figure (75). The amount of fuel used is 
inversely proportional to the efficiency; that is, 60 lbs. of fuel with 75% 
efficiency will do as much work as 75 lbs. with 60% efficiency. The 
saving of fuel is 15 lbs. which is 20% of 75 lbs. 



INTEREST AND DISCOUNT. 

Interest is money paid for the use of money for a given time; the 
factors are: 

p, the sum loaned, or the principal; 
t, the time in years; 
r, the rate of interest; 

i, the amount of interest for the given rate and time; 
a = p + i = the amount of the principal with interest 
at the end of the time. 
Formulae: 

vtt 
i = interest = principal X time X rate per cent = i = Jqq • 

ptr 
a •= amount ?= pnncipal + interest => p+ rr?^ • 

100^. 
r -= rate = • — t-; 
pt 

. . , lOOt ptr . 

p - principal = -^ = a - ^: 

e- time =- -^. 



INTEREST AND DISCOUNT. 13 

If the rate is expressed decimally, — thus, 6 per cent = .06, — the 
formulae become 



pt* pr* ^ tr 1-hrt 

Rules for finding Interest. — Multiply the principal by the rate per 
annum divided by 100, and by the time in years and fractions of a year. 

Tisxu*- • • -J '4. i principal X rate X no. of days 

If the time is given in days, interest = — C^^^ .. .Ir. ■■ ^* 

ooo X 100 

In banks interest is sometimes calculated on the basis of 360 days to a 
year, or 12 months of 30 days each. 

Short rules for interest at 6 per cent, when 360 days are taken as 1 year: 

Multiply the principal by number of days and divide by 6000. 

Multiply the principal by number of months and divide by 200. 

The interest of 1 dollar for one month is ^ cent. 



Interest of 100 Dollars for Different Times and Bates. 

Time 2% 3% 4% 5% 6% 8% 10% 

lyear $2.00 $3.00 $4.00 $5.00^ $6.00 $8.00 $10.00 

1 month .161 .25 .33| .4l| .50 .66| .83i 

lday=3iTjyear.0055f .0083^ .0111^ .0138| .01661 .0222f .0277| 
lday=5|s year .005479 .008219 .010959 .013699 .016438 .0219178 .0273973 

Discount is interest deducted for payment of money before it is due. 
' True discount is the difference between the amount of a debt payable 
at a future date without interest and its present worth. The present 
worth is that sum which put at interest at the legal rate will amount to 
the debt when it is due. 

To find the present worth of an amount due at a future date, divide the 
amount by the amount of $1 placed at interest for the given time. The 
discount ec[uals the amount minus the present worth. 

What discount should be allowed on $103 paid six months before it is 
due, interest being 6 per cent per annum? 

103 
■ = $100 present worth, discount ^ 3.00. 

1 + 1 X .06 X ^ 

Bank discount is the amount deducted by a bank as interest on money 
loaned on promissory notes. It is interest calculated not on the actual 
sum loaned, but on the gross amount of the note, from which the discount 
is deducted in advance. It is also calculated on the basis of 360 days 
in the year, and for 3 (in some banks 4) days more than the time specified 
in the note. These are called days of grace, and the note is not payable 
till the last of these days. In some States days of grace have been 
abohshed. 

What discount will be deducted by a bank in discounting a note for $103 
payable 6 months hence? Six months = 182 days, add 3 days grace = 185 

Compound Interest. — In compound interest the interest is added to 
the principal at the end of each year, (or shorter period if agreed upon). 

Let p = the principal, r = the rate expressed decimally, n = no. of 
years, and a the amount; 



a = amount « p(l + r)^; r =» rate = 4/^ - It 

. . t a - log a — log p 

p « pnncipal = (1 ^ .^p ; no. of years « n= ^^^ ^^ ^ y * 



14 



ARITHMETIC. 



Compound Interest Table, 

(Value of one dollar at compound interest, compounded yearly, at 
3, 4, 5, and 6 per cent, from. 1 to 50 years.) 



£ 


Per cent 


22 

1 


Per cent 


1 


3 


4 


5 


6 


3 


4 


5 


6 


, 


1.03 


1.04 


1.05 


1.06 


16 


1 .6047 


1.8730 


2.1829 


2.5403 


2 


1 .0609 


1.0816 


1.1025 


1.1236 


17 


1.6528 


1.9479 


2.2920 


2.6928 


3 


1.0927 


1.1249 


1.1576 


1 1910 


18 


1.7024 


2.0258 


2.4066 


2.8543 


4 


1.1255 


1.1699 


1.2155 


1 .2625 


19 


1.7535 


2.1068 


2.5269 


3.0256 


5 


1.1593 


1.2166 


1.2763 


1 .3382 


20 


1.8061 


2.1911 


2.6533 


3.2071 


6 


1.1941 


1 .2653 


1.3401 


1.4185 


21 


1 .8603 


2.2787 


2.7859 


3.3995 


7 


1 .2299 


1.3159 


1.4071 


1.5036 


22 


1.9161 


2.3699 


2.9252 


3.6035 


8 


1 .2668 


1 .3686 


1.4774 


1.5938 


23 


1.9736 


2.4647 


3.0715 


3.8197 


9 


1 .3048 


1 .4233 


1.5513 


1 .6895 


24 


2.0328 


2.5633 


3.2251 


4.0487 


10 


1.3439 


1.4802 


1.6289 


1.7908 


25 


2.0937 


2.6658 


3.3863 


4.2919 


11 


1.3842 


1.5394 


1.7103 


1.8983 


30 


2.4272 


3.2433 


4.3219 


5.7435 


12 


1.4258 


1.6010 


1.7958 


2.0122 


35 


2.8138 


3.9460 


5.5159 


7.6862 


13 


1 .4685 


1.6651 


1.8856 


2.1329 


40 


3.2620 


4.8009 


7.0398 


10.2858 


14 


1.5126 


1.7317 


1.9799 


2.2609 


45 


3.7815 


5.8410 


8.9847 


13.7648 


15 


1.5580 


1.8009 


2.0789 


2.3965 


50 


4.3838 


7.1064 


11.4670 


18.4204 



At compound interest at 3 per cent money will double itself in 23 I/2 years, 
at 4 per cent in 1 72/3 years, at 5 per cent in 14.2 years, and at 6 per cent in 
11.9 years. 

EQUATION OF PAYMENTS. 

By equation of payments we find the equivalent or average time in 
which one payment should be made to cancel a number of obligations due 
at different dates; also the number of days upon which to calculate interest 
or discount upon a gross sum which is composed of several smaller sums 
payable at different dates. 

Rule. — Multiply each item by the time of its maturity in days from a 
fixed date, taken as a standard, and divide the sum of the products by 
the sum of the items: the result is the average time in days from the stand- 
ard date. T 

A owes B SlOO due in 30 days, $200 due in 60 days, and $300 due in 90 
In how many days may the whole be paid in one sum of $600? 

100X30+200X60+300X90 = 42,000; 42,000 -^ 600 = 70 days, ans. 

A owes B $100, $200, and $300, which amounts are overdue respectively 
30, 60, and 90 days. If he now pays the whole amount, $600, how many 
days' interest should he pay on that sura? A7is. 70 days. 



PARTIAL PAYMENTS. 

To compute interest on notes and bonds when partial payments have 
been made. 

United States Rule. — Find the amount of the principal to the time 
of the first payment, and, subtracting the payment from it, find the 
amount of the remainder as a new principal to the time of the next pay« 
meat. 



ANNUITIES. 



15 



If the payment is less than the interest, find the amount of the principal 
to the time when the sum of the payments equals or exceeds the interest 
due, and subtract the sum of the payments from this amount. 

Proceed in this manner till the time of settlement. 

Note. — The principles upon wliich the preceding rule is founded are: 

1st. That payments must be applied first to discharge accrued interest, 
and then the remainder, if any, toward the discharge of the principal. 

2d. That only unpaid principal can draw interest. 

3Iercantile Method. — When partial payments are made on short 
notes or interest accounts, business men commonly employ the following 
method: 

Find the amount of the whole debt to the time of settlement; also find 
the amount of each payment from the time it was made to the time of 
settlement. Subtract the amount of payments from the amount of the 
debt: the remainder will be the balance due. 



ANIVTJITIES. 

An Annuity is a fixed sum of money paid yearly, or at other equal times 
agreed upon. The values of annuities are calculated by the principles of 
compound interest. 

1. Let I denote interest on $ 1 for a year, then at the end of a year the 
amount will be 1 -f i. At the end of n years it will be (1 + i)^. 

2. The sum which in n years will amount to 1 is or (1 +i) — ^, 



or the present value of 1 due in n years. 



(1 + i)^ 



3. The amount of an annuity of 1 in any number of years n is 



(i+i)^-i 



4. The present value of an annuity of 1 for any number of years n is 
1 - (1+ i)-n 



5. The annuity which 1 will purchase for any number of years n is 
i 



1 - (14- I) - 



6. The annuity which would amount to 1 in n years is 



(1 + i)^ 



Amounts, Present Values, etc., at 5% Interest. 





(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


Years 


(l + i)^ 


(1 + t)-'' 


(l+t)"-l 


l-Ci+t)-'' 


% 


i 




i 


% 


1-(l + i)-^ 


(1 + 1)^-1 


1 . . 


1.05 


.952381 


1.00 


.952381 


1.05 


1.00 


2. . 


1.1025 


.907029 


2.05 


1.859410 


.537805 


.487805 


3. . 


1.157625 


.863838 


3.1525 


2.723248 


.367209 


.317209 


4. . 


1.215506 


.822702 


4.310125 


3.545951 


.282012 


.232012 


5. . 


1.276282 


.783526 


5.525631 


4.329477 


.230975 


.180975 


6. . 


1.340096 


.746215 


6.801913 


5.075692 


.197017 


.147018 


7. . 


1.407100 


.710681 


8.142008 


5.786373 


.172820 


.122820 


8. . 


1.477455 


.676839 


9.549109 


6.463213 


.154722 


.104722 


9. . 


1.551328 


.644609 


1 1 .026564 


7.107822 


.140690 


.090690 


10. . 


1.628895 


.613913 


12.577893 


7.721735 


.129505 


.079505 



16 



ARITHMETIC. 



§ 

o 



© 
© 
© 



p^ 



3 

a* 



I 



ir»Tj-oorN«^ 
00 — tNt^Tj- 



«*^ f<^ r^l t^ 0> 

— p p 00 rs 
O^ — l>»iri vO 

— OQOr>.vO 



00^00 ^o in 

O*' (S t>.' psi oo' 



r^ioo^c^-tn 



vOmo^iA 
00 — cTir*.-^ 



fr\a>r>.»n-^ 



oo — r^^oo^^ 



a>0Or«^ (NOO 
00 — fAOO "^ 



"^ CvJ -^ 00 T 
O r^; '.r — rsi 

"T en C<^ C<^ (NJ 



vO(so^ t>.m 



OOin-f O 
"^cncvi — — 



ir> — vo o^ oq 
\0' o 't' O^' in 
>OvOin "^-^ 



OO^OO — 
cs a* — in p 
r4 oo* vo cK n* 

"^ C«^ C<^ C<N «N| 



m CO f^ ^«n 
00 in in rs in 
hs en O 00 >0 



O — vein- 
ed <smoo in 
"^rrvcq — — 



QOtj-- O0t>. 



a^ rqm oom 



p oq O^^ r<^ vO 
"T o 1^* in in 



Cvin — o^r>» 



Oin-^c^-'T 

P !>» — Tt vO 

rq r^i oo' t^i m' 
O^ <sm oom 



— t^ in — <N| 
O in r^i o oo 
fS — ' 



rqmo*>oO"^ 
o^ fNcn 00 in 
"^cnts — — 



f^ Tj- o\ o^in 
C^rgmoOin 
-^tnrq — — 



•^o^ 00 00 in 
ON vO r>. — m 
NO m* o oo' oo' 





493.83 
325.14 
240.84 
190.24 
156.56 


132.49 
114.47 
100.46 
89.25 
80.11 


a^-n'<rhNO 

T p in tN. nO 
fs" vd O in — 
t>.NO sOinin 


O^vOr^ — (N 
r> -"T — o" c^' 


OOO-Tl^vO 
I^(N0O<SrM 

(N od n-" rg o* 



•^•in — — r>» 
O^ (N '^ o^ m 
n-cnts — — 



•— 00 oo O* ^ 
jn/T/^p^ — 

fr( iK — O — * 

»n — oo^oo 



»n\0(S(Noo 
0><N'TOMn 



mom — r^ 
vO p m^ o^ oq 
^ o vd m' — 

Cs|(N — 



f^^tr^'^m>o r>»ooa*o— <st*\"^m>o r^ooo»om omomo 

— — • ^r^mmmmwm ^. «■ v- C4 C>) •*% «<^ '^ '^ lO 



WEIGHTS AND MEASURES. 



17 



TABLES FOR CALCULATING SEVKING-FUNDS AND 
PRESENT VALUES. 

Engineers and others connected with municipal work and industrial 
enterprises often find it necessary to calculate payments to sinking-funds 
which will provide a sura of money sufficient to pay off a bond issue or 
other debt at the end of a given period, or to determine the present value 
of certain annual charges. The accompanying tables were computed by 
Mr. John W. Hill, of Cincinnati, Eng'g News, Jan. 25, 1894. 

Table I (opposite page) shows the annual sum at various rates of interest 
required to net $1000 in from 2 to 50 years, and Table II shows the present 
value at various rates of interest of an annual charge of $1000 for from 5 
to 50 years, at five-year intervals, and for 100 years. 



Table II. 



- Capitalization of Annuity of $1000 for 
from 5 to 100 Years. 



^ 






Rate of Ii terest, per ( 


3ent. 








31/2 


3 


31/2 


4 


41/2 


5 


51/2 


6 


5 
10 
15 
20 
25 

30 
35 
40 
45 
50 
100 


4,645.88 
8,752.17 
12,381.41 
15,589.215 
18,424.67 

20,930.59 
23,145.31 
25,103.53 
26,833.15 
28,362.48 
36,614.21 


4.579.60 
8,530.13 
11,937.80 
14,877.27 
17,413.01 

19,600.21 
21,487.04 
23,114.36 
24,518.49 
25,729.58 
31,598.81 


4,514.92 
8,316.45 
11,517.23 
14,212.12 
16,481.28 

18,391.85 
20,000.43 
21,354.83 
22,495.23 
23,455.21 
27,655.36 


4,451.68 
8,110.74 
11,118.06 
13,590.21 
15,621.93 

17,291.86 
18,664.37 
19,792.65 
20,719.89 
21,482.08 
24,504.96 


4,389.91 
7,912.67 
10,739.42 
13,007.88 
14,828.12 

16,288.77 
17,460.89 
18,401.49 
19,156.24 
19,761.93 
21,949.21 


4,329.45 
7,721.73 
10,379.53 
12,462.13 
14,093.86 

15,372.36 
16,374.36 
17,159.01 
17,773.99 
18,255.86 
19,847.90 


4,268.09 
7,537.54 
10,037.48 
11,950.26 
13,413.82 

14,533.63 
15,390.48 
16,044.92 
16,547.65 
16,931.97 
18,095.83 


4,212.40 

7,360.19 

9,712.30 

11,469.96 

12,783.38 

13,764.85 
14,488.65 
15,046.31 
15,455.85 
15,761.87 
16,612.64 



WEIGHTS AND MEASURES. 

Long Measure. — Measures of Length. 

12 inches = 1 foot. 

3 feet = 1 yard. 

1760 yards, or 5280 feet = 1 mile. 

Additional measures of length in occasional use: 1000 mils = 1 inch; 
4 inches = 1 hand; 9 inches = 1 span; 2 1/2 feet = 1 military pace; 2 yards 
= 1 fathom; 51/2 yards, or I6I/2 feet = 1 rod (formerly also called pole or 
perch). 

Old Land Pleasure. — 7.92 inches = 1 link; 100 links, or 66 feet, or 4 
rods = 1 chain; 10 chains, or 220 yards = 1 furlong; 8 furlongs, or 80 
chains = 1 mile; 10 square chains = 1 acre. 

Nautical Measure. 

6080.26Jeet,.or 1.15156 stat- j ^^ ^^^t;,^, „i,e_ „, ,,„„t * 

3 nautical miles = 1 league. 

^ "^surutrmtfes""" ''•''' } =1 d^g^ee (at the equator). 
360 degrees = circumference of the earth at the equator. 

* The British Admiralty takes the round figure of 6080 ft. which is the 
length of the " measured mile" used in trials of vessels. The value varies 
from 6080.26 to 6088.44 ft. according to different measures of the earth's 
diameter. There is a difference of opinion among writers as to the use 
of the word " knot" to mean length or a distance — some holding that 
it should be used only to denote a rate of speed. The length between 
knots on the log line is 1/120 of a nautical mile, or 50.7 ft., when a half- 
minute glass is used; so that a speed of 10 knots is equal to 10 nautical 
miles per hour. 



18 ARITHMETIC. 

Square Measure. — Measures of Surface. 

144 square inches, or 183.35 circular ) , o^,,,,,.^ f^«* 

inches } = 1 square foot. 

9 square feet = 1 square yard. 

301/4 square yards, or 2721/4 square feet -= 1 square rod. 

10 sq. chains, or 160 sq. rods, or 4840 sq. ) _ -, ^^^^ 

yards, or 43560 sq. feet ) ~" ■"■ ^^^^• 

640 acres or 27 ,878,400 sq . f t . =1 square mile. 

An acre equals a square whose side is 208.71 feet. 

Circular Inch ; Circular 3Iil, — A circular inch is the area of a circle 

1 inch in diameter = 0.7854 square inch. 

1 square inch = 1.2732 circular inches. 

A circular mil is the area of a circle 1 mil, or 0.001 inch in diameter. 
10002 or 1,000,000 circular mils = 1 circular inch. 

1 square inch = 1,273,239 circular mils. 

The mil and circular mil are used in electrical calculations involving 
the diameter and area of wires. 

Solid or Cubic Measure. — Measures of Volume. 

1728 cubic inches = 1 cubic foot. 
27 cubic feet = 1 cubic yard. 
1 cord of wood = a pile, 4X4X8 feet = 128 cubic feet. 
1 perch of masonry = 16 1/2 X 1 1/2 X 1 foot =^ 243/4 cubic feet. 

Liquid Measure. 

4 gills = 1 pint. 
2 pints = 1 quart. 

4 nuartq = 1 gallon i ^' ^- ^31 cubic inches. 
4 quarts - 1 gallon ( ^^^^ 277.274 cubic inches. 

Old Liquid Measures. — 31 1/2 gaUons = l barrel; 42 gallons = 1 tierce; 

2 barrels, or 63 gallons = 1 hogshead; 84 gallons, or 2 tierces = 1 pun- 
cheon; 2 hogsheads, or 126 gallons = 1 pipe or butt; 2 pipes, or 3 pun- 
cheons = 1 tun. 

A gallon of water at 62° F. weighs 8.33561b. (air free, weighed in vacuo). 

The U. S. gallon contains 231 cubic inches; 7.4805 gallons = 1 cubic 
foot. A cyUnder 7 in. diam. and 6 in. high contains 1 gallon, very nearly, 
or 230.9 cubic inches. The British Imperial gallon contains 277.274 cubic 
inches = 1.20032 U. S. gallon, or 10 lbs. of water at 62° F. 

The gallon is a very troublesome unit for engineers. Much labor might 
be saved if it were abandoned and the cubic foot used instead. The 
capacity of a tank or reservoir should be stated in cubic feet, and the 
delivery of a pump in cubic feet per second or in millions of cubic feet in 
24 hours. One cubic foot per second = 86,400 cu. ft. in 24 hours. One 
million cu. ft. per 24 hours = 11.5741 cu. ft. per sec. 

The Miner's Inch. — (Western U. S. for measuring flow of a stream 
of water.) An act of the California legislature. May 23, 1901, makes the 
standard miner's inch 1.5 cu. ft. per minute, measured through any aper- 
ture or orifice. 

The term Miner's Inch is more or less indefinite, for the reason that Cali- 
fornia water companies do not all use the same head above the centre of 
the aperture, and the inch varies from 1.36 to 1.73 cu. ft. per min., but 
the most common measurement is through an aperture 2 ins. high and 
whatever length is required, and through a plank II/4 ins. thick. The 
lower edge of the aperture should be 2 ins. above the bottom of the meas- 
uring-box, and the plank 5 ins. high above the aperture, thus making a 6-in. 
head above the centre of the stream. Each square inch of this opening 
represents a miner's inch, which is equal to a flow of 1 V2 cu. ft. per min. 

Apothecaries' Fluid Measure. 

60 minims = 1 fluid drachm. 8 drachms = 1 fluid ounce. 

In the U. S. a fluid ounce is the 128th part of a U. S. gallon, or 1.805 
cu. ins. It contains 456.3 grains of water at 39° F. In Great Britain 
the fluid ounce is 1.732 cu. ins. and contains 1 ounce avoirdupois, or 437.5 
grains of water at 62° F. 



WEIGHTS AND MEASURES. 19 

Dry Measure, U. S. 

2 pints = 1 quart. 8 quarts = 1 peck. 4 pecks = 1 bushel. 

The standard U. S. bushel is the Winchester bushel, which is, in 
cylinder form, 18 1/2 inches diameter and 8 inches deep, and contains 
2150.42 cubic inches. 

A struck bushel contains 2150.42 cubic inches = 1.2445 cu. ft.; 1 
cubic foot = 0.80356 struck bushel. A heaped bushel is a cylinder 18 1/2 
inches diameter and 8 inches deep, with a heaped cone not less than 
6 inches high. It is equal to 1 1/4 struck bushels. (When applied to 
apples and pears the bushel should be heaped so as to contain 2737.715 
cu. in. = 1.2731 struck bushels. — Decision of U. S. Court of Customs 
Appeals, 1912.) 

The British Imperial bushel = 8 imperial gallons or 2218.192 cu. in. = 
1.2837 cu. ft. The British quarter = 8 imperial bushels. 

Capacity of a cylinder in U. S. gallons = square of diameter, in inches 
X height in inches X .0034. (Accurate within 1 part in 100,000.) 

Capacity of a cylinder in U. S. bushels = square of diameter in inches 
X height in inches X 0.0003652. 

Shipping Measure. 

Register Ton. — For register tonnage or for measurement of the entire 
internal capacity of a vessel: 

100 cubic feet = 1 register ton. 

This number is arbitrarily assumed to facilitate computation. 
Shipping Ton. — For the measurement of cargo: 

40 cubic feet = 1 U. S. shipping ton = 32.143 U. S. bushels. 

42 cubic feet = 1 British shipping ton = 32.719 imperial bushels. 

Carpenter's Rule. — Weight a vessel wiU carry = length of keel X 
breadth at main beam X depth of hold in feet ^ 95 (the cubic feet 
allowed for a ton). The result will be the tonnage. For a double- 
decker instead of the depth of the hold take half the breadth of the 
beam. 

Measures of Weight. — Avoirdupois or Commercial 
Weight. 

16 drachms, or 437.5 grains = 1 ounce, oz. 
16 ounces, or 7000 grains = 1 pound, lb. 
28 pounds = 1 quarter, qr. 

4 quarters = 1 hundredweight, cwt. = 112 lb. 

20 hundredweight = 1 ton of 2240 lb., gross or long ton. 

2000 pounds = 1 net, or short ton. 

2204.6 pounds = 1 metric ton. 

1 stone =14 pounds; 1 quintal =100 pounds. 

The drachm, quarter, hundredweight, stone, and quintal are now 
seldom used in the United States. 

Troy Weight 

24 grains = 1 pennyweight, dwt. 

20 pennyweights = 1 ounce, oz. = 480 grains. 

12 ounces = 1 poimd, lb. = 5760 grains. 

Troy weight is used for weighting gold and silver. The grain is the 
same in Avoirdupois, Troy, and Apothecaries' weights. A carat, for 
weighing diamonds = 3.086 grains = 0.200 gramme. (International 
Standard, 1913.) 

Apothecaries' Weight. 

20 grains — 1 scruple, 9 

3 scruples «= 1 drachm, 3 =^ 60 grains* 

8 drachms = 1 ounce, 5 =^ 480 grains. 

12 ounces =» 1 pound, lb. = 5760 grains. 



20 ARITHMETIC. 

To determine whether a balance has unequal arms. — After weigh- 
ing an article and obtaining equilibrium, transpose the article and the 
weights. If the balance is true, it will remain in equilibrium; if untrue, 
the pan suspended from the longer arm will descend. 

To weigh correctly on an incorrect balance. — First, by substitu- 
tion. Put the article to be weighed in one pan of the balance and counter- 
Soise it by any convenient heavy articles placed on the other pan. 
:,emove the article to be weighed and substitute for it standard weights 
until equipoise is again established. The amount of these weights is the 
weight of the article. 

Second, by transi)osition. Determine the apparent weight of the 
article as usual, then its apparent weight after transposing the article and 
the weights. If the difference is small, add half the difference to the 
smaller of the apparent weights to obtain the true weight. If the differ- 
ence is 2 per cent the error of this method is 1 part in 10,000. For larger 
differences, or to obtain a perfectly accurate result, multiply the two 
apparent weights together and extract the square root of the product. 

Circular Measure. 

60 seconds, " = 1 minute, '. 
60 minutes, ' = 1 degree, **. 
90 degrees = 1 quadrant. 
S80 '* = circumference. 

Arc of angle of 57.3°, or 360** -> 6.2832 = 1 radian = the arc whose length 
is equal to the radius. 

Time. 

60 seconds = 1 minute. 
60 minutes = 1 hour. 
24 hours = 1 day. 
7 days = 1 week. 
365 days, 5 hours, 48 minutes, 48 seconds = 1 year. 

By the Gregorian Calendar every year whose number is divisible by 4 
is a leap year, and contains 366 days, the other years containing 365 days, 
except that the centesimal years are leap years only when the number of 
the year is divisible by 400. 

The comparative values of mean solar and sidereal time are shown by 
the following relations according to Bessel: 

365.24222 mean solar days = 366.24222 sidereal days, whence 
1 mean solar day = 1.00273791 sidereal days; 
1 sidereal day = 0.99726957 mean solar day; 
24 hours mean solar time = 24^ 3 568.555 sidereal time; 
24 hours sidereal time = 23^^ 56w 4s.091 mean solar time, 

whence 1 mean solar day is 3»» 55«.91 longer than a sidereal day, reckoned 
In mean solar time. 

BOARD AND TIMBER MEASURE. 

Board Pleasure. 

In board measure boards are assumed to be one inch in thickness. To 
obtain the number of feet board measure (B. M.) of a board or stick of 
square timber, multiply together the length in feet, the breadth in feet, 
and the thickness in inches. 

To compute the measure or surface in square feet. — When all 
dimensions are in feet, multiply the length by the breadth, and the prod- 
uct will give the surface required. 

When either of the dimensions are in inches, multiply as above and 
divide the product by 12. 

When all dimensions are in inches, multiply as before and divide product 
by 144. 

Timber Measure. 

To compute the volume of round timber. — When all dimensions 
are in feet, multiply the length by one quarter of the product of the mean 



WEIGHTS AND MEASURES. 



21 



girth and diameter, and the product will give the measurement in cubic 
feet. When length is given in feet, and girth and diameter in Inches, 
divide the product by 144; when all the dimensions are in inches, divide 
by 1728. 

To compute the volume of square timber. — When all dimensions 
are in feet, multiply together the length, breadth, and depth; the product 
will be the volume in cubic feet. When one dimension is given in inches, 
divide by 12; when two dimensions are in inches, divide by 144; when all 
three dimensions are in inches, divide by 1728. 

Contents in Feet of Joists, Scantling, and Timber. 

Length in Feet. 



Size. 



12 


14 


16 


18 


20 


22 


24 


26 


28 



30 



Feet Board Measure, 



2X4 


8 


9 


11 


12 


13 


15 


16 


17 


19 


20 


2X6 


12 


14 


16 


18 


20 


22 


24 


26 


28 


30 


2X8 


16 


19 


21 


24 


11 


29 


32 


35 


37 


40 


2 X 10 


20 


23 


27 


30 


33 


37 


40 


43 


47 


50 


2X 12 


24 


28 


32 


36 


40 


44 


48 


52 


56 


60 


2 X 14 


28 


33 


37 


42 


47 


51 


56 


61 


65 


70 


3X8 


24 


28 


32 


36 


40 


44 


48 


52 


56 


60 


3 X 10 


30 


35 


40 


45 


50 


55 


60 


65 


70 


75 


3 X 12 


36 


42 


48 


54 


60 


66 


72 


78 


84 


90 


3 X 14 


42 


49 


56 


63 


70 


77 


84 


91 


98 


105 


4X4 


16 


19 


21 


24 


27 


29 


32 


35 


37 


40 


4X6 


24 


28 


32 


36 


40 


44 


48 


52 


56 


60 


4X8 


32 


37 


43 


43 


53 


59 


64 


69 


75 


80 


4 X 10 


40 


47 


53 


60 


67 


73 


80 


87 


93 


100 


4 X 12 


48 


56 


64 


72 


80 


88 


96 


104 


112 


120 


4 X 14 


56 


65 


75 


84 


93 


103 


112 


121 


131 


140 


6X6 


36 


42 


48 


54 


60 


66 


72 


78 


84 


90 


6X8 


48 


56 


64 


72 


80 


88 


96 


104 


112 


120 


6X10 


60 


70 


80 


90 


100 


110 


120 


130 


140 


150 


6X 12 


72 


84 


96 


108 


120 


132 


144 


156 


168 


180 


6X 14 


84 


98 


112 


126 


140 


154 


168 


182 


196 


210 


8X8 


64 


75 


85 


96 


107 


117 


128 


139 


149 


160 


8X10 


80 


93 


107 


120 


133 


147 


160 


173 


187 


200 


8 X 12 


96 


112 


128 


144 


160 


176 


192 


208 


224 


240 


8 X 14 


112 


131 


149 


168 


187 


205 


224 


243 


261 


280 


10 X 10 


100 


117 


133 


150 


167 


183 


200 


217 


233 


250 


10 X 12 


120 


140 


160 


180 


200 


220 


240 


260 


260 


300 


10 X 14 


140 


163 


187 


210 


233 


257 


280 


303 


327 


350 


12 X 12 


144 


168 


192 


216 


240 


264 


288 


312 


336 


360 


12 X 14 


168 


196 


224 


252 


280 


308 


336 


364 


392 


420 


14 X 14 


196 


229 


261 


294 


327 


359 


392 


425 


457 


490 



FRENCH OR METRIC HIEASURES. 

The metric unit of length is the metre = 39.37 inches. 

The metric unit of weight is the gram = 15.432 grains. 

The following prefixes are used for subdivisions and multiples: Milli « 
yiooo, Centi = i/ioo, Deci = i/io, Deca = 10, Hecto = 100, Kilo = 1000. 
Myna = 10,000. 



22 



ARITHMETIC. 



FEENCH AND BRITISH (AND AMERICAN) 
EQUrV ALENT MEASURES. 

Measures of Length. 

French. British and U. S. 

1 metre = 39.37 inches, or 3.28083 feet, or 1.09361 yards. 

0.3048 metre = 1 foot. 

1 centimetre = 0.3937 inch. 
2.54 centimetres = 1 inch. 

1 milUmetre = 0.03937 inch, or 1 /25 inch, nearly. 
25.4 millimetres = 1 inch. 

1 kilometre = 1093. Gl yards, or 0.62137 mile. 



Of Surface 



French 
1 square metre 

0.836 square metre 
0.0929 square metre 

1 square centimetre 

6.452 square centimetres 
1 square milhmetre 

645.2 square millimetres 
1 centiare = 1 sq. metre 
1 are = 1 sq. decametre 
1 hectare =100 ares 
1 sq. kilometre 
1 sq. myriametre 



H 



British and U. S. 

10.7639 square feet. 
1.196 square yards. 
1 square yard. 
1 square foot. 
0.15500 square inch. 
1 square inch. 

0.00155 sq. in. = 1973.5 circ. mils. 
1 square inch. 
10.764 square feet. 
1076.41 " 

107641 " " = 2.4711 acres. 
0.386109 sq. miles = 247.11 " 
38.6109 " 



Of 



French. 

1 cubic metre 

0.7645 cubic metre 
0.02832 cubic metre 

1 cubic decimetre 

28.32 cubic decimetres 
1 cubic centimetre 
16.387 cubic centimetres 
1 cubic centimetre = 1 millilitre 
1 deciUtre 
1 litre = 1 cubic decimetre 



H 



Volume 

British and U. S. 
35.314 cubic feet, 

1.308 cubic yards, 
cubic yard, 
cubic foot. 

61.0234 cubic inches. 
0.035314 cubic foot, 
cubic foot. 
0.061 cubic inch. 
1 cubic inch. 
0.061 cubic inch. 
6.102 
61.0234 " 



= 1 



1 hectolitre or decistere 

1 stere, kilolitre, or cubic metre = 1.308 cubic yards = 28.37 bu 



= 3.5314 cubic feet 



= 1.05671 

quarts, U. S. 
2.8375 bu., U.S. 



French. 



1 htre ( = 1 cubic decimetre) = 



28.317 litres 
4.543 Utres 
3.785 Utres 



French. 

1 gramme 

0.0648 gramme 

1 kilogramme 
0.4536 kilogramme 

1 tonne or metric ton I 
1000 kilogrammes j 

1.016 metric tons 



Of Capacity 

British and U. S. 
61.0234 cubic inches. 

0.03531 cubic foot. 

0.2642 gallon (American), 

2.202 pounds of water at 62° F. 
= 1 cubic foot. 
= 1 gallon (British). 
= 1 gallon (American). 

Of Weight. 



British and U. S. 
= 15,432 grains. 
= 1 grain. 
= 2.204622 pounds. 
= 1 pound. 

= \ 0.9842 ton of 2240 potmds. 
= ) 2204.6 pounds. 
= 1 ton of 2240 pounds. 



WEIGHTS AND MEASURES. 



23 



Mr. O. H. Titmaiin, in Bulletin No. 9 of the U. S. Coast and Geodetic 
Survey, discusses the work of various authorities who have compared the 
yard and the metre, and by referring all the observations to a common 
standard has succeeded in reconciling the discrepancies within very 
narrow hmits. The following are his results for the number of inches in a 
metre according to the comparisons of the authorities named: 1817. 
Hassler, 39.36994 in. 1818. Kater, 39.36990 in. 1835. Baily, 39.36973 
in. 1866. Clarke. 39. 36970 in. 1885. Comstock, 39.36984 in. The mean 
of these is 39.36982 in. 

The value of the m.etre is now defined in the U. S. laws as 39.37 mches. 



French and British Equivalents of Compound Units. 



French. 
1 gramme per square millimetre 
1 kilogramme per square " 
1 " " " centimetre 

1.0335 kg. per sq. cm. = 1 atmosphere 
0.070308 kilogramme per square centimetre 
1 kilogram metre 



British. 

1.422 lbs. per sq. in. 

1422.32 '' "■ '^ '' 

14.223 " '' '' " 

14.7 '* ^' " " 

1 lb. per square inch. 

7.2330 foot-pounds. 



1 gramme per litre = 0.062428 lb. per cu. ft. = 58.349 grains per U. S gal. 

of water at 62** F. 
1 grain per U. S. gallon = 1 part in 58,349 = 1.7138 parts per 100,000 

= 0.017138 grammes per litre. 



METRIC COIVVERSION TABLES. 

The following tables, with the subjoined memoranda, w^ere published 
in 1890 by the United States Coast and Geodetic Survey, office of standard 
weights and measures, T. C. Mendenhall, Superintendent. 

Tables for Converting U. S. Weights and Measures — 
Customary to Metric. 

LINEAR. 



Inches to Milli- 
metres. 



Feet to Metres. 



Yards to Metres. 



Miles to Kilo- 
metres. 



1 = 

2 = 

3 = 

4 = 

5 = 

6 = 

7 = 

8 = 

9 = 



25.4001 
50.8001 
76.2002 
101.6002 
127.0003 

152.4003 
177.8004 
203.2004 
228.6005 



0.304801 
0.609601 
0.914402 
1.219202 
1.524003 

1.828804 
2.133604 
2.438405 
2.743205 



0.914402 
1.828804 
2.743205 
3.657607 
4.572009 

5.486411 
6.400813 
7.315215 
8.229616 



1.60935 
3.21869 
4.82804 
6.43739 
8.04674 

9.65608 
11.26543 
12.87478 
14.48412 



SQUARE. 



quare Inches to 
Square Centi- 
metres. 



6.452 
12.903 
19.355 
25.807 
32.258 

38.710 
45.161 
51.613 
58.065 



Square !• eet to 
Square Deci- 
metres. 



9.290 
18.581 
27.871 
37.161 
46.452 

55.742 
65.032 
74.323 
83.613 



Square Yards to 
Square Metres. 



0.836 
1.672 
2.508 
3.344 
4.181 

5.017 
5.853 
6.689 
7.525 



Acres to 
Hectares. 



4047 
0.8094 
1.2141 
1.6187 
2.0234 

2.4281 
2.8328 
3.2375 
3.6422 



S4 



ARITHMETIC. 



CUBIC. 





Cubic incties to 


Cubic Feet to 


Cubic Yards to 


Bushels to 




Cubic Centi- 
metres. 


Cubic Metres. 


Cubic Metres. 


Hectolitres. 


1 = 


16.387 


0.02832 


0.765 


0.35242 


2 = 


32.774 


0.05663 


1.529 


0.70485 


3 = 


49.161 


0.08495 


2.294 


1.05727 


4 = 


65.549 


0.11327 


3.058 


1.40969 


5 = 


81.936 


0.14158 


3.823 


1.76211 


6 = 


98.323 


0.16990 


4.587 


2.11454 


7 = 


114.710 


0.19822 


5.352 


2.46696 


8 = 


131.097 


0.22654 


6.116 


2.81938 


9 = 


147.484 


0.25485 


6.881 


3.17181 



CAPACITY. 





Fluid DracHms 










to Millilitres or 
Cubic Centi- 


Fluid Ounces to 
Millilitres, 


Quarts to Litres. 


Gallons to 
Litres. 




metres. 








1 = 


3.70 


29.57 


0.94636 


3.78544 


2 = 


7.39 


59.15 


1.89272 


7.57088 


3 = 


11.09 


88.72 


2.83908 


11.35632 


4 = 


14.79 


118.30 


3.78544 


15.14176 


5 = 


18.48 


147.87 


4.73180 


18.92720 


6 = 


22.18 


177.44 


5.67816 


22.71264 


7 = 


25.88 


207.02 


6.62452 


26.49808 


8 = 


29.57 


236.59 


7.57088 


30.28352 


9 = 


33.28 


266.16 


8.51724 


34.06896 



WEIGHT. 



Grains to Milli- 
grammes. 



Avoirdupois 
Ounces to 
Grammes. 



Avoirdupois 

Pounds to Kilo- 

granmies. 



Troy Ounces to 
Grammes. 



64.7989 
129.5978 
194.3968 
259.1957 
323.9946 

388.7935 
453.5924 
518.3914 
583.1903 



28.3495 

56.6991 

85.0486 

113.3981 

141.7476 

170.0972 
198.4467 
226.7962 
255.1457 



0.45359 
0.90719 
1.36078 
1.81437 
2.26796 

2.72156 
3.17515 
3.62874 
4.08233 



31.10348 
62.20696 
93.31044 
124.41392 
155.51740 

186.62089 
217.72437 
248.82785 
279.93133 



1 chain 

1 square mile 

1 fathom 

1 nautical mile 

1 foot 

1 avoir, pound 

15432.35639 grains 



20. 11 69 metres. 
259 hectares. 
1 .829 metres. 
1853.27 metres. 
0.304801 metre. 
453.5924277 gram. 
1 kilogramme. 



METRIC CONVERSION TABLES. 



25 



Tables for Converting U. S. Weights and Measures- 
Metric to Customary. 

LINEAR. 





Metres to 
Inches. 


Metres to 
Feet. 


Metres to 
Yards. 


Kilometres to 
Miles. 


1 - 

2 = 

3 = 

4 = 

5 = 

6 = 

7 = 

8 = 

9 = 


39.3700 
78.7400 
118.1100 
157.4800 
196.8500 

236.2200 
275.5900 
314.9600 
354.3300 


3.28083 
6.56167 
9.84250 
13.12333 
16.40417 

19.68500 
22.96583 
26.24667 
29.52750 


1.093611 
2.187222 
3.280833 
4.374444 
5.468056 

6.561667 
7.655278 
8.748889 
9.842500 


0.62137 
1.24274 
1.86411 
2.48548 
3.10685 

3.72822 
4.34959 
4.97096 
5.59233 



SQUARE. 



Square Centi- 
metres to 
Square Inches. 



Square Metres 
to Square Feet. 



Square Metres 
to Square Yards. 



Hectares to 
Acres. 



0.1550 
0.3100 
0.4650 
0.6200 
0.7750 

0.9300 
1.0850 
1.2400 
1.3950 



10.764 
21.528 
32.292 
43.055 
53.819 

64.583 
75.347 
86.111 
96.874 



1.196 
2.392 
3.588 
4.784 
5.980 

7.176 
8.372 
9.568 
10.764 



2.471 
4.942 
7.413 
9.884 
12.355 

14.826 
17.297 
19.768 
22.239 



CUBIC. 



Cubic Centi- 
metres to Cubic 
Inches. 



0.0610 
0.1220 
0.1831 
0.2441 
0.3051 

0.3661 
0.4272 
0.4882 
0.5492 



Cubic Deci- 
metres to Cubic 
Inches. 



61.023 
122.047 
183.070 
244.093 
305.117 

366.140 
427.163 
488.187 
549.210 



Cubic Metres to 
Cubic Feet. 



35.314 
70.629 
105.943 
141.258 
176.572 

211.887 
247.201 
282.516 
317.830 



Cubic Metres to 
Cubic Yards. 



1.308 
2.616 
3.924 
5.232 
6.540 

7.848 
9.156 
10.464 
11.771 



CAPACITY. 





Millihtres or 
Cubic Centi- 
metres toFluid 
Drachms. 


Centimetres 
to Fluid 
Ounces. 


Litres to 
Quarts. 


Dekalitres 
to 
Gallons. 


Hektolitres 
to * 
Bushels. 


1 = 

2 = 

3 = 

4 = 

5 = 

6 = 

7 = 

8 = 

9 = 


0.27 
0.54 
0.81 
1.08 
1.35 

1.62 
1.89 
2.16 
2.43 


0.338 
0.676 
1.014 
1.352 
1.691 

2.029 
2.368 
2.706 
3.043 


1.0567 
2.1134 
3.1700 
4.2267 
5.2834 

6.3401 
7.3968 
8.4534 
9.5101 


2.6417 

5.2834 

7.9251 

10.5668 

13.2085 

15.8502 
18.4919 
21.1336 
23.7753 


2.8375 
5.6750 
8.5125 
11.3500 
14.1875 

17.0250 
19.8625 
22.7000 
25.5375 



26 



ARITHMETIC. 
WEIGHT. 





Milligrammes 
to Grains. 


Kilogrammes 
to Grains. 


Hectogrammes 
( 1 00 grammes) 
to Ounces Av. 


Kilogrammes 
to Pounds 
Avoirdupois. 


1 = 

2 = 

3 = 

4 = 

5 = 

6 = 

7 = 

8 = 

9 = 


0.01543 
0.03086 
0.04630 
0.06173 
0.07716 

0.09259 
0.10803 
0.12346 
0.13839 


15432.36 
30864.71 
46297.07 
61729.43 
77161.78 

92594.14 
108026.49 
123458.85 
138891.21 


3.5274 
7.0548 
10.5822 
14.1096 
17.6370 

21.1644 
24.6918 
28.2192 
31.7466 


2.20462 
4.40924 
6.61386 
8.81849 
11.02311 

13.22773 
15.43235 
17.63697 
19.84159 



1 = 

2 = 

3 = 

4 = 

5 = 

6 = 

7 = 

8 = 

9 = 



Quintals to 
Pounds Av. 



220.46 
440.92 
661.38 
881.84 
1102.30 

1322.76 
1543.22 
1763.68 
1984.14 



Milliers or Tonnes to 
Pounds Av. 



2204.6 
4409.2 
6613.8 
8818.4 
11023.0 

13227.6 
15432.2 
17636.8 
19841.4 



Grammes to Ounces. 
Troy. 



0.03215 
0.06430 
0.09645 
0.12860 
0.16075 

0.19290 
0.22505 
0.25721 
0.28936 



The British Avoirdupois pound was derived from the British standard 
Troy pound of 1758 by direct comparison, and it contains 7000 grains Troy. 

The grain Troy is therefore the same as the grain Avoirdupois, and the 
pound Avoirdupois in use in the United States is equal to the British 
pound Avoirdupois. 

By the concurrent action of the principal governments of the world an 
International Bureau of Weights and Measures has been established near 
Paris. 

The International Standard Metre is derived from the Mfetre des 
Archives, and its length is defined by the distance between two lines at 0° 
Centigrade, on a platinum-iridium bar deposited at the International 
Bureau. 

The International Standard Kilogramme is a mass of platinum-iridium 
deposited at the same place, and its weight in vacuo is the same as that of 
the Ivilogramme des Archives. 

Copies of these international standards are deposited in the office of 
standard weights and measures of the U. S. Coast and Geodetic Survey. 

The litre is equal to a cubic decimetre of water, and it is measured by 
the quantity of distilled water which, at its maximum density, will 
counterpoise the standard kilogramme in a vacuum; the volume of such 
a quantity of water b^ixig, as nearly as has been ascertained, equal to a 
cubic decimetre. 

The metric system was legalized in the United States in 1866. Many 
attempts were made during the 40 years following to have the U. S^ 
Congress pass laws to make the metric system the legal standard, but they 
have all failed. Similar attempts in Great Britain have also failed. For 
arguments for and against the metric system see the report of a committee 
of the American Society of Mechanical Engineers, 1903, Vol. 24. 



WEIGHTS AND MEASURES. 27 

COMPOUND UNITS. 

Measures of Pressure and Weight. 

One pound force (or pressure) = the force exerted by gravity on 1 lb. 
of matter at a place where the acceleration due to gravity is 32.1740 
feet-per-second per second ; that is (very nearly) the force of gravity on 
1 lb. of matter at latitude 45° at the sea level. 

il44 lb. per square foot. 
2.0355 in. of mercury at 32^ F. 
2.0416 " " " "62°F. 

2.309 ft. of water at 62° F. 
27.71 ins. " " " 62° F. 
1 ^,,^«« ^^^ cr. iry - J 0.1276 in. of mercury at 62° F. 

1 ounce per sq. m. - -j ^ 732 in. of water at 62° F. 

( 2116.3 lb. per square foot. 
1 ^ u^^r. MA -7 IK r.^^ ar. ir. ^ ' 33.947 ft. of watcr at 62° F. 

1 atmosphere (14.71b. per sq.m.) = ^ 29.921 m. of mercury at 32° F. 

( 760 milUmetres of mercury at 32° F. 
j 0.03609 lb. or .5774 oz. per sq. in. 
1 inch of water at 62° F. = ■{ 5.196 lb. per square foot. 

( 0.0735 in. of mercury at 62° F. 
1 f^^4- ^f „r^-^« r.-^ ano ^7^ _ j 0.433 lb. per square inch. 

1 foot of water at 62° F. = ] g2.355 lb. per square foot. 

j 0.491 lb. or 7.86 oz. per sq. in. 
1 inch of mercury at 62° F. = ■{ 1.134 ft. of water at 62° F. 

( 13.61 in. of water at 62° F. 

Weight of One Cubic Foot of Pure Water. 

At 32° F. (freezing-point) 62.418 lb. 

" 39.1° F. (maximum density) 62.425 " 

•' 62° F. (standard temperature) in vacuo 62.355 " 

" 212° F. (boihng-point, under 1 atmosphere) 59.76 " 

American gallon = 231 cubic ins. of water at 62° F. = 8.3356 lb. 

British " = 277.274 " " " " " " = 10 lb. 

Weight of 1 cu. ft. of air-free distilled water at 62°, weighed in air at 
62° with brass weights of 8. 4 density = 62.287 lb. = 8.32671b. per U. S. 
gallon. 

Weight and Volume of Air. 
1 cubic ft. of air at 32° F. and atmospheric pressure weighs 0.080728 lb. 
1 f^ in bPiVbt nf air at -^9° F - i 0.0005606 lb. per sq. in. 
1 tt. m height ot air at 32 i^ • - j 0.015534 inches of water at 62° F. 
For air at any other temperature T° Falu-. multiply by 492 ^ (460 + T). 
1 lb. pressure per sq. ft. = 12.387 ft. of air at 32° F. 

1 •' " " sq. in. = 1784. " " " •* 

1 inch of water at 62° F. = 64.37 " " " " 

For air at any other temperature multiply by (460 + T) -j- 492. 

At any fixed temperature the weight of a given volume is proportional 
to the absolute pressure. 

Measures of Worlc, Power, and Duty. 
Unit of worlf . — One foot^-pound, i.e., a pressure of one pound exerted 
through a space of one foot. 

Horse-power. — The rate of work. Unit of horse-power = 33,000 
ft.-lb. per minute, or 550 ft. -lb. per second = 1 ,980,000 ft.-lb. per hour. 
Heat unit. = heat required to raise 1 lb. of water 1° F. (see page 560). 

33 000 
Horse-power expressed in heat-units = ' - = 42.442 heat-units per 

minute = 0.7074 heat-unit per second = 2546.5 heat units per hour. 
1 lb. of fuel per H.P. per hour = 1,980.000 ft.-lb. per lb. of fuel. 
1,000,000 ft.-lb. per lb. of'fuel = 1.98 lb. of fuel per H.P. per hour. 

5280 22 
Velocity. — Feet per second = o^qq = t^X miles per hour. 

Gross tons per mile = 2240 ^ 14 ^^- P®^ ^^^^ (single rail). 



ARITHMETIC. 



WIRE AND SHEET.31ETAX GAUGES COMPARED. 



"S . 


lis. 


American or 

Brown and 

Sharpe Gauge. 


\^^^ 


11^ 


[British Imper- 
ial Standard 
Wire Gauge, 

1884. 


dfl^^ 


lard 
r 

late 
eel. 


o 


55 


f4 

£■22 


^ c ^ 

III 




fflC5 C3 5$ g 

•poll 


^ OCL-M 


1^ 




inch. 


inch. 


inch. 


inch. 


inch. 


inch. 


inch. 




0000000 






.49 




.500 


.6666 


.5 


7/'0 


000000 






.46 




464 


.625 


.469 


6.0 


00000 






.43 




.432 


.5883 


.438 


5/o 


0000 


.454 


.46 


.393 




.4 


.5416 


.406 


4/0 


000 


.425 


.40964 


.362 




.372 


.500 


.375 


3/0 

^6" 


00 


.38 


.3648 


.331 




.348 


.4452 


.344 





.34 


.32486 


.307 




.324 


.3964 


.313 


1 


.3 


.2893 


.283 


.227 


.3 


3532 


.281 


I 


2 


.284 


.25763 


.263 


.219 


.276 


.3147 


.266 


2 


3 


.259 


.22942 


.244 


.212 


.252 


.2804 


25 


3 


4 


.238 


.20431 


.225 


.207 


.232 


.250 


.234 


4 


5 


.22 


J8194 


.207 


.204 


.212 


.2225 


.219 


5 


6 


.203 


.16202 


.192 


.201 


.192 


.1981 


.203 


6 


7 


.18 


J 4428 


.177 


.199 


.176 


.1764 


.188 


7 


8 


.165 


.12849 


.162 


.197 


.16 


.1570 


.172 


8 


9 


.148 


.11443 


.148 


.194 


.144 


.1398 


.156 


9 


10 


.134 


.10189 


.135 


.191 


.128 


.1250 


.141 


10 


n 


.12 


.09074 


.12 


.188 


.116 


.1113 


.125 


11 


12 


.109 


.08081 


J05 


.185 


.104 


.0991 


.109 


12 


13 


.095 


.07196 


.092 


.182 


.092 


.0882 


.094 


13 


14 


.083 


.06408 


.08 


.180 


.08 


.0785 


.078 


14 


15 


.072 


.05707 


.072 


.178 


.072 


.0699 


.07 


15 


16 


.065 


.05082 


.063 


.175 


.064 


.0625 


.0625 


16 


17 


.05'8 


.04526 


.054 


.172 


.056 


.0556 


.0563 


17 


16 


.049 


.0403 


.047 


.168 


.048 


.0495 


.05 


18 


19 


.042 


.03589 


.041 


164 


.04 


.0440 


.0438 


19 


20 


.035 


.03196 


.035 


.161 


.036 


.0392 


.0375 


20 


21 


.032 


.02846 


.032 


.157 


.032 


.0349 


.0344 


21 


22 


.028 


.02535 


.028 


.155 


.028 


.03125 


.0313 


22 


23 


.025 


.02257 


.025 


.153 


.024 


.02782 


.0281 


23 


24 


.022 


.0201 


.023 


.151 


.022 


.02476 


.025 


24 


25 


.02 


.0179 


.02 


.148 


.02 


.02204 


.0219 


25 


26 


.018 


.01594 


.018 


.146 


.018 


.01961 


.0188 


26 


11 


.016 


.01419 


.017 


.143 


.0164 


.01745 


.0172 


27 


28 


.014 


.01264 


.016 


.139 


.0148 


.015625 


.0156 


28 


29 


.013 


.01126 


.015 


.134 


.0136 


.0139 


.0141 


29 


30 


.012 


.01002 


.014 


.127 


.0124 


.0123 


.0125 


30 


31 


.01 


.00893 


.013 


.120 


.0116 


.0110 


.0109 


31 


32 


.009 


.00795 


.013 


.115 


.0108 


.0098 


.0101 


32 


33 


.008 


.00708 


.011 


.112 


.01 


.0087 


.0094 


33 


34 


.007 


.0063 


.01 


.110 


.0092 


.0077 


.0086 


34 


35 


.005 


.00561 


.0095 


.108 


.0084 


.0069 


.0078 


35 


36 


.004 


.005 


.009 


.106 


.0076 


.0061 


.007 


36 


37 




.00445 


.0085 


.103 


.0068 


.0054 


.0066 


37 


38 




.00396 


.008 


.101 


.006 


.0048 


.0063 


38 


39 




.00353 


.0075 


.099 


.0052 


.0043 




39 


40 




.00314 


.007 


.097 


.0048 


.00386 




40 


41 








.095 


.0044 


.00343 




41 


42 








.092 


.004 


.00306 




42 


43 








.088 


.0036 


.00272 




43 


44 








.085 


.0032 


.00242 




44 


45 








.081 


.0028 


.00215 




45 


46 








.079 


.0024 


.00192 




46 


47 








.077 


.002 


.00170 




47 


48 








.075 


.0016 


.00152 




48 


49 








.072 


.0012 


.00135 


! 


49 


50 








.065 


.001 


.00120 


1 


50 



WIRE AND SHEET METAL GAUGES. 29 



THE EDISON OR CIRCULAR MIL, WIRE GAUGE. 

(For table of copper wires by this gauge, giving weights, electrical 
resistances, etc., see Copper Wire.) 

Mr. C. J. Field (Stevens Indicator, July, 1887) thus describes the origia 
of the Edison gauge: 

The Edison company experienced inconvenience and loss by not having 
a wide enough range nor sutficient number of sizes in the existing gauges. 
This was felt more particularly in the central-station work in making 
electrical determinations for the street system. They were compelled to 
make use of two of the existing gauges at least, thereby introducing a 
complication that was liable to lead to mistakes by the contractors and 
linemen. 

In the incandescent system an even distribution throughout the entire 
system and a uniform pressure at the point of delivery are obtained by 
calculating for a given maximum percentage of loss from the potential as 
dehvered from the dynamo. In carrying this out, on account of lack of 
regular sizes, it was often necessary to use larger sizes than the occasion 
demanded, and even to assume new sizes for large underground conductors. 
The engineering department of the Edison company, knowing the require- 
ments, have designed a gauge that has the widest range obtainable and 
a large number of sizes which increase in a regular and uniform manner. 
The basis of the graduation is the sectional area, and the number of the 
wire corresponds. A wire of 100,000 circular mils area is No. 100; a wire 
of one half the size will be No. 50; twice the size No. 200. 

In the older gauges, as the number increased the size decreased. With 
this gauge, however, the number increases with the wire, and the number 
multipUed by 1000 will give the circular mils. 

The weight per mil-foot, 0.00000302705 pounds, agrees with a specific 
gravity of 8.889, which is the latest figure given for copper. The ampere 
capacity which is given was deduced from experiments made in the com- 
pany's laboratory, and is based on a rise of temperature of 50° F. in the 
wire. 

In 1893 Mr. Field writes, concerning gauges in use by electrical engineers: 

The B. and S. gauge seems to be in general use for the smaller sizes, up 
to 100,000 cm., and in some cases a little larger. From between one ana 
two hundred thousand circular mils upwards, the Edison gauge or its 
equivalent is practically in use, and there is a general tendency to desig- 
nate all sizes above this in circular mils, specifying a wire as 200,000, 
400,000, 500,000, or 1,000,000 CM. 

In the electrical business there is a large use of copper wire and rod and 
other materials of these large sizes, and in ordering them, speaking of 
them, specifying, and in every other use, the general method is to simply 
specify the circular milage. I think it is going to be the only system in 
the future for the designation of wires, and the attaining of it means 
practically the adoption of the Edison gauge or the method and basis of 
this gauge as the correct one for wire sizes. 

THE U. S. STANDARD GAUGE FOR SHEET AND 
PLATE IRON AND STEEL, 1893. 

There is in this country no uniform or standard gauge, and the same 
numbers in different gauges represent different thicknesses of sheets or 
plates. This has given rise to much misunderstanding and friction 
between employers and workmen and mistakes and fraud between dealers 
and consumers. 

An Act of Congress in 1893 established the Standard Gauge for sheet 
iron and steel which is given on the next page. It is based on the fact that 
a cubic foot of iron weighs 480 pounds. 

A sheet of iron 1 foot square and 1 inch thick weighs 40 pounds, or 640 
ounces, and 1 ounce in weight should be 1/640 inch thick. The scale has 
been arranged so that each descriptive number represents a certain 
number of ounces in weight and an equal number of 640ths of an inch ia 
thickness. 

The law enacts that on and after July 1, 1893, the new gauge shall be 
used in determining duties and taxes levied on sheet and plate iron and 
{Continued on page 32.) 



30 



ARITHMETIC. 





Edison, or Circular Mil Gauge for Electrical Wires. 




Gauge 

Num- 
ber. 


Circular 

Mils. 


Diam- 
eter in 
Mils. 


Gauge 

Num- 
ber. 


Circular 
Mils. 


Diam- 
eter in 
Mils. 


Gauge 
Num- 
ber. 


Circular 
Mils. 


Diam- 
eter in 

Mils. 


3 
5 
8 
12 
15 

20 
25 
30 
35 
40 

45 
50 
55 
60 
65 


3,000 

5,000 

8,000 

12,000 

15,000 

20,000 
25,000 
30,000 
35,000 
40,000 

45,000 
50,000 
55,000 
60,000 
65,000 


54.78 

70.72 

89.45 

109.55 

122.48 

141.43 
158.12 
173.21 
187.09 
200.00 

212.14 
223.61 
234.53 
244.95 
254.96 


/O 
75 
80 
85 
90 

95 
100 
110 
120 
130 

140 
150 
160 
170 
180 


70,000 
75,000 
80,000 
85,000 
90,000 

95,000 
100,000 
110,000 
120,000 
130,000 

140,000 
150,000 
160,000 
170,000 
180,000 


264.58 
273.87 
282.85 
291.55 
300.00 

308.23 
316.23 
331.67 
346.42 
360.56 

374.17 
387.30 
400.00 
412.32 
424.27 


190 
200 
220 
240 
260 

280 
300 
320 
340 
360 


190,000 
200,000 
220,000 
240,000 
260,000 

280,000 
300,000 
320,000 
340,000 
360,000 


435.89 
447.22 
469.05 
489.90 
509.91 

529.16 
547.73 
565.69 
583.10 
600.00 



Twist Drill and Steel Wire Gauge. 

(Manufacturers Standard) 



No. 


Size. 


No. 


Size. 


No. 


Size. 


No. 


Size. 


No. 


Size. 


No. 


Size. 




inch. 




inch. 




inch. 




inch. 




inch. 




inch. 


1 


0.2280 


14 


0.1820 


n 


0.1440 


40 


0.0980 


53 


0.0595 


67 


0.0320 


2 


.2210 


15 


.1800 


28 


.1405 


41 


.0960 


54 


.0550 


68 


.0310 


3 


.2130 


16 


.1770 


29 


.1360 


42 


.0935 


55 


.0520 


69 


.0292 


4 


.2090 


17 


.1730 


30 


.1285 


43 


.0890 


56 


.0465 


70 


.0280 


5 


.2055 


18 


.1695 


31 


.1200 


44 


.0860 


57 


.0430 


71 


.0260 


6 


.2040 


19 


.1660 


32 


.1160 


45 


.0820 


58 


.0420 


72 


.0250 


7 


.2010 


20 


.1610 


33 


.1130 


46 


.0810 


59 


.0410 


73 


.0240 


8 


.1990 


21 


.1590 


34 


.1,110 


47 


.0785 


60 


.0400 


74 


.0225 


9 


.1960 


22 


.1570 


35 


.1100 


48 


.0760 


61 


.0390 


75 


.0210 


10 


.1935 


23 


.1540 


36 


.1065 


49 


.0730 


62 


.0380 


76 


.0200 


11 


.1910 


24 


.1520 


37 


.1040 


50 


.0700 


63 


.0370 


77 


.0180 


12 


.1890 


25 


.1495 


38 


.1015 


51 


.0670 


64 


.0360 


78 


.0160 


13 


.1850 


26 


.1470 


39 


.0995 


52 


.0635 


65 
66 


.0350 
.0330 


79 
80 


.0145 
.0135 



Stubs' Steel Wire Gauge. 

(For Nos. 1 to 50 see table on page 31.) 



No. 


Size. 


No. 


Size. 


No. 


Size. 


No. 


Size. 


No. 


Size. 


No. 


Size. 




inch. 


inch. 


inch. 


inch. 




inch. 


inch. 


Z 


.413 


P 


.323 


F 


.257 


51 


.066 


61 


.038 


71 


.026 


Y 


.404 


O 


.316 


E 


.250 


52 


.063 


62 


.037 


72 


.024 


X 


.397 


N 


.302 


D 


.246 


53 


.058 


63 


.036 


73 


.023 


W 


.386 


M 


.295 


C 


.242 


54 


.055 


64 


.035 


74 


.022 


V 


.377 


T. 


.290 


B 


.238 


55 


.050 


65 


.033 


75 


.020 


IT 


.368 


K 


.281 


A 


.234 


56 


.045 


66 


.032 


76 


.018 


T 


.358 


J 


.277 


1 


(See 


57 


.042 


67 


.031 


77 


.016 


S 


.348 


I 


.272 


to 


<page 


58 


.041 


68 


.030 


78 


.015 


R 


.339 


H 


.266 


50 


(29 


59 


.040 


69 


.029 


79 


.014 


Q 


.332 


G 


.261 






60 


.039 


70 


.027 


80 


.013 



The Stubs* Steel Wire Gauge is used in measuring drawn steel wire or 
drill rods of Stubs* make, and is also used by many makers of American 
drill rods. 



WIRE AND SHEET METAL GAUGES. 



31 



U. S. STANDARD GAUGE FOR SHEET AND PLATE 
IRON AND STEEL, 1893. 





Approximate 

Thickness in 

Fractions of 

an Inch. 


Approximate 

Thickness in 

Decimal 

Parts of an 

Inch. 


Approximate 
Thickness 

in 
MilHmeters. 


Weight per 

Square Foot 

in Ounces 

Avoirdupois. 


Weight per 

Square Foot 

in Pounds 

Avoirdupois. 


m 

til 




1 Weight per Sq. 

Meter in Pounds 

Avoirdupois. 


0000000 


1-2 


0.5 


12.7 


320 


20. 


9.072 


97.65 


215.28 


000000 


15-32 


0.46875 


11.90625 


300 


18.75 


8.505 


91.55 


201.82 


00000 


7-16 


0.4375 


11.1125 


280 


17.50 


7.938 


85.44 


188.37 


0000 


13-32 


0.40625 


10.31875 


260 


16.25 


7.371 


79.33 


174.91 


000 


3-8 


0.375 


9.525 


240 


15. 


6.804 


73.24 


161,46 


00 


11-32 


0.34375 


8.73125 


220 


13.75 


6.237 


67.13 


148.00 





5-16 


0.3125 


7.9375 


200 


12.50 


5.67 


61.03 


134.55 


1 


9-32 


0.28125 


7.14375 


180 


11.25 


5.103 


54.93 


121.09 


2 


17-64 


0.265625 


6.746875 


170 


10.625 


4.819 


51.88 


114.37 


3 


1-4 


0.25 


6.35 


160 


10. 


4.536 


48.82 


107.64 


4 


15-64 


0.234375 


5.953125 


150 


9.375 


4.252 


45.77 


100.91 


5 


7-32 


0.21875 


5.55625 


140 


8.75 


3.969 


42.72 


94.18 


6 


13-64 


0.203125 


5.159375 


130 


8.125 


3.685 


39.67 


87.45 


7 


3-16 


0.1875 


4.7625 


120 


7.5 


3.402 


36.62 


80.72 


8 


11-64 


0.171875 


4.365625 


110 


6.875 


3.118 


33.57 


74.00 


9 


5-32 


0.15625 


3.96875 


100 


6.25 


2.835 


30.52 


67.27 


10 


9-64 


0.140625 


3.571875 


90 


5.625 


2.552 


27.46 


60.55 


11 


1-8 


0.125 


3.175 


80 


5. 


2.268 


24.41 


53.82 


12 


7-64 


0.109375 


2.778125 


70 


4.375 


1.984 


21.36 


47.09 


13 


3-32 


0.09375 


2.38125 


60 


3.75 


1.701 


18.31 


40.36 


14 


5-64 


0.078125 


1.984375 


50 


3.125 


1.417 


15.26 


33.64 


15 


9-128 


0.0/03125 


1 .7859375 


45 


2.8125 


1.276 


13.73 


30.27 


16 


1-16 


0.0625 


1.5875 


40 


2.5 


1.134 


12.21 


26.91 


17 


9-160 


0.05625 


1.42875 


36 


2.25 


1.021 


10.99 


24.22 


18 


1-20 


0.05 


1.27 


32 


2. 


0.9072 


9.765 


21.53 


19 


7-160 


0.04375 


1.11125 


28 


1.75 


0.7938 


8.544 


18.84 


20 


3-80 


0.0375 


0.9525 


24 


1.50 


0.6804 


7.324 


16.15 


21 


1 1-320 


0.034375 


0.873125 


22 


1.375 


0.6237 


6.713 


14.80 


22 


1-32 


0.03125 


0.793750 


20 


1.25 


0.567 


6.103 


13.46 


23 


9-320 


0.028125 


0.714375 


18 


1.125 


0.5103 5.49 


12.11 


24 


1-40 


0.025 


0.635 


16 


1. 


0.4536, 4.882 


10.76 


25 


7-320 


0.021875 


0.555625 


14 


0.875 


0.3969, 4.272 


9.42 


26 


3-160 


0.01875 


0.47625 


12 


0.75 


0.3402 3.662 


8.07 


27 


1 1-640 


0.0171875 


0.4365625 


11 


0.6875 


0.3119! 3.357 


7.40 


28 


1-64 


0.015625 


0.396875 


10 


0.625 


0.2835 3.052 


6.73 


29 


9-640 


0.0140625 


0.3571875 


9 


0.5625 


0.2551 


2 746 


6.05 


30 


1-80 


0.0125 


0.3175 


8 


0.5 


0.2268 


2.441 


5.38 


31 


7-640 


0.0109375 


0.2778125 


7 


0.4375 


0.1984 2.136 


4.71 


32 


13-1280 


0.01015625 


0.25796875 


61/2 


0.40625 


0.1843 1.983 


4.37 


33 


3-320 


0.009375 


0.238125 


6 


0.375 


0.1701 


1.831 


4.04 


34 


11-1280 


0.00859375 


0.21828125 


51/2 


0.34375 


0.1559 


1.678 


3.70 


35 


5-640 


0.0078125 


0.1984375 


5 


0.3125 


0.1417 


1.526 


3.36 


36 


9-1280 


0.00703125 


0.17859375 


41/2 


0.28125 


0.1276 


1.373 


3.03 


37 


17-2560 


0.00664062 


0.16867187 


41/4 


0.26562 


0.1205 


1.297 


2.87 


38 


1-160 


0.00625 


0.15875 


4 


0.25 


0.1134 


1.221 


2.69 



32 



THE DECIMAL GAUGE. 



{continued from page 29) steel; and that in its application a variation of 
2 1/2 per cent either way may be allowed. 

The Decimal Gauge. — The legalization of the standard sheet- 
metal gauge of 1893 and its adoption by some manufacturers of 
sheet iron have only added to the existing confusion of gauges. A joint 
committee of the American Society of Mechanical Engineers and the 
American Railway Master Mechanics' Association in 1895 agreed to 
recommend the use of the decimal gauge, that is, a gauge whose number 
for each thickness is the number of thousandths of an inch in 'that thick- 
ness, and also to recommend " the abandonment and disuse of the various 
other gauges now in use, as tending to confusion and error." A no4;ched 
gauge of oval form, shown in the cut below, has come into use as a standard 
form of the decimal gauge. 

In 1904 The Westinghouse Electric & Mfg. Co. abandoned the use of 
gauge numbers in referring to wire, sheet metal, etc. 

Weight of Sheet Iron and Steel. Thickness by Decimal Gauge. 







£2 


Weight per 








Weight per 


1 


m 

o . 


Square Foot 


. 


S 


fe 


Square Foot 


a 


in Pounds. 


c3 


o 

II 


.§ 


in Pounds. 


tc 




m" 




o 


a 

< 


s 


^^ 


vO 


O 




r^J> 


vO 




s 




tk 


13 


X 03 


s 






*8 
Q 


o 

a 
< 






Q 


1- 

< 


>< 
2 
a 

< 


^0 

do 
2^ 




0.002 


1/500 


0.05 


0.08 


0.082 


0.060 


1/16- 


1.52 


2.40 


2.448 


0.004 


1/250 


0.10 


0.16 


0.163 


0.065 


13/200 


1.65 


2.60 


2.652 


0.006 


3/500 


0.15 


0.24 


0.245 


0.070 


7/100 


1.78 


2.80 


2.856 


0.008 


1/125 


0.20 


0.32 


0.326 


0.075 


3/40 


1.90 


3.00 


3.060 


0.010 


VlOO 


0.25 


0.40 


0.408 


0.080 


2/25 


2.03 


3.20 


3.264 


0.012 


3/250 


0.30 


0.48 


0.490 


0.085 


17/200 


2.16 


3.40 


3.468 


0.014 


7/500 


0.36 


0.56 


0.571 


0.090 


9/100 


.2.28 


3.60 


3.672 


0.016 


1/64 + 


0.41 


0.64 


0.653 


0.095 


19/200 


2.41 


3.80 


3.876 


0.018 


9/500 


0.46 


0.72 


0.734 


0.100 


i/io 


2.54 


4.00 


4.080 


0.020 


1/50 


0.51 


0.80 


0.816 


0.110 


11/100 


2.79 


4.40 


4.488 


0.022 


11/500 


0.56 


0.88 


0.898 


0.125 


1/8 


3.18 


5.00 


5.100 


0.025 


1/40 


0.64 


1.00 


1.020 


0.135 


27/200 


3.43 


5.40 


5.508 


0.028 


7/250* 


0.71 


1.12 


1.142 


0.150 


3/20 


3.81 


6.00 


6.120 


0.032 


1/32 + 


0.81 


1.28 


1.306 


0.165 


33/200 


4.19 


6.60 


6.732 


0.036 


9/250 


0.91 


1.44 


1.469 


0.180 


9/50 


4.57 


7.20 


7.344 


0.040 


1/25 


1.02 


1.60 


1.632 


0.200 


1/5 


5.08 


8.00 


8.160 


0.045 


9/200 


1.14 


1.80 


1.836 


0.220 


11/50 


5.59 


8.80 


8.976 


0.050 


1/20 


1.27 


2.00 


2.040 


0.240 


6/95 


6.101 9.60 


9.792 


0.055 


11/200 


1.40 


2.20 


2.244 


0.250 


^ 1/4 


6.35I 10.00 


10.200 






.020° 
.018° 

.N^ o 



:*.>^0IMALGa1;^/ 



O' 




STANDARD O 



o5er 



^^AST^RlN^HAn?^ 



ALGEBRA. 33 



ALGEBRA. 

Addition. — Add a, b, and — c. Ans. a -]- b - c. 

Add 2a and — 3a. Ans. — a. Add 2ab, — Sab, — c, — 3c. Ans. 

— ab — 4c. Add a^ and 2a. Ans. a^ + 2a. 

Subtraction. — Subtract a from 6. Ans. b ~ a. Subtract — a from 

— b. Ans. — & + a. 

Subtract b + c from a. Ans. a — 6 — c. Subtract Sa^b — 9c from 
4a26 4- c. Ans. a2& 4- 10c. Rule: Change the signs of the subtrahend 
and proceed as in addition. 

Multiplication. — Multiply a by b. Ans. ab. Multiply a& by a + b. 
Ans. a^b + ab^. 

Multiply a+ 6 by a + b. Ans. {a +b) (a +b)=a^-h 2ab-\-b^. 

Multiply — a by — b. Ans. ab. Multiply —a by b. Ans. — ab. 
Like signs give plus, unlike signs minus. 

Powers of numbers. — The product of two or more powers of any 
number is the number with an exponent equal to the sum of the powers: 
ai X a^ = a^: a'^b^ X ab = a^b^: - lab X 2ac = - 14a^bc. 

To multiply a polynomial by a monomial, multiply each term of the 
polynomial by the monomial and add the partial products: (6a — 3b) 
X 3c = 18ac - 9bc. 

To multiply two polynomials, multiply each term of one factor by each 
term of the other and add the partial products: (5a — 66) X (3a — 46) 
= 15a2 - 38a6 + 2462. 

The square of the sum of two numbers = sum of their squares + twice 
their product. 

The square of the difference of two numbers = the sum of their squares 

— twice their product. 

The product of the sum and difference of two numbers = the difference 
of their squares: 

(a + 6)2 = a2 + 2a6 + 62; (a - 6)2 = a^ - 2ab + 62; 
(a + 6) X (a - 6) = a2 - 62. 

The square of half the sums of two quantities is equal to their product 
plus the square of half their difference: ( — — ) = a6 + ( — 9~ ) ' 

The square of the sum of two quantities is equal to four times their 
products, plus the square of their difference: (a + 6)2 = 4a6 4- (a — 6)2. 

The sum of the squares of two quantities equals twice their product, 
plus the square of their difference: a2 + 62 = 2a6 + (a — 6)2. 

The square of a trinomial = square of each term + twice the product 
of each term bv each of the terms that follow it: (a 4- 6 + c)2 = a2 + 62 
+ c2 + 2a6 4- 2ac 4- 26c; (a - 6 - c)?= a2 4- 62 4- c* - 2a6- 2ac 4- 26c. 

The square of (any number 4- 1/2) = square of the number 4- the number 
4-1/4; ^ the number X (the number 4-1)4-1/4; (a 4- 1/2)^ = a2 4- a 4- 1/4. 
= a(a 4- 1)4-1/4. (41/2)2=424-44-1/4 = 4x54-1/4=201/4. 

The product of any number 4- 1/2 by any other number 4- 1/2 = product 
of the numbers 4- half their sum 4- 1/4. (a 4- 1/2) X (6 4- 1/2) = a6 4- i/2(a 4-6) 
4- 1/4. 41/2 X 6I/2 = 4 X 6 -f 1/2(4 -f 6) -h 1/4 = 24 4- 5 4- I/4 = 291/4. 

Square, cube, 4th power, etc., of a binomial a 4- 6. 

(a 4- 6)2 = a2 4- 2a6 4- 62; (a 4- 6)^ = a^ 4- 3a26 4- 3a62 4- 6^ 
(a 4- 6)* = a< 4- 4a36 4- 6a262 4- 4a63 4- b*. 

In each case the number of terms is one greater than the exponent of 
the power to which the binomial is raised. 

2. In the first term the exponent of a is the same as the exponent of the 
power to which the binomial is raised, and it decreases by 1 in each suc- 
ceeding term. 

3. 6 appears in the second term with the exponent 1, and its exponent 
increases by 1 in each succeeding term. 

4. The coefficient of the first term is 1. 

5. The coefficient of the second term is the exponent of the power to 
which the binomial is raised. 



34 ALGEBRA. 



6. The coefificient of each succeeding term is found from the next pre- 
ceding term by multiplying its coefficient by the exponent of a, and 
dividing the product by a number greater by 1 than the exponent of b. 
(See Binomial Theorem, below.) 

Parentheses. — When a parenthesis is preceded by a plus sign it may 
be removed without changing the value of the expression: a -\- b -h (a -i- 
6) = 2a + 2b. When a parenthesis is preceded by a minus sign it may 
be removed if we change the signs of all the terms within the parenthesis: 
I — (a — b — c) = l— a-\-b+c. When a parenthesis is within a 
parenthesis remove the inner one first: a —[b — -(c —{d — 6)}] = ^ ~ [^ ~ 
^c — d + eyj= a — [b — c + d — e] = a ~ b + c — d + e. 

A multipUcation sign, X, has the effect of a parenthesis, in that the 
operation indicated by it must be performed before the operations of 
addition or subtraction, a + b Xa-\-b = a-{-ab -f-6; while (a + b) 
X (a + 6) = a2 + 2ab + b~, and (a + 6) X a -h b = a^ -{- ab -\- b. 

The absence of any sign between two parentheses, or between a quan- 
tity and a parenthesis, indicates that the parenthesis is to be multiplied by 
the quantity or parenthesis: a{a + b + c) = a^ -{- ab -h ac. 

Division. — The quotient is positive when the dividend and divisor 
have like signs, and negative when they have unlike signs: abc -r- b = ac; 
abc -r- — b = — ac. 

To divide a monomial by a monomial, write the dividend over the 
divisor with a line between them. If the expressions have common factors, 
remove the common factors: 

„, , a^bx ax a* a^ 1 , 

a^bx -i- aby = -r— = — ;—, = a; -r = -^ = a~^, 
aby y a^ a^ a^ 

To divide a polynomial by a monomial, divide each term of the poly- 
nomial by the monomial: {Sab — 12ac) ^ 4a = 26 — 3c. 

To divide a polynomial by a polynomial, arrange both dividend and 
divisor in the order of the ascending or descending powers of some common 
letter, and keep this arrangement throughout the operation. 

Divide the first term of the dividend by the first term of the divisor, and 
write the result as the first term of the quotient. 

Multiply all the terms of the divisor by the first term of the quotient 
and subtract the product from the dividend. If there be a remainder, 
consider it as a new dividend and proceed as before: (a^ — b'^) -5- (a + b). 

a^ - b^ I a + b . 
a^ -\- ab \ a — b. 



- ab - b^. 

- ab - b\ 

The difference of two equal odd powers of any two numbers is divisible 

by their difference but not by their sum: 

(a3-&3)-f.(a-6)=a2-f-a& + 62; (a^-.j)2)^(^a-{-b) = a^-ab-b^+ • • • . 

The difference of two equal even powers of two numbers is divisible by 
their difference and also by their sum: (a^ ~ b^) -^ (a — b) = a -\- b. 

The sum of two equal even powers of two numbers is not divisible by 
either the difference or the sum of the numbers; but when the exponent 
of each of the two equal powers is composed of an odd and an even factor, 
the sum of the given power is divisible by the sum of the powers expressed 
by the even factor. Thus x^ + y^ is not divisible by x -h y ot by x ~ y, 
but is divisible by x^ + y^. 

Simple equations. — An equation is a statement of equality between 
two expressions; as, a 4- & = c + rf. 

A simple equation, or equation of the first degree, is one which contains 
only the first power of the unknown quantity. If equal changes be made 
(by addition, subtraction, multiplication, or division) in both sides of an 
equation, the results will be equal. 

Any term may be changed from one side of an equation to another, 
provided its sign be changed: a+b = c-{-d; a = c-\-d — b. To solve 



ALGEBRA. 35 

an equation having one unknown quantity, transpose all the terms involv- 
ing the unknown quantity to one side of the equation, and all the other 
terms to the other side; combine like terms, and divide both sides by the 
coefficient of the unknown quantity. 

Solve 8.T - 29 = 26 - Sx. Sx + 3x = 29 + 26; llx = 55; x = 5, ans. 

Simple algebraic problems containing one unknown quantity are solved 
by making x = the unknown quantity, and stating the conditions of the 
problem in the form of an algebraic equation, and then solving the equa- 
tion. What two numbers are those whose sum is 48 and difference 14? 
Let X = the smaller number, a; + 14 the greater, x •{- x + 14 = 48. 
2a: = 34, a: = 17; a; 4- 14 = 31, ans. 

Find a number whose treble exceeds 50 as much as its double falls short 
of 40. Let a; = the number. 3a; — 50 = 40 - 2a;; 5x = 90;a; = 18, ans. 
Proving, 54 - 50 = 40 - 36. 

Equations containing two unknown quantities. — If one equation 
contains two unknown quanfities, x and y, an indefinite number of pairs 
of values of x and y may be found that will satisfy the equation, but if a 
second equation be given only one pair of values can be found that will 
satisfy both equations. Simultaneous equations, or those that may be 
satisfied by the same values of the unknown quantities, are solved by 
combining the equations so as to obtain a single equation containing only 
one unknown quantity. This process is called elimination. 

Elimination by addition or subtraction. — Multiply the equation by 
such numbers as will make the coefficients of one of the unknown quanti- 
ties equal in the resulting equation. Add or subtract the resulting equa- 
tions according as they have unlike or like signs. 



9n7vp i 2a? + 3y =^ 7. Multiply by 2: 4a7 + 6?/ =14 

^^^^® t 407 - 5]/ = 3. Subtract : 4a? - 5y =3 Uy - 11 ; y 



= 1. 



Substituting value of y in first equation, 2a; + 3 = 7; x = 2. 

Elimination by substitution. — From one of the equations obtain the 
value of one of the unknown quantities in terms of the other. Substi- 
tute for this unknown quantity its value in the other equation and reduce 
the resulting equations. 

qolvp ! 2a; + 3?/ = 8. (1). From (1) we find x = ^ ~ ^^ » 
^°^^^l3a; +7y = 7, (2). 2 

Substitute this value in (2): 3 ( ^ ""^ ^^ ) +7y = 7; =24-92/ +142/ = 14. 

whence y = — 2. Substitute this value in (1): 2a; — 6 = 8; a; = 7. 

Elimination by comparison. — From each equation obtain the value of 
one of the unknown quantities in terms of the other. Form an equation 
from these equal values, and reduce this equation. 

Solve 2x - 9y = 11. (1) and 3a; - 4y = 7. (2). From (1) we find 

11 + 9v -n /ON « ^ 7 4- 4?; 

X = — ^. From (2) we find x = • r— ^« 

z o 

11 + 9?/ 7 4- Av 
Equating these values of a;, — • = — -^—^ ; 19y = ~ 19; 2/ = — 1. 

Substitute this value of ?/ in (1): 2a; + 9 = 11; a; = 1. 

If three simultaneous equations are given containing three unknown 
quantities, one of the unknown quantities must be eliminated between two 
pairs of the equations; then a second between the two resulting equations. 

Quadratic equations. — A quadratic equation contains the square of 
the unknown quantity, but no higher power. A pure quadratic contains 
the square only; an affected quadratic both the square and the first power. 

To solve a pure quadratic, collect the unknown quantities on one side, 
and the known quantities on the other; divide by the coefficient of the 
unknown quantity and extract the square root of each side of the resulting 
equation. 

Solve 3x2 - 15 = 0. 3a;2 = 15; x^ = 5; .t = V5. 

A root like ^^, which is indicated, but which can be found only approxi- 
mately, is called a surd. 



36 ALGEBRA. 

Solve 3x2 + 15 = 0. 3x'= ~ 15; a;2 = - 5; a; « vCr"5. 

The square root of — 5 cannot be found even approximately, for the 
square of any number positive or negative is positive; therefore a root 
which is indicated, but cannot be found even approximately, is called 
imaginary. 

To solve an affected quadratic, 1. Convert the equation into the form 
a^x^ ± 2abx = c, multiplying or dividing the equation if necessary, so as 
to make the coefficient of x^ a square number. 

2. Complete the square of the first member of the equation, so as to 
convert it to the form of a'^x^ ± 2abx + b^, which is the square of the 
binomial ax±b, as follows: add to each side of the equation the square of 
the quotient obtained by dividing the second term by twice the square 
root of the first term. 

3. Extract the square root of each side of the resulting equation. 
Solve 3x2 „ 4^= 32. To make the coefficient of x^ a square number, 

multiply by 3 : 9x2 - 12a; = 96; I2x -^ (2 X 3x) = 2; 22 = 4. 

Complete the square: 9x2 _ i2x + 4 = 100. Extract the root: 
3x — 2 = ± 10, whence x = 4 or — 22/3. The square root of 100 is 
either + 10 or — 10, since the square of — 10 as well as + 10^ = 100. 

Every affected quadratic may be reduced t o the form ax2+6x+c=f--0. 

The solution of this equation is x = • 

Problems involving quadratic equations have apparently two solutions, 
as a quadratic has two roots. Sometimes both will be true solutions, but 
generally one only will be a solution and the other be inconsistent with the 
conditions of the problem. 

The sum of the squares of two consecutive positive numbers is 481. 
Find the numbers. 

Let X = one number, x + 1 the other, x^ + (x + 1)2 = 481. 2x2 4. 
2x + 1 = 481. 

x2 + X = 240. Completing the square, x2 +x + 0.25 = 240.25. 
Extracting the root we obtain x+ 0.5 = db 15.5; x = 15 or — 16. The 
negative root — 16 is inconsistent with the conditions of the problem. 

Quadratic equations containing two unknown quantities require 
different methods for their solution, according to the form of the equations. 
For these methods reference must be made to works on algebra. 

Theory of exponents. — ^a when n is a positive integer is one of n 

equal factors of a. ya^ means a is to be raised to the mth power and the 
nth root extracted. 

^ means that the nth root of a is to be taken and the result 



( ^" 



={v-ay 



raised to the mth power, 
m 

a w. When the exponent is a" fraction, the numera- 
tor indicates a poweyr, and the denominator a root. a/2 = V'as = a'; 

To extract the root of a quantity raised to an indicated power, divide 
the exponent by the index of the required root; as, 

m 



y^^an- \/a^^a^l 



Subtracting 1 from the exponent of a is equivalent to dividing by a: 

a2-i== ai « a; ai-i = aO = -= 1; aO-» = a-> = -; a-i-i = a^2=l 
a a a2 

A number with a negative exponent denotes the reciprocal of the num- 
ber with the corresponding positive exponent. 

A factor under the radical sign whose root can be taken may, by having 
the root taken, be removed from under the radical sign: 

Vc^b « Va2X V6 = a v^6. 



GEOMETRICAL PROBLEMS. 



37 



A factor outside the radical sign may be raised to the corresponding 
power and placed under it: 

Binomial Theorem. — To obtain any power, as the nth, of an expres- 
sion of the form x + a ^_2 ^_, 



Va. 



etc 



x + 



n(n - l)a" 



• a:2 + 



n(n-l)(n-'2)a"' 



x^ + 



1.2 1.2.3. 

The following laws hold for any term in the expansion of (a + ic)^. 
The exponent of x is less by one than the number of terms. 
The exponent of a is n minus the exponent of x. 

The last factor of the numerator is greater by one than the exponent of a. 
The last factor of the denominator is the same as the exponent of x. 
In the rth term the exponent of x will be r — 1. 
The exponent of a will be n — (r — 1), or n — r + 1. 
The last factor of the numerator will be n — r + 2. 
The last factor of the denominator will be = r ~ 1. 



Hence the rth term = 



n(n - l){n - 2) 



1.2.3 (r- 1) 



(n-r-\-2) n^^i r^l^ 



GEOMETRICAL PROBLEMS. 




E ^3 ' A 

Fig. 4. 



1. To bisect a straight line, or 
an arc of a circle (Fig. 1). — From 
the ends A, B, as centres, describe 
arcs intersecting at C and D, and 
draw a line through C and D which 
will bisect the line at E or the arc 
at F. 

2. To draw a perpendicular to 
a straight line, or a radial line to 
a circular arc. — Same as in 
Problem 1. C D is perpendicular to 
the line A B, and also radial to the 
arc. 

3. To draw a perpendicular to 
a straight line frojn a given point 
in that line (Fig. 2). — With any 
radius, from the given point A in the 
line B C, cut the line at B and C. 
With a longer radius describe arcs 
from B and C, cutting each other at 
D, and draw the perpendicular D A, 

4. From the end A of a given 
line A D to erect a perpendicular 
AE (Fig. 3). — From any centre F, 
above A D, describe a circle passing 
through the given point A , and cut- 
ting the given line at D. Draw D F 
and produce it to cut the circle at E, 
and draw the perpendicular A E. 

Second Method (Fig. 4). — From 
the given point A set off a distance 
A E equal to three parts, by any 
scale; and on the centres A and E^ 
with radii of four and five parts 
respectively, describe arcs intersect- 
ing at C Draw the perpendicular 
A C. 

Note. — This method is most 
useful on very large scales, where 
straight edges are inapplicable. Any 
multiples of the numbers 3, 4, 5 may 
be taken with the same effect, as 6, & 
10, or 9, 12, 15. 



38 



GEOMETRICAL PROBLEMS. 



5. To draw a perpendicular to 
a straight line from any point 
without it (Fig. 5). — From the 
point A, with a sufficient radius cut 
the given line at F and G, and from 
these points describe arcs cutting at 
E. Draw the perpendicular A E. 



6. To draw a straight line 
parallel to a given line, at a given 
distance apart (Fig. 6). — From 
the centres A, B, in the given line, 
with the given distance as radius, 
describe arcs C, D, and draw the 
parallel lines C D touching the arcs. 



7. To divide a straight line into 
a number of equal parts (Fig. 7). 
— To divide the line A B into, say, 
five parts, draw the line A C at an 
angle from A ; set off five equal parts; 
draw B5 and draw parallels to it 
from the other points of division in 
A C. These parallels divide A B as 
required. 

Note. — Bj^ a similar process a 
line may be divided into a number 
of unequal parts; setting off divisions 
on A C, proportional by a scale to the 
required divisions, and drawing 
parallels cutting A B. The triangles 
All, A 22, ASS, etc., are similar 
triangles. 



8. Upon a straight line to draw 
an angle equal to a given angle 

(Fig. 8). — Let A be the given angle 
and 7^' G the line. From the point A 
with any radius describe the arc D E. 
From F with the same radius 
describe I H. Set off the arc / H 
equal to D E, and draw F H. The 
angle F is equal to A, as required. 



9. To draw angles of 60° and 

80° (Fig. 9). — From F, with any 
radius F I, describe an arc / H\ and 
from /, with the same radius, cut 
the arc at H and draw F H to form 
the required angle I F H. Draw the 
perpendicular H Kto the base line to 
form the angle of 30° F H K. 



10. To draw an angle of 45° 

(Fig. 10). — Set off the distance F 7; 
draw the perpendicular 7 H equal to 
/ F, and join H F to form the angle at 
F. The angle at 77 is also 45°. 




Fig. 5. 



c 


D 


■'--;'-> 


1 




1 




GEOMETRICAL PROBLEMS. 



39 




Fig. 11. 




Fig. 15, 



11. To bisect an angle (Fig. 11). 
— Let ACB be the angle; with C as 
a centre draw an arc cutting the 
sides at A, B. From A and B as 
centres, describe arcs cutting each 
other at D. Draw C D, dividing the 
angle into two equal parts. 

12. Through two given points 
to describe an arc of a circle with 
a given radius (Fig. 12). — From 
the points A and B as centres, with 
the given radius, describe arcs cut- 
ting at C; and from C with the same 
radius describe an arc A B. 



13. To find the centre of a circle 
or of an arc of a circle (Fig. 13). — 
Select three points. A, B, C, in the 
circumference, well apart; with the 
same radius describe arcs from these 
three points, cutting each other, and 
draw the two Hues, D E, F G, 
through their intersections. The 
point 0, where they cut, is the centre 
of the circle or arc. 

To describe a circle passing 
through three given points. — 
Let A, B, C be the given points, and 
proceed as in last problem to find the 
centre O, from which the circle may 
be described. 



14. To describe an arc of a 
circle passing through three 
given points when the centre is 
not available (Fig. 14). — From 
the extreme points A, B, as 
centres, describe arcs A H, B G. 
Through the third point C draw 
AE, BF, cutting the arcs. 
Divide A F and B E into any 
number of equal parts, and set 
off a series of equal parts of the 
same length on the upper por- 
tions of the arcs beyond the 
points EF. Draw straight 
lines, B L, B M, etc., to the 
divisions in A F, and AT, A K, 
etc., to the divisions in E G. 
The successive intersections iV, 
0, etc., of these lines are points 
in the circle required between the 
given points A and C, which may 
be drawn in; similarly the remain- 
ing part of the curve B C may 
be described, (See also Problem 
54.) 



15. To draw a tangent to a 
circle from a given point in the 
circumference (Fig. 15). — Through 
the given point A, draw the radial 
line A C, and a perpendicular to it, 
F G, which is the tangent required. 



40 



GEOMETKICAL PROBLEMS. 



16. To draw tangents to a 
circle from a point without it (Fig. 
16). — From A, with the radius 
A C, describe an arc BCD, and 
from C, with a radius equal to the 
diameter of the circle, cut the arc at 
BD. Join BC, CD, cutting the 
circle at E F, and draw AE, AF, 
the tangents. 

Note. — When a tangent is 
already drawn, the exact point of 
contact may be found by drawing a 
perpendicular to it from the centre. 

17. Between two inclined lines 
to draw a series of circles touching 
these lines and touching each 
other (Fig. 17). — Bisect the inclina- 
tion of the given lines AB, CD, by 
the line N O. From a point P in this 
line draw the perpendicular P J5 to the 
line A B, and on P describe the circle 
BD, touching the lines and cutting 
the centre line at E. From E draw 
E F perpendicular to the centre line, 
cutting AB at F, and from F 
describe an arc E G, cutting A 5 at 
G. Draw GH parallel to B P, 
giving H, the centre of the next 
circle, to be described with the 
radius HE, and so on for the next 
circle IN. 

Inversely, the largest circle may 
be described first, and the smaller 
ones in succession. This problem is 
of frequent use in scroll-work. 

18. Between two inclined lines 
to draw a circular segment tan- 
gent to the lines and passing 
through a point F on the line F C 
which bisects the angle of the 
lines (Fig. 18). — Through F draw 
DA at right angles to FC\ bisect 
the angles A and D, as in Problem 
11, by lines cutting at C, and from 
C with radius C F draw the arc H FG 
required. 

19. To draw a circular arc that 
will be tangent to two given lines 
AB and C D inclined to one another, 
one tangential point E being given 

(Fig. 19). — Draw the centre line 
G F. From E draw E F at right 
angles to A B: then F is the centre 
of the circle required. 

20. To describe a circular arc 
joining two circles, and touching 
one of them at a given point (Fig. 
20). — To join the circles AB, FG, 
by an arc touching one of them at 
F, draw the radius E F, and produce 
it both ways. Set off F H equal to 
the radius ^ C of the other circle; 
join C H and bisect it with the per- 
pendicular L I, cutting E F 2it I. 
On the centre /, with radius I F^ 
describe the arc F A d^^ required. 




GEOMETRICAL PROBLEMS. 



41 





Fig. 26. 



21. To draw a circle with a 
given radius R tiiat will be tan- 
gent to two given circles A and B 

(Fig. 21). — From centre of circle 
A with radius equal R plus radius 
of A, and from centre of B with 
radius equal to /^ 4- radius of B^ 
draw two arcs cutting each other in 
C, which will be the centre of the 
circle required. 



22. To construct an equilateral 
triangle, the sides being given 

(Fig. 22). — On the ends of one side, 
Ay B, with A ^ as radius, describe 
arcs cutting at C, and draw A C,C B. 



23. To construct a triangle of 
unequal sides (Fig. 23). — On 
either end of the base A D, with the 
side B as radius, describe an arc; 
and with the side C as radius, on the 
other end of the base as a centre, cut 
the arc at E, Join A E, D E, 



24. To construct a square on a 
given straight line A B (Fig. 24). 
— With A B a.s radius and A and B 
as centres, draw arcs A D and B C, 
intersecting at E. Bisect E B a.t 
F. With E as centre and E F 3iS 
radius, cut the arcs A D and B C 
in D and C. Join A C, C D, and 
D B to form the square. 



25. To construct a rectangle 
with gi ven base E F and height E H 

(Fig. 25). — On the base E F draw 
the perpendiculars E H, F G equal 
to the height, and join G H. 



26. To describe a circle about 
a triangle (Fig. 26). — Bisect two 
sides A B, A C oi the triangle at 
E F, and from these points draw 
perpendiculars cutting at K. On 
the centre K, with the radius K A, 
draw the circle ABC, 



27. To inscribe a circle in a 
triangle (Fig. 27). — Bisect two of 
the angles A, C, of the triangle by 



42 



GEOMETRICAL PROBLEMS. 



lines cutting at D; from D draw a 
perpendicular D E to any side, and 
with D E as radius describe a circle. 
When the triangle is equilateral, 
draw a perpendicular from one of the 
angles to the opposite side, and from 
the side set otf one third of the 
perpendicular. 

38. To describe a circle about 
a square, and to inscribe a square 
in a circle (Fig. 28). — To describe 
the circle, draw the diagonals A B, 
C D of the square, cutting at E. On 
the centre E, with the radius A E, 
describe the circle. 

To inscribe the square. — Draw 
the two diameters, A B, C D, at right 
angles, and join the points A, B, 
C D, to form the square. 

Note, — In the same way a circle 
may be described about a rectangle. 

29. To inscribe a circle in a 
Sjq[uare (Fig. 29). — To inscribe the 
circle, draw the diagonals A B, C D 
of the square, cutting at E; draw the 
perpendicular E F to one side, and 
with the radius E F describe the 
circle. 






30. To describe a square about 
a circle (Fig. 30). — Draw two 
diameters A B, C D Sit right angles. ' 
With the radius of the circle and 
A, B, C and D as centres, draw the 
four half circles which cross pne 
another in the corners of the square. 



31. To inscribe a pentagon in 
a circle (Fig. 31). — Draw diam- 
eters A C, B D 3it right angles, cut- 
ting at 0. Bisect A o at E, and from 
E, with radius E B, cut A C a.t F; 
from B, with radius B F, cut the 
circumference at G, H, and with the 
same radius step round the circle to 
/ and K; join the points so found to 
form the pentagon. 



32. To construct a pentagon 
on a given line A B (Fig. 32). — 
From B erect a perpendicular B C 
half the length of A B; join A C and 
prolong it to D, making C D = B C. 
Then B D is the radius of the circle 
circumscribing the pentagon. From 
A and B as centres, with B D a,s 
radius, draw arcs cutting each other 
in O, which is the centre of the circle. 





Fig. 32. 



GEOMETRICAL PROBLEMS. 



43 





m I 
Fig. 37. 



33. To construct a hexagon 
upon a given straight line (Fig. 
33). — From A and B, the ends of 
the given Une, with radius A B, 
describe arcs cutting at g; from g, 
with the radius g A, describe a circle; 
with the same radius set off the arcs 
A G, G F, and B D, D E. Join the 
points so found to form the hexagon. 
The side of a hexagon = radius of its 
circumscribed circle. 

34. To inscribe a hexagon in a 
circle (Fig. 34). — Draw a diam- 
eter A C B. From A and B as 
centres, with the radius of the circle 
A C, cut the circumference, at D, E, 
F, G, and draw A D, D E, etc., to 
form the hexagon. The radius of 
the circle is equal to the side of the 
hexagon; therefore the points D, E, 
etc., may also be found by stepping 
the radius six times round the circle. 
The angle between the diameter and 
the sides of a hexagon and also the 
exterior angle between a side and an 
adjacent side prolonged is 60 degrees; 
therefore a hexagon may conven- 
iently be drawn by the use of a 60- 
degree triangle. 

35. To describe a hexagon 
about a circle (Fig. 35). — Draw a 
diameter A D B, and with the radius 
A D, on the centre A, cut the circum- 
ference at C; join A C, and bisect it 
with the radius D E; through E draw 
FG, parallel to A C, cutting the diam- 
eter at F, and with the radius D F 
describe the circumscribing circle 
F H. Within this circle, describe a 
hexagon by the preceding problem. 
A more convenient method is by use 
of a 60-degree triangle. Four of the 
sides make angles of 60 degrees with 
the diameter, and the other two are 
parallel to the diameter. 

36. To describe an octagon on 
a given straight line (Fig. 36). — 
Produce the given line A B both 
ways, and draw^ perpendiculars A E, 
B F; bisect the external angles A and 
B by the lines AH, B C, which make 
equal to A B. Draw C D and // G 
parallel to A E, and equal to A B; 
from the centres G, D, with the 
radius A B, cut the perpendiculars at 
E, F, and draw E F to complete the 
octagon. 

37. To convert a square into 
an octagon (Fig. 37). — Draw the 
diagonals of the square cutting at e; 
from the corners A, B, C, D, with 
A e as radius, describe arcs cutting 
the sides at gn, fk, hm, and ol, and 
join the points so found to form the 
octagon. Adjacent sides of an octa- 
gon make an angle of 135 degrees. 



44 



GEOMETRIC AL PROBLEMS. 



38. To inscribe an octagon in 

a circle (Fig. 38). — Draw two 
diameters, A C, B D at right angles; 
bisect the arcs A B, B C, etc., at ef, 
etc., and join A e^e B^ etc., to form 
the octagon. 



39. To describe an octagon 
about a circle (Fig. 39). — Describe 
a square about the given circle A B; 
draw^ perpendiculars h k, etc., to the 
diagonals, touching the circle to 
form the octagon. 



40. To describe a polygon of 
any number of sides upon a given 
straight line (Fig. 40). — Produce 
the given line A B, and on A, with the 
radius A B, describe a semicircle; 
divide the semi-circumference into 
as many equal parts as there are to 
be sides in the polygon — say, in 
this example, five sides. Draw lines 
from A through the divisional points 
D, b, and c, omitting one point a; 
and on the centres B, D, with the 
radius A B, cut Ah &t J5/ and A c at F. 
Draw D E,E F,F BXo complete the 
polygon. 




E A; C 





1 




41. To inscribe a circle within 
a polygon (Figs. 41, 42), — When 
the polygon has an even number of 
sides (Fig. 41), bisect two opposite 
sides at A and B\ draw A B, and 
bisect it at C by a diagonal D E, and 
with the radius C A describe the 
circle. 

When the number of sides is odd 
(Fig. 42), bisect two of the sides at A 
and B, and draw lines A E, B Dto the 
opposite angles, intersecting at C; 
from C, with the radius C A, describe 
the circle. 



43. To describe a circle without 
a polygon (Figs. 41, 42). — Find 
the centre C as before, and with the 
radius C D describe the circlCo 

43. To inscribe a polygon of 
any number of sides within a circle 

(Fig. 43). — Draw the diameter A B 
and through the centre E draw the 




Fig. 42. 



GEOMETRICAL PROBLEMS. 



45 




perpendicular E C, cutting the circle 
at F. Divide E F into four equal 
parts, and set off three parts equal 
to those from F to C. Divide the 
diameter A B into as many equal 
parts as the polygon is to have sides; 
and from C draw C D, through the 
second point of division, cutting the 
circle at D. Then AD is equal to one 
side of the polygon, and by stepping 
round the circumference with the 
length A D the polygon may be com- 
pleted. 



Table of Polygonal Angles. 



Number 


Angle 


Number 


Angle 


Number 


Angle 


of Sides. 


at Centre. 


of Sides. 


at Centre. 


of Sides. 


at Centre. 


No. 


Degrees. 


No. 


Degrees. 


No. 


Degrees. 


3 


120 


9 


40 


15 


24 


4 


90 


10 


36 


16 


221/2 


5 


72 


n 


328/11 


17 


213/17 


6 


60 


12 


30 


18 


20 


7 


513/7 


13 


27 9/13 


19 


19 


8 


45 


14 


25 5/7 


20 


18 



In this table the angle at the centre is found by dividing 360 degrees, the 
number of degrees in a circle, by the number of sides in the polygon; and 
by setting off round the centre of the circle a succession of angles by means 
of the protractor, equal to the angle in the table due to a given number of 
sides, the radii so drawn will divide the circumference into the same num- 
ber of parts. 

44. To describe an ellipse when 
the length and breadth are given 
(Fig. 44). — A B, transverse axis; 
C D, conjugate axis; F G, foci. The 
sum of the distances from C to i^ 
and G, also the sum of the distances 
from F and G to any other point in 
the curve, is equal to the transverse 
axis. From the centre C, with A E 
as radius, cut the axis A J5 at F and 
G, the foci; fix a couple of pins into 
the axis at F and G, and loop on a 
thread or cord upon them equal in 
length to the axis A B, so as when 
stretched to reach to the extremity 
C of the conjugate axis, as shown in 
dot-lining. Place a pencil inside the 
cord as at H, and guiding the pencil 
in this way, keeping the cord equally 
in tension, carry the pencil round the 
pins F, G, and so describe the 
ellipse. 

Note. — This method is employed 
in setting off elliptical garden-plots, 
walks, etc. 

2d Method (Fig. 45). — Along the 
straight edge of a slip of stiff paper 
mark off a distance a c equal to A C, 
half the transverse axis; and from 




"Sia. 45. 



the same point a distance a b equal 
to C Dt halt the conjugate axis. 



46 



GEOMETRICAL PROBLEMS. 



Place the slip so as to bring the point b on the line A B of the transverse 
axis, and the point c on the line D E; and set off on the drawing the posi- 
tion of the point a. Shifting the slip so that the point b travels on the 
transverse axis, and the point c on the conjugate axis, any number of 
points in the curve may be found, through which the curve may be 

3d Method (Fig. 46). — The action 
of the preceding method may be 
embodied so as to afford the means 
of describing a large curve contin- 
uously by means of a bar m k, with 
steel points m, I, k, riveted into brass 
slides adjusted to the length of the 
semi-axis and fixed with set-screws. 
A rectangular cross E G, with guiding- 
slots is placed, coinciding with the 
two axes of the ellipse A C and B H. 
By sliding the points k, I in the slots, 
and carrying round the point m, the 
curve may be continuously described. 
A pen or pencil may be fixed at m. 

4th Method (Fig. 47). — Bisect the 
transverse axis at C, and through C 
draw the perpendicular D E, making 
C D and C E each equal to half the 
conjugate axis. From D or E, with 
the radius AC, cut the transverse 
axis at F, F\ for the foci. Divide 
A C into a number of parts at the 
points 1, 2, 3, etc. With the radius 
Al on F and F' as centres, describe 
arcs, and with the radius 5 1 on the 
same centres cut these arcs as shown. 
Repeat the operation for the other 
divisions of the transverse axis. The 
series of intersections thus made are 
points in the curve, through which 
the curve may be traced. 

Mh Method (Fig. 48). — On the 
two axes A B, D E eis diameters, on 
centre C, describe circles; from a 
number of points a, b, etc., in the 
circumference A F B, draw radii cut- 
ting the inner circle at a\ b\ etc. 
From a, &, etc., draw perpendiculars 
to AB; and from a', b\ etc., draw 
parallels to A B, cutting the respec- 
tive perpendiculars at n, o, etc. The 
intersections are points in the curve, 
through which the curve may be 
traced. 

eth Method (Fig. 49). — When the 
transverse and conjugate diameters 
are given, AB,C D, draw the tangent 
EF parallel to AB. Produce CD, 
and on the centre G with the radius 
of half A B, describe a semicircle 
H D K; from the centre G draw any 
number of straight lines to the points 
E, r, etc., in the Une E F, cutting the 
circumference at I, m, n, etc.; from 
the centre O of the ellipse draw 
straight lines to the points E, r, etc.; 
and from the points I, m, n, etc., 
draw parallels to GC, cutting the 
lines O E, Or, etc., at I, M, N, etc. 




GEOMETRICAL PROBLEMS. 



47 



/"""^ 


\r'' 1 


(/cfx«^ 


/e\J 




These are points in the circumference of the ellipse, and the curve may be 
traced through them. Points in the other half _ of the ellipse are form.ed 
by extending the intersecting hues as indicated in the figure. 

45. To describe an ellipse 
approximately by means of cir- 
cular arcs. — First. — With arcs 
of two radii (Fig. 50). — Find the 
difference of the semi-axes, and set 
it off from the centre O to a and c on 
O A and O C; draw a c, and set off 
^ half ac to d; draw d i parallel to a c; 

set off O e equal to d; join e i, and 
draw the parallels em, dm. From 
m, with radius m C, describe an arc 
through C; and from i describe an 
D arc through £>; from cZ and e describe 

Fig. 50. arcs through A and B. The four 

arcs form the eUipse approximately. 
Note. — This method does not 
apply satisfactorily when the con- 
jugate axis is less than tvv^o thirds of 
the transverse axis. 

2d Method (by Carl G. Barth, Fig. 
51\ — In Fig. 51 a 5 is the major and 
c d the minor axis of the ellipse to be 
approximated. Lay oft b e equal to 
the semi-minor axis c O, and use a e 
as radius for the arc at each extrem- 
ity of the minor axis. Bisect e oat f 
and lay off eg' equal toef, and use gb 
as radius for the arc at each extrem- 
ity of the major axis. 

The method is not considered applicable for cases in which the minor 
axis is less than two thirds of the major. 

Sd Method: With arcs of three radu 
(Fig. 52). — On the transverse axis 
A B draw the rectangle B G on the 
height O C; to the diagonal A C 
draw the perpendicular G H D\ set 
off O K equal to O C, and describe a 
semicircle on A K, and produce C 
to L; set off O M equal to C L, and 
from D describe an arc with radius 
D M; from A, with radius O L, cut 
A B 3bt N; from H, with radius HN^ 
cut arc a b Sit a. Thus the five 
centres D, a, b, H, H' are found, 
from which the arcs are described to 
form the elUpse. 

This process works well for nearly 
all proportions of ellipses. It is used 
in striking out vaults and stone 
bridges. 

Uh Method (by F. R. Honey, 
Figs. 53 and 54).— Three 
radii are employed. With 
the shortest radius describe 
the two arcs which pass 
through the vertices of the 
major axis, with the longest 
the two arcs which pass 
through the vertices of the 
minor axis, and with the third 
radius the four arcs which 
connect the former. 




48 



GEOMETRICAL PROBLEMS. 



A simple method of determining the radii of curvature is illustrated in 
Fig. 53. Draw the straight lines a f and a c, forming any angle at a. With 
a as a centre, and with radii a b and a c, respectively, equal to the semi- 
minor and semi-major axes, draw the arcs b e and c d. Join e d, and 
through b and c respectively draw h g and c f parallel to e d, intersecting 
a c at ^, and a f at f; a f is the radius of curvature at the vertex of 
the minor axis; and a g the radius of curvature at the vertex of the 
major axis. 

Lay ofl dh (Fig. 53) equal to one eighth of h d. Join e h, and draw c k 
and b I parallel to e h. Take a k for the longest radius (= R), a I ioT the 
shortest radius (= r), and the arithmetical mean, or one half the sum of 
the semi-axes, for the third radius (= p), and employ these radii for the 
eight-centred oval as follows: 

Let a b and c d (Fig. 54) 
be the major and minor 
axes. Lay off a e equal 
to r, and a f equal to p; 
also lay off c g equal to i?, 
and c h equal to p. With 
(7 as a centre and gh as a 
radius, draw the arc h k; 
with the centre e and 
radius e f draw the arc / k, q\ 
intersecting h k at k. 
Draw the line g k and 
produce it, making g I 
equal to R. Draw k e 
and produce it, making 
k m equal to p. With the 
centre g and radius g c 
{= R) draw the arc c I; 
with the centre k and 
radius k I (= p) draw the 
arc I rriy and with the 
centre e and radius e m 
(= r) draw the arc m a. 

The remainder of the 
axes. 

46. The Parabola. — A parabola (D A C, Fig. 55) is a curve such 
that every point in the curve is equally distant from the directrix K L 
and the focus F, The focus lies in the axis 
A B drawn from the vertex or head of the 
curve A, so as to divide the figure into two 
equal parts. The vertex A is equidistant 
from the directrix and the focus, oiA e = AF, 
Any line parallel to the axis is a diameter. 
A straight line, as E G or D C, drawn across 
the figure at right angles to the axis is a 
double ordinate, and either half of it is an 
ordinate. The ordinate to the axis E F G, 
drawn through the focus, is called the para- 
meter of the axis. A segment of the axis, 
reckoned from the vertex, is an abscissa of 
the axis, and it is an abscissa of the ordinate 
drawn from the base of the abscissa. Thus, 
A B is an abscissa of the ordinate B C. 




work is symmetrical with respect to the 



K 




5 


L 






A 




E 


/^ 


\N 


G 


"/ 


F 


\ 


^^ 


y 







vi 


u/ 





\ 


Xw 


/ 









D 


B 
b 




-i». c 



Fig. 55. 



Abscissae of a parabola are as the squares of their ordinates. 



To describe a parabola when an abscissa and Its ordinate are given 

(Fig. 55), — Bisect the given ordinate B C at a, draw A a, and then a b 
perpendicular to it, meeting the axis at 6. Set ofi A e, A F, each equal to 
B b; and draw K eL perpendicular to the axis. Then K L is the directrix 
and F is the focus. Through F and any number of points, o, o, etc., in the 
axis, draw double ordinates, n o n, etc., and from the centre F, with the 
radii F e, o e, etc., cut the respective ordinates at E, G, n, n, etc. The 
curve may be traced through these points as shown. 

2d Method: By means of a square and a cord (Fig. 56). — Place a 



GEOMETRICAL PROBLEMS. 



49 




straight-edge to the directrix E iST, 
and apply to it a square LEG, 
Fasten to the end G one end of a 
thread or cord equal in length to the 
edge E G, and attach the other end 
to the focus F\ slide the square along 
the straight-edge, holding the cord 
taut against the edge of the square 
by a pencil £>, by which the curve is 
described. 

Sd Method: When the height and 
the base are given (Fig. 57). — Let 
A B he the given axis, and C D b. 
double ordinate or base; to describe 
a parabola of which the vertex is at 
A. Through A draw E F parallel to 
C D, and through C and D draw C E 
and D F parallel to the axis. Divide 
B C and B D into any number of 
equal parts, say five, at a, b, etc., and 
divide C E and D F into the same 
number of parts. Through the 
points a, b, c, d in the base CD on 
each side of the axis draw perpen- 
diculars, and through a, b, c, dinC E 
and D F draw lines to the vertex A, 
cutting the perpendiculars at e, f, g, h. 
These are points in the parabola, and 
the curve CAD may be traced as 
shown, passing through them. 
47. The Hyperbola (Fig. 58). -- A hyperbola is a plane curve, such 
*t t.hP. difference of the distances from any pomt of it to two fixed pomts 

is equal to a given distance. The 
fixed points are called the foci. 

To construct a hyperbola. — 
Let F' and F be the foci, and F' P 
the distance between them. Take a 
ruler longer than the distance F' F^ 
and fasten one of its extremities at 
the focus F\ At the other extrem- 
ity, H, attach a thread of such a 
length that the length of the ruler 
shall exceed the length of the thread 
by a given distance A B. Attach 
the other extremity of the thread at 
the focus F. 

Press a pencil, P, against the ruler, 
and keep the thread constantly tense, 
w^hile the ruler is turned around F' as 
a centre. The point of the pencil 
will describe one branch of the curve. 
2d Method: By points (Fig. 59). — 
From the focus F' lay off a distance 
F' N equal to the transverse axis, or 
distance between the two branches of 
the curve, and take any other dis- 
tance, as F' //, greater than F' N. 

With F' as a centre and F' // as a 
radius describe the arc of a circle. 
Then with F as a centre and AT i? as a radius describe an arc intersecting 
the arc before described at p and q. These will be points of the hyper- 
bola, ioT F' q — F q is equal to the transverse axis A B. 

if, with F as a centre and F' // as a radius, an arc be described, and a 

second arc be described with F' as a centre and iV // as a radius, two points 

in the other branch of the curve will be determined. Hence, by changing 

the centres, each pair of radii will determine two points in each branch. 

The Equilateral Hyperbola. — The transverse axis of a hyperbola is 



C d cbaBabod 
Fig. 57. 



that the difference of the 




FlQ. 58. 




50 



GEOMETRICAL PROBLEMS. 




the distance, on a line joining the foci, between the two branches of the 
curve. The conjugate axis is a line perpendicular to the transverse axis, 
drawn from its centre, and of such a length that the diagonal of the rect- 
angle of the transverse and conjugate axes is equal to the distance between 
the foci. The diagonals of this rectangle, indehnitely prolonged, are the 
asymptotes of the hyperbola, lines which the curve continually approaches, 
but touches only at an infinite distance. If these asymptotes are perpen- 
dicular to each other, the hyperbola is called a rectangular or equilateral 
hyperbola. It is a property of this hyperbola that if the asymptotes are 
taken as axes of a rectangular system of coordinates (see Analytical Geom- 
etry), the product of the abscissa and ordinate of any point in the curve is 
equal to the product of the abscissa and ordinate of any other point; or, if 
p is the ordinate of any point and v its abscissa, and pi, and vi are the 
ordinate and abscissa of any other point, vv — pin; or pi; = a constant. 

48. The Cycloid (Fig. 

60). — If a circle A c? be 6 / 

rolled along a straight ^ ^^ — ^~ ''— - 

line A 6, any point of the 
circumference as A will 
describe a curve, which is 
called a cycloid. The 
circle is called the gene- 
rating circle, and A the 
generating point. 

To draw a cycloid. — 
Divide the circumference 
of the generating circle 

into an even number of equal parts, as A 1, 12, etc., and set off these dis- 
tances on the base. Through the points 1, 2, 3, etc., on 'the circle 
draw horizontal lines, and on them 
set off distances la = A\, 26 = A2, 3c== 
AZ, etc. The points A, a,h, c, etc., 
will be points in the cycloid, through 
which draw the curve. 

49. The Epicycloid (Fig. 61) is 
generated by a point D in one circle 
D C rolling upon the circumference of 
another circle A C B, instead of on a 
flat surface or line; the former being 
the generating circle, and the latter 
the fundamental circle. The generat- 
ing circle is shown in four positions, 
in which the generating point is 
successively marked D, D\ Z>", D"\ 
A D'" B is the epicycloid. 



50. The Hypocycloid (Fig. 62) 
is generated by a point in the gener- 
ating circle rolling on the inside of 
the fundamental circle. 

When the generating circle = 
radius of the other circle, the hypo- 
cycloid becomes a straight line. 



51. The Tractrix or Schiele's 
anti-friction curve (Fig. 63). — R 
is the radius of the shaft, C, 1,2, etc., 
the axis. From O set off on i2 a 
small distance, oa; with radius R and 
centre a cut the axis at 1, join a 1, 
and set off a like small distance a b; 
from b with radius R cut axis at 2, 
join b 2, and so on, thus finding 
points 0, a, b, c, rf, etc., through which 
the curve is to be drawUo 




1 33456 789 10 

Fig. 63, 



GEOMETRICAL PROBLEMS. 



51 





5'Z. The Spiral. — The spiral is a curve described by a point which 
moves along a straight line according to any given law, the line at the same 
time having a uniform angular motion. The line is called the radius vector. 

If the radius vector increases directly 
as the measuring angle, the spires, 
or parts described in each revolution, 
thus gradually increasing their dis- 
tance from each other, the curve is 
known as the spiral of Archimedes 
(Fig. 64). 

This curve is commonly used for 
cams. To describe it draw the 
radius vector in several different 
directions around the centre, with 
equal angles between them; set off 
the distances 1, 2, 3, 4, etc., corresponding to the scale upon which the 
curve is drawn, as shown in Fig. 64. 

In the common spiral (Fig. 64) the 
pitch is uniform; that is, the spires 
are equidistant. Such a spiral is 
made by rolling up a belt of uniform 
thickness. 

To construct a spiral with four 
centres (Fig. 65). — Given the 
pitch of the spiral, construct a square 
about the centre, with the sum of 
the four sides equal to the pitch. 
Prolong the sides in one direction as 
showm; the corners are the centres for 
each arc of the external^ angles, 
forming a quadrant of a spire. 

63. To find the diameter of a circle into which a certain number of 
rings will fit on its inside (Fig. 66). — For instance, w^hat is the diameter 
of a circle into which twelve 1/2-inch rings will fit, as per sketch? Assume 
that we have found the diameter of the required circle, and have drawn 

the rings inside of it. Join the 
centres of the rings by straight lines, 
as show-n: we then obtain a regular 

Eolygon with 12 sides, each side 
eing equal to the diameter of a 
given ring. We have now to find 
the diameter of a circle circum- 
scribed about this polygon, and add 
the diameter of one ring to it; the 
sum will be the diameter of the circle 
into which the rings will fit. 
Through the centres A and D of two 
adjacent rings draw the radii C A 
and C D ; since the polygon has twelve 
sides the angle A C D = 30° and 
AC 5 = 15°. One half of the side 
A Dis equal to A B. We now give 
the following proportion: The sine 
of the angle AC Bisio A B 2iS 1 is to 
the required radius. From this we 
get the following rule: Divide A B hy the sine of the angle A C B\ the 
quotient will be the radius of the circumscribed circle; add to the corre- 
sponding diameter the diameter of one ring; the sum will be the required 
diameter F G. 

54. To describe an arc of a circle which is too large to be drawn 
by a beam compass, by means of points in the arc, radius being given. 
— Suppose the radius is 20 feet and it is desired to obtain five points in an 
arc whose half chord is 4 feet. Draw a line equal to the half chord, full 
size, or on a smaller scale if more convenient, and erect a perpendicular at 
one end, thus making rectangular axes of coordinates. Erect perpen- 
diculars at points 1, 2, 3, and 4 feet from the first perpendicular. Find 
values of y in the formula of the circle, a:^ + j/2 = r'^^ by substituting for 




52 



GEOMETRICAL PROBLEMS. 



X the values 0, 1, 2, 3, and 4, etc .. and fo r R^ the squar_e_of the radiu s, or 
400. The values will be 2/ = Vi^a _ ^2 = V400, V399, V396, V39I. 

VssI; = 20, 19.975, 19.90, 19.774, 19.596.' 
Subtract the smallest, 

or 19.596. leaving 0.404. 0.379, 0.304, 0.178, feet. 

Lay off these distances on the five perpendiculars, as ordinates from the 
half chord, and the positions of five points on the arc will be found. 
Through these the curve may be 
drawn. (See also Problem 14.) 

55. The Catenary is the curve 
assumed bv a perfectly flexible cord 
when its ends are fastened at two 

Eoints, the weight of a unit length 
eing constant. 
The equation of the catenary is 



2/=-U*^ + e ^1, in wliich e is the 

base of the Napierian system of log- 
arithms. 

To plot the catenary. — Let 

(Fig. 67) be the origin of coordmates. 
Assigning to a any value as 3, the 
equation becomes 



'+e 



') 



To find the lowest point of the 
curve. 

Put a: = 0; " 




Fig. 67. 



•. 2/==^(eO+e-o)= - (l+l)=3. 



Then put 
Put 



X = l] 









, (1.396 +0.717) =3.17. 
\ (1.948 +0.513) =3.69. 



Put a: = 3, 4, 5, etc., etc., and find the corresponding values of y. For 
each value ofywe obtain two symmetrical points, as for example p and p\ 
In this way, by making a successively equal to 2, 3, 4, 5, 6, 7, and 8, the 
curves of Fig. 67 were plotted. 

In each case the distance from the origin to 
the lowest point of the curve is equal to a; for 
putting X = o, the general equation reduces to 
y = a. 

For values of o = 6, 7, and 8 the catenary 
closely approaches the parabola. For deriva- 
tion of the equation of the catenary see Bow- 
ser's Analytic Mechanics. 

56. The Involute is a name given to the 
curve which is formed by the end of a string 
which is unwound from a cyUnder and kept 
taut ; conseqiuently the string as it is unwound 
will always lie in the direction of a tangent 
to the cylinder. To describe the involute of 
any given circle, Fig. 68, take any point A on 
its circumference, draw a diameter A B, and 
from B draw B b perpendicular to A B. Make 
B b equal in length to half the circumference 
of the circle. Divide B b and the semi-circum- 
ference into the same number of equal parts, 
say six. From each point of division 1, 2, 
3, etc., on the circumference draw lines to the centre C of the circle. 
Then draw lai perpendicular to CI; 2 a2 perpendicular to C2; and 
so on. Make lai equal tob bi', 2 02 equal to 6 62; 3 03 equal to & 63; and 
so on. Join the points A, ai, 02, 03, etc., by a curve; this curve will be 
the required involute. 




GEOMETRICAL PROPOSITIONS. 53 

57. Method of plotting angles without using a protractor. — The 

radius of a circle whose circumference is 360 is 57.3 (more accurately 
57.296). Striking a semicircle with a radius 57.3 by any scale, spacers 
set to 10 by the same scale will divide the arc into 18 spaces of 10° each, 
and intermediates can be measured indirectly at the rate of 1 by scale for 
each 1°, or interpolated by eye according to the degree of accuracy required 
The following table shows the chords to the above-mentioned radius for 
every 10 degrees from 0° up to 110°, By means of one of these a 10° 
point is fixed upon the paper next less than the required angle, and the 
remainder is laid oft at the rate of 1 by scale for each degree. 

Angle. Chord. Angle. Chord. Angle. Chord. 

1° «... 0.999 40° 39.192 80° 73.658 

10° 9.988 50° 48.429 90° 81.029 

20° 19.899 60° 57.296 100° 87.782 

30° 29.658 70° 65.727 110° 93.869 



GEOMETRICAL PROPOSITIONS. 

In a right-angled triangle the square on the hypothenuse is equal to the 
sum of the squares on the other two sides. 

If a triangle is equilateral, it is equiangular, and vice versa. 

If a straight line from the vertex of an isosceles triangle bisects the base, 
it bisects the vertical angle and is perpendicular to the base. 

If one side of a triangle is produced, the exterior angle is equal to the 
sum of the two interior and opposite angles. 

If two triangles are mutually equiangular, they are similar and their 
corresponding sides are proportional. 

If the sides of a polygon are produced in the same order, the sum of the 
exterior angles equals four right angles. (Not true if the polygon has 
re-entering angles.) 

In a quadrilateral, the sum of the interior angles equals four right 
angles. 

In a parallelogram, the opposite sides are equal; the opposite angles are 
equal; it is bisected by its diagonal, and its diagonals bisect each other. 

If three points are not in the same straight line, a circle may be passed 
through them. 

If two arcs are intercepted on the same circle, they are proportional to 
the corresponding angles at the centre. 

If two arcs are similar, they are proportional to their radii. 

The areas of two circles are proportional to the squares of their radii. 

If a radius is perpendicular to a chord, it bisects the chord and it bisects 
the arc subtended by the chord. 

A straight line tangent to a circle meets it in only one point, and it is 
perpendicular to the radius drawn to that point. 

If from a point without a circle tangents are drawn to touch the circle, 
there are but two; they are equal, and they make equal angles with the 
chord joining the tangent points. 

If two lines are parallel chords or a tangent and parallel chord, they 
intercept equal arcs of a circle. 

If an angle at the circumference of a circle, between two chords, is sub- 
tended by the same arc as an angle at the centre, between two radii, the 
angle at the circumference is equal to half the angle at the centre. 

If a triangle is inscribed in a semicircle, it is right-angled. 

If two chords intersect each other in a circle, the rectangle of the seg- 
ments of the one equals the rectangle of the segments of the other. 

And if one chord is a diameter and the other perpendicular to it, the 
rectangle of the segments of thfe diameter is equal to the souare on 
half the other chord, and the half chord is a mean proportional Det ween 
the segments of the diameter. 

If an angle is formed by a tangent and chord, it is measured by one half 
of the arc intercepted by the chord; that is, it is equal to half the angle at 
the centre subtended by the chord. 



54 MENSURATION — PLANE SURFACES. 

Degree of a Railway Curve. — This last proposition is useful in staking 
out railway curves. A curve is designated as one of so many degrees, and 
the degree is the angle at the centre subtended by a chord of 100 ft. To 
lay out a curve of n degrees the transit is set at its beginning or " point of 
curve," pointed in the direction of the tangent, and turned through 1/2^ 
degrees; a point 100 ft. distant in the line of sight will be a point in the 
curve. The transit is then sw^ung 1/2^ degrees further and a 100 ft. chord 
is measured from the point already found to a point in the new line of 
sight, which is a second point or " station " in the curve. 

^The radius of a 1° curve is 5720.65 ft., and the radius of a curve of any 
degree is 5729.65 ft. divided by the number of degrees. 

Some authors use the angle subtended by an arc (instead of chord) of 
100 ft. in defining the degree of a curve. For a statement of the relative 
advantages of the two definitions, see Eng. News, Feb. 16, 1911. 

MENSURATION. 

PLANE SURFACES. 

Quadrilateral* — A four-sided figure. 

Parallelogram. — A quadrilateral with opposite sides parallel. 

Varieties. — Square: four sides equal, all angles right angles. Rect- 
angle: opposite sides equal, all angles right angles. Pi^hombus: four sides 
equal, opposite angles equal, angles not right angles. Rhomboid: opposite 
sides equal, opposite angles equal, angles not right angles. 

Trapezium. — A quadrilateral with unequal sides. 

Trapezoid. — A quadrilateral with only one pair of opposite sides 
parallel. 

Diagonal of a square = v^2 x side^ = 1.4142 X side. 

Diag. of a rectangle = Vsum of squares of two adjacent sides. 

Area of any parallelogram = base X altitude. 

Area of rhombus or rhomboid = product of two adjacent sides X sine 
of angle included between them. 

Area of a trapezoid = product of half the sum of the two parallel sides 
by the perpendicular distance between them. 

To find the area of any quadrilateral figure. — Divide the quad- 
rilateral into two triangles; the sum of the areas of the triangles is the 
area. 

Or, multiplj^ half the product of the two diagonals by the sine of the 
angle at their intersection. 

To find the area of a quadrilateral which may be inscribed in a 
circle. — From half the sum of the four sides subtract each side severally; 
multiply the four remainders together; the square root of the product is 
the area. 

Triangle. — A three-sided plane figure. 

Varieties. — Right-angled, having one right angle; obtuse-angled, hav- 
ing one obtuse angle; isosceles, having two equal angles and two equal 
sides; equilateral, having three equal sides and equal angles. 

The sum of the three angles of every triangle = 180°. 

The sum of the two acute angles of a right-angled triangle = 90°. 

Hypothe nuse of a right-angled triangle, the side opposite the right 
angle, = Vsum of the squares of the other two si des. If a and b are the 
two sides and c the hypothenuse, c2=a2+ b^; a = ^c^ — b^^'^ic-hb)(c — b). 

If the two sides are equal, side = hyp -5- 1.4142; or hyp X. 7071. 

To find the area of a triangle: 

Rule 1. Multiply the base by half the altitude. 

Rule 2. Multiply half the product of two sides by the sine of the 
included angle. 

Rule 3. From half the sum of the three sides subtract each side 
severally; multiply together the half sum and the three remainders, and 
extract the square root of the product. 

The area of an equilateral triangle is equal to one fourth ^he square of 

one of its sides multiplied by the square root of 3, =» — 7— 1 a being tbt 
side; or a^ X 0.433013, 



MENSURATION. 



56 



Area of a triangle given, to find base: Base = twice area -v- perp 3ndicular 
height. 

Area of a triangle given, to find height: Height == twice area -^ base. 

Two sides and base given, to find perpendicular height (in a triangle in 
which both of the angles at the base are acute). 

Rule. — As the base is to the sum of the sides, so is the difference of the 
sides to the difference of the divisions of the base made by drawing the 
perpendicular. Half this difference being added to or subtracted from 
half the base will give the two divisions thereof. As each side and its 
opposite division of the base constitutes a right-angled trian.gle, th e 
perpendicular is ascertained by the rule: Perpendicular = ^hyp^ — base^. 

Areas of similar figures are to each other as the squares of their 
respective linear dimensions. If the area of an equilateral triangle of 
side = 1 is 0.433013 and its height 0.86603, what is the area of a similar 
triangle whose height = 1? 0.866032 : 12 :: 0.433013 : 0.57735, Ans. 

Polygon. — A plane figure having three or more sides. Regular or 
irregular, according as the sides or angles are equal or unequal. Polygons 
are named from the number of their sides and angles. 

To find the area of an irregular polygon. — Draw diagonals dividing 
the polygon into triangles, and find the sum of the areas of these triangles. 

To find the area of a regular polygon: 

Rule. — Multiply the length of a side by the perpendicular distance to 
the centre; multiply the product by the number of sides, and divide it by 
2. Or, multiply half the perimeter by the perpendicular let fall from the 
centre on one of the sides. 

The perpendicular from the centre is equal to half of one of the sides of 
the polygon multipUed by the cotangent of the angle subtended by the 
half side. 

The angle at the centre = 360° divided by the number of sides. 



Table of Regular PolygonSo 









r-i 


Radius of Cir- 
















II 


cumscribed 


■^ . 


d o 




» 






'"' 


* 


Circle. 


■gii 


O 5 


J 


73 
< 








is 
II 

< 


1 

i 


1 


< 


2 

1 


£ 11 

5^ 








6 

s 

< 


3 


Triangle 


0.4330 


0.5773 


2.000 


0.5773 


0.2887 


1.732 


120° 


60° 


4 


Square 


1 . 0000 


1.0000 


1.414 


0.7071 


0.5000 


1.4142 


90 


90 


5 


Pentagon 


1 . 7205 


0.7265 


1.236 


0.8506 


0.6882 


1 . 1 756 


72 


108 


6 


Hexagon 


2.5981 


0.8660 


1.155 


1.0000 


0.866 


1.0000 


60 


120 


7 


Heptagon 


3.6339 


0.7572 


l.ll 


1.1524 


1.0383 


0.8677 


51 26' 


1284.7 


8 


Octagon 


4.8284 


0.8284 


1.082 


1.3066 


1.2071 


0.7653 


45 


135 


9 


Nonagon 


6.1818 


0.7688 


1.064 


1.4619 


1.3737 


0.684 


40 


140 


10 


Decagon 


7.6942 


0.8123 


1.051 


1.618 


1.5388 


0.618 


36 


144 


11 


Undecagon 


9.3656 


0.7744 


1.042 


1.7747 


1 . 7028 


0.5634 


32 43' 


1473-11 


12 


Dodecagon 


11.1962 


0.8038 


1.035 


1.9319 


1.866 


0.5176 


30 


150 



* Short diameter, even number of sides, => diam. of inscribed circle: 
short diam., odd number of sides, = rad. of inscribed circle -f rad. oi 
circumscribed circle. 



56 



AREA OF IRREGULAR FIGURES. 



To find the area of a regular polygon, when the length of a side 
only is given: „ o *, -^ 

Rule. — Multiply the square of the side by the figure for area, side — 
1," opposite to the name of the polygon in the table. 

Length of a side of a regular polygon inscribed in a circle = diam. 
X sin (180° -^ no. of sides). 

No. of 



of sides 


sin (180°/n) 


No. 


sin (180° //i) 


No. 


sin (1807n) 


3 


0.86603 


9 


0.34202 


15 


0.20791 


4 


.70711 


10 


.30902 


16 


.19509 


5 


.58778 


11 


.28173 


17 


.18375 


6 


.50000 


12 


.25882 


18 


.17365 


7 


.43388 


13 


.23931 


19 


.16458 


8 


.38268 


14 


.22252 


20 


.15643 




Lengtjh — 
Fig. 69. 



To find the area of an irregular 
figure (Fig. 69). — Draw ordinates 
across its breadth at equal distances 
apart, the first and the last ordinate 
each being one half space from the 
ends of the figure. Find the average 
breadth by adding together the 
lengths of these lines included be- 
tween the boundaries of the figure, 
and divide by the number of the lines 
added; multiply this mean breadth 
by the length. The greater the num- 
ber of lines the nearer the approxi- 
mation. 

In a figure of very irregular outline, as an indicator-diagram from a 
high-speed steam-engine, mean lines may be substituted for the actual 
lines of the figure, being so traced as to intersect the undulations, so that 
the total area of the spaces cut off may be compensated by that of the 
extra spaces inclosed. 

2d Method: The Trapezoidal Rule. — Divide the figure into any 
sufficient number of equal parts; add half the sum of the two end ordinates 
to the sum of all the other ordinates; divide by the number of spaces 
(that is, one less than the number of ordinates) to obtain the mean 
ordinate, and multiply this by the length to obtain the area. 

Sd Method: Simpson's Rule. — Divide the length of the figure into any 
even number of equal parts, at the common distance D apart, and draw 
ordinates through the points of division to touch the boundary lines 
Add together the first and last ordinates and call the sum A ; add together 
the even ordinates and call the sum B; add together the odd ordinates, 
except the first and last, and call the sum C. Then, 



area of the figure = 



A + 45+ ^C 



X D. 



Ath Method: Durand's Rule. — Add together 4/io the sum of the first 
and last ordinates, IViothe sum of the second and the next to the last 
(or the penultimates), and the sum of all the intermediate ordinates. 
Multiply the sum thus gained by the common distance between the ordi- 
nates to obtain the area, or divide this sum by the number of spaces to 
obtain the mean ordinate. 

Prof. Durand describes the method of obtaining his rule in Engineering 
News, Jan. 18, 1894. He claims that it is more accurate than Simpson's 
rule, and practically as simple as the trapezoidal rule. He thus describes 
its application for approximate integration of differential equations. Any 
definite integral may be represented graphically by an area. Thus, let 



Q =/u 



dx 



be an integral in which u is some function of x, either known or admitting 
of computation or measurement. Any curve plotted with x as abscissa 
and u as ordinate will then represent the variation of u with x, and the 



MENSURATION. 



area between such curve and the axis X will represent the integral in 
question, no matter how simple or complex may be the real nature of the 
function u. 

Substituting in the rule as above given the word " volume" for " area" 
and the word "section" for "ordinate," it becomes applicable to the 
determination of volumes from equidistant sections as well ^s of areas 
from equidistant ordinates. 

Having approximately obtained an area by the trapezoidal rule, the 
area by Durand's rule may be found by adding algebraically to the sum of 
the ordinates used in the trapezoidal rule (that is, half the sum of the end 
ordinates + sum of the other ordinates) Vio of (sum of penultimates 
- sum of first and last) and multiplying by the common distance between 
the ordinates. 

5th Method. — Draw the. figure on cross-section paper. Count the 
number of squares that are entirely included within the boundary; then 
estimate the fractional parts of squares that are cut by the boundary, add 
together these fractions, and add the sum to the number of whole squares. 
The result is the area in units of the dimensions of the squares. The finer 
tbe ruling of the cross-section paper the more accurate the result. 

6//i Method. — Use a planimeter. 

7th Method. — With a chemical balance, sensitive to one milligram, 
draw the figure on paper of uniform thickness and cut it out carefully; 
weigh the piece cut out, and compare its weight with the weight per 
square inch of the paper as tested by weighing a piece of rectangular shape. 



THE CIRCLE. 

Circumference = diameter X 3. 1416, nearly; more accurately, 3.14159265359. 

Approximations, -~ = 3.143; ^ = 3.1415929. 

The ratio of circum. to diam. is represented by the symbol ;: (called Pi). 
Area = 0.7854 X square of the diameter. 



Multiples of t:. 

In = 3.14159265359 
2;: = 6.28318530718 
St: = 9.42477796077 
At: = 12.56637061436 
57r = 15.70796326795 
6;: = 18.84955592154 
7;r = 21.99114857513 
8;r = 25.13274122872 
9^ = 28.27433388231 



Multiples of - 



^/4 



X 2 

X 3 

X 4 

X 5 

X 6 

X 7 

X 8 



= 0.7853982 
= 1.5707963 
= 2.3561945 
= 3.1415927 
= 3.9269908 
= 4.7123890 
= 5.4977871 
6.2831853 



X 9 = 7.0685835 



Ratio of diam. to circumference = reciprocal of ;: = 0.3183099. 



Reciprocal of 7r/4 =1.27324. 
Multiples of I/tt. 
I/tt = 0.31831 
2/7r = 0.63662 
S/tt = 0.95493 
4/7r= 1.27324 
5/7r= 1.59155 
6/7r= 1.90986 
7/7r= 2.22817 
S/tt = 2.54648 
9/7r = 2.86479 



10/ir = 

12/7r = 

ir/2 = 

7r/3 = 

7r/6 = 

7r/12 = 

7r/64 = 

■/360 = 

360/7r = 



3.18310 
3.81972 
1.570796 
1.047197 
0.523599 
0.261799 
0.049087 
0.0087266 
114.5915 
9.86960 



1/^^=0.101321 

Vx =1.772453 

VIT^ =0.564189 

V^ =0.886226 

LogTT =0.49714987 

Log TT 74^=1.895090 

Log vV =0.248575 

Log V^/4= 1.947545 



Diam. in ins. = 13.5405 >/area in sq. ft. 

Area in sq. ft. = (diam in inches) 2 x .0054542. 

D = diameter, R = radius, C = circumference, 



58 THE CIRCLE. . 

G=nD\ ^2r.R\ = ^ ; = 2\^7A\ = 3.545VJ; 

A = D2X.7854;= ^ ; = 42^2 X. 7854; = ;ri22; =4^:2)2; =11- ; = .07958C«;= ^• 
2 4 4?: 4 

/)=-;= 0.31831C; = 2 4/ - ; = 1.12838 v^; 
i^ = ^ ; = 0.159155C; = i/^ ; = 0.564189 v^2. 

Areas of circles are to each other as the squares of their diameters. 
To find the length of an arc of a circle : 

Rule 1. As 360 is to the number of degrees in the arc, so is the circum- 
ference of the circle to the length of the arc. 

Rule 2. Multiply the diameter of the circle by the number of degrees 
in the arc, and tliis product by 0.0087266. 

Relations of Arc, Chord, Chord of Half the Arc, etc. 

Let R = radius, D = diameter, L = length of arc, 
C = chord of the arc, c = chord of half the arc, 
V = rise, or height of the arc, 

8c — (7 2c X 10 V 

Length of the arc = L= — ^ — (very nearly), = gnD^^^27F "^^^' ^^^^^y» 

VC2 4- 472 X 1072 , ^ , 

= 1.502+33 72 + 2c, nearly. 



Chord of the arc C, = 2 ^c^ - 72 ; = Vi)2 _ (Z) _ 27)2; = 8c - 3L 

= 2 Vjg2 - (7 g -. F)2; == 2 V(D - 7 ) X 7. 
Chord of half the arc, c = 1/2 VC2+ 472; = Vdx 7; = (3L + C) -i- 8. 

C2 1/4 C2 + 72 

Diameter of the circle, -D = rr^ ; = . -^-^ p ; 

Rise of the arc, 7 = ^ ; = 1/2 (D - Vd2 _ (72), 



(or if 7 is greater than radius 1/2 (^ + ^D^ - C2); 

= Vc2 - 1/4 C^ 

Half the chord of the arc is a mean proportional b etween the rise and 
the diameter minus the rise: V2C = ^V X{ D— 7). 

Length of the Chord subtending an angle at the centre = twice the 
sine of half the angle. (See Table of Sines.) 

Ordinates to Circular Arcs. — C = chord, 7 = height of the arc, or 
middle ordinate, x = abscissa, or distance measured on the chord from its 
central point, y = or dinate, or d istance fr om the arc to the chord at the 
point X, V = R - Vi?2 _ 1/4 c'2; y = Vr2 _ x^ - (R - 7). 

Length of a Circular Arc. — Huyghens's Approximation. 

Length of the arc, L = (8c — C) -4- 3. Professor Williamson shows 
that when the arc subtends an angle of 30°, the radius being 100,000 feet 
(nearly 19 miles), the error by this formula is about two inches, or 1/600000 
part of the radius. When the length of the arc is equal to the radius, i.e., 
when it subtends an angle of 57°. 3, the error is less than 1/7680 part of the 
radius. Therefore, if the radius is 100,000 feet, the error is less than 
100000/7680 = 13 feet. The error increases rapidly with the increase of 
the angle subtended. For an arc of 1 20° the error is 1 part in 400; for an 
arc of 180° the error is 1.18%. 



MENSURATION. 



59 



In the measurement of an arc which is described with a short radius the 
error isso small that it may be neglected. Describing an arc with a radius 
of 12 inches subtending an angle of 30"^, the error is 1/50000 of an inch. 

To measure an arc when it subtends a large angle, bisect it and measure 
each half as before — in this case making 5 = length of the chord of half the 
arc, and 6 = length of the chord of one fourth the arc; then L = (16ft — 2B) -^ 3. 



Formulas for a Circular Curve. 

J. C. Locke, Eng. News, March 16, 1908. 




c = \^2Ra, = v'a2~+~62, 



= V^2i2 (R- ^{R +h) {R - b) 
= 2\^m {2R - m), = 2R sin 1/2/, 
= 2r cos 1/2/. 
e = R exsec 1/2 -f, = R tan 1/2/ tan 1/4/, 
= r tan 1/4/. 



■^'^(2l?^,=v/(c + |^)(c-^), 



= R sin I, = a cot 1/2'^. 

q2 + 52 _ c2 ^ C?2 

2a ' ~ 2a ' ~ 2m ' 



R = 



4m 2 



8m 



d= V2^ 

rf2 



V{2R + c) {2R - c)), = 2R sin 1/4/. 



i? T ^{R + 1){^~ I)' = ^ vers 1/2/, 



2i2 

R sin 1/2/ tan 1/4/, = V2C tan 1/4/. 
r2 



2R' 



R -V{R -i- b) (R - b), = 2R (sin l/2/)2, = R vers /, 



= J? sin / tan 1/2/, = ft tan 1/2/, =- ^ sin /. 



T = 72 tan 1/2/. 

L = IR X 0.01745329, = 

Area of Segment = 



/ =^X 57.295780° 
It 



R^jX 57.295780^ 



8d ~ c 



3 














LR 
2 


R^ 


sin 
2 


/ 


= 


L/2 
2 


i^ft 
2 



Relation of the Circle to its Equal, Inscribed, and Circum- 
scribed Squares. 



Diameter of circle X 

Circumference of circle X 

Circumference of circle X 1.1284 

Diameter of circle X 0.7071 ) 

Circumference of circle X 0.22508 [ 
Area of circle X 0.90031 ^diameter) 

Area of circle X 1.2732 

Area of circle X 0.63662 

Side of square X 1.4142 

X 4.4428 

X 1.1284 

** "X 3 5449 

Perimeter of square X o'.88623 

Square inche^^; X 1.2732 



28209 i "" ^^^^ ^^ equal square. 



perimeter of equal square. 

= side of inscribed square. 

= area of circumscribed square. 

= area of inscribed square. 

= diam. of circumscribed circle. 

= circum. 

= diam. of equal circle. 

= circum. " " 

41 14 4C 

= circular inches. 



60 MENSURATION. 

Sectors and Segments. — To find the area of a sector of a circle. 

Rule 1. MultipTj^ the arc of the sector by half its radius. 

Rule 2. As 360 is to the number of degrees in the arc, so is the area of 
the circle to the area of the sector. 

Rule 3. Multiply the number of degrees in the arc by the square of the 
radius and by 0.008727. 

To find the area of a segment of a circle: Find the area of the sector 
which has the same arc, and also the area of the triangle formed by the 
chord of the segment and the radii of the sector. 

Then take the sura of these areas, if the segment is greater than a semi- 
circle, but take their difference if it is less. (See Table of Segments.) 

Another Method: Area of segment = 1/2^^ (arc — sin A), in which A is 
the central angle, R the radius, and arc the length of arc to radius 1 . 

To find the area of a segment of a circle when its chord and height only 
are given. First find radius, as follows; 

J. 1 Psquare of half the chord , , . , ^ 1 
radius = 2 L ^^^^^ + height J . 

2. Find the angle subtended by the arc, as follows: half chord -4- 
radius = sine of half the angle. Take the corresponding angle from a 
table of sines, and double it to get the angle of the arc. 

3. Find area of the sector of which the segment is a part: 

area of sector = area of circle X degrees of arc -^ 360. 

4. Subtract area of triangle under the segment: 

Area of triangle = half chord X (radius — height of segment). 

The remainder is the area of the segment. 

When the chord, arc, and diameter are given, to find the area. From 
the length of the arc subtract the length of the chord. Multiply the 
remainder by the radius or one-half diameter; to the product add the 
chord multiplied by the height, and divide the sum by 2. 

Given diameter, d, and height of segment, h. 

When h is from to 1/4^, area = h^ l.lQtQdh ~ h^; 

♦• " " " i/id to 1/2^?, area = 71^0.017^2+ xj^h - h^ 

(approx.). Greatest error 0.23%, when h = Vid. 

To find the chord: From the diameter subtract the height; multiply 
the remainder by four times the height and extract the square root. 

When the chords of the arc and of half the arc and the rise are given: 
To the chord of the arc add four thirds of the chord of half the arc; mul- 
tiply the sum by the rise and the product by 0.40426 (approximate). 

Circular Ring. — To find the area of a ring included between the cir- 
cumferences of two concentric circles: Take the difference between the areas 
of the two circles; or, subtract the square of the less radius from the square 
of the greater, and multiply their difference by 3.14159. 

The area of the greater circle is equal to nR^; 
and the area of the smaller, 7:r^. 

Their difference, or the area of the ring, is 7:(R^ — r^). 
The Ellipse. — Area of an ellipse = product of its semi-axes X3. 14159 

= product of its axes X0. 785398. 

, /7)2_|_ ^2 

The Ellipse. — Circumference (approximate) = 3.1416 y — •, D 

and d being the two axes. 

Trautwine gives the following as more accurate: When the longer axis 
D is not more than five times the length of the shorter axis, d. 



{^ 



Circumference = 3.1416 J ^^ t ^ - ^^ g S^^^ 



MENSURATION. 61 

IThen D is more than 5cf, the divisor 8.8 is to be replaced by the followings 

ForD/d = 6 7 8 9 10 12 14 16 18 20 30 40 50 
Divisor = 9 9.2 9.3 9.35 9.4 9.5 9.6 9.68 9.75 9.8 9.92 9.98 10 

/ A"^ A* 4* 25A8 \ 

An accurate formula is C= rr(a + 6) 1 4- ^ + ~ + 7^ + r^ +...). 

\ 4 64 2o6 16384 / 

in which A = ~ , . — Ingenieurs Taschenbuch, 1896. (a and 6, semi-axes.) 

Carl G. Barth (Machinery, Sept., 1900) gives as a very close approxi- 
mation to this formula 

, . ^, 64 - 3A < 
^-^(^+^) 64-16A^ - 

Area of a segment of an ellipse the base of which is parallel to one of 
the axes of the elUpse. Divide the height of the segment by the axis of 
which it is part, and find the area of a circular segment, in a table of circu- 
lar segments, of which the height is equal to the quotient; multiply the 
area thus found by the product of the two axes of the ellipse. 

Cycloid. — A curve generated by the rolling of a circle on a plane. 

Length of a cycloidal curve = 4 X diameter of the generating circle. 
Length of the base= circumference of the generating circle. 
Area of a cycloid = 3 X area of generating circle. 

Helix (Screw). — A line generated by the progressive rotation of a 
point around an axis and equidistant from its center. 

Length of a helix. — To the square of the circumference described by the 
generating point add the square of the distance advanced in one revolution, 
and take the square root of their sum multipUed by the number of revolu- 
tions of the generating point. Or, 

n\/c2 4- /i2 = length, n being number of revolutions. 

Spirals. — Lines generated by the progressive rotation of a point 
around a fixed axis, with a constantly increasing distance from the axis. 

A plane spiral is made when the point rotates in one plane. 

A conical spiral is made when the point rotates around an axis at a 
progressing distance from its center, and advancing in the direction of the 
axis, as around a cone. 

Length of a plane spiral line. — When the distance between the coils is 
uniform. 

Rule. — Add together the greater and less diameters; divide their sum 
by 2; multiply the quotient by 3.1416, and again by the number of revo- 
lutions. Or, take the mean of the length of the greater and less circum- 
ferences and multiply it by the number of revolutions. Or, 

length = nniR +r), R and r being the outer and inner radii. To find n, 

j^ If ^ 

let t = thickness of coil or band, s = space between the coils, n = —rr. — • 

Length of a conical spiral line. — Add together the greater and less 
diameters; divide their sum by 2 and multiply the quotient by 3.1416. 
To the square of the product of this circumference and the number of 
revolutions of the spiral add the square of the height of its axis and take 
the square root of the sum. 

Or, length = \ {^^-^Y + ^'• 

SOLID BODIES. 

Surfaces and Volumes of Similar Solids. — The surfaces of twd 
similar sohds are to each other as the squares of their Unear dimensions: 
the volumes are as the cubes of their linear dimensions. If L = the side 



62 MENSURATION. 

of a cube or other solid, and I the side of a similar body of different size, 
S, s, the surfaces and V, v, the volumes respectively, S : s i: L^ : l^; 

The Prism. — To find the surface of a right prism: Multiply the perim- 
eter of the base by the altitude for the convex surface. To this add the 
areas of the two ends when the entire surface is required. 

Volume of a prism = area of its base X its altitude. 

The pyramid. — Convex surface of a regular pyramid = perimeter of 
its base X half the slant height. To this add area of the base if the whole 
surface is required. 

Volume of a pyram^id = area of base X one third of the altitude. 

To find the surface of a frustum of a regular pyramid: Multiply half the 
slant height by the sum of the perim.eters of the two bases for the convex 
surface. To thi^add the areas of the two bases when the entire surface is 
required . 

To find the volume of a frustum of a pyramid: Add together the areas of 
the two bases and a mean proportional between them, and multiply the 
sum by one third of the altitude. (Mean proportional between two 
numbers = square root of their product.) 

Wedge. — A wedge is a solid bounded by five planes, viz. : a rectangular 
base, two trapezoids, or two rectangles, meeting in an edge, and two 
triangular ends. The altitude is the perpendicular drawn from any point 
in the edge to the plane of the base. 

To find the volume of a wedge: Add the length of the edge to t\vice the 
length of the base, and multiply the sum by one sixth of the product of 
the height of the wedge and the breadth of the base. 

Rectangular prismoid. — A rectangular prismoid is a solid bounded 
by six planes, of which the two bases are rectangles, having their corre- 
sponding sides parallel, and the four upright sides of the solid are trape- 
zoids. 

To find the volume of a rectangular prismoid: Add together the areas of 
the two bases and four times the area of a parallel section equally distant 
from the bases, and multiply the sum by one sixth of the altitude. 

Cylinder. — Convex surface of a cylinder = perimeter of base X 
altitude. To this add the areas, of the two ends when the entire surface is 
required. 

Volume of a cylinder = area of base X altitude. 

Cone. — Convex surface of a cone = circumference of base X half the 
slant height. To this add the area of the base when the entire surface is 
required. 

Volume of a cone = area of base X one third of the altitude. 

To find the surface of a frustum of a cone: Multiply half the side by the 
sum of the circumferences of the two bases for the convex surface; to this 
add the areas of the two bases when the entire surface is required. 

To find the volume of a frustum of a cone: Add together the areas of 
the two bases and a mean proportional between them, and multiply 
the sum by one third of the altitude. Or, Vol. = 0.2618a(&2-f c2 4- hc)\ 
a = altitude; h and c, diams. of the two bases. 

Sphere. — To find the surface of a sphere: Multiply the diameter by the 
circumference of a great circle; or, multiply the square of the diameter by 
3.14159. 

Surface of sphere = 4 x area of its great circle. 
** ** " = convex surface of its circumscribing cylinder. 

Surfaces of spheres are to each other as the squares of their diameters. 
To find the volume of a sphere: Multiply the surface by one third of the 
radius; or, multiply the cube of the diameter by 7r/6; that is, by 0.5236, 
Value of ;r/6 to 10 decimal places = 0.5235987756. 
The volume of a sphere = 2/3 the volume of its circumscribing cylinder. 
Volumes of spheres are to each other as the cubes of their diameters. 



MENSURATION. . 63 



Spherical triangle. — To find the area of a spherical triangle: Compute 
the surface of the quadrantai triangle, or one eighth of the surface of 
the sphere. From the sum of the three angles subtract two right angles; 
divide the remainder by 90, and multiply the quotient by the area of the 
quadrantai triangle. 

Spherical polygon. — To find the area of a spherical polygon: Compute 
the surface of the quadrantai triangle. From the sum of all the angles 
subtract the product of two right angles by the number of sides less two; 
divide the remainder by 90 and multiply the quotient by the area of the 
quadrantai triangle. 

The prismoid. — The prisrooid is a solid having parallel end areas, and 
may be composed of any combination of prisms, cylinders, \vedges, pyra- 
mids, or cones or frustums of the same, whose bases and apices lie in the 
end areas. 

Inasmuch as cylinders and cones are but special forms of prisms and 
pyramids, and warped surface sohds may be divided into elementary 
forms of them, and since frustums may also be subdivided into the elemen- 
tary forms, it is sufficient to say that all prismoids may be decomposed 
into prisms, wedges, and pyramids. If a formula can be found which is 
equally apphcable to all of these forms, then it will apply to any combi- 
nation of them. Such a formula is called 



The Prismoidal Formula. 

Let A = area of the base of a prism, w^edge, or pyramid* 

Au Ai, Afn, = the two end and the middle areas of a prismoid, or of any of 
its elementary solids; h = altitude of the prismoid or elementary solid; 
V = its volume; 

For a prism, Ai, Aj^ and A2 are equal, = A\ 7=77X6^. = hA, 

For a wedge with parallel ends, ^2 = 0, A^= -'Av,V= -(Ai+2Ai)= — • 

For a cone or pyramid, A2 = 0, A^ = - Ai\ 7 = -^ {Ai + Ai) ^ -r- - 

The prismoidal formula is a rigid formula for all prismoids. The only 
approximation involved in its use is in the assumption that the given solid 
may be generated by a right line moving over the boundaries of the end 
areas. 

The area of the middle section is never the mean of the two end areas if 
the prismoid contains any pyramids or cones among its elementary forms. 
When the three sections are similar in form the dimensions of the middle 
area are always the means of the corresponding end dimensions. This 
fact often enables the dimensions, and hence the area of the middle section, 
to be computed from the end areas. 

Polyedrons. — A polyedron is a soUd bounded by plane polygons. A 
regular polvedron is one w^hose sides are all equal regular polygons. 

To find the surface of a regular polyedron. — Multiply the area of one of 
the faces by the number of faces; or, multiply the square of one of the 
edges by the surface of a similar solid whose edge is unity. 



A Table op the? Regular Polyedrons whose Edges are Unity. 

Names. No. of Faces. Surface. Volume. 

TetFaedron 4 1.7320508 0.1178513 

Hexaedron 6 6.0000000 1.0000000 

Octaedron 8 3.4641016 0.4714045 

Dodecaedron 12 20.6457288 7.6631189 

Icosaedroa 20 8.6602540 2.1816950 



64 MENSURATION. 

To find the volume of a regular polyedron. -— Multiply the surface 
by one third of the perpendicular let fall from the centre on one of the 
faces; or, multiply the cube of one of the edges by the soUdity of a similar 
polyedron whose edge is unity. 

Solid of revolution. — The volume of any sohd of revolution is equal 
to the product of the area of its generating surface by the length of the 
path of the centre of gravity of that surface. 

The convex surface of any soUd of revolution is equal to the product of 
the perimeter of its generating surface by the length of path of its centre 
of gravity. 

,, S^P^^T}^^^ ,^.^^^* ~- Let d = outer diameter; d' = inner diameter; 
V2(a - d) = thickness = t; i/i ttI^ = sectional area; 1/2(0? -hd') = mean 
diameter = M; nt = circumference of section; ;r ikf = mean circum- 
^^^o^Ja-t?^ ?^P ^iilt^^^ - rctXnM', =1/4 ;r2 (d^ - d'^); = 9.86965 t M; 
= 2.46741 ((^2 __ ci'^); volume = V^Ttt^ M r.\ = 2.467241 t^ M. 

Spherical zone. — Surface of a spherical zone or segment of a sphere 
— Its altitude X the circumference of a great circle of the sphere. A 



by the height and by 1.5708. 

Spherical segment. — Volume of a spherical segment with one base — 
Multiply half the height of the segment by the area of the base, and the 
cube of the height by 0.5236 and add the two products. Or, from three 
times the diameter of the sphere subtract twice the height of the segment- ' 
multiply the difference by the square of the height and by 0.5236 Or to 
three times the square of the radius of the base of the segment add the 
square of its height, and multiply the sum by the height and by 5236 

Spheroid or ellipsoid. — When the revolution of the generating sur- 
lace of the spheroid is about the transverse diameter the spheroid is 
prolate, and when about the conjugate it is oblate. 

Convex surface of a segment of a spheroid. — Square the diameters of the 
spheroid, and take the square root of half their sum; then, as the diameter 
from which the segment is cut is to this root so is the height of the segment 
to the proportionate height of the segment to the mean diameter. ' Multinlv 
the product of the other diameter and 3.1416 by the proportionate heieht 

Convex surface of a frustum or zone of a spheroid. — Proceed as by 
previous rule for the surface of a segment, and obtain the proportionate 
height of the frustum. Multiply the product of the diameter parallel to 
the base of the frustum and 3.1416 by the proportionate height of the 
frustum. 

Volume of a spheroid is equal to the product of the square of the revolv- 
ing axis by the fixed axis and by 0.5236. The volume of a spheroid is two 
thirds of that of the circumscribing cylinder. 

Volume of a segment of a spheroid. — 1. When the base is parallel to the 
revolving axis, multiply the difference between three times the fixed axis 
5 r^oP^^J",^ height of the segment, by the square of the height and bv 
0.5236. Multiply the product by the square of the revolving axis, and 
divide by the square of the fixed axis. 

2. When the base is perpendicular to the revolving axis, multiply the 
difference between three times the revolving axis and twice the height of 
the segment by the square of the height and by 0.5236. Multiply the 
product by the length of the fixed axis, and divide by the length of the 
revolving axis. 

Volume of the middle frustum of a spheroid. — 1. When the ends are 
circular, or parallel to the revolving axis; To twice the square of the middle 
diameter add the square of the diameter of one end; multiply the sum bv 
the length of the frustum and by 0.2618. 

2. When the ends are elliptical, or perpendicular to the revolving axis: 

■J'J^^^ ' product of the transverse and conjugate diameters of the 
middle section add the product of the transverse and conjugate diameters 
or one end; multiply the sum by the length of the frustum and by 0.2618. 

Spindles. — Figures generated by the revolution of a plane area, 
hounded by a curve other than a circle, when thi curve is revolved about 
a chord perpendicular to its axis, or about its double ordinate. They are 
designated by the name of the arc or curve from which they are generated, 
as Qrcular. ElUptic. Parabolic, etc., etc. ^ o «. 



MENSURATION. 65 



Convex surface of a circular spindle, zone, or segment of it. — Rule: Mul- 
tiply the length by the radius of the revolving arc; multiply this arc by the 
central distance, or distance between the centre of the spindle and centre 
of the revolving arc; subtract this product from the former, double the 
remainder, and multiply it by 3.1416. 

Volume of a circular spindle. — IMultiply the central distance by half 
the area of the revolving segment; subtract the product from one tliird of 
the cube of half the length, and multiply the remainder by 12.5664. 

Volume of frustum or zone of a circular spindle. — From the square of 
half the length of the whole spindle take one third of the square of half the 
length of the frustum, and multiply the remainder by the said half length 
of the frustum; multiply the central distance by the revolving area which 
generates the frustum; subtract this product from the former, and multi- 
ply the ren^ainder by 6.2832. 

Volume of a segment of a circular spindle, — Subtract the length of the 
segment from the half length of the spindle; double the remainder and 
ascertain the volume of a middle frustum of this length; subtract the 
result from the volume of the whole spindle and halve the remainder. 

Volume of a cycloidal spindle = five eighths of the volume of the circum- 
scribing cylinder. — Multiply the product of the square of twice the dia- 
meter of the generating circle and ck927 by its circumference, and divide 
tills product by 8. 

Parabolic conoid. — Volume of a parabolic conoid (generated by the 
revolution of a parabola on its axis). — Multiply the area of the base by 
half the height. 

Or multiply the square of the diameter of the base by the height and by 
0.3927. 

Volume of a frustum of a paraoolic conoid. — Multiply half the sum of 
xne areas of the two ends by the height. 

Volume of a parabolic spindle (generated by the revolution of a parabola 
on its base). — Multiply the square of the middle diameter by the length 
and by 0.4189. The volume of a parabolic spindle is to that of a cylinder 
of the same height and diameter as 8 to 15. 

Volume of the middle frustum of a parabolic spindle. — Add together 
8 times the square of the maximum diameter, 3 times the square of the 
end diameter, and 4 times the product of the diameters. Multiply the 
sum by the length of the frustum and by 0.05236. This rule is applicable 
for calculating the content of casks of parabolic form. 

Casks. — To find the volume of a cask of any form. — Add together 39 
times the square of the bung diameter, 25 times the square of the head 
diameter, and 26 times the product of the diameters. Multiply the sum 
by the length, and divide by 31,773 for the content in Imperial gallons, or 
by 26,470 for U. S. gallons. 

This rule was framed by Dr. Hutton, on the supposition that the middle 
third of the length of the cask was a frustum of a parabolic spindle, and 
each outer third was a frustum of a cone. 

To find the idlage of a cask, the quantity of liquor in it when it is not full. 
1. For a lying cask: Divide the number of wet or dry inches by the bung 
diameter in inches. If the quotient is less than 0.5, deduct from it one 
fourth part of what it wants of 0.5. If it exceeds 0.5, add to it one fourth 
part of the excess above 0.5. Multiply the remainder or the sum by the 
whole content of the cask. The product is the quantity of liquor in the 
cask, in gallons, when the di\ddend is wet inches; or the empty space, if 
dry inches. 

2. For a standing cask: Divide the number of wet or dry inches by the 
leogth of the cask. If the quotient exceeds 0.5, add to it one tenth of its 
excess above 0.5; if less than 0.5, subtract from it one tenth of what it 
wants of 0.5. Multiply the sum or the remainder by the whole content of 
the cask. The product is the quantity of liquor in the cask, when the 
dividend is wet inches; or the empty space, if dry inches. 

Volume of cask (approximate) U. S. gallons = square of mean diam. 
X length in inches X 0.0034. Mean diameter = half the sum of the 
bung and head diameters. 

Volume of an irregular solid. — Suppose it divided into parts, resem- 
bling prisms or other bodies measurable by preceding rules. Find the con- 
tent of each part; the sura of the contents is the cubic contents of the solid. 



66 PLANE TRIGONOMETRY. 



The content of a small part is found nearly by multiplying half the sum 
of the areas of each end bv the perpendicular distance between them. 

The contents of small irregular solids may sometimes be found by im- 
mersing them under water in a prismatic or cylindrical vessel, and observ- 
ing the amount by which the level of the water descends when the solid is 
withdrawn The sectional area of the vessei being multiphed by the 
descent of the level gives the cubic contents „.^,-„u. ^f 

Or weigh the soUd in air and in water; the difference is the weight of 
water it displaces. Divide the weight in pounds by 62.4 to obtain volume 
in cubic feet or multiply it bv 27.7 to obtain the volume in cubic inches. 

When the solid is very large and a great degree, of accuracy is not 
requisite, measure its length, breadth, and depth in several different 
places, and take the mean of the measurement for each dimension, and 
multiply the three means together. . .^ . -u *+ +^ Ai.riA^ h 

When the surface of the solid is very extensive it is better to divide it 
into triangles, to find the area of each triangle, and to multiply it by the 
mean depth of the triangle for the contents of each triangular portion; the 
contents of the triangular sections are to be added together. 

The mean depth of a triangular section is obtained by measuring the 
depth at each angle, adding together the tliree measurements, and taking 
one third of the sum. 



PLANE TRIGONOMETRY. 

Trigonometrical Functions. 

Every triangle has six parts — three angles and three sides When any 
three of these parts are given, provided one of them, is a side, the other 
m.rts mav be determined. By the solution of a triangle is meant the 
Setermination of the unknown parts of a triangle when certain parts are 

^^^he complement of^an angle or arc is what remains after subtracting the 

^""iJf gL^emlTwe^represent any arc by ^ its complement is 90° - A. 
Hence the complement of an arc that exceeds 90° is negative 

The supplement of an angle or arc is what remains after subtracting the 
angle or arc from 180°. If A is an arc its supplement is 180° - A. The 
suDDlement of an arc that exceeds 180° is negative. . 

^Thl^mof the three angles of a triangle is equal ^o 180°. . Either angle is 
the supplement of the other two. In a right-angled triangle, the right 
angle being equal to 90°, each of the acute angles is the complement ot 

^"^^naUHght-angled triangles having the same acute angle, the fdeshaveto 
each other the same ratio. These ratios have received special names, as 

^"^ k'a 'is one of the acute angles, a the opposite side, h the adjacent side, 
^''T^^^t^Ionu'Se A is the quotient of the opposite side divided by the 
hypothenuse. Sin A =^ -■ 

The tangent of the angle A is the quotient of the opposite side divided by 
the adjacent side. Tan A = y 

The secant of the angle A is the quotient of the hypothenuse divided by the 
adjacent side. Sec A = ~r' 

The cosine (cos), cotangent (cot), and cosecant (cosec) of an angle 
are respectively the sine, tangent, and secant of. the complement of that 
angle. The terms sine, cosine, etc., are called tri^;onometrical functions 

In a circle whose radius is unity, the sine of an arc or of the angle a the 
centre measured by that arc, is the perpendicular let fall from one extremity of 
the arc upon the diameter passing throiigh the other extremity. ,^,^,^ .. 

The tangent of an arc is the line which touches the circle at one extremit\f 



PLANE TRIGONOMETRY. 



67 



of the arc, and is limited by the diameter (produced) passing through the other 
extremity. 

The secant of an arc is that part of the produced diameter which is inter- 
cepted between the centre and the tangent. 

The versed sine of an arc is that part of the diameter intercepted between 
the extremity of the arc and the foot of the sine. 

In a circle whose radius is not unity, the trigonometric functions of an 
arc will be equal to the lines here defined, divided by the radius of the 
circle. 

li ICA (Fig. 71) is an angle in the first quadrant, and CF = radius, 

J rT.u^..:^^^,.u ..„ ^<^ r. CG KF 



DCotan. L/ 




The sine of t he ar^gle 
FA 



Rad 



Cos ■■ 



Tan - 



iiad 



Secant = -^^-r- 
Rad 



Cosec = 



CL 
Rad 



Versin = 



Rad' 

Cot = 

GA 
Rad ' 



Rad 
PL 
Rad 



If radius is 1, then Rad in the denominator is 
omitted, and sine = F G, etc. 

The sine of an arc = half the chord of twice the 
arc. 

The sine of the supplement of the arc is the 
same as that of the arc itself. Sine of arc B D F 
= F G = sin arc F A. 
The tangent of the supplement is equal to the tangent of the arc, but 
with a contrary sign. Tan BDF = — BM. 

The secant of the supplement is equal to the secant of the arc, but with 
a contrary sign. Sec BDF = — CM. 

Signs of the functions in the four quadrants. — If we divide a 
circle into four quadrants by a vertical arid a horizontal diameter, the 
upper right-hand quadrant is called the first, the upper left the second, 
the lower left the third, and the lower right the fourth. The signs of the 
functions in the four quadrants are as follows: 



Second quad 
+ 



Third quad. Fourth quad. 



First quad. 
Sine and cosecant, + 

Cosine and secant, + 

Tangent and cotangent, 4- — + — 

The values of the functions are as follows for the angles specified; 



Angle 

Sine 

Cosine 

Tangent . . . 
Cotangent . 

Secant 

Cosecant . . 
Versed sine 






o 





























30 


45 


60 


90 


120 


135 


150 


180 


270 





1 


1 


V3 


\ 


V3 


1 


1 





-1 


2 


V2 


2 




2 


V2 





1 


V3 


1 


1 





1 


1 


Vf 


-1 







2 


V2 


2 




2 


V2 


2 





1 

V3 


1 


1 

V3 


00 


-vs 


-1 


1 
V3 





00 


00 


V3 


1 





V3 


-1 


-V3 


00 





1 


2 


Vi 


2. 
2 


00 


-2 
2 


-V2 


2 
V3~ 


-1 


00 


00 


2 


v^ 


V3 


1 


V? 


V2 


2 


00 


-1 





2-V3 


^/2-l 


I, 

2 


1 


3 

2 


vT+i 


24-V3 


2 


1 


2 


V2 


V2 


2 



360 


1 



1 

«o 




68 PLANE TRIGONOMETRY. 



TRIGONOMETRICAL FORIVHILAE. 

The follow*ing relations are deduced from the properties of similar 
triangles (Radius = 1): 



cos A : sin A : : 1 : tan A, whence tan A = 
sin A : cos A : : I : cot A, " cotan A = 
cos ^ : 1 : : 1 : sec A, " sec A = 
sin All 111: cosec A, " cosec A = 

tan ^ : 1 : : 1 : cot J. ** tan A = 



sin A , 
cos A * 
cos A ^ 
sin A * 

1 
cos A' 

1 
sin A 

1 
cot A 



The sum of the square of the sine of an arc and the square of its cosine 
equals unity. Sin2 A 4- cos2 A = 1. 

Also, 1 + tan2 A = sec2 A; 1 + cot2 A = cosec2 A. 

Functions of the sum and difference of two angles: 

Let the two angles be denoted by A and B, their sum A 4- 5 = C, and 
their difference A — B by D. 

sin (A + 5) = sin A cos B + cos A sin 5; (1) 

cos (A 4- 5) = cos A cos 5 — sin A sin 5; (2) 

sin (A — B) = sin A cos B — cos A sin 5; (3) 

cos (a — B) = cos A cos ^ + sin A sin -S (4) 

From these four formulae by addition and subtraction we obtain 

sin (A + 5) + sin (A - ^) = 2 sin A cos 5; . . . . (5) 

sin {A -h B) - sin (A - 5) = 2 cos A sinB; , . . . (6) 

cos (A + jB) + cos (A - 5) = 2 cos A cos 5; .... (7) 

cos (A - 5) - cos (A 4- 5) = 2 sin A sin 5 (8) 

If we put A 4- 5 = C, and A - B = D, then A = 1/2 (C 4- D) and 5 = 
V2(C' — D), and we have 

(9) 
(10) 
(11) 
(12) 

Equation (9) may be enunciated thus: The sum of the sines of any two 
angles is equal to twice the sine of half the sum of the angles multiplied by 
the cosine of half their difference. These formulae enable us to transform 
a sum or difference into a product. 

The sum of the sines of two angles is to their difference as the tangent of 
half the sum of those angles is to the tangent of half their difference. 

sin A 4- sin ^ ^ 2 sin 1/2 (A 4- B) cos V2 (A -B) ^ tan 1/2 (A + B) 
sin A - sin 5 2 cos 1/2 (A 4- B) sin 1/2 (A - B) tan 1/2 (A - B) ' ^ ^ 

The sum of the cosines of two angles is to their difference as the cotan- 
gent of half the sum of those angles is to the tangent of half their difference. 

cos A 4- cos g ^ 2 cos 1/2 (A 4- B) cos 1/2 (A - B) ^ cot V2 (A 4- B) 
cos 5 - cos A 2 sin 1/2 (A 4- B) sin 1/2 (A -g) tan 1/2 (A - B)' ^ ^ 

The sine of the sum of two angles is to the sine of their difference as the 
sum of the tangents of those angles is to the difference of the tangents. 

sin (A 4- B) tan A 4- tan B ,, ,, 

-^ * (lo) 



sin C + sin D = 2 sin 1/2 (C 4- D) cos 1/2 (C - D) 
sin C - sin Z) = 2 cos 1/2 (C 4- D) sin 1/2 (C - D) 
cos C 4- cos D = 2 cos 1/2 (C 4- D) cos 1/2 (C - D), 
cosD - cosC = 2 sin 1/2 (C 4- D) sin 1/2 (C - Z)). 



sin (A — JB) tan A — tan B 



PLANE TRIGONOMETRY. 



69 



sin (A + B) 
cos A cos B 
sin (A - B) 
cos A cos B 
cos (A + B) 
cos vl cos B 
cos (^ - B) 
cos ^4 cos i^ 

Functions of twice an angle: 
sin 2.4. = 2 sin yl cos A ; 

^ , 2 tan .4 

tan 2.4 = :; ^ — ^-r ; 

1 — tan2 A 

Functions of half an angle: 



— tan A + tan B; 
= tan A — tan i?; 
= 1 —tan A tan B; 
= 14- tan A tan B; 



sin 1/2^= ± 



v'^ 



— cos A 



tani/2A=± i/i-^ . 

* 1 + cos A 



cos J. 



tan (A + B)^ 
tan (A - i?) = 
cot (A + B) --= 
cot (A - B) = 



tan A + tan B , 
1— tan A tan B ' 

tan A — tan B 

1 -f tan A tan 5 ' 
cot A cot ^ — 1 . 

cot 5 + cot A ' 
cot A cot JJ4- 1 ^ 

cot B — cot A 



cos 2 A =- cos2 A 

_. COt2A 

cot 2A = 



sin2 A; 
1 



2 cot A 



cos 1/2^ = ± 



cot 1/2^ 






COS A 



cos A 



COS A 

For tables of Trigonometric Functions, see Mathematical Tables. 



Solution of Plane Right-angled Triangles. 

Let A and B be the two acute ang:Ies and C the right angle, and a, 5, and 
c the sides opposite these angles, respectively, then we have 



1. sin A = cos B 



3. tan A = cot i? = r ; 




2. cos A = sin 5 = -; 4. cot A = tan B = -- 
c a 

1. In any plane right-angled triangle the sine of either of the acute 
angles is equal to the quotient of the opposite leg divided by the hypothe- 
nuse. 

2. The cosine of either of the acute angles is equal to the quotient of 
the adjacent leg divided by the hypothenuse. 

3. The tangent of either of the acute angles is equal to the quotient of 
the opposite leg divided by the adjacent leg. 

4. The cotangent of either of the acute angles is equal to the quotient 
of the adjacent leg divided by the opposite leg. 

5. The square of the hypothenuse equals the sum of the squares of the 
other two sides. 



Solution of Oblique-angled Triangles. 

The following propositions are proved in works on plane trigonometry. 
In any plane triangle — 

Theorem 1. The sines of the angles are proportional to the opposite 
sides. 

Theorem 2. The sum of any two sides is to their difference as the tan- 
gent of half the sum of the opposite angles is to the tangent of half their 
difference. 

Theorem 3. If from any angle of a triangle a perpendicular be drawn to 
the opposite side or base, the whole base will be to the sum of the other 
two sides as the difference of those two sides is to the difference of the 
segments of the base. 

Case I. Given two angles and a side, to find the third angle and the 
other two sides. 1. The third angle = 180° — sum of the two angles. 
2. The sides may be found by the following proportion; 



70 ANALYTICAL GEOMETRY. 

The sine of the angle opposite the given side is to the sine of the angle 
opposite the required side as the given side is to the required side. 

Case II. Given two sides and an angle opposite one of them, to find 
the third side and the remaining angles. 

The side of)posite the given angle is to the side opposite the required 
angle as the sine of the given angle is to the sine of the required angle. 

The third angle is found by subtracting the sum of the other two from 
180°, and the third side is found as in Case I. 

Case III. Given two sides and the included angle, to find the third 
side and the remaining angles. 

The sum of the required angles is found by subtracting the given angle 
from 180°. The difference of the required angles is then found by Theorem 
II. Half the difference added to half the sum gives the greater angle, and 
half the difference subtracted from half the sum gives the less angle. The 
third side is then found by Theorem I. 

Another method: 

Given the sides c, b, and the included angle A, to find the remaining side 
a and the remaining angles B and C. 

From either of the unknown angles, as B, draw a perpendicular Be to 
the opposite side. 

Then 

Ae = c cos A, Be = c sin A, eC — h — Ae Be -^ eC = tan C. 

Or, in other words, solve Be, Ae and BeC as right-angled triangles. 

Case IV. Given the three sides, to find the angles. 

Let fall a perpendicular upon the longest side from the opposite angle, 
dividing the given triangle into two right-angled triangles. The two seg- 
ments of the base may be found by Theorem III. There will then be 
given the hypothenuse and one side of a right-angled triangle to find the 
angles. 

For areas of triangles, see Mensuration. 



ANALYTICAL GEOMETRY. 

Analytical geometry is that branch of Mathematics wiiich has for its 
object the determination of the" forms and magnitudes of geometrical 
magnitudes by means of analysis. 

Ordinates and abscissas. -7 In analytical geometry two intersecting 
lines YY', XX' are used as coordinate axes, 
XX' being the axis of abscissas or axis of X, 
and YY' the axis of ordinates or axis of Y, 
A, the intersection, is called the origin of co- 
ordinates. The distance of any point P 
from the axis of Y measured parallel to the 
axis of X is called the abscissa of the point, 
as AD or CP, Fig. 72. Its distance from the 
axis of X, measured parallel to the axis of 
y, is called the ordinate, as ^C or PD. 
The abscissa and ordinate taken together 
are called the coordinates of the point P, 
The angle of intersection is usually taken as 
a right angle, in which case the axes of X 
and Y are called rectangular coordinates. 

The abscissa of a point is designated by the letter x and the ordinate 
ojy. 

The equations of a point are the equations which express the distances 
of the point from the axis. Thus z ^ a, y = b are the equations of the 
point P. 

Equations referred to rectangular coordinates. — The equation of 
a line expresses the relation which exists between the coordinates of every 
point of the line. 

Equation of a straight line, 7/ = ax ± 5, in which a is the tangent of the 
angle the line makes with the axis of X, and b the distance above A in 
which the fine cuts the axis of Y. 

Every equation of the first degree between two variables is the equation 




ANALYTICAL GEOMETRY. 71 

of a straight line, as Ay ■¥ Bx +C = 0, which can be reduced to the form 
y == ax ± h. 

Equation of the distance between two points: 

D = '^{x" - x')2 + {y~- y')\ 

in which x'y\ x"y" are the coordinates of the two pointSo 
Equation of a line passing through a given point: 

' y - y' = a{x - x'), 

in which x'y' are the coordinates of the given point, a, the tangent of the 
angle the line makes with che axis of x, being undetermined, since any 
number of hnes may be drawn through a given point. 
Equation of a line passing through two given points: 

y-y' - f^3|^(^ - ^'). 

Equation of a hne parallel to a given line and through a given point : 

y — y' = cl{x — x'). 
Equation of an angle V included between two given lines: 

a' — a 



tang V ■■ 



1 + a'a 



in which a and a' are the tangents of the angles the lines make with the 
axis of abscissas. 

If the lines are at right angles to each other tang y = oo , and 

1 -{- a'a = 0. 

Equations of an intersection of two lines, whose equations are 

y = ax -1- &, and y = a'x + h\ 

h — h' , ah' — a'h 

X == 7, and y = r— 

a — a' a — a 

Equation of a perpendicular from a given point to a given line: 
Equation of the length of the perpendicular P% 

p = y' - Q^' - ^ 

The circle. — Equation of a circle, the origin of coordinates being at 
the centre, and radius = H: 

0:2 + 2/2 = 7^2, 

If the origin is at the left extremity of the diameter, on the axis of X: 

2/2 = 2Rx - x^. 

If the origin is at any point, and the coordinates of the centre are x'y' 

ix - x')^ + (y - ?/)2 = R\ 

Equation of a tangent to a circle, the coordinates of the point of tan- 
gency being x"y" and the origin at the centre, 

yy" 4- XX" = R\ 

The ellipse. — Equation of an ellipse, referred to rectansrular coordi- 
nates with axis at the centre: 

A^y^ + B^x-2 = AW\ 

in which A is half the transverse axis and B half the conjugate axis. 



72 ANALYTICAL GEOMETRY. 

Equation of the ellipse wiien the origin is at the vertex of the transverse 
axis: 

7/2 = 4t(2Ax ~ a;2). 

The eccentricity of an ellipse is the distance from the centre to either 
focus, divided by the semi-transverse axis, or 



A 

The parameter of an ellipse is the double ordinate passing through the 
focus. It is a third proportional to the transverse axis and its conjugate, 
or 

2A : 2B II 2B : parameter, or parameter = —.— 

Any ordinate of a circle circumscribing an ellipse is to the corresponding 
ordinate of the ellipse as the semi -transverse axis to the semi-conjugate. 
Any ordinate of a circle inscribed in an ellipse is to the corresponding 
ordinate of the ellipse as the semi-conjugate axis to the semi-transverseo 

Equation of the tangent to an ellipse, origin of axes at the centre: 

A^yy" + B'^xx" = A^B"^, 

y"x" being the coordinates of the point of tangency. 

Equation of the normal, passing through the point of tangency, and 
perpendicular to the tangent: 

A-^y'' 

y - y = :b2p^^ - ^^- 

The normal bisects the angle of the two lines drawn from the point of 
tangency to the foci. 

The lines drawn from the foci make equal angles with the tangent. 

The parabola. — Equation of the parabola referred to rectangular 
coordinates, the origin being at the vertex of its axis, ?/2 = 2px, in which 
2p is the parameter or double ordinate through the focus. 

The parameter is a third proportional to any abscissa and its correspond- 
ing ordinate, or 

X : y M y : 2p. 

Equation of the tangent: 

yy" = 7?(x 4- x"). 

y"x" being coordinates of the point of tangency. 
Equation of the normal: 

The sub-normal, or projection of the normal on the axis, is constant, and 
equal to half the parameter. 

The tangent at any point makes equal angles with the axis and with the 
line drawn from the point of tangency to tlie focus. 

The hyperbola. — Equation of the hyperbola referred to rectangular 
coordinates, origin at the centre: 

^2^2 _ 52jp2 = ^ ^2/^2^ 

in wliich A is the semi-transverse axis and B the semi-conjugate axis. 
Equation when the origin is at the right vertex of the transverse axis: 

i?2 

7/2 = ii_^ (2Aa: + x2). 
A'' 

Conjugate and equilateral hyperbolas. — If on the conjugate axis, 



DIFFERENTIAL CALCULUSo 73 



as a transverse, and a focal distance equal to ^A^ + B"^, we construct 
the two branches of a hj'perbola, the two hyperbolas thus constructed are 
called conjugate hyperbolas. If the transverse and conjugate axes are 
equal, the hyperbolas are called equilateral, in which case y^ — x^= — A'^ 
when A is the transverse axis, and x^ — y- = — B^ when B is the trans- 
verse axis. 

The parameter of the transverse axis is a third proportional to the trans- 
verse axis and its conjugate. 

2 A : 2B :: 2B : parameter. 

The tangent to a hyperbola bisects the angle of the two lines drawn from 
the point of tangency to the foci. 

The asymptotes of a hyperbola are the diagonals of the rectangle 
described on the axes, indehnitely produced in both directions. 

The asymototes continually approach the hyperbola, and become 
tangent to it "at an infinite distance from the centre. 

Equilateral hyperbola, — In an equilateral hyperbola the asymptotes 
make equal angles with the transverse axis, and are at right angles to each 
other. With the asymptotes as axes, and P = ordinate, V = abscissa, 
PV = a constant. This equation is that of the expansion of a perfect 
gas, in which P = absolute pressure, V = volume. 

Curveof Expansion of Gases.— Py^ = a constant, or Pi Fi^ = P2y2'^, 
in which Vi and V2 are the volumes at the pressures Pi and P2, When 
these are given, the exponent n may be found from the formula 

^ log Pi - log P2 
log V2 - log Vi' 

Conic sections = — Every equation of the second degree between two 
variables will represent either a circle, an ellipse, a parabola or a hyperbola. 
These curves are those which are obtained by intersecting the surface of a 
cone by planes, and for this reason they are called conic sections. 

Logarithmic curve- — A logarithmic curve is one in which one of the 
coordinates of any point is the logarithm of the other. 

The coordmate axis to which the lines denoting the logarithms are 
parallel is called the axis of logarithms, and the other the axis of numbers. 
If y is the axis of logarithms and a: the axis of numbers, the equation of the 
curve is y = log x. 

If the base of a system of logarithms is a, we have a^ = x, in which y is 
the logarithm of x. 

Each system of logarithms will give a different logarithmic curve. If 
y -^ 0, a* = 1. Hence every logarithmic curve will intersect the axis of 
numbers at a distance from the origin equal to 1. 



DIFFERENTIAL CALCULUS. 

The differential of a variable quantity is the difference between any two 
of its consecutive values; hence it is indefinitely small. It is expressed by 
writmg (i before the quantity, as dx, which is read differential of x. 

The term | is called the differential coefficient of y regarded as a func- 
tion of x. It is also called the first derived function or the derivative. 

The differential of a function is equal to its differential coefficient mul- 
tiplied .by the differential of the independent variable; thus, —dx = dy. 

The limit of a variable quantity is that value to which it continually 
approaches, so as at last to differ from it by less than any assignable 
quantity. 

The differential coefficient is the limit of the ratio of the increment of 
the independent variable to the increment of the function. 

The differential of. a constant quantity is equal to 0. 

The differential of a product of a constant by a variable is equal to the 
constant raultipUed by the differential of the variable. 

If u -= Av, du = A dv. 



74 DIFFERENTIAL CALCULUS. 

In any curve whose equation is 2/ = fix), the differential coefficient 

~ = tan a; hence, the rate of increase of the function, or the ascension of 

ax 

the curve at any point, is equal to the tangent of the angle which the 

tangent line makes with the axis of abscissas. 

All the operations of the Differential Calculus comprise but two objects: 

1. To find the rate of change in a function when it passes from one state 
of value to another, consecutive with it. 

2. To find the actual change in the function: The rate of change is the 
differential coefficient, and the actual change the differential. 

Differentials of algebraic functions. — The differential of the sum 
or difference of any number of functions, dependent on the same variable, 
is equal to the sum or difference of their differentials taken separately: 

If u = y + z — w, du = dy -h dz — dw. 

The differential of a product of two functions dependent on the same 
variable is equal to the sum of the products of each by the differential of 
the other: 

_,. . ^ , J d(uv) du , dv 

d(uv) = vdu+ udv. • = {- 

uv u V 

The differential of the product of any number of functions is equal to 
the sum of the products which arise by multiplying the differential of each 
function by the product of all the others: 

d(uts) = tsdu + usdt + utds. 

The differential of a fraction equals the denominator into the diffeiential 
of the numerator minus the numerator into the differential of the denom- 
inator, divided by the square of the denominator: 

,, ■, / ^ » J du— udv 
dt 



J {u\ V du — 



If the denominator is constant, dv = 0, and dt = — ^ = — • 

v^ V 

udv 
If the numerator is constant, du = 0, and dt = ^» 

The differential of the square root of a quantity is equal to the differen- 
tial of the quantity di^dded by twice the square root of the quantity: 

If V = wV2, OT V =- V^ dv = -^; = i u-^^2du. 

2Vw ^ 

The differential of any power of a function is equal to the exponent multi- 
plied by the function raised to a powerless one, multiplied by the differen- 
tial of the function, d(u^) = nu^~^du. 

Formulas for differentiating algebraic functions. 

1. d (a) = 0. 

2. d {ax) = a dx. 

3. d {x + y) = dx -^ dy. 

4. d (x — y) = dx — dy. 

5. d (xy) = x dy -\- y dx. 

To find the differential of the form u = (a + bx^)^: 
Multiply the exponent of the parenthesis into the exponent of the vari- 
able within the parenthesis, into the coefficient of the variable, into the 



6. 


'© = 


y dx - 


xdy 




7. 


d (x'") = 


mx"^-' 


dx. 




8. 


d (\^x) = 


dx 

2\^x 






9. 


d (r^l 


r 
s 


r 


-1 

dx. 



DIFFERENTIAL CALCULUS. 75 

binomial raised to a power less 1, intr- the variable within the parenthesis 
raised to a power less 1, into the differential of the variable. 

du = d{a + bx^)^ = mnb{a + bx^)"^'^ x^~^ dx. 

To find the rate of change for a given value of the variable: 
Find the differential coefficient, and substitute the value of the variable 
in the second member of the equation. 

Example. — If x is the side of a cube and u its volume, w = x^, -— = 3x2. 

dx 
Hence the rate of change in the volume is three times the square of the 
edge. If the edge is denoted by 1, the rate of change is 3. 

Application. The coefficient of expansion by heat of the volume of a 
body is three times the linear coefficient of expansion. Thus if the side 
of a cube expands 0.001 inch, its volume expands 0.003 cubic inch. l.OOl^ 
= 1.003003001. 

A partial differential coefficient is the differential coefficient of a 
function of two or more variables under the supposition that only one 
of them has changed its value. 

A partial differential is the differential of a function of two or more 
variables under the supposition that only one of them has changed its 
value. 

The total differential of a function of any number of variables is equal 
to the sum of the partial differentials. 

If li = / (X7j), the partial differentials are — dx, -r-dij. 

Ifu -0:2 + 2/3 _ ^ du = ^-^ dx + ^ dy + ^ dz; ='2xdx ^3y^ dy- dz. 
^ dx dy dz 

Integrals. — An integral is a functional expression derived from a 
differential. Integration is the operation of hnding the piiraitive func- 
tion from the differential function. It is indicated by the sign /, which is 

read "the integral of." Thus flxdx = a:2; read, the integral of 2xdx 
equals x"^. 

To integrate an expression of the form mx^~^dx or x^dx, add 1 to the 
exponent of the variable, and divide by the new exponent and by the 

differential of the variable: fzx'^dx = x^. (Applicable in all cases except 

when m = — 1. For /i dx see formula 2, page 81.) 

The integral of the product of a constant by the differential of a vari- 
able is equal to the constant multiplied by the integral of the differential: 



\ ax^ dx = a i a 



m + 1 ■ 



„m+i 



The integral of the algebraic sum of any number of differentials is 
equal to the algebraic sum of their integrals: 



/2 b 

du-= - ax^ - -y^ - 



Since the differential of a constant is 0, a constant connected with a 
variable by the sign 4- or — disappears in the differentiation; thus 
d(a + x^) = dx^ = mx'^ ^ dx. Hence in integrating a differential 
expression we must annex to the integral obtained a constant represented 
by C to compensate for the term which may have been lost in differen- 
tiation. Thus if we have dy = a dx ; /dy = aydx. Integratiug, 

y = ax ± C, 



76 DIFFERENTIAL CALCULUS. 

The constant C, which is added to the first integral, must have such a 
value as to render the functional equation true for every possible value 
that may be attributed to the variable. Hence, after having found the 
first integral equation and added the constant C, if we then make 
the variable equal to zero, the value wliich the function assumes wiU be 
the true value of C. . 

An indefinite integral is the first integral obtained before the value of 
the constant C is determined. 

A particular integral is the integral after the value of C has been found. 

A definite integral is the integral corresponding to a given value of the 
variable. 

Integration between limits. — Having found the indefinite integral 
and the particular integral, the next step is to find the definite integral, 
and then the definite integral between given limits of the variable. 

The integral of a function, taken between two limits, indicated by given 
values of x, is equal to the difference of the definite integrals correspond- 
ing to those limits. The expression 



•^ X 



dy 



is read: Integral of the differential of y, taken between the limits x' and 
x": the least limit, or the limit corresponding to the subtractive integral, 
being placed below. 

Integrate du = 9x-2 dx between the limits x = 1 and a: = 3, w being equal 

to 81 when x = 0. fdu = /9c2 dx = 2>x^ + C; C = 81 when x = 0, then 



X 



.r=3 

du = 3(3)3 -I- 81, minus 3(1)3 + gl = 78. 
x= i 



Integration of particular forms. __ 

To integrate a differential of the form du = (a + bx^)^^x'^ ^ dx. 

1. If there is a constant factor, place it without the sign of the integral, 
and omit the power of the variably without the parenthesis and the differ- 
ential ; 

2. Augment the exponent of the parenthesis by 1, and then divide 
this quantity, with the exponent so increased, by the exponent of the 
parenthesis, into the exponent of the variable within the parenthesis, 
into the coefficient of the variable. Whence 



/ 



(m+ l)no 



The differential of an arc is the hypothenuse of a right-angle triangle of 
which the base is dx and the perpendicular dy. 

If z is an arc, dz ^^dx^Tdy^ z =y^dx^ + dy^. 

Quadrature of a plane figure. 

The differential of the area of a plane surface is equal to the ordinate mto 
the differential of the abscissa. 

ds = y dx. 

To apply the principle enunciated in the last equation, in finding the area 
of any particular plane surface: ^ , .. rx,_ u ^- i- 

Find the value of y in terms of x, from the equation of the boundmg hne; 
substitute this value in the differential equation, and then mtegrate 
between the required limits of x. . x- * ^u 

Area of the parabola. -— Find the area of any portion of the com- 
mon parabola whose equation is 

2/2 = 2px] whence?/ =-= v^2px. 



DIFFERENTIAL CALCULUS. 77 

Substituting this value of y in the differential equation ds = y dx givea 

fds = fvj^ dx ^V2iCx^^-dx =?-^^a;^/2^. c, 
or, s ^ ^^ Xx = ^xy + C, 

If we estimate the area from the principal vertex, x = 0, y = 0, and 

2 
C = 0; and denoting the particular integral by s\ s' = - a:?/. 

That is, the area of any portion of the parabola, estimated from the 
vertex, is equal to 2/3 of the rectangle of the abscissa and ordinate of the 
extreme point. The curve is therefore quadrable. 

Quadrature of surfaces of revolution. — The differential of a surface 
of revolution is equal to the circumference of a circle perpendicular to the 
axis into the differential of the arc of the meridian curve. 

ds = 2r.y'^dx^ + dy^ 

in which y is the radius of a circle of the bounding surface in a plane per- 
pendicular to the axis of revolution, and r is the abscissa, or distance of 
the plane from the origin of coordinate axes. 

Therefore, to find the volume of any surface of revolution: 

Find the value of y and di.i from the equation of the meridian curve in 
terms of x and dx, then substitute these values in the differential equation, 
and integrate between the proper limits of x. 

By application of this rule we may find: 

The curved surface of a cylinder equals the product of the circum- 
ference of the base into the altitude. 

The convex surface of a cone equals the product of the circumference of 
the base into half the slant height. 

The surface of a sphere is equal to the area of four great circles, or equal 
to the curved surface of the circumscribing cylinder. 

Cubature of volumes, of revolution. — A volume of revolution is a 
volume generated by the revolution of a plane figure about a fixed line 
called the axis. 

If we denote the volume by T, dV = ny"^ dx. 

The area of a circle described by any ordinate y is ny'^-, hence the differ- 
ential of a volume of revolution is equal to the area of a circle perpendicular 
to the axis into the differential of the axis. 

The differential of a volume generated by the revolution of a plane 
figure about the axis of Y is r.x"^ dy. 

To find the value of V for any given volume of revolution : 

Find the value of ?/2 in terms of x from the equation of the meridian 
curve, substitute this value in the differential equation, and then integrate 
between the required limits of x. 

By application of this rule we may find: 

The volume of a cylinder is equal to the area of the base multiplied 
by the altitude. 

The volume of a cone is equal to the area of the base into one third the 
altitude. 

The volume of a prolate spheroid and of an oblate spheroid (formed by 
the revolution of an ellipse around its transverse and its conjugate axis 
respectively) are each equal to two thirds of the circumscribing cylinder. 

If the axes are equal, the spheroid becomes a sphere and its volume = 

- TzR"^ X D = - 7rZ)3; R being radius and D diameter. 

The volume of a paraboloid is equal to half the cylinder having the same 
base and altitude. 

The volume of a pyramid equals the area of the base multiplied by one 
third the altitude. 

Second, third, etc., differentials. — The differential coefficient being 
a function of the independent variable, it may be differentiated, and we 
thus obtain the second differential coefficient: 



78 DIFFERENTIAL CALCULUS 

d(-r^\ =» -- — Dividing by dx^ we have for the second differential 
\dxj dx 
d^u 
coefficient -^, which is read : second differential of u divided by the square 

of the differential of x (or dx squared). 

The third differential coefficient -r-^ is read: third differential of u 

divided by dx cubed. 

The differentials of the different orders are obtained by multiplying 
the differential coefficient by the corresponding powers of dx; thus 

d^u 

-T-^ dx^ = third differential of u. 

dx^ 

Sign of the first differential coefficient. — If we have a curve 
Nhose equation is y = fx, referred to rectangular coordinates, the curve 

will recede from the axis of X when -- is positive, and approach the 

axis when it is negative, when the curve Ues within the first angle of the 
coordinate axes. For all angles and every relation of ?/ and x the curve 
will recede from the axis of X when the ordinate and first differential 
coefficient have the same sign, and approach it when they have different 
signs. If the tangent of the curve becomes parallel to the axis of X at any 

point ~ = 0. If the tangent becomes perpendicular to the axis of X at 

. , dv 
any pointy, = oo. 

Sign of the second dififerential coefficient. — The second differential 
coefficient has the same sign as the ordinate when the curve is convex 
toward the axis of abscissa and a contrary sign when it is concave. 

Maclaurin's Theorem. — For developing into a series any function 
of a single variable as ii = A -h Bx + Cx^ + Dx^ + Ex^, etc., in which 
A, B, C, etc., are independent of x: 

In applying the formula, omit the expressions a; = 0, although the 
coefficients are always found under this hypothesis. 
Examples: 

(a + xf = a" + ma""-' x +^^I!L^\'^-'x^ 

a + x ~ a a^ a^ a* o^ + 1' ^ ^* 

Taylor's Theorem. — For developing into a series any function of the 
sum or difference of two independent variables, as u' = f(x ± y): 

, , du , d'^u ?/2 dhc y^ , ^ 

u^^u + ^^y+^,—^+^,-^-^+etc., 

du du^ 

in which u is what u' becomes when y = 0, y- is what -tt becomes when 

y => 0, etc. 

3Iaxima and minima. — To find the maximum or minimum value 
of a function of a single variable: 

1. Find the first differential coefficient of the function, place it equal 
to 0, and determine the roots of the equation. 

2. Find the second differential coefficient, and substitute each real root, 



DIFFERENTIAL CALCULUS. 79 

in succession, for the variable in the second member of the equation. 
Each root which gives a negative result will corresi)ond to a maximum 
value of the function, and each which gives a positive result will corre- 
spond to a minimum value. 

Example. — To find the value of x which will render the function y a 
maximum or minimum in the equation of the circle, y^ + x^ = R^-, 

dv X . . X ^ . - 

~ = ; making — - = o gives x = 0. 

dx y y 

d^V x^ + y^ 

The second differential coefficient is: :r4 = :—■ — 

dx^ y^ 

When a; = 0, y = R; hence w^ = ~ "B' which being negative, y is a, 

maximum for 7^ positive. 

In applying the rule to practical examples we first find an expression for 
the function which is to be made a maximum or minimum. 

2. If in such expression a constant quantity is found as a factor, it may 
be omitted in the operation; for the product will be a maximum or a mini- 
mum when the variable factor is a maximum, or a minimum. 

3. Any value of the independent variable which renders a function a 
maximum or a minimum will render any power or root of that function a 
maximum or minimum; hence we may square both members of an equa- 
tion to free it of radicals before differentiating. 

By these rules we may find: 

The maximum rectangle which can be inscribed in a triangle is one 
whose altitude is half the altitude of the triangle. 

The altitude of the maximum cylinder which can be inscribed in a cone 
is one third the altitude of the cone. 

The surface of a cylindrical vessel of a given volume, open at the top, 
is a minimum when the altitude equals half the diameter. 

The altitude of a cyhnder inscribed in a sphere when its convex surface is 
a maximum is r v^2. r = radius. 

The altitude of a odinder inscribed in a sphere when the volume is a 
maximum is 2r -j- V3. 

Maxima and Minima without the Calculus. — In the equation 
y ^ a -{- bx + CX-, in which a, b, and c are constants, either positive or 
negative, if c be positive y is a minimum when .t = — & -^ 2c; if c be 
negative ?/ is a maximum when x = — b -^ 2c. In the equation y = a -h 
bx 4-C/.T, ?/ is a minimum when bx = c/x. 

Application. — The cost of electrical transmission is made up (1) of 
fixed charges, such as superintendence, repairs, cost of poles, etc., which 
may be represented by a; (2) of interest on cost of the wire, which varies 
with the sectional area, and may be represented by bx; and (3) of cost of 
the energy wasted in transmission, which varies inversely with the area 
of the wire, or c/x. The total cost, y = a -i- bx + c/x, is a minimum 
when item 2 = item 3, or bx = c/x. 

Differential of an exponential function. 

If w = a^ c . . . (1) 

then du = da^ = a^k dx (2) 

in which fc is a constant dependent on a. 

1 

The relation between a and fc is a* = e; whence a = 6* .... (3) 
in which e = 2.7182818 . . . the base of the Naperian system of loga- 
rithms. 

Logarithms. — The logarithms in the Naperian system are denoted by 
f, Nap. log or hyperbolic log, hyp. log, or log^ ; and in the common system 
always by log. 

k « Nap. log a; log a = k log e , , . ^ . < (4) 



go DlFFERiENTIAL CALCULUS. 

The common logarithm of e, = log 2.7182818 . . . = 0.4342945 . . . ♦ 
is called the modulus of the common system, and is denoted by M. 
Hence, if we have the Naperian logarithm of a number we can find the 
common logarithm of the same number by multiplying by the modulus. 
Reciprocally, Nap. log = com. log X 2.3025851. 

If in equation (4) we make a = 10, we have 

1 = ^• log e, or T = log e = M. 

That is, the modulus of the common system is equal to 1, divided by the 
Naperian logarithm of the common base. 
From equation (2) we have 

du da^ 

u a^ 

If we make a = 10, the base of the common system, x = log w, and 

d{\ogu) =^dx = ~x\--~XM. 

That is, the differential of a common logarithm of a quantity is equal to 
the differential of the quantity divided by the quantity, into the modulusc 
If we make a = e, the base of the Naperian system, x becomes the Nape- 
rian logarithm of u, and k becomes 1 (see equation (3)); hence M == 1, 
and 

d (Nap. log u) = dx = -— ; = — • 
a^ u 

That is, the differential of a Naperian logarithm of a quantity is equal to 
the differential of the quantity divided by the quantity; and in the 
Naperian system the modulus is 1. 

Since k is the Naperian logarithm of a, du = a^ I a dx. That is, the 
differential of a function of the form a^ is equal to the function, into the 
Naperian logarithm of the base a, into the differential of the exponent. 

If we have a differential in a fractional form, in which the numerator is 
the differential of the denominator, the integral is the Naperian logarithm 
of the denominator. Integrals of fractional differentials of other forms 
are given below: 

Differential forms which have known integrals; exponential 
functions. (I = Nap. log.) 

1. Ca^ladx = a^ + C: 

2. r^ = Cdx x-'^ '^Ix-hC; 

3. C(xy^''^dy -h y^ ly X dx) = 2/* 4- C; 

4. (*—=£= = l(x + \^x^ ± a2) + C; 

6. r , ^"^ ^l(x ±a+ Vx2 ± 2ax) -»- C; 

J Vx^ ± 2ax 



DIFFERENTIAL CALCULUS. 



81 



7. 



10. 



/ 2adx _ / Va2 4-a:2- a \ 
a:Va2 + a:2 \\/a2 + a;2+a/ 

/ 2a(fx ^ jl a - ^a^ - xA 
X Va2 - a- 2 V a + Va2 _ a;2/ 

/ a^^^c/x _ ^ 14-^1 + a3i-2 ^ , ^ 



Circular functions. — Let z denote an arc in ihe first quadrant, ?/ its 
sine, X its cosine, v its versed sine, and t its tangent ; and the following nota- 
tion be employed to designate an arc by any one of its functions, viz., 

sin~i y denotes an arc of which y is the sine, 



cos~^ X 
tan~i t 



" a: is the cosine, 
" t is the tangent, 



(read "arc whose sine is ?/," etc.), — we have the following differential 
forms which have known integrals (r = radius): 



/ 



cos z dz = sin 2 4- C\ 
^in zdz = cos 2 4- C; 

= sin— 1 2/ 4- C\ 
= cos— 1 x+ C\ 
= versin— 1 v+ C\ 



— dx 
Vi -a:2 

dv 



J \^2v - V' 

flfr^ =tan-ii4-C; 

, = sm ^ y+ C 

VV2 _ y2 



J Vr 



r dx 



x^ 



■■ cos— 1 x+ C\ 



z dz == versin2 4- C\ 
tan 2 4- C; 
= versin" 1 v+ C\ 



z 
r dv 



Jsin 

r dz 

J COS2 Z 

/ 

/.- 

/ 

J Va2 - u 

r du 

J V2 cm - w2 

/ a du _ 
a2 4-w2 ~ 



V2rv 4- V 

24- t^ 
du 



Va2 - u 
— du 



= tan-i^4-C; 
-= sin-i-4-C; 



= cos-i - 4-C; 



-+C; 



tan -1 -4-C. 
a 



The cycloid. — If a circle be rolled along a straight line, any point of 
the circumference, as P, will describe a curve which is called a cycloid. 
The circle is called the generating circle, and P the generating point. 



82 THE SLIDE RULE. 

The transcendental equation of the cycloid is 



. _. y 



n-i-^ - ^2ry - y\ 



and the differential equation is dx = 



y dx 



^2ry - 



V' 



The area of the cycloid is equal to three times the 
area of the generating circle. 

The surface described by the arc of a cycloid when 
revolved about its base is equal to 64 thirds of the 
generating circle. 

The volume of the solid generated by revolving 
a cycloid about its base is equal to five eighths of the 
circumscribing cylinder. 

Integral calculus. — In the integral calculus we 
have to return from the differential to the function 
from which it was derived. A number of differential 
expressions are given above, each of which has a 
known integral corresponding to it, which, being 
differentiated, will produce the given differential. 

In all classes of functions any differential expression 
may be integrated when it is reduced to one of the 
known forms; and the operations of the integral cal- 
culus consist mainly in making such transformations 
of given differential expressions as shall reduce them 
to equivalent ones whose integrals are known. 

For methods of making these transformations 
reference m.ust be made to the text-books on differen- 
tial and integral calculus. 



:| 



i: 



:| *" 



THE SLIDE RULE. 



The slide rule is based on the principles that the 
addition of logarithms multiplies the numbers which 
they represent, and subtracting logarithms divides 
the numbers. By its use the operations of multiplica- 
tion, division, the finding of powers and the extraction 
of roots, may be performed rapidly and with an ap- 
proximation to accuracy which is sufficient for many 
purposes. With a good 10-inch Mannheim rule the 
results obtained are usually accurate to 1/4 of 1 per 
cent. Much greater accuracy is obtained with cylin- 
drical rules like the Thacher. 

The rule (see Fig. 73) consists of a fixed and a 
sliding part both of which are ruled with logarithmic 
scales; that is, with consecutive divisions spaced not 
equally, as in an ordinary scale, but in proportion 
to the logarithms of a series of numbers from 1 to 
10. By moving the slide to the right or left the loga- 
rithms are added or subtracted, and multiplication 
or division of the numbers thereby effected. The 
scales on the fixed part of the rule are known as the 
A and D scales, and those on the slide as the B and 
C scales. A and B are the upper and C and D 
are the lower scales. The A and B scales are each 
divided into two, left hand and right hand, each 
being a reproduction, one half the size, of the C and 
D scales. A "runner," which consists of a framed 
glass plate with a fine vertical line on it, is used to 
facilitate some of the operations. The numbering on 
each scale begins with the figure 1, which is called 



=1. 

'I 



i |£"^ 



Fig. 73. 



THE SLIDE RULE. 83 

the "index" of the scale. In using the scale the figures 1, 2, 3, etc., are 
to be taken either as representing these numbers, or as 10, 20, 30, etc., 
100, 200, 300, etc., 0.1, 0.2, 0.3, etc.. that is, the numbers multiplied or 
iiivided by 10, 100, etc., as may be most convenient for the solution of a 
given problem. 

The following examples will give an idea of the method of using the 
elide rulec 

Proportion. — Set the first term of a proportion on the C scale opposite 
the second term on the D scale, then opposite the third term on the C 
scale read the fourth term on the D scale. 

Example — Find the fourth term in the proportion 12 : 21 :: 30 : x. 
Move the slide to the right until 12 on C coincides with 21 on D, then 
opposite 30 on C read re on D = 52.5. The A and B scales may be used 
instead of C and D. 

Multiplication. — Set the index or figure 1 of the C scale to one of the 
factors on D 

Example. — 25 X 3. Move the slide to the right until the left index 
of C coincides with 25 on the D scale. Under 3 on the C scale will be 
found the product on the D scale, = 75. 

Division — Place the divisor on C opposite the dividend on D, and the 
quotient will be found on D under the index of C. 

Example. — 750 ^ 25. Move the slide to the right until 25 on C coin- 
cides with 750 on D. Under the left index of C is found the quotient on 
Z>, = 30. 

Combined Multiplication and Division. — Arrange the factors to be 
multiplied and divided in the form of a fraction with one more factor in 
the numerator than in the denominator, supplying the factor 1 if necessary. 
Then perform alternate division and multiplication, using the runner to 
indicate the several partial results. 

4X5X8 
Example — • — „ = 8.9 nearly. Set 3 on C over 4 on D, set 

o X t) 

runner to 5 on C, then set 6 on C under the runner, and read under 8 on 
C the result 8.9 - on Z). 

Involution and Evolution. — The numbers on scales A and B are the 
squares of their coinciding numbers on the scales C and D, and also the 
numbers on scales C and D are the square roots of their coinciding num- 
bers on scales A and B. 

Example — 4^ = 16. Set the runner over 4 on scale D and read 16 
on A^ 

^^16 = 4. Set the runner over 16 on A and read 4 on D. 

In extracting square roots, if the namber of digits is odd, take the num- 
ber on the left-hand scale of A : if the number of digits is even, take the 
number on the right-hand scale of A. 

To cube a number, perform the operations of squaring and multiplica- 
tion. 

Example. — 2^ == 8. Set the index of C over 2 on D, and above 2 
on B read the result 8 on Ac 

Extraction of the Cube Root. — Set the runner over the number on A, 
then move the slide until there is found under the runner on B, the same 
number which is found under the index of C on D; this number is the 
cube root desired. 

Example — yjs = 2. Set the runner over 8 on A, move the slide 
along until the same number appears under the runner on B and under 
the index of C on D; this will be the number 2. 

Trigonometrical Computations. — On the under side of the slide (which 
is reversible) are i)laced three scales, a scale of natural sines marked S, 
a scale of natural tangents marked T, and between these a scale of equal 
parts To use these scales, reverse the slide, bringing its under side to 
the top. Coinciding with an angle on S its sine will be found on A, and 
coinciding with an angle on T will be found the tangent on D. Sines and 
tangents can be multiplied or divided like numbers. 



g4 LOGARITHMIC RULED PAPER, 

LOGARITHMIC RULED PAPER. 

W. F. Durand {Eng, News, Sept. 28, 1893.) 

As plotted on ordinary cross-section paper the lines which express 
relations between two variables are usually curved, and must be plotted 
point by point from a table previously computed. It is only where the 
exponents involved in the relationship are unity that the line becomes 
straight and may be drawn immediately on the determination of two of 
its points. It is the pecuhar property of logarithmic section paper that 
for all relationships which involve multiplication, division, raising to 
powers, or extraction of roots, the lines representing them are straight. 
Any such relationship may be represented by an equation of the form: 
y = Bx*^. Taking logarithms we have: log y = log B +n log x. 

Logarithmic section paper is a short and ready means of plotting such 
logarithmic equations. The scales on each side are logarithmic instead 
of uniform, as in ordinary cross-section paper. The numbers and divi- 
sions marked are placed at such points that their distances from the origin 
are proportional to the logarithms of such numbers instead of to the 
numbers themselves. If we take any point, as 3, for example, on such a 
scale, the real distance we are dealing with is log 3 to some particular 
base, and not 3 itself. The number at the origin of such a scale is always 
1 and not 0, because 1 is the number whose logarithm is 0. This 1 may, 
however, represent a unit of any order, so that quantities of any size 
whatever may be dealt with. 

If we have a series of values of x and of 5x , and plot on logarithmic 
section paper x horizontally and Bx'"' vertically, the actual distances 
Involved will be log x and log (Bx'^), or log 5 + n log x. But these dis- 
tances ^^ill give a straight line as the locus. Hence all relationships 
expressible in tliis form are represented on logarithmic section paper by 
straight lines. It follows that the entire locus may be determined from 
any two points; that is, from any two values of Bx^^; or, again, by any one 
point and the angle of inclination; that is, by one value of Bx^^ and the 
value of n, remembering that n is the tangent of the angle of inclination 
to the horizontal. 

A single square plotted on each edge with a logarithmic scale from 1 
to 10 may be made to serve for any number whatever from to oo. Thus 
to express graphically the locus of the equation: y = 3-^/2. Let Fig. 74 
denote a square cross-sectioned vv^ith logarithmic scales, as described. 
Suppose that there were joined to it and to each other on the right and 
above, an indefinite series of such squares similarly divided. Then, con- 
sidering, in pa^ssing from one square to an adjacent one to the right or 
above, that the unit becomes of next higher order, such a series of squares 
would, with the proper variation of the unit, represent all values of either 
X or y between and go. 

Suppose the original square divided on the horizontal edge into 3 parts, 
and on the vertical edge into 2 parts, the points of division being at A, 
B, D, F, G, I. Then lines joining these points, as shown, wiU be at an 
inclination to the horizontal whose tangent is 3/2. Now, beginning at O, 
OF will give the value of 2:^/2 for values of x fromi 1 to that denoted by HF, 
or OB, or about 4.6. For greater values of .f the line would run into the 
adjacent square above, but the location of this line, if continued, would 
be exactly similar to that of BD in the square before us. Therefore the 
line BD will give values of .r^/2 for x between B and C, or 4.6 and 10, the 
corresponding values of ?/ being of the order of tens, and ranging from 10 
to 31.3. For larger values of x the unit of x is of the higher order, and 
we run into an adjacent square to the right without change of unit for y. 
In this square we should traverse a line similar to 10. Therefore, by a 
proper choice of units we may make use of IG for the determination of 
values of .t^/2 where x hes between 10 and the value at G, or about 21.5. 
We should then run into an adjacent square above, requiring the unit on 
y to be of the next higher order, and traverse a line similar to AE, which 



LOGARITHMIC RULED PAPER. 



85 



takes us finally to the opposite corner and completes the cycle. Follow- 
ing this, the same series of lines would result for numbers of succeeding 
orders. 

The value of a; /2 for any value of x between 1 and oo may thus be read 
from one or another of these. lines, and likewise for any value between 
and 1. The location of the decimal point is readily found by a little 
attention to the numbers involved. The limiting values of x for any 
given line may be marked on it, thus enabling a proper choice to be readily 
made. Thus, in Fig. 74 we mark OF as - 4.6, BD as 4.6 - 10, IG as 



H 

in ^ 


G 3 Q i 


F 


-^ 












d 




10 


9 i- 

8 ^^ - 


=^- 4_...__UC 




I 

t 

i 


8 
6 


1 1 i / : 1 1 ' 1 ; .. — ^^- 

1 / ! 1 i M 1 ■ 1 ■ 

'mmWm 


#^- ' ■ ' 


- 


r/ 


5 

1 

D 

3 


3 1 i ! u ' 


/ ^ ' 


'' 




-^^ ' T > 




/ 






TT-^^ 


/ -^ 






y 






M-A 


A ^ ^" 1-"^' i 1 


/ 






/ 










i^ ^^ p / ! 1 


/ 








/ 




l''i 




1 // 


-!/ ^ 






/ 








/ 


'r. 


I'll 




\//i 


T T \ 


xiLL 


; J 


; , 








/ 




1 ' 




/A 


IT ± T+ ZT " M 




ll/i 


i! 


i 1 




-'/ 




z 






/] 


A- - ---^ ^-^ 


1 


T/i 1 




!l' 




2 _::::c::: 


"^ JI _ 5^1. Ml 




/ ' 










o 


'^^k^ 


1 Ml /uk4Tti^ 


J / 










-1 1 i4^--|--r-l r 

i IJfem] 


trpi|l!i)f|'l||M^ 


1 \: 






/ / 


/ ' ' / 








/ , 


y r- ■/- ' j -^ 






/ / 


2 ^ ' 








-^ X ' / ; " 




t t "±":[: j+ 


/—t y/ ' ■— ' 






/ / 






^ ^ 


/- — y^: 


1 




a: > ± 


_- V ~~ "4i""I 






^ t 


z A 1 


/ i 1 




it ±_ I___ 


/ / 


1/ T' M-'i^iiniii liiiiii^ihuiiiiiii 


1 



o p 



2 A 



3 ' P 4 

Fig. 74. 



B 5 



10 

C 



10 - 21.5, and AE as 21.5 - 100. If values of x less than 1 are to be 
dealt with, AE will serve for values of x between 1 and 0.215, IG for 
values between 0.215 and 0.1, BZ) for values between 0.1 and 0.046, and 
OF for values between 0.046 and 0.001. 

The principles involved in this case may be readily extended to any 
other, and in general if the exponent be represented by min, the complete 
set of Unes may be drawn by dividing one side of the square into m and 
the other into n parts, and joining the points of division as in Fig. 74. In 
all there will be (m 4- n — 1) lines, and opposite to any point on X there 
will be n lines corresponding to the n different beginnings of the nth root 



86 MATHEMATICAL TABLES. 

oi the mth power, while opposite to any point on Y will be m lines corre- 
sponding to the different beginnings of the ?7ith root of the nth power. 
Where the complete number of lines would be quite large, it is usually 
unnecessary to draw them all, and the number may be limited to those 
necessary to cover the needed range in the values of x. 

If, instead of the equation y = x^, we have a constant term as a multi- 
plier, gi\dng an equation in the more general form y =Bx^, or Bx mm, 
there will be the same number of lines and at the same inclination, but 
all shifted vertically through a distance equal to log B. If, therefore, 
we start on the axis of Y at the point B, we may draw in the same series 
of lines and in a similar manner. In this way PQ represents the locr.s 
giving the values of the areas of circles in terms of their diameters, being 
the locus of the equation A = 1/4 ^ d^ or ?/ = 1/4 "^ ^'^. 

If in any case we have x in the denominator such that the equation is 
in the form ?/ =B/x^, this is equal to ?/ = Bx~^^, and the same general 
rules hold. The lines in such case slant downward to the right instead of 
upward. Logarithmic ruled paper, with directions for the use, may be 
obtained from Keuffel & Esser Co., 127 Fulton St., New York. 



MATHEMATICAL TABLES. 

Formula for Interpolation. 

, / -.N^ . (^-1) (^^-2) , , (n-1) (n-2) (n-3) ^ . 

ai = the first term of the series; n, number of the required term; a^, the 
required term; di, di, ds, first terms of successive orders of differences 
between ai, a2, as, a^, successive terms. 

Example. — Required the log of 40.7, logs of 40, 41, 42, 43 being given as 
below. 

Terms ai, 02, ^3, 04,: 1.6021 1.6128 1.6232 1.6335 

1st differences: 0.0107 0.0104 0.0103 
2d " - 0.0003 - 0.0001 

3d " + 0.0002 

For log. 40, n = 1; log 41, n= 2; for log 40.7, n = 1.7; n - 1 =» 0.7: n-2 
= - 0.3; n - 3 =- 1.3. 

a, =1.6021+0.7 (0.0107) ^(0.7)( -0.3)( -0.0003) _^ (0.7)( -0.3)(- O KO^OOOg) 

2 6 

= X.6021 + 0.00749 + 0.000031 + 0.000009 = 1.6096 +, 



RECIPROCALS OF NUMBERS. 



87 







RECIPROCALS 


OF NU3IBERS. 






No. 


Recipro- 
cal. 


No. 
64 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal, 


1 


l.OOOOOOUO 


01562500 


127 


•00/8/402 


190 


.00526316 


253 


.00395257 


2 


.50000000 


5 


01538461 


8 


•00781250 


1 


.00523560 


4 .00393701 


3 


.33333333 


6 


01515151 


9 


00775194 


2 


.00520833 


5 


.00392157 


4 


.25000000 


7 


01492537 


130 


•00769231 


3 


.00518135 


6 


.00390625 


5 


.20000000 


8 


01470588 


1 


00763359 


4 


.00515464 


7 


.00389105 


6 


.16666667 


9 


01449275 


2 


00757576 


5 


.00512820 


8 


.0038/597 


7 


.14285714 


70 


•01428571 


3 


•00751880 


6 


.00510204 


9 


.00386100 


8 


.12500C00 


] 


■01408451 


4 


00746269 


7 


.00507614 


260 


.00384615 


9 


.11111111 


2 


•01388889 


5 


•00740741 


8 


.00505051 


1 


.00383142 


10 


.10000000 


3 


•01369863 


6 


00735294 


9 


.00502513 


2 


.00381679 


11 


.09090909 


4 


•01351351 


7 


•00729927 


200 


.00500000 


3 


.00380228 


12 


.08333333 


5 


•01333333 


8 


•00724638 


1 


.00497512 


4 


.00378788 


'13 


.07692308 


6 


01315789 


9 


•00719424 


2 


.00495049 


5 


.00377358 


14 


.07142857 


7 


•01298701 


140 


00714286 


3 


.00492611 


6 


.00375940 


15 


.06666667 


8 


•01282051 


1 


00709220 


4 


.00490196 


7 


.00374532 


16 


.06250000 


9 


•01265823 


2 


.00704225 


5 


.00487805 


8 


.00373134 


17 


.05882353 


80 


•01250000 


3 


00699301 


6 


.00485437 


9 


.00371747 


18 


.05555556 


1 


•01234568 


4 


.00694444 


7 


.00483092 


270 


.00370370 


19 


.05263158 


2 


01219512 


5 


.00689655 


8 


.00480769 


1 


.00369004 


20 


.05000000 


3 


•01204819 


6 


.00684931 


9 


.00478469 


2 


.00367647 


1 


.04761905 


4 


•01190476 


7 


.00680272 


210 


.00476190 


3 


.00366300 


2 


.04545455 


5 


•01176471 


8 


.00675676 


11 


.00473934 


4 


.00364%3 


3 


.04347826 


6 


•01162791 


9 


.00671141 


12 


.00471698 


5 


.00363636 


4 


.04166667 


7 


•01149425 


150 


.00666667 


13 


.00469434 


6 


.00362319 


5 


.04000000 


8 


•01136364 


1 


.00662252 


14 


.00467290 


7 


.00361011 


6 


.03846154 


9 


01123595 


2 


.00657895 


15 


.00465116 


8 


.00359712 


7 


.03703704 


90 


01111111 


3 


.00653595 


16 


.00462963 


9 


.00358423 


8 


.03571429 


1 


•01093901 


4 


.00649351 


17 


.00460829 


280 


.00357143 


9 


.03448276 


2 


01036956 


5 


.00645161 


18 


.00458716 


1 


.00355872 


30 


.03333333 


3 


01075269 


6 


.00641026 


19 


.00456621 


2 


.00354610 


1 


.03225806 


4 


•01063830 


7 


.00636943 


220 


.00454545 


3 


.00353357 


2 


.03125000 


5 


•01052632 


8 


.0063291 1 


1 


.00452489 


4 


.00352113 


3 


.03030303 


6 


•01041667 


9 


.00628931 


2 


.00450450 


5 


.00350877 


4 


.02941176 


7 


•01030928 


160 


.00625000 


3 


.00448430 


6 


.00349650 


5 


.02857143 


8 


•01020408 


1 


.00621118 


4 


.00446429 


7 


.00348432 


6 


.027/7778 


9 


•01010101 


2 


.00617284 


5 


.00444444 


8 


.00347222 


7 


.02702703 


100 


01000000 


3 


.00613497 


6 


.00442478 


9 


.00346021 


8 


.02631579 


1 


00990099 


4 


.00609756 


7 


.00440529 


290 


.00344828 


9 


.02564103 


2 


•00980392 


5 


.00606061 


8 


.00438596 


1 


.00343643 


40 


.02500000 


3 


■00970874 


6 


.00602410 


9 


.00436681 


2 


.00342466 


1 


.02439024 


4 


•00961538 


7 


.00598802 


230 


.00434783 


3 


.00341297 


2 


.02380952 


5 


•00952381 


8 


.00595233 


1 


.00432900 


4;. 00340 136 


3 


.02325581 


6 


•00943396 


9 


00591716 


2 


.00431034 


5 '00333983 


4 


.02272727 


7 


•00934579 


170 


.00588235 


3 


.00429184 


61.00337838 


5 


.02222222 


8 


.00925926 


1 


.00584795 


4 


.00427350 


71.00336700 


6 


.02173913 


9 


.00917431 


2 


.00581395 


5 


.00425532 


8 


.00335570 


7 


.02127660 


110 


.00909091 


3 


.00578035 


6 


.00423729 


9 


.00334448 


8 


.02083333 


11 


.00900901 


4 


.00574713 


7 


.00421941 


300 


.00333333 


9 


.02040816 


12 


.00892857 


5 


.00571429 


8 


.00420168 


1 


.00332226 


50 


.02000000 


13 


.00884956 


6 


.00568182 


9 


.00418410 


2 


.00331126 


1 


.01960784 


14 


.00877193 


7 


.00564972 


240 


.00416667 


3 


.00330033 


2 


.01923077 


15 


.00869565 


8 


.00561798 


1 


.00414938 


4 


.00328947 


3 


.01886792 


16 


.00862069 


9 


.00558659 


2 


.00413223 


5 


.00327869 


4 


.01851852 


17 


.00854701 


180 


.00555556 


3 


.00411523 


6;. 00326797 


5 


.01818182 


18 


.00847458 


1 


.00552486 


4 


.00409836 


7 .00325733 


6 


.01785714 


19 


.00840336 


2 


.00549451 


5 


.00408163 


8 .00324675 


7 


.01754386 


120 


.00833333 


3 


.00546448 


6 


.00406504 


91.00323625 


8 


.01724138 


\ 


.00826446 


4 


.00543478 


7 


.00404858 


310 


.00322581 


9 


.01694915 


2 


.00819672 


5 


.00540540 


8 


.00403226 


11 


.00321543 


60 


.01666667 


3 


.00813008 


6 


.00537634 


9 


.00401606 


12 


.00320513 


1 


.01639344 


4 


.00806452 


7 


.00534759 


250 


.00400000 


13 


.00319489 


2 


.01612903 


5 


.00800000 


8 


.00531914 


1 


.00398406 


14 


.00318471 


3 


.01587302 


6 


.00793651 


9 


.00529100 


2 .00396825 


15.00317460 



88 



MATHEMATICAL TABLES. 



No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No 


Recipro- 
cal. 


No 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


3ie 


.00316456 


'38^ 


.00262467 


^46|.002242T5' 


" TT 


1 .00195695 


576 00173611 


17 


.00315457 


^ 


'00261780 


7 1.002237 14 


12|.00195312 


7 .00173310 


18 


.00314465 




'.00261097 


8!. 002232 14 


13 .00194932 


8 00173010 


19 


.00313480 


I 


1 .00260417 


9| .002227 17 


141.00194552 


9' 00172712 


320 


.00312500 




.00259740 


450,. 00222222 


If 


) .00194175 


580l 00172414 


1 


.00311526 


\ 


) .00259067 


1 1.00221729 


1( 


) .00193798 




.00172117 


2 


.00310559 


/ 


.00258398 


2,. 0022 1239 


1; 


.00193424 




.00171821 


3 


.00309597 


f 


.00257732 


3 .00220751 


\l 


.00193050 


3 


.00171527 


^ 


.00308642 


9 


.00257069 


4;. 00220264 


ic 


.00192678 


A 


.00171233 


5 


.00307692 


39C 


.00256410 


5 1.002 19780 


52f 


.00192308 


5 


.00170940 


6 


.00306748 


1 


.00255754 


6 .00219298 


1 


.00191939 


6 


.00170648 


7 


.00305810 


2 


.00255102 


7 


1.00218818 


2 


.00191571 


7 


.00170358 


8 


.00304878 


3 


.00254453 


8 


! 002 18341 


3 


.00191205 


8 


00170068 


9 
330 


.00303951 


4 


.00253807 


9 


.00217865 


4 


.00190840 


9 


.00169779 


.00303030 


5 


.00253165 


460 


j. 002 17391 


5 


.00190476 


590 


.00169491 


1 


.00302115 


6 


.00252525 


1 


1.00216920 


6 


.00190114 


1 


00169205 


2 


.00301205 


7 


.00251889 


2 


1.00216450 


7 


.00189753 


2 


.00168919 


3 


.00300300 


8 


.00251256 


3 


1.00215983 


8 


.00189394 


3 


00168634 


4 


.00299401 


9 


.00250627 


4 


.00215517 


9 


.00189036 


4 


.00168350 


5 


.00298507 


400 


.00250000 


5 


.00215054 


530 


.00188679 


5 


00168067 


6 


.00297619 


1 


.00249377 


6 


.00214592 


1 


.00188324 


6 


00167785 


7 


.00296736 


2 


.00248756 


7 


.00214133 


2 


.00187970 


7 


.00167504 


8 


.00295858 


3 


.00248139 


8 


.00213675 


3 


.00187617 


8 


.00167224 


9 
340 


.00294985 


4 


.00247525 


9 


.00213220 


4 


.00187266 


9 


00166945 


.00294118 


5 


.00246914 


470 


.00212766 


5 


.00186916 


600 


00166667 


1 


.00293255 


6 


.00246305 


1 


.00212314 


6 


.00186567 


1 


00166389 


2 


.00292398 


7 


.00245700 


2 


.00211864 


7 


.00186220 


2 


.00166113 


3 


.00291545 


8 


.00245098 


3 


.00211416 


8 


.00185874 


3 


00165837 


4 


.00290698 


9 


.00244499 


4 


.00210970 


9 


.00185528 


4 


.00165563 


5 


.00289855 


410 


.00243902 


5 


.00210526 


540 


.(50185185 


5 


00165289 


6 


.00289017 


11 


.00243309 


6 


.00210084 


1 


.00184843 


6 


00165016 


7 
8 


.00288184 
.00287356 


12 
13 


.00242718 
.00242131 


7 
8 


.00209644 
.00209205 


2 
3 


.00184502 
.00184162 


7 

8 


.00164745 
00164474 


9 

350 


.00286533 


14 


.00241546 


9 


.00208768 


4 


.00183823 


9 


00164204 > 


,00285714 


15 


.00240964 


•480 


.00208333 


5 


.00183486 


610 


00163934 


1 


.00284900 


16 


.00240385 


1 


.00207900 


6 


.00183150 


11 


00163666 


2 


.00284091 


17 


.00239808 


2 


.00207469 


7 


.00182815 


12 


00163399 


3 


.00283286 


18 


.00239234 


3 


.00207039 


8 


.00182482 


13 


00163132 


4 


.00282486 


19 


.00238663 


4 


.00206612 


9 


.00182149 


14 


00162866 


5 


.00281690 


420 


.00238095 


5 


.00206186 


550 


.00181818 


15i 


00162602 


6 


.00280899 


1 


.00237530 


6 


.00205761 


1 


.00181488 


161 


00162338 


7 


.00280112 


2 


.00236967 


7 


.00205339 


2 


.00181159 


I7I 


00162075 


8 


.00279330 


3 


.00236407 


8 


.00204918 


3 


.00180832 


18 


00161812 


9 
360 


.00278551 


4 


.00235849 


9' 


.00204499 


4 


.00180505 


19' 


00161551 


.00277778 


5 


.00235294 


490 ; 


.00204082 


5 


.00180180 


620 


00161290 


1 


.00277008 


6 


.00234742 


1, 


.00203666 


6 


.00179856 


1 


00161031 


2 


.00276243 


7 


.00234192 


2; 


.00203252 


7 


.00179533 


2 


.00160772 


3 


.00275482 


8 


.00233645 


3, 


.00202840 


8 


.00179211 


3: 


00160514 


4 


.00274725 


9 


.00233100 


4 


.00202429 


9 


.00178891 


4' 


00160256 


5 


.00273973 


430 


.00232558 


5; 


.00202020 


560 


.00178571 


5 


00160000 


6 


.00273224 


1 


.00232019 


6 


.00201613 


1 


.00178253 


6' 


00159744 


7 


.00272480 


2 


.00231481 


7: 


.00201207 


2 


.00177936 


7' 


00159490 


8 


.0027 1 739 


3 


.00230947 


8 


00200803 


3 


.00177620 


8 


00159236 


9 
370 


.00271003 


4 


.00230415 


9 


00200401 


4, 


.00177305 


9 


00158982 


.00270270 


5 


.00229885 


500 


00200000 


5| 


.00176991 


630 


00158730 


1 


.00269542 


6 


.00229358 


1 


00199601 


6 


00176678 


li 


00158479 


2 


.00268817 


7 


00228833 


2 


00199203 


7 


00176367 


2\ 


00158228 


3 


.002680% 


8 


00228310 


3 


00198807 


8 


00176056 


3 


00157978 


4 


.00267380 


9 


00227790 


4 


00198413 


9 


00175747 


4! 


00157729 


5 


.00266667 


440 


00227273 


5 


00198020 


570 


00175439 


5 


00157480 


6 


.00265957 


1 


00226757 


6' 


00197628 


1 


00175131 


6 


00157233 


7 


.00265252 


2 


00226244 


7:' 


00197239 


2 


00174825 


7 


00156986 


8 


.00264550 


3 


00225734 


8i 


00196850 


3 


00174520 


8 


00156740 


9 
380 


.00263852 


4 


00225225 


9 


00196464 


4 


00174216 


9 


00156494 


.00263158 


5 


00224719 


5101 


00196078 


5 .00173913 ' 


640 . 


00156250 



RECIPROCALS OF NUMBERS. 



89 



No. 


Recipro- 
cal. 


xVo. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


641 


.00156006 


706 


.00141643 


771 


.00129702 


836 


.00119617 


901 


.00110988 


2 


.00155763 


7 


.00141443 


2 


.00129534 


7 


.00119474 


2 


.00110865 


3 


.00155521 


8 


.00141243 


■ 3 


.00129366 


8 


.00119332 


3 


.00110742 


4 


.00155279 


9 


.00141044 


4 


.00129199 


9 


.00119189 


4 


.00110619 


5 


.00155039 


710 


.00140345 


5 


.00129032 


840 


.00119048 


5 


.00110497 


6 


.00154799 


11 


.00140647 


6 


.00128866 


1 


.00118906 


6 


.00110375 


7 


.00154559 


12 


,00140449 


7 


.00128700 


2 


.001 18765 


7 


.00110254 


8 


.00154321 


13 


.00140252 


8 


.00128535 


3 


.00118624 


8 


.00110132 


9 


.00154083 


14 


.0014(X)56 


9 


.00128370 


4 


.00118483 


9 


.00110011 


650 


.00153846 


15 


.00139860 


780 


.00128205 


5 


.00118343 


910 


.00109890 


I 


.00153610 


16 


.00139665 


1 


.00128041 


6 


.00118203 


11 


.00109769 


2 


.00153374 


17 


.00139470 


2 


.00127877 


7 


.001 18064 


12 


.00109649 


3 


.00153140 


18 


.00139276 


3 


.00127714 


8 


.00117924 


13 


.00109529 


4 


.00152905 


19 


.00139032 


4 


.00127551 


9 


.00117786 


14 


.00109409 


5 


.00152672 


720 


.00138889 


5 


.0012738? 


850 


.00117647 


15 


.00109290 


6 


.00152439 


1 


.00138696 


6 


.00127226 


1 


.00117509 


16 


.00109170 


7 


.00152207 


2 


.00138504 


7 


.00127065 


2 


.00117371 


17 


.00109051 


8 


.00151975 


3 


.00138313 


8 


.00126904 


3 


.00117233 


18 


.00108932 


9 


.00151745 


4 


.00138121 


9 


.00126743 


4 


.00117096 


19 


00108814 


660 


.00151515 


5 


.00137931 


790 


.00126582 


5 


.00116959 


920 


.00108696 


1 


.00151286 


6 


.00137741 


1 


.00126422 


6 


.00116822 


1 


.00108578 


2 


.00151057 


7 


.00137552 


2 


.00126263 


7 


.00116686 


2 


.00108460 


3 


.00150830 


8 


.00137363 


3 


.00126103 


8 


.00116550 


3 


.00108342 


4 


.00150502 


9 


.00137174 


4 


.00125945 


9 


.00116414 


4 


.00108225 


5 


.00150376 


730 


.00136936 


5 


.00125786 


860 


.00116279 


5 


.00108108 


6 


.00150150 


1 


.00136799 


6 


.00125623 


1 


.00116144 


6 


.00107991 


7 


.00149925 


2 


.00136612 


7 


.00125470 


2 


.00116009 


7 


.00107875 


8 


.00149701 


3 


.00135426 


8 


.00125313 


3 


.00115875 


8 


.00107759 


9 


.00149477 


4 


.00136240 


9 


.00125156 


4 


.00115741 


9 


.00107.643 


670 


.00149254 


5 


.00136054 


800 


.00125000 


5 


.00115607 


930 


.00107527 


I 


.00149031 


6 


.00135870 


1 


.00124844 


6 


.00115473 


1 


.00107411 


2 


,00148809 


7 


.00135685 


2 


.00124688 


7 


.00115340 


2 


.00107296 


■a 


.00148588 


8 


00135501 


3 


.00124533 


8 


.00115207 


3 


.00107181 


4 


.00148368 


9 


.00135318 


4 


.00124378 


9 


.00115075 


4 


.00107066 


5 


.00148143 


740 


.00135135 


5 


.00124224 


870 


.00114942 


5 


.00106952 


6 


.00147929 


1 


00134953 


6 


.00124069 


1 


.00114811 


6 


.00106838 


7 


.00147710 


2 


.00134771 


7 


.00123916 


2 


.00114679 


7 


.00106724 


8 


.00147493 


3 


.00134589 


8 


.00123762 


3 


.00114547 


8 


.00105610 


9 


.00147275 


4 


.00134409 


9 


00123609 


4 


.00114416 


9 


.00106496 


680 


.00147059 


5 


.00134228 


810 


.00123457 


5 .00114286 


940 


.00106383 


1 


.00146843 


6 


.00134048 


11 


.00123305 


6 


.00114155 


1 


.00106270 


2 


.00146628 


7 


.00133869 


12 


.00123153 


7 


.00114025 


2 


.00106157 


3 


.00146413 


8 


.00133690 


13 


.00123001 


8 


.00113895 


3 


.00106044 


4 


.00146199 


9 


.00133511 


14 


.00122850 


9 


.00113766 


4 


.00105932 


5 


.00145985 


750 


.00133333 


15 


.00122699 


830 


.00113636 


5 


.00105820 


6 


.00145773 


1 


.00133156 


16 


.00122549 


1 


.00113507 


6 


00105708 


7 


.00145560 


2 


.00132979 


17 


.00122399 


2 


.00113379 


7 


.00105597 


8 


.00145349 


3 


.00132802 


18 


.00122249 


3 


.00113250 


8 


.00105485 


9 


.00145137 


4 


.00132626 


19 


.00122100 


4 


.00113122 


9 


.00105374 


690 


.00144927 


5 


.00132450 


820 


.00121951 


5 


.0^' 12994 


950 


.00105263 


1 


.00144718 


6 


.00132275 


1 


.00121803 


6 


.00 1 i2867 


1 


.00105152 


2 


.00144509 


7 


.00132100 


2 


.00121654 


7 


.00112740 


2 


.00105042 


3 


.00144300 


8 


.00131926 


3 


.00121507 


8 


.00112613 


3 


.00104932 


4 


.00144092 


9 


.00131752 


4 


.00121359 


9 


.00112486 


4 


.00104822 


5 


.00143385 


760 


.00131579 


5 


.00121212 


890 


.00112360 


5 


.00104712 


6 


.00143678 


1 


.00131406 


6 


.00121065 


1 


00112233 


6 


.00104602 


7 


.00143472 


2 


.00131234 


7 


.00120919 


2 


00112108 


7 


.00104493 


8 


.00143266 


3 


.00131062 


8 


.00120773 


3 


00111982 


8 


.00104384 


9 


.00143061 


4 


.00130890 


9 


.00120627 


4 


.00111857 


9 


.00104275 


700 


.00142857 


5 


.00130719 


830 


.00120482 


5 


.00111732 


960 


.00104167 


1 


.00142653 


6 


.00130548 


1 


.00120337 


6 


.00111607 


1 


.00104058 


2 


.00142450 


7 


.00130378 


2 


.00120192 


7 


.00111483 


2 


.00103950 


3 


.00142247 


8 


.00130208 


3 


.00120048 


8 


.00111359 


3 


.00103842 


4 


.00142045 


9 


.00130039 


4 


.00119904 


9 


.00! 11235 


4 


.00103734 


5 


.00141844 


770 .00129870 ' 


5 


.00119760 


900.00111111 * 


5 


.00103627 



90 



MATHEjfATICAL TABLES. 



No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 


966 


.00103520 


1031 


.000969932 


10% 


.00091.2409 


1161 


.000861326 


1226 


.000815661 


7 


.00103413 


2 


.000968992 


7 


.000911577 


2 


.000860585 


7 


.000814996 


8 


.00103306 


3 


.000968054 


8 


.000910747 


3 


.000859845 


8 


.000814332 


9 


.00103199 


4 


.000967118 


9 


.000909918 


4 


.000859106 


9 


.000813670 


970 


.00103093 


5 


.000966184 


1100 


.000909091 


5 


.000358369 


1230 


.000813008 


1 


.00102937 


6 


.000965251 


1 


.000903265 


6 


.000857633 


1 


.000812348 


2 


.00102881 


7 


.000964320 


2 


.000907441 


7 


.000356898 


2 


.000811688 


3 


.00102775 


8 


.000963391 


3 


.000906618 


8 


.000856164 


3 


.000811030 


4 


.00102669 


9 


.000962464 


4 


.000905797 


9 


.000855432 


4 


.000810373 


5 


.00102564 


1040 


.000961538 


5 


.000904977 


1170 


.000354701 


5 


.000309717 


6 


.00102459 


1 


.000960615 


6 


.000904159 


1 


.000853971 


6 


.000809061 


7 


.00102354 


2 


.000959693 


7 


.000903342 


2 


.000853242 


7 


.000808407 


8 


.00102250 


3 


.000958774 


8 


.000902527 


3 


.000852515 


8 


.000807754 


9 


.00102145 


4 


.000957854 


9 


.000901713 


4 


.000851789 


9 


.000807102 


980 


.00102041 


5 


.000956938 


1110 


.000900901 


5 


.000851064 


1240 


.000806452 


1 


.00101937 


6 


.000956023 


11 


.000900090 


6 


.00085034C 


1 


.000805302 


2 


.00101833 


7 


.000955110 


12 


.000399231 


7 


.000849618 


2 


.000805153 


3 


.00101729 


8 


.000954198 


13 


.000898473 


8 


.000848396 


3 


.000804505 


4 


.00101626 


9 


.000953289 


14 


.000897666 


9 


.000848176 


4 


.000803858 


5 


.00101523 


1050 


.000952381 


15 


.000896861 


1180 


.000847457 


5 


.000803213 


6 


.00101420 


1 


.000951475 


16 


.000896057 


1 


.000846740 


6 


.000802568 


7 


.00101317 


2 


.000950570 


17 


.000895255 


2 


.000846024 


7 


.000801925 


8 


.00101215 


3 


.000949668 


18 


.000894454 


3 


.000845308 


8 


.000801282 


9 


.00101112 


4 


.000948767 


19 


.000893655 


4 


.000844595 


9 


.000800640 


990 


.00101010 


5 


.000947867 


1120 


.000892857 


5 


.000843882 


1250 


.0008000C0 


1 


.00100908 


6 


.000946970 


1 


.000392061 


6 


.000343170 


1 


.00079936C 


2 


.00100806 


7 


.000946074 


2 


.000891266 


7 


.000842460 


2 


.000798722 


3 


.00100705 


8 


.000945180 


3 


.000890472 


8 


.000841751 


3 


.000798035 


4 


.00100604 


9 


.000944287 


4 


.000889680 


9 


.000841043 


4 


.000797448 


5 


.00100502 


1060 


.000943396 


5 


.000888889 


1190 


.000840336 


5 


.000796813 


6 


.00100402 


1 


.000942507 


6 


.000888099 


1 


.000839631 


6 


.0C0796173 


7 


.00100301 


2 


.000941620 


7 


.000887311 


2 


000838926 


•7 


.000795545 


8 


.00100200 


3 


.000940734 


8 


.000886525 


3 


.000838222 


8 


.000794913 


9 


.00100100 


4 


.000939350 


9 


.000885740 


4 


.000837521 


9 


.000794281 


1000 


.00100000 


5 


.000938967 


1130 


.000884956 


5 


.000836820 


1260 


.000793651 


1 


.000999001 


6 


.000938086 


• 1 


.000884173 


6 


.000836120 


1 


.000793021 


2 


.000998004 


7 


.00093720; 


2 


.000883392 


7 


.000835422 


2 


.000792393 


3 


.000997009 


8 


.000936330 


3 


.000882612 


8 


.000834724 


3 


.000791766 


4 


.000996016 


9 


.000935454 


4 


.000881834 


9 


.000834028 


4 


.000791139 


5 


.000995025 


1070 


.000934579 


5 


.000881057 


1200 


.000833333 


5 


.000790514 


6 


.000994036 


1 


.000933707 


6 


.000880282 


1 


.000832639 


6 


.000789889 


7 


.000993049 


2 


.000932836 


7 


.000879503 


2 


.000831947 


7 


.000789266 


8 


.000992063 


3 


.000931966 


8 


.000878735 


3 


.000331255 


8 


.000788643 


9 


.000991080 


4 


.000931099 


9 


.000877963 


4 


.000830565 


9 


.000788022 


1010 


.000990099 


5 


.000930233 


1140 


.000877193 


5 


.000329875 


1270 


.000787402 


11 


.000989120 


6 


.000929368 


1 


.000376424 


6 


.000829187 


1 


.000786782 


12 


.000988142 


7 


.000928505 


2 


.000375657 


7 


.000828500 


2 


.000786163 


13 


.000987167 


8 


.000927644 


3 


.000874391 


8 


.000827815 


3 


.000785546 


14 


.000986193 


9 


.000926784 


4 


.000374126 


9 


.000827130 


4 


.000784929 


15 


.000935222 


1030 


.000925926 


5 


.000873362 


1210 


.000826446 


5 


.000784314 


16 


.000984252 


1 


.000925069 


6 


.000872600 


11 


.000825764 


6 


.000783699 


17 


.000983284 


2 


.000924214 


7 


.000871840 


12 


.000825082 


7 


.000783083 


18 


.000932318 


3 


.000923361 


8 


.000871030 


13 


.000324402 


8 


.000782473 


19 


.000981354 


4 


.000922509 


9 


.000870322 


14 


000323723 


9 


.000781861 


1020 


.000980392 


5 


.000921659 


1150 


.000869565 


15 


.000323045 


1280 


.000781250 


1 


.000979432 


6 


000920310 


1 


000368810 


16 


.000322368 


1 


.000780640 


2 


.000978474 


7 


.000919963 


2 


.000868056 


17 


.000821693 


2 


.000780031 


3 


.000977517 


8 


.000919118 


3 


.000867303 


18 


.000321018 


3 


.000779423 


4 


.000976562 


9 


.000918274 


4 


.000866551 


19 


.000320344 


4 


.000778816 


5 


.000975610 


1090 


.000917431 


5 


.000865801 


1220 


.000319672 


5 


.000778210 


6 


.000974659 


1 


.000916590 


6 


.000865052 


1 


.000819001 


6 


.000777605 


7 


.000973710 


2 


.00091575 


7 


.000864304 


2 


.000818331 


7 


.000777001 


8 


.000972763 


3 


.000914913 


8 


.000863558 


3 


.000817661 


8 


.000776397 


9 


.000971817 


4 


.00091407 


9 


.000862813 


4 


.000816993 


9 


.000775795 


10301 .000970874] 


5 


.000913242 


1160 


.000862069 


5 


.000816326 


12901.000775194 



RECIPEOCALS OF NUMBERS. 



91 



No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. • 


xVo. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


1291 


.000774593 


1356 


.000737463 


1421 


.000703730 


1486 


.000672948 


1551 .000644745 


2 


.000773994 


7 


.000736920 


2 


.000703235 


7 


.000672495 


21.000644330 


3 


.000773395 


8 


.000736377 


3 


.000702741 


8 


.000672043 


3 


.000643915 


4 


.000772797 


9 


.000735835 


4 


.000702247 


9 


.000671592 


4 


.000643501 


5 


.000772201 


1360 


.000735294 


5 


.000701754 


1490 


.000671141 


5 


.000643087 


6 


.000771605 


1 


.000734754 


6 


.000701262 


1 


.000670691 


6 


.000642673 


7 


.000771010 


2 


.000734214 


7 


.000700771 


2 


.000670241 


7 


.000642261 


8 


.000770416 


3 


.000733676 


8 


.000700280 


3 


.000669792 


8 


.000641848 


9 


.000769823 


4 


.000733138 


9 


.000699790 


4 


.000669344 


9 


.000641437 


1300 


.000769231 


5 


.000732601 


1430 


.000699301 


5 


.000668896 


1560 


.000641026 


1 


.000768639 


61.000732064 


1 


.000698812 


6 


.000668449 


J 


.000640615 


2 


.000768049 


71.000731529 


2 


.000698324 


7 


.000668003 


2 


.000640205 


3 


.000767459 


8 


.000730994 


3 


.000697837 


8 


.000667557 


3 


.000639795 


4 


.000766871 


9 


.000730460 


4 


.000697350 


9 


.000667111 


4 


.000639386 


5 


.000766283 


1370 


.000729927 


5 


.000696864 


1500 


.000666667 


5 


.000638978 


6 


.000765697 


1 


.000729395 


6 


.000696379 


1 


.000666223 


6 


.000638570 


7 


.000765111 


2 


.000728863 


7 


.000695894 


2 


.000665779 


7 


.000638162 


8 


.000764526 


3 


.000723332 


8 


.000695410 


3 


.000665336 


8 


.000637755 


9 


.000763942 


4 


.000727802 


9 


.000694927 


4 


.000664894 


9 


.000637349 


1310 


.000763359 


5 


.000727273 


1440 


.000694444 


5 


.000664452 


1570 


.000636943 


11 


.000762776 


6 


.000726744 


1 


.000693962 


6 


.000664011 


1 


.000636.537 


12 


.000762195 


7 


.000726216 


2 


.000693481 


7 


.000663570 


2 


.000636132 


13 


.000761615 


8 


.000725689 


3 


.000693001 


8 


.000663130 


3 


.000635728 


14 


.000761035 


9 


.000725163 


4 


.000692521 


9 


.000662691 


4 


.000635324 


15 


.000760456 


1380 


.000724638 


5 


.000692041 


1510 


.000662252 


5 


.000634921 


16 


.000759878 


1 


.000724113 


6 


.000691563 


11 


.000661813 


6 


.000634518 


17 


.000759301 


2 


.000723589 


7 


.000691035 


12 


.000661376 


7 


.000634115 


18 


.000758725 


3 


.000723066 


8 


.000690608 


13 


.000660939 


8 


.000633714 


19 


.000758150 


4 


.000722543 


9 


.000690131 


14 


.000660502 


9 


.000633312 


1320 


.000757576 


5 


.000722022 


1450 


.0006S%55 


15 


.000660066 


1580 


.00063291 1 


1 


.000757002 


6 


.000721501 


1 


.000689180 


16 


.00065963 1 


1 


.000632511 


2 


.000756430 


7 


.000720930 


2 


.000638705 


17 


.000659196 


2 


.000632111 


3 


.000755858 


8 


.000720461 


3 


.000688231 


18 


.000658761 


3 


.000631712 


4 


.000755287 


9 


.000719942 


4 


.000687753 


19 


.000658328 


4 


.000631313 


5 


.000754717 


1390 


.000719424 


5 


.000687285 


1520 


.000657895 


5 


.000630915 


6 


.000754148 


1 


.000718907 


6 


.000686813 


1 


.000657462 


6 


.000630517 


7 


.000753579 


2 


.000718391 


7 


.000636341 


2 


.000657030 


7 


.000630120 


8 


.000753012 


3 


.000717875 


8 


.000685871 


3 


.000656598 


8 


.000629723 


9 


.000752445 


4 


.00071736C 


9 


.000635401 


A 


.000656168 


9 


.000629327 


1330 


.000751880 


5 


.000716846 


1460 


.000684932 


5 


.000655738 


1590 


.000628931 


1 


.000751315 


6 


.000716332 


1 


.000634463 


6 


.000655308 


1 


.000628536 


2 


.000750750 


7 


.000715820 


2 


.000683994 


7 


.000654879 


2 


.000628141 


3 


.000750187 


8 


.000715308 


3 


.000633527 


8 


.000654450 


3 


.000627746 


4 


.00074%25 


9 


.000714796 


4 


.000633060 


9 


.000654022 


4 


.000627353 


5 


.000749064 


1400 


.000714286 


5 


.000682594 


1530 


.000653595 


5 


.000626959 


6 


.000748503 


1 


.000713776 


6 


.000682128 


1 


.000653168 


6 


.000626566 


7 


.000747943 


2 


.000713267 


7 


.000681663 


2 


.000652742 


7 


.000626174 


8 


.000747384 


3 


.000712758 


8 


.000681199 


3 


.000652316 


8 


.000625782 


9 


.000746826 


4 


.000712251 


.9 


.000680735 


4 


.000651890 


9 


.000625391 


1340 


.000746269 


5 


.000711744 


1470 


.000630272 


5 


.000651466 


1600 


.000625000 


1 


.000745712 


6 


.000711238 


1 


.000679810 


6 


.000651042 


2 


.000624219 


2 


.000745156 


7 


.000710732 


2 


.000679348 


7 


.000650618 


4 


.000623441 


3 


.000744602 


8 


.000710227 


3 


.000678887 


8 


.000650195 


6 


.000622665 


4 


.000744046 


9 


.000709723 


4 


.000678426 


9 


.000649773 


8 


.000621890 


5 


.000743494 


1410 


.000709220 


5 


.000677966 


1540 


.000649351 


1610 


.000621118 


6 


.000742942 


11 


.000708717 


6 


.000677507 


1 


.000648929 


12 


.000620347 


7 


.000742390 


12 


.000703215 


7 


.000677048 


2 


.000648508 


14 


.000619578 


8 


.000741840 


13 


.000707714 


8 


.000676590 


3 


.000648088 


16 


.000618812 


9 


.000741290 


14 


.000707214 


9 


.000676132 


4 


.000647668 


18 


.000618047 


!350 


.000740741 


15 


.000706714 


1480 


.000675676 


5 


.000647249 


1620 


.000617284 


1 


.000740192 


16 


.000706215 


1 


.000675219 


6 


.000646830 


2 


.000616523 


2 


.000739645 


17 


.000705716 


2 


.000674764 


7 


.000646412 


4 


.000615763 


3 


.000739098 


J8 


.000705219 


3 


.000674309 


8 


.000645995 


6 


.000615006 


4 


.000738552 


19 


.000704722 


4 


.000673854 


9 


.000645578 


8 


.000614250 


5 


.000738007 


1420 .000704225 


5 


.000673401 


1550 


.000645161 


1630 


.000613497 



92 



MATHEMATICAL TABLES. 



No. 


Recipro- 
caL 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


No. 


Recipro- 
cal. 


1632 


.000612745 


1706 


.000586166 


1780 


.000561798 


1854 


.000539374 


1928 


.000518672 


4 


.00061 1995 


8 


.000585480 


2 


.000561167 


6 


.000538793 


1930 


.000518135 


6 


.00061 1247 


1710 


.000584795 


4 


.000560538 


8 


.000538213 


2 


.000517599 


8 


.000610500 


12 


.000584112 


6 


.000559910 


1860 


.000537634 


4 


.000517063 


1640 


.000609756 


14 


.000583430 


8 


.000559284 


2 


.000537057 


6 


.000516528 


2 


.000609013 


16 


.000582750 


1790 


.000558659 


4 


.000536480 


8 


.000515996 


4 


.000603272 


18 


.000582072 


2 


.000558035 


6 


.000535905 


1940 


.000515464 


6 


.000607533 


1720 


.000581395 


4 


.000557413 


8 


.000535332 


2 


.000514933 


8 


.0006067% 


2 


.000580720 


6 


.000556793 


1870 


.000534759 


4 


.000514403 


1650 


.000606061 


4 


.000580046 


8 


.000556174 


2 


.000534188 


6 


.000513874 


2 


.000605327 


6 


.000579374 


1800 


.000555556 


4 


.000533618 


8 


.000513347 


4 


.000604595 


8 


.000578704 


2 


.000554939 


6 


.000533049 


1950 


.000512820 


6 


.000603865 


1730 


.000578035 


4 


.000554324 


8 


.000532481 


2 


.000512295 


8 


.000603136 


2 


.000577367 


6 


.000553710 


1880 


.000531915 


4 


.000511770 


1660 


.000602410 


4 


.000576701 


8 


.000553097 


2 


.000531350 


6 


.000511247 


2 


.000601685 


6 


.000576037 


1810 


.000552486 


4 


.000530785 


8 


.000510725 


4 


.000500962 


8 


.000575374 


12 


.000551876 


6 


.000530222 


1960 


.000510204 


6 


.000600240 


1740 


.000574713 


14 


.000551268 


8 


.000529661 


2 


.000509684 


8 


.000599520 


2 


.000574053 


16 


.000550661 


1890 


.000529100 


4 


.000509165 


1670 


.000598802 


4 


.000573394 


18 


.000550055 


2 


.000528541 


6 


.000508647 


2 


.000598086 


6 


.000572737 


1820 


.000549451 


4 


.000527983 


8 


.000508130 


4 


.000597371 


8 


.000572082 


2 


.000548848 


6 


.000527426 


1970 


.000507614 


6 


.000596658 


1750 


.000571429 


4 


.000548246 


8 


.000526870 


2 


.000507099 


8 


000595947 


2 


.000570776 


6 


.000547645 


1900 


.000526316 


4 


.000506585 


1680 


.000595238 


4 


.000570125 


8 


.000547046 


2 


.000525762 


6 


.000506073 


2 


000594530 


6 


000569476 


1830 


.000546448 


4 


.000525210 


8 


.000505561 


4 


.000593824 


8 


.000568828 


2 


.000545851 


6 


.000524659 


1980 


.000505051 


6 


.000593120 


1760 


.000568182 


4 


.000545256 


8 


.000524109 


2 


.000504541 


8 


.000592417 


2 


.000567537 


6 


.000544662 


1910 


.000523560 


4 


.000504032 


1690 


.000591716 


4 


.000566893 


8 


.000544069 


12 


.000523012 


6 


.000503524 


2 


.000591017 


6 


.000566251 


1840 


.000543478 


14 


.000522466 


8 


.000503018 


4 


.000590319 


8 


.00056561 1 


2 


.000542888 


16 


.000521920 


1990 


.000502513 


6 


.000589622 


1770 


.000564972 


4 


.000542299 


18 


.000521376 


2 


.000502008 


8 


.000588928 


2 


.000564334 


6 


.000541711 


1920 


.000520833 


4 


.000501504 


1700 


.000588235 


4 


.000563698 


, 8 


.000541125 


2 


.000520291 


6 


.000501002 


2 


.000587544 


6 


.000563063 


1850 


.000540540 


4 


.000519750 


8 


.000500501 


4 


.000586854 


8 


.000562430 


2 


.000539957 


6 


.000519211 


2000 


.000500000 



Use of reciprocals. — Reciprocals may be conveniently used to facili- 
tate computations in long division. Instead of dividing as usual, multiply 
the dividend by the reciprocal of the divisor. The method is especially 
useful when many different dividends are required to be divided by the 
same divisor. In this case find the reciprocal of the divisor, and make a 
small table of its multiples up to 9 times, and use this as a multiplication- 
table instead of actually performing the multiplication in each case. 

Example. — 9871 and several other numbers are to be divided by 1638. 
The reciprocal of 1638 is .000610500. 
Multiples of the 
reciprocal: 

1. .0006105 The table of multiples is made by continuous addi- 

2. .0012210 tion of 6105. The tenth line is written to check the 

3. .0018315 accuracy of the addition, but it is not afterwards used. 

4. .0024420 Operation: 

5. .0030525 Dividend 9871 

6. .0036630 Take from table 1 0006105 

7. .0042735 7 0.042735 

8. .0048840 8 00.48840 

9. .0054945 9 005.4945 

10. .0061050 

Quotient 6.0262455 

Correct quotient by direct division 6.0262515 

The result will generally be correct to as many figures as there are signi- 
ficant figures in the reciprocal, less one, and the error of the next figure will 
in general not exceed one. In the above example the reciprocal has six 
significant figures, 610500, and the result is correct to five places of figures. 



SQUARES, CUBES, SQUARE AND CUBE ROOTS. 93 



SQUARES, CUBES, SQUARE ROOTS AND CUBE ROOTS OF 
NU3IBERS FR03I 0.1 TO 1600. 



No. 


Square. 


Cube. 


Sq. 
Root. 


Cube 
Root. 


No. 


Square, 


Cube. 


Sq. 
Root. 


Cube 
Root. 


1 


.01 


.001 


.3162 


.4642 


3.1 


9.61 


29.791 


1.761 


1.458 


.15 


.0225 


.0034 


.3873 


.5313 


.2 


10.24 


32.768 


1.789 


1.474 


2 


.04 


.008 


.4472 


.5846 


.3 


10.89 


35.937 


1.817 


1.489 


.25 


.0625 


.0156 


.500 


.6300 


.4 


11.56 


39.304 


1.844 


1.504 


.3 


o09 


.027 


.5477 


.6694 


,5 


12.2!) 


42.875 


1.871 


1.518 


.35 


.1225 


.0429 


.5916 


.7047 


.6 


12.96 


46.656 


1.897 


1.533 


.4 


16 


.064 


.6325 


.7368 


.7 


13.69 


50.653 


1.924 


1.547 


.45 


.2025 


.0911 


.6708 


.7663 


.8 


14.44 


54.872 


1.949 


1.560 


.5 


.25 


.125 


.7071 


.7937 


.9 


15.21 


59.319 


1.975 


1.574 


.55 


.3025 


.1664 


.7416 


.8193 


4. 


16. 


64. 


2. 


1.5874 


.6 


.36 


.216 


.7746 


.8434 


.1 


16.81 


68.921 


2.025 


1.601 


.65 


.4225 


.2746 


.8062 


.8662 


.2 


17.64 


74.088 


2.049 


1.613 


.7 


.49 


.343 


.8367 


.8879 


.3 


18.49 


79.507 


2.074 


1.626 


.75 


.5625 


.4219 


.8660 


.9086 


.4 


19.36 


85.184 


2.098 


1.639 


,8 


.64 


.512 


.8944 


.9283 


.5 


20.25 


91.125 


2.121 


1.651 


.85 


.7225 


.6141 


.9219 


.9473 


.6 


21.16 


97.336 


2.145 


1.663 


.9 


.81 


.729 


.9487 


.9655 


.7 


22.09 


103.823 


2.168 


1.675 


.95 


.9025 


.8574 


.9747 


.9830 


.8 


23.04 


n 0.592 


2.191 


1.687 


1. 


1. 


1. 


1. 


1. 


.9 


24.01 


117.649 


2.214 


1.698 


1.05 


1.1025 


1.158 


1.025 


1.016 


5. 


25. 


125. 


2.2361 


1.7100 


1.1 


1.21 


1.331 


1.049 


1.032 


.1 


26.01 


132.651 


2.258 


1.721 


1.15 


1.3225 


1.521 


1.072 


1.048 


.2 


27.04 


140.608 


2.280 


1.732 


1.2 


1.44 


1.728 


1.095 


1.063 


.3 


28.09 


148.877 


2.302 


1.744 


1.25 


1.5625 


1.953 


1.118 


1.077 


.4 


29.16 


157.464 


2.324 


1.754 


1.3 


1.69 


2.197 


1.140 


1.091 


.5 


30.25 


166.375 


2.345 


1.765 


1.35 


1.8225 


2.460 


1.162 


1.105 


.6 


31.36 


175.616 


2.366 


1.776 


1.4 


1.96 


2.744 


1.183 


1.119 


.7 


32.49 


185.193 


2.387 


1.786 


1.45 


2.1025 


3.049 


1.204 


1.132 


.8 


33.64 


195.112 


2.408 


1.797 


1.5 


2.25 


3.375 


1.2247 


1.1447 


.9 


34.81 


205.379 


2.429 


1.807 


1.55 


2.4025 


3.724 


1.245 


1.157 


G. 


36. 


216. 


2.4495 


1.81^1 


1.6 


2.56 


4.096 


1.265 


1.170 


.1 


37.21 


226.981 


2.470 


1.827 


1.65 


2.7225 


4.492 


1.285 


1.182 


.2 


38.44 


238.328 


2.490 


1.837 


1.7 


2.89 


4.913 


1.304 


1.193 


.3 


39.69 


250.047 


2.510 


1.847 


1.75 


3.0625 


5.359 


1.323 


1.205 


.4 


40.96 


262.144 


2.530 


1.85/ 


1.8 


3.24 


5.832 


1.342 


1.216 


.5 


42.25 


274.625 


2.550 


1.866 


1.85 


3.4225 


6.332 


1.360 


1.228 


.6 


43.56 


287.496 


2.569 


1.876 


1.9 


3.61 


6.859 


1.378 


1.239 


.7 


44.89 


300.763 


2.588 


1.885 


1.95 


3.8025 


7.415 


1.396 


1.249 


.8 


46.24 


314.432 


2.608 


1.895 


2. 


4. 


8. 


1.4142 


1.2599 


.9 


47.61 


328.509 


2.627 


1.904 


.1 


4.41 


9.261 


1.449 


1.281 


7. 


49. 


343. 


2.6458 


1.9129 


.2 


4.84 


10.648 


1.483 


1.301 


o1 


50.41 


357.911 


2.665 


1.922 


.3 


5.29 


12.167 


1.517 


1.320 


.2 


51.84 


373.248 


2.683 


1.931 


.4 


5.76 


13.824 


1.549 


1.339 


.3 


53.29 


389.017 


2.702 


1.940 


.5 


6.25 


15.625 


1.581 


1.357 


.4 


54.76 


405.224 


2.720 


1.949 


.6 


6.76 


17.576 


1.612 


1.375 


.5 


56.25 


421.875 


2.739 


1.957 


.7 


7.29 


19.683 


1.643 


1.392 


.6 


57.76 


438.976 


2.757 


1.966 


,8 


7.84 


21.952 


1.673 


1.409 


.7 


59.29 


456.533 


2.775 


1.975 


.9 


8.41 


24.389 


1.703 


1.426 


.8 


60.84 


474.552 


2.793 


1.983 


3. 


9, 


27. 


1.7321 


1,4422 


.9 


62.41 


493.039 


2.811 


1.992 



94 



MATHEMATICAL TABLES. 



No. 


Square. 


Cube. 


Sq. 
Root. 


Cube 
Root. 


No. 


Square 


Cube. 


Sq. 
Root. 


Cube 

Root. 


8. 


64. 


512. 


2.8284 


2. 


45 


2025 


9112.1 


6.7082 


3.5569 


.1 


65.61 


531.441 


2.846 


2.008 


46 


2116 


97336 


6.7823 


3.5830 


.2 


67.24 


551.368 


2.864 


2.017 


47 


2209 


103823 


6.8557 


3.6088 


.3 


68.89 


571.787 


2.881 


2.025 


48 


2304 


110592 


6.9282 


3.6342 


.4 


70.56 


592.704 


2.898 


2.033 


49 


2401 


1 1 7649 


7. 


3.6593 


.5 


72.25 


614.125 


2.915 


2.041 


50 


2500 


125000 


7.0711 


3.6840 


.6 


73.96 


636.056 


2.933 


2.049 


51 


2601 


132651 


7.1414 


3.7084 


.7 


75.69 


658.503 


2.950 


2.057 


52 


2704 


1 40608 


7.2111 


3.7325 


.8 


77.44 


681.472 


2.966 


2.065 


53 


2809 


148877 


7.2801 


3.7563 


.9 


79.21 


704.969 


2.983 


2.072 


54 


2916 


157464 


7.3485 


3.7798 


9. 


81. 


729. 


3. 


2.0801 


55 


3025 


166375 


7.4162 


3.8030 


.1 


82.81 


753.571 


3.017 


2.088 


56 


3136 


175616 


7.4833 


3.8259 


.2 


84.64 


778.688 


3.033 


2.095 


57 


3249 


185193 


7.5498 


3.8485 


.3 


86.49 


804.357 


3.050 


2.103 


58 


3364 


195112 


7.6158 


3.8709 


.4 


88.36 


830.584 


3.066 


2.110 


59 


3481 


205379 


7.6811 


3.6930 


.5 


90.25 


857.375 


3.082 


2.118 


60 


3600 


2 1 6000 


7.7460 


3.9149 


.6 


92.16 


884.736 


3.098 


2.125 


61 


3721 


226981 


7.8102 


3.9365 


.7 


94.09 


912.673 


3.114 


2.133 


62 


3844 


238328 


7.8740 


3.9579 


.8 


96.04 


941.192 


3.130 


2.140 


63 


3969 


250047 


7.9373 


3.9791 


.9 


98.01 


970.299 


3.146 


2.147 


64 


4096 


262144 


8. 


4. 


10 


100 


1000 


3.1623 


2.1544 


65 


4225 


274625 


8.0623 


4.0207 


11 


121 


1331 


3.3166 


2.2240 


66 


4356 


287496 


8.1240 


4.0412 


12 


144 


1728 


3.4641 


2.2894 


67 


4489 


300763 


8.1854 


4.0615 


13 


169 


2197 


3.6056 


2.3513 


68 


4624 


314432 


8.2462 


4.0817 


14 


196 


2744 


3.7417 


2.4101 


69 


4761 


328509 


8.3066 


4.1016 


15 


225 


3375 


3.8730 


2.4662 


70 


4900 


343000 


8.3666 


4.1213 


16 


256 


4096 


4. 


2.5198 


71 


5041 


357911 


8.4261 


4.1408 


17 


289 


4913 


4.1231 


2.5713 


72 


5184 


373248 


8.4853 


4.1602 


18 


324 


5832 


4.2426 


2.6207 


73 


5329 


389017 


8.5440 


4.1793 


19 


361 


6859 


4.3589 


2.6684 


74 


5476 


405224 


8.6023 


4.1983 


20 


400 


8000 


4.4721 


2.7144 


75 


5625 


421875 


8.6603 


4.2172 


21 


441 


9261 


4.5826 


2.7589 


76 


5776 


438976 


8.7178 


4.2358 


22 


484 


10648 


4.6904 


2.8020 


77 


5929 


456533 


8.7750 


4.2543 


23 


529 


12167 


4.7958 


2.8439 


78 


6084 


474552 


8.8318 


4.2727 


24 


576 


13824 


4.8990 


2.8845 


79 


6241 


493039 


8.8882 


4.2908 


25 


625 


15625 


5. 


2.9240 


80 


6400 


512000 


8.9443 


4.3089 


26 


676 


17576 


5.0990 


2.9625 


81 


6561 


531441 


9. 


4.3267 


27 


729 


19683 


5.1962 


3. 


82 


6724 


551368 


9.0554 


4.3445 


28 


784 


21952 


5.2915 


3.0366 


83 


6889 


571787 


9.1104 


4.3621 


29 


841 


24389 


5.3852 


3.0723 


84 


7056 


592704 


9.1652 


4.3795 


30 


900 


27000 


5.4772 


3.1072 


85 


7225 


614125 


9.2195 


4.3968 


31 


961 


29791 


5.5678 


3.1414 


86 


7396 


636056 


9.2736 


4.4140 


32 


1024 


32768 


5.6569 


3.1748 


87 


7569 


658503 


9.3276 


4.4310 


33 


1089 


35937 


5.7446 


3.2075 


88 


7744' 


681472 


9.3808 


4.448u 


34 


1156 


39304 


5.8310 


3.2396 


89 


7921 


704969 


9.4340 


4.4647 


35 


1225 


42875 


5.9161 


3.2711 


90 


8100 


729000 


9.4868 


4.4814 


36 


1296 


46656 


6. 


3.3019 


91 


8281 


753571 


9.5394 


4.4979 


37 


1369 


50653 


6.0828 


3.3322 


92 


8464 


778688 


9.5917 


4.5144 


38 


1444 


54872 


6.1644 


3.3620 


93 


8649 


804357 


9.6437 


4.5307 


39 


1521 


59319 


6.2450 


3.3912 


94 


8836 


830584 


9.6954 


4.5468 


40 


1600 


64000 


6.3246 


3.4200 


95 


9025 


857375 


9.7468 


4.5629 


41 


1681 


68921 


6 4031 


3.4482 


96 


9216 


884736 


9.7980 


4.5789 


42 


1764 


74088 


6.4807 


3.4760 


97 


9409 


912673 


9.8489 


4.5947 


43 


1849 


79507 


6.5574 


3.5034 


98 


9604 


941192 


9.8995 


4.6104 


44 


1936 


85184 


6.6332 


3.5303 


99 


9801 


970299J 


9.9499 


4.6261 



SQUARES, CUBES, SQUARE AND CUBE ROOTS. 95 



No. 


Sq. 


Cube- 


Sq. 
Root. 


Cube 
Root. 


No. 


Square. 


Cube. 


Sq. 
Root. 


Cube 
Root. 


100 


10000 


1000000 


10. 


4.6416 


155 


24025 


3723875 


12.4499 


5.3717 


101 


10201 


1030301 


10.0499 


4.6570 


156 


24336 


3796416 


12.4900 


5.3832 


102 


10404 


1061208 


10.0995 


4.6723 


157 


24649 


3869893 


12.5300 


5.3947 


103 


10609 


1092727 


10.1489 


4.6875 


158 


24964 


3944312 


12.5698 


5.4061 


104 


10816 


1124864 


10.1980 


4.7027 


159 


25281 


4019679 


12.6095 


5.4175 


105 


11025 


1157625 


10.2470 


4.7177 


160 


25600 


4096000 


12.6491 


5.4288 


106 


11236 


1191016 


10.2956 


4.7326 


161 


25921 


4173281 


12.6886 


5.4401 


107 


11449 


1225043 


10.3441 


4.7475 


162 


26244 


4251528 


12.7279 


5.4514 


lOS 


11664 


1259712 


10.3923 


4.7622 


163 


26569 


4330747 


12.7671 


5.4626 


109 


11881 


1295029 


10.4403 


4.7769 


164 


26896 


4410944 


12.8062 


5.4737 


110 


12100 


1331000 


10.4881 


4.7914 


165 


27225 


4492125 


12.8452 


5.4848 


111 


12321 


1367631 


10.5357 


4.8059 


166 


27556 


4574296 


12.8841 


5.4959 


112 


12544 


1404928 


10.5830 


4.8203 


167 


27889 


4657463 


12.9228 


5.5069 


113 


12769 


1442897 


10.6301 


4.8346 


168 


28224 


4741632 


12.9615 


5.5178 


114 


12996 


1481544 


10.6771 


4.8488 


169 


28561 


4826809 


13.0000 


5.5288 


115 


13225 


1520875 


10.7238 


4.8629 


170 


28900 


4913000 


13.0384 


5.5397 


116 


13456 


1560896 


10.7703 


4.8770 


171 


29241 


50002 1 1 


13.0767 


5.5505 


117 


13689 


1601613 


10.8167 


4.8910 


172 


29584 


5088448 


13.1149 


5.5613 


113 


13924 


1643032 


10.8628 


4.9049 


173 


29929 


5177747 


13.1529 


5.5721 


119 


14161 


1685159 


10.9087 


4.9187 


174 


30276 


5268024 


13.1909 


5.5828 


120 


14400 


1728000 


10.9545 


4.9324 


175 


30625 


5359375 


13.2288 


5.5934 


121 


14641 


1771561 


1 1 .0000 


4.9461 


176 


30976 


5451776 


13.2665 


5.6041 


122 


14884 


1815848 


11.0454 


4.9597 


177 


31329 


5545233 


13.3041 


5.6147 


123 


15129 


1860867 


1 1 .0905 


4.9732 


178 


31684 


5639752 


13.3417 


5.6252 


124 


15376 


1 906624 


11.1355 


4.9866 


179 


32041 


5735339 


13.3791 


5.6357 


125 


15625 


1953125 


11.1803 


5.0000 


180 


32400 


5832000 


13.4164 


5.6462 


126 


15876 


2000376 


11.2250 


5.0133 


181 


32761 


5929741 


13.4536 


5.6567 


127 


16129 


2048383 


11.2694 


5.0265 


182 


33124 


6028568 


13.4907 


5.6671 


123 


16384 


2097152 


11.3137 


5.0397 


183 


33489 


6128487 


13.5277 


5.6774 


129 


16641 


2146639 


11.3578 


5.0528 


184 


33856 


6229504 


13.5647 


5.6877 


130 


16900 


2197000 


11.4018 


5.0658 


185 


34225 


6331625 


13.6015 


5.6980 


131 


17161 


2248091 


11.4455 


5.0788 


186 


34596 


6434856 


13.6382 


5.7083 


132 


17424 


2299968 


11.4891 


5.0916 


187 


34969 


6539203 


13.6748 


5.7185 


133 


17639 


2352637 


11.5326 


5.1045 


188 


35344 


6644672 


13.7113 


5.7287 


134 


17956 


2406104 


11.5758 


5.1172 


189 


35721 


6751269 


13.7477 


5.7388 


135 


18225 


2460375 


11.6190 


5.1299 


190 


36100 


6859000 


13.7840 


5.7489 


136 


18496 


2515456 


11.6619 


5.1426 


191 


36481 


6967871 


13.8203 


5.7590 


137 


18769 


2571353 


11.7047 


5.1551 


192 


36864 


7077888 


13.8564 


5.7690 


133 


19044 


2628072 


11.7473 


5.1676 


193 


37249 


7189057 


13.8924 


5.7790 


139 


19321 


2685619 


11.7898 


5.1801 


194 


37636 


7301384 


13.9284 


5.7890 


140 


19600 


2744000 


11.8322 


5.1925 


195 


38025 


7414875 


13.9642 


5.7989 


141 


19331 


2803221 


11.8743 


5.2048 


196 


38416 


7529536 


14.0000 


5.8088 


142 


20164 


2863288 


11.9164 


5.2171 


197 


38809 


7645373 


14.0357 


5.8186 


143 


20449 


2924207 


11.9583 


5.2293 


198 


39204 


7762392 


14.0712 


5.8285 


144 


20736 


2985984 


12.0000 


5.2415 


199 


39601 


7880599 


14.1067 


5.8383 


145 


21025 


3048625 


12.0416 


5.2536 


200 


40000 


8000000 


14.1421 


5.8480 


146 


21316 


3112136 


12.0830 


5.2656 


201 


40401 


8120601 


14.1774 


5.8578 


147 


21609 


3176523 


12.1244 


5.2776 


202 


40804 


8242408 


14.2127 


5.8675 


148 


21904 


3241792 


12.1655 


5.2896 


203 


41209 


8365427 


14.2478 


5.8771 


!49 


22201 


3307949 


12.2066 


5.3015 


204 


41616 


8489664 


14.2829 


5.8868 


150 


22500 


3375000 


12.2474 


5.3133 


205 


42025 


8615125 


14.3178 


5.8964 


151 


22801 


3442951 


12.2882 


5.3251 


206 


42436 


8741816 


14.3527 


5.9059 


152 


23104 


3511808 


12.3288 


5.3368 


207 


42849 


8869743 


14.3875 


5.9155 


153 


23409 


3581577 


12.3693 


5.3485 


208 


43264 


8998912 


14.4222 


5.9250 


154 


23716 


3652264 


' 12.4097 


5.3601 


209 


43681 


9129329 


14.4568 


5.9345 



96 



MATHEMATICAL TABLES. 



No. 


Sq. 


Cube. 


Sq. 
Root. 


Cube 
Root. 


No. 


Square. 


Cube. 


Sq. 
Root. 


Cube 
Root. 


210 


44100 


9261000 


14.4914 


5.9439 


265 


70225 


1 8609625 


16.2788 


6.4232 


211 


44521 


9393931 


14.5258 


5.9533 


266 


70756 


18821096 


16.3095 


6.4312 


212 


44944 


9528128 


14.5602 


5.9627 


267 


71289 


19034163 


16.3401 


6.4393 


213 


45369 


9663597 


14.5945 


5.9721 


268 


71824 


19248832 


16.3707 


6.4473 


214 


45796 


9800344 


14.6287 


5.9814 


269 


72361 


19465109 


16.4012 


6.4553 


215 


46225 


9938375 


14.6629 


5.9907 


270 


72900 


19683000 


16.4317 


6.4633 


216 


46656 


10077696 


14.6969 


6.0000 


271 


73441 


19902511 


16.4621 


6.4713 


217 


47089 


10218313 


14.7309 


6.0092 


272 


73984 


20123648 


16.4924 


6.4792 


218 


47524 


10360232 


14.7648 


6.0185 


273 


74529 


20346417 16.5227 


6.4872 


219 


47961 


10503459 


14.7986 


6.0277 


274 


75076 


20570824 16.5529 


6.4951 


220 


48400 


10648000 


14.8324 


6.0368 


275 


75625 


20796875 16.5831 


6.5030 


221 


48841 


10793861 


14.8661 


6.0459 


276 


76176 


21024576 16.6132 


6.5108 


222 


49284 


10941048 


14.8997 


6.0550 


277 


76729 


21253933 


16.6433 


6.5187 


223 


49729 


11089567 


14.9332 


6.0641 


278 


77284 


21484952 


16.6733 


6.5265 


224 


50176 


11239424 


14.9666 


6.0732 


279 


77841 


21717639 


16.7033 


6.5343 


225 


50625 


11390625 


15.0000 


6.0822 


280 


78400 


21952000 


16.7332 


6.542i 


226 


51076 


11543176 


15.0333 


6.0912 


281 


78961 


22188041 


16.7631 


6.5499 


227 


51529 


11697083 


15.0665 


6.1002 


282 


79524 


22425768 


16.7929 


6.5577 


228 


51984 


11852352 


15.0997 


6.1091 


283 


80089 


22665187 


16.8226 


6.5654 


229 


52441 


12008989 


15.1327 


6.1180 


284 


80656 


22906304 


16.8523 


6.5731 


230 


52900 


12167000 


15.1658 


6.1269 


285 


81225 


23149125 


16.8819 


6.5808 


231 


53361 


12326391 


15.1987 


6.1358 


286 


81796 


23393656 16.9115 


6.5885 


232 


53824 


12487168 


15.2315 


6.1446 


287 


82369 


23639903 16.9411 


6.5962 


233 


54289 


12649337 


15.2643 


6.1534 


288 


82944 


23887872 16.9706 


6.6039 


.234 


54756 


12812904 


152971 


6.1622 


289 


83521 


24137569 17.0000 


6.6115 


235 


55225 


12977875 


15.3297 


6.1710 


290 


84100 


24389000 17.0294 6.6191 


236 


55696 


13144256 


15.3623 


6.1797 


291 


84681 


24642171 17.05871 6.6267 


237 


56169 


13312053 


15.3948 


6.1885 


292 


85264 


24897088 


17.0880 6.63.43 


238 


56644 


13481272 


15.4272 


6.1972 


293 


85849 


25153757 


17.1172 


6.6419 


239 


57121 


13651919 


15.4596 


6.2058 


294 


86436 


25412184 


17.1464 


6.6494 


240 


57600 


13824000 


15.4919 


6.2145 


295 


87025 


25672375 


17.1756 


6.6569 


241 


58081 


13997521 


15.5242 


6.2231 


296 


87616 


25934336 


17.2047 


6.6644 


242 


58564 


14172488 


15.5563 


6.2317 


297 


88209 


26198073 


17.2337 


6.6719 


243 


59049 


14348907 


15.5885 


6.2403 


298 


88804 


26463592 


17.2627 


6.6794 


244 


59536 


14526784 


15.6205 


6.2488 


299 


89401 


26730899 17.2916 


6.6869 


245 


60025 


14706125 


15.6525 


6.2573 


300 


90000 


27000000 17.3205 


6.6943 


246 


60516 


14886936 


15.6844 


6.2658 


301 


90601 


27270901 


17.3494 


6.7018 


247 


61009 


15069223 


15.7162 


6.2743 


302 


91204 


27543608 


17.3781 


6.7092 


248 


61504 


15252992 


15.7480 


6.2828 


303 


91809 


27818127 


17.4069 


6.7166 


249 


62001 


15438249 


15.7797 


6.2912 


304 


92416 


28094464 


17.4356 


6.7240 


250 


62500 


15625000 


15.8114 


6.2996 


305 


93025 


28372625 


17.4642 


6.7313 


251 


63001 


15813251 


15.8430 


6.3080 


306 


93636 


28652616117.4929 


6.7387 


252 


63504 


16003008 


15.8745 


6.3164 


307 


94249 


28934443117.5214 


6.7460 


253 


64009 


16194277 


15.9060 


6.3247 


308 


94864 


29218112117.5499 


6.7533 


254 


64516 


16387064 


15.9374 


6.3330 


309 


95481 


29503629117.5784 


6.7606 


255 


65025 


16581375 


15.9687 


6.3413 


310 


96100 


29791000 17.6068 


6.7679 


256 


65536 


16777216 


16.0000 


6.3496 


311 


96721 


3008023 l| 17.6352 


6.7752 


257 


66049 


16974593 


16.0312 


63579 


312 


97344 


30371328 


17.6635 


6.7824 


258 


66564 


17173512 


16.0624 


6.3661 


313 


97969 


30664297 


17.6918 


6.7897 


259 


67081 


17373979 


16.0935 


6.3743 


314 


98596 


30959144 


17.7200 


6.7969 


260 


67600 


17576000 


16.1245 


6.3825 


315 


99225 


31255875 


17.7482 


6.8041 


261 


68121 


17779581 


16.1555 


6.3907 


316 


99856 


31554496 


17.7764 


6.8113 


262 


68644 


17984723 


16.1864 


6.3988 


317 


1 00489 


31855013 


17.8045 


6.8185 


263 


69169 


18191447 


16.2173 


6.4070 


318 


101124 


32157432 


17.8326 


6.825e 


264 


69696 


' 18399744 


16.2481 


6.4151 


319 


101761 


32461759 


17.8606 


6.8326 



SQUARES, CUBES, SQUARE AND CUBE ROOTS. 97 



Cube. 



Sq. 
Root. 



32768000 
33076161 
33386248 
33698267 
34012224 



Cube 
Root. 



34328125 
34645976 
34965783 
35287552 
356112891 



17.8885 6.8399 
17.9165 6.8470 
17.94446.8541 
17.9722 6.8612 
18.0000j6.8683 

18.0278'6.8753 
18.0555 6.8824 
18.0831 6.8894 
18.1108 6.8964 
18. 138416.9034 



35937000, 18. 1659!6. 9104 
36264691 18.1934 6.9174 
36594368 18.2209 6.9244 
36926037J18.2483i6.9313 
37259704 18.2757 6.9382 

37595375,18.3030 6.9451 
37933056 18.3303 6.9521 
38272753 18 3576 6.9589 
38614472 18.3848 6.9658 
38958219] 18.4120 6.9727 

39304000 18.4391:6.9795 
39651821 18.4662 6.9864 
40001688 18.4932 6.9932 
40353607 18.5203 7.0000 
40707584118.5472 7.0068 

41063625 18.5742 7.0136 
41421736 18.6011 7.0203 
41781923^8.6279 7.0271 
42144192118.6548 7.0338 
42508549.1 8.681 5i7.0406 



42875000; 18.7083 7.0473 
43243551 1 8.7350:7.0540 
43614208 18.7617 7.0607 
43986977 18.7883 7.0674 
44361864 18.8149 7.0740 

44738875 18.8414 7.0807 
45118016 18.8680 7.0873 
45499293 18.8944 7.0940 
458827121 18.9209 7.1006 
46268279 18.94737.1072 

46656000 18 9737 7.1138 
47045881 '19.0000 7.1204 
47437928 19.0263 7.1269 
47832147 19.05267.1335 
482285441 19.0788 7.1400 

48627125 19.10507.1466 
49027896 19.1311 7.1531 
49430863 19.1572 7.1596 
49836032 19.1833 7.1661 
50243409 19.2094 7.1726 

50653000 19.2354 7.1791 
51064811 19.2614 7.1855 
51478848 19.2873 7. 1920 
51895117|19.31327.1984 
52313624'l9.339r7.2048 



No. Square 



3751140625 

376 141376 

377 142129 

378 142884 
379,143641 

38o' 144400 

381 145161 

382 145924 

383 146689 

384 147456 



385 
386 
387 
38S 
389 



390 



1 48225 
1 48996 
149769 
150544 
151321 



1^2100 

391 1 152881 
392' 153664 
3931154449 
394:155236 

395 156025 
396*156816 
397=157609 
398 158404 
399:159201 

400 160000 
401 1160801 
402 161604 
4031162409 
404!l63216 



405 
406 

407 



164025 
164836 
165649 
408| 166464 
409 167281 



410 168100 

411 168921 

412 169744 
41 3! 170569 
4141171396 

415 172225 
4'6! 173056 
4171173889 
4181174724 
419.175561 

420 1 76400 

421 177241 

422 178084 
4231 178929 

424 1 79776 

425 180625 

426 18M76 

427 182329 
428,183184 
429' 184041 



Cube. 



52734375 
53157376 
53582633 
54010152 
54439939 

54872000 
55306341 
55 742968 
56181887 
56623104 

57066625 
57512456 
57960603 
58411072 
58863869 

59319000 
59776471 
60236288 
60698457 
61162984 

61629875 
62099136 
62570773 
63044792 
63521199 



Sq. 
Root. 



19.3649 
19.3907 
19.4165 
19.4422 
19.4679 

19.4936 
19.5192 
19.5448 
19.5704 
19.5959 

19.6214 
19.6469 
19.6723 
19.6977 
19.7231 

19.7484 
19.7737 
19.7990 
19.8242 
1 9.8494 

19.8746 
19.8997 
19.9249 
19.9499 
19.9750 



64000000 2O.C0OO 
64481201 20.0250 
64964808 20.0499 
65450827|20.0749 
65939264j20.0998 

66430125 20.1246 
66923416 20.1494 
67419143 20.1742 
67917312120.1990 
68417929 20.2237 

68921000 20 2^85 
69426531:20.2731 
69934528 20.2978 
70444997120.3224 
70957944120.3470 

71473375 20.3715 
71991296120. 3961 
72511713:20.4206 
73034632 20.4450 
73560059:20.4695 

74088000'20.4939 
74618461120.5183 
75151448 20.5426 
75686967 20.5670 
76225024120.5913 

76765625 20.6155 
77308776 20.6398 
77854483 20.6640 
78402752120.6882 
78953589'20.7123 



98 



MATHEMATICAL TABLES. 



No. 


Square 


Cube. 


Sq, 
Root. 


Cube 
Root. 


No. 


Square 


Cube. 


Sq. 
Root. 


Cub© 
Root. 


430 


1 84900 


79507000 


20.7364 7.5478 


485 


235225 


114084125 


22.0227 


7.8568 


431 


185761 


80062991 


20.7605 7.5537 


486 


236196 


114791256 


22.0454 


7 8622 


432 


186624 


80621568 


20.7846'7.5595 


487 


237169 


115501303 


22.0681 


7.8676 


433 


187489 


81182737 


20.8087 


7.5654 


488 


238144 


116214272 22.09071 


7.8730 


434 


188356 


81746504 


20.8327 


7.5712 


489 


239121 


116930169 


22.1133 


7.8784 


435 


189225 


82312875 


20.8567 


7.5770 


490 


240100 


117649000 


22.1359 


7.8837 


436 


1 90096 


82881856 


20.8806 


7.5828 


491 


241081 


118370771 


22.1585 


7.8891 


437 


190969 


83453453 


20.9045 


7.5886 


492 


242064 


119095488 


22.1811 


7.8944 


438 


191844 


84027672 


20.9284 


7.5944 


493 


243049 


119823157 


22.2036 


7.8998 


439 


192721 


84604519 


20.9523 


7.6001 


494 


244036 


120553784 


22.2261 


7.9051 


440 


193600 


85184000 


20.9762 


7.6059 


495 


245025 


121287375 


22.2486 


7.9105 


441 


194481 


85766121 


21.0000 


7.6117 


496 


246016 


122023936 


22.2711 


7.9158 


442 


195364 


86350888 


21.0238 


7.6174 


497 


247009 


122763473 


22.2935 


7.9211 


443 


196249 


86938307 


21.0476 


7.6232 


498 


248004 


123505992 


22.3159 


7.9264 


444 


197136 


87528384 


21.0713 


7.6289 


499 


249001 


124251499 


22.3383 


^93 17 


445 


198025 


88121125 


2\ .0950 


7.6346 


500 


250000 


125000000 


22.3607 


7.9370 


446 


198916 


88716536 


21.1187 


7.6403 


501 


251001 


125751501 


22.3830 


7.9423 
7.9476 


447 


199809 


89314623 


21.1424 


7.6460 


502 


252004 


126506008 


22.4054 


448 


200704 


89915392 


21.1660 


7.6517 


503 


253009 


127263527 


22.4277 


7.9528 


449 


201601 


905 1 8849 


21.1896 


7.6574 


504 


254016 


128024064 


22.4499 


7.9581 


450 


202500 


91125000 


21.2132 


7.6631 


505 


255025 


128787625 


22..'.722 


7.9634 


451 


203401 


91733851 


21.2368 


7.6688 


506 


256036 


129554216 


22.4944 


7.9686 


452 


204304 


92345408 


21.2603 


7.6744 


507 


257049 


130323843 


22.5167 


7 9739 


453 


205209 


92959677 


21.2838 


7.6800 


508 


258064 


131096512 


22.5389 


7.9791 


454 


206116 


93576664 


21.3073 


7.6857 


509 


259081 


131872229 


22.5610 


7.9843 


455 


207025 


94196375 


21.3307 


7.6914 


510 


260100 


132651000 


22.5832 


7.9896 


456 


207936 


94818816 


21.3542 


7.6970 


511 


261121 


13343283 1 


22.6053 


7.9948 


457 


208849 


95443993 


21.3776 


7.7026 


512 


262144 


134217728 


22.6274 


8.0000 


458 


209764 


96071912 


21.4009 


7.7082 


513 


263169 


135005697 


22.6495 


8.0052 


459 


210681 


96702579 


21.4243 


7.7138 


514 


264196 


135796744 


22.6716 


8.0104 


460 


211600 


97336000 


21.4476 


7.7194 


515 


265225 


136590875 


22.6936 


8.0156 


461 


212521 


97972181 


21.4709 


7.7250 


516 


266256 


137388096 


22.7156 


8.0208 


462 


213444 


9861 1128 


2 1 .4942 


7.7306 


517 


267289 


138188413 


22.7376 


8.0260 


463 


214369 


99252847 


21.5174 


7.7362 


518 


268324 


138991832 


22.7596 


8.0311 


464 


215296 


99897344 


21.5407 


7.7418 


519 


269361 


139798359 


22.7816 


8.0363 


465 


216225 


100544625 


21.5639 


7.7473 


520 


270400 


140608000 


22.8035 


8.0415 


466 


217156 


101194696 


21.5870 


7.7529 


521 


271441 


141420761 


22.8254 


8.0466 


467 


218089 


101847563 


21.6102 


7.7584 


522 


272484 


142236648 


22.8473 


8.0517 


468 


219024 


102503232 


21.6333 


7.7639 


523 


273529 


143055667 


22.8692 


8.0569 


469 


219961 


103161709 


21.6564 


7.7695 


524 


274576 


143877824 


22.8910 


8.062C 


470 


220900 


103823000 


21.6795 


7.7750 


525 


275625 


144703125 


22.9129 


8.0671 


471 


221841 


1044871 11 


21.7025 


7.7805 


526 


276676 


145531576 


22.9347 


8.0723 


472 


222784 


105154048 


21.7256 


7.7860 


527 


277729 


146363183 


22.9565 


8.0774 


473 


223729 


105823817 


21.7486 


7.7915 


528 


278784 


147197952 


22.9783 


8.0825 


474 


224676 


106496424 


21.7715 


7.7970 


529 


279841 


148035889 


23.0000 


8.0876 


475 


225625 


107171875 


21.7945 


7.8025 


530 


280900 


148877000 


23.0217 


8.0927 


476 


226576 


107850176 


21.8174 


7.8079 


531 


281961 


149721291 


23.0434 


8.0978 


477 


227529 


108531333 


21.8403 


7.8134 


532 


283024 


150568768 


23.0651 


8.1028 


478 


228484 


109215352 


21.8632 


7.8188 


533 


284089 


151419437 


23.0868 


8.1075 


479 


229441 


109902239 


21.8861 


7.8243 


534 


285156 


152273304 


23.1084 


8.1 13C 


480 


230400 


1 1 0592000 


21.9089 


7.8297 


535 


286225 


153130375 


23.1301 


8.n8C 


481 


231361 


1 1 1284641 


21.9317 


7.8352 


536 


287296 


153990656 


23.1517 


8.1231 


482 


232324 


1 11980168 


21.9545 


7.8406 


537 


288369 


154854153 


23.1733 


8.1281 


483 


233289 


112678587 


21.9773 


7.8460 


538 


289444 


155720872 


23.1948 


8.1332 


484 


234256 


113379904 


22.0000 


7.8514 


539 


290521 


156590819 


23.2164 


8.1382 



SQUARES, CUBES, SQUARE AND CUBE ROOTS. 99 



No. Square. 



540 291600 
541) 292681 
542 293764 
294849 
295936 

297025 
298116 
299209 
300304 
301401 

302500 
303601 
304704 
305809 
306916 

308025 
309136 
310249 
311364 
312481 

313600 
314721 
315844 
316969 
318096 

319225 
320356 
321489 
322624 
323761 

324900 
326041 
327184 
328329 
329476 

575 330625 

576 331776 
332929 
334084 
335241 

336400 
337561 
338724 
339889 
341056 

342225 
343396 
344569 
345744 
34692 1 



Cube. 



Sq. Cube 
Root. Root. 



157464000 23.2379 8.1433 
158340421;23.2594 8.1483 
15922008SI 23. 2809 8.1533 
160103007 23.3b24 8.1583 
160989184 23.3238 8.1633 



161878625 
162771336 
163667323 
164566592 
165469149 

166375000 
167284151 
168196608 
169112377 
170031464 



23.3452 8.1683 
23.3666 8.1733 



23.3880 
23.4094 
23.4307 

23.4521 
23.4734 
23.4947 
23.5160 
23.5372 



170953875 23.5584 
171879616123.5797 
172808693123.6008 
1 73741 112|23. 6220 
174676879 23.6432 



8.1783 
8.1833 
8.1882 

8.1932 
8.1982 
8.2031 
8.2081 
8.2130 

8.2180 
8.2229 
8.2278 
8.2327 
8.2377 



175616000 23.6643 8.2426 
176558481 23. 6854 8.2475 
177504328 23.7065 8.2524 



178453547 23.7276 
179406144 23.7487 



180362125 
181321496 
182284263 
183250432 
184220009 

185193000 
186169411 
187149248 
188132517 
189119224 

190109375 
191102976 
192100033 
193100552 
194104539 

195112000 
196122941 
197137368 
198155287 
199176704 



23.7697 
23.7908 
23.8118 
23.8328 
23.8537 

23.8747 
23.8956 
23.9165 
23.9374 
23.9583 



8.2573 
8.2621 

8.2670 
8.2719 
8.2763 
8.2816 
8.2865 

8.2913 
8.2962 
8.3010 
8.3059 
8.3107 



23.9792 8.3155 
24.0000; 8.3203 
24.0208:8.3251 
24.0416;8.3300 
24.0624 8.3348 



24.0832 
24.1039 
24.1247 
24.1454 
24.1661 



8.3396 
8.3443 
8.3491 
8.3539 
8.3587 



200201625 24.1868 8.3634 
201230056 24.2074 8.3682 
202262003; 24.2281 8.3730 
203297472' 24.2487 8.3777 
204336469124.2693 8.3825 

590 348100 205379000 24.2899 8.3872 

591i 349281 206425071 [24.3105 8 3919 

592 350464 207474688 24.33 1 1 8.3967 

593 35 1 649|208527857|24.35 1 618.401 4 
594' 352836^209584584 24. 3721 '8 4061 



No. 



595 

596 
597 
598 
599 

600 
601 
602 
603 
604 

605 
606 
607 
608 
609 

610 
611 
612 
613 
614 

615 
616 
617 
618 
619 

620 
621 
622 
623 
624 

625 
626 
627 
628 
629 

630 
631 
632 
633 
634 

635 
636 
637 

638 
639 



640 
641 
642 



Square 



354025 
355216 
356409 
357604 
358801 

360000 
361201 
362404 
363609 
364816 

366025 
367236 
36S449 
369664 
370881 

372100 
373321 
374544 
375769 
376996 

378225 
379456 
380689 
381924 
383161 

384400 
385641 
386884 
388129 
389376 

390625 
391876 
393129 
394384 
395641 

396900 
398161 
399424 
400689 
401956 

403225 
404496 
405769 
407044 
408321 



210644875 24.3926 
211708736 24.4131 



409600 
410881 
412164 

643 413449 

644 414736 



645 
646 
647 
648 
649 



Cube. 



Sq. 
Root. 



212776173 
213847192 
214921799 

216000000 
217081801 
218167203 
219256227 
220348864 

221445125 
222545016 
223648543 
224755712 
225866529 

226981000 
228099131 
229220928 
230346397 
231475544 

232608375 
233744896 
234885113 
236029032 
237176659 

238328000 
239483061 
240641848 
241804367 
242970624 

244140625 
245314376 
246491883 
247673152 
248858189 

250047000 
251239591 
252435968 
253636137 
254840104 

256047875 
257259456 
258474853 
259694072 
260917119 

262144000 
263374721 
264609288 
265847707 
267089984 



416025 263336125 
417316 269586136 
418609 270840O73 
4199041 272097792 
421201 273359449 



24.4336 
24.4540 
24.4745 

24.4949 8.4343 
24.5153 8.4390 
24.5357 
24.5561 
24.5764 

24.5967 
24.6171 
24.6374 
24.6577 
24.6779 

24.6982 
24.7184 
24.7386 
24.7588 
24.7790 

24.7992 
24.8193 
24.8395 
24.8596 
24.8797 

24.8998 
24.9199 
24.9399 
24.9600 
24.9800 

25.0000 
25.0200 
25.0400 
25.0599 
25.0799 

25.0998 
25.1197 
25.1396 
25.1595 
25.1794 

25.1992 
25.2190 
25.2389 
25.2587 
25.2784 

25.2982 
25.3180 
25.3377 
25.3574 
25.3772 

25.3969 
25.4165 
25.4362 
25.4558 
25.4755 



100 



MATHEMATICAL TABLES. 



Ko 


Square. 


Cube. 


Sq. 
Root. 


Cube 
Root. 


No. 


Square 


Cube. 


Sq. 
Root. 


Cube 
Root. 


650 


422500 


274625000 


25.4951 


8.6624 


705 


497025 


350402625 


26.5518 


8.9001 


651 


423801 


275894451 


25.5147 


8.6668 


706 


498436 


351895816 


26.5707 


8.9043 


652 


425104 


277167808 


25.5343 


8.6713 


707 


499849 


353393243 


26.5895 


8.9085 


653 


426409 


278445077 


25.5539 


8.6757 


708 


501264 


354894912 


26.6083 


8.9127 


654 


427716 


279726264 


25.5734 


8.6801 


709 


502681 


356400829 


26.6271 


8.9169 


655 


429025 


281011375 


25.5930 


8.6845 


710 


504100 


357911000 


26.6458 


8.9211 


656 


430336 


282300416 


25.6125 


8.6890 


711 


505521 


359425431 


26.6646 


8.9253 


657 


431649 


283593393 


25.6320 


8.6934 


712 


506944 


360944128 


26.6833 


8.9295 


658 


432964 


284890312 


25.6515 


8.6978 


713 


508369 


362467097 


26.7021 


8.9337 


659 


434281 


286191179 


25.6710 


8.7022 


714 


509796 


363994344 


26.7208 


8.9378 


660 


435600 


287496000 


25.6905 


8.7066 


715 


511225 


365525875 


26.7395 


8.9420 


661 


436921 


288804781 


25.7099 


8.7110 


716 


512656 


367061696 


26.7582 


8.9462 


662 


438244 


290117528 


25.7294 


8.7154 


717 


514089 


368601813 


26.7769 


8.9503 


663 


439569 


291434247 


25.7488 


8.7198 


718 


515524 


370146232 


26.7955 


8.9545 


664 


440896 


292754944 


25.7682 


8.7241 


719 


516961 


371694959 


26.8142 


8.9587 


665 


442225 


294079625 


25.7876 


8.7285 


720 


518400 


373248000 


26.8328 


8.9628 


666 


443556 


295408296 


25.8070 


8.7329 


721 


519841 


374805361 


26.8514 


8.9670 


667 


444889 


296740963 


25.8263 


8.7373 


722 


521284 


376367048 


26.8701 


8.9711 


663 


446224 


298077632 


25.8457 


8.7<16 


723 


522729 


377933067 


26.8887 


8.9752 


669 


447561 


299418309 


25.8650 


8.7460 


724 


524176 


379503424 


26.9072 


8.9794 


670 


448900 


300763000 


25.8844 


8.7503 


725 


525625 


381078125 


26.9258 


8.9835 


671 


450241 


302111711 


25.9037 


8.7547 


726 


527076 


382657176 


26.9444 


8.9876 


672 


451584 


303464448 


25.9230 


8.7590 


727 


528529 


384240583 


26.9629 


8.9918 


673 


452929 


304821217 


25.9422 


8.7634 


728 


529984 


385828352 


26.9815 


8.9959 


674 


454276 


306182024 


25.9615 


8.7677 


729 


531441 


387420489 


27.0000 


9.0000 


675 


455625 


307546875 


25.9808 


8.7721 


730 


532900 


389017000 


27.0185 


9.0041 


676 


456976 


308915776 


26.00Q0 


8.7764 


731 


534361 


390617891 


27.0370 


9.0082 


677 


458329 


310288733 


26 0192 


8.7807 


732 


535824 


392223168 


27.0555 


9.0123 


678 


459684 


311665752 


26.0384 


8.7850 


733 


537289 


393832837 


27.0740 


9.0164 


679 


461041 


313046839 


26.0576 


8.7893 


734 


538756 


395446904 


27.0924 


9.0205 


680 


462400 


314432000 


26.0768 


8.7937 


735 


540225 


397065375 


27.1109 


9.0246 


681 


463761 


315821241 


26.0960 


8.7980 


736 


541696 


398688256 


27.1293 


9.0287 


682 


465124 


317214568 


26.1151 


8.8023 


737 


543169 


400315553 


27.1477 


9.0328 


683 


466489 


318611987 


26.1343 


8.8066 


738 


544644 


401947272 


27.1662 


9.0369 


684 


467856 


320013504 


26.1534 


8.8109 


739 


546121 


403583419 


27.1846 


9.0410 


685 


469225 


321419125 


26.1725 


8.8152 


740 


547600 


405224000 


27.2029 


9.0450 


686 


470596 


322828856 


26.1916 


8.8194 


741 


54908! 


40686902 ! 


27.2213 


9 0491 


687 


471969 


324242703 


26.2107 


8.8237 


742 


550564 


408518488 


27.2397 


9.0532 


688 


473344 


325660672 


26.2298 


8.8280- 


743 


552049 


410172407 


27.2580 


9.0572 


689 


474721 


327082769 


26.2488 


8.8323 


744 


553536 


411830784 


27.2764 


9.0613 


690 


476100 


328509000 


26.2679 


8.8366 


745 


555025 


413493625 


27.2947 


9.0654 


691 


477481 


329939371 


26.2869 


8.8408 


746 


556516 


415160936 


27.3130 


9.0694 


692 


478864 


331373888 


26.3059 


8.8451 


747 


558009 


416832723 


27.3313 


9.0735 


693 


480249 


332812557 


26.3249 


8.8493 


748 


559504 


418508992 


27.3496 


9.0775 


694 


481636 


334255384 


26.3439 


8.8536 


749 


561001 


420189749 


27.3679 


9.0816 


695 


483025 


335702375 


26.3629 


8.8578 


750 


562500 


421875000 


27.3861 


9.0856 


696 


484416 


337153536 


26.3818 


8.8621 


751 


564001 


423564751 


27.4044 


9.0896 


697 


485809 


338608873 


26.4008 


8.8663 


752 


565504 


425259008 


27.4226 


9.0937 


698 


487204 


340068392 


26.4197 


8.8706 


753 


567009 


426957777 


27.4408 


9.0977 


699 


48860 1 


341532099 


26.4386 


8.8748 


754 


568516 


428661061 


27.4591 


9.1017 


700 


490000 


343000000 


26.4575 


8.8790 


755 


570025 


430368875 


27.4773 


9.1057' 


701 


491401 


344472101 


26.4764 


8.8833 


756 


571536 


432081216 


27.4955 


9.1098 


702 


492804 


345948408 


26.4953 


8.8875 


757 


573049 


433798093 


27.5136 


9.1138 


703 


494209 


347428927 


26.5141 


8.8917 


758 


574564 


435519512 


27.5318 


9.1178 


704 


495616 


348913664 


26.5330 


8.8959 


759 


576081 


437245479 


27.5500 


9.1218 



SQUARES, CUBES, SQUARE AND CUBE ROOTS. 101 



No 


. Square 


Cube. 


Sq. 
Root. 


) Cube 
Root. 


No 


Square 


Cube. 


Sq. 
Root. 


Cube 
Root. 


76C 


) 57760C 


43897600C 


27.5681 


9.1258 


815 


664225 


541343375 


28.5482 


9.3408 


761 


579121 


440711081 


27.5862 


9.1298 


816 


665856 


543338496|28.5657 


9.3447 


762 


580644 


44245072S 


27.6043 


9.1338 


817 


667489 


545338513 28.5832 


9.3485 


763 


582169 


444194947 


27.6225 


9.1378 


81£ 


669124 


547343432 28.6007 


9.3523 


764 


583696 


445943744 


27.6405 


9.1418 


81^ 


670761 


549353259 28.6182 


9.3561 


765 


585225 


447697125 


27.6586 


9.1458 


82C 


672400 


55136800C 


28.6356 


9.3599 


766 


586756 


449455096 


27.6767 


9.1498 


821 


674041 


553387661 


28.6531 


9.3637 


767 


588289 


451217663 


27.6948 


9.1537 


822 


675684 


555412248 


28.6705 


9.3675 


768 


589824 


452984832 


27.7128 


9.1577 


823 


677329 


557441767 


28.688C 


9.3713 


769 


591361 


454756609 


27.7308 


9.1617 


824 


678976 


559476224 


28.7054 


9.3751 


770 


592900 


456533000 


27.7489 


9.1657 


825 


680625 


561515625 


28.7228 


9.3789 


771 


594441 


458314011 


27.7669 


9.1696 


826 


682276 


563559976 


28.7402 


9.3827 


772 


595984 


460099648 


27.7849 


9.1736 


827 


683929 


565609283 


28.7576 


9.3865 


773 


597529 


461889917 


27.8029 


9.1775 


828 


685584 


567663552 


28.7750 


9.3902 


774 


599076 


463684824 


27.8209 


9.1815 


829 


687241 


569722789 


28.7924 


9.3940 


775 


600625 


465484375 


27.8388 


9.1855 


830 


688900 


571787000 


28.8097 


9.3978 


776 


602176 


467288576 


27.8568 


9.1894 


831 


690561 


573856191 


28.8271 


9.4016 


777 


603729 


469097433 


27.8747 


9.1933 


832 


692224 


575930368 


28.8444 


9.4053 


778 


605284 


470910952 


27.8927 


9.1973 


833 


693889 


578009537 


28.8617 


9.4091 


779 


606841 


472729139 


27.9106 


9.2012 


834 


695556 


580093 704 


28.8791 


9.4129 


780 


608400 


474552000 


27.9285 


9.2052 


835 


697225 


582182875 


28.8964 


9.4166 


781 


609961 


476379541 


27.9464 


9.2091 


836 


698896 


584277056 


28.9131 


9.4204 


782 


611524 


478211768 


27.9643 


9.2130 


837 


700569 


586376253 


28.9310 


9.4241 


783 


613089 


480048687 


27.9821 


9.2170 


838 


702244 


588480472 


28.9482 


9.4279 


784 


614656 


481890304 


28.0000 


9.2209 


839 


703921 


590589719 


28.9655 


9.4316 


785 


616225 


483736625 


28.0179 


9.2248 


840 


705600 


592704000 


28.9828 


9.4354 


786 


617796 


485587656 


28.0357 


9.2287 


841 


707281 


594823321 


29.0000 


9.4391 


787 


619369 


487443403 


28.0535 


9.2326 


842 


708964 


596947688 


29.0172 


9.4429 


788 


620944 


489303872 


28.0713 


9.2365 


843 


710649 


599077107 


29.0345 


9.4466 


789 


622521 


491169069 


28.0891 


9.2404 


844 


712336 


601211584 


29.0517 


9.4503 


790 


624100 


493039000 


28.1069 


9.2443 


845 


714025 


603351125 


29.0689 


9.4541 


791 


625681 


494913671 


28.1247 


9.2482 


846 


715716 


605495736 


29.0861 


9.4578 


792 


627264 


496793088 


28.1425 


9.2521 


8471717409 


607645423 


29.1033 


9.4615 


793 


628849 


498677257 


28.1603 


9.2560 


848 


719104 


609800192 


29.1204 


9.4652 


794 


630436 


500566184 


28.1780 


9.2599 


849 


720801 


611960049 


29.1376 


9.4690 


795 


632025 


502459875 


28.1957 


9.2638 


850 


722500 


614125000 


29.1548 


9.4727 


796 


633616 


504358336 


28.2135 


9.2677 


851 


724201 


616295051 


29.1719 


9.4764 


797 


635209 


506261573 


28.2312 


9.2716 


852 


725904 


618470208 


29. 1 890 


9.4801 


798 


636804 


508169592 


28.2489 


9.2754 


853 


727609 


620650477 


29.2062 


9.4838 


799 


638401 


510082399 


28.2666 


9.2793 


854 


729316 


622835864 


29.2233 


9.4875 


800 


640000 


512000000 


28.2843 


9.2832 


855 


731025 


625026375 


29.2404 


9.4912 


801 


641601 


513922401 


28.3019 


9.2870 


856 


732736 


627222016 


29.2575 


9.4949 


802 


643204 


515849608 


28.3196 


9.2909 


857 


734449 


629422793 


29.2746 


9.4986 


803 


644809 


517781627 


28.3373 


9.2948 


858 


736164 


6316287121 


29.2916 


9.5023 


804 


646416 


519718464 


28.3549 


9.2986 


859 


737881 


633839779 


29.3087 


9.5060 


805 


648025 


521660125 


28.3725 


9.3025 


860 


739600 


636056000 


29.3258 


9.5097 


806 


649636 


523606616 


28.3901 


9.3063 


861 


741321 


638277381 


29.3428 


9.5134 


807 


651249 


525557943 


28.4077 


9.3102 


862 


743044 


640503928 


29.3598 


9.5171 


808 


652864 


527514112 


28.4253 


9.3140 


863 


744769 


642735647 


29.3769 


9.5207 


809 


654481 


529475129 


28.4429 


9.3179 


864 


746496 


644972544 


29.3939 


9.5244 


810 


656100 


531441000 


28.4605 


9.3217 


865 


748225 


647214625 


29.4109 


9.5281 


811 


657721 


533411731 


28.4781 


9.3255 


866 


749956 


64946 1896 1 


29.4279 


9.5317 


812 


659344 


535387328 


28.4956 


9.3294 


867 


751689 


6517143631 


29.4449 


9.5354 


813 


660969 


537367797 


28.5132 


9.3332 


868 


753424 


6539720321 


29.4618 


9.5391 


814 


662596 


539353144 


28.5307 


9.3370 


869 


755161 


656234909L 


29.47881 


9.5427 



102 



MATHEMATICAL TABLES. 



No. 


Square 


Cube. 


Sq. 
Root. 


Cube 
Root. 


No. 


Square 


Cube. 


Sq. 
Root. 


Cube 
Root. 


870 


756900 


658503000 


29.4958 


9.5464 


925 


855625 


791453125 


30.4138 


9.7435 


871 


758641 


660776311 


29.5127 


9.5501 


926 


857476 


79402277630.4302 


9.7470 


872 


760384 


603054848 


29.5296 


9.5537 


927 


859329 


796597983 


30.4467 


9.7505 


873 


762129 


665338617 


29.5466 


9.5574 


928 


861184 


799178752 


30.4631 


9.7540 


874 


763876 


667627624 


29.5635 


9.5610 


929 


863041 


801765089 


30.4795 


9.7575 


875 


765625 


669921875 


29.5804 


9.5647 


930 


86490C 


804357000 


30.4959 


9.7610 


876 


767376 


672221376 


29.5973 


9.5683 


931 


866761 


806954491 


30.5123 


9.7645 


877 


769129 


674526133 


29.6142 


9.5719 


932 


868624 


809557568 


30.5287 


9.7680 


878 


770884 


676836152 


29.63 H 


9.5756 


933 


870489 


812166237 


30.5450 


9.7715 


879 


772641 


679151439 


29.6479 


9.5792 


934 


872356 


814780504 


30.5614 


9.7750 


880 


774400 


681472000 


29.6648 


9.5828 


935 


874225 


817400375 


30.5778 


9.7785 


881 


776161 


683797841 


29.6816 


9.5865 


936 


876096 


820025856 


30.5941 


9.7819 


882 


777924 


686128968 


29.6985 


9.5901 


937 


877969 


822656953 


30.6105 


9.7854 


883 


779689 


688465387 


29.7153 


9.5937 


938 


879844 


825293672 


30.6268 


9.7889 


884 


781456 


690807104 


29.7321 


9.5973 


939 


881721 


827936019 


30.6431 


9.7924 


885 


783225 


693154125 


29.7489 


9.6010 


940 


883600 


830584000 


30.6594 


9.7959 


886 


784996 


695506456 


29.7658 


9.6046 


941 


885481 


833237621 


30.6757 


9.7993 


887 


786769 


697864103 


29.7825 


9.6082 


942 


887364 


8358968^8 


30.6920 


9.8028 


888 


788544 


700227072 


29.7993 


9.6118 


943 


889249 


838561807 


30.7083 


9.8063 


889 


790321 


702595369 


29.8161 


9.6154 


944 


891136 


841232384 


30.7246 


9.8097 


890 


792100 


704969000 


29.8329 


9.6190 


945 


893025 


843908625 


30.7409 


9.8132 


891 


793881 


707347971 


29.8496 


9.6226 


946 


894916 


846590536 


30.7571 


9.8167 


892 


795664 


709732288 


29.8664 


9.6262 


947 


896809 


849278123 


30.7734 


9.8201 


893 


797449 


712121957 


29.8831 


9.6298 


948 


898704 


851971392 


30.7896 


9.8236 


894 


799236 


714516984 


29.8998 


9.6334 


949 


90060 1 


854670349 


30.8058 


9.8270 


895 


801025 


716917375 


29.9166 


9.6370 


950 


902500 


857375000 


30.8221 


9.8305 


896 


802816 


719323136 


29.9333 


9.6406 


951 


904401 


860085351 


30.8383 


9.8339 


897 


804609 


721734273 


29.9500 


9.6442 


952 


906304 


862801408 


30.8545 


9.8374 


898 


806404 


724150792 


29.9666 


9.6477 


953 


908209 


865523177 


30.8707 


9.8408 


899 


808201 


726572699 


29.9833 


9.6513 


954 


910116 


868250664 


30.8869 


9.8443 


900 


810000 


729000000 


30.0000 


9.6549 


955 


912025 


870983875 


30.9031 


9.8477 


901 


811801 


731432701 


30.0167 


9.6585 


956 


913936 


873722816 


30.9192 


9.8511 


902 


813604 


733870808 


30.0333 


9.6620 


957 


915849 


876467493 


30.9354 


9.8546 


903 


815409 


736314327 


30.0500 


9.6656 


958 


917764 


879217912 


30.9516 


9.8580 


904 


817216 


738763264 


30.0666 


9.6692 


959 


919681 


881974079 


30.9677 


9.8614 


905 


819025 


741217625 


30.0832 


9.6727 


960 


921600 


884736000 


30.9839 


9.8648 


906 


820836 


743677416 


30.0998 


9.6763 


961 


923521 


887503681 


31.0000 


9.8683 


907 


822649 


746142643 


30.1164 


9.6799 


962 


925444 


890277128 


31.0161 


9.8717 


908 


824464 


748613312 


30.1330 


9.6834 


963 


927369 


893056347 


31.0322 


9.8751 


909 


826281 


751089429 


30.1496 


9.6870 


964 


929296 


895841344 


31.0483 


9.8785 


910 


828100 


753571000 


30.1662 


9.6905 


965 


931225 


898632125 


31.0644 


9.8819 


911 


82992 1 


756058031 


30.1828 


9.6941 


966 


933156 


901428696 


31.0805 


9.8854 


912 


831744 


758550528 


30.1993 


9.6976 


967 


935089 


904231063 


31.0966 


9.8888 


913 


833569 


761048497 


30.2159 


9.7012 


968 


937024 


907039232 


31.1127 


9.8922 


914 


835396 


763551944 


30.2324 


9.7047 


969 


938961 


909853209 


31.1288 


9.8956 


915 


837225 


766060875 


30.2490 


9.7082 


970 


940900 


912673000 


3 1 . 1 448 


9.8990 


916 


839056 


768575296 


30.2655 


9.7118 


971 


942841 


915498611 


31.1609 


9.9024 


917 


840889 


771095213 


30.2820 


9.7153 


972 


944784 


918330048 


3 1 . 1 769 


9.9058 


918 


842724 


773620632 


30.2985 


9.7188 


973 


946729 


921167317 


31.1929 


9.9092 


919 


844561 


776151559 


30.3150 


9.7224 


974 


948676 


924010424 


31.2090 


9.9126 


920 


846400 


778688000 


30.3315 


9.7259 


975 


950625 


926859375 


31.2250 


9.9160 


921 


848241 


781229961 


30.3480 


9.7294 


976 


952576 


929714176 


31.2410 


99194 


922 


850084 


783777448 


30.3645 


9.7329 


977 


954529 


932574833 


31.2570 


9.9227 


923 


851929 


786330467 


30.3809 


9.7364 


978 


956484 


935441352 


3 J. 2730 


9.9261 


924 


853776 7888890241 


30.3974 9.7400 1 


979 


958441 


938313739 


31.2890 


9.9295 



SQUARES, CUBES, SQUARE AND CUBE ROOTS. 103 



Square. 



960400 
962361 
964324 
966289 
968256 

970225 
972196 
974169 
976144 
978121 

980100 
982081 
984064 
986049 
988036 

990025 
992016 
994009 
996004 
998001 

1000000 
100200! 
1004004 
1006009 
1008016 

1010025 
1012036 
1014049 
1016064 
1018081 

T020100 
1022121 
1024144 
1026169 
1028196 

1030225 
1032256 
1034289 
1036324 
1038361 

1040400 
1042441 
1044484 
1046529 
1048576 

1050625 
1052676 
1054729 
1056784 
1058841 



1060900 
1062961 
1065024 



Cube. 



941 192000 
944076141 
946966168 
949862087 
952763904 



Sq. 
Root. 



31.3050 
31.3209 
31.3369 
31.3528 
31.3688 



955671625 
958585256 
961504803 
964430272 31.4325 
%7361669;3 1.4484 



31.3847 
31.4006 
31.4166 



970299000 31.4643 
973242271 31.4802 



976191488 
979146657 
982107784 

985074875 
988047936 
991026973 
99401 1992 
997002999 

1000000000 
1003003001 
1006012008 
1009027027 



31.4960 
31.5119 
31.5278 

31.5436 
31.5595 
31.5753 
31.5911 
31.6070 

31.6228 
31.6386 
31.6544 
31.6702 



1012048064 31.6860 

1015075125 31.7017 
1018108216 31.7175 
1021147343 31.7333 
1024192512 31.7490 
1027243729 31.7648 



1030301000 
1033364331 
1036433728 
1039509197 
1042590744 



31.7805 
31.7962 
31.8119 
31.8277 
31.8434 



1045678375 31.8591 
1048772096 31.8748 
1051871913,31.8904 
1 054977832 j 3 1.9061 
1058089859 31.9218 

1061208000 31.9374 
1064332261 31.9531 
1067462648 1 3 1.9687 
1070599167 31.9844 
1073741824 32.0000 

1076890625 32.0156 
1080045576 32.0312 
10S3206683 
1086373952 
1089547389 



' 1092727000 
1095912791 
1099104768 
1067089; 1102302937 
1069156' 1105507304 



32.0468 
32.0624 
32.0780 



32.0936 
32.1092 
32.1248 
32.1403 
32.1559 



Cube 
Root. 



9.9329 
9.9363 
9.9396 
9.9430 
9.9464 

9.9497 
9.9531 
9.9565 
9.9598 
9.%32 

9.9666 
9.%99 
9.9733 
9.9766 
9.9800 

9.9833 
9.9866 
9.9900 
9.9933 
9.9967 

10.0000 
10.0033 
10.0067 
10.0100 
10.0133 

10.0166 
10.0200 
10.0233 
10.0266 
10.0299 

10.0332 
10.0365 
10.0398 
10.0431 
10.0465 

10.0498 
10.0531 
10.0563 
10.0596 
10.0629 

10.0662 
10.0695 
10.0728 
10.0761 
10.0794 

10.0826 
10.0859 
10.0892 
10.0925 
10.0957 

10.0990 
10.1023 
10.1055 
10.1088 
10.1121 



No. 

1035 
1036 
1037 
1038 
1039 

1040 
1041 
1042 
1043 
1044 

1045 
1046 
1047 
1048 
1049 

1050 
1051 
1052 
1053 
1054 

1055 
1056 
1057 
1058 
1059 

1060 
1061 
1062 
1063 
1064 

1065 
1066 
1067 
1063 
1069 

1070 
1071 
1072 
1073 
1074 

1075 
107o 
1077 
1078 
1079 

1080 
1081 
1082 
1083 
1034 

1085 
1086 
1087 
1088 
1089 



Square. 



Cube. 



1071225 1108717875 
1073296 1111934656 
1075369^1115157653 
1077444,1118386872 
1079521 1121622319 



1081600 
1083681 
1085764 
1087849 
1089936 

1092025 
1094116 
1096209 
1098304 
1100401 

1 102500 
1104601 
1106704 
1108809 
1110916 

1113025 
1115136 
1117249 
1 1 19364 
1121481 

1123600 
1125721 
1 127844 
1129969 
1132096 

1134225 
1136356 
1138489 
1140624 
1142761 

1144900 
1147041 
1149184 
1151329 
1153476 

1155625 
1157776 
1159929 
1162084 
1164241 

1166400 
1168561 
1170724 
1172889 
1175056 



1177225 
1179396 
1181569 



1124864000 
1128111921 
1131366088 
1134626507 
1137893184 

1141166125 
1144445336 
1147730823 
1151022592 
1154320649 



1157625000 32.4037 
1160935651 32.4191 



Sq. 
Root. 



32.1714 
32.1870 
32.2025 
32.2180 
32.2335 

32.2490 
32.2645 
32.2800 
32.2955 
32.3110 

32.3265 
32.3419 
32.3574 
32.3728 
32.3883 



1164252608 
1167575877 
1170905464 

1174241375 
1177583616 
1180932193 
1184287112 
1187648379 

1191016000 
1194389981 
1197770328 
1201157047 
1204550144 

120794%25 
1211355496 
1214767763 
1218186432 
1221611509 

1225043000 
1228480911 
1231925248 
1235376017 
1238833224 



32.4345 
32.4500 
32.4654 

32.4808 
32.4962 
32.5115 
32.5269 
32.5423 

32.5576 
32.5730 
32.5883 
32.6036 
32.6190 

32.6343 
32.6497 
32.6650 
32.6803 
32.6956 

32.7109 
32.7261 
32.7414 
32.7567 
32.7719 



1242296875 32.7872 10.2440 
1245766976 32.8024 10.2472 
1249243533 32.8177 10.2503 



1252726552 
1256216039 

1259712000 
1263214441 
1266723368 
1270238787 
1273760704 



1277289125 
1280824056 
1284365503 
118374411287913472 
18592111291467969 



32.8329 10.2535 
32.8481 10.2567 

32.8634 
32.8786 
32.8938 
32.9090 
32.9242 

32.9393 
32.9545 
32.9697 
32.9848 10.2851 
33.0000' 10.7^3 



104 



MATHEMATICAL TABLES. 



Square. 



Cube. 



1188100 
1190281 
1192464 
1194649 
1196836 

1199025 
1201216 
1203409 
1205604 
1207801 

1210000 
1212201 
1214404 
1216609 
1218816 

1221025 
1223236 
1225449 
1227664 
1229881 

1232100 
1234321 
1236544 
1238769 
12409% 

1243225 
1245456 
1247689 
1249924 
1252161 

1254400 
1256641 
1258884 
1261129 
1263376 

1265625 
1267876 
1270129 
1272384 
1274641 

1276900 
1279161 
1281424 
1283689 
1285956 

1288225 
1290496 
1292769 



1295029000 
12985%571 
1302170688 
1305751357 
1309338584 

1312932375 
1316532736 
1320139673 
1323753192 
1327373299 

1331000000 
1334633301 
1338273208 
1341919727 
1345572864 

1349232625 
1352899016 
1356572043 
1360251712 
1363938029 

1367631000 
1371330631 
1375036928 
1378749897 
1382469544 

1386195875 
1389928896 
1393668613 
1397415032 
1401168159 

1404928000 
1408694561 
1412467848 
1416247867 
1420034624 

1423828125 
1427628376 
1431435383 
1435249152 
1439069689 

1442897000 
1446731091 
1450571968 
1454419637 
1458274104 



Sq. 
Root. 



33.0151 
33.0303 
33.0454 
33.0606 
33.0757 

33.0908 
33.1059 
33.1210 
33.1361 
33.1512 

33.1662 
33.1813 
33.1964 
33.2114 
33.2264 

33.2415 
33.2566 
33.2716 
33.2866 
33.3017 

33.3167 
33.3317 
33.3467 
33.3617 
33.3766 

33.3916 
33.4066 
33.4215 
33.4365 
33.4515 

33.4664 
33.4813 
33.4%3 
33.5112 
33.5261 



Cube 
Root. 



10.2914 
10.2946 
10.2977 
10.3009 
10.3040 

10.3071 
10.3103 
10.3134 
10.3165 
10.3197 

10.3228 
10.3259 
10.3290 
10.3322 
10 3353 

10.3384 
10.3415 
10.3447 
10.3478 
10.3509 

10.3540 
10.3571 
10.3602 
10.3633 
10.3664 

10.3695 
10.3726 
10.3757 
10.3788 
10.3819 

10.3850 
10.3881 
10.3912 
10.3943 
10.3973 



No. 



33.5410 10.4004 
33.5559 10.4035 
33.5708 10.4066 



33.5857 
33.6006 

33.6155 
33.6303 
33.6452 
33.6601 
33.6749 



1462135375|33.6898 
1466003456133.7046 



1469878353 
1295044 1473760072 
1297321 1477648619 



1299600 
1301881 
1304164 
1306449 
1308736 



1481544000 
1485446221 
1489355288 
1493271207 
1497193984 



33.7174 
33.7342 
33.7491 

33.7639 
33.7787 
33.7935 
33.8083 
33.8231 



10.4097 
10.4127 

10.4158 
10.4189 
10.4219 
10.4250 
10.4281 

10.4311 
10.4342 
10.4373 
10.4404 
10.4434 

10.4464 
10.4495 
10.4525 
10.4556 
10.4586 



Square. 



1145 
1146 
1147 
1148 
1149 

1150 
1151 
1152 
1153 
1154 

1155 
1156 
1157 
1158 
1159 

1160 
1161 
1162 
1163 
1164 

1165 
1166 
1167 
1168 
1169 

1170 
1171 
1172 
1173 
1174 

1175 
1176 
1177 
1178 
1179 

1180 
1181 
1182 
1183 
1184 

1185 
1186 
1187 
1188 
1189 

1190 
1191 
1192 
1193 
1194 

1195 
11% 
1197 
1198 
1199 



Cube. 



1311025 
1313316 
1315609 
1317904 
1320201 

1322500 
1324801 
1327104 
1329409 
1331716 

1334025 
1336336 
1338649 
1340964 
1343281 

1345600 
1347921 
1350244 
1352569 
13548% 

1357225 
1359556 
1361889 
1364224 
1366561 

1368900 
1371241 
1373584 
1375929 
1378276 

1380625 
1382976 
1385329 
1387684 
1390041 

1392400 
1394761 
1397124 
1399489 
1401856 

1404225 
14065% 
1408%9 
1411344 
1413721 

1416100 
1418481 
1420864 
1423249 
1425636 

1428025 
1430416 
1432809 
1435204 
1437601 



1501123625 
1505060136 
1509003523 
1512953792 
1516910949 

1520875000 
1524845951 
1528823808 
1532808577 
1536800264 

1540798875 
1544804416 
1548816893 
1552836312 
1556862679 

1560896000 
1564936281 
1568983528 
1573037747 
1577098944 

1581167125 
15852422% 
1589324463 
1593413632 
1597509809 

1601613000 
1605723211 
1609840448 
1613964717 
1618096024 

1622234375 
1626379776 
1630532233 
1634691752 
1638858339 



Sq. 
Root. 



33.8378 
33.8526 
33.8674 
33.8821 
33.8%9 

33.9116 
33.9264 
33.9411 
33.9559 
33.9706 

33.9853 
34.0000 
34.0147 
34.0294 
34.0441 

34.0588 
34.0735 
34.0881 
34.1028 
34.1174 

34.1321 
34.1467 
34.1614 
34.1760 
34.1906 

34.2053 
34.2199 
34.2345 
34.2491 
34.2637 

34.2783 
34.2929 
34.3074 
34.3220 
34.3366 



1643032000 34.3511 
1647212741 34.3657 
1651400568^34.3802 
1655595487 34.3948 
1659797504 34.4093 



1664006625 
1668222856 
1672446203 
1676676672 
1680914269 

1685159000 
1689410871 
1693669888 
1697936057 
1702209384 

1706489875 
1710777536 
1715072373 
1719374392 
1723683599 



34.4238 
34.4384 
34.4529 
34.4674 
34.4819 

34.4964 
34.5109 
34.5254 
34.5398 
34.5543 

34.5688 
34.5832 
34.5977 
34.6121 
34.6266 



Cube 
Root. 

10.4617 
10.4647 
10.4678 
10.4708 
10.4739 

10.4769 
10.4799 
10.4830 
10.4860 
10.4890 

10.4921 
10.4951 
10.4981 
10.5011 
10.5042 

10.5072 
10.5102 
10.5132 
10.5162 
10.5192 

10.5223 
10.5253 
10.5283 
10.5313 
10.5343 

10.5373 
10.5403 
10.5433 
10.5463 
10.5493 

10.5523 
10.5553 
10.5583 
10.5612 
10.5642 

10.5672 
10.5702 
10.5732 
10.5762 
10.5791 

10.5821 
10.5851 
10.5881 
10.5910 
10.5940 

10.5970 
10.6000 
10.6029 
10.6059 
10.6085 

10.6118 
10.6148 
10.6177 
10.6207 
10.6236 



SQUARES, CUBES, SQUARE AND CUBE ROOTS. 105 



Square. 



1440000 
1442401 
1444804 
1447209 
144%] 6 

1452025 
1454436 
1456849 
1459264 
1461681 

1464100 
1466521 
1468944 
1471369 
14737% 

1476225 
1478656 
1481089 
1483524 
1485%1 

1488400 
1490841 
1493284 
1495729 
1498176 

1500625 
1503076 
1505529 
1507984 
1510441 

1512900 
1515361 
1517824 
1520289 
1522756 

1525225 
1527696 
1530169 
1532644 
1535121 

1537600 
1540081 
1542564 
1545049 
1547536 

1550025 
1552516 
1555009 
1557504 
1560001 

1562500 
1565031 
1567504 
1570009 
1572516 



Cube. 



1728000000 
1732323601 
1 736654408 
1740992427 
1745337664 

174%90125 
1754049816 
1758416743 
1762790912 
1767172329 

1771561000 
1775956931 
1780360128 
1784770597 
1789188344 

1793613375 
17980456% 
1802485313 
1806932232 
1811386459 

1815848000 
1820316861 
1824793048 
1829276567 
1833767424 

1838265625 
1842771176 
1847284083 
1851804352 
1856331989 

1860867000 
1865409391 
1869959168 
1874516337 
1879080904 

1883652875 
1888232256 
1892819053 
1897413272 
1902014919 

1906624000 
1911240521 
1915864488 
1920495907 
1925134784 

1929781125 
1934434936 
1939096223 
1943764992 
1948441249 

1953125000 
1957816251 
1962515008 
1%7221277 
1971935064 



Sq. 
Root. 



34.6410 
34.6554 
34.6699 
34.6843 
34.6987 

34.7131 
34.7275 
34.7419 
34.7563 
34.7707 

34.7851 
34.7994 
34.8138 
34.8281 
34.8425 

34.8569 
34.8712 
34.8855 
34.8999 
34.9142 

34.9285 
34.9428 
34.9571 
34.9714 
34.9857 

35.0000 
35.0143 
35.0286 
35.0428 
35.0571 

35.0714 
35.0856 
35.0999 
35.1141 
35.1283 

35.1426 
35.1568 
35.1710 
35.1852 
35.1994 

35.2136 
35.2278 
35.2420 
35.2562 
35.2704 

35.2846 
35.2987 
35.3129 
35.3270 
35.3412 

35.3553 
35.3695 
35.3836 
35.3977 
35.4119 



Cube 
Root. 



10.6266 
10.6295 
10.6325 
10.6354 
10.6384 

10.6413 
10.6443 
10.6472 
1C.6501 
10.6530 

10.6560 
10.6590 
10.6619 
10.6648 
10.6678 

10.6707 
10.6736 
10.6765 
10.6795 
10.6824 

10.6853 
10.6882 
10.6911 
10.6940 
10.6970 

10.6999 
10.7028 
10.7057 
10.7086 
10.7115 

10.7144 
10.7173 
10.7202 
10.7231 
10.7260 

10.7289 
10.7318 
10.7347 
10.7376 
10.7405 

10.7434 
10.7463 
10.7491 
10.7520 
10.7549 

10.7578 
10.7607 
10.7635 
10.7664 
10.7693 

10.7722 
10.7750 
10.7779 
10.7808 
10.7837 



No. 



1255 
1256 
1257 
1258 
1259 

1260 
1261 
1262 
1263 
1264 

1265 
1266 
1267 
1268 
1269 

1270 
1271 
1272 
1273 
1274 

1275 
1276 
1277 
1278 
1279 

1280 
1281 
1282 
1283 
1284 

1285 
1286 
1287 
1288 
1289 

1290 
1291 
1292 
1293 
1294 

1295 
12% 
1297 
1298 
1299 

1300 
1301 
1302 
1303 
1304 

1305 
1306 
1307 
1308 
1309 



Square. 



1575025 
1577536 
1580049 
1582564 
1585081 

1587600 
1590121 
1592644 
1595169 
15976% 

1600225 
1602756 
1605289 
1607824 
1610361 

1612900 
1615441 
1617984 
1620529 
1623076 

1625625 
1628176 
1630729 
1633284 
1635841 

1638400 
1640%! 
1643524 
1646089 
1648656 

1651225 
16537% 
1656369 
1658944 
1661521 

1664100 
1666681 
1669264 
1671849 
1674436 

1677025 
167%16 
1682209 
1684804 
1687401 

1690000 
1692601 
1695204 
1697809 
1700416 

1703025 
1705636 
1708249 
1710864 
1713481 



Cube. 



1976656375 
1981385216 
1986121593 
1990865512 
1995616979 

2000376000 
2005142581 
2009916728 
2014698447 
2019487744 

2024284625 
20290890% 
2033901163 
2038720832 
2043548109 

2048383000 
2053225511 
2058075648 
2062933417 
2067798824 

2072671875 
2077552576 
2082440933 
2087336952 
2092240639 

2097152000 
2102071041 
2106997768 
2111932187 
2116874304 

2121824125 
2126781656 
2131746903 
2136719872 
2141700569 

2146689000 
2151685171 
2156689088 
2161700757 
2166720184 

2171747375 
2176782336 
2181825073 
2186875592 
2191933899 

2197000000 
2^02073901 
2207155608 
2212245127 
2217342464 

2222447625 
2227560616 
2232681443 
2237810112 
2242946629 



Sq. 
Root. 



35.4260 
35.4401 
35.4542 
35.4683 
35.4824 

35.4%5 
35.5106 
35.5246 
35.5387 
35.5528 

35.5668 
35.5809 
35.5949 
35.6090 
35.6230 

35.6371 
35.6511 
35.6651 
35.6791 
35.6931 

35.7071 
35.7211 
35.7351 
35.7491 
35.7631 

35.7771 
35.7911 
35.8050 
35.8190 
35.8329 

35.8469 
35.8608 
35.8748 
35.8887 
35.9026 

35.9166 
35.9305 
35.9444 
35.9583 
35.9722 

35.9861 
36.0000 
36.0139 
36.0278 
36.0416 

36.0555 
36.0694 
36.0832 
36.0971 
36.1109 

36.1248 
36.1386 
36.1525 
36.1663 
36.1801 



106 



MATHEMATICAL TABLES. 



Square. 



1716100 
1718721 
1721344 
1723969 
17265% 

1729225 
1731856 
1734489 
1737124 
1739761 

1742400 
1745041 
1747684 
1750329 
1752976 



Cube. 



2248091000 
2253243231 
2258403328 
2263571297 
2268747144 

2273930875 
2279122496 
2284322013 
2289529432 
2294744759 

2299968000 
2305199161 
2310438248 
2315685267 
2320940224 



1755625 2326203125 
1758276 2331473976 
1760929 2336752783 
1763584 2342039552 
1766241 2347334289 



1768900 
1771561 
1774224 
1776889 
1779556 

1782225 
17848% 
1787569 
1790244 
1792921 

1795600 
1798281 
1800964 
1803649 
1806336 

1809025 
1811716 
1814409 
1817104 
1819801 

1822500 
1825201 
1827904 
1830609 
1833316 

1836025 
1838736 
1841449 
1844164 
1846881 

1849600 
1852321 
1855044 
1857769 
18604% 



2352637000 
2357947691 
2363266368 
2368593037 
2373927704 

2379270375 
2384621056 
2389979753 
2395346472 
2400721219 

2406104000 
2411494821 
2416893688 
2422300607 
2427715584 



2433138625 
2438569736 
2444008923 
2449456192 36.7151 
2454911549 36.7287 



Cube 
Root. 



Sq. 
Root, 

36.1939 
36.2077 
36.2215 
36.2353 
36.2491 

36.2629 
36.2767 
36.2905 
36.3043 
36.3180 

36.3318 
36.3456 
36.3593 
36.3731 
36.3868 

36.4005 
36.4143 
36.4280 
36.4417 
36.4555 

36.4692 
36.4829 
36.4966 
36.5103 
36.5240 

36.5377 
36.5513 
36.5650 
36.5787 
36.5923 

36.6060 
36.6197 
36.6333 
36.6469 
36.6606 1 1 .0357 



10.9418 
10.9446 
10.9474 
10.9502 
10.9530 

10.9557 
10.9585 
10.9613 
10.9640 
10.9668 

10.%96 
10.9724 
10.9752 
10.9779 
10.9807 

10.9834 
10.9862 
10.9890 
10.9917 
10.9945 

10.9972 
11.0000 
1 1 .0028 
1 1 .0055 
11.0083 

11.0110 
11.0138 
11.0165 
11.0193 
1 1 .0320 

11.0247 
1 1 .0275 
1 1 .0302 
11.0330 



No. 



2460375000 
2465846551 
2471326208 
2476813977 
2482309864 

2487813875 
2493326016 
2498846293 
2504374712 
2509911279 

2515456000 
2521008881 
2526569928 
2532139147 
2537716544 



36.6742 1 1 .0384 

36.6879 11.0412 

36.7015 11.0439 

1 1 .0466 

1 1 .0494 






36.7423 
36.7560 
36.7696 
36.7831 
36.7967 

36.8103 
36.8239 
36.8375 
36.8511 
36.8646 

36.8782 
36.8917 
36.9053 
36.9188 
36.9324 



11.0521 
1 1 .0548 
1 1 .0575 
1 1 .0603 
1 1 .0630 

11.0657 
11.0684 
11.0712 
1 1 .0739 
1 1 .0766 

1 1 .0793 
1 1 .0820 
1 1 .0847 
1 1 .0875 
11.0902 



Square. 



1365 
1366 
1367 
1368 
1369 

1370 
1371 
1372 
1373 
1374 

1375 
1376 
1377 
1378 
1379 

1380 
1381 
1382 
1383 
1384 

1385 
1386 
1387 
1388 
1389 

1390 
1391 
1392 
1393 
1394 

1395 
1396 
1397 
1398 
1399 

1400 
1401 
1402 
1403 
1404 

1405 
1406 
1407 
1408 
1409 

1410 
1411 
1412 
1413 
1414 

1415 
1416 
1417 
1418 
1419 



Cube. 



1863225 2543302125 36.9459 
1865956 2548895896 36.9594 



Sq. 
Root. 



1868689 
1871424 
1874161 



2554497863 
2560108032 
2565726409 



1876900 2571353000 
1879641 12576987811 



1882384 
1885129 
1887876 



2582630848 
2588282117 
2593941624 



1890625 2599609375 
1893376 1 2605285376 



1896129 
1898884 
1901641 



2610969633 
2616662152 
2622362939 



1904400 2628072000 
190716112633789341 
1909924 2639514968 
1912689 2645248887 
1915456 2650991104 



1918225 
1920996 
1923769 
1926544 
1929321 

1932100 
1934881 
1937664 
1940449 
1943236 

1946025 
1948816 
1951609 
1954404 
1957201 

1960000 
1962801 
1965604 
1968409 
1971216 

1974025 
1976836 
1979649 
1982464 
1985281 

1988100 
1990921 
1993744 
19%569 
1999396 

2002225 
2005056 
2007889 
2010724 
2013561 



2656741625 
2662500456 
2668267603 
2674043072 
2679826869 

2685619000 
2691419471 
2697228288 
2703045457 
2708870984 

2714704875 
2720547136 
2726397773 
2732256792 
2738124199 

2744000000 
2749884201 
2755776808 
2761677827 
2767587264 

2773505125 
2779431416 
2785366143 
2791309312 
2797260929 

2803221000 
2809189531 
2815166528 
2821151997 
2827145944 

2833148375 
2839159296 
2845178713 
2851206632 
2857243059 



36.9730 
36.9865 
37.0000 

37.0135 
37.0270 
37.0405 
37.0540 
37.0675 

37.0810 
37.0945 
37.1080 
37.1214 
37.1349 

37.1484 
37.1618 
37.1753 
37.1887 
37.2021 

37.2156 
37.2290 
37.2424 
37.2559 
37.2693 

37.2827 
37.2961 
37.3095 
37.3229 
37.3363 

37.3497 
37.3631 
37.3765 
37.3898 
37.4032 

37.4166 11.1869 
37.4299 11.1896 
37.443311 1.1922 
37.4566 11.1949 
37.4700 11.1975 



37.4833 
37.4967 
37.5100 
37.5233 
37.5366 

37.5500 
37.5633 
37.5766 
37.5899 
37.6032 

37.6165 
37.6298 
37.6431 
37.6563 
37.66% 



1 1 .2002 
1 1 .2028 
1 1 .2055 
1 1 .2082 
11.2108 

11.2135. 
11.216r 
11.2188 
11.2214 
1 1 .2240 

1 1 .2267 
11.2293 
1 1 .2320 
1 1 2346 
1 1 2373 



SQUARES, CUBES, SQUARE AND CUBE ROOTS. 107 



Square. 



2016400 
2019241 
2022034 
2024929 
2021776 

2030625 
2033476 
2036329 
2039184 
2042041 

2044900 
2047761 
2050624 
20534S9 
2056356 

2059225 
2062096 
2064969 
2067844 
2070721 

2073600 
2076481 
2079364 
2082249 
2085136 

2088025 
2090916 
2093809 
2096704 
2099601 

2102500 
2105401 
2108304 
2111209 
2114116 

2117025 
2119936 
2122849 
2125764 
2128681 

2131600 
2134521 
2137444 
2140369 
2143296 

2146225 
2149156 
2152039 
2155024 
2157961 

2160900 
2163841 
2166784 
2169729 
2172676 



Cube. 



2863288000 
2869341461 
2875403448 
2881473967 
2887553024 

2893640625 
2899736776 
2905841483 
2911954752 
2918076589 

2924207000 
2930345991 
2936493568 
2942649737 
2948814504 

2954987875 
2961169856 
2967360453 
2973559672 
2979767519 

2985984000 
2992209121 
2998442888 
3004685307 
3010936384 

3017196125 
3023464536 
3029741623 
3036027392 
3042321849 

3048625000 
3054936851 
3061257408 
3067586677 
3073924664 

3030271375 
3086626816 
3092990993 
3099363912 
3105745579 

3112136000 
3118535181 
3124943128 
3131359847 
3137785344 

314421%25 
3150662696 
3157114563 
3163575232 
3170044709 

3176523000 
3183010111 
3189506048 
3196010817 
3202524424 



Sq. 
Root. 



37.6829 
37.6%2 
37.7094 
37.7227 
37.7359 

37.7492 
37.7624 
37.7757 
37.7889 
37.8021 

37.8153 
37.8286 
37.8418 
37.8550 
37.8682 

37.8814 
37.8946 
37.9078 
37.9210 
37.9342 

37.9473 
37.9605 
37.9737 
37.9868 
38.0000 

38.0132 
38.0263 
38.0395 
38.0526 
38.0657 

38.0789 
38.0920 
38.1051 
38.1182 
38.1314 

38.1445 
38.1576 
38.1707 
38.1838 
38.1969 

38.2099 
38.2230 
38.2361 
38.2492 
38.2623 

38.2753 
38.2884 
38.3014 
38.3145 
38.3275 

38.3406 
38.3536 
38.3667 
38.3797 
38.3927 



Cube 
Root. 



1 1 .2399 
1 1 .2425 
1 1 .2452 
11.2478 
11.2505 

11.2531 
1 1 .2557 
11.2583 
11.2610 
1 1 .2636 

11.2662 
1 1 .2689 
11.2715 
11.2741 
1 1 .2767 

11.2793 
11.2820 
11.2846 
11.2872 
11.2898 

11.2924 
1 1 .2950 
11.2977 
1 1 .3003 
1 1 .3029 

11.3055 
11.3081 
11.3107 
11.3133 
11.3159 

11.3185 
11.3211 
1 1 .3237 
1 1 .3263 
11.3289 

11.3315 
11.3341 
1 1 .3367 
1 1 .3393 
11.3419 

11.3445 
11.3471 
1 1 .3496 
1 1 .3522 
11.3548 

11.3574 
11.3600 
1 1 .3626 
1 1 .3652 
11.3677 

1 1 .3703 
1 1 .3729 
11.3755 
11.3780 
11.3806 



No. 



1475 
1476 
1477 
1478 
1479 

1480 
1481 
1482 
1483 
1484 



Square. 



2175625 
2178576 
2181529 
2184484 
2187441 

2190400 
2193361 
2196324 
2199289 
2202256 



1485 2205225 

1486 2208196 



1487 
1488 
1489 

1490 
1491 
1492 
1493 
1494 

1495 
1496 
1497 
1498 
1499 

1500 
1501 
1502 
1503 
1504 

1505 
1506 
1507 
1508 
1509 

1510 
1511 
1512 
1513 
1514 

1515 
1516 
1517 
1518 
1519 

1520 
1521 
1522 
1523 
1524 

1525 
1526 
1527 
1528 
1529 



2211169 
2214144 
2217121 

2220100 
2223081 
2226064 
2229049 
2232036 

2235025 
2238016 
2241009 
2244004 
2247001 

2250000 
2253001 
2256004 
2259009 
2262016 

2265025 
2268036 
2271049 
2274064 
2277081 

2280100 
2283121 
2286144 
2289169 
2292196 

2295225 
2298256 
2301289 
2304324 
2307361 

2310400 
2313441 
2316484 
2319529 
2322576 

2325625 
2328676 
2331729 
2334784 
2337841 



Cube. 



3209046875 
3215578176 
3222118333 
3228667352 
3235225239 

3241792000 
3248367641 
3254952168 
3261545587 
3268147904 

3274759125 
3281379256 
3288008303 
3294646272 
3301293169 

3307949000 
3314613771 
3321287488 
3327970157 
3334661784 

3341362375 
3348071936 
3354790473 
3361517992 
3368254499 

3375000000 
3381754501 
3388518008 
3395290527 
3402072064 

3408862625 
3415662216 
3422470843 
3429288512 
3436115229 

3442951000 
3449795831 
3456649728 
3463512697 
3470384744 

3477265875 
3484156096 
3491055413 
3497%3832 
3504881359 

3511808000 
3518743761 
3525688648 
3532642667 
3539605824 

3546578125 
3553559576 
3560550183 
3567549952 
3574558889 



Sq. 
Root. 



38.4057 
38.4187 
38.4318 
38.4448 
38.4578 

38.4708 
38.4838 
38.4968 
38.5097 
38.5227 

38.5357 

38.5487 
38.5616 
38.5746 
38.5876 

38.6005 
38.6135 
38.6264 
38.6394 
38.6523 

38.6652 
38.6782 
38.6911 
38.7040 
38.7169 

38.7298 
38.7427 
38.7556 
38.7685 
38.7814 

38.7943 
38.8072 
38.8201 
38.8330 
38.8458 

38.8587 
38.8716 
38.8844 
38.8973 
38.9102 

38.9230 
38.9358 
38.9487 
38.9615 
38.9744 

38.9872 
39.0000 
39.0128 
39.0256 
39.0384 

39.0512 
39.0640 
39.0768 
39.0896 
39.1024 



Cube 
Root. 



11.3832 
11.3858 
11.3883 
11.3909 
11.3935 

11.3960 
11.3986 
11.4012 
11.4037 
11.4063 

11.4089 
11.4114 
11.4140 
11.4165 
11.4191 

11.4216 
1 1 .4242 
11.4268 
1 1 .4293 
11.4319 

11.4344 
11.4370 
11.4395 
11.4421 
11.4446 

11.4471 
11.4497 
1 1 .4522 
1 1 .4548 
11.4573 

11.4598 
11.4624 
11.4649 
11.4675 
11.4700 

11.4725 
11.4751 
1K4776 
11.4801 
11.4826 

11.4852 
11.4877 
11.4902 
11.4927 
11.4953 

11.4978 
11.5003 
11.5028 
11.5054 
11.5079 

11.5104 
11.5129 
11.5154 
11.5179 
11.5204 



108 



MATHEMATICAL TABLES. 



No. 


Square. 


1530 


2340900 


1531 


2343% 1 


1532 


2347024 


1533 


2350089 


1534 


2353156 


1535 


2356225 


1536 


23592% 


1537 


2362369 


1538 


2365444 


1539 


2368521 


1540 


2371600 


1541 


2374681 


1542 


2377764 


1543 


2380849 


1544 


2383936 


1545 


2387025 


1546 


2390116 


1547 


2393209 


1548 


23%304 


1549 


2399401 


1550 


2402500 


1551 


2405601 


1552 


2408704 


1553 


2411809 


1554 


2414916 


1555 


2418025 


1556 


2421136 


1557 


2424249 


1558 


2427364 


1559 


2430481 


1560 


2433600 


1561 


2436721 


1562 


2439844 


1563 


2442%9 


1564 


24460% 



Cube. 



3581577000 
3588604291 
3595640768 
3602686437 
3609741304 

3616805375 
3623878656 
3630% 1153 
3638052872 
3645153819 

3652264000 
3659383421 
3666512088 
3673650007 
3680797184 

3687953625 
3695119336 
3702294323 
3709478592 
3716672149 

3723875000 
3731087151 
3738308608 
3745539377 
3752779464 

3760028875 
3767287616 
3774555693 
3781833112 
3789119879 

3796416000 
3803721481 
3811036328 
3818360547 
3825694144 



Sq. 
Root. 



39.1152 
39.1280 
39.1408 
39.1535 
39.1663 

39.1791 
39.1918 
39.2046 
39.2173 
39.2301 

39.2428 
39.2556 
39.2683 
39.2810 
39.2938 

39.3065 
39.3192 
39.3319 
39.3446 
39.3573 

39.3700 
39.3827 
39.3954 
39.4081 
39.4208 

39.4335 
39.4462 
39.4588 
39.4715 
39.4842 

39.4968 
39.5095 
39.5221 
39.5348 
39.5474 



Cube 
Root. 



1 1 .5230 
11.5255 
11.5280 
11.5305 
11.5330 

11.5355 
1 1 .5380 
11.5405 
1 1 .5430 
11.5455 

11.5480 
11.5505 
11.5530 
11.5555 
11.5580 

11.5605 
11.5630 
1 1 .5655 
1 1 .5680 
11,5705 

11.5729 
11.5754 
11.5779 
1 1 .5804 
1 1 .5829 

11.5854 
11.5879 
11.5903 
11.5928 
1 1 .5953 

11.5978 
11.6003 
1 1 .6027 
11.6052 
11.6077 



No. 



1565 
1566 
1567 
1568 
1569 

1570 
1571 
1572 
1573 
1574 

1575 
1576 
1577 
1578 
1579 

1580 
1581 
1582 
1583 
1584 

1585 

1586 

1587 

If 

1589 

1590 
1591 
1592 
1593 
1594 

1595 
1596 
1597 
1598 
1599 

1600 



Square. 



2449225 
2452356 
2455489 
2458624 
2461761 

2464900 
2468041 
2471184 
2474329 
2477476 

2480625 
2483776 
2486929 
2490084 
2493241 

2496400 
2499561 
2502724 
2505889 
2509056 

2512225 
2515396 
2518569 
2521744 
2524921 

2528100 
2531281 
2534464 
2537649 
2540836 

2544025 
2547216 
2550409 
2553604 
2556801 

2560000 



Cube. 



3833037125 
38403894% 
3847751263 
3855123432 
3862503009 

3869893000 
3877292411 
3884701248 
3892119517 
3899547224 

3906984375 
3914430976 
3921887033 
3929352552 
3936827539 

3944312000 
3951805941 
3959309368 
3966822287 
3974344704 

3981876625 
3989418056 
3996969003 
4004529472 
4012099469 

4019679000 
4027268071 
4034866688 
4042474857 
4050092584 

4057719875 
4065356736 
4073003173 
4080659192 
4088324799 

4096000000 



Sq. 
Root. 



39.5601 
39.5727 
39.5854 
39.5980 
39.6106 

39.6232 
39.6358 
39.6485 
39.661 1 
39.6737 

39.6863 
39.6989 
39.7115 
39.7240 
39.7366 

39.7492 
39.7618 
39.7744 
39.7869 
39.7995 

39.8121 
39.8246 
39.8372 
39.8497 
39.8623 

39.8748 
39.8873 
39.8999 
39.9124 
39.9249 

39.9375 
39.9500 
39.%25 
39.9750 
39.9875 

40.0000 



SQUARES AND CUBES OF DECI3IAUS. 



No. 


Square 


Cube. 


No. 


Square 


Cube. 


No. 


Square. 


Cube. 


I 


.01 


.001 


.01 


.0001 


.000 001 


.001 


.00 00 01 


.000 000 001 


7 


.04 


.008 


.02 


.0004 


.000 008 


.002 


.00 00 04 


.000 000 008 


3 


.09 


.027 


.03 


.0009 


.000 027 


.003 


.00 00 09 


.000 000 027 


4 


.16 


.064 


.04 


.0016 


.000 064 


.004 


.00 00 16 


.000 000 064 


5 


.25 


.125 


.05 


.0025 


.000 125 


.005 


.00 00 25 


.000 000 125 


6 


.36 


.216 


.06 


.0036 


.000 216 


.006 


.00 00 36 


.000 000 216 


7 


.49 


.343 


,07 


.0049 


.000 343 


.007 


.00 00 49 


.000 000 343 


8 


.64 


.512 


08 


.0064 


.000 512 


.008 


.09 00 64 


.000 000 512 


9 


.81 


.729 


09 


.0081 


.000 729 


.009 


.00 00 81 


.000 000 729 


1 


1.00 


1.000 


,10 


.0100 


.001 000 


.010 


.00 01 00 


.000 001 000 


1.2 


1.44 


1.728 


.12 


.0144 


.001 728 


.012 


.00 01 44 


.000 001 728 



Note that the square has twice as many decimal places, and the cube 
>hree times as many decimal places, as the root. 



FIFTH ROOTS AND FIFTH POWERS. 



109 



FIFTH ROOTS AND FIFTH POWERS. 

(Abridged from Trautwine.) 



0^ 




o -te 




-^^ 




o -^ 




o^ 




oS 


Power. 


oj 


Power. 


dS 


Power. 


68 


Power. 


6S 


Power. 


&^ 




i^ 




i^ 




^^ 




i^ 




"jo 


.000010 


T7 


693.440 


9.8 


90392 


21.8 


4923597 


40 


102400000 


.15 


.000075 


3.8 


792.352 


9.9 


95099 


22.0 


5153632 


41 


115856201 


.20 


.000320 


3.9 


902.242 


10.0 


100000 


22.2 


5392186 


42 


130691232 


.25 


.000977 


4.0 


1024.00 


10.2 


110408 


22.4 


5639493 


43 


147008443 


.30 


.002430 


4.1 


1158.56 


10.4 


121665 


22.6 


5895793 


44 


164916224 


.35 


.005252 


4.2 


1306.91 


10.6 


133823 


22.8 


6161327 


45 


184528125 


.40 


.010240 


4.3 


1470.08 


10.8 


146933 


23.0 


6436343 


46 


205962976 


.45 


.018453 


4.4 


1 649. 1 6 


11.0 


161051 


23.2 


6721093 


47 


229345007 


.50 


.031250 


4.5 


1845.28 


11.2 


17623-1 


23.4 


7015834 


48 


254803968 


.55 


.050328 


4.6 


2059.63 


11.4 


192541 


23.6 


7320825 


49 


282475249 


.60 


.077760 


4.7 


.2293.45 


11.6 


210034 


23.8 


7636332 


50 


312500000 


.65 


.116029 


4.8 


2548.04 


11.8 


228776 


24.0 


7962624 


51 


345025251 


.70 


.168070 


4.9 


2824.75 


12.0 


248832 


24.2 


8299976 


52 


380204032 


.75 


.237305 


5.0 


3125.00 


12.2 


270271 


24.4 


8648666 


53 


418195493 


.80 


.327680 


5.1 


3450.25 


12.4 


293163 


24.6 


9008978 


54 


459165024 


.85 


.443705 


5.2 


3802.04 


12.6 


317580 


24.8 


9381200 


55 


503284375 


.90 


.590490 


5.3 


4181.95 


12.8 


343597 


25.0 


9765625 


56 


550731776 


.95 


.773781 


5.4 


4591.65 


13.0 


371293 


25.2 


10162550 


57 


601692057 


1.00 


1.00000 


5.5 


5032.84 


13.2 


400746 


25.4 


10572278 


58 


656356768 


1.05 


1.27628 


5.6 


5507.32 


13.4 


432040 


25.6 


10995116 


59 


7 1 4924299 


1.10 


1.61051 


5.7 


6016.92 


13.6 


465259 


25.8 


11431377 


60 


777600000 


1.15 


2.01135 


5.8 


6563.57 


13.8 


500490 


26.0 


11881376 


61 


844596301 


1.20 


2.48832 


5.9 


7149.24 


14.0 


537824 


26.2 


12345437 


62 


916132832 


1.25 


3.05176 


6.0 


7776.00 


14.2 


577353 


26.4 


12823886 


63 


992436543 


1.30 


3.71293 


6.1 


8445.96 


14.4 


619174 


26.6 


13317055 


64 


1073741824 


1.35 


4.48403 


6.2 


9161.33 


14.6 


663383 


26.8 


13825281 


65 


1160290625 


1.40 


5.37824 


6.3 


9924.37 


14.8 


710082 


27.0 


14348907 


66 


1252332576 


1.45 


6.40973 


6.4 


10737 


15.0 


759375 


27.2 


14888280 


67 


1350125107 


1.50 


7.59375 


6.5 


11603 


15.2 


811368 


27.4 


15443752 


68 


1453933568 


1.55 


8.94661 


6.6 


12523 


15.4 


866171 


27.6 


16015681 


69 


1564031349 


1.60 


10.4858 


6.7 


13501 


15.6 


923896 


27.8 


16604430 


70 


1680700000 


1.65 


12.2298 


6.8 


14539 


15.8 


984658 


28.0 


17210368 


71 


1804229351 


1.70 


14.1986 


6.9 


15640 


16.0 


1048576 


28.2 


1 7833868 


72 


1934917632 


1.75 


16.4131 


7.0 


16807 


16.2 


1115771 


28.4 


18475309 


73 


2073071593 


1.80 


18.8957 


7.1 


18042 


16.4 


1186367 


28.6 


19135075 


74 


2219006624 


1.85 


21.6700 


7.2 


19349 


16.6 


1260493 


28.8 


19813557 


75 


2373046875 


1.90 


24.7610 


7.3 


20731 


16.8 


1338278 


29.0 


20511149 


76 


2535525376 


1.95 


28.1951 


7.4 


22190 


17.0 


1419857 


29.2 


21228253 


77 


2706784157 


2.00 


32.0000 


7.5 


23730 


17.2 


1505366 


29.4 


21965275 


78 


2887174368 


2.05 


36.2051 


7.6 


25355 


17.4 


1594947 


29.6 


22722628 


79 


3077056399 


2.10 


40.8410 


7.7 


27068 


17.6 


1688742 


29.8 


23500728 


80 


3276800000 


2.15 


45.9401 


7.8 


28872 


17.8 


1786899 


30.0 


24300000 


81 


3486784401 


2.20 


51.5363 


7.9 


30771 


18.0 


1889568 


30.5 


26393634 


82 


3707398432 


2.25 


57.6650 


8.0 


32768 


18.2 


1996903 


31.0 


28629151 


83 


3939040643 


2.30 


64.3634 


8.1 


34868 


18.4 


2109061 


31.5 


31013642 


84 


4182119424 


2.35 


71.6703 


8.2 


37074 


18.6 


2226203 


32.0 


33554432 


85 


4437053125 


2.40 


79.6262 


8.3 


39390 


18.8 


2348493 


32.5 


36259082 


86 


4704270176 


2.45 


88.2735 


8.4 


41821 


19.0 


2476099 


33.0 


39135393 


87 


4984209207 


2.50 


97.6562 


8.5 


44371 


19.2 


2609193 


33.5 


42191410 


88 


5277319168 


2.55 


107.820 


8.6 


47043 


19.4 


2747949 


34.0 


45435424 


89 


5584059449 


2.60 


118.814 


8.7 


49842 


19.6 


2892547 


34.5 


48875980 


90 


5904900000 


2.70 


143.489 


8.8 


52773 


19.8 


3043168 


35.0 


52521875 


91 


6240321451 


2.80 


172.104 


8.9 


55841 


20.0 


3,200000 


35.5 


56382167 


92 


6590815232 


2.90 


205.111 


9.0 


59049 


20.2 


3363232 


36.0 


60466176 


93 


6956883693 


3.00 


243.000 


9.1 


62403 


20.4 


3533059 


36.5 


64783487 


94 


7339040224 


3.10 


286.292 


9.2 


65908 


20.6 


3709677 


37.0 


69343957 


95 


7737809375 


3.20 


335.544 


9.3 


69569 


20.8 


3893289 


37.5 


74157715 


96 


8153726976 


3.30 


391.354 


9.4 


73390 


21.0 


4084101 


38.0 


79235168 


97 


8587340257 


3.40 


454.354 


9.5 


77378 


21.2 


4282322 


38.5 


84587005 


98 


9039207968 


3.50 


525.219 


9.6 


81537 


21.4 


4488 1 66 


39.0 


90224199 


99 


9509900499 


3.60 


604.662 


9.7 85873 


21.6 


4701850 


39.5'96158012| 







110 



MATHEMATICAL TABLES. 



'^ 



rs)cr\ooor>.\Of<^coo^or^osOsOLn<N<^c7vOrs.— QOr>,oOint>Ncoro(NO 
«£^<^OrnTr'^rTj-ro-— oolnfNooT^c^Lr^O'r(:^■^oocNsOpoor^f<^o^u^o 



0<NvOfNT^^r^sOv0^^t^O^ 



'I 



CN -"T rsj OO m OO t>. <N O^ r<M~>. LTi sO O -_.,.,_.- 






^>-^ 
'^ 



< 



vO O^ ^«0 "O nO ^O ^O ^O ^O vO ^O ^O 



> 



Ou^fAOin(^OmoO<-nu^coOc^r<^oOOOOOr^wOOOoOc^mf<-Mi->oooOOO 
inr^Lnot>.OLncNr>s,'rrv)OOooirMnrsirgooor->itorvicoovor>.aMnvom 

-^- - — ^ "--OfSvOOr-xi^cNjc^iooooMj^ 

-r^^rr^^^r^vOvOr>»ooooo^O 



ICQirHli— lo O — — <— — r^irvjrvjr^rqrvir^irsirsj<^fOr<^co«^r<^fOfO(^cO(^rO'^ 



'I 



_ _ -OO'^O 



— roLOoofNoo''*- — oc^Of<^^>lfsr>soor>.r^J■<r'^fSC^■^^«.o — I 



= £"■ 



TJ< (N T}< 

;ir ^ ??• — <N c'^ -^ in vo r>. CO o^ o — <N fT^ -^t- in SO oo o fs ■«*• vo 00 o «N ""I- vo oo o 
— — — — — — — — fscNcsr-^ fsroc<^c^^c<^c«^'!^ 



0(^oOLnoOOOOOiAOf<^OOOtOOOrOOOOOcOmOf<^rAOoOu-Mnwnu^ 
com — 1>*. — ro,osOLnOf<^\Ooot>.oor>.0'^vocNooun'^r<^r>,rNicom 

cr\|>>, — Tt-COO^NOO<^r<^ — O^— l-inOc*^- Tj-rM-^o^^^Ln — rN,vOfN 

■^jTvjrviTro — avt>.oo — r^-^fN ^i>>.r>.vomoo(Nf<^r>,«n-<roO'^r>N.r>N 
t^Of<^oocoLnT}-^ooro, — rs. — (^uMn — Lnr^NOoa^Ooou-vcsicoo 
mo^<^"^f>.Of<^mr>.osfNfOLnot>»o^ — fscrMnNOsoooooo^oocN 

— — — <N (N <N CN rsj (N (N CN <N r<> rK r<*i 



l(MICglt-l|rH|r-IO o o o o - 



'^ 



ooo 
m <^in 
tno^ sO 

oo 



— r<^0 
m sO t^ 
O — fN 
ro vO — 



vO — vO sO 

— OinO^O^invO*— sO~>0 

t>,OsrvivOvO — rsO'roNOvOt>.ooro — r^vOi>i 
cooc^moo — rvjo<Noo — -^coirr — rrMr>rt-oooOfncN 



ooooo— 



<N(r^^000v0c<^r^^r<-^^„OO0^0^t^^00O^^0Q000r<^ — 

— — cNcoTr-irNor>.oorvjso 



ga3 = 



(Nf'^'^sOCOOrO^OO'^OcnOLnOOOOsONOOOrslfSCSf^ — — 



ooooo— —- 



«NCNcrirOTj-T}-tnvOr>.t>,ooo — rgf<-iT}-tnsOt>,a\ 



O N 



r-i 1-1 n r-t CO 



^^ -^ -Si -sj QP\C\ 

— — p-cNP^ifOr<^Tr'«j-ir\vorsoooNO — fsro«rmQQQ 



CIRCUMFERENCES AND AREAS OF CIRCLES. 
CIRCUMFERENCES AND AREAS OF CIRCLES. 



Ill 



Diani. 


Circum. 


Area. 


Diam. 


Circum. 


Area. 


Diam. 


Circum. 


Area. 


1/64 


. 04909 


. 000 1 9 


33/8 


7.4613 


4.4301 


61/8 


19.242 


29.465 


1/32 


.09818 


.00077 


7/16 


7.6576 


4.6664 


1/4 


19.635 


30.680 


3/64 


.14726 


.00173 


1/2 


7.8540 


4.9087 


3/8 


20.028 


31 919 


1/16 


.19635 


.00307 


9/16 


8.0503 


5.1572 


1/2 


20.420 


33. 183 


3/32 


.29452 


. 00690 


5/8 


8.2467 


5.4119 


5/8 


20.813 


34 472 


1/8 


.39270 


.01227 


11/16 


8.4430 


5.6727 


3/4 


21.206 


35.785 


5/32 


.49087 


.01917 


3/4 


8.6394 


5.9396 


7/8 


21.598 


37.122 


3/16 


.58905 


.02761 


13/18 


8.8357 


6.2126 


7. 


21.991 


38.485 


7/32 


.68722 


.03758 


7/8 


9.0321 


6.4918 


1/8 


22.384 


39.871 








15/16 


9.2284 


6.7771 


1/4 


22.776 


41.282 


1/4 


.78540 


.04909 








3/8 


23.169 


42.718 


9/32 


.88357 


. 062 1 3 


3. 


9.4248 


7.0686 


1/9 


23.562 


44.179 


5/16 


.98175 


.07670 


1/16 


9.6211 


7.3662 


5/8 


23.955 


45 . 664 


11/32 


1.0799 


.09281 


1/8 


9.8175 


7 . 6699 


3/4 


24.347 


47.173 


3/8 


1.1781 


.11045 


3/16 


10.014 


7.9798 


7/8 


24.740 


48.707 


13/32 


1.2763 


.12962 


1/4 


10.210 


8.2958 


8. 


25.133 


50.265 


7/16 


1.3744 


.15033 


5/16 


10.407 


8.6179 


1/8 


25.525 


51.849 


15/32 


1.4726 


.17257 


3/8 


10.603 


8.9462 


1/4 


25.918 


53.456 








7/16 


10.799 


9.2806 


3/8 


26.311 


55.088 


1/2 


1.5708 


.19635 


1/2 


1 . 996 


9 . 62 1 1 


1/2 


26.704 


56.745 


17/32 


1 . 6690 


.22166 


9/16 


11.192 


9.9678 


5/8 


27.096 


58.426 


9/16 


1.7671 


.24850 


5/8 


11.388 


10.321 


3/4 


27.489 


60.132 


19' 32 


1.8653 


.27688 


11/16 


11.585 


10.680 


7/8 


27.882 


61.862 


5/8 


1.9635 


. 30680 


3/4 


11.781 


11.045 


9. 


28.274 


63.617 


21,32 


2.0617 


.33824 


13/16 


11.977 


11.416 


1/8 


28.667 


65.397 


iVl6 


2.1598 


.37122 


7/8 


12.174 


1 1 . 793 


1/4 


29.060 


67.201 


23/32 


2.2580 


.40574 


15/16 


12.370 


12.177 


3/8 


29.452 


69.029 








4. 


12.566 


12.566 


1/2 


29.845 


70.882 


3/4 


2.3562 


.44179 


1/16 


12.763 


12.962 


5/8 


30.238 


72.760 


25/32 


2.4544 


.47937 


1/8 


12.959 


13.364 


3/4 


30.631 


74.662 


13/16 


2.5525 


.51849 


3/16 


13.155 


13.772 


7/8 


31.023 


76.589 


27/32 


2.6507 


.55914 


1/4 


13.352 


14. 186 


10. 


31.416 


78.540 


21^ 


2.7489 


.60132 


5/16 


13.548 


14.607 


1/8 


31.809 


80.516 


29/32 


2.8471 


.64504 


3/8 


13.744 


15.033 


1/4 


32.201 


82.516 


15/16 


2.9452 


. 69029 


7/16 


13.941 


1 5 . 466 


3/8 


32.594 


84.541 


31/32 


3.0434 


.73708 


1/2 


14.137 


15.904 


1/2 


32.987 


86.590 








9/16 


14.334 


16.349 


5/8 


33.379 


88 . 664 


1. 


3.1416 


.7854 


5/8 


14.530 


16.800 


3/4 


33.772 


90.763 


1/16 


3.3379 


.8866 


11/16 


14.726 


17.257 


7/8 


34.165 


92.886 


0^8 


3.5343 


.9940 


3/4 


14.923 


17.721 


11. 


34.558 


95.033 


3/16 


3.7306 


1.1075 


13/16 


15.119 


18.190 


1/8 


34.950 


97.205 


1/4 


3.9270 


1.2272 


7/8 


15.315 


18.665 


1/4 


35.343 


99.402 


5/16 


4.1233 


1.3530 


15/16 


15.512 


19.147 


• 3/8 


35.736 


101.62 


3/8 


4.3197 


1.4849 


5. 


15.708 


19.635 


1/2 


36.128 


103.87 


7/16 


4.5160 


1.6230 


1/16 


15.904 


20.129 


5/8 


36.521 


106.14 


V'' 


4.7124 


1.7671 


1/8 


16.101 


20.629 


3/4 


36.914 


108.43 


9/16 


4.9087 


1.9175 


3/16 


16.297 


21.135 


7/8 


37.306 


110.75 


5/8 


5.1051 


2.0739 


1/4 


16.493 


21.648 


12. 


37.699 


113.10 


11/16 


5.3014 


2.2365 


5/l6 


16.690 


22.166 


1/8 


38.092 


115.47 


3/4 


5.4978 


2.4053 


3/8 


16.886 


22.691 


1/4 


38.485 


117.86 


13/16 


5.6941 


2.5802 


7/16 


17.082 


23.221 


3/8 


38.877 


120.28 


.V^ 


5.8905 


2.7612 


1/2 


17.279 


23.758 


1/2 


39.270 


122.72 


15/16 


6.0868 


2.9483 


9/16 


17.475 


24.301 


5/8 


39.663 


125.19 








5/8 


17.671 


24.850 


3/4 


40.055 


127.68 


S. 


6.2832 


3.1416 


11/16 


1 7 . 868 


25.406 


7/8 


40.448 


130.19 


1/16 


6.4795 


3.3410 


3/4 


18.064 


25.967 


13. 


40.841 


132.73 


1/8 


6.6759 


3.5466 


13/16 


18.261 


26.535 


1/8 


41.233 


135 30 


3/16 


6.8722 


3.7583 


7/8 


18.457 


27.109 


1/4 


41.626 


137.89 


1/4 


7 . 0686 


3.9761 


15/16 


18.653 


27.688 


3/8 


42.019 


140.50 


5/16 


7.2649 


4.2000 


6. 


18.850 


28.274 


1/2 


42.412 


143.14 



112 



MATHEMATICAL TABLES. 



Diam. 


Circura. 


Area. 


Diam. 


Circum. 


Area. 


Diam. 


Circura. 


Area. 


135/8 


42.804 


145.80 


^tVs 


68.722 


375.83 


30 Vs 


94.640 


712.76 


3/4 


43. 197 


148.49 


23. 


69.115 


380. 13 


1/4 


95.033 


718.69 


7/8 


43.590 


151.20 


1/8 


69.508 


384.46 


8/8 


95.426 


724.64 


14. 


43.982 


153.94 


1/4 


69.900 


388.82 


1/2 


95.819 


730.62 


1/8 


44.375 


156.70 


3/8 


70.293 


393.20 


5/8 


96.211 


736.62 


Va 


44.768 


159.48 


1/2 


70.686 


397.61 


3/4 


96.604 


742.64 


38 


45.160 


162.30 


5/8 


71.079 


402.04 


7/8 


96.997 


748.69 


1/2 


45.553 


165.13 


3/4 


71.471 


406.49 


31. 


97.389 


754.77 


5/8 


45.946 


167.99 


7/8 


71.864 


410.97 


1/8 


97.782 


760.87 


3/4 


46.338 


170.87 


23. 


72.257 


415.48 


1/4 


98.175 


766.99 


7/8 


46.731 


173.78 


i/s 


72.649 


420.00 


3/8 


98.567 


773.14 


15. 


47.124 


176.71 


1/4 


73.042 


424.56 


1/2 


98.960 


779.31 


1/8 


47.517 


179.67 


3/8 


73.435 


429.13 


5/8 


99.353 


785.51 


1/4 


47.909 


182.65 


1/2 


73.827 


433.74 


3/4 


99.746 


791 73 


8/8 


48.302 


185.66 


5/8 


74.220 


438.36 


7/8 


100.138 


797.98 


1/2 


48.695 


188.69 


3/4 


74.613 


443.01 


32. 


100.531 


804.25 


5/8 


49.087 


191.75 


7/8 


75.006 


447.69 


1/8 


100.924 


810.54 


3/4 


49.480 


194.83 


24. 


75.398 


452.39 


1/4 


101.316 


816.86 


7/8 


49.873 


197.93 


1/8 


75.791 


457.11 


3/8 


101.709 


823.21 


16. 


50.265 


201.06 


1/4 


76.184 


461.86 


1/2 


102.102 


829.58 


1/8 


50.658 


204.22 


3/8 


76.576 


466.64 


5/8 


102.494 


835.97 


1/4 


51.051 


207.39 


1/2 


76.969 


471.44 


8/4 


102.887 


842.39 


8/8 


51.444 


210.60 


5/8 


77.362 


476.26 


7/8 


103.280 


848.83 


1/2 


51.836 


213.82 


3/4 


77.754 


481. 11 


33. 


103.673 


855.30 


5/8 


52.229 


217.08 


7/8 


78.147 


485.98 


1/8 


104.065 


861.79 


3/4 


52.622 


220.35 


25. 


78.540 


490.87 


1/4 


104.458 


868.31 


7/8 


53.014 


223.65 


Vs 


78.933 


495.79 


8/8 


104.851 


874.85 


17. 


53.407 


226.98 


1/4 


79.325 


500.74 


1/2 


105.243 


881.41 


1/8 


53.800 


230.33 


3/8 


79.718 


505.71 


5/8 


105.636 


888.00 


1/4 


54.192 


233.71 


1/2 


80.111 


510.71 


3/4 


106.029 


894.62 


3/8 


54.585 


237.10 


5/8 


80.503 


515.72 


7/8 


106.421 


901.26 


1/2 


54.978 


240.53 


3/4 


80.896 


520.77 


34. 


106.814 


907.92 


5/8 


55.371 


243.98 


7/8 


81.289 


525.84 


1/8 


107.207 


914.61 


3/4 


55.763 


247.45 


2G. 


8 1 . 68 1 


530.93 


1/4 


107.600 


921.32 


7/8 


56.156 


250.95 


i/s 


82.074 


536.05 


3/8 


107.992 


928.06 


18. 


56.549 


254.47 


1/4 


82.467 


541.19 


1/2 


108.385 


934.82 


1/8 


56.941 


258.02 


3/8 


82.860 


546.35 


5/8 


108.778 


941.61 


1/4 


57.334 


261.59 


1/2 


83.252 


551.55 


3/4 


109.170 


948.42 


3/8 


57.727 


265.18 


5/8 


83.645 


556.76 


7/8 


109.563 


955.25 


1/2 


58.119 


268.80 


3/4 


84.038 


562.00 


35. 


109.956 


962.11 


5/8 


58.512 


272.45 


7/8 


84.430 


567.27 


1/8 


110.348 


969 . 00 


3/4 


58.905 


276.12 


27. 


84.823 


572.56 


1/4 


110.741 


975.91 


7/8 


59.298 


279.81 


1/8 


85.216 


577.87 


3/8 


111.134 


982.84 


19. 


59.690 


283.53 


1/4 


85.608 


583.21 


1/2 


111.527 


989.80 


1/8 


60.083 


287.27 


3/8 


86.001 


588.57 


5/8 


111.919 


996.78 


1/4 


60.476 


291.04 


1/2 


86.394 


593.96 


3/4 


112.312 


1003.8 


3/8 


60.868 


294.83 ■ 


5/8 


86.786 


599.37 


7/8 


112.705 


1010.8 


1/2 


61.261 


298.65 


3/4 


87.179 


604.81 


36. 


113.097 


1017.9 


5/8 


61.654 


302.49 


7/8 


87.572 


610.27 


1/8 


113.490 


1025.0 


3/4 


62.046 


306.35 


28. 


87.965 


615.75 


1/4 


113.883 


1032.1 


7/8 


62.439 


310.24 


i/s 


88,357 


621.26 


3/8 


114.275 


1039.2 


20. 


62.832 


314.16 


1/4 


88.750 


626.80 


1/2 


114.668 


1046.3 


1/8 


63.225 


318.10 


3/8 


89.143 


632.36 


5/8 


115.061 


1053.5 


1/4 


63.617 


322.06 


1/2 


89.535 


637.94 


3/4 


115.454 


1060.7 


3/8 


64.010 


326.05 


5/8 


89.928 


643.55 


7/8 


115.846 


1068.0 


1/2 


64.403 


330.06 


3/4 


90.321 


649.18 


37. 


116.239 


1075.2 


5/8 


64.795 


334.10 


7/8 


90.713 


654.84 


1/8 


116.632 


1082.5 


3/4 


65.188 


338.16 


29. 


91.106 


660.52 


1/4 


117.024 


1089.8 


7/8 


65.581 


342.25 


Vs 


91.499 


666.23 


3/8 


117.417 


1097.1 


31. 


65.973 


346.36 


1/4 


91.892 


671.96 


1/2 


117.810 


1104.5 


1/8 


66.366 


350.50 


3/8 


92.284 


677.71 


5/8 


118.202 


1111.8 


1/4 


66.759 


354.66 


1/2 


92.677 


683 . 49 


8/4 


118.596 


1119.2 


3/8 


67.152 


358.84 


5/8 


93.070 


689.30 


7/8 


118.988 


1126.7 


1/2 


67.544 


363.05 


3/4 


93.462 


695.13 


38. 


119.381 


1134.1 


5/8 


67.937 


367.28 


7/8 


93.855 


700.98 


1/8 


119.773 


1141.6 


3/4 


68.330 


371.54 


30. 


94.248 


706.86 


1/4 


120.166 


1149.1 



CIRCUMFERENCES AND AREAS OF CIRCLES. 113 



Diam 


. Circum. 


Area. 


Diam 


Circum. 


Area. 


Diam 


. Circum. 


Area. 


383/8 


120.559 


1156.6 


465/8 


146.477 


1707.4 


547/8 


172.395 


2365.0 


V2 


120.951 


1164.2 


3/4 


146.869 


1716.5 


55. 


172.788 


2375.8 


5/8 


121.344 


1171.7 


7/8 


147.262 


1725.7 


Vs 


173. 180 


2386.6 


3/4 


121.737 


1179.3 


47. 


147.655 


1734.9 


V4 


173.573 


2397.5 


7/8 


122.129 


1186.9 


Vs 


148.048 


1744.2 


3/8 


173.966 


2408.3 


39. 


122.522 


1194.6 


1/4 


148.440 


1753.5 


V2 


174.358 


2419.2 


Vs 


122.915 


1202.3 


3/8 


148.833 


1762.7 


5/8 


174.751 


2430.1 


1/4 


123.308 


1210.0 


1/2 


149.226 


1772.1 


3/4 


175. 144 


2441. 1 


8/8 


123.700 


1217.7 


5/8 


149.618 


1781.4 


7/8 


175.536 


2452.0 


1/2 


124.093 


1225.4 


3/4 


150.011 


1790.8 


56. 


175.929 


2463.0 


5/8 


124.486 


1233.2 


7/8 


150.404 


1800.1 


Vs 


176.322 


2474.0 


3/4 


124.878 


1241.0 


48. 


150.796 


1809.6 


V4 


176.715 


2485.0 


7/8 


125.271 


1248.8 


1/8 


151.189 


1819.0 


3/8 


177.107 


2496.1 


40. 


125.664 


1256.6 


1/4 


151.582 


1828.5 


V2 


177.500 


2507.2 


Vs 


126.056 


1264.5 


3/8 


151.975 


1837.9 


5/8 


177.893 


2518.3 


1/4 


126.449 


1272.4 


1/2 


152.367 


1847.5 


3/4 


178.285 


2529.4 


3/8 


126.842 


1280.3 


5/8 


152.760 


1857.0 


7/8 


178.678 


2540.6 


V2 


127.235 


1288.2 


3/4 


153.153 


1866.5 


57. 


179.071 


2551.8 


5/8 


127.627 


1296.2 


7/8 


153.545 


1876. 1 


Vs 


179.463 


2563.0 


3/4 


128.020 


1304.2 


49. 


153.938 


1885.7 


V4 


179.856 


2574.2 


7/8 


128.413 


1312.2 


1/8 


154.331 


1895.4 


3/8 


180.249 


2585.4 


41. 


128.805 


1320.3 


1/4 


154.723 


1905.0 


V2 


180.642 


2596.7 


1/8 


129.198 


1328.3 


3/8 


155.116 


1914.7 


5/8 


181.034 


2608.0 


1/4 


129.591 


1336.4 


1/2 


155.509 


1924.4 


3/4 


181.427 


2619.4 


3/8 


129.983 


1344.5 


5/8 


155.902 


1934.2 


7/8 


181.820 


2630.7 


V2 


130.376 


1352.7 


3/4 


156.294 


1943.9 


58. 


182.212 


2642. 1 


5/8 


130.769 


1360.8 


7/8 


156.687 


1953.7 


Vs 


182.605 


2653.5 


8/4 


131.161 


1369.0 


50. 


157.080 


1963.5 


V4 


182.998 


2664.9 


7/8 


131.554 


1377.2 


Vs 


157.472 


1973.3 


3/s 


183.390 


2676.4 


43. 


131.947 


1385.4 


1/4 


157.865 


1983.2 


V2 


183.783 


2687.8 


1/8 


132.340 


1393.7 


3/8 


158.258 


1993.1 


5/8 


184. 176 


2699.3 


1/4 


132.732 


1402.0 


!/•> 


158.650 


2003.0 


3/4 


184.569 


2710.9 


3/8 


133.125 


1410.3 


5/8 


159.043 


2012.9 


7/s 


184.961 


2722.4 


1/2 


133.518 


1418.6 


3/4 


159.436 


2022.8 


59. 


185.354 


2734.0 


5/8 


133.910 


1427.0 


7/8 


159.829 


2032.8 


Vs 


185.747 


2745.6 


3/4 


134.303 


1435.4 


51. 


160.221 


2042.8 


V4 


186.139 


2757.2 


7/8 


134.696 


1443.8 


Vs 


160.614 


2052.8 


3/8 


186.532 


2768.8 


43. 


135.088 


1452.2 


1/4 


161.007 


2062.9 


V2 


186.925 


2780.5 


1/8 


135.481 


1460.7 


3/8 


161.399 


2073.0 


5/8 


187.317 


2792.2 


1/4 


135.874 


1469.1 


1/2 


161.792 


2083.1 


3/4 


187.710 


2803.9 


3/8 


136.267 


1477.6 


5/8 


162.185 


2093.2 


7/8 


188.103 


2815.7 


1/2 


136.659 


1486.2 


3/4 


162.577 


2103.3 


60. 


188.496 


2827.4 


5/8 


137.052 


1494.7 


7/8 


162.970 


2113.5 


Vs 


188.888 


2839.2 


3/4 


137.445 


1503.3 


53. 


163.363 


2123.7 


V4 


189.281 


2851.0 


7/8 


137.837 


1511.9 


V8 


163.756 


2133.9 


3/s 


189.674 


2862.9 


44. 


138.230 


1520.5 


1/4 


164.148 


2144.2 


V2 


190.066 


2874.8 


1/8 


138.623 


1529.2 


3/8 


164.541 


2154.5 


5/8 


190.459 


2886.6 


V4 


139.015 


1537.9 


V2 


164.934 


2164.8 


3/4 


190.852 


2898.6 


3/8 


139.408 


1546.6 


5/8 


165.326 


2175.1 


7/s 


191.244 


2910.5 


V2 


139.801 


1555.3 


3/4 


165.719 


2185.4 


61. 


191.637 


2922.5 


5/8 


140.194 


1564.0 


7/8 


166.112 


2195.8 


Vs 


192.030 


2934.5 


3/4 


140.586 


1572.8 


53. 


166.504 


2206.2 


V4 


192.423 


2946.5 


7/8 


140.979 


1581.6 


1/8 


166.897 


2216.6 


3/8 


192.815 


2958.5 


45. 


141.372 


1590.4 


V4 


167.290 


2227.0 


V2 


193.208 


2970.6 


V8 


141.764 


1599.3 


3/8 


167.683 


2237.5 


5/s 


193.601 


2982.7 


1/4 


142.157 


1608.2 


V2 


168.075 


2248.0 


3/4 


193.993 


2994.8 


3/8 


142.550 


1617.0 


5/8 


168.468 


2258.5 


7/8 


194.386 


3006.9 


V2 


142.942 


1626.0 


3/4 


168.861 


2269.1 


63. 


194.779 


3019.1 


5/8 


143.335 


1634.9 


7/8 


169.253 


2279.6 


i/s 


195.171 


3031.3 


3/4 


143.728 


1643.9 


54. 


169.646 


2290.2 


V4 


195.564 


3043.5 


7/8 


144.121 


1652.9 


Vs 


170.039 


2300.8 


3/8 


195.957 


3055.7 


46. 


144.513 


1661.9 


V4 


170.431 


2311.5 


V2 


196.350 


3068.0 


1/8 


144.906 


1670.9 


3/8 


170.824 


2322.1 


5/8 


196.742 


3080.3 


1/4 


145.299 


1680.0 


V2 


171.217 


2332.8 


3/4 


197.135 


3092.6 


3/8 


145.691 


1689.1 


5/8 


171.609 


2343.5 


7/s 


197.528 


3104.9 


, V2 


146.084 


1698,2 


3/4 


172.002 


2354.3 


63. 


197.920 


3117.2 



114 



MATHEMATICAL TABLES. 



Diara. 


Circura. 


Area. 


Diam. 


Circum. 


Area. 


Diam. 


Circum. 


Area. 


63 Vi" 


198.313 


3129.6 


224.23 1 


400 1 . 1 


795/8 


250.149 


4979.5 


V4 


198.706 


3142.0 


1/2 224.624 


4015.2 


3/4 


250.542 


4995.2 


3/8 


199.098 


3154.5 


5/8 


225.017 


4029.2 


7/8 


250.935 


5010.9 


1/2 


199.491 


3166.9 


3/4 


223.409 


4043.3 


80. 


251.327 


5026.5 


5/8 


199.884 


3179.4 


7/8 


225.802 


4057.4 


I'S 


251.720 


5042.3 


3/4 


200.277 


3191.9 


72. 


226.195 


4071.5 


1/4 


252.113 


5058.0 


'/8 


200.669 


3204.4 


1/8 


226.587 


4085.7 


3/8 


252.506 


5073.8 


64. 


201.062 


3217.0 


1/4 


226.980 


4099.8 


1/2 


252.898 


5089.6 


1/8 


201.455 


3229.6 


3/8 


227.373 


4114.0 


5/8 


253.291 


5105.4 


1/4 


201.847 


3242.2 


1/2 


227.765 


4128.2 


3/4 


253.684 


5121.2 


3/8 


202.240 


3254.8 


5/8 


228.158 


4142.5 


7/8 


254.076 


5137.1 


1/2 


202.633 


3267.5 


3/4 


228.551 


4156.8 


81. 


254.469 


5153.0 


5/8 


203.025 


3280.1 


7/8 


228.944 


4171.1 


1'8 


254.862 


5168.9 


3/4 


203.418 


3292.8 


73. 


229.336 


4185.4 


1/4 


255.254 


5184.9 


7/8 


203.811 


3305.6 


1/8 


229.729 


4199.7 


3/8 


255.647 


5200.8 


65. 


204.204 


3318.3 


1/4 


230.122 


4214.1 


1/2 


256.040 


5216.8 


1/8 


204.596 


3331.1 


3/8 


230.514 


4228.5 


5/8 


256.433 


5232.8 


1/4 


204.989 


3343.9 


1/2 


230.907 


4242.9 


3/4 


256.825 


5248.9 


3/8 


205.382 


3356.7 


5/8 


231.300 


4257.4 


7/8 


257.218 


5264.9 


V2 


205.774 


3369.6 


3/4 


23 1 . 692 


4271.8 


83. 


257.611 


5281.0 


5/8 


206.167 


3382.4 


7/8 


232.085 


4286.3 


1/8 


258.003 


5297.1 


3/4 


206.560 


3395.3 


74. 


232.478 


4300.8 


1/4 


258.396 


5313.3 


7/8 


206.952 


3408.2 


1/8 


232.871 


4315.4 


3/8 


258.789 


5329.4 


66. 


207.345 


3421.2 


1/4 


233.263 


4329.9 


1/2 


259.181 


5345.6 


1/8 


207.738 


3434.2 


3/8 


233.656 


4344.5 


5/8 


259.574 


5361.8 


1/4 


208.131 


3447.2 


1/2 


234.049 


4359.2 


3/4 


259.967 


5378.) 


3/8 


208.523 


3460.2 


5/8 


234.441 


4373.8 


7/8 


260.359 


5394.3 


1/2 


208.916 


3473.2 


3/4 


234.834 


4388.5 


83. 


260.752 


5410.6 


5/8 


209.309 


3486.3 


7/8 


235.227 


4403.1 


1/8 


261.145 


5426.9 


3/4 


209.701 


3499.4 


75. 


235.619 


4417.9 


1/4 


261.538 


5443.3 


7/8 


210.094 


3512.5 


1/8 


236.012 


4432.6 


3/8 


261.930 


5459.6 


67. 


210.487 


3525.7 


1/4 


236.405 


4447.4 


1/2 


262.323 


5476.0 


1/8 


210.879 


3538.8 


3/8 


236.798 


4462.2 


5/8 


262.716 


5492.4 


1/4 


211.272 


3552.0 


1/2 


237.190 


4477.0 


3/4 


263.108 


5508.8 


3/8 


2H.665 


3565.2 


5/8 


237.583 


4491.8 


7/8 


263.501 


5525.3 


1/2 


212.058 


3578.5 


3/4 


237.976 


4506.7 


84. 


263.894 


5541.8 


5/8 


212.450 


3591.7 


7/8 


238.368 


4521.5 


1/8 


264.286 


5558.3 


3/4 


212.843 


3605.0 


76. 


238.761 


4536.5 


1/4 


264.679 


5574.8 


7/8 


213.236 


3618.3 


1/8 


239.154 


4551.4 


3/8 


265.072 


5591.4 


68. 


213.628 


3631.7 


1/4 


239.546 


4566.4 


1/2 


265.465 


5607.9 


1/8 


214.021 


3645.0 


3/8 


239.939 


4581.3 


5/8 


265.857 


5624.5 


1/4 


214.414 


3658.4 


1/2 


240.332 


4596.3 


3/4 


266.250 


5641.2 


3/8 


214.806 


3671.8 


5/8 


240.725 


4611.4 


7/8 


266.643 


5657.8 


1/2 


215.199 


3685.3 


Vi 


241.117 


4626.4 


85. 


267.035 


5674.5 


5/8 


215.592 


3698.7 


7/8 


241.510 


4641.5 


1/8 


267.428 


5691.2 


3/4 


2 1 5 . 984 


3712.2 


77. 


241.903 


4656.6 


1/4 


267.821 


5707.9 


7/8 


216.377 


3725.7 


1/8 


242.295 


4671.8 


3/8 


268.213 


5724.7 


69. 


216.770 


3739.3 


1/4 


242.688 


4686.9 


l/o 


268.606 


5741.5 


1/8 


217.163 


3752.8 


3/8 


243.081 


4702.1 


5/8 


268.999 


5758.3 


1/4 


217.555 


3766.4 


1/2 


243.473 


4717.3 


3/4 


269.392 


5775.1 


3/8 


217.948 


3780.0 


5/8 


243.866 


4732.5 


7/8 


269.784 


5791.9 


1/2 


218.341 


3793.7 


3/4 


244.259 


4747.8 


86. 


270.177 


5808.8 


5/8 


218.733 


3807.3 


7/8 


244.652 


4763.1 


1/8 


270.570 


5825.7 


3/4 


219.126 


3821.0 


78. 


245.044 


4778.4 


1/4 


270.962 


5842.6 


7/8 


219.519 


3834.7 


1/8 


245.437 


4793.7 


3/8 


271.355 


5859.6 


70. 


219.911 


3848.5 


1/4 


245.830 


4809.0 


1/2 


271.748 


5876.5 


1/8 


220.304 


3862.2 


3/8 


246.222 


4824.4 


5/8 


272.140 


5893.5 


1/4 


220.697 


3876.0 


l/o 


246.615 


4839.8 


3/4 


272.533 


5910.6 


3/8 


22 1 . 090 


3889.8 


5/8 


247.008 


4855.2 


7/8 


272.926 


5927.6 


1/2 


221.482 


3903.6 


3/4 


247 400 


4870.7 


87. 


273.319 


5944.7 


5/8 


221.875 


3917.5 


7/8 


247.793 


4886.2 


1/8 


273.711 


5961.8 


3/4 


222.268 


3931.4 


79. 


248. 186 


4901.7 


1/4 


274.104 


5978.9 


7/H 


222.660 


3945 3 


1/8 


248.579 


4917.2 


3/8 


274.497 


5996.0 


71. 


223.053 


3959 2 


V4 


248.971 


4932.7 


1/2 


274.889 


6013.2 


1/8 


223.446 


3973 1 


3/8 


249.364 


4948.3 


5/8 


275.282 


6030.4 


1/4 


223.838 


3987.1 


1/3 


249.757 


4963.9 


3/4 


275.675 


6047.6 



CIRCUMFERENCES AND AREAS OF CIRCLES. 115 



Diain 


. Circum. 


Area. 


Diam 


. Circum. 


Area. 


Diam 


. Circum. 


Area. 


87 7/8 


276.065 


6064.9 


957/8 


301.20C 


7219.4 


130 


408.41 


13273.23 


88. 


276. 46C 


) 6082.1 


96. 


301.593 


7238.2 


131 


411.55 


13478.22 


1/8 


276.853 


6099.4 


1/8 


301.986 


7257.1 


132 


414.69 


13684.78 


V4 


277.246 


6116.7 


1/4 


302.378 


7276.0 


133 


417.83 


13892.91 


S/8 


277.638 


6134.1 


3/8 


i 302.771 


7294.9 


134 


420.97 


14102.61 


1/2 


278.031 


6151.4 


1/2 


303.164 


7313.8 


135 


424.12 


14313.88 


5/8 


278.424 


6168.8 


5/8 


303.556 


7332.8 


136 


427.26 


14526.72 


3/4 


278.816 


6186.2 


3/4 


303.949 


7351.8 


137 


430.40 


14741.14 


7/8 


279.209 


6203.7 


7/8 


304.342 


7370.8 


138 


433.54 


14957.12 


89. 


279.602 


6221.1 


97. 


304.734 


7389.8 


139 


436.68 


15174.68 


1/8 


279.994 


6238.6 


1/8 


305.127 


7408.9 


140 


439.82 


15393.80 


1/4 


280.387 


6256.1 


1/4 


305.520 


7428.0 


141 


442.96 


15614.50 


3/8 


280.780 


6273.7 


3/8 


305.913 


7447.1 


142 


446.11 


15836.77 


1/2 


281.173 


6291.2 


1/2 


306.305 


7466.2 


143 


449.25 


16060.61 


5/8 


281.565 


6308.8 


5/8 


306.698 


7485.3 


144 


452.39 


16286.02 


3/4 


281.958 


6326.4 


3/4 


307.091 


7504.5 


145 


455.53 


16513.00 


7/8 


282.351 


6344.1 


7/8 


307.483 


7523.7 


146 


458.67 


16741.55 


90. 


282.743 


6361.7 


98. 


307.876 


7543.0 


147 


461.81 


16971.67 


1/8 


283.136 


6379.4 


1/8 


308.269 


7562.2 


148 


464.96 


17203.36 


1/4 


283.529 


6397.1 


1/4 


308.661 


7581.5 


149 


468.10 


17436.62 


3/8 


283.921 


64 1 4 . 9 


3/8 


309.054 


7600.8 


150 


471.24 


17671.46 


!/•> 


284.314 


6432.6 


1/2 


309.447 


7620. 1 


151 


474.38 


17907.86 


4 


284.707 


6450.4 


5/8 


309.840 


7639.5 


152 


477.52 


18145.84 


3/4 


285. 100 


6468.2 


8/4 


310.232 


7658.9 


153 


480.66 


18385.39 


7/8 


285.492 


6486.0 


7/8 


310.625 


7678.3 


154 


483.81 


18626.50 


91. 


285 . 885 


6503.9 


99. 


311.018 


7697.7 


155 


486.95 


18869.19 


1/8 


286.278 


6521.8 


1/8 


311.410 


7717.1 


156 


490.09 


19113.45 


1/4 


286.670 


6539.7 


1/4 


311.803 


7736.6 


157 


493.23 


19359.28 


3/8 


287.063 


6557.6 


3/8 


312.196 


7756.1 


158 


496.37 


19606.68 


1/2 


287.456 


6575.5 


1/2 


312.588 


7775.6 


159 


499.51 


19855.65 


5/8 


287.848 


6593.5 


5/8 


312.981 


7795.2 


160 


502.65 


20106.19 


3/4 


288.241 


6611.5 


3/4 


313.374 


7814.8 


161 


505.80 


20358.31 


7/8 


288.634 


6629.6 


7/8 


313.767 


7834.4 


162 


508.94 


20611.99 


92. 


289.027 


6647.6 


100 


314.159 


7854.0 


163 


512.08 


20867.24 


1/8 


289.419 


6665 . 7 


101 


317.30 


8011.85 


164 


515.22 


21124.07 


1/4 


289.812 


6683.8 


102 


320.44 


8171.28 


165 


518.36 


21382.46 


3/8 


290.205 


6701.9 


103 


323.58 


8332.29 


166 


521.50 


21642.43 


1/2 


290.597 


6720.1 


104 


326.73 


8494.87 


167 


524.65 


21903.97 


5/8 


290.990 


6738.2 


105 


329.87 


8659.01 


168 


527.79 


22167.08 


3/4 


291.383 


6756.4 


106 


333.01 


8824.73 


169 


530.93 


22431.76 


7/8 


291.775 


6774.7 


107 


336.15 


8992.02 


170 


534.07 


22698.01 


dS. 


292.168 


6792.9 


108 


339.29 


9160.88 


171 


537.21 


22965.83 


1/8 


292.561 


6811.2 


109 


342.43 


9331.32 


172 


540.35 


23235.22 


1/4 


292.954 


6829.5 


110 


345.58 


9503.32 


173 


543.50 


23506.18 


3/8 


293.346 


6847.8 


111 


348.72 


9676.89 


174 


546.64 


23778.71 


1/2 


293.739 


6866.1 


112 


351.86 


9852.03 


175 


549.78 


24052.82 


5/8 


294.132 


6884.5 


113 


355.00 


10028.75 


176 


552.92 


24328.49 


3/4 


294.524 


6902.9 


114 


358.14 


10207.03 


177 


556.06 


24605 . 74 


7/8 


294.917 


6921.3 


115 


361.28 


10386.89 


178 


559.20 


24884.56 


»4. 


295.310 


6939.8 


116 


364.42 


10568.32 


179 


562.35 


25164.94 


1/8 


295.702 


6958.2 


117 


367.57 


10751.32 


180 


565.49 


25446.90 


1/4 


296.095 


6976.7 


118 


370.71 


10935.88 


181 


568.63 


25730.43 


S/8 


296.488 


6995.3 


119 


373.85 


11122.02 


182 


571.77 


26015.53 


1/2 


296.881 


7013.8 


120 


376.99 


11309.73 


183 


574.91 


26302.20 


5/8 


297.273 


7032.4 


121 


380.13 


11499.01 


184 


578.05 


26590.44 


3/4 


297.666 


7051.0 


122 


383.27 


11689.87 


185 


581.19 


26880.25 


7/8 


298.059 


7069.6 


123 


386.42 


11882.29 


186 


584.34 


27171.63 


»5. 


298.451 


7088.2 


124 


389.56 


12076.28 


187 


587.48 


27464.59 


1/8 


298.844 


7106.9 


125 


392.70 


12271.85 


188 


590.62 


27759.11 


1/4 


299.237 


7125.6 


126 


395.84 


12468.98 


189 


593.76 


28055.21 


3/8 


299.629 


7144.3 


127 


398.98 


12667.69 


190 


596.90 


28352.87 


1/2 


300.022 


7163.0 


128 


402.12 


12867.96 


191 


600.04 


28652.11 


5/8 


300.415 


7181.8 


129 


405.27 


13069.81 


192 


603.19 


28952.92 


3/4 


300.807 


7200.6 






1 







116 



MATHEMATICAL TABLES. 



Diam. 


Circum. 


Area. 


Diam 


jcircum. 


Area. 


Diam 


Circum. 


Area. 


193 


606.33 


29255.30 


260 


816.81 


53092.92 


327 


1027.30 


83981.84 


194 


609.47 


29559.25 


261 


819.96 


53502.11 


328 


1030.44 


84496.28 


195 


612.61 


29864.77 


262 


823.10 


53912.87 


329 


1033.58 


85012.28 


196 


615.75 


30171.86 


263 


826.24 


54325.21 


330 


1036.73 


85529.86 


197 


618.89 


30480.52 


264 


829.38 


54739. 11 


331 


1039.87 


86049.01 


198 


622.04 


30790.75 


265 


832.52 


55154.59 


332 


1043.01 


86569.73 


199 


625.18 


31102.55 


266 


835.66 


55571.63 


333 


1046. 15 


87092.02 


200 


628.32 


31415.93 


267 


838.81 


55990.25 


334 


1049.29 


87615.88 


201 


63 1 . 46 


31730.87 


268 


841.95 


56410.44 


335 


1052.43 


88141.31 


202 


634.60 


32047.39 


269 


845.09 


56832.20 


336 


1055.58 


88668.31 


203 


637.74 


32365.47 


270 


848.23 


57255.53 


337 


1058.72 


89196.88 


204 


640.88 


32685. 13 


271 


851.37 


57680.43 


338 


1061.86 


89727.03 


205 


644.03 


33006.36 


272 


854.51 


58106.90 


339 


1065.00 


90258.74 


206 


647. 17 


33329. 16 


273 


857.65 


58534.94 


340 


1068. 14 


90792.03 


207 


650.31 


33653.53 


274 


860.80 


58964.55 


341 


1071.28 


91326.88 


208 


653.45 


33979.47 


275 


863.94 


59395.74 


342 


1074.42 


91863.31 


209 


656.59 


34306.98 


276 


867.08 


59828.49 


343 


1077.57 


92401.31 


210 


659.73 


34636.06 


277 


870.22 


60262.82 


344 


1080.71 


92940.88 


211 


662.88 


34966.71 


278 


873.36 


60698.71 


345 


1083.85 


93482.02 


212 


666.02 


35298.94 


279 


876.50 


61136. 18 


346 


1086.99 


94024.73 


213 


669.16 


35632.73 


280 


879.65 


61575.22 


347 


1090. 13 


94569.01 


214 


672.30 


35968.09 


281 


882.79 


62015.82 


348 


1093.27 


95114.86 


215 


675.44 


36305.03 


282 


885.93 


62458.00 


349 


1096.42 


95662.28 


216 


678.58 


36643.54 


283 


889.07 


62901.75 


350 


1099.56 


96211.28 


217 


681.73 


36983.61 


284 


892.21 


63347.07 


351 


1102.70 


96761.84 


218 


684.87 


37325.26 


285 


895.35 


63793.97 


352 


1105.84 


97313.97 


219 


688.01 


37668.48 


286 


898.50 


64242.43 


353 


1108.98 


97867.68 


220 


691. 15 


38013.27 


287 


901.64 


64692.46 


354 


1112.12 


98422.96 


221 


694.29 


38359.63 


288 


904.78 


65144.07 


355 


1115.27 


98979.80 


222 


697.43 


38707.56 


289 


907.92 


65597.24 


356 


1118.41 


99538.22 


223 


700.58 


39057.07 


290 


911.06 


66051.99 


357 


1121.55 


100098.21 


224 


703.72 


39408. 14 


291 


914.20 


66508.30 


358 


1124.69 


100659.77 


225 


706.86 


39760.78 


292 


917.35 


66966. 19 


359 


1127.83 


101222.90 


226 


710.00 


401 15.00 


293 


920.49 


67425.65 


360 


1130.97 


101787.60 


227 


713.14 


40470.78 


294 


923.63 


67886.68 


361 


1134.11 


102353.87 


228 


716.28 


40828. 14 


295 


926.77 


68349.28 


362 


1137.26 


102921.72 


229 


719.42 


41187.07 


296 


929.91 


68813.45 


363 


1140.40 


103491. 13 


230 


722.57 


41547.56 


297 


933.05 


69279.19 


364 


1143.54 


104062. 12 


231 


725.71 


41909.63 


298 


936.19 


69746.50 


365 


1146.68 


104634.67 


232 


728.85 


42273.27 


299 


939.34 


70215.38 


366 


1149.82 


105208.80 


233 


73 1 . 99 


42638.48 


300 


942.48 


70685 . 83 


367 


1152.96 


105784.49 


234 


735.13 


43005.26 


301 


945.62 


71157.86 


368 


1156. 11 


106361.76 


235 


738.27 


43373.61 


302 


948.76 


71631.45 


369 


1159.25 


106940.60 


236 


741.42 


43743.54 


303 


951.90 


72106.62 


370 


1162.39 


107521.01 


237 


744.56 


441 15.03 


304 


955.04 


72583.36 


371 


1165.53 


108102.99 


238 


747.70 


44488.09 


305 


958.19 


73061.66 


372 


1168.67 


108686.54 


239 


750.84 


44862.73 


306 


961.33 


73541.54 


373 


1171.81 


109271.66 


240 


753.98 


45238.93 


307 


964.47 


74022.99 


374 


1174.96 


109858.35 


241 


757.12 


45616.71 


308 


967.61 


74506.01 


375 


1178. 10 


110446.62 


242 


760.27 


45996.06 


309 


970.75 


74990.60 


376 


1181.24 


111036.45 


243 


763.41 


46376.98 


310 


973.89 


75476.76 


377 


1184.33 


111627.86 


244 


766.55 


46759.47 


311 


977.04 


75964.50 


378 


1187.52 


112220.83 


245 


769.69 


47143.52 


312 


980. 18 


76453.80 


379 


1190.66 


112815.38 


246 


772.83 


47529. 16 


313 


983.32 


76944.67 


380 


1193.81 


113411.49 


247 


775.97 


47916.36 


314 


986.46 


77437.12 


381 


1196.95 


114009.18 


248 


779. 11 


48305. 13 


315 


989.60 


77931.13 


382 


1200.09 


114608.44 


249 


782.26 


48695.47 


316 


992.74 


78426.72 


383 


1203.23 


115209.27 


250 


785.40 


49087.39 


317 


995.88 


78923.88 


384 


1206.37 


115811.67 


251 


788.54 


49480.87 


318 


999.03 


79422.60 


385 


1209.51 


116415.64 


252 


791.68 


49875.92 


319 


1002.17 


79922 . 90 


386 


1212.65 


117021.18 


253 


794.82 


50272.55 


320 


1005.31 


80424.77 


387 


1215.80 


117628.30 


254 


797.96 


50670.75 


321 


1008.45 


80928.21 


388 


1218.94 


118236.98 


255 


801.11 


51070.52 


322 


1011.59 


81433.22 


389 


1222.08 


118847.24 


256 


804.25 


51471.85 


323 


1014.73 


81939.80 


390 


1225.22 


119459.06 


257 


807.39 


51874.76 


324 


1017.88 


82447.96 


391 


1228.36 


120072.46 


258 


810.53 


52279.24 


325 


1021.02 


82957.68 


392 


1231.50 


120687.46 


259 


813.67 


52685 29 326 1 


1024. 16 


83468.98 


393 


1234.65 


121303.96 



CIKCUMFERENCE8 AND AREAS OP CIRCLES. 



117 



Diam. Circum Area. Diam. Circum. Area. Diam. Circum. Area. 



1237 

1240 

1244 

1247 

1250 

1253 

1256 

1259 

1262 

1266 

1269 

1272 

1275 

1278 

1281 

1284 

1288 

1291 

1294 

1297 

1300 

1303. 

1306. 

1310. 

1313. 

1316. 

1319. 

1322. 

1325. 

1328. 

1332. 

1335. 

1338. 

1341. 

1344. 

1347. 

1350. 

1354. 

1357. 

1360. 

1363. 

1366. 

1369. 

1372. 

1376. 

1379. 

1382. 

1385. 

1388. 

1391. 

1394 

1398. 

1401. 

1404. 

1407. 

1410. 

1413. 

1416. 

1420. 

1423. 

1426. 

1429. 

1432. 

1435. 

1438. 

1441. 

1445. 



.79 

.93 

.07 

.21 

.35 

.50 

.64 

78 

92 

06 

20 

35 

49 

.63 

77 

91 

05 

.19 

.34 

.48 

.62 

.76 

.90 

.04 

.19 

.33 

.47 

.61 

.75 

.89 

.04 

.18 

.32 

.46 

.60 

.74 

.88 

.03 

17 

31 

45 

59 

73 

88 

02 

16 

30 

44I 

58 
73 
87 
01 
15 
29 
43 
58 
72 
86 
00 
14 
28 
42 
57 
71 
85 
99 
13 



121922.07 
122541.75 
123163.00 
123785.82 
124410.21 
125036.17 
125663.71 
126292.81 
126923.48 
127555.73 
128189.55 
128824.93 
129461.89 
130100.42 
130740.52 
131382.19 
132025.43 
132670.24 
133316.63 
133964.58 
134614.10 
135265.20 
135917.86 
136572.10 
137227.91 
137885.29 
138544.24 
139204.76 
139866.85 
140530.51 
141195.74 
141862.54 
142530.92 
143200.86 
143872.38 
144545.46 
145220.12 
145896.35 
146574.15 
147253.52 
147934.46 
148616.97 
149301.05 
149986.70 
150673.93 
151362.72 
152053.08 
152745.02 
153438.53 
154133.60 
154830.25 
155528.47 
156228.26 
156929.62 
157632.55 
158337.06 
159043.13 
159750.77 
160459.99 
161170.77 
161883.13 
162597.05 
163312.55 
164029.62 
164748.26 
165468.47 
166190.25 



461 

462 

463 

464 

465 

466 

467 

468 

469 

470 

471 

472 

473 

474 

475 

476 

477 

478 

479 

480 

481 

482 

483 

484 

485 

486 

487 

488 

489 

490 

491 

492 

493 

494 

495 

496 

497 

498 

499 

500 

501 

502 

503 

504 

505 

506 

507 

508 

509 

510 

511 

512 

513 

514 

515 

516 

517 

518 

519 

520 

521 

522 

523 

524 

525 

526 

527 



1448 

1451 

1454 

1457 

1460 

1463 

1467 

1470 

1473 

1476 

1479 

1482 

1485 

1489 

1492 

1495 

1498 

1501 

1504. 

1507. 

1511. 

1514. 

1517. 

1520. 

1523. 

1526. 

1529. 

1533. 

1536. 

1539. 

1542. 

1545. 

1548. 

1551. 

1555. 

1558. 

1561. 

1564. 

1567. 

1570. 

1573. 

1577. 

1580. 

1583. 

1586. 

1589. 

1592. 

1595. 

1599. 

1602. 

1605. 

1608. 

1611. 

1614. 

1617. 

1621. 

1624. 

1627. 

1630. 

1633. 

1636. 

1639. 

1643. 

1646. 

1649. 

1652. 

1655. 



27i 166913.60 
42 167638.53 
.56 168365.02 



70 
.84 
98 
12 
27 
41 
55 
69 
83 
.97 
.11 
26 
.40 
.54 
68 
82 
96 
11 
25 
39 
53 
67 
81 
96 
10 
24 
38 
52 
66 
81 
95 
09 
23 
37 
51 
65 
80 
94 
08 
22 
36 
50 
65 
79 
93 
07 
21 
35 
50 
64 
78 
92 
06 
20 
34 
49 
63 
77 
91 
05 
19 
34 
48 
62 



1 69093 . 08 

169822.72 

170553.92 

171286.70 

172021.05 

172756.97 

173494.45 

174233.51 

174974.14 

175716.35 

176460.12 

177205.46 

177952.37 

178700.86 

179450.91 

180202.54 

180955.74 

181710.50 

182466.84 

183224.75 

183984.23 

184745.28 

185507.90 

186272.10 

187037.86 

187805.19 

188574.10 

189344.5 

190116.62 

190890.24 

191665.43 

192442.18 

193220.51 

194000.41 

194781.89 

195564.93 

196349.54 

197135.72 

197923.48 

198712.80 

199503.70 

200296.17 

201090.20 

201885.81 

202682.99 

203481.74 

204282.06 

205083.95 

205887.42 

206692 . 45 

207499.05 

208307.23 

209116.97 

209928.29 

210741.18 

211555.63 

212371.66 

213189.26 

214008.43 

214829.17 

215651.49 

216475.37 

217300.82 

218127.85 



528 

529 

530 

531 

532 

533 

534 

535 

536 

537 

538 

539 

540 

541 

542 

543 

544 

545 

546 

547 

548 

549 

550 

551 

552 

553 

554 

555 

556 

557 

558 

559 

560 

561 

562 

563 

564 

565 

566 

567 

568 

569 

570 

571 

572 

573 

574 

575 

576 

577 

578 

579 

580 

581 

582 

583 

584 

585 

586 

587 

588 

589 

590 

591 

592 

593 

594 



1658 

1661 

1665 

1668 

1671 

1674 

1677 

1680 

1683 

1687 

1690 

1693 

1696 

1699 

1702 

1705 

1709 

1712 

1715 

1718 

1721. 

1724. 

1727. 

1731. 

1734. 

1737. 

1740. 

1743. 

1746. 

1749. 

1753. 

1756. 

1759. 

1762. 

1765. 

1768. 

1771. 

1775. 

1778. 

1781. 

1784. 

1787. 

1790. 

1793. 

1796. 

1800. 

1803. 

1806. 

1809. 

1812. 

1815. 

1818. 

1822. 

1825. 

1828. 

1831. 

1834. 

1837. 

1840. 

1844. 

1847. 

1850. 

1853. 

1856. 

1859. 

1862. 

1866. 



76 
90 
04 
.19 
.33 
.47 
.61 
75 
.89 
.04 
18 
.32 
46 
.60 
.74 
.88 
.03 
.17 
.31 
.45 
.59 
.73 
.88 
.02 
.16 
.30 
.44 
.58 
.73 
.87 
.01 
.15 
29 
43 
58 
72 
86 
00 
14 
28 
42 
57 
71 
85 
99 
13 
27 
42 



218956.44 
219786.61 
220618.34 
221451.65 
222286.53 
223122.98 
223961.00 
224800.59 
225641.75 
226484.48 
227328.79 
228174.66 
229022. 10 
229871.12 
230721.71 
231573.86 
232427.59 
233282.89 
234139.76 
234998.20 
235858.21 
236719.79 
237582.94 
238447.67 
239313.96 
240181.83 
241051.26 
241922.27 
242794.85 
243668.99 
244544.71 
245422.00 
246300.86 
247181.30 
248063.30 
248946.87 
249832.01 
250718.73 
251607.01 
252496.87 
253388.30 
254281.29 
255175.86 
256072.00 
256969.71 
257868.99 
258769.85 
259672.27 
56;260576.26 
70 261481.83 
84262388.96 
98^263297.67 
121264207.94 
27 265119.79 
4l'266033.21 
55;266948.20 



267864.76 
268782.89 
269702.59 
270623.86 
271546.70 
40272471.12 
54[273397.10 
68 274324.66 
821275253.78 
961276184.48 
11777116.75 



118 



MATHEMATICAL TABLES. 



Diam. 


Circum. 


595 


1869.25 


596 


1872.39 


597 


1875.53 


598 


1878.67 


599 


1881.81 


600 


1884.96 


601 


1888. 10 


602 


1891.24 


603 


1894.38 


604 


1897.52 


605 


1900.66 


606 


1903.81 


607 


1906.95 


608 


1910.09 


609 


1913.23 


610 


1916.37 


611 


1919.51 


612 


1922.65 


613 


1925.80 


614 


1928.94 


615 


1932.08 


616 


1935.22 


617 


1938.36 


618 


1941.50 


619 


1944.65 


620 


1947.79 


621 


1950.93 


622 


1954.07 


623 


1957.21 


624 


1960.35 


625 


1963.50 


626 


1966.64 


627 


1969.78 


628 


1972.92 


629 


1976.06 


630 


1979.20 


631 


1982.35 


632 


1985.49 


633 


1988.63 


634 


1991.77 


635 


1994.91 


636 


1998.05 


637 


2001.19 


638 


2004.34 


639 


2007.48 


640 


2010.62 


641 


2013.76 


642 


2016.90 


643 


2020.04 


644 


2023. 19 


645 


2026.33 


646 


2029.47 


647 


2032.61 


648 


2035.75 


649 


2038.89 


650 


2042.04 


651 


2045.18 


652 


2048.32 


653 


2051.46 


654 


2054.60 


655 


2057.74 


656 


2060.88 


657 


2064.03 


658 


2067.17 


659 


2070.31 


660 


2073.45 


661 


2076.59 


662 


2079.73 



Area. 



278050.58 
278985.99 
279922.97 
280861.52 
281801.65 
282743.34 
283686.60 
284631.44 
285577.84 
286525.82 
287475.36 
288426.48 
289379.17 
290333.43 
291289.26 
292246.66 
293205.63 
294166.17 
295128.28 
296091.97 
297057.22 
298024.05 
298992.44 
299962.41 
300933.95 
301907.05 
302881.73 
303857.98 
304835.80 
305815.20 
306796. 16 
307778.69 
308762.79 
309748.47 
310735.71 
311724.53 
312714.92 
313706.88 
314700.40 
315695.50 
316692.17 
317690.42 
318690.23 
319691.61 
320694.56 
321699.09 
322705.18 
323712.85 
324722.09 
325732.89 
326745.27 
327759.22 
328774.74 
329791.83 
330810.49 
331830.72 
332852.53 
333875.90 
334900.85 
335927.36 
336955.45 
337985.10 
339016.33 
340049.13 
341083.50 
342119.44 
343156.95 
344196.03 



Diam. Circum. 



663 

664 

665 

666 

667 

668 

669 

670 

671 

672 

673 

674 

675 

676 

677 

678 

679 

680 

681 

682 

683 

684 

685 

686 

687 

688 

689 

690 

691 

692 

693 

694 

695 

696 

697 

698 

699 

700 

701 

702 

703 

704 

705 

706 

707 

708 

709 

710 

711 

712 

713 

714 

715 

716 

717 

718 

719 

720 

721 

722 

723 

724 

725 

726 

727 



2082 

2086 

2089 

2092 

2095 

2098 

2101 

2104 

2108 

2111 

2114 

2117 

2120 

2123 

2126 

2130 

2133 

2136 

2139 

2142 

2145 

2148 

2151 

2155 

2158 

2161 

2164 

2167 

2170 

2173 

2177 

2180 

2183 

2186, 

2189 

2192 

2195. 

2199 

2202 

2205 

2208 

2211 

2214 

2217 

2221. 

2224. 

2227 

2230 

2233. 

2236. 

2239 

2243. 

2246. 

2249. 

2252 

2255 

2258. 

2261 

2265. 

2268 

2271. 

2274. 

2277. 

2280 

2283 



Area. 



728 12287 

729 12290 

730 12293 



345236.69 
346278.91 
347322.70 
1348368.07 
349415.00 
350463.51 
351513.59 
352565.24 
353618.45 
354673.24 
355729.60 
356787.54 
357847.04 
358908.11 
359970.75 
361034.97 
362100.75 
363168.11 
364237.04 
365307.54 
366379.60 
367453.24 
368528.45 
369605.23 
370683.59 
371763.51 
372845.00 
373928.07 
375012.70 
376098.91 
377186.68 
378276.03 
379366.95 
380459.44 
381553.50 
382649.13 
383746.33 
384845.10 
385945.44 
387047.36 
388150.84 
389255.90 
390362.52 
391470.72 
392580.49 
393691.82 
394804.73 
395919.21 
397035.26 
398152.89 
399272.08 
400392.84 
401515.18 
402639.08 
403764.56 
404891.60 
406020.22 
407150.41 
408282.17 
409415.50 
410550.40 
411686.87 
412824.91 
413964.52 
415105.71 
416248.46 
417392.79 
418538.68 



Diam. Circum. Area. 



731 
732 
733 

734 
735 
736 

737 
738 
739 
740 

741 

742 

743 

744 

745 

746 

747 

748 

749 

750 

751 

752 

753 

754 

755 

756 

757 

758 

759 

760 

761 

762 

763 

764 

765 

766 

767 

768 

769 

770 

771 

772 

773 

774 

775 

776 

111 

11% 

779 

780 

781 

782 

783 

784 

785 

786 

787 

788 

789 

790 

791 

792 

793 

794 

795 

796 

797 

798 



2296.501419686.15 
2299.65 420835.19 



2302.79 
2305.93 
2309.07 
2312.21 
2315.35 
2318.50 
2321.64 
2324.78 
2327.92 



421985.79 
423137.97 
424291.72 
425447.04 
426603 . 94 
427762.40 
428922.43 
430084.03 

431247.21 

2331.06 432411.95 
2334.20 433578.27 
2337.34 434746.16 
2340.49 435915.62 
2343.63 437086.64 
2346.77 438259.24 
2349.91 439433.41 
2353.05 440609.16 
2356. 19 441786.47 
2359.34 442965.35 
444145.80 
445327.83 
446511.42 
447696.59 
448883.32 
450071.63 
45126K51 
452452.96 
453645.98 
454840.57 
456036.73 
457234.46 
458433.77 
459634.64 
460837.08 
462041.10 
463246.69 
464453.84 
465662.57 
466872.87 
468084.74 
469298.18 
470513.19 
471729.77 
472947.92 
474167.65 
475388.94 
476611.81 
477836.24 
479062.25 
480289.83 
481518.97 
482749.69 
483981.98 
485215.84 
486451.28 
487688.28 
488926.85 



2362.48 
2365.62 
2368.76 
2371.90 
2375.04 
2378.19 
2381.33 
2384.47 
2387.61 
2390.75 
2393.89 
2397.04 
2400.18 
2403.32 
2406.46 
2409.60 
2412.74 
2415.88 
2419.03 
2422.17 
2425.31 
7428.45 
2431.59 
2434.73 
2437.88 
2441.02 
2444.16 
2447.30 
2450.44 
2453.58 
2456.73 
2459.87 
2463.01 
2466.15 
2469.29 
2472.43 
2475.58 

2478.72 

2481.86 490166.99 
2485.00 491408.71 
2488. 14 492651.99 
2491.28 493896.85 
2494.42 495143.28 
2497.57[496391.27 
2500.71 497640.84 
2503.85 498891.98 
2506. 9915001 44. 69 



CIRCUMFERENCES AND AREAS OF CIRCLES. 119 



Diam Circum.l Area. 



2510. 

2513. 

2516. 

2519. 

2522. 

2525. 

2528. 

2532. 

2535. 

2538. 

2541. 

2544. 

2547. 

2550. 

2554. 

2557. 

2560. 

2563. 

2566. 

2569. 

2572. 

2576. 

2579 

2582. 

2585. 

2588. 

2591. 

2594. 

2598. 

2601. 

2604. 

2607. 

2610. 

2613. 

2616. 

2620. 

2623. 

2626. 

2629. 

2632. 

2635. 

2638. 

2642. 

2645 

2648 

2651 

2654 

2657. 

2660 

2664 

2667. 

2670. 

2673. 

2676. 

2679. 

2682. 

2686. 

2689. 

2692. 

2695. 

2698. 

2701. 

2704. 

2708. 

2711. 

2714. 

2717. 

12720. 



13501398 
27 502654 
42 503912 
56 505171 
70 506431 
84 507693. 
98 508957. 
12 510222. 
27 511489. 
41 512758. 
55 514028. 
69515299. 
83 516572. 
97517847. 
11519123. 
26 520401. 
40,521681. 
54!522962. 
68 524244. 
82i525528. 
96526814. 



Diam. Circum.l Area. Diam.'circiim.l Area. 



528101 

529390. 

530680, 

531972. 

533266. 

534561. 

535858. 

537156. 

538456. 

539757. 
52J541060. 
66 542365. 

543671. 

544979. 

546288. 

547599. 

548911. 

550225. 

551541. 

552858. 

554176. 

555497. 

556819. 

558142. 

559467. 

560793. 

562122. 

563451. 
071564782. 
21 566115. 
35:567450. 
50,568786. 
64|570123. 
78 571462. 
92 572803. 
06 574145. 
20575489. 
34576834. 
49578181 



579530 
580880 
582232 
583585 
19584940 
34 586296 
48 587654 
62 589014 



97 

82 
25 
.24 
80 
94 
64 
92 
77 
19 
1 

74 

87 

57 

84 

68 

10 

08 

63 

76 

46 

73 

56 

97 

95 

50 

62 

32 

58 

41 

82 

79 

34 

46 

15 

40 

23 

63 

6 

15 

26 

94 

20 

02 

42 

39 

92 

.03 

.71 

.96 

.78 

.17 

.14 

.67 

.77 

.45 

.69 

.51 

.90 

.85 

.38 

.48 

.15 

39 

20 

59 

.54 

.07 



867 
868 
869 
870 

871 

872 

873 

874 

875 

876 

877 

878 

879 

880 

881 

882 

883 

884 

885 

886 

887 

888 

889 

890 

891 

892 

893 

894 

895 

896 

897 

898 

899 

900 

901 

902 

903 

904 

905 

906 

907 

908 

909 

910 

911 

912 

913 

914 

915 

916 

917 

918 

919 

920 

921 

922 

923 

924 

925 

926 

927 

928 

929 

930 

931 

932 

933 

934 



2723 

2726 

2730 

2733 

2736 

2739. 

2742. 

2745. 

2748. 

2752. 

2755. 

2758. 

2761. 

2764. 

2767. 

2770. 

2774. 

2777. 

2780. 

2783. 

2786. 

2789. 

2792. 

2796. 

2799. 

2802. 

2805. 

2808. 

2811. 

2814. 

2818. 

2821. 

2824. 

2827. 

2830. 

2833. 

2836. 

2840. 

2843 

2846 

2849 

2852 

2855. 

2858. 

2861. 

2865 

2868. 

2871 

2874. 

2877. 

2880. 

2883. 

2887. 

2890. 

2893. 

2896. 

2899. 

2902. 

2905. 

2909. 

2912. 

2915. 

2918. 

2921. 

2924. 

12927. 

12931. 

2934 



.76590375 
90 591737 
.04 593102 
.19 594467 
33 595835 
47 597204 
61,598574 
75,599946 
89 601320, 
04 '602695, 
18604072, 
32 605450, 
46i606830, 
60608212. 
741609595. 
88610980. 
03 612366. 
17613754. 
31 615143. 
45 616534. 
59617926. 
73 619321. 
88 620716. 
02 622113 



623512 
624913 
626314 
627718 
629123 
630530 
631938 
633348 
634759 
431636172 
58637587 
72 639003 



640420, 
641839, 
643260, 
644683, 
646107, 
647532, 
648959, 
650388, 
651818, 
653250, 
654683, 
656118, 
657554, 
658993, 
84|660432, 
98,661873 
12 663316 



664761 

666206 

667654 

669103 

.83'670554 

.97 672006 

.11 673460 

.26674915 

.40 676372 

.54 677830 

.68 679290 

.82 680752 

.96 682215 

. 1 1 683680 

.25 685146 



935 
936 
937 
938 
939 
940 
941 
942 
943 
944 
945 
946 
947 
948 
949 
9.50 
951 
952 
953 
954 
955 
956 
957 
958 
959 
960 
961 
962 
963 
964 
965 
966 
967 
968 
969 
970 
971 
972 
973 
974 
975 
976 
977 
978 
979 
980 
981 
982 
983 
984 
985 
986 
987 
988 
989 
990 
991 
992 
993 
994 
995 
996 
997 
998 
999 
1000 



2937 

2940 

2943 

2946 

2949 

2953 

2956 

2959, 

2962, 

2965, 

2968, 

2971, 

2975. 

2978. 

2981. 

2984. 

2987. 

2990 

2993 

2997 

3000 

3003 

3006 

3009 

3012 

3015. 

3019 

3022 

3025. 

3028. 

3031. 

3034 

3037 

3041. 

3044 

3047. 

3050. 

3053. 

3056 

3059. 

3063. 

3066. 

3069 

3072. 

3075 

3078 

3081 

3085 

3088 

3091 

3094 

3097 

3100 

3103 

3107 

3110 

3113 

3116 

3119. 

3122. 

3125. 

3129. 

3132. 

3135. 

3138. 

3141. 



.39686614.71 
.53 688084. 19 
.67,689555.24 
.81|691027.8e 
,96 692502.05 
, 101693977.82 
24;695455.15 
38 696934.06 
52698414.53 
66 699896.58 
81 701380. 19 
951702865.38 
09 704352.14 
23 705840.47 
37,707330.37 
51 708821.84 



710314.88 
711809.50 
713305.68 
714803.43 
716302.76 
717803.66 
.^,719306.12 
65 720810.16 
79 722315.77 
93 723822.95 
07 725331.70 
21 726842.02 
35 728353.91 
50 729867.37 
64 731382.40 
78 732899.01 
92 734417.18 
06 735936.93 
20 737458.24 
34 738981.13 
49 740505.59 
63 742031.62 
77 743559.22 
91 745088.39 
05 746619.13 
19 748151.44 
34 749685.32 
48 751220.78 
62 752757.80 
76 754296.40 
90 755836.56 
04 757378.30 
19 758921.61 
33 760466.48 
47 762012.93 
61 763560.95 
75 765110.54 
89 766661.70 
04 768214.44 
18 769768.74 
32 771324.61 
46 772882.06 
60:774441.07 
74,776001.66 
88 777563.82 
779127.54 
780692.84 
782259.71 
783828.15 
785398.16 



120 CIRCUMFERENCE OF CIRCLES, FEET AND INCHES. 






c<:-<. 



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AREAS OF THE SEGMENTS OF A CIRCLE. 



121 



AREAS OF THE SEGMENTS OF A CIRCLE. 

(Dlaineter=l; Rise or Height in parts of Diameter being given.) 

Rule for Use of the Table. — Divide the rise or height of the segment 
by the diameter. Multiply the area in the table corresponding to the 
quotient thus found by the square of the diameter. 

// the segment exceeds a semicircle its area is area of circle — area of seg- 
ment whose rise i^ (diam. of circle — rise of given segment). 

Given chord and rise, to find diameter. Diam. = (square of half chord -j- 
rise) + rise. The half chord is a mean proportional between the two parts 
into which the chord divides the diameter which is perpendicular to it. 



Rise 




Rise 




Rise 




Rise 




Rise 




-t- 


Area. 


-f- 


Area. 


-r- 


Area. 


■4- 


Area. 


-;- 


Area. 


ttam. 




Diam. 




Diam. 




Diam. 




Diam. 




.001 


.00004 


.054 


•01646 


.107 


.04514 


.16 


.08111 


.213 


.12235 


.002 


.00012 


.055 


.01691 


.108 


.04576 


.161 


.08185 


.214 


.12317 


.003 


.00022 


.056 


.01737 


.109 


.04638 


.162 


.08258 


.215 


.12399 


.004 


.00034 


.057 


.01783 


] ] 


.04701 


.163 


.08332 


.216 


.12481 


.005 


.00047 


.058 


.01830 


.111 


.04763 


.164 


.08406 


.217 


.12563 


.006 


.00062 


.059 


.01877 


.112 


.04826 


.165 


.08480 


.218 


. 1 2646 


.007 


.00078 


.06 


.01924 


.113 


.04889 


.166 


.08554 


.219 


.12729 


.008 


.00095 


.061 


.01972 


.114 


.04953 


.167 


.08629 


.22 


.12811 


.009 


.00113 


.062 


.02020 


.115 


.05016 


.168 


.08704 


.221 


.12894 


.01 


.00133 


.063 


.02068 


.116 


.05080 


.169 


.08779 


.222 


.12977 


.011 


.00153 


.064 


.02117 


.117 


.05145 


.17 


.08854 


.223 


.13060 


.012 


.00175 


.065 


.02166 


.118 


.05209 


.171 


.08929 


.224 


.13144 


.013 


.00197 


.066 


.02215 


.119 


.05274 


.172 


.09004 


.225 


.13227 


.014 


.0022 


.067 


.02265 


.12 


.05338 


.173 


.09080 


.226 


.13311 


.015 


.00244 


.068 


.02315 


.121 


.05404 


.174 


.09155 


.227 


.13395 


.016 


.00268 


.069 


.02366 


.122 


.05469 


.175 


.09231 


.228 


.13478 


.017 


.00294 


.07 


.02417 


.123 


.05535 


.176 


.09307 


.229 


.13562 


.018 


.0032 


.071 


.02468 


.124 


.05600 


.177 


.09384 


.23 


.13646 


.019 


.00347 


.072 


.02520 


.125 


.05666 


.178 


.09460 


.231 


.13731 


.02 


.00375 


.073 


.02571 


.126 


.05733 


.179 


.09337 


.232 


.13815 


.021 


.00403 


.074 


.02624 


.127 


.05799 


.18 


.09613 


.233 


.13900 


.022 


00432 


.075 


.02676 


.128 


.05866 


.181 


.09690 


.234 


.13984 


.023 


.00462 


.076 


.02729 


.129 


.05933 


.182 


.09767 


.235 


.14069 


.024 


.0Q492 


.077 


.02782 


.13 


.06000 


.183 


.09845 


.236 


.14154 


.025 


.00523 


.078 


.02836 


.131 


.06067 


.184 


.09922 


.237 


.14239 


.026 


.00555 


.079 


.02889 


.132 


.06135 


.185 


.10000 


,238 


.14324 


.027 


.00587 


.08 


.02943 


.133 


.06203 


.186 


.10077 


.239 


.14409 


.028 


.00619 


.081 


.02998 


.134 


.06271 


.187 


.10155 


.24 


.14494 


.029 


.00653 


.082 


.03053 


.135 


.06339 


.188 


.10233 


.241 


.14580 


.03 


.00687 


.083 


.03108 


.136 


.06407 


.189 


.10312 


.242 


.14666 


.031 


.00721 


.084 


.03 1 63 


.137 


.06476 


.19 


.10390 


.243 


.14751 


.032 


.00756 


.085 


.03219 


.138 


.06545 


.191 


. 1 0469 


.244 


.14837 


.033 


.00791 


.086 


.03275 


.139 


.06614 


.192 


.10547 


.245 


.14923 


.034 


.00827 


.087 


.03331 


.14 


.06683 


.193 


.10626 


.246 


.15009 


.035 


.00864 


.088 


.03387 


.141 


.06753 


.194 


.10705 


.247 


.15095 


.036 


.00901 


.089 


.03444 


.142 


.06822 


.195 


.10784 


.248 


.15182 


.037 


.00938 


.09 


.03501 


.143 


.06892 


.196 


.10864 


.249 


.15268 


.038 


.00976 


091 


.03559 


.144 


.06963 


.197 


.10943 


.25 


.15355 


.039 


.01015 


.092 


.03616 


.145 


.07033 


.198 


.11023 


.251 


.15441 


.04 


.01054 


.093 


.03674 


.146 


.07103 


.199 


.11102 


.252 


.15528 


.041 


.01093 


.094 


.03732 


.147 


.07174 


.2 


.11182 


.253 


.15615 


.042 


.01133 


.095 


.03791 


.148 


.07245 


.201 


.11262 


.254 


.15702 


.043 


.01173 


.096 


.03850 


.149 


.07316 


.202 


.11343 


.255 


.15789 


.044 


.01214 


.097 


.03909 


.15 


.07387 


.203 


.11423 


.256 


.15876 


.045 


.01255 


.098 


.03968 


.151 


.07459 


.204 


.11504 


.257 


.15964 


.046 


.01297 


.099 


.04028 


.152 


.07531 


.205 


.11584 


.258 


.16051 


.047 


.01339 


1 


.04087 


.153 


.07603 


.206 


.11665 


.259 


.16139 


.048 


.01382 


;ioi 


.04148 


.154 


.07675 


.207 


.11746 


.26 


.16226 


.049 


.01425 


.102 


.04208 


.155 


.07747 


.208 


.11827 


.261 


.16314 


.05 


.01468 


.103 


.04269 


.156 


.07819 


.209 


.11908 


.262 


.16402 


.051 


.01512 


.104 


.04330 


.157 


.07892 


.21 


.11990 


.263 


.16490 


.052 


.01556 


.105 


.04391 


.158 


.07965 


.211 


.12071 


.264 


.16578 


,053 


.01601 


.106 


.04452 


.159 


.08038 


.212 


.12153 


.265 


.16666 



122 



MATHEMATICAL TABLES. 



Rise 




Rise 




Rise 




Rise 




Rise 




-h 


Area. 


-1- 


Area. 


-»- 


Area. 


-4- 


Area. 


•«- 


Area. 


Diam . 




Diam. 




Diam. 




Diam. 




Diam. 




.266 


.16755 


.313 


.21015 


.36 


.25455 


.407 


.30024 


.454 


.34676 


.267 


.16543 


.314 


.21108 


.36! 


.25551 


.408 


.30122 


.455 


.34776 


.268 


.16932 


315 


.21201 


.362 


.25647 


.409 


.30220 


.456 


.34876 


.269 


17020 


316 


.21294 


.363 


.25743 


.41 


.30319 


.457 


.34975 


.27 


. 1 7 1 09 


.317 


.21387 


.364 


.25839 


.411 


.30417 


.458 


.35075 


.271 


.17198 


.318 


.21480 


.365 


.25936 


.412 


.30516 


.459 


.35175 


.272 


.17287 


.319 


.21573 


.366 


.26032 


.413 


.30614 


.46 


.35274 


.273 


.17376 


32 


.21667 


.367 


.26128 


.414 


.30712 


.461 


.35374 


.274 


.17465 


.321 


.21760 


.368 


.26225 


.415 


.30811 


.462 


.35474 


.275 


.17554 


.322 


.21853 


.369 


.26321 


.416 


.30910 


.463 


.35573 


.276 


.17644 


.323 


.21947 


.37 


.26418 


.417 


.3 1 008 


.464 


.35673 


.277 


.17733 


.324 


.22040 


.371 


.26514 


.418 


.31107 


.465 


.35773 


.278 


.17823 


.325 


.22134 


.372 


.26611 


.419 


.31205 


.466 


.35873 


.279 


.17912 


.326 


.22228 


.373 


.26708 


.42 


.31304 


.467 


.35972 


.28 


.18002 


.327 


.22322 


.374 


.26805 


.421 


.31403 


.468 


.36072 


.281 


.18092 


.328 


.22415 


.375 


.26901 


.422 


.31502 


.469 


.36172 


.282 


.18182 


.329 


.22509 


.376 


.26998 


.423 


.31600 


.47 


.36272 


.283 


.18272 


.33 


.22603 


.377 


.27095 


.424 


.31699 


.471 


.36372 


.284 


.18362 


.331 


.22697 


.378 


.27192 


.425 


.31798 


.472 


.36471 


.285 


.18452 


.332 


.22792 


.379 


.27289 


.426 


.31897 


.473 


.36571 


.286 


.18542 


.333 


.22886 


.38 


.27386 


.427 


.3 1 996 


.474 


.36671 


.287 


.18633 


.334 


.22980 


.381 


.27483 


.428 


.32095 


.475 


.36771 


.288 


.18723 


.335 


.23074 


.382 


.27580 


.429 


.32194 


.476 


.36871 


.289 


.18814 


.336 


.23169 


.383 


.27678 


.43 


.32293 


.477 


.36971 


.29 


.18905 


.337 


.23263 


.384 


.27775 


.431 


.32392 


.478 


.37071 


.291 


.18996 


.338 


.23358 


.385 


.27872 


.432 


.32491 


.479 


.37171 


292 


.19086 


.339 


.23453 


.386 


.27969 


.433 


.32590 


.48 


.37270 


.293 


.19177 


.34 


.23547 


.387 


.28067 


.434 


.32689 


.481 


.37370 


.294 


.19268 


.341 


.23642 


.388 


.28164 


.435 


.32788 


.482 


.37470 


.295 


.19360 


.342 


.23737 


.389 


.28262 


.436 


.32887 


.483 


.37570 


.296 


.19451 


.343 


.23832 


.39 


.28359 


.437 


.32987 


.484 


.37670 


.297 


.19542 


.344 


.23927 


.391 


.28457 


.438 


.33086 


.485 


.37770 


.298 


.19634 


.345 


.24022 


.392 


.28554 


.439 


.33185 


.486 


.37870 


299 


.19725 


.346 


.24117 


.393 


.28652 


.44 


.33284 


.487 


.37970 


.3 


.19817 


.347 


.24212 


.394 


.28750 


.441 


.33384 


.488 


.38070 


.301 


.19908 


.348 


.24307 


.395 


.28848 


.442 


.33483 


.489 


.38170 


.302 


.20000 


.349 


.24403 


.396 


.28945 


.443 


.33582 


.49 


.38270 


.303 


.20092 


.35 


.24498 


.397 


.29043 


.444 


.33682 


.491 


.38370 


.304 


.20184 


.351 


.24593 


.398 


.29141 


.445 


.33781 


.492 


.38470 


.305 


.20276 


.352 


.24689 


.399 


.29239 


.446 


.33880 


.493 


.38570 


.306 


.20368 


.353 


.24784 


.4 


.29337 


.447 


.33980 


.494 


.38670 


307 


.20460 


.354 


.24880 


.401 


.29435 


.448 


.34079 


.495 


38770 


.308 


.20553 


.355 


.24976 


.402 


.29533 


.449 


.34179 


.496 


.38870 


.309 


.20645 


.356 


.25071 


.403 


.29631 


.45 


.34278 


.497 


.38970 


.31 


.20738 


.357 


.25167 


.404 


.29729 


.451 


.34378 


.498 


.39070 


.311 


.20830 


.358 


.25263 


.405 


.29827 


.452 


.34477 


.499 


.39170 


.312 


.20923 


.359 


.25359 


.406 


.29926 


.453 


.34577 


.5 


.39270 



For rules for finding the area of a segment see Mensuration, page 60. 

LENGTHS OF CIRCULAR ARCS. 

(Degrees being given. Radius of Circle = 1.) 

Formula. — Length of arc = X radius X number of degrees. 

Rule. — Multiply the factor in the table (see next page) for any given 
aumber of degrees by the radius. 
Example. — Given a curve of a radius of 55 feet and an angle of 78° 20'. 

Factor from table for 78° 1 .3613568 

Factor from table for 20' 0058178 

Factor 1.3671746 

1.3671746X55 = 75.19 feet. 



LENGTHS OF CIRCULAR ARCS. 



123 



Factors for Lengths of Circular Arcs. 



Degrees. 


Minutes. 


1 


.0174533 


61 


1.0646508 


121 


2.1118484 


1 


.0002909 


2 


.0349066 


62 


1.0821041 


122 


2.1293017 


2 


.0005818 


3 


.0523599 


63 


1.0995574 


123 


2.1467550 


3 


.0008727 


4 


.0698 1 32 


64 


1.1170107 


124 


2.1642083 


4 


.001 1636 


5 


.0872665 


65 


1.1344640 


125 


2.1816616 


5 


.0014544 


6 


.1047198 


66 


1.1519173 


126 


2.1991149 


6 


.0017453 


7 


.1221730 


67 


1.1693706 


127 


2.2165682 


7 


.0020362 


6 


.1396263 


68 


1.1868239 


128 


2.2340214 


8 


.0023271 


9 


.1570796 


69 


1.2042772 


129 


2.2514747 


9 


.0026180 


10 


.1745329 


70 


1.2217305 


130 


2.2689280 


10 


.0029089 


11 


.1919862 


71 


1.2391838 


131 


2.2863813 


11 


.0031998 


12 


.2094395 


72 


1.2566371 


132 


2.3038346 


12 


.0034907 


13 


.2268928 


73 


1.2740904 


133 


2.3212879 


13 


.0037815 


14 


.2443461 


74 


1.2915436 


134 


2.3387412 


14 


.0040724 


15 


.2617994 


75 


1.3089969 


135 


2.3561945 


15 


.0043633 


16 


.2792527 


76 


1.3264502 


136 


2.3736478 


16 


.0046542 


17 


.2967060 


77 


1.3439035 


137 


2.3911011 


17 


.0049451 


18 


.3141593 


78 


1.3613568 


138 


2.4085544 


18 


.0052360 


19 


.3316126 


79 


1.3788101 


139 


2.4260077 


19 


.0055269 


20 


.3490659 


80 


1.3962634 


140 


2.4434610 


20 


.0058178 


21 


.3665191 


81 


1.4137167 


141 


2.4609142 


21 


.0061087 


22 


.3839724 


82 


1.4311700 


142 


2.4783675 


22 


.0063995 


23 


.4014257 


83 


1.4486233 


143 


2.4958208 


23 


.0066904 


24 


.4188790 


84 


1.4660766 


144 


2.5132741 


24 


.0069813 


25 


.4363323 


85 


1.4835299 


145 


2.5307274 


25 


.0072722 


26 


.4537856 


86 


1.5009832 


146 


2.5481807 


26 


.0075631 


27 


.4712389 


87 


1.5184364 


147 


2.5656340 


27 


.0078540 


28 


.4886922 


88 


1.5358897 


148 


2.5830873 


28 


.0081449 


29 


.5061455 


89 


1.5533430 


149 


2.6005406 


29 


.0084358 


30 


.5235988 


90 


1.5707963 


150 


2.6179939 


30 


.0087266 


31 


.5410521 


91 


1.5882496 


151 


2.6354472 


31 


.0090175 


32 


.5585054 


92 


1.6057029 


152 


2.6529005 


32 


.0093084 


33 


.5759587 


93 


1 .623 1 562 


153 


2.6703538 


33 


.0095993 


34 


.5934119 


94 


1 .6406095 


154 


2.6878070 


34 


.0098902 


35 


.6108652 


95 


1 .6580628 


155 


2.7052603 


35 


.0101811 


36 


.6283185 


96 


1.6755161 


156 


2.7227136 


36 


.0104720 


37 


.6457718 


97 


1 .6929694 


157 


2.7401669 


37 


.0107629 


38 


.6632251 


98 


1.7104227 


158 


2.7576202 


38 


.0110538 


39 


.6806784 


99 


1.7278760 


159 


2.7750735 


39 


.0113446 


40 


.6981317 


100 


1.7453293- 


160 


2.792526S 


40 


.0116355 


41 


.7155850 


101 


1.7627825 


161 


2.8099801 


41 


.0119264 


42 


.7330383 


102 


1.7802358 


162 


2.8274334 


42 


.0122173 


43 


.7504916 


103 


1.7976891 


163 


2.8448867 


43 


.0125082 


44 


.7679449 


104 


1.8151424 


164 


2.8623400 


44 


.0127991 


45 


.7853982 


105 


1.8325957 


165 


2.8797933 


45 


.0130900 


46 


.8028515 


106 


1 .8500490 


166 


2.8972466 


46 


.0133809 


47 


.8203047 


107 


1.8675023 


167 


2.9146999 


47 


.0136717 


48 


.8377580 


108 


1.8849556 


168 


2.9321531 


48 


.0139626 


49 


.8552113 


109 


1.9024089 


169 


2.9496064 


49 


.0142535 


50 


.8726646 


110 


1.9198622 


170 


2.9670597 


50 


.0145444 


51 


.8901179 


111 


1.9373155 


171 


2.9845130 


51 


.0148353 


52 


.9075712 


112 


1.9547688 


172 


3.0019663 


52 


.0151262 


53 


.9250245 


113 


1.9722221 


173 


3.0194196 


53 


.0154171 


54 


.9424778 


114 


1.9896753 


174 


3.0368729 


54 


.0157080 


55 


.9599311 


115 


2.0071286 


175 


3.0543262 


55 


.0159989 


56 


.9773844 


116 


2.0245819 


176 


3.0717795 


56 


.0162897 


57 


.9948377 


117 


2.0420352 


177 


3.0892328 


57 


.0165806 


58 


1.0122910 


118 


2.0594885 


178 


3.1066861 


58 


.0168715 


59 


1.0297443 


119 


2.0769418 


179 


3.1241394 


59 


.0171624 


60 


1.0471976 


120 


2.0943951 


180 


3.1415927 


60 


.0174533 



124 



MATHEMATICAL TABLES. 



I.BNGTHS OF CIRCXJIAR ARCS. 

(Diameter = 1. Given the Chord and Height of the Arc.) 

Rule for Use of the Table. — Divide the height by the chord. Find 
in the column of heights the number equal to this quotient. Take out the 
corresponding number from the column of lengths. Multiply this last 
number by the length of the given chord; the product will be length of the 
arc. 

// the arc is greater than a semicircle, first find the diameter from the 
formula, Diam. = (square of half chord -^ rise) + rise; the formula is true 
whether the arc exceeds a semicircle or not. Then find the circumference. 
From the diameter subtract the given height of arc, the remainder will be 
height of the smaller arc of the circle; find its length according to the rule, 
and subtract it from- the circumference. 



Hgts. 


Lgths. 


Hgts. 


Lgths. 


Hgts. 


Lgths. 


Hgts. 


Lgths. 


Hgts. 


Lgths. 


0,001 


1.00002 


0.15 


1.05896 


0.238 


1.14480 


0.326 


1.26288 


0.414 


1.40788 


.005 


1.00007 


.152 


1.06051 


.24 


1.14714 


.328 


1.26588 


.416 


1.41145 


.01 


1.00027 


.154 


1.06209 


.242 


1.14951 


.33 


1.26892 


.418 


1.41503 


.015 


1.00061 


.156 


1.06368 


.244 


1.15189 


.332 


1.27196 


.42 


1.41861 


.02 


1.00107 


.158 


1.06530 


.246 


1.15428 


.334 


1.27502 


.422 


1.42221 


.025 


1.00167 


.16 


1.06693 


.248 


1.15670 


.336 


1.27810 


.424 


1.42583 


.03 


1.00240 


.162 


1.06858 


.25 


1.15912 


.338 


1.28118 


.426 


1.42945 


.035 


1.00327 


.164 


1.07025 


.252 


1.16156 


.34 


1.28428 


.428 


1.43309 


.04 


1.00426 


.166 


1.07194 


.254 


1.16402 


.342 


1.28739 


.43 


1.43673 


.045 


1.00539 


.168 


1.07365 


.256 


1.16650 


.344 


1.29052 


.432 


1.44039 


.05 


1.00665 


.17 


1.07537 


.258 


1.16899 


.346 


1.29366 


.434 


1.44405 


.055 


1.00805 


.172 


1.07711 


.26 


1.17150 


.348 


1.29681 


.436 


1.44773 


.06 


1.00957 


.174 


1.07888 


.262 


1.17403 


.35 


1.29997 


.438 


1.45142 


.065 


1.01123 


.176 


1.08066 


.264 


1.17657 


.352 


1.30315 


.44 


1.45512 


.07 


1.01302 


.178 


1.08246 


.266 


1.17912 


.354 


1.30634 


.442 


1.45883 


.075 


1.01493 


.18 


1.08428 


.268 


1.18169 


.356 


1.30954 


.444 


1.46255 


.08 


1.01698 


.182 


1.08611 


.27 


1.18429 


.358 


1.31276 


.446 


1.46628 


.085 


1.01916 


.184 


1.08797 


.272 


1.18689 


.36 


1.31599 


.448 


1.47002 


.09 


1.02146 


.186 


1.08984 


.274 


1.18951 


.362 


1.31923 


.45 


1.47377 


.095 


1.02389 


.188 


1.09174 


.276 


1.19214 


.364 


1.32249 


.452 


1.47753 


.10 


1.02646 


.19 


1.09365 


.278 


1.19479 


.366 


1.32577 


.454 


1.48131 


.102 


1.02752 


.192 


1.09557 


.28 


1.19746 


.368 


1.32905 


.456 


1.48509 


.104 


1.02860 


.194 


1.09752 


.282 


1.20014 


.37 


1.33234 


.458 


1.48889 


.106 


1.02970 


.196 


1.09949 


.284 


1.20284 


.372 


1.33564 


.46 


1.49269 


.108 


1.03082 


.198 


1.10147 


.286 


1.20555 


.374 


1.33896 


.462 


1.49651 


.11 


1.03196 


.20 


1.10347 


.288 


1.20827 


.376 


1.34229 


.464 


1.50033 


.112 


1.03312 


.202 


1.10548 


.29 


1.21102 


.378 


1.34563 


.466 


1.50416 


.114 


1.03430 


.204 


1.10752 


.292 


1.21377 


.38 


1.34899 


.468 


1.50800 


.116 


1.03551 


.206 


1.10958 


.294 


1.21654 


.382 


1.35237 


.47 


1.51185 


.118 


1.03672 


.208 


1.11165 


.296 


1.21933 


.384 


1.35575 


.472 


1.51571 


.12 


1.03797 


.21 


1.11374 


.298 


1.22213 


.386 


1.35914 


.474 


1.51958 


.122 


1.03923 


.212 


1.11584 


.30 


1.22495 


.388 


K 36254 


.476 


1.52346 


.124 


1.04051 


.214 


1.11796 


.302 


1.22778 


.39 


1.36596 


.478 


1.52736 


.126 


1.04181 


.216 


1.12011 


.304 


1.23063 


.392 


1.36939 


.48 


1.53126 


.128 


1.04313 


.218 


1.12225 


.306 


1.23349 


.394 


1.37283 


.482 


1.53518 


.13 


1.04447 


.22 


1.12444 


.308 


1.23636 


.396 


1.37628 


.484 


1.53910 


.132 


1.04584 


.222 


1.12664 


.31 


1.23926 


.398 


1.37974 


.486 


1.54302 


.134 


1.04722 


.224 


1.12885 


.312 


1.24216 


.40 


1.38322 


.488 


1.54696 


.136 


1.04862 


.226 


1.13108 


.314 


1.24507 


.402 


1.38671 


.49 


1.55091 


.138 


1.05003 


.228 


1.13331 


.316 


1.2^801 


.404 


1.39021 


.492 


1.55487 


.14 


1.05147 


.23 


1.13557 


.318 


1.25095 


.406 


1.39372 


.494 


1.55854 


.142 


1.05293 


.232 


1.13785 


.32 


1.25391 


.408 


1.39724 


.496 


1.56282 


.144 


1.05441 


.234 


1.14015 


.322 


1.25689 


.41 


1.40077 


.498 


1.56681 


.146 


1.05591 


.236 


1.14247 


.324 


1.25988 


.412 


1.40432 


.50 


1.57080 


.148 


1.05743 



















CIRCLES AND SQUARES OF EQUAL AREA. 



125 



Diameters of Circles and Sides of Squares of Same Area. 

Diameter of circle = 1.128379 X side of square of same area. 
Side of square = 0.886227 X diameter of circle of same area. . 





Side of 


•s^'^ 


Square 


J^CQ 


Equiva- 


^>^ 


lent to 


.2 w o 
0. 


Circle. 


1 


0.886 


2 


1.772 


3 


2.689 


4 


3.545 


5 


4.431 


6 


5.317 


7 


6.204 


8 


7.090 


9 


7.976 


10 


8.862 


II 


9.748 


12 


10.635 


13 


11.521 


14 


12.407 


15 


13.293 


16 


14.180 


17 


15.066 


18 


15.952 


19 


16.838 


20 


17.725 


21 


18.611 


22 


19.497 


23 


20.383 


24 


21.269 


25 


22.156 


26 


23.042 


27 


23.928 


28 


24.814 


29 


25.701 


30 


26.587 


31 


27.473 


32 


28.359 


33 


29.245 



Diam. of 


Hi 


Side of 


Circle 




Square 


Equiva- 


Equiva- 


lent to 


1-2 «- 


lent to 


Square. 


.2 y o 
Q 


Circle. 


1.128 


34 


30.132 


2.257 


35 


31.018 


3.385 


36 


31.904 


4.514 


37 


32.790 


5.642 


38 


33.677 


6.770 


39 


34.563 


7.899 


40 


35.449 


9.027 


41 


36.335 


10.155 


42 


37.222 


11.284 


43 


38.108 


12.412 


44 


38.994 


13.541. 


45 


39.880 


14.669 


46 


40.766 


15.797 


47 


41.653 


16.926 


48 


42.539 


18.054 


49 


43.425 


19.182 


50 


44.311 


20.311 


51 


45.198 


21.439 


52 


46.084 


22.568 


53 


46.970 


23.696 


54 


47.856 


24.824 


55 


48.742 


25.953 


56 


49.625 


27.081 


57 


50.515 


28.209 


58 


51.401 


29.338 


59 


52.287 


30.466 


60 


53.174 


31.595 


61 


54.060 


32.723 


62 


54.946 


33.851 


63 


55.832 


34.980 


64 


56.719 


36.108 


65 


57.605 


37.237 


66 


58.491 





^ ^ m 




Diam. of 


^■^^S 


Side of 


Circle 




Square 


Equiva- 


Equiva- 


lent to 


1-2 «- 


lent to 


Square. 


S"° 


Circle. 
59.377 


38.365 


67 


39.493 


68 


60.263 


40.622 


69 


61.150 


41.750 


70 


62.036 


42.878 


71 


62.922 


44.007 


72 


63.808 


45.135 


73 


64.695 


46.264 


74 


65.581 


47.392 


75 


66.467 


48.520 


76 


67.353 


49.649 


77 


68.239 


50.777 


78 


69.126 


51.905 


79 


70.012 


53.034 


80 


70.898 


54.162 


81 


71.784 


55.291 


82 


72.671 


56.419 


83 


73.557 


57.547 


84 


74.443 


58.676 


85 


75.330 


59.804 


86 


76.216 


60.932 


87 


77.102 


62.061 


88 


77.988 


63.189 


89 


78.874 


64.318 


90 


79.760 


65.446 


91 


80.647 


66.574 


92 


81.533 


67.703 


93 


82.419 


68.831 


94 


83.305 


69.959 


95 


84.192 


71.088 


96 


85.078 


72.216 


97 


85.964 


73.345 


98 


86.850 


74.473 


99 


87.736 



Diam. of 
Circle 

Equiva- 
lent to 
Square. 

75.601 
76.730 
77.858 
78.987 
80.115 
81.243 
82.372 
83.500 
84.628 
85.757 
86.885 
88.104 
89.142 
90.270 
91 .399 
92.527 
93.655 
94.784 
95.912 
97.041 
98.169 
99.297 
100.426 
101.554 
102.682 
103.811 
104.939 
106.068 
107.196 
108.324 
109.453 
110.581 
111.710 



Number of Circles that can be Inscribed witliin a Larger Circle. 

A^ = Nimiber of circles; D = diam. of enclosing circle; d = diam. of 
inscribed circles. 

Obtain the ratio of D -^ d and find the value nearest to it in the 
table. Opposite this value under N, find the nmnber of circles of 
diameter d that can be inscribed in a circle of diameter D, 



N 


D/d 


N 


D/d 


N 


D/d 


N 


D/d 


N 


D/d 


N 


D/d 


N 


D/d 


2 


2.00 


13 


4.23 


24 


5.72 


35 


6.86 


46 


7.81 


85 


10.46 


140 


13.26 


3 


2.15 


14 


4.41 


25 


5.81 


36 


7.00 


47 


7.92 


90 


10.73 


145 


13.49 


4 


2.41 


13 


4.55 


26 


5.92 


37 


7.00 


48 


8.00 


95 


11.15 


150 


13.72 


5 


2.70 


16 


4.70 


27 


6.00 


38 


7.08 


49 


8.03 


100 


11.34 


155 


13.95 


6 


3.00 


17 


4.86 


28 


6.13 


39 


7.18 


50 


8.13 


105 


11.60 


160 


14.17 


7 


3.00 


18 


5.00 


29 


6.23 


40 


7.31 


55 


8.21 


no 


11.85 


165 


14.39 


8 


3.31 


19 


5.00 


30 


6.40 


41 


7.39 


60 


8.94 


115 


12.10 


170 


14.60 


9 


3.61 


20 


5.18 


31 


6.44 


42 


7.43 


65 


9.25 


120 


12.34 


175 


14.81 


10 


3.80 


21 


5.31 


32 


6.55 


43 


7.61 


70 


9.61 


125 


12.57 


180 


15.01 


11 


3.92 


22 


5.49 


33 


6.70 


44 


7.70 


75 


9.93 


130 12.80 


185 


15.20 


12 


4.05 


23 


5.61 


34 


6.76 


45 


7.72 


80 


10.20 


135! 13.06 


190| 15.39 



126 



MATHEMATICAL TABLES. 



SPHERES. 

(Some errors of 1 in the last figure only. From Trautwine.) 



Diam. 


Sur- 
face. 


Vol- 
ume. 


Diam. 


Sur- 
face. 


Vol- 
ume. 


Diam. 


Sur- 
face. 


Vol- 
ume. 


1/32 


.00307 


.00002 


31/4 


33.183 


17.974 


97/8 


306.36 


504.21 


Vl6 


.01227 


.00013 


5/16 


34.472 


19.031 


10. 


314.16 


523.60 


3/32 


.02761 


.00043 


3/8 


35.78^ 


20.129 


1/8 


322.06 


543.48 


1/8 


.04909 


.00102 


7/16 


37.122 


21.268 


1/4 


330.06 


563.86 


5/32 


.07670 


.0020C 


1/2 


38.484 


22.449 


3/8 


333.16 


584.74 


3/16 


.11045 


.00345 


9/16 


39.872 


23.674 


1/2 


346.36 


606.13 


7/32 


.15033 


.0054fi 


5/8 


41.283 


24.942 


5/8 


354.66 


628.04 


1/4 


.19635 


.00818 


11/16 


42.719 


26.254 


3/4 


363.05 


650.46 


9/32 


.24851 


.01165 


3/4 


44.179 


27.611 


7/8 


371.54 


673,42 


5/16 


.30680 


.01598 


13/16 


45.664 


29.016 


11. 


380.13 


696.91 


11/32 


.37123 


.02127 


7/8 


47.173 


30.466 


1/8 


388.83 


720.95 


3/8 


.44179 


.02761 


15/16 


48.708 


31.965 


1/4 


397.61 


745.51 


13/32 


.51848 


.03511 


4. 


50.265 


33.510 


3/8 


406.49 


770.64 


7/16 


.60132 


.04385 


1/8 


53.456 


36.751 


1/2 


415.48 


796.33 


15/32 


.69028 


.05393 


1/4 


56.745 


40.195 


5/8 


424.50 


822.58 


1/2 


.78540 


.06545 


3/8 


60. 1 33 


43.847 


3/4 


433.73 


849.40 


9/16 


.99403 


.09319 


1/2 


63.617 


47.713 


7/8 


443.01 


876.79 


5/8 


1.2272 


.12783 


5/8 


67.201 


51.801 


13. 


452.39 


904.78 


11/16 


1 .4849 


.17014 


3/4 


70.883 


56.116 


1/4 


471.44 


962.52 


3/4 


1.7671 


.22089 


7/8 


74.663 


60.663 


1/2 


490.87 


1 022.7 


13/16 


2.0739 


.28084 


5. 


78.540 


65.450 


3/4 


510.71 


1085.3 


7/8 


2.4053 


.35077 


1/8 


82.516 


70.482 


13. 


530.93 


1150.3 


15/16 


2.7611 


.43143 


1/4 


86.591 


75.767 


1/4 


551.55 


1218.0 


1 


3.1416 


.52360 


3/8 


90.763 


81 .308 


1/2 


572.55 


1288.3 


1/16 


3.5466 


.62804 


1/2 


95.033 


87.113 


3/4 


593.95 


1361.2 


1/8 


3.9761 


.74551 


5/8 


99.401 


93.189 


14. 


615.75 


1436.8 


3/16 


4.4301 


.87681 


3/4 


103.87 


99.541 


1/4 


637.95 


1515,1 


1/4 


4.9088 


1.0227 


7/8 


108.44 


106.18 


1/2 


660.52 


1596.3 


5/16 


5.4119 


1.1839 


6. 


, 113.10 


113.10 


3/4 


683.49 


1680.3 


3/8 


5.9396 


1.3611 


1/8 


117.87 


120.31 


15. 


706.85 


1767.2 


7/16 


6.4919 


1.5553 


1/4 


122.72 


127.83 


1/4 


730.63 


1857.0 


1/2 


7.0686 


1.7671 


3/8 


127.68 


135.66 


1/2 


754.77 


1949.8 


9/16 


7.6699 


1.9974 


1/2 


132.73 


143.79 


3/4 


779.32 


2045.7 


5/8 


8.2957 


2.2468 


5/8 


137.89 


152.25 


16. 


804.25 


2144.7 


11/16 


8.9461 


2.5161 


3/4 


143.14 


161.03 


1/4 


829.57 


2246,8 


3/4 


9.6211 


2.8062 


7/8 


148.49 


170.14 


1/2 


855.29 


2352.1 


13/16 


10.321 


3.1177 


7. 


153.94 


179.59 


3/4 


881.42 


2460.6 


7/8 


1 1 .044 


3.4514 


1/8 


159.49 


189.39 


17. 


907.93 


2572.4 


15/16 


11.793 


3.8083 


1/4 


165.13 


199.53 


1/4 


934.83 


2687.6 


2. 


12.566 


4.1888 


3/8 


170.87 


210.03 


1/2 


962.12 


2806.2 


1/16 


13.364 


4.5939 


1/2 


176.71 


220.89 


3/4 


989.80 


2928.2 


1/8 


14.186 


5.0243 


5/8 


182.66 


232.13 


18. 


1017.9 


3053.6 


3/16 


15.033 


5.4809 


3/4 


188.69 


243.73 


1/4 


1046.4 


3182.e 


1/4 


15.904 


5.9641 


7/8 


194.83 


255.72 


1/2 


1075.2 


3315.3 


5/16 


16.800 


6.4751 


8. 


201.06 


268.08 


3/4 


1104.5 


3451.5 


3/8 


17.721 


7.0144 


1/8 


207.39 


280.85 


19. 


1134.1 


3591.4 


Vl6 


18.666 


7.5829 


1/4 


213.82 


294.01 


1/4 


1164.2 


3735.0 


1/2 


19.635 


8.1813 


3/8 


220.36 


307.58 


1/2 


1194.6 


3882.5 


9/16 


20.629 


8.8103 


1/2 


226.98 


321.56 


3/4 


1225.4 


4033.7 


5/8 


21.648 


9.4708 


5/8 


233.71 


335.95 


20. 


1256.7 


4188.8 


11/16 


22.691 


10.1j4 


3/4 


240.53 


350.77 


1/4 


1288.3 


4347.8 


3/4 


23.758 


1J.889 


7/8 


247.45 


366.02 


1/2 


1320.3 


4510.9 


13/16 


24.850 


1 1 .649 


9. 


254.47 


381.70 


3/4 


1352.7 


4677.9 


,1(8 


25.967 


12.443 


1/8 


261.59 


397.83 


21. 


1385.5 


4849.1 


15/16 


27.109 


13.272 


1/4 


268.81 


414.41 


1/4 


1418.6 


5024.3 


3. 


28.274 


14.137 


3/8 


270.12 


431.44 


1/' 


1452.2 


5203.7 


1/16 


29.465 


15.039 


1/2 


283.53 


448.92 


3/4 


1486.2 


5387.4 


1/8 


J0.680 


15.979 


5/8 


291.04 


466.87 


22. 


1520.5 


5575.3 


3/16 31.919 '16.957 | 


3/4 


289.65 485.31 1 


1/4 


1555.3 


5767.6 



SPHERES. 



127 



SPHERES — Continued, 



Diam 


Sur- 
face. 


1 
Vol- 
ume. 


Diam 


Sur. 
face 


Vol- 
ume 


Diam. 


Sur- 
face. 

1 


Vol- 
ume. 


23 1/2 


1590.4 


5964.1 


40 1/2 


5153.1 


34/33 


70 1/2 


; 15615 


183471 


3/4 


1626.0 


6165.2 


41. 


5281.1 


36087 


71. 


15837 


187402 


33. 


1661.9 


6370.6 


1/2 


5410.7 


37423 


1/2 


16061 


191389 


1/4 


1698.2 


6580.6 


43. 


5541.9 


38792 


73. 


16286 


195433 


1/2 


1735.0 


6795.2 


1/2 


5674.5 


40194 


1/2 


16513 


199532 


3/4 


1772.1 


7014.3 


43. 


5808.8 


41630 


73. 


16742 


203689 


34. 


1809.6 


7238.2 


1/2 


5944.7 


43099 


1/2 


16972 


207903 


1/4 


1847.5 


7466.7 


44. 


6082.1 


44602 


74. 


17204 


212175 


1/2 


1885.8 


7700.1 


1/2 


6221.2 


46141 


1/2 


17437 


216505 


3/4 


1924.4 


7938.3 


45. 


6361.7 


47713 


75. 


, 17672 


220894 


35. 


1963.5 


8181.3 


1/2 


6503.9 


49321 


1/2 


i 17908 


225341 


1/4 


2002.9 


8429.2 


46. 


6647.6 


50965 


76. 


18146 


229848 


1/2 


2042.8 


8682.0 


1/2 


6792.9 


52645 


1/2 


' 18386 


234414 


3/4 


2083.0 


8939.9 


47. 


6939.9 


54362 


77. 


18626 


239041 


36. 


2123.7 


9202.8 


1/2 


7088.3 


56115 


1/2 


18869 


243728 


1/4 


2164.7 


9470.8 


48. 


7238.3 


57906 


78. 


19114 


248475 


1/2 


2206.2 


9744.0 


1/9 


7389.9 


59734 


1/2 


19360 


253284 


3/4 


2248.0 


10022 


49. 


7543.1 


61601 


79. 


19607 


258155 


37. 


2290.2 


10306 


1/2 


7697.7 


63506 


1/2 


19856 


263088 


1/4 


2332.8 


10595 


50. 


7854.0 


65450 


80. 


20106 


268083 


1/2 


2375.8 


10889 


1/2 


8011.8 


67433 


1/2 


20358 


273141 


3/4 


2419.2 


11189 


51. 


8171.2 


69456 


81. 


20612 


278263 


38. 


2463.0 


11494 


1/2 


8332.3 


71519 


1/2 


20867 


283447 


1/4 


2507.2 


11805 


53. 


8494.8 


73622 


83. 


21124 


288696 


1/2 


2551.8 


12121 


1/2 


8658.9 


75767 


1/2 


21382 


294010 


3/4 


2596.7 


12443 


53. 


8824.8 


77952 


83. 


21642 


299388 


39. 


2642.1 


12770 


1/2 


8992.0 


80178 


1/2 


21904 


304831 


1/4 


2687.8 


13103 


54. 


9160.8 


82448 


84. 


22167 


310340 


1/2 


2734.0 


13442 


1/2 


9331.2 


84760 


1/2 


22432 


315915 


3/4 


2780.5 


13787 


55. 


9503.2 


87114 


85. 


22698 


321556 


30. 


2827.4 


14137 


1/2 


9676.8 


89511 


1/2 


22966 


327264 


1/4 


2874.8 


14494 


56. 


9852.0 


91953 


86. 


23235 


333039 


1/2 


2922.5 


14856 


1/2 


10029 


94438 


1/2 


23506 


338882 


3/4 


2970.6 


15224 


57. 


10207 


96967 


87. 


23779 


344792 


31c 


3019.1 


15599 


1/2 


10387 


99541 


1/2 


24053 


350771 


1/4 


3068.0 


15979 


58. 


10568 


102161 


88. 


24328 


356819 


1/2 


3117.3 


16366 


1/2 


10751 


104826 


1/2 


24606 


362935 


3/4 


3166.9 


16758 


59. 


10936 


107536 


89. 


24885 


369122 


33. 


3217.0 


17157 


1/2 


11122 


110294 


1/2 


25165 


375378 


1/4 


3267.4 


17563 


60. 


11310 


113098 


90. 


25447 


381704 


1/2 


3318.3 


17974 


1/2 


11499 


115949 


1/2 


25730 


388102 


3/4 


3369.6 


18392 


61. 


11690 


118847 


91. 


26016 


394570 


33. 


3421.2 


18817 


1/2 


11882 


121794 


1/2 


26302 


401109 


1/4 


3473.3 


19248 


63. 


12076 


124789 


93. 


26590 


407721 


1/2 


3525.7 


19685 


1/2 


12272 


127832 


1/2 


26880 


414405 


3/4 


3578.5 


20129 


63. 


12469 


130925 


93. 


27172 


421161 


34. 


3631.7 


20580 


1/2 


12668 


134067 


1/2 


27464 


427991 


1/4 


3685.3 


21037 


64. 


12868 


137259 


94. 


27759 


434894 


1/2 


3739.3 


21501 


1/2 


13070 


140501 


1/2 


28055 


441871 


35. 


3848.5 


22449 


65. 


13273 


143794 


95. 


28353 


448920 


1/2 


3959.2 


23425 


1/2 


13478 


147138 


1/2 


28652 


456047 


36. 


4071.5 


24429 


66. 


13685 


150533 


96. 


28953 


463248 


1/2 


4185.5 


25461 


1/2 


13893 


153980 


1/2 


29255 


470524 


37. 


4300.9 


26522 


67. 


14103 


157480 


97. 


29559 


477874 


1/2 


4417.9 


27612 


1/2 


14314 


161032 


1/2 


29865 


485302 


38. 


4536.5 


28731 


68. 


14527 


164637 


98. 


30172 


492808 


1/2 


4656.7 


29880 


1/2 


14741 


168295 


1/2 


30481 


500388 


39. 


4778.4 


31059 


69. 


14957 


172007 


99. 


30791 


508047 


1/2 


4901.7 


32270 


1/2 


15175 


175774 


1/2 


31103 


515785 


40. 


5026.5 


33510 


70. 


15394 


179595 


100. 


31416 


523598 



128 



MATHEMATICAL TABLES. 



NUMBER OF SQUARE FEET IN PLATES 3 TO 32 FEET 
LONG, AND 1 INCH WIDE. 

Forotherwidths.multiply by the width in inches. 1 sq. in. = 0.0069V9 sq.ft. 



Ft. and 

Ins. 
Long. 


Ins. 


Square 
Feet. 


Ft. and 

Ins. 

Long. 


Ins. 


Square 


Ft. and 

Ins. 
Long. 


Ins. 


Square 


Long. 


Long. 


Feet. 


Long. 


Feet. 


3. 


36 


.25 


7. 10 


94 


.6528 


13. 8 


152 


1.056 


1 


37 


.2569 


11 


95 


.6597 


9 


153 


1.063 


2 


38 


.2639 


8. 


96 


.6667 


10 


154 


1.069 


3 


39 


.2708 


1 


97 


.6736 


11 


155 


1.076 


4 


40 


.2778 


2 


98 


.6806 


13. 


156 


1.083 


5 


41 


.2847 


3 


99 


.6875 




157 


1.09 


6 


42 


.2917 


4 


100 


.6944 


2 


158 


1.097 


7 


43 


.2986 


5 


101 


.7014 


3 


159 


1.104 


8 


44 


.3056 


6 


102 


.7083 


4 


160 


1.114 


9 


45 


.3125 


7 


103 


.7153 


5 


161 


1.118 


10 


46 


.3194 


8 


104 


.7222 


6 


162 


1.125 


11 


47 


.3264 


9 


105 


.7292 


7 


163 


1.132 


4. 


48 


.3333 


10 


106 


.7361 


8 


164 


1.139 


1 


49 


.3403 


11 


107 


.7431 


9 


165 


1.146 


2 


50 


.3472 


9. 


108 


.75 


10 


166 


1.153 


3 


51 


.3542 


1 


109 


.7569 


11 


167 


1.159 


4 


52 


.3611 


2 


110 


.7639 


14. 


168 


1.167 


5 


53 


.3681 


3 


111 


.7708 


1 


169 


1.174 


6 


54 


.375 


4 


112 


.7778 


2 


170 


1.181 


7 


55 


.3819 


5 


113 


.7847 


3 


171 


1.188 


8 


56 


.3889 


6 


114 


.7917 


4 


172 


1.194 


9 


57 


.3958 


7 


115 


.7986 


5 


173 


1.201 


10 


58 


.4028 


8 


116 


.8056 


6 


174 


1.208 


11 


59 


.4097 


9 


117 


.8125 


7 


175 


1.215 


6. 


60 


.4167 


10 


118 


.8194 


8 


176 


1.222 


1 


61 


.4236 


11 


119 


.8264 


9 


177 


1.229 


2 


62 


.4306 


10. 


120 


.8333 


10 


178 


1.236 


3 


63 


.4375 


1 


121 


.8403 


11 


179 


1.243 


4 


64 


.4444 


2 


122 


.8472 


15. 


180 


1.25 


5 


65 


.4514 


3 


• 123 


.8542 


1 


181 


1.257 


6 


66 


.4583 


4 


124 


.8611 


2 


182 


1.264 


7 


67 


.4653 


5 


125 


.8681 


3 


183 


1.271 


8 


68 


.4722 


6 


126 


.875 


4 


184 


1.278 


9 


69 


.4792 


7 


127 


.8819 


5 


185 


1.285 


10 


70 


.4861 


8 


128 


.8889 


6 


186 


1.292 


11 


71 


.4931 


9 


129 


.8958 


7 


187 


1.299 


6. 


72 


.5 


10 


130 


.9028 


8 


188 


1.306 


1 


73 


.5069 


11 


131 


.9097 


9 


189 


1.313 


2 


74 


.5139 


11. 


132 


.9167 


10 


190 


1.319 


3 


75 


.5208 


1 


133 


.9236 


11 


191 


1.326 


4 


76 


.5278 


2 


134 


.9306 


16. 


192 


1.333 


5 


77 


.5347 


3 


135 


.9375 


1 


193 


1.34 


6 


78 


.5417 


4 


136 


.9444 


2 


194 


1.347 


7 


79 


.5486 


5 


137 


.9514 


3 


195 


1.354 


8 


80 


.5556 


6 


138 


.9583 


4 


196 


1.361 


9 


81 


.5625 


7 


139 


.9653 


5 


197 


1.368 


10 


82 


.5694 


8 


140 


.9722 


6 


198 


1.375 


11 


83 


.5764 


9 


141 


.9792 


7 


199 


1.382 


7. 


84 


.5834 


10 


142 


.9861 


8 


200 


1.389 


1 


85 


.5993 


11 


143 


.9931 


9 


201 


1.396 


2 


86 


.5972 


13. 


144 


1.000 


10 


202 


1.403 


3 


87 


.6042 


1 


145 


1.007 


11 


203 


1.41 


4 


88 


.6111 


2 


146 


1.014 


17. 


204 


1.417 


5 


89 


.6181 


3 


147 


1.021 


1 


205 


1.424 


6 


90 


.625 


4 


148 


1.028 


2 


206 


1.431 


7 


91 


.6319 


5 


149 


1.035 


3 


207 


1.438 


8 


92 


.6389 


6 


150 


1.042 


4 


208 


1.444 


9 


93 


.6458 


7 


151 


1.049 


5 


209 


1.451 



NUMBER OF SQUARE FEET IN PLATES. 



129 





SQUARE FEET 


IN PISTES.— 


Continued. 




Ft.anc 

Ins. 

Long. 


Ins. 
Long. 


Square 
Feet. 


Ft. and 

Ins. 
Long. 


Ins. 
Long. 


Square 
Feet. 


Ft. and 

Ins.- 

Long. 


Ins. 
Long 


Square 
Feet. 


17. 6 


210 


1.458 


22. 5 


269 


1.868 


27o 4 


328 


2.278 


7 


211 


1.465 


6 


270 


1.875 


5 


329 


2.285 


8 


212 


1.472 


7 


271 


1.882 


6 


330 


2.292 


9 


213 


1.479 


8 


272 


1.889 


7 


331 


2.299 


10 


214 


1.486 


9 


273 


1.896 


8 


332 


2.306 


1] 


215 


1.493 


10 


274 


1.903 


9 


333 


2.313 


18. 


216 


1.5 


11 


275 


1.91 


10 


334 


2.319 


1 


217 


1.507 


23. 


276 


1.917 


11 


335 


2.326 


2 


218 


1.514 


1 


277 


1.924 


28. 


336 


2.333 


3 


219 


1.521 


2 


278 


1.931 


1 


337 


2.34 


4 


220 


1.528 


3 


279 


1.938 


2 


338 


2.347 


5 


221 


1.535 


4 


280 


1.944 


3 


339 


2.354 


6 


222 


1.542 


5 


281 


1.951 


4 


340 


2.361 


7 


223 


1.549 


6 


282 


1.958 


5 


341 


2.368 


8 


224 


1.556 


7 


283 


1.965 


6 


342 


2.375 


9 


225 


1.563 


8 


284 


1.972 


7 


343 


2.382 


10 


226 


1.569 


9 


285 


1.979 


8 


344 


2.389 


11 


227 


1.576 


10 


286 


1.986 


9 


345 


2.396 


19. 


228 


1.583 


11 


287 


1.993 


10 


346 


2.403 


1 


229 


1.59 


24. 


288 


2. 


11 


347 


2.41 


2 


230 


1.597 


1 


289 


2.007 


29. 


348 


2.417 


3 


231 


1.604 


2 


290 


2.014 


1 


349 


2.424 


4 


232 


1.611 


3 


291 


2.021 


2 


350 


2.431 


5 


233 


1.618 


4 


292 


2.028 


3 


351 


2.438 


6 


234 


1.625 


5 


293 


2.035 


4 


352 


2.444 


7 


235 


1.632 


6 


294 


2.042 


5 


353 


2.451 


8 


236 


1.639 


7 


295 


2.049 


6 


354 


2.458 


9 


237 


1.645 


8 


296 


2.056 


7 


355 


2.465 


10 


238 


1.653 


9 


297 


2.063 


8 


356 


2.472 


11 


239 


1 .659 


10 


298 


2.069 


9 


357 


2.479 


20. 


240 


1.667 


11 


299 


2.076 


10 


358 


2.486 


1 


241 


1.674 


25. 


300 


2.083 


11 


359 


2.493 


2 


242 


1.681 


1 


301 


2.09 


30. 


360 


2.5 


3 


243 


1.688 


2 


302 


2.097 


1 


361 


2.507 


4 


244 


1.694 


3 


303 


2.104 


2 


362 


2.514 


5 


245 


1.701 


4 


304 


2.111 


3 


363 


2.521 


6 


246 


1.708 


5 


305 


2.118 


4 


364 


2.528 


7 


247 


1.715 


6 


306 


2.125 


5 


365 


2.535 


8 


248 


1.722 


7 


307 


2.132 


• 6 


366 


2.542 


9 


249 


1.729 


8 


308 


2.139 


7 


367 


2.549 


10 


250 


1.736 


9 


309 


2.146 


8 


368 


2.556 


11 


251 


1.743 


10 


310 


2.153 


9 


369 


2.563 


21. 


252 


1.75 


11 


311 


2.16 


10 


370 


2.569 


I 


253 


1.757 


26. 


312 


2.167 




371 


2.576 


2 


254 


1.764 


1 


313 


2.174 


31. 


372 


2.583 


3 


255 


1.771 


2 


314 


2.181 


1 


373 


2.59 


4 


256 


1.778 


3 


315 


2.188 


2 


374 


2.597 


5 


257 


1.785 


4 


316 


2.194 


3 


375 


2.604 


6 


258 


1.792 


5 


317 


2.201 


4 


376 


2.611 


7 


259 


1.799 


6 


318 


2.208 


5 


377 


2.618 


8 


260 


1.806 


7 


319 


2.215 


6 


378 


2.625 


9 


261 


1.813 


8 


320 


2.222 


7 


379 


2.632 


10 


262 


1.819 


9 


321 


2.229 


8 


380 


2.639 


11 


263 


1.826 


10 


322 


2.236 


9 


381 


2.64^ 


22. 


264 


1.833 


11 


323 


2.243 


10 


382 


2.653 


1 


265 


1.84 


27. 


324 


2.25 


11 


383 


2.66 


2 


266 


1.847 


1 


325 


2.257 


32. 


384 


2.667 


3 


267 


1.854 


2 


326 


2.264 


1 


385 


2.674 


4 


268 


1.861 


3 


327 


2.271 


2 


386 


2.681 



130 



MATHEMATICAL TABLES. 



GALLONS AND CUBIC FEET, 

United Sta^tes Gallons in a given Number of Cubic Feet. 



1 cubic foot = 


=7.480519 U 


.S. gallons; 


1 gallon = 2[ 


Jlcu.in. = u.ic 


};5b»ui5t)cu.u. 


Cubic Ft. 


Gallons. 


Cubic Ft. 


Gallons. 


Cubic Ft. 


Gallons. 


0.1 
0.2 
0.3 
0.4 
0.5 


0.75 
1.50 
2.24 
2.99 
3.74 


50 
60 • 
70 
80 
90 


374.0 
448,8 
523.6 
598.4 
673.2 


8,000 

9,000 

10,000 

20,000 

30,000 


59,844.2 

67,324.7 

74,805.2 

149,610.4 

224,415.6 


0.6 
0.7 
0.8 
0.9 

1 


4.49 
5.24 
5.98 
6.73 
7.48 


100 
200 
300 
400 
500 


748.0 
1,496.1 
2,244.2 
2,992.2 
3,740.3 


40,000 
50,000 
60,000 
70,000 
80,000 


299,220.8 
374.025.9 
448,831.1 
523,636.3 
598,441.5 


2 
3 
4 
5 
6 


14.96 
22.44 
29.92 
37.40 
44.88 


600 
700 
800 
900 
1,000 


4,488.3 
5,236.4 
5,984.4 
6,732.5 
7,480.5 


90,000 
100,000 
200,000 
300,000 
400,000 


673,246. 

748,051.9 
1,496,103.8 
2,244.155.7 
2,992.207.6 


7 
8 
9 
10 
20 


52.36 
59.84 
67.32 
74.80 
149.6 


2,000 
3,000 
4,000 
5,000 
6,000 


14,961.0 
22,441.6 
29,922.1 
37,402.6 
44,883.1 


500,000 
600,000 
700,000 
800,000 
900,000 


3,740,259.5 
4,488,311.4 
5,236,363.3 
5,984,415.2 
6,732,467.1 


30 
40 


224.4 
299.2 


7,000 


52,363.6 


1,000,000 


7.480.519.0 



Cubic Feet in a given Number of Gallons. 



Gallons. 



Cubic Ft. 



1 

2 
3 
4 
5 

6 
7 

8 
9 
10 



.134 
.267 
.401 
.535 
.668 

.802 
.936 
1.069 
1.203 
1.337 



Gallons. 



1,000 
2,000 
3,000 
4,000 
5,000 

6,000 
7,000 
8,000 
9,000 
10,000 



Cubic Ft. 



133.681 
267.361 
401.04: 
534.722 
668.403 

802.083 

935.764 

1,069.444 

1,203.125 

1,336.806 



Gallons. 



1,000,000 
2,000,000 
3,000,000 
4,000,000 
5,000,000 

6,000,000 
7,000,000 
8 000,000 
9,000.000 
10,000,000 



Cubic Ft. 



133,680.6 
267,361.1 
401,041.7 
534,722.2 
668,402.8 

802,083.3 

935,763.9 

1,069.444.4 

1,203,125.0 

1,336,805.6 



Cubic Feet per Second, Gallons in 24 hours, etc. 



1 

60 

448.83 
646,317 



Cu. ft. per sec. Veo 

Cu. ft, per min. 1 

U. S. Gals, per min. 7.480519 

* 24hrs. 10,771.95 

Pounds of water ) ao qc^f^ •^74.1 s 
(at 62° F.) per min. f ^^"^^^ "^^^^ "^ 
The gallon is a troublesome and unnecessary measure. ^. ..,, — «--- 
engineers and pump manufacturers would stop using it, and use cubic 
leet instead, many tedious calculations would be saved. 



1.5472 
92.834 
694.444 
1,000,000 

5788.66 



2.2800 
133.681 
1,000. 
1,440,000 

8335.65 



If hydraulic 



CAPACITY OF CYLINDRICAL VESSELS. 



131 



CONTENTS IN CUBIC FEET AND U. S. GALLONS OF PIPES 

AND CYLINDERS OF VARIOUS DIA3IETERS AND ONE 

FOOT IN LENGTH. 





1 gallon 


= 231 cubic inches. 1 cubic foot 


= 7.4805 gallons 






For 1 Foot in 


c 


For 1 Foot in 




For 1 Foot Id 


1" 


Length. 


Length. 




Length. 


Cu.Ft. 


U.S. 


Cu.Ft. 


U.S. 


Cu.Ft. 


U.S. 


C fl 


also 


Gals.. 


also 


Gals., 


also 


Gals.. 


'sT 


Area in 


231 


Q 


Area in* 


231 


5 


Area in 


231 


Sq.Ft. 


Cu.In. 




Sq.Ft. 


Cu.In. 


Sq.Ft. 


Cu. In. 


1/4 


.0003 


.0025 


63/4 


.2485 


1 .859 


19 


1.969 


14.73 


5/16 


.0005 


.004 


7 


.2673 


1.999 


191/0 


2 074 


15.51 


3/8 


.0003 


.0057 


71/4 


.2867 


2.145 


20 ^ 


2.182 


16.32 


7/16 


.001 


.0078 


71/2 


.3068 


2.295 


201/2 


2.292 


17.15 


1/2 


,0014 


.0102 


73/4 


.3276 


2.45 


21 


2.405 


17,99 


9/16 


.0017 


.0129 


8 


.3491 


2.611 


211/2 


2.521 


18.86 


B/8 


.0021 


.0159 


81/4 


.3712 


2.777 


22 


2.640 


19.75 


n/ie 


.0026 


.0193 


81/2 


.3941 


2.948 


221/2 


2.761 


20.66 


3/4 


.0031 


.0230 


83/4 


.4176 


3.125 


23 


2.885 


21.58 


13/16 


.0036 


.0269 


9 


.4418 


3.305 


231/2 


3.012 


22.53 


7/8 


.0042 


.0312 


91/4 


.4667 


3.491 


24 


3.142 


23.50 


15/16 


.0048 


.0359 


91/2 


.4922 


3.632 


25 


3.409 


25.50 


1 


.0055 


.0408 


93/4 


.5185 


3.879 


26 


3.687 


27.58 


11/4 


.0035 


.0638 


10 


.5454 


4.08 


27 


3.976 


29.74 


U/2 


.0123 


.0918 


101/4 


.5730 


4.286 


28 


4.276 


31.99 


13/4 


.0167 


.1249 


101/9 


,6013 


4.498 


29 


4.587 


34.31 


2 


.0218 


.1632 


103/4 


.6303 


4.715 


30 


4 909 


36.72 


21/4 


.0276 


.2066 


11 


.66 


4.937 


31 


5.241 


39.21 


21/2 


.0341 


.2550 


111/4 


.6903 


5.164 


32 


5.585 


41.78 


23/4 


.0412 


.3085 


111/2 


.7213 


5.396 


33 


5.940 


44.43 


3 


.0491 


.3672 


1 1 3/4 


,7530 


5.633 


34 


6.305 


47.16 


31/4 


.0576 


.4309 


12 


,7854 


5.875 


35 


6.631 


49.98 


31/2 


.0668 


,4998 


121/2 


.8522 


6.375 


36 


7.069 


52.88 


33/4 


.0767 


.5733 


13 


.9218 


6.895 


37 


7.467 


55.86 


4 


.0873 


.6528 


131/2 


.994. 


7.436 


38 


7.876 


58.92 


41/4 


.0935 


.7369 


14 


1.069 


7.997 


39 


8.296 


62.06 


41/2 


.1104 


.8263 


141/2 


1.147 


8.578 


40 


8.727 


65.28 


43/4 


.1231 


.9206 


15 


1.227 


9.180 


41 


9.168 


68.58 


5 


.1364 


1.020 


151/2 


1.310 


9.801 


42 


9.621 


71.97 


51/4 


.1503 


1.125 


16 


1.396 


10.44 


43 


10.085 


75.44 


51/2 


,1650 


1.234 


16 1/2 


1.485 


11.11 


44 


10.559 


78.99 


53/4 


.1803 


1.349 


17 


1.576 


11.79 


45 


11.045 


82.62 


6 


.1963 


1.469 


171/2 


1.670 


12.49 


46 


11.541 


86.33 


61/4 


.2131 


1.594 


18 


1.768 


13.22 


47 


12.048 


90.10 


6 1/2 


.2304 


1.724 


18 1/2 


1.867 


13.96 


48 


12.566 


94.00 



To find the capacity of pipes greater than the largest given in the table, 
look in the table for a pipe of one-half the given size, and multiply its capa- 
city by 4; or one of one-third its size, and ni.ultiply its capacity by 9, etc. 

To find theweight of water in any of the given sizes, multiply the capacity 
in cubic feet by 621/4 or the gallons by 8 1/3. or, if a closer approximation is 
required, by the weight of a cubic foot of water at the actual temperature 
in the pipe. 

Given the dimensions of a cylinder in inches, to find its capacity in U. S. 
gallons: Square the diameter, multiply by the length and by 0.0034. If d== 

diameter, I = length, gallons- ^' ^ Vo^,""^ ^ ^ =0.0034 d2«. If DandLare 



in feet, gallons - 5.875 D^L, 



231 



132 MATHEMATICAL TABLES. 

CYLINDRICAL VESSELS, TANKS, CISTERNS, ETC. 

Diameter in Feet and Inches, Area in Square Feet, and U. S. 
Uiameier igj^^^^ Capacity for One Foot in Depth. 

1 gallon = 231 cubic inches = ^^y^|^* = 0-13368 cubic feet. 



Diam. Area. 



Ft. In. 

1 
I 

I 
I 
I 
I 
1 
1 
I 
\ 



1 

2 
3 
4 
5 
6 
7 
8 
9 

1 10 
I 11 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
2 
3 
3 
3 
3 
3 

3 
3 

3 

3 

3 

3 

3 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

4 

5 

5 

5 

5 

5 

5 

5 

5 



Gals. 



Sq.ft. 

-.785 
.922 
1.069 
1.227 
1.396 
1.576 
1.767 
1.969 
2.182 
2.405 
2.640 
2.885 
3.142 
3.409 
3.687 
3.976 
4.276 
4.587 
4.909 
5.241 
5.585 
5.940 
6.305 
6.681 
7.069 
7.467 
7.876 
8.296 
8.727 
9.168 
9.621 
10.085 
10.559 
11.045 
11.541 
12.048 
12.566 
13.095 
13.635 
14.186 
14.748 
15.321 
15.90 
16.50 
17.10 
17.72 
18.35 
18.99 
19.63 
20.29 
20.97 
21.65 
22.34 
23.04 
23.76 
24.48 



Diam. Area. 



1 foot 

depth. 
5.87 
6.89 
8.00 
9.18 
10.44 
11.79 
13.22 
14.73 
16.32 
17.99 
19.75 
21.58 
23.50 
25.50 
27.58 
29.74 
31.99 
34.31 
36.72 
39.21 
41.78 
44.43 
47.16 
49.98 
52.88 
55.86 
58.92 
62.06 
65.28 
68.58 
71.97 
75.44 
78.99 
82.62 
86.33 
90.13 
94.00 
97.96 
102.00 
106.12 
110.32 
114.61 
118.97 
123.42 
127.95 
132.56 
137.25 
142.02 
146.88 
151.82 
156.83 
161.93 
167.12 
172.38 
177.72 
183.15 



Ft. In. 

5 8 
5 9 
5 10 
5 11 
6 



6 3 

6 ( 

6 < 

7 

7 : 

7 ( 
7 ' 
8 
8 
8 
8 
9 
9 
9 
9 
10 
10 
10 
10 

11 

11 
11 
11 

13 

12 
12 
12 
13 
13 
13 
13 
14 
14 
14 
14 
15 
15 
15 
15 
16 
16 
16 
16 
17 
17 
17 
17 
18 
18 
18 
18 



Gals. Diam. Area 



Sq. ft. 
25.22 
25.97 
26.73 
27.49 
28.27 
30.68 
33.18 
35.78 
38.48 
41.28 
44.18 
47.17 
50.27 
53.46 
56.75 
60.13 
63.62 
67.20 
70.88 
74.66 
78.54 
82.52 
86.59 
90.76 
95.03 
99.40 
103.87 
108.43 
113.10 
117.86 
122.72 
127.68 
132.73 
137.89 
143.14 
148.49 
153.94 
159.48 
165.13 
170.87 
176.71 
182.65 
188.69 
194.83 
201.06 
207.39 
213.82 
220.35 
226.98 
233.71 
240.53 
247.45 
254.47 
261.59 
268.80 
276.12 



1 foot 

depth 
188.66 
194.25 
199.92 
205.67 
211.51 
229.50 
248.23 
267.69 
287.88 
308.81 
330.48 
352.88 
376.01 
399.88 
424.48 
449.82 
475.89 
502.70 
530.24 
558.51 
587.52 
617.26 
647.74 
678.95 
710.90 
743.58 
776.99 
811.14 
846.03 
881.65 
918.00 
955.09 
992.91 
1031.5 
1070.8 
1110.8 
1151.5 
1193.0 
1235.3 
1278.2 
1321.9 
1366.4 
1411.5 
1457.4 
1504.1 
1551.4 
1 599.5 
1648.4 
1697.9 
1748.2 
1799.3 
1851.1 
1903.6 
1956.8 
2010.8 
2065.5 



Gals. 



Ft. In 

19 

19 : 
19 ( 
19 « 
20 
20 
20 
20 
21 
21 
21 
21 
22 
22 
22 
22 
23 
23 

23 

23 
24 

24 

24 

24 
25 

25 

25 

25 
26 

26 

26 

26 

27 

27 

27 

27 

28 

28 3] 

28 6' 

28 9 

29 

29 

29 
29 

30 
30 
30 
30 

31 
31 
31 
31 

32 
32 
32 
32 



Sq.ft. 

283 .53 

291.04 

298.65 

306.35 

314.16 

322.06 

330.06 

338.16 

346.36 

354.66 

363.05 

371.54 

380.13 

388.82 

397.61 

406.49 

415.48 

424.56 

433.74 

443.01 

452.39 

461.86 

471.44 

481.11 

490.87 

500.74 

510.71 

520.77 

530.93 

541.19 

551.55 

562.00 

572.56 

583.21 

593.96 

604.81 

615.75 

626.80 

637.94 

649.18 

660.52 

671.96 

683.49 

695.13 

706.86 

718.69 

730.62 

742.64 

754.77 

766.99 

779.31 

791.73 

804.25 

816.86 

829.58 

842.39 



1 foot 

depth. 

2120.9 

2177.1 

2234.0 

2291.7 

2350.1 

2409.2 

2469.1 

2529.6 

2591.0 

2653.0 

2715.8 

2779.3 

2843.6 

2908.6 

2974.3 

3040.8 

3108.0 

3175.9 

3244.6 

3314.0 

3384.1 

3455.0 

3526.6 

3598.9 

3672.0 

3745.8 

3820.3 

3895.6 

3971.6 

4048.4 

4125.9 

4204.1 

4283.0 

4362.7 

4443.1 

4524.3 

4606.2 

4688.8 

4772.1 

4856.2 

4941.0 

5026.6 

5112.9 

5199.9 

5287.7 

5376.2 

5465.4 

5555.4 

5646.1 

5737.5 

5829.7 

5922.6 

6016.2 

6110.6 

6205.7 

6301.5 



CAPACITIES OF RECTANGULAR TANKS. 



133 



CAPACITIES OF RECTANGULAR TANKS IN U. S. 
GALLONS, FOR EACH FOOT IN DEPTH. 

1 cubic foot = 7.4805 U. S. gallons. 



Width 


Length of Tank. 


of 
Tank. 


feet. 
2 


ft. in. 
2 6 


feet. 
3 


ft. in. 
3 6 


feet. 
4 


ft. in. 
4 6 


feet. 
5 


ft. in. 
5 6 


feet. 
6 


ft. in. 
6 6 


feet. 
7 


ft. in. 
2 

2 6 
3 

3 6 
4 

4 6 
5 

5 6 
6 

6 6 

7 


29.92 


37.40 
46.75 


44.88 
56.10 
67.32 


52.36 
65.45 
78.54 
91.64 


59.84 

74.80 

89.77 

104.73 

119.69 


67.32 
84.16 
100.99 
117.82 
134.65 

151.48 


74.81 
93.51 
112.21 
130.91 
149.61 

168.31 
187.01 


82.29 
102.86 
123.43 
144.00 
164.57 

185.14 
205.71 
226.28 


89.77 
112.21 
134.65 
157.09 
179.53 

201.97 
224.41 
246.86 
269.30 


97.25 
121.56 
145.87 
170.18 
194.49 

218.80 
243.11 
267.43 
291.74 
316.05 


104.73 
130.91 
157.09 
183.27 
209.45 

235.62 
261.82 
288.00 
314.18 
340.36 

366.54 





Length of Tank. 


Width 




of 






















Tank. 


ft. in 


feet. 


ft. in 


feet. 


ft. in. 


feet. 


ft. in. 


feet. 


ft. in. 


feet. 




7 6 


8 


8 6 


9 


9 6 


10 


10 6 


11 


11 6 


13 


ft. in. 
2 


112.21 


119.69 


127.17 


134.65 


142.13 


149.61 


157.09 


164.57 


172.05 


179.53 


2 6 


140.26 


149.61 


158.96 


168.31 


177.66 


187.01 


196.36 


205.71 


215.06 


224.41 


3 


168.31 


179.53 


190.75 


202.97 


213.19 


224.41 


235.63 


246.86 


258.07 


269.30 


3 6 


196.36 


209.45 


222.5^ 


235.63 


248.73 


261.82 


274.90 


288.00 


301.09 


314.13 


4 


224.41 


239.37 


254.34 


269.30 


284.26 


299.22 


314.18 


329.14 


344.10 


359.06 


4 6 


25247 


269.30 


286.13 


302.96 


319.79 


336.62 


353.45 


370.28 


387.11 


403.94 


5 


280.52 


299.22 


317.92 


336.62 


355.32 


374.03 


392.72 


411.43 


430.13 


448.83 


5 6 


303.57 


329.14 


349.71 


370.28 


390.85 


4 1 1 .43 


432.00 


452.57 


473.14 


493.71 


6 


336.62 


359.06 


381.50 


403.94 


426.39 


448.83 


471.27 


493.71 


516.15 


538.59 


6 6 


364.67 


388.98 


413.30 


437.60 


461.92 


486.23 


510.54 


534.85 


559.16 


583.47 


7 


392.72 


418.91 


445.09 


471.27 


497.45 


523.64 


549.81 


575.99 


602.18 


628.36 


7 6 


420.78 


448.83 


476.88 


504.93 


532.98 


561.04 


589.08 


617.14 


645.19 


673.24 


8 




478.75 


508.67 


538.59 


568.51 


598.44 


628.36 


658.28 


688.20 


718.12 


8 6 






540.46 


572.25 


604.05 


635.84 


667.63 


699.42 


731.21 


763.00 


9 








605.92 


639.58 


673.25 


706.90 


740.56 


774.23 


807.69 


9 6 










675.11 


710.65 


746.17 


781.71 


817.24 


852.77 


10 












748.05 


785.45 


822.86 


860.26 


897.66 


10 6 














824.73 


864.00 


903.26 


942.56 


11 
















905.14 


946.27 


987.43 


11 6 


















989.29 


1032.3 


12 




















1077.2 



134 



MATHEMATICAL TABLES. 



NUMBER OF BARRELS (31 1-3 GALLONS) IN 
CISTERNS AND TANKS. 

baiTel = 31 3^ gallons = ^^ ^^2^^ =4.21094 cu. ft. Reciprocal = 0.2 37 477 



Depth 








Diameter 


in Feet 


• 








Feet. 


5 

4.663 
23.3 

28.0 
32.6 
37.3 


6 


7 


8 


9 


10 


11 


13 


13 


14 


1 

5 
6 
7 
8 


6.714 

33.6 

40.3 

47.0 

53.7 


9.139 

45.7 

54.8 

64.0 

73.1 


11.937 
59.7 
71.6 
83.6 
95.5 


15.108 
75.5 
90.6 
105.8 
120.9 


18.652 
93.3 
111.9 
130.6 
149.2 


22.569 

112.8 

135.4 

158.0 

180.6 


26.859 

134.3 

161.2 

188.0 
214.9 


31.522 

157.6 

189.1 

220.7 

252.2 


36.557 

182.8 

219.3 

255.9 

292.5 


9 
10 
11 
12 
13 


42.0 
46.6 
51.3 
56.0 
60.6 


60.4 
67.1 
73.9 
80.6 
87.3 


62.3 

91.4 
100.5 
109.7 
118.8 


107.4 
119.4 
131.3 
143.2 
155.2 


136.0 
151.1 
166.2 
181.3 
196.4 


167.9 
186.5 
205.2 
223.8 
242.5 


203.1 

225.7 
248.3 
270.8 
293.4 


241.7 
268.6 
295.4 
322.3 
349.2 


283.7 
315.2 
346.7 
378.3 
409.8 


329.0 
365.6 
402.1 
438.7 
475.2 


14 
15 
16 
17 

18 


65.3 
69.9 
74.6 
79.3 
83.9 


94.0 
100.7 
107.4 
114.1 
120.9 


127.9 
137.1 
146.2 
155.4 
164.5 


167.1 
179.1 
191.0 
202.9 
214.9 


211.5 
226.6 
241.7 
256.8 
271.9 


261.1 
279.8 
298.4 
317.1 
335.7 


316.0 
338.5 
361.1 
383.7 
406.2 


376.0 
402.9 
429.7 
456.6 

483.5 


441.3 
472.8 
504.4 
535.9 
567.4 


511.8 
548.4 
584.9 
621.5 
658.0 


19 
20 


88.6 
93.3 


127.6 

134.3 


173.6 
182.8 


226.8 
238.7 


287,1 
302.2 


354.4 
373.0 


428.8 
451.4 


510.3 
5372 


598.9 
630.4 


6Q4.6 
731.1 



Depth 
in 








Diameter 


in Feet. 








Feet. 




















15 


16 


17 


18 


19 


20 


21 


22 


1 


41.966 


47.748 


53.903 


60.431 


67.332 


74.606 


82.253 


90.273 


5 


209.8 


238.7 


269.5 


302.2 


3367 


373.0 


411.3 


451.4 


6 


251.8 


286.5 


323.4 


362.6 


404.0 


447.6 


493.5 


541.6 


7 


293.8 


334.2 


377.3 


423.0 


471.3 


522.2 


575.8 


631.9 


8 


335.7 


382.0 


431.2 


483.4 


538.7 


596.8 


658.0 


722.2 


9 


377.7 


429.7 


485.1 


543.9 


606.0 


671.5 


740.3 


812.5 


10 


419.7 


477.5 


539.0 


604.3 


673.3 


746.1 


822.5 


902.7 


11 


461.6 


525.2 


592.9 


664.7 


740.7 


820.7 904.8 


993.0 


12 


503.6 


573.0 


646.8 


725.2 


808.0 


895.3 i 987.0 


1083.3 


13 


545.6 


620.7 


700.7 


785.6 


875.3 


969.9 


1069.3 


1173.5 


14 


587.5 


668.5 


754.6 


846.0 


942.6 


1044.5 


1151.5 


1263.8 


15 


629.5 


716.2 


808.5 


906.5 


1010.0 


1119.1 


1233.8 


1354.1 


16 


671.5 


764.0 


862.4 


966.9 


1077.3 


1193.7 


1316.0 


1444.4 


17 


713.4 


811.7 


9164 


1027.3 


1144.6 


1268.3 


1398.3 


1534.5 


18 


755.4 


859.5 


970.3 


1087.8 


1212.0 


1342.9 


1480.6 


1624.9 


19 


797.4 


907.2 


1024.2 


1148.2 


1279.3 


1417.5 


1562.8 


1715.2 


20 


839.3 


955.0 


1078.1 


1208.6 


1346.6 


1492.1 


1645.1 


1805.5 



LOGARITHMS OF NUMBERS. 



135 



NUMBER OF BARRELS (31 1-3 GALLONS) IN CISTERNS 

AND TANKS. — Continued. 



Depth 








Diameter 


in Feet 








m 
Feet. 


23 


24 


25 


26 


27 


1 

28 


1 29 


30 


1 
5 
6 
7 
8 


98.666 

493.3 

592.0 

690.7 

789.3 


107.432 
537.2 
644.6 
752.0 
859.5 


116.571 
582.9 
699.4 
816.0 
932.6 


126.083 
630.4 
756.5 
882.6 

1008.7 


135.968 
679.8 
815.8 
951.8 

1087.7 


14"6.226 
731.1 
877.4 
1023.6 
1169.8 


156.858 
784.3 
941.1 
1098.0 
1254.9 


167.863 
839.3 
1007.2 
1175.0 
1342.9 


9 
10 
11 
12 
13 


888.0 
986.7 
1085.3 
1184.0 
1282.7 


966.9 
1074.3 
1181.8 
1289.2 
1396.6 


1049.1 
1165.7 
1282.3 
1398.8 
1515.4 


1134.7 
1260.8 
1386.9 
1513.0 
1639.1 


1223.7 
1359.7 
1495.6 
1631.6 
1767.6 


1316.0 

1462.2 
1608.5 
1754.7 
1900.9 


1411.7 
1568.6 
1725.4 
1882.3 
2039.2 


1510.8 
1678.6 
1846.5 
2014.4 
2182.2 


14 
15 
16 

17 
18 


1381.3 
1480.0 
1578.7 
1677.3 
1776.0 


1504.0 
1611.5 
1718.9 
1826.3 
1933.8 


1632.0 
1748.6 
1865.1 
1981.7 
2098.3 


1765.2 
1891.2 
2017.3 
2143.4 
2269.5 


1903.6 
2039.5 

2175.5 
2311.5 
2447.4 


2047.2 
2193.4 
2339.6 
2485.8 
2632.0 


2196.0 
2352.9 
2509.7 
2666.6 
2823.4 


2350.1 
2517.9 
2685.8 
2853.7 
3021.5 


19 
20 


1874.7 
1973.3 


2041.2 
2148.6 


2214.8 
2321.4 


2395.6 
2521.7 


2583.4 
2719.4 


2778.3 
2924.5 


2980.3 
3137.2 


3189.4 
3357.3 



LOGARITHMS. 

Logarithms (abbreviation log). — The log of a number is the exponent 
of the power to which it is necessary to raise a fixed number to produce 
the given number. The fixed number is called the base. Thus if the 
base is 10, the log of 1000 is 3, for 10^ = 1000. There are two systems 
of logs in general use, the common, in which the base is 10, and the Naperian, 
or /i?/pe?-6o^ic, in which the base is 2.718281828 .... The Naperian base 
is commonly denoted by e, as in the equation e^ = x, in which y is the 
Nap. log of X. The abbreviation logg is commonly used to denote the 
Nap log. 

In any system of logs, the log of 1 is 0; the log of the base, taken in that 
system, is 1. In any system the base of which is greater than 1, the logs of 
all numbers greater than 1 are positive and the logs of all numbers less 
than 1 are negative. 

The modulus of any system is equal to the reciprocal of the Naperian log 
of the base of that system. The modulus of the Naperian system is 1, that 
of the common system is 0.4342945. 

The log of a number in any system equals the modulus of that system X 
the Naperian log of the number. 

The hi/perbolic or Naperian log of any number equals the common 
logX 2.3025851. 

Every log consists of two parts, an entire part called the characteristic. 
or index, and the decimal part, or mantissa. The mantissa only is given 
in the usual tables of common logs, with the decimal point omitted. The 
characteristic is found by a simple rule, viz., it is one less than the number 
of figures to the left of the decimal point in the number whose log is to be 
found. Thus the characteristic of numbers from 1 to 9.99 + is 0, from 
10 to 99.99 + is 1, from 100 to 999 + is 2, from 0.1 to 0.99 + is - 1, from 
0.01 to 0.099 + is - 2, etc. Thus 

log of 2000 is 3.30103; log of 0.2 is - 1.30103, or 9.30103 - 10 

" " 200 " 2.30103; " " 0.02 " - 2.30103, " 8.30103 - 10 

" " 20 " 1.30103; " " 0.002 " - 3.30103, " 7.30103 - 10 

♦* •* 2 •' 0.30103; ** *' 0.0002 " - 4.30103, " 6.30103 - 10 



136 LOGARITHMS OF NUMBERS. 

The minus sign is frequently written above the characteristic thus: 
log 0.002 = 3.30103. The characteristic only is negative, the decimal part^ 
or mantissa, being always positive. 

When a log consists of a negative index and a positive mantissa, it is 
usual to write the negative sign over the index, or else to add 10 to the 
index, and to indicate the subtraction of 10 from the resulting logarithm. 

Thus log 0.2 = 1.30103, and this may be written 9.30103 - 10. 

In tables of logarithmic sines, etc., the — 10 is generally omitted, as 
being understood. 

Rules for use of the table of logarithms. — To find the log of any 
whole number. — For 1 to 100 inclusive the log is given complete in the 
small table on page 137. 

For 100 to 999 inclusive the decimal part of the log is given opposite the 
given number in the column headed in the table (including the two 
figures to the left, making six figures). Prefix the characteristic, or 
index, 2. 

For 1000 to 9999 inclusive: The last four figures of the log are found 
opposite the first three figures of the given number and in the vertical 
column headed with the fourth figure of the given number; prefix the two 
figures under column 0, and the index, which is 3. 

For numbers over 10,000 having five or more digits: Find the decimal 
part of the log for the first four digits as above, multiply the difference 
figure in the last column by the remaining digit or digits, and divide by 10 
if there be only one digit more, by 100 if there be two more, and so on: 
add the quotient to the log of the first four digits and prefix the index, 
which is 4 if there are five digits, 5 if there are six digits, and so on. The 
table of proportional parts may be used, as shown below. 

To find the log of a decimal fraction or of a whole number and a 
decimal. — First find the log of the quantity as if there were no decimal 
point, then prefix the index according to rule: the index is one less than 
the number of figures to the left of the decimal point. 

Example, log of 3.14159. log of 3.141 = 0.497068. Diff. = 138 
From proportional parts 5 — 690 

09= 1242 

log 3.14159 0.4971494 

If the number is a decimal le^s than unity, the index is negative 
and is one more than thj^ number of zeros to the right of the decimal 
point. Log of 0.0682 = *^. 833784 = 8.833784 - 10. 

To find the number corresponding to a given log. — Find in the 
table the log nearest to the decimal part of the given log and take the 
first four digits of the required number from the column N and the top or 
foot of the column containing the logwhich is the next less thanthegiven 
log. To find the 5th and 6th digits subtract the log in the table from the 
given log, multiply the difference by 100, and divide by the figure in the 
Diff. column opposite the log; annex the quotient to the four digits 
already found, and place the decimal point according to the rule; the 
number of figures to the left of the decimal point is one greater than the 
index. The number corresponding to a log is called the antl-logaritlun. 

Find the anti-log of 0.497150 

Next lowest log in table corresponds to 3141 0.497068 Diff. = 82 

Tabular diff. = 138; 82 -^ 138 = 0.59 + 
The index being 0, the number is therefore 3.14159 +. 

To multiply two numbers by the use of logarithms. — Add together 
the logs of the two numbers, and find the number whose log is the sum. 

To divide two numbers. — Subtract the log of the divisor from the 
log of the dividend, and find the number whose log is the difference. 
Log of a fraction. Log of a/b = log a — log b. 

To raise a number to any given power. — Multiply the log of the 
number by the exponent of the power, and find the number whose log 
is the product. 

To find any root of a given number. — Divide the log of the number 
by the index of the root. The quotient is the log of the root. 



LOGARITHMS OF NUMBERS. 



137 



To find the reciprocal of a number. — Subtract the decimal pait 
of the log of the number from 0, add 1 to the index and change the sign of 
the index. The result Is the log of the reciprocal. 

Required the reciprocal of 3.141593. 

Log of 3.141593, as found above 0.4971498 

Subtract decimal part from gives 0.5028502 

Add 1 to the index, and changing sign of the index gives. . 1.5028502 
which- is the log of 0.31831. 

To find the fourth term of a proportion by logarithms. — Add 
the logarithms of the ftccond and third terms, and from their sum subtract 
the logarithm of the first term. 

When one logaithm is to be subtracted from another, it may be more 
convenient to convert the subtraction into an addition, which may be 
done by first subtracting the given logarithm from 10, adding the difference 
to the other logarithm, and afterwards rejecting the 10. 

The difference between a given logarithm and 10 is called its arithmetical 
complement, or cologarithm. 

To subtract one logarithm from another is the same as to add its com- 
plement and then reject 10 from the result. For a — b = 10 — & 4- a — 10. 

To work a proportion, then, by logarithms, add the complement of the 
logarithm of the first term to the logarithms of the second and third terms. 
The characteristic must afterwards be diminished by 10. 

Example In logarithms with a negative index. — Solve by 



logarithms 



/ 526 V 
VlOll/ 



which means divide 526 by 1011 and raise the 



quotient to the 2.45 powder. 

log 526 = 2.720986 
log 1011 = 3.004751 



log of quotient = 
Multiply by 



9.716235 - 10 
2.45 



.48581175 
3.8864940 
19.432470 



23.80477575 - (10 X 2.45) = 1.30477575 = 0.20173, ^ns. 



Logarithms of Numbers from 1 to 100. 



N. 


Log. 


N. 


Log. 


N. 


Log. 


N. 


Log. 


N. 
81 


Log. 


1 


0.000000 


21 


1.322219 


41 


1.612784 


61 


1.785330 


1 .908485 


2 


0.301030 


22 


1 .342423 


42 


1 .623249 


62 


1.792392 


82 


1.913814 


3 


0.477121 


23 


1.361728 


43 


1.633468 


63 


1.799341 


83 


1.919078 


4 


0.602060 


24 


1.380211 


44 


1.643453 


64 


1.806180 


84 


1.924279 


5 


0.698970 


25 


1 .397940 


45 


1.653213 


65 


1.812913 


85 


1.929419 


6 


0.778151 


26 


1.414973 


46 


1 .662758 


66 


1.819544 


86 


1 .934498 


7 


0.845098 


27 


1.431364 


47 


1 .672098 


67 


1.826075 


87 


1.939519 


8 


0.903090 


28 


1.447158 


48 


1.681241 


68 


1.832509 


88 


1 .944483 


9 


0.954243 


29 


1 .462398 


49 


1.690196 


69 


1 .838849 


89 


1 .949390 


10 


1.000000 


30 


1.477121 


50 


1 .698970 


70 


1 .845098 


90 


1 .954243 


11 


1.041393 


31 


1.491362 


51 


1.707570 


71 


1.851258 


91 


1.959041 


12 


1.079181 


32 


1.505150 


52 


1.716003 


72 


1.857332 


92 


1.963788 


13 


1.113943 


33 


1.518514 


53 


1.724276 


73 


1.863323 


93 


1 .968483 


14 


1.146128 


34 


1.531479 


54 


1.732394 


74 


1.869232 


94 


1.973128 


15 


1.176091 


35 


1 .544068 


55 


1.740363 


75 


1.875061 


95 


1 977724 


16 


1.204120 


36 


1.556303 


56 


1.748188 


76 


1.880814 


96 


1.982271 


17 


1 .230449 


37 


1.568202 


57 


1.755875 


77 


1.886491 


97 


1.966772 


18 


1.255273 


38 


1.579784 


58 


1.763428 


78 


1.892095 


98 


1.991226 


19 


1.278754 


39 


1.591065 


59 


1.770852 


79 


1.897627 


99 


1.995635 


20 


1.301030 


40 


1 .602060 


60 


1.778151 


80 


1.903090 


100 


2.000000 



For four-place logarithms see page 167. 



138 



LOGARITHMS OF NUMBERS. 



No. 100 L. OOO.J 














[No. 


109 L 


.040, 


N. 


1 


2 

0868 
5181 
9451 


3 


4 


5 


6 


7 


8 

3461 

7748 


9 

3891 
8174 


Diff. 


100 
2 


000000 
4321 
8600 


0434 
4751 
9026 


1301 
5609 
9876 


1734 
6038 


2166 
6466 


2598 
6894 


3029 
7321 


432 
428 


0300 
4521 
8700 


0724 
4940 
9116 


1147 
5360 
9532 


1570 
5779 
9947 


1993 
6197 


2415 
6616 


424 


3 

4 


012837 
7033 


3259 
7451 


3680 
7868 


4100 
8284 


420 


0361 
4486 
8571 


0775 
4896 
8978 


416 
412 
408 


5 
6 
7 


02 1 1 89 
5306 
9384 


1603 
5715 
9789 


2016 
6125 


2428 
6533 


2841 
6942 


3252 
7350 


3664 

7757 


4075 
8164 




0195 
4227 
8223 


0600 

4628 
8620 


1004 
5029 
9017 


1408 
5430 
9414 


1812 
5830 
9811 


2216 
6230 


2619 
6629 


3021 
7028 


404 
400 


8 
9 


033424 
7426 
04 


3826 
7825 


0207 


0602 


0998 


397 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


434 


43.4 


86.8 


130.2 


173.6 


217.0 


260.4 


303.8 


347.2 


390.6 


433 


43.3 


86.6 


129.9 


173.2 


216.5 


259.8 


303.1 


346.4 


389.7 


432 


43.2 


86.4 


129.6 


172.8 


216.0 


259.2 


302.4 


345.6 


388.8 


431 


43.1 


86.2 


129.3 


172.4 


215.5 


258.6 


301.7 


344.8 


387.9 


430 


43.0 


86.0 


129.0 


172.0 


215.0 


258.0 


301.0 


344.0 


387.0 


429 


42.9 


85.8 


128.7 


171.6 


214.5 


257.4 


300.3 


343.2 


386.1 


428 


42.8 


85.6 


128.4 


171.2 


214.0 


256.8 


299.6 


342.4 


385.2 


427 


42.7 


85.4 


128.1 


170.8 


213.5 


256.2 


298.9 


341.6 


384.3 


426 


42.6 


85.2 


127.8 


170.4 


213.0 


255.6 


298.2 


340.8 


383.4 


425 


42.5 


85.0 


127.5 


170.0 


212.5 


255.0 


297.5 


340.0 


382.5 


424 


42.4 


84.8 


127.2 


169.6 


212.0 


254.4 


296.8 


339.2 


381.6 


423 


42.3 


84.6 


126.9 


169.2 


,211.5 


253.8 


296.1 


338.4 


380.7 


422 


42.2 


84.4 


126.6 


168.8 


211.0 


253.2 


295.4 


337.6 


379.8 


421 


42.1 


84.2 


126.3 


168.4 


210.5 


252.6 


294.7 


336.8 


378.9 


420 


42.0 


84.0 


126.0 


168.0 


210.0 


252.0 


294.0 


336.0 


373.0 


419 


41.9 


83.8 


125.7 


167.6 


209.5 


251.4 


293.3 


335.2 


377.1 


418 


41.8 


83.6 


125.4 


167.2 


209.0 


250.8 


292.6 


334:4 


376.2 


417 


41.7 


83.4 


125.1 


166.8 


208.5 


250.2 


291.9 


333.6 


375.3 


416 


41.6 


83.2 


124.8 


166.4 


208.0 


249.6 


291.2 


332.8 


374.4 


415 


41.5 


83.0 


124.5 


166.0 


207.5 


249.0 


290.5 


332.0 


373.5 


414 


41.4 


82.8 


124.2 


165.6 


207.0 


248.4 


289.8 


331.2 


372.6 


413 


41.3 


82.6 


123.9 


165.2 


206.5 


247.8 


289.1 


330.4 


371.7 


412 


41.2 


82.4 


123.6 


164.8 


206.0 


247.2 


288.4 


329.6 


370.8 


411 


41.1 


82.2 


123.3 


164.4 


205.5 


246.6 


287.7 


328.8 


369.9 


410 


41.0 


82.0 


123.0 


164.0 


205.0 


246.0 


287.0 


328.0 


369.0 


409 


40.9 


81.8 


122.7 


163.6 


204.5 


245.4 


286.3 


327.2 


368.1 


408 


40.8 


81.6 


122.4 


163.2 


204.0 


244.8 


285.6 


326.4 


367.2 


407 


40.7 


81.4 


122.1 


162.8 


203.5 


244.2 


284.9 


325.6 


366.3 


406 


40.6 


81.2 


121.8 


162.4 


203.0 


243.6 


284.2 


324.8 


365.4 


405 


40.5 


81.0 


121.5 


162.0 


202.5 


243.0 


283.5 


324.0 


364.5 


404 


40.4 


80.8 


121.2 


161.6 


202.0 


242.4 


282.8 


323.2 


363.6 


403 


40.3 


80.6 


120.9 


161.2 


201.5 


241.8 


282.1 


322.4 


362.7 


402 


40.2 


80.4 


120.6 


160.8 


201.0 


241.2 


281.4 


321.6 


361.8 


401 


40.1 


80.2 


120.3 


160.4 


200.5 


240.6 


280.7 


320.8 


360.9 


400 


40.0 


80.0 


120.0 


160.0 


200.0 


240.0 


280.0 


320.0 


360.0 


399 


39.9 


79.8 


119.7 


159.6 


199.5 


239.4 


279.3 


319.2 


359.1 


398 


39.8 


79.6 


119.4 


159.2 


199.0 


238.8 


278.6 


318.4 


358.2 


397 


39.7 


79.4 


119.1 


158.8 


198.5 


238.2 


277.9 


317.6 


357.3 


396 


39.6 


79.2 


118.8 


158.4 


198.0 


237.6 


277.2 


316.8 


356.4 


395 


39.5 


79.0 


118.5 


158.0 


197.5 


237.0 


276.5 


316.0 


355.5 



LOGARITHMS OF NUMBEBS. 



139 



No. 110 L. 041.] 














[No 


. 119 L. 078. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


no 

I 

2 


041393 
5323 
9218 


1787 
5714 
9606 


2182 
6105 
9993 


2576 
6495 


2yo9 
6885 


3362 
7275 


3755 
7664 


4148 
8053 


4540 
8442 


4932 
8830 


393 
390 


0330 
4230 
8046 


0766 
4613 
8426 


1153 
4996 
8505 


1538 
5378 
9185 


1924 
5760 
9563 


2309 
6142 
9942 


2694 
6524 

0320 
4083 
7815 


386 
383 

379 
376 
373 


3 
4 


053078 
6905 


3463 
7286 


3846 
7666 


5 

6 

7 


060693 
4453 
8186 


1075 

4832 
8557 


1452 
5206 
8928 


1829 
5580 
9298 


2206 
5953 
9668 


2582 
6326 


2958 
6699 


3333 
7071 


3709 
7443 




0038 
3718 
7368 


0407 
4085 
7731 


0776 
4451 
8094 


1145 
4816 
8457 


1514 
5182 
8819 


370 
366 
363 


8 
9 


071882 
5547 


2250 
5912 


2617 
6276 


2935 
6640 


3352 
7004 



Proportional Parts. 



Diff. 


1 


3 


3 


4 


5 


« 


7 


8 


9 


395 


39.5 


79.0 


118.5 


158.0 


197.5 


237.0 


276.5 


316.0 


355.5 


394 


39.4 


78.8 


118.2 


157.6 


197.0 


236.4 


275.8 


315.2 


354.6 


393 


39.3 


78.6 


117.9 


157.2 


196.5 


235.8 


275.1 


314.4 


353.7 


392 


39.2 


78.4 


117.6 


156.8 


196.0 


235.2 


274.4 


313.6 


352.8 


391 


39.1 


78.2 


117.3 


156.4 


195.5 


234.6 


273.7 


312.8 


351.9 


390 


39.0 


78.0 


117.0 


156.0 


195.0 


234.0 


273.0 


312.0 


351.0 


389 


38.9 


77.8 


116.7 


155.6 


194.5 


233.4 


272.3 


311.2 


350.1 


388 


38.8 


77.6 


116.4 


155.2 


194.0 


232.8 


271.6 


310.4 


349.2 


387 


38.7 


77.4 


116.1 


154.8 


193.5 


232.2 


270.9 


309.6 


348.3 


386 


38.6 


77.2 


115.8 


154.4 


193.0 


231.6 


270.2 


308.8 


347.4 


385 


38.5 


77.0 


115.5 


154.0 


192.5 


231.0 


269.5 


308.0 


346.5 


384 


38.4 


76.8 


115.2 


153.6 


192.0 


230.4 


268.8 


307.2 


345.6 


383 


38.3 


76.6 


114.9 


153.2 


191.5 


229.8 


268.1 


306.4 


344.7 


382 


38.2 


76.4 


114.6 


152.8 


191.0 


229.2 


267.4 


305.6 


343.8 


381 


38.1 


76.2 


114.3 


152.4 


190.5 


228.6 


266.7 


304.8 


342.9 


380 


38.0 


76.0 


114.0 


152.0 


190.0 


223.0 


266.0 


304.0 


342.0 


379 


37.9 


75.8 


113.7 


151.6 


189.5 


227.4 


265.3 


303.2 


341.1 


378 


37.8 


75.6 


113.4 


151.2 


189.0 


226.8 


264.6 


302.4 


340.2 


377 


37.7 


75.4 


113.1 


150.8 


188.5 


226.2 


263.9 


301.6 


339.3 


376 


37.6 


75.2 


112.8 


150.4 


188.0 


225.6 


263.2 


300.8 


338.4 


375 


37.5 


75.0 


112.5 


150.0 


187.5 


225.0 


262.5 


300.0 


337.5 


374 


37.4 


74.8 


112.2 


149.6 


187.0 


224.4 


261.8 


299.2 


336.6 


373 


37.3 


74.6 


111.9 


149.2 


186.5 


223.8 


261.1 


298.4 


335.7 


372 


37.2 


74.4 


111.6 


148.8 


186.0 


223.2 


260.4 


297.6 


334.8 


371 


37.1 


74.2 


111.3 


148.4 


185.5 


222.6 


259.7 


296.8 


333.9 


370 


37.0 


74.0 


111.0 


148.0 


185.0 


222.0 


259.0 


296.0 


333.0 


369 


36.9 


73.8 


110.7 


147.6 


184.5 


221.4 


258.3 


295.2 


332.1 


368 


36.8 


73.6 


110.4 


147.2 


184.0 


220.8 


257.6 


294.4 


331.2 


367 


36.7 


73.4 


110.1 


146.8 


183.5 


220.2 


256.9 


293.6 


330.3 


366 


36.6 


73.2 


109.8 


146.4 


183.0 


219.6 


256.2 


292.8 


329.4 


365 


36.5 


73.0 


109.5 


146.0 


182.5 


219.0 


255.5 


292.0 


328.5 


364 


36.4 


72.8 


109.2 


145.6 


182.0 


218.4 


254.8 


291.2 


327.6 


363 


36.3 


72.6 


108.9 


145.2 


181.5 


217.8 


254.1 


290.4 


326.7 


362 


36.2 


72.4 


103.6 


144.8 


181.0 


217.2 


253.4 


289.6 


325.8 


361 


36.1 


72.2 


108.3 


144.4 


180.5 


216.6 


252.7 


288.8 


324.9 


360 


36.0 


72.0 


103.0 


144.0 


180.0 


216.0 


252.0 


288.0 


324.0 


359 


35.9 


71.8 


107.7 


143.6 


179.5 


215.4 


251.3 


287.2 


323.1 


358 


35.8 


71.6 


107.4 


143.2 


179.0 


214.8 


250.6 


286.4 


322.2 


357 


35.7 


71.4 


107.1 


142.8 


178.5 


214.2 


249.9 


285.6 


321.3 


356 


35.6 


71.2 


106.8 


142.4 


178.0 


213.6 


249.2 


284.8 


320.4 



140 



LOGARITHMS OP NUMBERS. 



No. 120 L. 079.] 














[No. 


134 L 


. 130. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Difif. 


120 


079181 


9543 


9904 


















0266 
3861 
7426 


0626 
4219 
7781 


0987 
4576 
8136 


1347 
4934 
8490 


1707 
5291 
8845 


2067 
5647 
9198 


2426 
6004 
9552 


360 
357 
355 


1 

2 
3 


082785 
6360 
9905 


3144 
6716 


3503 
7071 


0258 
3772 
7257 


0611 
4122 
7604 


0963 

4471 
7951 


1315 
4320 
8298 


1667 
5169 
8644 


2018 
5518 
8990 


2370 
5866 
9335 


2721 
6215 
9681 


3071 
6562 


352 


4 
5 


093422 
6910 


349 


0026 
3462 
6871 

0253 
3609 

6940 


346 
343 
341 

338 
335 

333 


6 
7 
8 


100371 
3804 
7210 


0715 
4146 
7549 


1059 

4487 
7888 


1403 
4828 
8227 


1747 
5169 
8565 


2091 
5510 
8903 


2434 
5851 
9241 


27.-'7 
6191 
9579 


3119 
6531 
9916 


9 

130 
1 


110590 

3943 
7271 


0926 

4277 
7603 


1263 

4611 
7934 


1599 

4944 
8265 


1934 

5278 
8595 


2270 

5611 
8926 


2605 

5943 
9256 


2940 

6276 
9586 


3275 

6608 
9915 




0245 
3525 
6781 


330 
328 
325 


2 
3 
4 


120574 
3852 
7105 

13 


0903 
4178 
7429 


1231 
4504 
7753 


1560 
4830 
8076 


1888 
5156 
8399 


2216 
5481 
8722 


2544 
5806 
9045 


2871 
6131 
9368 


3198 
6456 
9690 


0012 


323 



Proportional Parts. 



Di£f. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


355 


35.5 


71.0 


106.5 


142.0 


177.5 


213.0 


248.5 


284.0 


319.5 


354 


35.4 


70.8 


106.2 


141.6 


177.0 


212.4 


247.8 


283.2 


318.6 


353 


35.3 


70.6 


105.9 


141.2 


176.5 


211.8 


247.1 


282.4 


317.7 


352 


35.2 


70.4 


105.6 


140.8 


176.0 


211.2 


246.4 


281.6 


316.8 


351 


35.1 


70.2 


105.3 


140.4 


175.5 


210.6 


245.7 


280.8 


315.9 


350 


35.0 


70.0 


105.0 


140.0 


175.0 


210.0 


245.0 


280.0 


315.0 


349 


34.9 


69.8 


104.7 


139.6 


.174.5 


209.4 


244.3 


279.2 


314.1 


348 


34.8 


69.6 


104.4 


139.2 


174.0 


208.8 


243.6 


278.4 


313.2 


347 


34.7 


69.4 


104.1 


138.8 


173.5 


208.2 


242.9 


277.6 


312.3 


346 


34.6 


69.2 


103.8 


138.4 


173.0 


207.6 


242.2 


276.8 


311 4 


345 


34.5 


69.0 


103.5 


138.0 


172.5 


207.0 


241.5 


276.0 


310.5 


344 


34.4 


68.8 


103.2 


137.6 


172.0 


206.4 


240.8 


275.2 


309.6 


343 


34.3 


68.6 


102.9 


137.2 


171.5 


205.8 


240.1 


274.4 


308.7 


342 


34.2 


68.4 


102.6 


136.8 


171.0 


205.2 


239.4 


273.6 


307.8 


341 


34.1 


68.2 


102.3 


136.4 


170.5 


204.6 


238.7 


272.8 


306.9 


340 


34.0 


68.0 


102.0 


136.0 


170.0 


204.0 


238.0 


272.0 


306.0 


339 


33.9 


67.8 


101.7 


135.6 


169.5 


203.4 


237.3 


271.2 


305.1 


338 


33.8 


67.6 


101.4 


135.2 


169.0 


202.8 


236.6 


270.4 


304.2 


337 


33.7 


67.4 


101.1 


134.8 


168.5 


202.2 


235.9 


269.6 


303.3 


336 


33.6 


67.2 


100.8 


134.4 


168.0 


201.6 


235.2 


268.8 


302.4 


335 


33.5 


67.0 


100.5 


134.0 


167.5 


201.0 


234.5 


268.0 


301.5 


334 


33.4 


66.8 


100.2 


133.6 


167.0 


200.4 


233.8 


267.2 


300.6 


333 


33.3 


66.6 


99.9 


133.2 


166.5 


199.8 


233.1 


266.4 


299.7 


332 


33.2 


66.4 


99.6 


132.8 


166.0 


199.2 


232.4 


265.6 


298.8 


331 


33.1 


66.2 


99.3 


132.4 


165.5 


198.6 


231.7 


264.8 


297.9 


330 


33.0 


66.0 


99.0 


132.0 


165.0 


193.0 


231.0 


264.0 


297.0 


329 


32.9 


65.8 


98.7 


131.6 


164.5 


197.4 


230.3 


263.2 


296.1 


328 


32.8 


65.6 


98.4 


131.2 


164.0 


196.8 


229.6 


262.4 


295.2 


327 


32.7 


65.4 


98.1 


130.8 


163.5 


196.2 


228.9 


261.6 


294.3 


326 


32.6 


65.2 


97.8 


130.4 


163.0 


195.6 


228.2 


260.8 


293.4 


325 


32.5 


65.0 


97.5 


130.0 


162.5 


195.0 


227.5 


260.0 


292.5 


324 


32.4 


64.8 


97.2 


129.6 


162.0 


194.4 


226.8 


259.2 


291.6 


323 


32.3 


64.6 


96.9 


129.2 


161.5 


193.8 


226.1 


258.4 


290.7 


322 


32.2 


64.4 


96.6 


128.8 


161.0 


193.2 


225.4 


257.6 


289.8 



LOGAEITHMS OF NUMBERS. 



141 



No. 135 L. 130.] 














[No 


. 149 L. 175. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Difif. 


135 
6 

7 
8 


130334 
3539 
6721 
9879 


0655 

3858 
7037 


0977 
4177 
7354 


1298 
4496 
7671 


1619 

4814 
7987 


1939 

5133 
8303 


2260 
5451 
8618 


2580 
5769 
8934 


2900 
6086 
9249 


3219 
6403 
9564 


321 
318 
3,16 


0194 
3327 

6438 
9527 


0508 
3639 

6748 
9835 


0822 
3951 

7058 


1136 
4263 

7367 


1450 
4574 

7676 


1763 
4885 

7985 


2076 
5196 

8294 


2389 
5507 

8603 


2702 
5818 

8911 


314 
311 

309 


9 

140 
1 


143015 

6128 
9219 




0142 
3205 
6246 
9266 


0449 
3510 
6549 
9567 


0756 
3815 
6852 
9868 


1063 
4120 
7154 


1370 
4424 
7457 


1676 
4728 
7759 


1982 
5032 
8061 


307 
305 
303 


2 
3 
4 


152288 
5336 
8362 


2594 
5640 
8664 


2900 
5943 
8965 


0168 
3161 
6134 
9086 


0469 
3460 
6430 
9380 


0769 
3758 
6726 
9674 


1068 
4055 
7022 
9968 


301 
299 
297 
295 


5 
6 
7 


161368 
4353 
7317 


1667 
4650 
7613 


1967 
4947 
7908 


2266 
5244 
8203 


2564 
5541 
8497 


2863 
5838 
8792 


8 
9 


170262 
3186 


0555 

3478 


0848 
3769 


1141 
4060 


1434 
4351 


1726 
4641 


2019 
4932 


2311 
5222 


2603 
5512 


2895 
5802 


293 
291 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


321 


32.1 


64.2 


96.3 


128.4 


160.5 


192.6 


224.7 


256.8 


288.9 


320 


32.0 


64.0 


96.0 


128.0 


160.0 


192.0 


224.0 


256.0 


288 


319 


31.9 


63.8 


95.7 


127.6 


159.5 


191.4 


223.3 


255.2 


287.1 


318 


31.8 


63.6 


95.4 


127.2 


159.C 


190.8 


222.6 


254.4 


286.2 


317 


31.7 


63.4 


95.1 


126.8 


158.5 


190.2 


221.9 


253.6 


285.3 


316 


31.6 


63.2 


94.8 


126.4 


158.0 


189.6 


221.2 


252.8 


284.4 


315 


31.5 


63.0 


94.5 


126.0 


157.5 


189.0 


220.5 


252.0 


283.5 


314 


31.4 


62.8 


94.2 


125.6 


157.0 


188.4 


219.8 


251.2 


282.6 


313 


31.3 


62.6 


93.9 


125.2 


156.5 


187.8 


219.1 


250.4 


281.7 


312 


31.2 


62.4 


93.6 


124.8 


156.0 


187.2 


218.4 


249.6 


280.8 


311 


31.1 


62.2 


93.3 


124.4 


155.5 


186.6 


217.7 


248.8 


279.9 


310 


31.0 


62.0 


93.0 


124.0 


155.0 


186.0 


217.0 


248.0 


279.0 


309 


30.9 


61.8 


92.7 


123.6 


154.5 


185.4 


216.3 


247.2 


278.1 


308 


30.8 


61.6 


92.4 


123.2 


154.0 


184.8 


215.6 


246.4 


277.2 


307 


30.7 


61.4 


92.1 


122.8 


153.5 


184.2 


214.9 


245.6 


276.3 


306 


30.6 


61.2 


91.8 


122.4 


153.0 


183.6 


214.2 


244.8 


275.4 


305 


30.5 


61.0 


91.5 


122.0 


152.5 


183.0 


213.5 


244.0 


274.5 


304 


30.4 


60.8 


91.2 


121.6 


152.0 


182.4 


212.8 


243.2 


273.6 


303 


30.3 


60.6 


90.9 


121.2 


151.5 


181.8 


212.1 


242.4 


272.7 


302 


30.2 


60.4 


90.6 


120.8 


151.0 


181.2 


211.4 


241.6 


271.8 


301 


30.1 


60.2 


90.3 


120.4 


150.5 


180 6 


210.7 


240.8 


270.9 


300 


30.0 


60.0 


90.0 


120.0 


150.0 


180.0 


210.0 


240.0 


270.0 


299 


29.9 


59.8 


89.7 


119.6 


149.5 


179.4 


209.3 


239.2 


269.1 


298 


29.8 


59.6 


89.4 


119.2 


149.0 


178.8 


208.6 


238.4 


268.2 


297 


29.7 


59.4 


89.1 


118.8 


148.5 


178.2 


207.9 


237.6 


267.3 


296 


29.6 


59.2 


88.8 


118.4 


148.0 


177.6 


207.2 


236.8 


266.4 


295 


29.5 


59.0 


88.5 


118.0 


147.5 


177.0 


206.5 


236.0 


265.5 


294 


29.4 


58.8 


88.2 


117.6 


147.0 


176.4 


205.8 


235.2 


264.6 


293 


29.3 


58.6 


87.9 


117.2 


146.5 


175.8 


205.1 


234.4 


263.7 


292 


29.2 


58.4 


87.6 


116.8 


146.0 


175.2 


204.4 


233.6 


262.8 


291 


29.1 


58.2 


87.3 


116.4 


145.5 


174.6 


203.7 


232.8 


261.9 


290 


29.0 


58.0 


87.0 


116.0 


145.0 


174.0 


203.0 


232.0 


261.0 


289 


28.9 


57.8 


86.7 


115.6 


144.5 


173.4 


202.3 


231.2 


260.1 


288 


28.8 


57.6 


86.4 


115.2 


144.0 


172.8 


201.6 


230.4 


259.2 


287 


28.7 


57.4 


86.1 


114.8 


143.5 


172.2 


200.9 


229.6 


258.3 


286 


28.6 


57.2 


85.8 


114.4 


143.0 


171.6 


200.2 


228.8 


257.4 



142 



LOGARITHMS OF NUMBERS. 



No. 150 L. 176.] 














[No. 


16PL 


.230 


N. 





1 


3 


3 


4 


5 


6 


7 


8 


9 


Din 


150 


176091 
8977 


6381 
9264 


6670 
9552 


6959 
9839 


7248 


7536 


7825 


8113 


8401 


8689 


289 




0126 
2985 
5825 
8647 


0413 
3270 
6108 

8928 


0699 
3555 
6391 
9209 


0986 
3839 
6674 
9490 


1272 
4123 
6956 
9771 


1558 
4407 
7239 


287 


2 
3 
4 


181844 
4691 
7521 


2129 
4975 
7803 


2415 
5259 
8034 


2700 
5542 
8366 


285 
283 


0051 

2846 
5623 
6382 


281 
279 
278 
270 


5 
6 
7 
8 


190332 
3125 
5900 
8657 


0612 
3403 
6176 
8932 


0392 
3681 
6453 
9206 


1171 
3959 
6729 
9481 


1451 
4237 
7005 
9755 


1730 
4514 
7281 


2010 
4792 
7556 


2289 
5069 

7832 


2567 
5346 
8107 


0029 
2761 

5475 
8173 


0303 
3033 

5746 
8441 


0577 
3305 

60i6 
8710 


0850 

3577 

6286 
8979 


1124 
3848 

6556 
9247 


274 

272 

271 
269 


9 

160 

I 
2 


201397 

4120 
6826 
9515 


1670 

4391 
7096 
9783 


1943 

4663 
7365 


2216 

4934 
7634 


2488 

5204 
7904 


0051 
2720 
5373 
8010 


0319 
2986 
5638 
8273 


0586 
3252 
5902 
8536 


0853 
3518 
6166 
8798 


1121 
3783 
6430 
9060 


1388 
4049 
6694 
9323 


1654 
4314 
6957 
9585 


1921 
4579 
7221 
9846 

2456 
5051 
7630 


267 
266 
264 
262 


3 
4 
5 


21218S 
4844 
7484 


2454 
5109 
7747 


6 

7 
8 
9 


220108 
2716 
5309 
7887 

23 


0370 
2976 
5568 
8144 


0631 
3236 
5826 
8400 


0892 
3496 
6084 
8657 


1153 
3755 
6342 
8913 


1414 
4015 
6600 
9170 


1675 
4274 
6858 
9426 


1936 
4533 
7115 
9682 


2196 
4792 
7372 
9938 


261 
259 

258 


0193 


256 



Proportional Parts. 



Difif. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


285 


28.5 


57.0 


85.5 


114.0 


142.5 


171.0 


199.5 


228.0 


256.5 


284 


28.4 


56.8 


85.2 


113.6 


142.0 


170.4 


198.8 


227.2 


255.6 


283 


28.3 


56.6 


84.9 


113.2- 


141.5 


169.8 


198.1 


226.4 


254.7 


282 


23.2 


56.4 


84.6 


112.8 


141.0 


169.2 


197.4 


225.6 


253.8 


281 


23.1 


56.2 


84.3 


112.4 


140.5 


168.6 


196.7 


224.8 


252.9 


280 


23.0 


56.0 


84.0 


112.0 


140.0 


168.0 


196.0 


224.0 


252.0 


279 


27.9 


55.8 


83.7 


111.6 


139.5 


167.4 


195.3 


223.2 


251.1 


278 


27.8 


55.6 


83.4 


111.2 


139.0 


166.8 


194.6 


222.4 


250.2 


277 


27.7 


55.4 


83.1 


110.8 


138.5 


166.2 


193.9 


221.6 


249.3 


276 


27.6 


55.2 


82.8 


110.4 


138.0 


165.6 


193.2 


220.8 


248.4 


275 


27.5 


55.0 


82.5 


110.0 


137.5 


165.0 


192.5 


220.0 


247.3 


274 


27.4 


54.8 


82.2 


109.6 


137.0 


164.4 


191.8 


219.2 


246.6 


273 


27.3 


54.6 


81.9 


109.2 


136.5 


163.8 


191.1 


218.4 


245.7 


272 


27.2 


54.4 


81.6 


108.8 


136.0 


163.2 


190.4 


217.6 


244.8 


271 


27 1 


54.2 


81.3 


108.4 


135.5 


162.6 


189.7 


216.8 


243.9 


270 


270 


54.0 


81.0 


103.0 


135.0 


162.0 


189.0 


2160 


243.0 


269 


26.9 


53.8 


80.7 


107.6 


134.5 


161.4 


188.3 


215.2 


242.1 


268 


26.8 


53.6 


80.4 


107.2 


134.0 


160.8 


187.6 


214.4 


241.2 


267 


26.7 


53.4 


80.1 


106 8 


133.5 


160.2 


186.9 


213.6 


240.3 


266 


26.6 


53.2 


79.8 


106.4 


133.0 


159.6 


186.2 


212.8 


239.4 


265 


26.5 


53.0 


795 


106.0 


132.5 


159.0 


185.5 


212.0 


238.3 


264 


26.4 J 


52.8 


79.2 


105.6 


132.0 


158.^. 


184.8 


211.2 


237.6 


263 


26.3 


52.6 


789 


105.2 


131.5 


1578 


184.1 


210.4 


236.7 


262 


26.2 


52.4 


78 6 


104.8 


131.0 


1572 


183.4 


209.6 


235.8 


261 


26.1 


52.2 


78.3 


104 4 


130.5 


156.6 


182.7 


208.8 


234.9 


260 


26.0 


52.0 


78.0 


1040 


130.0 


156.0 


182.0 


208.0 


234.0 


259 


25 9 


51.8 


77.7 


103.6 


129.5 


155.4 


181.3 


207.2 


233.1 


25S 


25.8 


51.6 


77.4 


103.2 


129.0 


154.8 


1806 


206.4 


232.2 


257 


25.7 


51.4 


77 1 


102.8 


128.5 


154.2 


179 9 


205.6 


231.3 


256 


25.6 


51.2 


76.8 


102.4 


128.0 


153 6 


179.2 


2048 


230.4 


255 


25.5 


51.0 


76.5 


102.0 


127.5 


1530 


17^.5 


204 


229.3 



LOGARITHMS OF NUMBERS. 



143 



No. 170 L. 230. 
















[No 


. 189 L. 278. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


170 

1 

2 
3 


230449 
2996 
5523 
8046 


0704 
3250 
5781 
8297 


0960 
3504 
6033 

8548 


1215 
3757 
6285 
8799 


1470 
4011 
6537 
9049 


1724 
4264 
6789 
9299 


19/9 
4517 
7041 
9550 


2234 
4770 
7292 
9800 


2488 
5023 

7544 


2742 
5276 
7795 


255 
253 
252 




0050 

2541 
5019 
7482 

00^-7 


0300 
2790 
5266 
7728 


250 

249 
248 
246 


4 
5 
6 
7 


240549 
3033 
5513 
7973 


0799 
3286 
5759 
8219 


1048 
3534 
6006 
8464 


1297 
3782 
6252 
8709 


1546 
4030 
6499 
8954 


1795 
4277 
6745 
9198 


2044 
4525 
6991 
9443 


2293 
4772 
7237 




0176 
2610 
5031 

7439 
9833 


245 
243 
242 

241 
239 


8 
9 

180 
I 


250420 
2853 

5273 
7679 


0664 
3096 

5514 
7918 


0908 
3338 

5755 
8158 


1151 
3580 

5996 
8398 


1395 
3822 

6237 
8637 


1638 
4064 

6477 
8877 


1881 
4306 

6718 
9116 


2125 
4548 

6958 
9355 


2368 
4790 

7198 
9594 


2 
3 
4 
5 
6 


260071 
2451 
4318 
7172 
9513 


0310 
2683 
5054 
7406 
9746 


0548, 0787 
2925 i 3162 
5290 5525 
7641 7875 

OOMO 


1025 
3399 
5761 
8110 


1263 
3636 
5996 
8344 


1501 
3373 
6232 
8578 


1739 
4109 
6467 
8812 


1976 
4346 
6702 
9046 


2214 
4582 
6937 
9279 


238 
237 
235 
234 




0213 
2538 
4850 
7151 


0446 
2770 
5031 
7380 


0679 
3001 
5311 
7609 


0912 
3233 
5542 
7838 


1144 
3464 
bill 
8061 


1377 
3696 
6002 
8296 


1609 
3927 
6232 
8525 


233 
232 
230 
229 


7 
8 
9 


271842 
4158 
6462 


2074 
4389 
6692 


2306 
4620 
6921 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


255 


25.5 


51.0 


76.5 


102.0 


127.5 


153.0 


178.5 


204.0 


229.5 


254 


25.4 


50.8 


76.2 


101.6 


127.0 


152.4 


177.8 


203.2 


228.6 


253 


25.3 


50.6 


75.9 


101.2 


126.5 


151.8 


177.1 


202.4 


227.7 


252 


25.2 


50.4 


75.6 


100.8 


126.0 


151.2 


176.4 


201.6 


226.8 


251 


25.1 


50.2 


75.3 


100.4 


125.5 


150.6 


175.7 


200.8 


225.9 


250 


25.0 


50.0 


75.0 


100.0 


125.0 


150.0 


175.0 


200.0 


225.0 


249 


24.9 


49.8 


74.7 


99.6 


124.5 


149.4 


174.3 


199.2 


224.1 


248 


24.8 


49.6 


74.4 


99.2 


124.0 


148.8 


173.6 


198.4 


223.2 


247 


24.7 


49.4 


74.1 


98.8 


123.5 


148.2 


172.9 


197.6 


222.3 


246 


24.6 


49.2 


73.8 


98.4 


123.0 


147.6 


172.2 


196.8 


221.4 


245 


24.5 


49.0 


73.5 


98.0 


122.5 


147.0 


171.5 


196.0 


220.5 


244 


24.4 


48.8 


73.2 


97.6 


122.0 


146.4 


170.8 


195.2 


219.6 


243 


24.3 


48.6 


72.9 


97.2 


121.5 


145.8 


170.1 


194.4 


218.7 


242. 


24.2 


48.4 


72.6 


96.8 


121.0 


145.2 


169.4 


193.6 


217.8 


241 


24.1 


48.2 


72.3 


96.4 


120.5 


144.6 


168.7 


192.8 


216.9 


240 


24.0 


48.0 


72.0 


96.0 


120.0 


144.0 


168.0 


192.0 


216.0 


239 


23.9 


47.8 


71.7 


95.6 


119.5 


143.4 


167.3 


191.2 


215.1 


238 


23.8 


47.6 


71.4 


95.2 


119.0 


142.8 


166.6 


190.4 


214.2 


237 


23.7 


47.4 


71.1 


94.8 


118.5 


142.2 


165.9 


189.6 


213.3 


236 


23.6 


47.2 


70.8 


94.4 


118.0 


141.6 


165.2 


188.8 


212.4 


235 


23.5 


47.0 


70.5 


94.0 


117.5 


141.0 


164.5 


188.0 


211.5 


234 


23.4 


46.8 


70.2 


93.6 


117.0 


140.4 


163.8 


187.2 


210.6 


233 


23.3 


46.6 


69.9 


93.2 


116.5 


139.8 


163.1 


186.4 


209.7 


232 


23.2 


46.4 


69.6 


92.8 


116.0 


"139.2 


162.4 


185.6 


208.8 


231 


23.1 


46.2 


69.3 


92.4 


115.5 


138.6 


161.7 


184.8 


207.9 


230 


23.0 


46.0 


69.0 


92.0 


115.0 


138.0 


161.0 


184.0 


207.0 


229 


22.9 


45.8 


68.7 


91.6 


114.5 


137.4 


160.3 


183.2 


206.1 


228 


22.8 


45.6 


68.4 


91.2 


114.0 


136.8 


159.6 


182.4 


205.2 


227 


22.7 


45.4 


68.1 


90.8 


113.5 


136.2 


158.9 


181.6 


204.3 


226 


22.6 


45.2 


67.8 


90.4 


113.0 


135.6 


158.2 


180.8 


203.4 



144 



LOGARITHMS OF NUMBERS. 



No. 190 L. 278.1 














[No. 


214 L 


.332. 


N. 





1 


2 


3 4 


5 


6 


7 


8 


9 


Diff. 


190 


278754 


8982 


9211 


9439 


9667 


9895 












0123 
2396 
4656 
6905 
9143 


0351 
2622 
4882 
7130 
9366 


0578 
2849 
5107 
7354 
9589 


0806 
3075 
5332 
7578 
9812 


228 
227 
226 
225 
223 


1 

2 
3 
4 


281033 
3301 
5557 
7802 


1261 
3527 

5782 
8026 


1488 
3753 
6007 
8249 


1715 
3979 
6232 
8473 


1942 
4205 
6456 
8696 


2169 
4431 
6681 
8920 


5 
6 
7 
8 
9 


290035 
2256 
4466 
6665 
8853 


0257 
2478 
4687 
6884 
9071 


0480 
2699 
4907 
7104 
9289 


0702 
2920 
5 127 
7323 
9507 


0925 

3141 
5347 
7542 
9725 


1147 
3363 
5567 
7761 
9943 


1369 
3584 
5787 
7979 


1591 
3804 
6007 
8198 


1813 
4025 
6226 
8416 


2034 
4246 
6446 
8635 


222 
221 
220 
219 


0161 

2331 
4491 
6639 
8778 


0378 

2547 
4706 
6854 
8991 


0595 

2764 
4921 
7068 
9204 


0813 

2980 
5136 
7282 
9417 


218 

217 
216 
215 
213 


200 
1 

2 
3 
4 


301030 
3196 
5351 
7496 
9630 


1247 
3412 
5566 
7710 
9843 


1464 
3628 
5781 
7924 


1681 
3844 
5996 
8137 


1898 
4059 
6211 
8351 


2114 
4275 
6425 
8564 


0056 
2177 
4289 
6390 
8481 


0268 
2389 
4499 
6599 
8689 


0481 
2600 
4710 
6809 
8898 


0693 
2812 
4920 
7018 
9106 


0906 
3023 
5130 

7227 
9314 


1118 
3234 
5340 
7436 
9522 


1330 

3445 
5551 
7646 
9730 


1542 
3656 
5760 
7854 
9938 


212 
211 
210 
209 
208 


5 
6 
7 
8 


311754 
3867 
5970 
8063 


1966 
4078 
6180 
8272 


9 

210 
1 

2 
3 


320146 

2219 
4282 
6336 
8380 


0354 

2426 
4488 
6541 
8583 


0562 

2633 
4694 
6745 
8787 


0769 

2839 
4899 
6950 
8991 


0977 

3046 
5105 
7155 

Q 1 Oil 


1184 

3252 
5310 
7359 

oaoQ 


1391 

3458 
5516 
7563 
9601 


1598 

3665 
5721 
7767 
9805 


1805 

3871 
5926 
7972 


2012 

4077 
6131 
8176 


207 

206 
205 
204 




0008 
2034 


0211 
2236 


203 
202 


4 


330414 


0617 


0819 


1022 


1225 


14271 


1630 


1832 



Proportional Parts. 



22.5 
22.4 
22.3 
22.2 
22.1 
22.0 
21.9 
21.8 

21.7 
21.6 
21.5 
21.4 
21.3 
21.2 
21.1 
21.0 

20.9 
20.8 
20.7 
20.6 
20.5 
20.4 
20.3 
20.2 



45.0 

44.8 
44.6 
44.4 
44.2 
44.0 
43.8 
43.6 

43.4 
43.2 
43.0 
42.8 
42.6 
42.4 
42.2 
42.0 

41.8 
41.6 
41.4 
41.2 
41.0 
40.8 
40.6 
40.4 



67.5 
67.2 
66.9 
66.6 
66.3 
66.0 
65.7 
65.4 

65.1 
64.8 
64.5 
64.2 
63.9 
63.6 
63.3 
63.0 

62.7 
62.4 
62.1 
61.8 
61.5 
61.2 
60.9 
60.6 



90.0 
89.6 
89.2 
88.8 
88.4 
88.0 
87.6 
87.2 

86.8 
86.4 
86.0 
85.6 
85.2 
84.8 
84.4 
84.0 

83.6 
83.2 
82.8 
82.4 
82.0 
81.6 
81.2 
80.8 



112.5 
112.0 
111.5 
111.0 
110.5 
110.0 
109.5 
109.0 

108.5 
108.0 
107.5 
107.0 
106.5 
106.0 
105.5 
105.0 

104.5 
104.0 
103.5 
103.0 
102.5 
102.0 
101.5 
101.0 I 



135.0 
134.4 
133.8 
133.2 
132.6 
132.0 
131.4 
130.8 

130.2 
129.6 
129.0 
128.4 
127.8 
127.2 
126.6 
126.0 

125.4 
124.8 
124.2 
123.6 
123.0 
122.4 
121.8 
121.2 



157.5 
156.8 
156.1 
155.4 
154.7 
154.0 
153.3 
152.6 

151.9 
151.2 
150.5 
149.8 
149.1 
148.4 
147.7 
147.0 

146.3 
145.6 
144.9 
144.2 
143.5 
142.8 
142.1 
141.4 



8 



180.0 
179.2 
178.4 
177.6 
176.8 
176.0 
175.2 
174.4 

173.6 
172.8 
172.0 
171.2 
170.4 
169.6 
168.8 
168.0 

167.2 
166.4 
165.6 
164.8 
164.0 
163.2 
162.4 
161.6 



9 

"^0275 
201.6 
200.7 
199.8 
198.9 
198.0 
197.1 
196.2 

195.3 
194.4 
193.5 
192.6 
191.7 
190.8 
189.9 
189.0 

188.1 
187.2 
186.3 
185.4 
184.5 
183.6 
182.7 
181.8 



LOGARITHMS OP NUMBERS. 



145 



No. 215 L. 332.] 














(No. 


239 L 


.380. 


N. 





1 


2 1 3 


4 


5 


6 


7 


8 


9 

4253 
6260 
8257 


Diff. 


215 

6 

7 
8 


332438 
4454 
6460 
8456 


2640 
4655 
6660 
8656 


2842; 3044 
4856 5057 
6860 7060 
88551 Qni^A 


3246 
5257 
7260 
9253 


3447 
5458 
7459 
9451 


3649 
5658 
7659 
9650 


3850 
5859 

7858 

QH40 


4051 
6059 
8058 


202 
201 
200 








0047 
2028 

3999 
5962 
7915 
9860 


0246 

2225 

4196 
6157 
8110 


199 
198 

197 
196 
195 


9 

220 

1 

2 
3 


340444 

2423 
4392 
6353 
8305 


0642 

2620 
4589 
6549 
8500 


0841 

2817 
4785 
6744 
8694 


1039 

3014 
4981 
6939 
8889 


1237 

3212 
5178 
7135 
9083 


1435 

3409 
5374 
7330 
9278 


1632 

3606 
5570 
7525 
9472 


1830 

3802 
5766 
7720 
9666 


0054 
1989 
3916 
5834 
7744 
9646 


194 
193 
193 
192 
191 
190 


4 
5 
6 
7 
8 
9 


350248 
2183 
4108 
6026 
7935 
9835 


0442 
2375 
4301 
6217 
8125 


0636 
2568 
4493 
6408 
8316 


0829 
2761 
4685 
6599 
8506 


1023 
2954 
4876 
6790 
8696 


1216 
3147 
5068 
6981 
8886 


1410 
3339 
5260 
7172 
9076 


1603 
3532 
5452 
7363 
9266 


1796 
3724 
5643 
7554 
9456 


0025 

1917 
3800 
5675 
7542 
9^01 


0215 

2105 
3988 
5862 
7729 
9587 


0404 

2294 
4176 
6049 
7915 
9772 


0593 

2482 
4363 
6236 
8101 
9958 


0783 

2671 
4551 
6423 

8287 


0972 

2859 
4739 
6610 
8473 


1161 

3048 
4926 
6796 
8659 


1350 

3236 
5113 
6983 
8845 


1539 

3424 
5301 
7169 
9030 


189 

188 
188 
187 
186 


230 
1 

2 
3 
4 


361728 
3612 
5488 
7356 
9216 


0143 
1991 
3831 
5664 
7488 
9306 


0328 
2175 
4015 
5846 
7670 
9487 


0513 
2360 
4198 
6029 
7852 
9668 


0698 
2544 
4382 
6212 
8034 
9849 


0883 
2728 
4565 
6394 
8216 


185 
184 
184 
183 
182 


5 
6 
7 
8 
9 


371068 
2912 
4748 
6577 
8398 

38 


1253 
3096 
4932 
6759 
8580 


1437 
3280 
5115 
6942 
8761 


1622 
3464 
5298 
7124 
8943 


1806 
3647 
5481 
7306 
9124 


0030 


181 











Proportional 


Parts. 








DifiP. 


1 


3 


3 


4 


5 


6 


7 


8 


9 


202 


20.2 


40.4 


60.6 


80.8 


101.0 


121.2 


141.4 


161.6 


181.8 


201 


20.1 


40.2 


60.3 


80.4 


100.5 


120.6 


140.7 


160.8 


180.9 


200 


20.0 


40.0 


60.0 


80.0 


100.0 


120.0 


140.0 


160.0 


180.0 


199 


19.9 


39.8 


59.7 


79.6 


99.5 


119.4 


139.3 


159.2 


179.1 


198 


19.8 


39.6 


59.4 


79.2 


99.0 


118.8 


138.6 


158.4 


178.2 


197 


19.7 


39.4 


59.1 


78.8 


98.5 


118.2 


137.9 


157.6 


177.3 


196 


19.6 


39.2 


58.8 


78.4 


98.0 


117.6 


137.2 


156.8 


176.4 


195 


19.5 


39.0 


58.5 


78.0 


97.5 


117.0 


136.5 


156.0 


175.5 


194 


19.4 


38.8 


58.2 


77.6 


97.0 


116.4 


135.8 


155.2 


174.6 


193 


19.3 


38.6 


57.9 


77.2 


96.5 


115.8 


135.1 


154.4 


173.7 


192 


19.2 


38.4 


57.6 


76.8 


96.0 


115.2 


134.4 


153.6 


172.8 


191 


19.1 


38.2 


57.3 


76.4 


95.5 


114.6 


133.7 


152.8 


171.9 


190 


19.0 


38.0 


57.0 


76.0 


95.0 


114.0 


133.0 


152.0 


171.0 


189 


18.9 


37.8 


56.7 


75.6 


94.5 


113.4 


132.3 


151.2 


170.1 


188 


18.8 


37.6 


56.4 


75.2 


94.0 


112.8 


131.6 


150.4 


169.2 


187 


18.7 


37.4 


56.1 


74.8 


93.5 


112.2 


130.9 


149.6 


168.3 


186 


18.6 


37.2 


55.5 


74.4 


93.0 


111.6 


130.2 


148.8 


167.4 


185 


18.5 


37.0 


55.5 


74.0 


92.5 


111.0 


129.5 


148.0 


166.5 


184 


18.4 


36.8 


55.2 


73.6 


92.0 


110.4 


128.8 


147.2 


165.6 


183 


183 


36.6 


54.9 


73.2 


91.5 


109.8 


128.1 


146.4 


164.7 


182 


18.2 


36.4 


54.6 


72.8 


91.0 


109.2 


127.4 


145.6 


163.8 


181 


18.1 


36.2 


54.3 


72.4 


90.5 


108.6 


126.7 


144.8 


162.9 


180 


18.0 


36.0 


54.0 


72.0 


90.0 


108.0 


126.0 


144.0 


162.0 


179 


17.9 


35.8 


53.7 


71.6 


89.5 


107.4 


125.3 


143.2 


161.1 



LOGARITHMS OF NUMBERS. 



Wo. 240 L. 380.1 



[No. 269 L. 431 



N. 


« 


1 


3 1 3 


4 


5 


6 


7 


8 

1656 
3456 
5249 
7034 
8811 


9 


Difif. 


240 
1 

2 
3 
4 
5 


380211 
2017 
3815 
5606 
7390 
9166 


0392 
2197 
3995 
5785 
7568 
9343 


0573 

2377 
4174 
5964 
7746 
9520 


0754 
2557 
4353 
6142 
7924 
9698 


0934 
2737 
4533 
6321 
810! 
9875 


1115 
2917 
4712 
6499 

8279 


1296 
3097 
489! 
6677 
8456 


1476 
3277 
5070 
6856 
8634 


1837 
3636 
5428 
7212 
8989 


181 
180 
179 
178 
178 


0051 
1817 
3575 
5326 
7071 

8803 


0228 
1993 
3751 
550! 
7245 

8981 


0405 
2169 
3926 
5676 
7419 

9154 


0582 
2345 
4!0! 
5850 
7592 

9328 


0759 
2521 
4277 
6025 
7766 

9501 


177 
176 
176 
175 
174 

173 


6 

7 
8 
9 

250 
1 


390935 
2697 
4452 
6199 

7940 
9674 


1112 
2873 
4627 
6374 

8114 
9847 


1288 
3048 
4802 
6548 

8287 


1464 
3224 
4977 
6722 

8461 


1641 
3400 
5152 
6896 

8634 




0020 
1745 
3464 
5176 
6881 
8579 


0192 
1917 
3635 
5346 
7051 
8749 


0365 
2039 
3807 
5517 
7221 
8918 


0538 
226! 
3978 
5638 
739! 
9087 


0711 
2433 
4149 
5858 
7561 
9257 


0883 
2605 
4320 
6029 
7731 
9426 


1056 
2777 
4492 
6199 
7901 
9595 


1228 
2949 
4663 
6370 
8070 
9764 


173 

172 
171 

171 
170 
169 


2 
3 
4 
5 
6 
7 


401401 
3121 
4834 
6540 
8240 
9933 


1573 
3292 
5005 
6710 
8410 


0102 
1788 
3467 

5140 
6307 
8467 


0271 
1956 
3635 

5307 
6973 
8633 


0440 
2124 
3803 

5474 
7139 
8798 


0609 
2293 
3970 

564! 
7306 
8964 


0777 
246! 
4137 

5808 

7472 
9129 


0946 
2629 
4305 

5974 
7638 
9295 


1114 
2796 
4472 

614! 
7804 
9460 


1283 
2964 
4639 

6308 
7970 
9625 


1451 
3132 
4806 

6474 
8135 
9791 


169 
168 
167 

167 
166 
165 


8 
9 

260 
1 

2 
3 


411620 
3300 

4973 
6641 
8301 
9956 


0121 
1768 
3410 
5045 
6674 
8297 
9914 


0286 
1933 
3574 
5208 
6836 
8459 


045! 
2097 
3737 
5371 
6999 
8621 


0616 
2261 
3901 
5534 
7161 
8783 


078! 
2426 
4065 
5697 
7324 
8944 


0945 
2590 
4228 
5860 
7486 
9106 


1110 
2754 
4392 
6023 
7648 
9268 


1275 
2918 
4555 
6186 
7811 
9429 


1439 
3082 
4718 
6349 
7973 
9591 


165 
164 
164 
163 
162 
162 


4 
5 
6 
7 
8 
9 


421604 
3246 
4832 
6511 
8135 
9752 

43 


0075 


0236 


0398 


0559 


0720 


0881 


1042 


1203 


161 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


178 


17.8 


35.6 


53.4 


71.2 


89.0 


106.8 


124.6 


142.4 


160.2 


177 


17.7 


35.4 


53.1 


70.8 


88.5 


106.2 


123.9 


141.6 


159.3 


176 


17.6 


35.2 


52.8 


70.4 


88.0 


105.6 


123.2 


140.8 


158.4 


175 


17.5 


35.0 


52.5 


70.0 


87.5 


105.0 


122.5 


140.0 


157.5 


174 


17.4 


34.8 


52.2 


69.6 


87.0 


104.4 


121.8 


139.2 


156.6 


173 


173 


34.6 


51.9 


69.2 


86.5 


103.8 


121.1 


138.4 


155.7 


172 


17.2 


34.4 


51.6 


68.8 


86.0 


103.2 


120.4 


137.6 


154.8 


171 


17.1 


34.2 


51.3 


68.4 


85.5 


102.6 


119.7 


136.8 


153.9 


170 


17.0 


34.0 


51=0 


68.0 


85.0 


102.0 


119.0 


136.0 


153.0 


169 


16.9 


33.8 


50.7 


67.6 


84.5 


101.4 


118.3 


135.2 


152.1 


168 


16.8 


33.6 


50.4 


67.2 


84.0 


100.8 


117.6 


134.4 


151.2 


167 


16.7 


33.4 


50.1 


66.8 


83.5 


100.2 


116.9 


133.6 


150.3 


166 


16.6 


33.2 


49.8 


66.4 


83.0 


99.6 


116.2 


132.8 


149.4 


165 


16.5 


33.0 


49.5 


66.0 


82.5 


99.0 


115.5 


132.0 


148.5 


164 


16.4 


32.8 


49.2 


65.6 


82.0 


98.4 


114.8 


131.2 


147.6 


163 


16.3 


32.6 


48.9 


65.2 


81.5 


97.8 


114.1 


130.4 


146.7 


162 


16.2 


32.4 


48.5 


64.8 


81.0 


97.2 


113.4 


129.6 


145.8 


161 


16.1 


32.2 


48.3 


64.4 


80.5 


96.6 


112.7 


128.8 


144.9 



LOGARITHMS OP NUMBERS. 



147 



No. 270 L. 431.] 














[No. 


299 L 


. 476. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


270 
1 

2 
3 
4 
5 


431364 
2969 
4569 
6163 
7751 
9333 


1525 
3130 
4729 
6322 
7909 
9491 


1685 
3290 
4888 
6481 
8067 
9648 


1646 
3450 
5048 
6640 
8226 
9806 


2007 
3610 
5207 
6799 
8384 
9964 


2167 
3770 
5367 
6957 

8542 


2328 
3930 
5526 
7116 
8701 


246^ 
4090 
5685 
7275 
8859 


2649 
4249 
5844 
7433 
9017 


2809 
4409 
6004 
7592 
9175 


161 
160 
159 
159 
158 


0122 
1695 
3263 
4825 
6382 

7933 
9478 


0279 
1852 
3419 
4981 
6537 

8088 
9633 


0437 
2009 
3576 
5137 
6692 

8242 
9787 


0594 
2166 
3732 
5293 
6848 

8397 
9941 


0752 
2323 
3889 
5449 
7003 

8552 


158 
157 
157 
156 
155 

155 


6 

7 
8 
9 

280 


440909 
2430 
4045 
5604 

7158 
8706 


1066 
2637 
4201 
5760 

7313 
8361 


1224 
2793 
4357 
5915 

7468 
O015 


1381 
2950 
4513 
6071 

7623 
9170 


1538 
3106 
4669 
6226 

7778 
9324 




0095 
1633 
3165 
4692 
6214 
7731 
9242 


154 
154 
153 
153 
152 
152 
151 


2 
3 
4 
5 
6 


450249 
1786 
3318 
4345 
6366 
7882 
9392 


0403 
1940 
3471 
4997 
6518 
8033 
9543 


0557 
2093 
3624 
5150 
6670 
8184 
9694 


0711 
2247 
3777 
5302 
6821 
8336 
9845 


0865 
2400 
3930 
5454 
6973 
8437 
9995 


1018 
2553 
4082 
5606 

7125 
8638 


1172 
2706 
4235 
5758 
7276 
8789 


1326 
2859 
4387 
5910 
7428 
8940 


1479 
3012 
4540 
6062 
7579 
9091 


0146 
1649 

3146 
4639 
6126 
7608 
9085 


0296 
1799 

3296 
4788 
6274 
7756 
9233 


0447 
1948 

3445 
4936 
6423 
7904 
9380 


0597 
2098 

3594 
5085 
6571 
8052 
9527 


0748 
2248 

3744 
5234 
6719 
8200 
9675 


151 
150 

150 
149 
149 
148 
148 


9 

290 
1 

2 
3 
4 
5 


460398 

2393 
3393 
5333 
6363 
8347 
9322 


1048 

2548 
4042 
5532 
7016 
8495 
9969 


1193 

2697 
4191 
5680 
7164 
8643 


1348 

2847 
4340 
5829 
7312 
8790 


1499 

2997 
4490 
5977 
7460 
8938 




0116 
1535 
3049 
4503 
5962 


0263 
1732 
3195 
4653 
6107 


0410 
1878 
3341 
4799 
6252 


0557 
2025 
3487 
4944 
6397 


0704 
2171 
3633 
5090 
6542 


0351 
2318 
3779 
5235 
6687 


0998 
2464 
3925 
5381 
6832 


1145 
2610 
4071 
5526 
6976 


147 
146 
146 
146 
145 


6 

7 
8 
9 


471292 
2756 
4216 
5671 


1433 
2903 
4362 
5316 











Proportional 


Parts. 








Diff. 


1 


2 


3 


4 


5 


1 ^ 


7 


8 


9 


161 


16.1 


32.2 


43.3 


64.4 


80.5 


96.6 


112.7 


128.8 


144.9 


160 


16.0 


32.0 


48.0 


64.0 


80.0 


96.0 


112.0 


128.0 


144.0 


159 


15.9 


31.8 


47.7 


63.6 


79.5 


95.4 


111.3 


127.2 


143.1 


158 


15.8 


31.6 


47.4 


63.2 


79.0 


94.8 


110.6 


126.4 


142.2 


157 


15.7 


31.4 


47.1 


62.8 


78.5 


94.2 


109.9 


125.6 


141.3 


156 


15.6 


31.2 


46.8 


62.4 


78.0 


93.6 


109.2 


\24.6 


140.4 


155 


15.5 


31.0 


46.5 


62.0 


77.5 


93.0 


108.5 


124.0 


139.5 


154 


15.4 


30.8 


46.2 


61.6 


77.0 


92.4 


107.8 


123.2 


138.6 


153 


15.3 


30.6 


45.9 


61.2 


76.5 


91.8 


107.1 


122.4 


137.7 


152 


15.2 


30.4 


45.6 


60.8 


76.0 


91.2 


106.4 


I2I.6 


136.8 


151 


15.1 


30.2 


45.3 


60.4 


75.5 


90.6 


105.7 


120.8 


135.9 


150 


15.0 


30.0 


45.0 


60.0 


75.0 


90.0 


105.0 


120.0 


135.0 


149 


14.9 


29.8 


44.7 


59.6 


74.5 


89.4 


104.3 


119.2 


134.1 


148 


14.8 


29.6 


44.4 


59.2 


74.0 


88.8 


103.6 


118.4 


133.2 


147 


14.7 


29.4 


44.1 


58.8 


73.5 


88.2 


102.9 


117.6 


132.3 


146 


14.6 


29.2 


43.8 


58.4 


73.0 


87.6 


102.2 


116.8 


131.4 


145 


14.5 


29.0 


43.5 


58.0 


72.5 


87.0 


101.5 


1160 


130.5 


144 


14.4 


28.8 


43.2 


57.6 


72.0 


86.4 


100.8 


115.2 


129.6 


143 


14.3 


28.6 


42.9 


57.2 


71.5 


85.8 


100.1 


114.4 


128.7 


142 


14.2 


28.4 


42.6 


56.8 


71.0 


85.2 


99.4 


113.6 


127.8 


141 


14.1 


28.2 


42.3 


56.4 


70.5 


84.6 


98.7 


112.8 


126.9 


140 


14.0 


23.0 


42.0 ' 


56.0 


70.0 


84.0 


98.0 


112.0 


126.0 



148 



LOGARITHMS OF KUMBERS. 



No. 300 L. 477.] 














[No. 


339 L 


.531. 


N. 





1 


3 


3 


4 


5 


6 


7 


S 


9 


Diff. 


300 


477121 


7266 


7411 


7555 


7700 


7844 


7989 


8133 


8278 


8422 


145 


1 


8566 


8711 


8855 


8999 


9143 


9287 


9431 


9575 


9719 


9863 


144 


2 


480007 


0151 


0294 


0438 


0582 


0725 


0869 


1012 


1156 


1299 


144 


3 


1443 


1586 


1729 


1372 


2016 


2159 


2302 


2445 


2583 


2731 


143 


4 


2874 


3016 


3159 


3302 


3445 


3587 


3730 


3872 


4015 


4157 


143 


5 


4300 


4442 


4585 


4727 


4869 


5011 


5153 


5295 


5437 


5579 


142 


6 


5721 


5863 


6005 


6147 


6289 


6430 


6572 


6714 


6855 


6997 


142 


7 


7138 


7280 


7421 


7563 


7704 


7845 


7986 


8127 


8269 


8410 


141 


8 


8551 
9958 


8692 


8833 


8974 


9114 


9255 


9396 


9537 


9677 


9313 


141 


9 


0099 
1502 


0239 
1642 


0380 
1782 


0520 
1922 


0661 
2062 


0801 
2201 


0941 
2341 


1081 
2481 


1222 
2621 


140 


310 


491362 


140 


1 


2760 


2900 


3040 


3179 


3319 


3458 


3597 


3737 


3876 


4015 


139 


1 


4155 


4294 


4433 


4572 


4711 


4850 


4989 


5128 


5267 


5406 


139 


3 


5544 


5683 


5822 


5960 


6099 


6238 


6376 


6515 


6653 


6791 


139 


4 


6930 


7068 


7206 


7344 


7483 


7621 


7759 


7897 


8035 


8173 


138 


5 


8311 
9687 


8448 
9824 


8586 
9962 


8724 


8862 


8999 


9137 


9275 


9412 


9550 


138 


6 


0099 
1470 


0236 
1607 


0374 
1744 


0511 
1880 


0643 
2017 


0735 
2154 


0922 
2291 


137 


7 


501059 


1196 


1333 


137 


8 


2427 


2564 


2700 


2837 


2973 


3109 


3246 


3382 


3518 


3655 


136 


9 


3791 


3927 


4063 


4199 


4335 


4471 


4607 


4743 


4878 


5014 


136 


320 


5150 


5286 


5421 


5557 


5693 


5828 


5964 


6099 


6234 


6370 


136 


1 


6505 


6640 


6776 


6911 


7046 


7181 


7316 


7451 


7586 


7721 


135 


2 


7856 


7991 


8126 


8260 


8395 


8530 


8664 


8799 


8934 


9068 


135 


3 


9203 


9337 


9471 


9606 


9740 


9874 


0009 
1349 


0143 

1482 


0277 
1616 


0411 
1750 


134 


4 


510545 


0679 


0813 


0947 


1081 


1215 


134 


5 


1883 


2017 


2151 


2284 


2418 


2551 


2684 


2818 


2951 


3034 


133 


6 


3218 


3351 


3484 


3617 


3750 


3333 


4016 


4149 


4282 


4415 


133 


7 


4548 


4631 


4813 


4946 


5079 


5211 


5344 


5476 


5609 


5741 


133 


8 


5874 


6006 


6139 


6271 


6403 


6535 


6668 


6800 


6932 


7064 


132 


9 


7196 


7328 


7460 


7592 


7724 


7855 


7987 


8119 


8251 


8382 


132 


330 


8514 
9828 


8646 
9959 


8777 


8909 


9040 


9171 


9303 


9434 


9566 


9697 


131 


1 


0090 
1400 


0221 
1530 


0353 
1661 


0484 
1792 


0615 
1922 


0745 
2053 


0876 
2133 


1007 
2314 


131 


2 


521138 


1269 


131 


3 


2444 


2575 


2705 


2835 


2966 


3096 


3226 


3356 


3486 


3616 


130 


4 


3746 


3876 


4006 


4136 


4266 


4396 


4526 


4656 


4785 


4915 


130 


5 


5045 


5174 


5304 


5434 


5563 


5693 


5822 


5951 


6081 


6210 


129 


6 


6339 


6469 


6598 


6727 


6856 


6985 


7114 


7243 


7372 


7501 


129 


7 


7630 


7759 


7888 


8016 


8145 


8274 


8402 


8531 


8660 


8783 


129 


8 


8917 


9045 


9174 


9302 


9430 


9559 


9687 


9815 


9943 


0072 
1351 


128 


9 


530200 


0328 


0456 


0584 


0712 


0840 


0968 


1096 


1223 


128 









Proportional Parts. 








Diff. 


1 


3 


3 


4 


5 


6 


7 


8 


9 


139 


13.9 


27.8 


41.7 


55.6 


69.5 


83.4 


97.3 


111.2 


125.1 


138 


13.8 


27.6 


41.4 


55.2 


69.0 


82.8 


96.6 


110.4 


124.2 


137 


13.7 


27.4 


41.1 


54.8 


68.5 


82.2 


95.9 


109.6 


123.3 


136 


13.6 


27.2 


40.8 


54.4 


68.0 


81.6 


95.2 


108.8 


122.4 


135 


13.5 


27.0 


40.5 


54.0 


67.5 


81.0 


94.5 


108.0 


121.5 


134 


13.4 


26.8 


40.2 


53.6 


67.0 


80.4 


93.8 


107.2 


120.6 


133 


13.3 


26.6 


39.9 


53.2 


66.5 


79.8 


93.1 


106.4 


119.7 


132 


13.2 


26.4 


39.6 


52.8 


66.0 


79.2 


92.4 


105.6 


118.8 


131 


13.1 


26.2 


39.3 


52.4 


65.5 


78.6 


91.7 


104.8 


117.9 


130 


13.0 


26.0 


39.0 


52.0 


65.0 


78.0 


91.0 


104.0 


117.0 


129 


12.9 


25.8 


38.7 


51.6 


64.5 


77.4 


90.3 


103.2 


116.1 


128 


12.8 


25.6 


33.4 


51.2 


64.0 


76.8 


89.6 


102.4 


115.2 


127 


12.7 


25.4 


38.1 


50.8 


63.5 


76.2 


83.9 


101.6 


114.3 



LOGARITHMS OP NUMBERS. 



149 



No. 340 L. 531.1 














INo. 


379 L 


. 579. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


IW 


531479 


1607 


1734 


1862 


1990 


~1aT7 


2245 


2372 


2500 


2627 


128 


\ 


2754 


2882 


3009 


3136 


3264 


3391 


3518 


3645 


3772 


3899 


127 


2 


4026 


4153 


4280 


4407 


4534 


4661 


4787 


4914 


5041 


5167 


127 


3 


5294 


5421 


5547 


5674 


5800 


5927 


6053 


6180 


6306 


6432 


126 


4 


6558 


6685 


6811 


6937 


7063 


7189 


7315 


7441 


7567 


7693 


126 


5 


7819 


7945 


8071 


8197 


8322 


8448 


8574 


8699 


8825 


8951 


126 


6 


9076 


9202 


9327 


9452 


9578 


9703 


9829 


9954 








0079 


0204 


125 




















7 


540329 


0455 


0580 


0705 


0830 


0955 


1080 


1205 


1330 


1454 


125 


8 


1579 


1704 


1829 


1953 


2078 


2203 


2327 


2452 


2576 


2701 


125 


9 


2825 


2950 


3074 


3199 


3323 


3447 


3571 


3696 


3820 


3944 


124 


350 


4068 


4192 


4316 


4440 


4564 


4688 


4812 


4936 


5060 


5183 


124 


1 


5307 


5431 


5555 


5678 


5802 


5925 


6049 


6172 


6296 


6419 


124 


2 


6543 


6666 


6} 89 


6913 


7036 


7159 


7282 


7405 


7529 


7652 


123 


3 


7775 


7898 


8021 


8144 


8267 


8389 


8512 


8635 


8758 


8881 


123 


4 


9003 


9126 


9249 


9371 


9494 


9616 


9739 


9861 


9984 


0106 
1328 


123 
122 


5 


550228 


0351 


0473 


0595 


0717 


0840 


0962 


1084 


1206 


6 


1450 


1572 


1694 


1816 


1938 


2060 


2181 


2303 


2425 


2547 


122 


7 


2668 


2790 


2911 


3033 


3155 


3276 


3398 


3519 


3640 


3762 


121 


8 


3883 


4004 


4126 


4247 


4368 


4489 


4610 


4731 


4852 


4973 


121 


9 


5094 


5215 


5336 


5457 


5578 


5699 


5820 


5940 


6061 


ei82 


121 


360 


6303 


6423 


6544 


6664 


6785 


6905 


7026 


7146 


7267 


7387 


120 


1 


7507 


7627 


7748 


7868 


7988 


8108 


8228 


8349 


8469 


8589 


120 


2 


8709 


8829 


8948 


9068 


9188 


9308 


9428 


9548 


9667 


9787 


120 


3 


9907 






















0026 


0146 


0265 


0385 


0504 


0624 


0743 


0863 


0982 


119 






4 


561101 


1221 


1340 


1459 


1578 


1698 


1817 


1936 


2053 


2174 


119 


5 


2293 


2412 


2531 


2650 


2769 


2887 


3006 


3125 


3244 


3362 


119 


6 


3481 


3600 


3718 


3837 


3955 


4074 


4192 


4311 


4429 


4548 


119 


7 


4666 


4784 


4903 


5021 


5139 


5257 


5376 


5494 


5612 


5730 


118 


8 


5848 


5966 


6084 


6202 


6320 


6437 


6555 


6673 


6791 


6909 


118 


9 


7026 


7144 


7262 


7379 


7497 


7614 


7732 


7849 


7967 


8084 


118 


370 


8202 


8319 


8436 


8554 


8671 


8788 


8905 


9023 


9140 


9257 


117 


1 


9374 


9491 


9608 


9725 


9842 


9959 


















0076 


0193 


0309 


0426 


117 
















2 


570543 


0660 


0776 


0893 


1010 


1126 


1243 


1359 


1476 


1592 


117 


3 


1709 


1825 


1942 


2058 


2174 


2291 


2407 


2523 


2639 


2755 


116 


4 


2872 


2988 


3104 


3220 


3336 


3452 


3568 


3684 


3800 


3915 


116 


5 


4031 


4147 


4263 


4379 


4494 


4610 


4726 


4841 


4957 


5072 


116 


6 


5188 


5303 


5419 


5534 


5650 


5765 


5880 


5996 


6111 


6226 


115 


7 


6341 


6457 


6572 


6687 


6802 


6917 


7032 


7147 


7262 


7377 


115 


8 


7492 


7607 


7722 


7836 


7951 


8066 


8181 


8295 


8410 


8525 


115 


9 


8639 


8754 


8868 


8983 


9097 


9212 


9326 


9441 


9555 


9669 


114 



Proportional, Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


128 


12.8 


25.6 


38.4 


51.2 


64.0 


76.8 


89.6 


102.4 


115.2 


12/ 


12.7 


25.4 


38.1 


50.8 


63.5 


76.2 


88.9 


101.6 


114.3 


126 


12.6 


25.2 


37.8 


50.4 


63.0 


75.6 


88.2 


100.8 


113.4 


125 


12.5 


25.0 


37.5 


50.0 


62.5 


75.0 


87.5 


100.0 


1 12 5 


124 


12.4 


24.8 


37.2 


49.6 


62.0 


74.4 


86.8 


99.2 


11 1.6 


123 


12.3 


24.6 


36.9 


49.2 


61.5 


73.8 


86.1 


98.4 


110.7 


122 


12.2 


24.4 


36.6 


48.8 


61.0 


73.2 


85.4 


97.6 


109.8 


121 


12.1 


24.2 


36.3 


48.4 


60.5 


72.6 


84.7 


96.8 


108.9 


120 


12.0 


24.0 


36.0 


48.0 


60.0 


72.0 


84.0 


96.0 


108.0 


119 


11.9 


23.8 


35.7 


47.6 


59.5 


71.4 


83.3 


95.2 


107.1 



150 



LOGARITHMS OF NUMBERS. 



No. 380 L. 579.1 



[No. 414 L. 617. 



N. 





1 


3 


3 


4 


5 


6 


7 


8 


9 


Diff. 


380 


579784 


9898 


nni? 


f\\ '>A 


0241 


0355 


0469 


0583 


0697 


081 1 












1 14 


1 


580925 


1039 


1153 


1267 


1381 


1495 


1608 


1722 


1836 


1950 




2 


2063 


2177 


2291 


2404 


2518 


2631 


2745 


2858 


2972 


3085 




3 


3199 


3312 


3426 


3539 


3652 


3765 


3879 


3992 


4105 


4218 




4 


4331 


4444 


4557 


4670 


4783 


4896 


5009 


5122 


5235 


5348 


1 13 


5 


5461 


5574 


5686 


5799 


5912 


6024 


6137 


6250 


6362 


6475 




6 


6587 


6700 


6812 


6925 


7037 


7149 


7262 


7374 


7486 


7599 




y 


7711 


7823 


7935 


8047 


8160 


8272 


8384 


8496 


8608 


8720 


112 


8 
9 


8832 
9950 


8944 


9056 


9167 


9279 


9391 


9503 


9615 


9726 


9838 




0061 


0173 


0284 


0396 


0507 


0619 


0730 


0842 


095i 










390 


591065 


1176 


1287 


1399 


1510 


1621 


1732 


1843 


1955 


2066 




1 


2177 


2288 


2399 


2510 


2621 


2732 


2843 


2954 


3064 


3175 


1 1 1 


2 


3286 


3397 


3508 


3618 


3729 


3840 


3950 


4061 


4171 


4282 




3 


4393 


4503 


4614 


4724 


4834 


4945 


5055 


5165 


5276 


5386 




4 


5496 


5606 


5717 


5827 


5937 


6047 


6157 


6267 


6377 


6487 




5 


6597 


6707 


6817 


6927 


7037 


7146 


7256 


7366 


7476 


7586 


1 10 


6 


7695 


7805 


7914 


8024 


8134 


8243 


8353 


8462 


8572 


8681 




7 
8 


8791 
9883 


8900 
9992 


9009 


9119 


9228 


9337 


9446 


9556 


9665 


9774 






0101 


0210 


0319 


0428 


0537 


0646 


0755 


0864 


109 










9 


600973 


1082 


1191 


1299 


1406 


1517 


1625 


1734 


1843 


1951 




400 


2060 


2169 


2277 


2386 


2494 


2603 


2711 


2819 


2928 


3036 




I 


3144 


3253 


3361 


3469 


3577 


3686 


3794 


3902 


4010 


41 18 


108 


2 


4226 


4334 


4442 


4550 


4658 


4766 


4874 


4982 


5089 


5197 




3 


5305 


5413 


5521 


5628 


5736 


5844 


5951 


6059 


6166 


6274 




4 


6381 


6489 


6596 


6704 


6811 


6919 


7026 


7133 


7241 


7348 




5 


7455 


7562 


7669 


7777 


7884 


7991 


8098 


8205 


8312 


8419 


107 


6 


8526 


8633 


8740 


8847 


8954 


9061 


9167 


9274 


9381 


9488 




7 


9594 


9701 


9808 


9914 


















0021 


0128 


0234 


0341 


0447 


0554 
















8 


610660 


0767 


0873 


0979 


1086 


1192 


1298 


1405 


151 1 


1617 




9 


1723 


1829 


1936 


2042 


2148 


2254 


2360 


2466 


2572 


2678 


106 


410 


2784 


2890 


2996 


3102 


3207 


3313 


3419 


3525 


3630 


3736 




1 


3842 


3947 


4053 


4159 


4264 


4370 


4475 


4581 


4686 


4792 




2 
3 


4897 


5003 5108 


5213 


5319 


5424 


5529 


5634 


5740 


5845 




5950 


6055 6160 


6265 


6370 


6476 


6581 


6686 


6790 


6895 


105 


4 


7000 


7105 7210 73151 7420| 


7525 7629' 


7734 


7839 


7943 





Proportional Parts. 



11.8 
11.7 
11.6 
11.5 
11.4 
11.3 
11.2 

11.1 
11.0 
10.9 
10.8 
10.7 
10.6 
10.5 
10.4 



23.6 
23.4 
23.2 
23.0 
22.8 
22.6 
22.4 

22.2 
22.0 
21.8 
21.6 
21.4 
21.2 
21.0 
20.8 



35.4 
35.1 
34.8 
34.5 
34.2 
33.9 
33.6 

33.3 
33.0 
32.7 
32.4 
32.1 
31.8 
31.5 
31.2 



47.2 
46.8 
46.4 
46.0 
45.6 
45.2 
44.8 

44.4 
44.0 
43.6 
43.2 
42.8 
42.4 
42.0 
41.6 



5 



59.0 
58.5 
58.0 



57.5 


57.0 


56.5 


56.0 


55.5 


55.0 


54.5 


54.0 


53.5 


53.0 


52.5 


52.0 



70.8 
70.2 
69.6 
69.0 
68.4 
67.8 
67.2 

66.6 
66.0 
65.4 
64.fi 
64.2 
63.6 
63.0 
62.4 



82.6 
81.9 
81.2 
80.5 
79.8 
79.1 
78.4 

77.7 
77.0 
76.3 
75.6 
74.9 
74.2 
73.5 
72.8 



8 



94.4 
93.6 
92.8 
92.0 
91.2 
90.4 
89.6 

88.8 
88.0 
87.2 
86.4 
85.6 
84.8 
84.0 
83.2 



LOGARITHMS OF NUMBERS. 



151 



No. 415 L. 618.] 














[No. 


459 L. 662. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Difif. 


415 


618046 


8153 


8257 


8362 


8466 


8571 


8676 


8780 


8884 


8989 


105 


6 


9093 


9198 


9302 


9406 


9511 


9615 


9719 


9824 


9928 


0032 
1072 




7 


620136 


0240 


0344 


0448 


0552 


0656 


0760 


0864 


0968 


104 


8 


1176 


1280 


1384 


1483 


1592 


1695 


1799 


1903 


2007 


2110 




9 


2214 


2318 


2421 


2525 


2628 


2732 


2835 


2939 


3042 


3146 




420 


3249 


3353 


3456 


3559 


3663 


3766 


3869 


3973 


4076 


4179 




1 


4232 


4335 


4433 


4591 


4695 


4793 


4901 


5004 


5107 


5210 


103 


2 


5312 


5415 


5518 


5621 


5724 


5827 


5929 


6032 


6135 


6238 




3 


6340 


6443 


6546 


6648 


6751 


6853 


6956 


7058 


7161 


7263 




4 


7366 


7463 


7571 


7673 


7775 


7878 


7980 


8082 


8185 


8287 




5 


8389 


8491 


8593 


8695 


8797 


8900 


9002 


9104 


9206 


9308 


102 


6 


9410 


9512 


9613 


9715 


9817 


9919 


0021 
1038 


0123 
1139 


0224 
1241 


0326 
1342 




7 


630428 


0530 


0631 


0733 


0835 


0936 




8 


1444 


1545 


1647 


1748 


1849 


1951 


2052 


2153 


2255 


2356 




9 


2457 


2559 


2660 


2761 


2862 


2963 


3064 


3165 


3266 


3367 




430 


3468 


3569 


3670 


3771 


3872 


3973 


4074 


4175 


4276 


4376 


101 


1 


4477 


4573 


4679 


4779 


4880 


4981 


5081 


5182 


5283 


5383 




2 


5434 


55S4 


5635 


5785 


5886 


5936 


6087 


6187 


6287 


6388 




3 


6433 


6538 


6638 


6789 


6389 


6939 


7039 


7189 


7290 


7390 




4 


7490 


7590 


7690 


7790 


7890 


7990 


8090 


8190 


8290 


8389 


100 


5 


8439 


8539 


8639 


8789 


8838 


8988 


903S 


9188 


9287 


9387 




6 


9436 
640431 


9536 


9686 


9785 


9835 


9934 


0084 
1077 


0183 
1177 


0283 
1276 


0382 
1375 




7 


0581 


0630 


0779 


0879 


0978 




8 


1474 


1573 


1672 


1771 


1871 


1970 


2069 


2168 


2267 


2366 




9 


2465 


2563 


2662 


2761 


2860 


2959 


3058 


3156 


3255 


3354 


99 


440 


3453 


3551 


3650 


3749 


3847 


3946 


4044 


4143 


4242 


4340 




1 


4439 


4537 


4636 


4734 


4832 


4931 


5029 


5127 


5226 


5324 




2 


5422 


5521 


5619 


5717 


5815 


5913 


6011 


6110 


6203 


6306 




3 


6404 


6502 


6600 


6698 


6796 


6894 


6992 


7089 


7187 


7285 


98 


4 


7333 


7481 


7579 


7676 


7774 


7872 


7969 


8067 


8165 


8262 




5 


8360 


8458 


8555 


8653 


8750 


8848 


8945 


9043 


9140 


9237 




6 


9335 


9432 


9530 


9627 


9724 


9821 


9919 


0016 
0987 


0113 
1084 


0210 
1181 




7 


650303 


0405 


0502 


0599 


0696 


0793 


0890 




8 


1278 


1375 


1472 


1569 


1666 


1762 


1859 


1956 


2053 


2150 


97 


9 


2246 


2343 


2440 


2536 


2633 


2730 


2826 


2923 


3019 


3116 




450 


3213 


3309 


3405 


3502 


3598 


3695 


3791 


3888 


3984 


4080 




1 


4177 


4273 


4369 


4465 


4562 


4658 


4754 


4850 


4946 


5042 




2 


5138 


5235 


5331 


5427 


5523 


5619 


5715 


5810 


5906 


6002 


96 


3 


6098 


6194 


6290 


6386 


6482 


6577 


6673 


6769 


6864 


6960 




4 


7056 


7152 


7247 


7343 


7438 


7534 


7629 


7725 


7820 


7916 




5 


8011 


8107 


8202 


8298 


8393 


8488 


8584 


8679 


8774 


8870 




6 

7 


8965 
9916 


9C60 


9155 


9250 


9346 


9441 


9536 


9631 


9726 


9821 




0011 
0960 


0106 
1055 


0201 
1150 


0296 
1245 


0391 
1339 


0486 
1434 


0581 
1529 


0676 
1623 


0771 
1718 


95 


8 


660865 




9 


1813 


1907 


2002 


2096 


2191 


2286 


2380 


2475 


2569 


2663 





Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 
84.0 


9 


105 


10.5 


21.0 


31.5 


42.0 


52.5 


63.0 


73.5 


945 


104 


10.4 


20.8 


31.2 


41.6 


52.0 


62.4 


72.8 


83.2 


93.6 


103 


10.3 


20/ 


30.9 


41.2 


51.5 


61.8 


72.1 


82.4 


92.7 


102 


10.2 


20.4 


30.6 


40.8 


51.0 


61.2 


71.4 


81.6 


91 8 


101 


10.1 


20.2 


30.3 


40.4 


50.5 


60.6 


70.7 


80.8 


90.9 


100 


10.0 


20.0 


30.0 


40.0 


50.0 


60.0 


70.0 


80.0 


90.0 


99 


9.9 


19.8 


29.7 


39.6 


49.5 


59.4 


69.3 


79.2 


89.1 



152 



LOGARITHMS OF NUMBERS. 



No. 460 L. 662.] 



[No. 499 L. 698. 



N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diflf. 


460 
1 

2 
3 
4 
5 
6 
7 


662758 
3701 
4642 
5581 
6518 
7453 
83S6 
9317 


2852 
3795 
4736 
5675 
6612 
7546 
8479 
9410 


2947 
3889 
4830 
5769 
6705 
7640 
8572 
9503 


3041 
3983 
4924 
5862 
6799 
7733 
8665 
9596 


3135 
4078 
5018 
5956 
6892 
7826 
8759 
9689 


3230 
4172 
5112 
6050 
6936 
7920 
8852 
9782 


3324 
4266 
5206 
6143 
7079 
8013 
8945 
9875 


3418 
4360 
5299 
6237 
7173 
8106 
9038 
9967 


3512 

4454 
5393 
6331 
7266 
8199 
9131 


3607 

4548 
5487 
6424 
7360 
8293 
9224 


94 


0060 
0988 
1913 

2836 
3758 
4677 
5595 
6511 
7424 
8336 
9246 


0153 
1080 
2005 

2929 
3850 
4769 
5687 
6602 
7516 
8427 
9337 


93 

92 
91 


8 
9 

470 
I 

2 
3 
4 
5 
6 
7 
8 


670246 
1173 

2098 
3021 
3942 
4861 
5778 
6694 
7607 
8518 
9428 


0339 
1265 

2190 
3113 
4034 
4953 
5870 
6785 
7698 
8609 
9319 


0431 
1358 

2283 
3205 
4126 
5045 
5962 
6876 
7789 
8700 
9610 


0524 
1451 

2375 
3297 
4218 
5137 
6053 
6968 
7881 
8791 
9700 


0617 
1543 

2467 
3390 
4310 
5228 
6145 
7059 
7972 
8882 
9791 


0710 
1636 

2560 
3482 
4402 
5320 
6236 
7151 
8063 
8973 
9882 


0802 
1728 

2652 
3574 
4494 
5412 
6328 
7242 
8154 
9064 
9973 


0895 
1821 

2744 
3666 
4586 
5503 
6419 
7333 
8245 
9155 


0063 
0970 

1874 
2777 
3677 
4576 
5473 
6368 
7261 
8153 
9042 
9930 


0154 
1060 

1%4 
2867 
3767 
4666 
5563 
6458 
7351 
8242 
9131 


0245 
1151 

2055 
2957 
3857 
4756 
5652 
6547 
7440 
8331 
9220 




9 

480 
1 

2 
3 
4 
5 
6 
7 
8 
9 


680336 

1241 
2145 
3047 
3947 
4845 
5742 
6636 
7529 
8420 
9309 


0426 

1332 
2235 
3137 
4037 
4935 
5831 
6726 
7618 
8509 
9398 


0517 

1422 
2326 
3227 
4127 
5025 
5921 
6815 
7707 
8598 
9486 


0607 

1513 
2416 
3317 
4217 
5114 
6010 
6904 
7796 
8687 
9575 


0698 

1603 
2506 
3407 
4307 
5204 
6100 
6994 
7886 
8776 
9664 


0789 

1693 
2596 
3497 
4396 
5294 
6189 
7083 
7975 
8865 
9753 


0879 

1784 
2686 
3587 
4486 
5383 
6279 
7172 
8064 
8953 
9841 


90 

89 




0019 

0905 
1789 
2671 
3551 
4430 
5307 
6182 
7055 
7926 
8796 


0107 

0993 
1877 
2759 
3639 
4517 
5394 
6269 
7142 
8014 
8883 




490 
1 

2 
3 
4 
5 
6 
7 
8 
9 


690196 
1081 
1965 
2847 
3727 
4605 
5482 
6356 
7229 
8100 


0285 
1170 
2053 
2935 
3815 
4693 
5569 
6444 
7317 
81881 


0373 
1258 
2142 
3023 
3903 
4781 
5657 
6531 
7404 
8275 


0462 
1347 
2230 
3111 
3991 
4868 
5744 
6618 
7491 
8362 


0550 
1435 

2318 
3199 
4078 
4956 
5832 
6706 
7578 
8449 


0639 
1524 
2406 
3287 
4166 
5044 
5919 
6793 
7665 
8535 


0728 
1612 
2494 
3375 
4254 
5131 
6007 
6880 
7752 
8622 


0816 
1700 

2583 
3463 
4342 
5219 
6094 
6968 
7839 
8709 


88 
87 



Proportional Parts. 



Diff. 


1 
9.8 


2 


3 


4 


5 


6 


7 


8 


9 


98 


19.6 


29.4 


39.2 


49.0 


58.8 


68.6 


78.4 


88.2 


9; 


9.7 


19.4 


29.1 


38.8 


48.5 


58.2 


67.9 


77.6 


87.3 


96 


9.6 


19.2 


28.8 


38.4 


48.0 


57.6 


67.2 


76.8 


86.4 


9b 


9.5 


19.0 


28.5 


38.0 


47.5 


57.0 


66.5 


76.0 


85.3 


94 


9.4 


18.8 


28.2 


37.6 


47.0 


56.4 


65.8 


75.2 


84.6 


93 


9.3 


18.6 


27.9 


37.2 


46.5 


55.8 


65.1 


74.4 


83.7 


92 


9.2 


18.4 


27.6 


36.8 


46.0 


55.2 


64.4 


73.6 


82.8 


91 


9.1 


18.2 


27.3 


36.4 


45.5 


54.6 


63.7 


72.8 


81.9 


90 


9.0 


18.0 


27.0 


36.0 


45.0 


54.0 


63.0 


72.0 


81.0 


89 


8.9 


17.8 


26.7 


35.6 


44.5 


53.4 


62.3 


71.2 


80.1 


88 


8.8 


17.6 


26.4 


35.2 


44.0 


52.8 


61.6 


70.4 


79.2 


87 


8.7 


17.4 


26.1 


34.8 


43.5 


52.2 


60.9 


69.6 


78.3 


86 


8.6 


17.2 


25.8 


34.4 


43.0 


51.6 


60.2 


68.8 


77.4 



LOGARITHMS OF NUMBERS. 



153 



So. 500 L. 698.1 



[No. 544 L. 736, 



N. 





1 


2 


3 

9231 


4 


5 


6 


7 


8 


9 


Diff. 


500 


6989/0 


905; 


9144 


9317 


9404 


9491 


9578 


9664 


9751 




1 


9838 


992^ 
























0011 


0098 


0184 


0271 


0358 


0444 


0531 


0617 












2 


700704 


0790 


0877 


0963 


1050 


1136 


1222 


1309 


1395 


1482 




3 


1568 


1654 


1741 


1827 


1913 


1999 


2086 


2172 


2258 


2344 




4 


2431 


2517 


2603 


2689 


2775 


2861 


2947 


3033 


3119 


3205 




•y 


3291 


3377 


3463 


3549 


3635 


3721 


3807 


3893 


3979 


4065 


86 


6 


4151 


4236 


4322 


4408 


4494 


4579 


4665 


4751 


4837 


4922 




7 


5003 


5094 


5179 


5265 


5350 


5436 


5522 


5607 


5693 


5778 




8 


5864 


5949 


6035 


6120 


6206 


6291 


6376 


6462 


6547 


6632 




9 


6718 


6803 


6888 


6974 


7059 


7144 


7229 


7315 


7400 


7485 




510 


7570 


7655 


7740 


7826 


7911 


7996 


8081 


8166 


8251 


8336 




1 


8421 


8506 


8591 


8676 


8761 


8346 


8931 


9015 


9100 


9185 


85 


2 


9270 


9355 


9440 


9524 


9609 


9694 


9779 


9863 


9948 






3 


710117 


0202 


0287 


0371 


0456 


0540 


0625 


0710 


0794 


0033 
0879 




4 


0963 


1048 


1132 


1217 


1301 


1385 


1470 


1554 


1639 


1723 




!) 


1807 


1892 


1976 


2060 


2144 


2229 


2313 


2397 


2481 


2566 




b 


2650 


2734 


2818 


2902 


2936 


3070 


3154 


3238 


33?3 


3407 




y 


3491 


3575 


3659 


3742 


3826 


3910 


3994 


4078 


4162 


4246 


84 


8 


4330 


4414 


4497 


4581 


4665 


4749 


4833 


4916 


5000 


5084 




9 


5167 


5251 


5335 


5418 


5502 


5586 


5669 


5753 


5836 


5920 




7 20 


6003 


6087 


6170 


6254 


6337 


6421 


6504 


6588 


6671 


6754 




1 


6838 


6921 


7004 


7088 


7171 


7254 


7338 


7421 


7504 


7587 




2 


7671 


7754 


7837 


7920 


8003 


8086 


8169 


8253 


8336 


8419 


83 


3 


8502 


8585 


8668 


8751 


8834 


8917 


9000 


9083 


9165 


9248 




4 


9331 


9414 


9497 


9580 


9663 


9745 


9828 


9911 


9994 






5 


720159 


0242 


0325 


0407 


0490 


0573 


0655 


0738 


0821 


0077 
0903 




6 


0986 


1063 


1151 


1233 


1316 


1393 


1481 


1563 


1646 


1728 




7 


1811 


1893 


1975 


2058 


2140 


2222 


2305 


2387 


2469 


2 552 




8 


2634 


2716 


2798 


2881 


2963 


3045 


3127 


3209 


3291 


3374 




9 


3456 


3538 


3620 


3702 


3784 


3866 


3948 


4030 


4112 


4194 


82 


530 


4276 


4358 


4440 


4522 


4604 


4685 


4767 


4849 


4931 


5013 




1 


5095 


5176 


5258 


5340 


5422 


5503 


5585 


5667 


5748 


5830 




2 


5912 


5993 


6075 


6156 


6238 


6320 


6401 


6483 


6564 


6646 




3 


6727 


6809 


6890 


6972 


7053 


7134 


7216 


7297 


7379 


7460 




4 • 


7541 


7623 


7704 


7785 


7866 


7948 


8029 


8110 


8191 


8273 




5 


8354 


8435 


8516 


8597 


8678 


8759 


8841 


8922 


9003 


9084 




6 

7 


9165 
9974 


9246 


9327 


9408 


9489 


9570 


9651 


9732 


9813 


9893 


81 




0055 


0136 


0217 


0298 


0378 


0459 


0540 


0621 


0702 






:?30782 




8 


0863 


0944 


1024 


1105 


1186 


1266 


1347 


1428 


1508 




9 


1589 


1669 


1750 


1830 


1911 


1991 


2072 


2152 


2233 


2313 




540 


2394 


2474 


2555 


2635 


2715 


2796 


2876 


2956 


3037 


3117 




1 


3197 


3278 


3358 


3438 


3518 


3598 


3679 


3759 


3839 


3919 




2 
3 


3999 


4079 


4160 


4240 


4320 


4400 


4480 4560 


4640 


4720 


80 


4800 


4880 


4960 


5040 


5120 


5200 


5279 5359 


5439 


5519 




4 


5599 


5679 


5759 5838' 59181 


5998 6078' 61571 


6237 


6317 





8.7 
8.6 
8.5 
8.4 



17.4 
17.2 
17.0 
16.8 



Proportional Parts. 



26.1 
25.8 
25.5 
25.2 



34.8 
34.4 
34.0 
33.6 



5 

43.5 
43.0 
42.5 
42.0 



I 



6 

52.2 
51.6 
51.0 
50.4 



60.9 
60.2 
59.5 

58.8 



8 

69.6 
68.8 
68.0 
67.2 



9 

"78T 
77.4 
76.5 
75.6 



154 



LOGARITHMS Of NUMBERS. 



No. 545 L. 736.] 














INo 


. 584 L. 767 


N. 





1 


3 


3 


4 


5 


6 


7 


8 


9 


Diff. 


545 
6 

7 
6 
9 


736397 
7193 
7987 
8781 
9572 


6476 
7272 
8067 
8860 
9651 


6556 
7352 
8146 
8939 
9731 


6635 

7431 
8225 
9018 
9810 


6715 
7511 
8305 
9097 
9889 


6795 
7590 
8384 
9177 
9968 


6874 
7670 
8463 
9256 


6954 
7749 
8543 
9335 


7034 
7829 
8622 
9414 


7113 
7908 
8701 
9493 




0047 

0836 
1624 
2411 
3196 
3980 
4762 
5543 
6323 
7101 
7878 

8653 
9427 


0126 

0915 
1703 
2489 
3275 
4053 
4840 
5621 
6401 
7179 
7955 

8731 
9504 


0205 

0994 
1782 
2568 
3353 
4136 
4919 
5699 
6479 
7256 
8033 

8808 
9582 


0284 

1073 
I860 
2647 
3431 
4215 
4997 
5777 
6556 
7334 
8110 

8885 
9659 


79 

78 


550 
1 

2 
3 
4 
5 
6 
7 
8 
9 

560 

I 
2 


740363 
1152 
1939 
2725 
3510 
4293 
5075 
5855 
6634 
7412 

8188 
8963 
9736 


0442 
1230 
2018 
2804 
3588 
4371 
5153 
5933 
6712 
7489 

8266 
9040 
9314 


0521 
1309 
2096 
2882 
3667 
4449 
5231 
6011 
6790 
7567 

8343 
9118 
9891 


0600 

1388 
2175 
2961 
3745 
4328 
5309 
6089 
6868 
7645 

8421 
9195 
9968 


0678 
1467 
2254 
3039 
3823 
4606 
5387 
6167 
6945 
7722 

8498 
9272 


0757 
1546 
2332 
3118 
3902 
4684 
5465 
6245 
7023 
7800 

8576 
9350 


0045 
0817 
1587 
2356 
3123 
3889 
4654 
5417 

6180 
6940 
7700 
8458 
9214 
9970 


0123 
0894 
1664 
2433 
3200 
3966 
4730 
5494 

6256 
7016 
7775 
8533 
9290 


0200 
0971 
1741 
2509 
3277 
4042 
4807 
5570 

6332 
7092 
7851 
8609 
9366 


0277 
1048 
1818 
2586 
3353 
4119 
4883 
5646 

6408 
7168 
7927 
8685 
9441 


0354 
1125 
1895 
2663 
3430 
4195 
4960 
5722 

6484 
7244 
8003 
8761 
9517 


0431 
1202 
1972 
2740 
3506 
4272 
5036 
5799 

6560 
7320 
8079 
8836 
9592 




3 
4 
5 
6 
7 
8 
9 

570 
I 

2 
3 
4 
5 


75050S 
1279 
2048 
2816 
3583 
4348 
5112 

5875 
6636 
7396 
8155 
8912 
9668 


0586 
1356 
2125 
2893 
3660 
4425 
5189 

5951 
6712 
7472 
8230 
8988 
9743 


0663 
1433 
2202 
2970 
3736 
4501 
5265 

6027 
6788 
7548 
8306 
9063 
9819 


0740 
1510 
2279 
3047 
3813 
4578 
5341 

6103 
6864 
7624 
8382 
9139 
9894 


77 

76 


0045 
0799 
1552 
2303 
3053 

3802 
4550 
5296 
6041 
6785 


0121 
0875 
1627 
2378 
3128 

3877 
4624 
5370 
6115 
6859 


0196 
0950 
1702 
2453 
3203 

3952 
4699 
5445 
6190 
6933 


0272 
1025 
1778 
2529 
3278 

4027 
4774 
5520 
6264 
7007 


0347 
1101 
1853 
2604 
3353 

4101 
4848 
5594 
6338 
7082 




6 

7 
8 
9 

580 
1 

2 
3 
4 


760422 
1176 
1928 
2679 

3428 
4176 
4923 
5669 
6413 


0498 
1251 
2003 
2754 

3503 

4251 
4998 
5743 
6487 


0573 
1326 
2078 
2829 

3578 
4326 
5072 
5818 
6562 


0649 
1402 
2153 
2904 

3653 
4400 
5147 
5892 
6636 


0724 
1477 
2228 
2978 

3727 
4475 
5221 
5966 
6710 


75 



Proportional Parts. 



Diff. 


1 
~8.3~ 


2 

16.6 


3 


4 


5 


6 


7 


8 


9 


83 


24.9 


33.2 


41.5 


49.8 


58.1 


66.4 


74.7 


82 


8.2 


16.4 


24.6 


32.8 


41.0 


49.2 


57.4 


65.6 


73.8 


81 


8.1 


16.2 


24.3 


32.4 


40.5 


48.6 


56.7 


64.8 


72.9 


80 


8.0 


16.0 


24.0 


32.0 


40.0 


48.0 


56.0 


64.0 


72.0 


79 


7.9 


15.8 


23.7 


31.6 


39.5 


47.4 


55.3 


63.2 


71.1 


78 


7.8 


15.6 


23.4 


31.2 


39.0 


46.8 


54.6 


62.4 


70.2 


77 


77 


15.4 


23.1 


30.8 


38.5 


46.2 


53.9 


61.6 


69.3 


76 


7.6 


15.2 


22.8 


30.4 


38.0 


45.6 


53.2 


60.8 


68.4 


75 


7.5 


15.0 


22.5 


30.0 


37.5 


45.0 


52.5 


60.0 


67.5 


74 


7.4 


14.8 


22.2 


296 


37.0 


44.4 


51.8 


59.2 


66.6 



LOGARITHMS OF NUMBERS. 



155 



No. 685 L. 767.1 














[No. 629 L. 799 


N. 




767156 
7898 
8638 
9377 


1 


2 


3 

7379 
8120 
8860 
9599 


4 


5 


6 

7601 

. 8342 

9082 

9820 


7 


8 


9 


Diff. 


585 
6 
7 
8 


7230 
7972 
8712 
9451 


7304 
8046 
8786 
9525 


7453 
8194 
8934 
9673 


7527 
8263 
9008 
9746 


7675 
8416 
9156 
9894 


7749 
8490 
9230 
9968 


7823 
8564 
9303 


74 


0042 
0778 

1514 
2248 
2981 
3713 
4444 
5173 
5902 
6629 
7354 
8079 

8802 
9524 




9 

590 
1 

2 
3 
4 
5 
6 
7 
8 
9 

600 

1 
2 


770115 

0852 
1587 
2322 
3055 
3786 
4517 
5246 
5974 
6701 
7427 

8151 
8874 
9596 


0189 

0926 
1661 
2395 
3128 
3360 
4590 
5319 
6047 
6774 
7499 

8224 
8947 
9669 


0263 

0999 
1734 
2463 
3201 
3933 
4663 
5392 
6120 
6846 
7572 

8296 
9019 
9741 


0336 

1073 
1803 
2542 
3274 
4006 
4736 
5465 
6193 
6919 
7644 

8368 
9091 
9313 


0410 

1146 
1881 
2615 
3348 
4079 
4809 
5538 
6265 
6992 
7717 

8441 
9163 
9885 


0484 

1220 
1955 
2688 
3421 
4152 
4832 
5610 
6338 
7064 
7789 

8513 
9236 
9957 


0557 

1293 
2028 
2762 
3494 
4225 
4955 
5683 
6411 
7137 
7862 

8585 
9303 


0631 

1367 
2102 
2835 
3567 
4293 
5028 
5756 
6483 
7209 
7934 

8658 
9380 


0705 

1440 
2175 
2908 
3640 
4371 
5100 
5829 
6556 
7282 
8006 

8730 
9452 


73 


0029 
0749 
1463 
2186 
2902 
3618 
4332 
5045 

5757 
6467 
7177 
7885 
8593 
9299 


0101 
0821 
1540 
2258 
2974 
3689 
4403 
5116 

5828 
6538 
7248 
7956 
8663 
9369 


0173 
0893 
1612 
2329 
3046 
3761 
4475 
5187 

5899 
6609 
7319 
8027 
8734 
9440 


0245 
0965 
1684 
2401 
3117 
3832 
4546 
5259 

5970 
6680 
7390 
8093 
8804 
9510 




3 
A 
5 
6 

7 
8 
9 

610 

1 

2 
3 
4 
5 
6 


780317 
1037 
1755 
2473 
3189 
3904 
4617 

5330 
6041 
6751 
7460 
8168 
8875 
9581 


0389 
1109 
1827 
2544 
3260 
3975 
4689 

5401 
6112 
6822 
7531 
8239 
8946 
9651 


0461 
1181 
1899 
2616 
3332 
4046 
4760 

5472 
6183 
6393 
7602 
8310 
9016 
9722 


0533 
1253 
1971 
26? 1 
3403 
4113 
4831 

5543 
6254 
6964 
7673 
8381 
9087 
9792 


0605 
1324 
2042 
2759 
3475 
4189 
4902 

5615 
6325 
7035 
7744 
8451 
9157 
9863 


0677 
1396 
2114 
2831 
3546 
4261 
4974 

5686 
6396 
7106 
7815 
8522 
9228 
9933 


72 
71 


0004 
0707 
1410 
2111 

2812 
3511 
4209 
4906 
5602 
6297 
6990 
7683 
8374 
9065 


0074 
0778 
1480 
2181 

2882 
3581 
4279 
4976 
5672 
6366 
7060 
7752 
8443 
9134 


0144 
0848 
1550 
2252 

2952 
3651 
4349 
5045 
5741 
6436 
7129 
7821 
8513 
9203 


0215 
0918 
1620 
2322 

3022 
3721 
4418 
5115 
5811 
6505 
7198 
7890 
8582 
9272 




7 
8 
9 

620 

1 

2 
3 
4 
5 
6 
7 
8 
9 


790285 
0988 
1691 

2392 
3092 
3790 
4488 
5185 
5880 
6574 
7268 
7960 
8651 


0356 
1059 
1761 

2462 
3162 
3860 
4558 
5254 
5949 
6644 
7337 
8029 
8720 


0426 
1129 
1831 

2532 
3231 
3930 
4627 
5324 
6019 
6713 
7406 
8098 
8789 


0496 
1199 
1901 

2602 
3301 
4000 
4697 
5393 
6038 
6782 
7475 
8167 
8858 


0567 
1269 
1971 

2672 
3371 
4070 
4767 
5463 
6158 
6852 
7545 
8236 
8927 


0637 
1340 
2041 

2742 
3441 
4139 
4836 
5532 
6227 
6921 
7614 
8305 
8996 


70 
69 



Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


75 


7.5 


15.0 


22.5 


30.0 


37.5 


45.0 


52.5 


60.0 


67.5 


74 


7.4 


14.8 


22.2 


29.6 


37.0 


44.4 


51.8 


59.2 


66.6 


73 


7.3 


14.6 


21.9 


29.2 


36.5 


43.8 


51.1 


58.4 


65.7 


72 


7.2 


14.4 


21.6 


28.8 


36.0 


43.2 


50.4 


57.6 


64.8 


71 


7.1 


14.2 


21.3 


28.4 


35.5 


42.6 


49 7 


56.8 


63.9 


70 


7.0 


14.0 


21.0 


28.0 


35.0 


42.0 


49.0 


56.0 


63.0 


69 


6.9 


13.8 


20.7 


27.6 


34.5 


41.4 


48.3 


55.2 


62.1 



156 



LOGARITHMS OF NUMBERS. 



No. 630 L. 799.! 














{No 


. 674 L. 829. 


N. 


« 


1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


"63or 


799341 


9409 


"9478 


9547 


9616 


96S5 


9754 


9823 


9892 


9961 




1 


800029 


0098 


0167 


0236 


0305 


0373 


0442 


0511 


0580 


0648 


2 


0717 


0786 


0854 


0923 


0992 


1061 


1129 


1198 


1266 


1335 




3 


1404 


1472 


1541 


1609 


1678 


1747 


1815 


1884 


1952 


2021 




4 


2089 


2158 


2226 


2295 


2363 


2432 


2500 


2568 


2637 


2705 




5 


2774 


2842 


2910 


2979 


3047 


3116 


31 84 


3252 


3321 


3389 




6 


3457 


3525 


3594 


3662 


3730 


3798 


3867 


3935 


4003 


4071 




7 


4139 


4208 


4276 


4344 


4412 


4480 


4548 


4616 


4685 


4753 




8 


4821 


4889 


4957 


5025 


5093 


5161 


5229 


5297 


5365 


5433 


68 


9 


5501 


5569 


5637 


5705 


5773 


5841 


5908 


5976 


6044 


6112 




640 


806180 


6248 


6316 


6384 


6451 


6519 


6587 


6655 


6723 


6790 




I 


6858 


6926 


6994 


7061 


7129 


7197 


7264 


7332 


7400 


7467 




2 


7535 


7603 


7670 


7738 


7806 


7873 


7941 


8008 


8076 


8143 




3 


8211 


8279 


8346 


8414 


8481 


8549 


8616 


8684 


8751 


8818 




4 


8886 


8953 


9021 


9088 


9156 


9223 


-9290 


9358 


9425 


9492 




5 


9560 


9627 


9694 


9762 


9829 


9896 


9964 










0031 


0098 


0165 




6 


810233 


0300 


0367 


0434 


0501 


0569 


0636 


0703 


0770 


0837 




7 


0904 


0971 


1039 


1106 


1173 


1240 


1307 


1374 


1441 


1508 


65 


6 


1575 


1642 


1709 


1776 


1843 


1910 


1977 


2044 


2111 


2178 




9 


2245 


2312 


2379 


2445 


2512 


2579 


2646 


2713 


2780 


2847 




650 


2913 


2980 


3047 


3114 


3181 


3247 


3314 


3381 


3448 


3514 




1 


3581 


3648 


3714 


3781 


3848 


3914 


3981 


4048 


4114 


4181 




2 


4248 


4314 


4381 


4447 


4514 


4581 


4647 


4714 


4780 


4847 




3 


4913 


4980 


5046 


5113 


5179 


5246 


5312 


5378 


5445 


5511 




4 


5578 


5644 


5711 


5777 


5843 


5910 


5976 


6042 


6109 


6175 




5 


6241 


6308 


6374 


6440 


6506 


6573 


6639 


6705 


6771 


6838 




6 


6904 


6970 


7036 


7102 


7169 


7235 


7301 


7367 


7433 


7499 




7 


7565 


7631 


7698 


7764 


7830 


7896 


7962 


8028 


8094 


8160 




8 


8226 


8292 


8358 


8424 


8490 


8556 


8622 


8688 


8754 


8820 


66 


9 


8885 


8951 


9017 


9083 


9149 


9215 


9281 


9346 


9412 


9478 




660 


9544 


9610 


9676 


9741 


9807 


9873 


9939 










0004 
0661 


0070 
0727 


0136 
0792 




1 


820201 


0267 


0333 


0399 


0464 


0530 


0595 




2 


0858 


0924 


0989 


1055 


1120 


1186 


1251 


1317 


1382 


1448 




3 


1514 


1579 


1645 


1710 


1775 


1841 


1906 


1972 


2037 


2103 




4 


2168 


2233 


2299 


2364 


2430 


2495 


2560 


2626 


2691 


2756 




5 


2822 


2887 


2952 


3018 


3083 


3148 


3213 


3279 


3344 


3409 




6 


3474 


3539 


3605 


3670 


3735 


3800 


3865 


3930 


3996 


4061 




7 


4126 


4191 


4256 


4321 


4386 


4451 


4516 


4581 


4646 


4711 




8 


4776 


4841 


4906 


4971 


5036 


5101 


5166 


5231 


5296 


5361 


65 


9 


5426 


5491 


5556 


5621 


5686 


5751 


5815 


5880 


5945 


6010 




670 


6075 


6140 


6204 


6269 


6334 


6399 


6464 


6528 


6593 


6658 




1 


6723 


6787 


6852 


6917 


6981 


7046 


7111 


7175 


7240 


7305 




2 


7369 


7434 


7499 


7563 


7628 


7692 


7757 


7821 


7886 


7951 




3 


8015 


8080 


8144 


8209 


8273 


8338 


8402 


8467 


8531 


8595 




4 


8660 


8724 


8789 


8853 


8918 


8982 


9046 


9111 


9175 


9239 





Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


68 


6.8 


13.6 


20.4 


27.2 


34.0 


40.8 


47.6 


54.4 


61.2 


67 


6.7 


13.4 


20.1 


26.8 


33.5 


40.2 


46.9 


53.6 


60.3 


66 


6.6 


13.2 


19.8 


26.4 


33.0 


39.6 


46.2 


52.8 


59.4 


65 


6.5 


13.0 


19.5 


26.0 


32.5 


39.0 


45.5 


52.0 


58.5 


64 


6.4 


12.8 


19.2 


25.6 


32.0 


38.4 


44.8 


51.2 


57.6 























LOGARITHMS OS" NUMBERS. 



167 



No. 675 L. 829.] 














[N0.719L. 85r 


N. 





1 


2 


3 


4 


5 


6 


4 


8 


9 


Diff. 


675 


829304 


9368 


9432 


9497 


9561 


9625 


9690 


9754 


9818 


9882 




6 


9947 






















0011 
0653 


0075 
0717 


0139 


0204 
0345 


0268 
0909 


0332 


0396 
1037 


0460 
1102 


0525 
1166 




7 


830589 


0781 


0973 




8 


1230 


1294 


1358 


1422 


1486 


1550 


1614 


1678 


1742 


1806 


64 


9 


1870 


1934 


1998 


2062 


2126 


2139 


2253 


2317 


2331 


2445 




680 


2509 


2573 


2637 


2700 


2764 


2828 


2892 


2956 


3020 


3083 




1 


3147 


3211 


3275 


3338 


3402 


3466 


3530 


3593 


3657 


3721 




2 


3784 


3843 


3912 


3975 


4039 


4103 


4166 


4230 


4294 


4357 




3 


4421 


4484 


4548 


4611 


4675 


4739 


4302 


4866 


4929 


4993 




4 


5056 


5120 


5183 


5247 


5310 


5373 


5437 


5500 


5564 


5627 




5 


5691 


5754 


5817 


5831 


5944 


6007 


6071 


6134 


6197 


6261 




6 


6324 


6387 


6451 


6514 


6577 


6641 


6704 


6767 


6330 


6894 




7 


6957 


7020 


7083 


7146 


7210 


7273 


7336 


7399 


7462 


7525 




6 


7588 


7652 


7715 


7778 


7841 


7904 


7967 


8030 


8093 


8156 


63 


9 


8219 


8282 


8345 


8408 


8471 


8534 


8597 


8660 


8723 


8786 




690 


8849 


8912 


8975 


9038 


9101 


9164 


9227 


9239 


9352 


9415 




1 


9478 


9541 


9604 


9667 


9729 


9792 


9355 


9918 


9981 






1 




0043 
0671 




2 


840106 


0169 


0232 


0294 


0357 


0420 


0482 


0545 


0608 




3 


0733 


0796 


0859 


0921 


0984 


1046 


1109 


1172 


1234 


1297 




4 


1359 


1422 


1485 


1547 


1610 


1672 


1735 


1797 


1860 


1922 




5 


1985 


2047 


2110 


2172 


2235 


2297 


2360 


2422 


2484 


2547 




6 


2609 


2672 


2734 


2796 


2359 


2921 


2933 


3046 


3108 


3170 




7 


3233 


3295 


3357 


3420 


3432 


3544 


3606 


3669 


3731 


3793 




8 


3855 


3918 


3930 


4042 


4104 


4166 


4229 


4291 


4353 


4415 




9 


4477 


4539 


4601 


4664 


4726 


4738 


4850 


4912 


4974 


5036 




700 


5093 


5160 


5222 


5284 


5346 


5408 


5470 


5532 


5594 


5656 


62 


1 


5718 


5780 


5842 


5904 


5966 


6028 


6090 


6151 


6213 


6275 




2 


6337 


6399 


6461 


6523 


6585 


6646 


6708 


6770 


6832 


6894 




3 


6955 


7017 


7079 


7141 


7202 


7264 


7326 


7383 


7449 


7511 




4 


7573 


7634 


7696 


7758 


7819 


7881 


7943 


8004 


8066 


8128 




5 


8189 


8251 


8312 


8374 


8435 


8497 


8559 


8620 


8682 


8743 




6 


8305 


8866 


8928 


8989 


9051 


9112 


9174 


9235 


9297 


9358 




7 


9419 


9481 


9542 


9604 


9665 


9726 


9788 


9849 


9911 


9972 




8 


850033 


0095 


0156 


0217 


0279 


0340 


0401 


0462 


0524 


0585 




9 


0646 


0707 


0769 


0330 


0391 


0952 


1014 


1075 


1136 


1197 




710 


1258 


1320 


1381 


1442 


1503 


1564 


1625 


1686 


1747 


1809 




1 


1870 


1931 


1992 


2053 


2114 


2175 


2236 


2297 


2358 


2419 


6! 


2 


2480 


2541 


2602 


2663 


2724 


2785 


2846 


2907 


2968 


3029 




3 


3090 


3150 


3211 


3272 


3333 


3394 


3455 


3516 


3577 


3637 




4 


3698 


3759 


3320 


3831 


3941 


4002 


4063 


4124 


4185 


4245 




5 


4306 


4367 


4428 


4488 


4549 


4610 


4670 


4731 


4792 


4852 




6 


4913 


4974 


5034 


5095 


5156 


5216 


5277 


5337 


5398 


5459 




7 


5519 


5530 


5640 


5701 


5761 


5822 


5882 


5943 


6003 


6064 




8 


6124 


6185 


6245 


6306 


6366 


6427 


6437 


6548 


6608 


6668 




9 


6729 


6789 


6850 


6910 


6970 


7031 


7091 


7152 


7212 


7272 





Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


65 


6.5 


13.0 


19.5 


26.0 


32.5 


39.0 


45.5 


52.0 


58.5 


64 


6.4 


12.8 


19.2 


25.6 


32.0 


38.4 


44.8 


51.2 


57.6 


63 


6.3 


12.6 


18.9 


25.2 


31.5 


37.8 


44.1 


50.4 


56.7 


62 


6.2 


12.4 


18.6 


24.8 


31.0 


37.2 


43.4 


49.6 


55.8 


61 


6.1 


12.2 


18.3 


24.4 


30.5 


36.6 


42.7 


48.8 


54.9 


60 


6.0 


12.0 


18.0 


24.0 


30.0 


36.0 


42.0 


48.0 


34.0 



158 



LOGARITHMS OF NUMBERS. 



No. 720 L. 857.] 



[No. 764 L. 883. 



N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


720 


857332 


7393 


7453 


7513 


7574 


/634 


7694 


7755 


7815 


7875 




1 


7935 


7995 


8056 


8116 


S176 


8236 


8297 


8357 


8417 


8477 




2 


8537 


8597 


8657 


8718 


8778 


8838 


8898 


8958 


9018 


9078 




3 


9138 


9198 


9258 


9318 


9379 


9439 


9499 


9559 


9619 


9679 


60 


4 


9739 


9799 


9859 


9918 


9978 






































0038 


0098 


0158 


0? 18 


0278 
0877 




5 


860338 


0398 


0458 


0518 


0578 


0637 


0697 


0757 


0817 




6 


0937 


0996 


1056 


1116 


1176 


1236 


1295 


1355 


1415 


1475 




7 


1534 


1594 


1654 


1714 


1773 


1833 


1893 


1952 


2012 


2072 




8 


2131 


2191 


2251 


2310 


2370 


2430 


2489 


2549 


2608 


2668 




9 


2728 


2787 


2847 


2906 


2966 


3025 


3085 


3144 


3204 


3263 




730 


3323 


3382 


3442 


3501 


3561 


3620 


3680 


3739 


3799 


3858 




1 


3917 


3977 


4036 


4096 


4155 


4214 


4274 


4333 


4392 


4452 




2 


4511 


4570 


4630 


4689 


4748 


4808 


4867 


4926 


4985 


5045 




3 


5104 


5163 


5222 


5282 


5341 


5400 


5459 


5519 


5578 


5637 




4 


5696 


5755 


5314 


5874 


5933 


5992 


6051 


6110 


6169 


6228 




5 


6287 


6346 


6405 


6465 


6524 


6583 


6642 


6701 


6760 


6819 




6 


6878 


6937 


6996 


7055 


71 14 


7173 


7232 


7291 


7350 


7409 


59 


7 


7467 


7526 


7585 


7644 


7703 


7762 


7821 


7880 


7939 


7998 




8 


8056 


8115 


8174 


8233 


8292 


8350 


8409 


8468 


8527 


8586 




9 


8644 


8703 


8762 


8821 


8879 


8938 


8997 


9056 


9114 


9173 




740 
1 


9232 
9818 


9290 
9377 


9349 
9935 


9408 
9994 


9466 


9525 


9584 


9642 


9701 


9760 




1 


0053 
063 « 


01 1 1 


0170 


0228 


0237 


0345 




2 


870404 


0462 


0521 


0579 


C696 


0755 


0313 


0872 


C930 




3 


0989 


1047 


1106 


1164 


1223 


1281 


1339 


1398 


1456 


1515 




4 


1573 


1631 


1690 


1748 


1806 


1865 


1923 


1931 


2040 


2098 




5 


2156 


2215 


2273 


2331 


2389 


2448 


2506 


2564 


2622 


2681 




6 


2739 


2797 


2855 


2913 


2972 


3030 


3083 


3146 


3204 


3262 




7 


3321 


3379 


3437 


3495 


3553 


3611 


3669 


3727 


3785 


3844 




8 


3902 


3960 


4018 


4076 


4134 


4192 


4250 


4308 


4366 


4424 


58 


9 


4482 


4540 


4598 


4656 


4714 


4772 


4830 


4888 


4945 


5003 




750 


5061 


5119 


5177 


5235 


5293 


5351 


5409 


5466 


5524 


5582 






5640 


5698 


5756 


5813 


5871 


5929 


5987 


6045 


6102 


6160 




2 


6218 


6276 


6333 


6391 


6449 


6507 


6564 


6622 


6680 


6737 




3 


6795 


6853 


6910 


6968 


7026 


7083 


7141 


7199 


7256 


7314 




4 


7371 


7429 


7487 


7544 


7602 


7659 


7717 


7774 


7832 


7889 




5 


7947 


8004 


8062 


8119 


8177 


8234 


8292 


8349 


8407 


8464 




6 


8522 


8579 


8637 


8694 


8752 


8809 


8866 


8924 


8981 


9039 




7 


9096 


9153 


9211 


9268 


9325 


9383 


9440 


9497 


9555 


9612 




8 


9669 


9726 


9784 


9841 


9898 


9956 












0013 


0070 


0127 


0185 
0756 




9 


880242 


0299 


0356 


0413 


0471 


0528 


0585 


0642 


0699 




760 


0814 


0871 


0928 


0985 


1042 


1099 


1156 


1213 


1271 


1328 




1 


1385 


1442 


1499 


1556 


1613 


1670 


1727 


1784 


1841 


1898 




2 


1955 


2012 


2069 


2126 


2183 


2240 


2297 


2354 


2411 


2468 


57 


3 


2525 


2581 


2638 


2695 


2752 


2809 


2866 


2923 


2980 


3037 




4 


3093 


3150 


3207 


3264 


3321 


3377 


3434 


3491 


3548 


3605 





Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


59 


5.9 


11.8 


17.7 


23.6 


29.5 


35.4 


41.3 


47.2 


53.1 


58 


5.8 


11.6 


17.4 


23.2 


29.0 


34.8 


40.6 


46.4 


52.2 


57 


5.7 


11.4 


17.1 


22.8 


28.5 


34.2 


39.9 


45.6 


51.3 


56 


5.6 


11.2 


16.8 


22.4 


28.0 


33.6 


39.2 


44.8 


50.4 



LOGARITHMS OF NUMBERS. 



159 



No. 765 L. 883.] 














(No 


. 809 L. 908. 


N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


765 


883661 


3718 


3775 


3832 


3888 


3945 


4002 


4059 


4115 


4172 




6 


4229 


4285 


4342 


4399 


4455 


4512 


4569 


462!? 


4682 


4739 




7 


4795 


4852 


4909 


4965 


5022 


5078 


5135 


5192 


5248 


5305 




8 


5361 


5418 


5474 


5531 


5587 


5644 


5700 


5757 


5813 


5870 




9 


5926 


5983 


6039 


6096 


6152 


6209 


6265 


6321 


6378 


6434 




770 


6491 


6547 


6604 


6660 


6716 


6773 


6829 


6885 


6942 


6998 




1 


7054 


7111 


7167 


7223 


7280 


7336 


7392 


7449 


7505 


7561 




2 


7617 


7674 


7730 


7786 


7842 


7898 


7955 


8011 


8067 


8123 




3 


8179 


8236 


8292 


8348 


8404 


8460 


8516 


8573 


8629 


8685 




4 


8741 


8797 


8353 


8909 


8965 


9021 


9077 


9134 


9190 


9246 




5 


9302 


9358 


9414 


9470 


9526 


9582 


9638 


9694 


9750 


9806 


56 


6 


9862 


9918 


9974 


















0030 


0086 


0141 
0700 


0197 
0756 


0253 


0309 


0365 




7 


890421 


0477 


0533 


0589 


0645 


0812 


0868 


0924 




8 


0980 


1035 


1091 


1147 


1203 


1259 


1314 


1370 


1426 


1482 




9 


1537 


1593 


1649 


1705 


1760 


1816 


1872 


1928 


1983 


2039 




780 


2095 


2150 


2206 


2262 


2317 


2373 


2429 


2484 


2540 


2595 




1 


2651 


2707 


2762 


2818 


2873 


2929 


2985 


3040 


3096 


3151 




2 


3207 


3262 


3318 


3373 


3429 


3484 


3540 


3595 


3651 


3706 




3 


3762 


3317 


3873 


3928 


3984 


4039 


4094 


4150 


4205 


4261 




4 


4316 


4371 


4427 


4482 


4538 


4593 


4648 


4704 


4759 


4814 




5 


4870 


4925 


4930 


5036 


5091 


5146 


5201 


5257 


5312 


5367 




6 


5423 


5478 


5533 


5588 


5644 


5699 


5754 


5809 


5864 


5920 




7 


5975 


6030 


6085 


6140 


6195 


6251 


6306 


6361 


6416 


6471 




8 


6526 


6581 


6636 


6692 


6747 


6802 


6857 


6912 


6967 


7022 




9 


7077 


7132 


7187 


7242 


7297 


7352 


7407 


7462 


7517 


7572 


55 


790 


7627 


7682 


7737 


7792 


7847 


7902 


7957 


8012 


8067 


8122 


1 


8176 


8231 


8286 


8341 


8396 


8451 


8506 


8561 


8615 


8670 




2 


8725 


8780 


8835 


8890 


8944 


8999 


9054 


9109 


9164 


9218 




3 


9273 


9328 


9383 


9437 


9492 


9547 


9602 


9656 


9711 


9766 




4 


9821 


9875 


9930 


9985 
















0039 
0586 


0094 
0640 


0149 
0695 


0203 
0749 


0258 
0804 


0312 
0859 




5 


900367 


0422 


0476 


0531 




6 


0913 


0968 


1022 


1077 


1131 


1186 


1240 


1295 


1349 


1404 




7 


1458 


1513 


1567 


1622 


1676 


1731 


1785 


1840 


1894 


1948 




8 


2003 


2057 


2112 


2166 


2221 


2275 


2329 


2384 


2438 


2492 




9 


2547 


2601 


2655 


2710 


2764 


2818 


2873 


2927 


2981 


3036 




800 


3090 


3144 


3199 


3253 


3307 


3361 


3416 


3470 


3524 


3578 




1 


3633 


36S7 


3741 


3795 


3849 


3904 


3958 


4012 


4066 


4120 




2 


4174 


4229 


4283 


4337 


4391 


4445 


4499 


4553 


4607 


4661 




3 


4716 


4770 


4824 


4878 


4932 


4986 


5040 


5094 


5148 


5202 




4 


5256 


5310 


5364 


5418 


5472 


5526 


5580 


5634 


5688 


5742 


54 


5 


5796 


5850 


5904 


5958 


6012 


6066 


6119 


6173 


6227 


6281 




6 


6335 


6389 


6443 


6497 


6551 


6604 


6658 


6712 


6766 


6820 




7 


6874 


6927 


6981 


7035 


7089 


7143 


7196 


7250 


7304 


7358 




8 


7411 


7465 


7519 


7573 


7626 


7680 


7734 


7787 


7841 


7895 




9 


7949 


8002 


8056 


8110 


8163 


8217 


8270 


8324 


8378 


8431 





Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


57 


5.7 


11.4 


17.1 


22.8 


28.5 


34.2 


39.9 


45.6 


51.3 


56 


5.6 


11.2 


16.8 


22.4 


28.0 


33.6 


39.2 


44.8 


50.4 


55 


5.5 


11.0 


16.5 


22.0 


27.5 


33.0 


38.5 


44.0 


49.5 


54 


5.4 


10.8 


16.2 


21.6 


27.0 


32.4 


37.8 


43.2 


48.6 



160 



LOGARITHMS OF NUMBERS. 



No. 810 L. 908.) 



[No. 854 L. 931 



N. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


810 

1 
2 


908485 
9021 
9556 


8539 
9074 
9610 


8592 
9128 
9663 


8646 
9181 
9716 


8699 
9235 
9770 


8753 
9289 
9823 


8807 
9342 
9877 


8860 
9396 
9930 


8914 
9449 
9984 


8967 
9503 




0037 
0571 
1104 
1637 
2169 
2700 
3231 
3761 

4290 
4819 
5347 
5875 
6401 
6927 
7453 
7978 
8502 
9026 

9549 




8 
9 

620 
1 

2 
3 
4 
5 
6 
7 
8 
9 

830 
1 


910091 
0624 
1158 
1690 
2222 
2753 
3284 

3814 
4343 
4872 
5400 
5927 
6454 
6980 
7506 
8030 
8555 

9078 
9601 


0144 
0678 
1211 
1743 
2275 
2806 
3337 

3867 
4396 
4925 
5453 
5980 
6507 
7033 
7558 
8083 
8607 

9130 
9653 


0197 
0731 
1264 
1797 
2328 
2859 
3390 

3920 
4449 
4977 
5505 
6033 
6559 
7085 
7611 
8135 
8659 

9183 
9706 


0251 
0784 
1317 
1850 
2381 
2913 
3443 

3973 
4502 
5030 
5558 
6085 
6612 
7138 
7663 
8188 
8712 

9235 
9758 


0304 
0838 
1371 
1903 
2435 
2966 
3496 

4026 
4555 
5083 
5611 
6138 
6664 
7190 
7716 
8240 
8764 

9287 
9810 


0358 
0891 
1424 
1956 
2488 
3019 
3549 

4079 
4608 
5136 
5664 
6191 
6717 
7243 
7768 
8293 
8816 

9340 
9862 


0411 
0944 
1477 
2009 
2541 
3072 
3602 

4132 
4660 
5189 
5716 
6243 
6770 
7295 
7820 
8345 
8869 

9392 
9914 


0464 
0998 
1530 
2063 
2594 
3125 
3655 

4184 
4713 
5241 
5769 
6296 
6822 
7348 
7873 
8397 
8921 

9444 
9967 


0518 
1051 
1584 
2116 
2647 
3178 
3708 

4237 
4766 
5294 
5822 
6349 
6875 
7400 
7925 
8450 
8973 

9496 


53 




0019 
0541 
1062 
1582 
2102 
2622 
3140 
3658 
4176 

4693 
5209 
5725 
6240 
6754 
7268 
7781 
8293 
8805 
9317 

9827 


0071 
0593 
1114 
1634 
2154 
2674 
3192 
3710 
4228 

4744 
5261 
5776 
6291 
6805 
7319 
7832 
8345 
8857 
9368 

9879 

0389 
0898 
1407 
1915 




2 
3 

4 
5 
6 
7 
8 
9 

840 
1 

2 
3 
4 
5 
6 
7 
8 
9 

850 

1 


920123 
0645 
1166 
1686 
2206 
2725 
3244 
3762 

4279 
4796 
5312 
5828 
6342 
6857 
7370 
7883 
8396 
8908 

9419 
9930 


0176 
0697 
1218 
1738 
2258 
2777 
3296 
3814 

4331 
4848 
5364 
5879 
6394 
6908 
7422 
7935 
8447 
8959 

9470 
9981 


0228 
0749 
1270 
1790 
2310 
2829 
3348 
3865 

4383 
4899 
5415 
5931 
6445 
6959 
7473 
7986 
8498 
9010 

9521 


0280 
0801 
1322 
1842 
2362 
2881 
3399 
3917 

4434 
4951 
5467 
5982 
6497 
7011 
7524 
8037 
8549 
9061 

9572 


0332 
0853 
1374 
1894 
2414 
2933 
3451 
3969 

4486 
5003 
5518 
6034 
6548 
7062 
7576 
8088 
8601 
9112 

9623 


0384 
0906 
1426 
1946 
2466 
2985 
3503 
4021 

4538 
5054 
5570 
6085 
6600 
7114 
7627 
8140 
8652 
9163 

9674 


0436 
0958 
1478 
1998 
2518 
3037 
3555 
4072 

4589 
5106 
5621 
6137 
6651 
7165 
7678 
8191 
8703 
9215 

9725 


0489 
1010 
1530 
2050 
2570 
3089 
3607 
4124 

4641 
5157 
5673 
6188 
6702 
7216 
7730 
8242 
8754 
9266 

9776 


52 
51 


0032 
0542 
1051 
1560 


0083 
0592 
1102 
1610 


0134 
0643 
1153 
1661 


0185 
0694 
1204 
1712 


0236 
0745 
1254 
1763 


0287 
0796 
1305 
1814 


0338 
0847 
1356 
1865 


2 
3 

4 


930440 
0949 
1458 


0491 
1000 
1509 





Proportional Parts. 



Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


53 
52 
51 
50 


5.3 
5.2 
5.1 
5.0 


10.6 
10.4 
10.2 
10.0 


15.9 
15.6 
15.3 
15.0 


21.2 
20.8 
20.4 
20.0 


26.5 
26.0 
25.5 
25.0 


31.8 
31.2 
30.6 
30.0 


37.1 
36.4 
35.7 
35.0 


42.4 
41.6 
40.8 
40.0 


47.7 
A6.Q 
45.9 
45.0 



LOGARITHMS OF NUMBERS. 



161 



No. 855 L. 931.1 



[No. 899 L. 954, 



N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


853 


931966 


2017 


2068 


2118 


2169 


2220 


2271 


2322 


2372 


2423 




6 


2474 


2524 


2575 


2626 


2677 


2727 


2778 


2829 


2879 


2930 




7 


2981 


3031 


3082 


3133 


3183 


3234 


3285 


3335 


3386 


3437 




8 


3487 


3538 


3589 


3639 


3690 


3740 


3791 


3841 


3892 


3943 




9 


3993 


4044 


4094 


4145 


4195 


4246 


4296 


4347 


4397 


4448 




860 


4498 


4549 


4599 


4650 


4700 


4751 


4801 


4852 


4902 


4953 




1 


5003 


5054 


5104 


5154 


5205 


5255 


5306 


5356 


5406 


5457 




2 


5507 


5558 


560S 


5658 


5709 


5759 


5809 


5860 


5910 


5960 




3 


6011 


6061 


61il 


6162 


6212 


6262 


6313 


6363 


6413 


6463 




4 


6514 


6564 


6614 


6665 


6715 


6765 


6815 


6865 


6916 


6966 




5 


7016 


7066 


7116 


7167 


7217 


7267 


7317 


7367 


7418 


7468 




6 


7518 


7568 


7618 


7668 


7718 


7769 


7819 


7869 


7919 


7969 




7 


8019 


8069 


8119 


8169 


8219 


8269 


8320 


8370 


8420 


8470 


50 


8 


8520 


8570 


8620 


8670 


8720 


8770 


8820 


8870 


8920 


8970 




9 


9020 


9070 


9120 


9170 


9220 


9270 


9320 


9369 


9419 


9469 




870 


9519 


9569 


9619 


9669 


9719 


9769 


9819 


9869 


9918 


9968 




1 


940018 


0068 


0118 


0168 


0218 


0267 


0317 


0367 


0417 


0467 




2 


0516 


0566 


0616 


0666 


0716 


0765 


0815 


0865 


0915 


0964 




3 


1014 


1064 


1114 


1163 


1213 


1263 


1313 


1362 


1412 


1462 




4 


1511 


1561 


1611 


1660 


1710 


1760 


1809 


1859 


1909 


1958 




5 


2003 


2058 


2107 


2157 


2207 


2256 


2306 


2355 


2405 


2455 




6 


2504 


2554 


2603 


2653 


2702 


2752 


2801 


2851 


2901 


2950 




7 


3000 


3049 


3099 


3148 


3198 


3247 


3297 


3346 


3396 


3445 




8 


3495 


3544 


3593 


3643 


3692 


3742 


3791 


3841 


3890 


3939 




9 


3989 


4038 


4088 


4137 


4186 


4236 


4285 


4335 


4384 


4433 




880 


4483 


4532 


4581 


4631 


4680 


4729 


4779 


4828 


4877 


4927 




1 


4976 


5025 


5074 


5124 


5173 


5222 


5272 


5321 


5370 


5419 




2 


5469 


5518 


5567 


5616 


5665 


5715 


5764 


5813 


5862 


5912 




3 


5961 


6010 


6059 


6108 


6157 


6207 


6256 


6305 


6354 


6403 




4 


6452 


6501 


6551 


6600 


6649 


6698 


6747 


6796 


6845 


6894 




5 


6943 


6992 


7041 


7090 


7139 


7189 


7238 


7287 


7336 


7385 




6 


7434 


7483 


7532 


7581 


7630 


7679 


7728 


7777 


7826 


7875 


4Q 


7 


7924 


7973 


8022 


8070 


8119 


8168 


8217 


8266 


8315 


8364 




8 


8413 


8462 


8511 


8560 


8608 


8657 


8706 


8755 


8804 


8853 




9 


8902 


8951 


8999 


9048 


9097 


9146 


9195 


9244 


9292 


9341 




890 


9390 


9439 


9488 


9536 


9585 


9634 


9683 


9731 


9780 


9829 




1 


9878 


9926 


9975 




















0024 
0511 


0073 
0560 


0121 
0608 


0170 
0657 


0219 
0706 


0267 
0754 


0316 
0303 




2 


950365 


0414 


0462 




3 


0851 


0900 


0949 


0997 


1046 


1095 


1143 


1192 


1240 


1289 




4 


1338 


1386 


1435 


1483 


1532 


1580 


1629 


1677 


1726 


1775 




5 


1823 


1872 


1920 


1969 


2017 


2066 


2114 


2163 


2211 


2260 




6 


2308 


2356 


2405 


2453 


2502 


2550 


2599 


2647 


2696 


2744 




7 


2792 


2341 


2889 


2933 


2986 


3034 


3083 


3131 


3180 


3228 




8 


3276 


3325 


3373 


3421 


3470 


3518 


3566 


3615 


3663 


3711 




9 


3760 


3808 


3856 


3905 


3953 


4001 


4049 


4098 


4146 


4194 





Proportional- Parts. 



8 



9 



5.1 
5.0 
4.9 
48 



10.2 
lO.O 
9.8 
9.6 



15.3 
15.0 
14.7 
14.4 



20.4 
20.0 
19.6 
19.2 



25.5 
25.0 
24.5 
24.0 



30.6 
30.0 
29.4 
28.8 



35.7 
35.0 
34.3 
33.6 



40.8 
40.0 
39.2 
38.4 



45.9 
45.0 
44.1 
43.2 



162 



LOGARITHMS OF NUMBERS. 



No. 900 L. 954.1 



[No. 944 L. 975. 



N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diflf. 


900 
1 

2 
3 

4 
5 
6 
7 
8 
9 

910 

1 
2 


954243 
4725 
5207 
5633 
6163 
6649 
7128 
7607 
8086 
8564 

9041 
9518 
9995 


4291 
4773 
5255 
5736 
6216 
6697 
7176 
7655 
8134 
8612 

9089 
9566 


4339 

4821 
5303 
5784 
6265 
6745 
7224 
7703 
8181 
8659 

9137 
9614 


4387 
4869 
5351 
5832 
6313 
6793 
7272 
7751 
8229 
8707 

9185 
9661 


4435 
4918 
5399 
5880 
6361 
6840 
7320 
7799 
8277 
8755 

9232 
9709 


4484 
4966 
5447 
5928 
6409 
6888 
7368 
7847 
8325 
8803 

9280 
9757 


4532 
5014 
5495 
5976 
6457 
6936 
7416 
7894 
8373 
8850 

9328 
9804 


4580 
5062 
5543 
6024 
6505 
6934 
7464 
7942 
842 1 
8898 

9375 
9852 


4628 
5110 
5592 
6072 
6553 
7032 
7512 
7990 
8468 
8946 

9423 
9900 


4677 
5158 
5640 
6120 
6601 
7080 
7559 
8038 
8516 
8994 

9471 
9947 


48 


0042 
0518 
0994 
1469 
1943 
2417 
2890 
3363 

3835 
4307 
4778 
5249 
5719 
6189 
6658 
7127 
7595 
8062 

8530 
8996 
9463 
9928 


0090 
0566 
1041 
1516 
1990 
2464 
2937 
3410 

3882 
4354 
4825 
5296 
5766 
6236 
6705 
7173 
7642 
8109 

8576 
9043 
9509 
9975 


0138 
0613 
1039 
1563 
2038 
2511 
2985 
3457 

3929 
4401 
4872 
5343 
5813 
6283 
6752 
7220 
7688 
8156 

8623 
9090 
9556 


0185 
0661 
1136 
1611 
2035 
2559 
3032 
3504 

3977 

4448 
4919 
5390 
5860 
6329 
6799 
7267 
7735 
8203 

8670 
9136 
9602 


0233 
0709 
1184 
1658 
2132 
2606 
3079 
3552 

4024 
4495 
4966 
5437 
5907 
6376 
6345 
7314 
7782 
8249 

8716 
9183 
9649 


0280 
0756 
1231 
1706 
2180 
2653 
3126 
3599 

4071 
4542 
5013 
5484 
5954 
6423 
6892 
7361 
7829 
8296 

8763 
9229 
9695 


0328 
0804 
1279 
1753 
2227 
2701 
3174 
3646 

4118 
4590 
5061 
5531 
6001 
6470 
6939 
7408 
7875 
8343 

8810 
9276 
9742 


0376 
0851 
1326 
1801 
2275 
2748 
3221 
3693 

4165 
4637 
5108 
5578 
6048 
6517 
6986 
7454 
7922 
8390 

8856 
9323 
9789 


0423 
0899 
1374 
1848 
2322 
2795 
3268 
3741 

4212 
4684 
5155 
5625 
6095 
6564 
7033 
7501 
7969 
8436 

8903 
9369 
9835 




3 

4 

5 

^ 

8 
9 

920 
1 
2 

3 
4 
5 
6 
7 
8 
9 

930 

1 

2 
3 


960471 
0946 
1421 
1895 
2369 
2843 
3316 

3788 
4260 
4731 
5202 
5672 
6142 
6611 
7080 
7548 
8016 

8483 
8950 
9416 
9882 


47 


0021 
0486 
0951 
1415 
1879 
2342 
2804 

3266 
3728 
4189 
4650 
5110 


0068 
0533 
0997 
1461 
1925 
2388 
2851 

3313 
3774 
4235 
4696 
5156 


0114 
0579 
1044 
1508 
1971 
2434 
2897 

3359 
3820 
4281 
4742 
5202 


0161 
0626 
1090 
1554 
2018 
2481 
2943 

3405 
3866 
4327 
4788 
5248 


0207 
0672 
1137 
1601 
2064 
2527 
2989 

3451 
3913 
4374 
4834 
5294 


0254 
0719 
1183 
1647 
2110 
2573 
3035 

3497 
3959 
4420 
4880 
5340 


0300 
0765 
1229 
1693 
2157 
2619 
3082 

3543 
4005 
4466 
4926 
5386 




4 

5 
6 
7 
8 
9 

940 

1 

2 
3 
4 


970347 
0812 
1276 
1740 
2203 
2666 

3128 
3590 
4051 
4512 
4972 


0393 
0858 
1322 
1786 
2249 
2712 

3174 
3636 
4097 
4558 
5018 


0440 
0904 
1369 
1832 
2295 
2758 

3220 
3682 
4143 
4604 
5064 


46 









Proportional Parts. 








Diff. 


1 


2 


3 


4 


5 


6 


7 


8 


9 i 


47 
46 


4.7 
4.6 


9.4 
9.2 


14.1 
13.8 


18.8 
18.4 


23.5 
23.0 


28.2 
27.6 


32.9 
32.2 


37.6 
36.8 


42.3 
41.4 























LOGARITHMS OF NUMBERS. 



163 



No. 945 L. 975.] 



[No. 989 L. 995. 



N. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


945 


975432 


5478 


5524 


5570 


5616 


5662 


5707 


5753 


5799 


5845 




6 


5891 


5937 


5983 


6029 


6075 


6121 


6167 


6212 


6258 


6304 




7 


6350 


6396 


6442 


6488 


6533 


6579 


6625 


6671 


6717 


6763 




8 


6808 


6854 


6900 


6946 


6992 


7037 


7083 


7129 


7175 


7220 




9 


7266 


7312 


7358 


7403 


7449 


7495 


7541 


7586 


7632 


7678 




950 


7724 


7769 


7815 


7861 


7906 


7952 


7998 


8043 


8089 


8135 




1 


8181 


8226 


8272 


8317 


8363 


8409 


8454 


8500 


8546 


8591 




2 


8637 


8633 


8728 


8774 


8819 


8865 


8911 


8956 


9002 


9047 




3 


9093 


913S 


9184 


9230 


9275 


9321 


9366 


9412 


9457 


9503 




4 


9548 


9594 


9639 


9685 


9730 


9776 


9821 


9867 


9912 


9958 




5 


980003 


0049 


0094 


0140 


0185 


0231 


0276 


0322 


0367 


0412 




6 


0458 


0503 


0549 


0594 


0640 


06851 0730 


0776 


0821 


0867 




7 


0912 


0957 


1003 


1048 


1093 


1139 


1184 


1229 


1275 


1320 




8 


1366 


1411 


1456 


1501 


1547 


1592 


1637 


1683 


1728 


1773 




9 


1819 


1864 


1909 


1954 


2000 


2045 


2090 


2135 


2181 


2226 




960 


2271 


2316 


2362 


2407 


2452 


2497 


2543 


2588 


2633 


2678 




1 


2723 


2769 


2814 


2859 


2904 


2949 


2994 


3040 


3085 


3130 




2 


3175 


3220 


3265 


3310 


3356 


3401 


3446 


3491 


3536 


3581 




3 


3626 


3671 


3716 


3762 


3807 


3852 


3897 


3942 


3987 


4032 




4 


4077 


4122 


4167 


4212 


4257 


4302 


4347 


4392 


4437 


4482 




5 


4527 


4372 


4617 


4662 


4707 


4752 


4797 


4842 


4887 


4932 


45 


6 


4977 


5022 


5067 


5112 


5157 


5202 


5247 


5292 


5337 


5382 




7 


5426 


5471 


5516 


5561 


5606 


5651 


5696 


5741 


5786 


5830 




8 


5875 


5920 


5965 


6010 


6055 


6100 


6144 


6189 


6234 


6279 




9 


6324 


6369 


6413 


6458 


6503 


6548 


6593 


6637 


6682 


6727 




970 


6772 


6817 


6861 


6906 


6951 


6996 


7040 


7085 


7130 


7175 




1 


7219 


7264 


7309 


7353 


7398 


7443 


7488 


7532 


7577 


7622 




2 


7666 


7711 


7756 


7800 


7845 


7890 


7934 


7979 


8024 


8068 




3 


8113 


8157 


8202 


8247 


8291 


8336 


8381 


8425 


8470 


8514 




4 


8559 


8604 


8648 


8693 


8737 


8782 


8826 


8871 


8916 


8960 


■" 


5 


9005 


9049 


9094 


9138 


9183 


9227 


9272 


9316 


9361 


9405 




6 


9450 


9494 


9339 


9583 


9628 


9672 


9717 


9761 


9806 


9850 




7 


9895 


9939 


9983 






















0028 


0072 


0117 


0161 


0206 


0250 


0294 














8 


990339 


0383 


0428 


0472 


0516 


0561 


0605 


0650 


0694 


0738 




9 


0783 


0327 


0871 


0916 


0960 


1004 


1049 


1093 


1137 


1182 




980 


1226 


1270 


1315 


1359 


1403 


1448 


1492 


1536 


1580 


1625 




1 


1669 


1713 


1758 


1802 


1846 


1890 


1935 


1979 


2023 


2067 




2 


2111 


2156 


2200 


2244 


2288 


2333 


2377 


2421 


2465 


2509 




3 


2554 


2593 


2642 


2686 


2730 


2774 


2819 


2863 


2907 


2951 




4 


2995 


3039 


3033 


3127 


3172 


3216 


3260 


3304 


3348 


3392 




5 


3436 


3430 


3524 


3568 


3613 


3657 


3701 


3745 


3789 


3833 




6 


3877 


3921 


3965 


4009 


4053 


4097 


4141 


4185 


4229 


4273 




7 


4317 


4361 4405 


4449 4493 


4537 


4581 


4625 


4669 


4713 


44 


8 


4757 


4801 4845 


4889 4933 


4977 


5021 


5065 51GG 


5152 




9 1 


5196 


5240 5284 5328| 5372| 


5416 


5460 


5504 5547 


5591 













Proportional Parts. 








Difif. 


1 


2 


3 


4 


5 


6 


7 


8 


9 


46 
45 
44 
43 


4.6 
4.5 

4.4 
4.3 


9.2 
9.0 

8.8 
8.6 


13.8 
13.5 
13.2 
12.9 


18.4 
18.0 
17.6 
17.2 


23.0 
22.5 
22.0 
21.5 


27.6 
27.0 
26.4 
25.8 


32.2 
31.5 
30.8 
30.1 


36.8 
36.0 
35.2 
34.4 


41.4 
40.5 
39.6 
38.7 



164 



HYPERBOLIC LOGARITHMS. 



No. 990 L. 995.1 














[No 


.999 L. 999. 


N. 





1 


3 


3 


4 


5 


6 


7 


8 


9 


Diff. 


990 


995635 


5679 


5723 


5767 


5811 


5854 


5898 


5942 


5986 


6030 






6074 


6117 


6161 


6205 


6249 


6293 


6337 


6380 


6424 


6468 


44 




6512 


6555 


6599 


6643 


6687 


6731 


6774 


6818 


6862 


6906 






6949 


6993 


7037 


7080 


7124 


7168 


7212 


7255 


7299 


7343 






7386 


7430 


7474 


7517 


7561 


7605 


7648 


7692 


7736 


7779 






7823 


7867 


7910 


7954 


7998 


8041 


8085 


8129 


8172 


8216 






8259 


8303 


8347 


8390 


8434 


8477 


8521 


8564 


8608 


8652 






8695 


8739 


8782 


8826 


8869 


8913 


8956 


9000 


9043 


9087 






9131 


9174 


9218 


9261 


9305 


9348 


9392 


9435 


9479 


9522 






9565 


9609 


9652 


9696 


9739 


9783 


9826 


9870 


9913 


9957 


43 



HYPERBOLIC LOGARITH3IS. 



No. Log. No. 



.0099 

.0198 

.0296 

.0392 

.0488 

.0583 

.0677 

.0770 

.0862 

.0953 

.1044 

.1133 

.1222 

.1310 

.1398 

.1484 

.1570 

J655 

.1740 

.1823 

.1906 

.1988 

.2070 

.2151 

.2231 

.2311 

.2390 

.2469 

.2546 

.2624 

.2700 

.2776 

.2852 

.2927 

.3001 

.3075 

.3148 

.3221 

.3293 

.3365 

.3436 

.3507 

.3577 

.3646 



1.45 

1.46 

1.47 

1.48 

1.49 

1.50 

1.51 

1.52 

1.53 

1.54 

1.55 

1.56 

1.57 

1.58 

1.59 

1.60 

1.61 

1.62 

1.63 

1.64 

1.65 

1.66 

1.67 

1.68 

1.69 

1.70 

1.71 

1.72 

1.73 

1.74 

1.75 

1.76 

1.77 

1.78 

1.79 

1.80 

1.81 

1.82 

1.83 

1.84 

1.85 

1.86 

1.87 

1.88 



Log. 



.3716 

.3784 

.3853 

.3920 

.3988 

.4055 

.4121 

.4187 

.4253 

.4318 

.4383 

.4447 

.4511 

.4574 

.4637 

.4700 

.4762 

.4824 

.4886 

.4947 

.5008 

.5068 

.5128 

.5188 

.5247 

.5306 

.5365 

.5423 

.5481 

.5539 

.5596 

.5653 

.5710 

.5766 

.5822 

.5878 

.5933 

.5988 

.6043 

.6098 

.6152 

.6206 

.6259 

.6313 



No. 



Log. 



1.89 

1.90 

1.91 

1.92 

1.93 

1.94 

1.95 

1.96 

1.97 

1.98 

1.99 

2.00 

2.01 

2.02 

2.03 

2.04 

2.05 

2.06 

2.07 

2.08 

2.09 

2.10 

2.11 

2.12 

2.13 

2.14 

2.15 

2.16 

2.17 

2.18 

2.19 

2.20 

2.21 

2.22 

2.23 

2.24 

2.25 

2.26 

2.27 

2.28 

2.29 

2.30 

2.31 

2.32 



.6366 

.6419 

.6471 

.6523 

.6575 

.6627 

.6678 

.6729 

.6780 

.6831 

.6881 

.6931 

.6981 

.7031 

.7080 

.7129 

.7178 

.7227 

.7275 

.7324 

.7372 

.7419 

.7467 

.7514 

.7561 

.7608 

.7655 

.7701 

.7747 

.7793 

.7839 

.7885 

.7930 

.7975 

.8020 

.8065 

.8109 

.8154 

.8198 

.8242 

.8286 

.8329 

.8372 

.8416 



No. 



2.33 

2.34 

2.35 

2.36 

2.37 

2.38 

2.39 

2.40 

2.41 

2.42 

2.43 

2.44 

2.45 

2.46 

2.47 

2.48 

2.49 

2.50 

2.51 

2.52 

2.53 

2.54 

2.55 

2.56 

2.57 

2.58 

2.59 

2.60 

2.61 

2.62 

2.63 

2.64 

2.65 

2.66 

2.67 

2.68 

2.69 

2.70 

2.71 

2.72 

2.73 

2.74 

2.75 

2.76 



Log. 



.8458 
.8502 
.8544 
.8587 
.8629 
.8671 
.8713 
.8755 
.8796 
.8838 
.8879 
.8920 
.8961 
.9002 
.9042 
.9083 
.9123 
.9163 
.9203 
.9243 
.9282 
.9322 
.9361 
.9400 
.9439 
.9478 
.9517 
.9555 
.9594 
.9632 
.9670 
.9708 
.9746 
.9783 
.9821 
.9858 
.9895 
.9933 
.9969 
1 .0006 
1 .0043 
1 .0080 
1.0116 
1.0152 



No. 



2.77 
2.78 
2.79 
2.80 
2.81 
2.82 
2.83 
2.84 
2.85 
2.86 
2.87 
2.88 
2.89 
2.90 
2.91 
2.92 
2.93 
2.94 
2.95 
2.96 
2.97 
2.98 
2.99 
3.00 
3.01 
3.02 
3.03 
3.04 
3.05 
3.06 
3.07 
3.08 
3.09 
3.10 



Log. 



11 

12 

13 

14 

15 

16 

17 

3.18 

3.19 

3.20 



1.0188 
1 .0225 
1 .0260 
1 .0296 
1 .0332 
1.0367 
1 .0403 
1.0438 
1.0473 
1.0508 
1.0543 
1.0578 
1.0613 
1 .0647 
1 .0682 
1.0716 
1.0750 
1.0784 
1.0818 
1 .0852 
1 .0886 
1.0919 
1.0953 
1 .0986 
1.1019 
1.1056 
1.1081 
1.1113 
1.1154 
1.1187 
1.1219 
1.1246 
1.1284 
1.1312 
1.1349 
1.1378 
1.1410 
1.1442 
1.1474 
1.1506 
1.1537 
1.1569 
1.1600 
1.1632 



HYPERBOLIC LOGARITHMS. 



165 



No. 


Log. 


No. 


Log. 


No. 


Log. 


No. 


Log. 


No. 


Log. 


3.21 


1.1663 


3.87 


1.3533 


4.53 


1.5107 


5.19 


1 .6467 


5.85 


1.7664 


3.22 


1.1694 


3.88 


1.3558 


4.54 


1.5129 


5.20 


1 .6487 


5.86 


1.7681 


3.23 


1.1725 


3.89 


1.3584 


4.55 


1.5151 


5.21 


1.6506 


5.87 


1 .7699 


3.24 


1.1756 


3.90 


1.3610 


4.56 


1.5173 


5.22 


1.6525 


5.88 


1.7716 


3.25 


1.1787 


3.91 


1.3635 


4.57 


1.5195 


5.23 


1.6544 


5.89 


1.7733 


3.26 


1.1817 


3.92 


1.3661 


4.58 


1.5217 


5.24 


1.6563 


5.90 


1.7750 


3.27 


1.1848 


3.93 


1 .3686 


4.59 


1.5239 


5.25 


1.6582 


5.91 


1.7766 


3.28 


1.1878 


3.94 


1.3712 


4.60 


1.5261 


5.26 


1.6601 


5.92 


1.7783 


3.29 


1.1909 


3.95 


1.3737 


4.61 


1.5282 


5.27 


1 .6620 


5.93 


1.7800 


3.30 


1.1939 


3.96 


1.3762 


4.62 


1.5304 


5.28 


1 .6639 


5.94 


1.7817 


3.31 


1.1969 


3.97 


1.3788 


4.63 


1.5326 


5.29 


1 .6658 


5.95 


1.7834 


3.32 


1.1999 


3.98 


1.3813 


4.64 


1.5347 


5.30 


1.6677 


5.96 


1.7851 


3.33 


1 .2030 


3.99 


1.3838 


4.65 


1.5369 


5.31 


1 .6696 


5.97 


1.7867 


3.34 


1 .2060 


4.00 


1.3863 


4.66 


1.5390 


5.32 


1.6715 


5.98 


1.7884 


3.35 


1.2090 


4.01 


1.3838 


4.67 


1.5412 


5.33 


1.6734 


5.99 


1.7901 


3.36 


1.2119 


4.02 


1.3913 


4.68 


1.5433 


5.34 


1.6752 


6.00 


1.7918 


3.37 


1.2149 


4.03 


1.3933 


4.69 


1.5454 


5.35 


1.6771 


6.01 


1.7934 


3.38 


1.2179 


4.04 


1.3962 


4.70 


1.5476 


5.36 


1.6790 


6.02 


1.7951 


3.39 


1 .2208 


4.05 


1.3987 


4.71 


1.5497 


5.37 


1 .6808 


6.03 


1.7967 


3.40 


1.2238 


4.06 


1.4012 


4.72 


1.5518 


5.38 


1.6827 


6.04 


1.7984 


3.41 


1.2267 


4.07 


1.4036 


4.73 


1.5539 


5.39 


1 .6845 


6.05 


1.8001 


3.42 


1 .2296 


4.08 


1.4061 


4.74 


1.5560 


5.40 


1 .6864 


6 06 


1.8017 


3.43 


1.2326 


4.09 


1.4085 


4.75 


1.5581 


5.41 


1 .6882 


6.07 


1 .8034 


3.44 


1.2355 


4.10 


1.4110 


4.76 


1.5602 


5.42 


1.6901 


6.08 


1.8050 


3.45 


1 .2384 


4.11 


1.4134 


4.77 


1.5623 


5.43 


1.6919 


6.09 


1 .8066 


3.46 


1.2413 


4.12 


1.4159 


4.78 


1.5644 


5.44 


1 .6938 


6.10 


1 .8083 


3.47 


1 .2442 


4.13 


1.4183 


4.79 


1.5665 


5.45 


1 .6956 


6.11 


1 .8099 


3.48 


1.2470 


4.14 


1 .4207 


4.80 


1.5686 


5.46 


1 .6974 


6.12 


1.8116 


3.49 


1 .2499 


4.15 


1 .423 1 


4.81 


1.5707 


5.47 


1 .6993 


6.13 


1.8132 


3.50 


1.2528 


4.16 


1.4255 


4.82 


1.5728 


5.48 


1.7011 


6.14 


1.8148 


3.51 


1.2556 


4.17 


1.4279 


4.83 


1.5748 


5.49 


1.7029 


6.15 


1.8165 


3.52 


1.2585 


4.18 


1.4303 


4.84 


1.5769 


5.50 


1.7047 


6.16 


1.8181 


3.53 


1.2613 


4.19 


1.4327 


4.85 


1.5790 


5.51 


1.7066 


6.17 


1.8197 


3.54 


1.2641 


4.20 


1.4351 


4.86 


1.5810 


5.52 


1.7084 


6.18 


1.8213 


3.55 


1 .2669 


4.21 


1.4375 


4.87 


1.5831 


5.53 


1.7102 


6.19 


1 .8229 


3.56 


1 .2698 


4.22 


1.4398 


4.88 


1.5851 


5.54 


1.7120 


6.20 


1.8245 


3.57 


1.2726 


4.23 


1 .4422 


4.89 


1.5872 


5.55 


1.7138 


6.21 


1 .8262 


3.58 


1.2754 


4.24 


1.4446 


4.90 


1.5892 


5.56 


1.7156 


6.22 


1 .8278 


3.59 


1.2782 


4.25 


1.4469 


4.91 


1.5913 


5.57 


1.7174 


6.23 


1 .8294 


3.60 


1 .2809 


4.26 


1 .4493 


4.92 


1.5933 


5.58 


1.7192 


6.24 


1.8310 


3.61 


1.2837 


4.27 


1.4516 


4.93 


1.5953 


5.59 


1.7210 


6.25 


1.8326 


3.62 


1 .2865 


4.28 


1.4540 


4.94 


1.5974 


5.60 


1.7228 


6.26 


1.8342 


3.63 


1 .2892 


4.29 


1.4563 


4.95 


1.5994 


5.61 


1.7246 


6.27 


1.8358 


3.64 


1 .2920 


4.30 


1.4586 


4.96 


1.6014 


5.62 


1.7263 


6.28 


1.8374 


3 65 


1.2947 


4.31 


1 .4609 


4.97 


1 .6034 


5.63 


1.7281 


6.29 


1.8390 


3.66 


1.2975 


4.32 


1.4633 


4.98 


1.6054 


5.64 


1.7299 


6.30 


1.8405 


3.67 


1 .3002 


4.33 


1.4656 


4.99 


1.6074 


5.65 


1.7317 


6.31 


1.8421 


3.68 


1.3029 


4.34 


1 .4679 


5.00 


1 .6094 


5.66 


1.7334 


6.32 


1.8437 


3.69 


1.3056 


4.35 


1 .4702 


5.01 


1.6114 


5.67 


1.7352 


6.33 


1 .8453 


3.70 


1.3083 


4.36 


1 .4725 


5.02 


1.6134 


5.68 


1.7370 


6.34 


1 .8469 


3.71 


1.3110 


4.37 


i.4748 


5.03 


1.6154 


5.69 


1.7387 


6.35 


1 .8485 


3.72 


1.3137 


4.38 


1.4770 


5.04 


1.6174 


5.70 


1.7405 


6.36 


1 .8500 


3.73 


1.3164 


4.39 


1.4793 


5.05 


1.6194 


5.71 


1.7422 


6.37 


1.8516 


3.74 


1.3191 


4.40 


1.4816 


5.06 


1.6214 


5.72 


1.7440 


6.38 


1.8532 


3.75 


1.3218 


4.41 


1.4839 


5.07 


1.6233 


5.73 


1.7457 


6.39 


1.8547 


3.76 


1.3244 


4.42 


1.4861 


5.08 


1.6253 


5.74 


1.7475 


6.40 


1.8563 


3.77 


1.3271 


4.43 


1 .4884 


5.09 


1.6273 


5.75 


1.7492 


6.41 


1.8579 


3.78 


1.3297 


4.44 


1 .4907 


5.10 


1 .6292 


5.76 


1.7509 


6.42 


1 .8594 


3.79 


1.3324 


4.45 


1.4929 


5.11 


1.6312 


5.77 


1.7527 


6.43 


1.8610 


3.80 


1.3350 


4.46 


1.4951 


5.12 


1.6332 


5.78 


1.7544 


6.44 


1 .8625 


3.8^ 


1.3376 


4.47 


1.4974 


5.13 


1.6351 


5.79 


1.7561 


6.45 


1.8641 


3.82 


1.3403 


4.48 


1 .4996 


5.14 


1.6371 


5.80 


1.7579 


6.46 


1 .8656 


3.83 


1.3429 


4.49 


1.5019 


5.15 


1.6390 


5.81 


1.7596 


6.47 


1 .8672 


3.84 


1.3455 


4.50 


1.5041 


5.16 


1 .6409 


5.82 


1.7613 


6.48 


1.8687 


3.85 


1.3481 


4.51 


1.5063 


5.17 


1 .6429 


5.83 


1.7630 


6.49 


1 .8703 


3.86 


1.3507 


4.52 


1.5085 


5.18 


1 .6448 


5.84 


1.7647 


6.50 


1.8718 



166 



HYPERBOLIC LOGARITHMS. 



No. 


Log. 


No. 


Log. 


No. 


Log. 


No. 


Log. 


No 


Log. 


6.51 


1.8733 


7.15 


1.9671 


7.79 


2.0528 


8.66 


2.1587 


9.94 


2.2966 


6.52 


1.8749 


7.16 


1.9685 


7.80 


2.0541 


8.68 


2.1610 


9.96 


2.2986 


6.53 


1 .8764 


7.17 


1 .9699 


7.81 


2.0554 


8.70 


2.1633 


9.98 


2.3006 


6.54 


1.8779 


7.18 


1.9713 


7.82 


2.0567 


8.72 


2 1656 


10.00 


2.3026 


6.55 


1.8795 


7.19 


1.9727 


7.83 


2.0580 


8.74 


2.1679 


10.25 


2.3279 


6.56 


1.8810 


7.20 


1.9741 


7.84 


2.0592 


8.76 


2.1702 


10 50 


2.3513 


6.57 


1.8825 


7.21 


1.9754 


7.85 


2.0605 


8.78 


2.1725 


10.75 


2.3749 


6.58 


1 .8840 


7.22 


1 .9769 


7.86 


2.0618 


8.80 


2.1748 


11.00 


2.3979 


6.59 


1.8856 


7.23 


1.9782 


7.87 


2.0631 


8.82 


2.1770 


11.25 


2.4201 


6.60 


1.8871 


7.24 


1.9796 


7.88 


2.0643 


8.84 


2.1793 


11.50 


2.4430 


6.61 


1 .8886 


7.25 


1.9810 


7.89 


2.0656 


8.86 


2.1815 


11.75 


2.4636 


6.62 


1.8901 


7.26 


1 .9824 


7.90 


2.0669 


8.88 


2.1838 


12.00 


2.4849 


6.63 


1.8916 


7.27 


1 .9838 


7.91 


2.0681 


8.90 


2.1861 


12.25 


2.5052 


6.64 


1 .893 1 


7.28 


1.9851 


7.92 


2.0694 


8.92 


2.1883 


12.50 


2.5262 


6.65 


1 .8946 


7.29 


1 .9865 


7.93 


2.0707 


8.94 


2.1905 


12.75 


2.5455 


6.66 


1 8961 


7.30 


1.9879 


7.94 


2.0719 


8.96 


2.1928 


13.00 


2.5649 


6.67 


1 .8976 


7.31 


1 .9892 


7.95 


2.0732 


8.98 


2.1950 


13.25 


2.5840 


6.68 


1.8991 


7.32 


1 .9906 


7.96 


2.0744 


9.00 


2.1972 


13.50 


2.6027 


6.69 


1 .9006 


7.33 


1 .9920 


7.97 


2.0757 


9.02 


2.1994 


13.75 


2.6211 


6.70 


1.9021 


7.34 


1.9933 


7.93 


2.0769 


9.04 


2.2017 


14.00 


2.6391 


6.71 


1.9036 


7.35 


1.9947 


7.99 


2.0782 


9.06 


2.2039 


14.25 


2.6567 


6.72 


1.9051 


7.36 


1.9961 


8.00 


2.0794 


9.03 


2.2061 


14.50 


2.6740 


6.73 


1 .9066 


7.37 


1.9974 


8.01 


2.0807 


9.10 


2.2083 


14.75 


2.6913 


6.74 


1.9081 


7.38 


1 .9938 


8.02 


2.0819 


9.12 


2.2105 


15.00 


2.7081 


6.75 


1.9095 


7.39 


2.0001 


8.03 


2.0832 


9.14 


2.2127 


15.50 


2.7408 


6.76 


1.9110 


7.40 


2.0015 


8.04 


2.0844 


9.16 


2.2148 


16.00 


2.7726 


6.77 


1.9125 


7.41 


2.0028 


8.05 


2.0857 


9.18 


2.2170 


16.50 


2.8034 


6.78 


1.9140 


7.42 


2.0041 


8.06 


2.0869 


9.20 


2.2192 


17.00 


2.8332 


6.79 


1.9155 


7.43 


2.0055 


8.07 


2.0882 


9.22 


2.2214 


17.50 


2.8621 


6.80 


1.9169 


7.44 


2.0069 


8.08 


2.0894 


9.24 


2.2235 


18.00 


2.8904 


6.81 


1.9184 


7.45 


2.0082 


8.09 


2.0906 


9.26 


2.2257 


18.50 


2.9178 


6.82 


1.9199 


7.46 


2.0096 


8.10 


2.0919 


9.28 


2.2279 


19.00 


2.9444 


6.83 


1.9213 


7.47 


2.0108 


8.11 


2.0931 


9.30 


2.2300 


19.50 


2.9703 


6.84 


1 .9228 


7.48 


2.0122 


8.12 


2.0943 


9.32 


2.2322 


20.00 


2.9957 


6.85 


1.9242 


7.49 


2.0136 


8.13. 


2.0956 


9.34 


2.2343 


21 


3.0445 


6.86 


1.9257 


7.50 


2.0149 


8 14 


2.0963 


9.36 


2.2364 


22 


3.0910 


6.87 


1.9272 


7.51 


2.0162 


8.15 


2.0980 


9.38 


2.2386 


23 


3.1355 


6.88 


1 .9286 


7.52 


2.0176 


8.16 


2.0992 


9.40 


2.2407 


24 


3.1781 


6.89 


1.9301 


7.53 


2.0189 


8.17 


2.1005 


9.42 


2.2428 


25 


3.2189 


6.90 


1.9315 


7.54 


2.0202 


8.18 


2.1017 


9.44 


2.2450 


26 


3.2581 


6.91 


1.9330 


7.55 


2.0215 


8.19 


2.1029 


9.46 


2.2471 


27 


3.2958 


6.92 


1.9344 


7.56 


2.0229 


8.20 


2.1041 


9.48 


2.2492 


28 


3.3322 


6.93 


1.9359 


7.57 


2.0242 


8.22 


2.1066 


9.50 


2.2513 


29 


3.3673 


6.94 


1.9373 


7.58 


2.0255 


8.24 


2.1090 


9.52 


2.2534 


30 


3.4012 


6.95 


1.9387 


7.59 


2.0268 


8.26 


2.1114 


9.54 


2.2555 


31 


3.4340 


6.96 


1.9402 


7.60 


2.0281 


8.28 


2.1138 


9.56 


2.2576 


32 


3.4657 


6.97 


1.9416 


7.61 


2.0295 


8.30 


2.1163 


9.58 


2.2597 


33 


3.4965 


6.98 


1.9430 


7.62 


2.0308 


8.32 


2.1187 


9.60 


2.2618 


34 


3.5263 


6.99 


1.9445 


7.63 


2.0321 


8.34 


2.1211 


9.62 


2.2638 


35 


3.5553 


7.00 


1.9459 


7.64 


2.0334 


8.36 


2.1235 


9.64 


2.2659 


36 


3.5835 


7.C1 


1.9473 


7.65 


2.0347 


8.38 


2.1258 


9.66 


2.2680 


37 


3.6109 


7.02 


1 .9488 


7.66 


2.0360 


8.40 


2.1282 


9.68 


2.2701 


38 


3.6376 


7.03 


1.9502 


7.67 


2.0373 


8.42 


2.1306 


9.70 


2.2721 


39 


3.6636 


7.04 


1.9516 


7.68 


2.0386 


8.44 


2.1330 


9.72 


2.2742 


40 


3.6889 


7.05 


1.9530 


7.69 


2.0399 


8.46 


2.1353 


9.74 


2.2762 


41 


3.7136 


7.06 


1.9544 


7.70 


2.0412 


8.48 


2.1377 


9.76 


2.2783 


42 


3.73/7 


7.07 


1.9559 


7.71 


2.0425 


8.50 


2.1401 


9.78 


2.2803 


43 


3.7612 


7.08 


1.9573 


7.72 


2.0438 


8.52 


2.1424 


9.80 


2.2824 


44 


3.7842 


7.09 


1.9587 


7.73 


2.0451 


8.54 


2.1448 


9.82 


2.2844 


45 


3.8067 


7.10 


1.9601 


7.74 


2.0464 


8.56 


2.1471 


9.84 


2.2865 


46 


3.8286 


7.11 


1.9615 


7.75 


2.0477 


8.58 


2.1494 


9.86 


2.2885 


47 


3.8501 


7.12 


1 .9629 


7.76 


2.0490 


8.60 


2.1518 


9.88 


2.2905 


48 


3.8712 


7.13 


1.9643 


7.77 


2.0503 


8.62 


2.1541 


9.90 


2.2925 


49 


3.8918 


7.14 


1.9657 


7.78 


2.0516 


8.64 


2.1564 


9.92 


2.2946 


50 


3.9120 



LOGARITHMIC TRIGONOMETRICAL FUNCTIONS. 167 



LOGARITHMIC SINES, ETC. 



W) 
P 


Sine. 


Cosec, 


Vers in. 


Tangent 


Cotan. Covers. 


Secant. 


Cosine. 


ft 





In.Neg. 


Infinite. 


In.Neg. 


In.Neg. 


Infinite. 


1 0.00000 


1 0.00000 


10.00000 


90 


1 


8.24186 


11.75814 


6.18271 


8.24192 


11.75808 


9.99235 


10.00007 


9.99993 


89 


2 


8.54282 


11.45718 


6.78474 


8.54308 


11.45692 


9.98457 


10.00026 


9.99974 


88 


3 


8.71880 


11.28120 


7.13687 


8.71940 


1 1 .28060 


9.97665 


10.00060 


9.99940 


87 


4 


8.84358 


11.15642 


7.38667 


8.84464 


11.15536 


9.96860 


10.00106 


9.99894 


86 


5 


8.94030 


11.05970 


7.58039 


8.94195 


11.05805 


9.96040 


10.00166 


9.99834 


85 


6 


9.01923 


10.98077 


7.73863 


9.02162 


10.97838 


9.95205 


10.00239 


9 99761 


84 


7 


9.08589 10.91411 


7.87238 


9.03914 


10.91086 


9.94356 


10.00325 


9.99675 


83 


8 


9.14356 10.85644 


7.98820 


9.14780 


10.85220 


9.93492 


10.00425 


9.99575 


82 


9 


9.19433 


10.80567 


8.09032 


9.19971 


10.80029 


9.92612 


10.00538 


9.99462 


81 


10 


9.23967 


10.76033 


8.18162 


9.24632 


10.75368 


9.91717 


10.00665 


9.99335 


80 


11 


9.28060 


10.71940 


8.26418 


9.28865 


10.71135 


9.90805 


10.00805 


9.99195 


79 


12 


9.31788 


10.68212 


8.33950 


9.32747 


10.67253 


9.89877 


10.00960 


9.99040 


78 


13 


9.35209 


10.64791 


8.40375 


9.36336 


10.63664 


9.88933 


10.01128 


9.98872 


77 


14 


9.38368 


10.61632 


8.47282 


9.39677 


10.60323 


9.87971 


10.01310 


9.98690 


76 


15 


9.41300 


10.58700 


8.53243 


9.42805 


10.57195 


9.86992 


10.01506 


9.98494 


75 


16 


9.44034 


10.55966 


8.58814 


9.45750 


10.54250 


9.85996 


10.01716 


9.98284 


74 


17 


9.46594 


10.53406 


8.64043 


9.48534 


10.51466 


9.84981 


10.01940 


9.98060 


73 


18 


9.48998 


10.51002 


8.68969 


9.51178 


10.48822 


9.83947 


10.02179 


9.97821 


72 


19 


9.51264 


10.48736 


8.73625 


9.53697 


10.46303 


9.82894 


10.02433 


9.97567 


71 


20 


9.53405 


10.46595 


8.78037 


9.56107 


10.43893 


9.81821 


10.02701 


9.97299 


70 


21 


9.55433 


10.44567 


8.82230 


9.58418 


10.41582 


9.80729 


10.02985 


9.97015 


69 


22 


9.57358 


10.42642 


8.86223 


9.60641 


10.39359 


9.79615 


10.03283 


9.96717 


68 


23 


9.59188 


10.40812 


8.90034 


9.62785 


10.37215 


9.78481 


10.03597 


9.96403 


67 


24 


9.60931 


10.39069 


8.93679 


9.64858 


10.35142 


9.77325 


10.03927 


9.96073 


66 


25 


9.62595 


10.37405 


8.97170 


9.66867 


10.33133 


9.76146 


10.04272 


9.95728 


65 


26 


9.64184 


10.35816 


9.00521 


9.68818 


10.31182 


9.74945 


10.04634 


9.95366 


64 


27 


9.65705 


10.34295 


9.03740 


9.70717 


10.29283 


9.73720 


10.05012 


9.94988 


63 


28 


9.67161 


10.32839 


9.06838 


9.72567 


10.27433 


9.72471 


10.05407 


9.94593 


62 


29 


9.68557 


10.31443 


9.09823 


9.74375 


10.25625 


9.71197 


10.05818 


9.94182 


61 


30 


9.69897 


10.30103 


9.12702 


9.76144 


10.23856 


9.69897 


10.06247 


9.93753 


60 


31 


9.71184 


10.28816 


9.15483 


9.77877 


10.22123 


9.68571 


10.06693 


9.93307 


59 


32 


9.72421 


10.27579 


9.18171 


9.79579 


10.20421 


9.67217 


10.07158 


9.92842 


58 


33 


9.73611 


10.26389 


9.20771 


9.81252 


10.18748 


9.65836 


10.07641 


9.92359 


57 


34 


9.74756 


10.25244 


9.23290 


9.82899 


10.17101 


9.64425 


10.08143 


9.91857 


56 


35 


9.75859 10.24141 


9.25731 


9.84523 


10.15477 


9.62984 


10.08664 


9.91336 


55 


36 


9.76922:10.23078 


9.28099 


9.86126 


10.13874 


9.61512 


10.09204 


9.90796 


54 


37 


9.77946 10.22054 


9.30398 


9.87711 


10.12289 


9.60008 


10.09765 


9.90235 


53 


38 


9.78934,10.21066 


9.32631 


9.89281 


10.10719 


9.58471 


10.10347 


9.89653 


52 


39 


9.79887 


10.20113 


9.34802 


9.90837 


10.09163 


9.56900 


10.10950 


9.89050 


51 


40 


9.80807 


10.19193 


9.36913 


9.92381 


10.07619 


9.55293 


10.11575 


9.88425 


50 


41 


9.81694 


10.18306 


9.38968 


9.93916 


10.06084 


9.53648 


10.12222 


9.87778 


49 


42 


9.82551 


10.17449 


9.40969 


9.95444 


10.04556 


9.51966 


10.12893 


9.87107 


48 


43 


9.83378 


10.16622 


9.42018 


9.96966 


10.03034 


9.50243 


10.13587 


9.86413 


47 


44 


9.84177 


10.15823 


9.44818 


9.98484 


10.01516 


9.48479 


10.14307 


9.85693 


46 


45 


9.84949 


10.15052 


9.46671 


10.00000 


10.00000 


9.46671 


10.15052 


9.84949 


45 




Cosine. 


Secant. 


Covers. 


Cotan. 


Tangent 


Vers in. 


Cosec. 


Sine. 





From 45° to 90° read from bottomi of table up\^ards. 



168 



LOGARITHMS OF NUMBERS. 



Four-place Logarithms of Numbers to 1000. 

For six-piace logarithms of numbers to 10,000, see pp. 137 to 164. 



No. 





1 


2 


3 


4 


^ 


6 


7 


8 


9 


No. 







0000 


3010 


4771 


6021 


6990 


7782 


8451 


9031 


9542 





2 
3 


0000 
3010 
4771 


0414 
3222 
4914 


0792 

3424 
5052 


1139 
3617 
5185 


1461 
3802 
5315 


1761 
3979 
544! 


2041 
4150 
5563 


2304 
4314 
5682 


2553 

4472 
5798 


2788 
4624 
5911 


1 
2 

3 


4 
5 
6 


6021 
6990 
7782 


6128 
7076 
7853 


6232 
7160 
7924 


6335 
7243 
7993 


6435 

7324 
8062 


6532 
7404 
8129 


6628 
7482 
8195 


6721 
7559 
8261 


6812 
7634 
8325 


6902 
7709 
8388 


4 
5 
6 


7 
8 
9 


8451 
9031 
9542 


8513 
9085 
9590 


8573 
9138 
9638 


8633 
9191 
9685 


8692 
9243 
9731 


8751 
9294 
9777 


8808 
9345 
9823 


8865 
9395 
9868 


8921 
9445 
9912 


8976 
9494 
9956 


7 
8 
9 


10 


0000 


0043 


0086 


0128 


0170 


'0212 


0253 


0294 


0334 


0374 


10 


11 
12 
13 


0414 
0792 
1139 


0453 
0828 
1173 


0492 
0864 
1206 


0531 
0899 
1239 


0569 
0934 
1271 


0607 
0969 
1303 


0645 
1004 
1335 


0682 
1038 
1367 


0719 
1072 
1399 


0755 
1106 
1430 


11 
12 
13 


14 
15 
16 


1461 
1761 
2041 


1492 
1790 
2068 


1523 
1818 
2095 


1553 
1847 
2122 


1584 
1875 
2148 


1614 
1903 
2175 


1644 
1931 
2201 


1673 
1959 
2227 


1703 
1987 
2253 


1732 
2014 
2279 


14 
15 
16 


17 
18 
19 


2304 
2553 
2788 


2330 
2577 
2810 


2355 
2601 
2833 


2380 
2625 
2856 


2405 
2648 
2878 


2430 
2672 
2900 


2455 
2695 
2923 


2480 
2718 
2945 


2504 
2742 
2967 


2529 
2765 
2989 


17 
18 
19 


20 


3010 


3032 


3054 


3075 


3096 


3118 


3139 


3160 


3181 


3201 


20 


21 
22 
23 


3222 
3424 
3617 


3243 
3444 
3636 


3263 
3464 
3655 


3284 
3483 
3674 


3304 
3502 
3692 


3324 
3522 
3711 


3345 
3541 
3729 


3365 
3560 

3747 


3385 
3579 
3766 


3404 
3598 
3784 


21 
22 
23 


24 
25 
26 


3802 
3979 
4150 


3820 
3997 
4166 


3838 
4014 
4183 


3856 
4031 
4200 


3874 
4048 
4216 


3892 
4065 
4232 


3909 3927 
4082 4099 
4249 4265 


3945 
4116 
4281 


3962 
4133 
4298 


24 
25 
26 


27 
28 
29 


4314 
4472 
4624 


4330 
4487 
4639 


4346 
4502 
4654 


4362 
4518 
4669 


4378 
4533- 
4683 


4393 

4548 
4698 


4409 
4564 
4713 


4425 
4579 
4728 


4440 
4594 
4742 


4456 
4609 
4757 


27 
28 
29 


30 


4771 


4786 


4800 


4814 


4829 


4843 


4857 


4871 


4886 


4900 


30 


31 
32 
33 


4914 
5052 
5185 


4928 
5065 
5198 


4942 
5079 
5211 


4955 
5092 
5224 


4969 
5105 
5237 


4983 
5119 
5250 


4997 
5132 
5263 


5011 
5145 
5276 


5024 
5159 
5289 


5038 
5172 
5302 


31 
32 
33 


34 
35 
36 


5315 
5441 
5563 


5328 
5453 
5575 


5340 
5465 
5587 


5355 
5478 
5599 


5366 
5490 
5611 


5378 
5502 
5623 


5391 
5515 
5635 


5403 
5527 
5647 


5416 
5539 
5658 


5428 
5551 
5670 


34 
35 
36 


37 
38 
39 


5682 
5798 
5911 


5694 
5809 
5922 


5705 
5821 
5933 


5717 
5832 
5944 


5729 
5843 
5955 


5740 
5855 
5966 


5752 
5866 
5977 


5763 
5877 
5988 


5775 
5888 
5999 


5786 
5899 
6010 


37 
38 
39 


40 


6021 


6031 


6042 


6053 


6064 


6075 


6085 


6096 


6107 


6117 


40 


41 
42 
43 


6128 
6232 
6335 


6138 
6243 
6345 


6149 
6253 
6355 


6160 
6263 
6365 


6170 
6274 
6375 


6180 

6284 
6385 


6191 
6294 
6395 


6201 
6304 
6405 


6212 
6314 
6415 


6222 
6325 
6425 


41 

42 
43 


44 
45 
46 


6435 
6532 
6628 


6444 
6542 
6637 


6454 
6551 
6646 


6464 
6561 
6656 


6474 
6571 
6665 


6484 
6580 
.6675 


6493 
6590 
6684 


6503 
6599 
6693 


6513 
6609 
6702 


6522 
6618 
6712 


44 
45 
46 


47 
48 
49 


6721 
6812 
6902 


6730 
6821 
6911 


6739 
6830 
6920 


6749 
6839 
6928 


6758 
6848 
6937 


6767 
6857 
6946 


6776 
6866 
6955 


6785 
6875 
6964 


6794 
6884 
6972 


6803 
6893 
6981 


47 
48 
49 


50 


6990 


6998 


7007 


7016 


7024 


7033 


7042 


7050 


7059 


7067 


50 



LOGARITHMS OF NUMBERS. 



169 



Four-place Logarithms of Numbers to 1000. 

For six-place logarithms of numbers to 10,000, see pp. 137 to 164. 



No. 





1 


2 


3 


4 


5 


6 


7 


8 


9 


No. 


50 


6990 


6998 


7007 


7016 


7024 


7033 


7042 


7050 


7059 


7067 


50 


51 
52 
53 


7076 
7160 
7243. 


7084 
7168 
7251 


7093 
7177 
7259 


7101 
7185 
7267 


7110 
7193 
7275 


7118 
7202 
7284 


7126 
7210 
7292 


7135 
7218 
7300 


7143 
7226 
7308 


7152 
7235 
7316 


51 
52 
53 


54 
55 
56 


7324 
7404 
7482 


7332 
7412 
7490 


7340 
7419 
7497 


7348 
7427 
7505 


7356 
7435 
7513 


7364 
7443 
7520 


7372 
7451 
7528 


7380 
7459 
7536 


7388 
7466 
7543 


7396 
7474 
7551 


54 
55 
56 


57 
58 
59 


7559 
7634 
7709 


7566 
7642 
7716 


7574 
7649 
7723 


7582 
7657 
7731 


7589 
7664 
7738 


7597 
7672 
7745 


7604 
7679 
7752 


7612 
7686 
7760 


7619 
7694 
7767 


7627 
7701 
7774 


57 
58 
59 


60 


7782 


7789 


7796 


7803 


7810 


7818 


7825 


7832 


7839 


7846 


60 


61 
62 
63 


7853 
7924 
7993 


7860 
7931 
8000 


7868 
7938 
8007 


7875 
7945 
8014 


7882 
7952 
8021 


7889 
7959 
8028 


7896 
7966 
8035 


7903 
7973 
8041 


7910 
7980 
8048 


7917 
7987 
8055 


61 
62 
63 


64 
65 
66 


8062 
8129 
8195 


8069 
8136 
8202 


8075 
8142 
8209 


8082 
8149 
8215 


8089 
8156 
8222 


8096 
8162 
8228 


8102 
8169 
8235 


8109 
8176 
8241 


8116 
8182 
8248 


8122 
8189 
8254 


64 
65 
66 


67 
68 
69 


8261 
8325 
8388 


8267 
8331 
8395 


8274 
8338 
8401 


8280 
8344 
8407 


8287 
8351 
8414 


8293 
8357 
8420 


8299 8306 
8363 8370 
8426 8432 


8312 8319 
8376 8382 
8439 8445 


67 
68 
69 


70 


8451 


8457 


8463 


8470 


8476 


8482 


8488 


8494 


8500 8506 


70 


71 
72 
73 


8513 
8573 
8633 


8519 
8579 
8639 


8525 
8585 
8645 


8531 
8591 
8651 


8537 
8597 
8657 


8543 
8603 
8663 


8549 
8609 
8669 


8555 
8615 
8675 


8561 
8621 
8681 


8567 
8627 
8686 


71 
72 
73 


74 
75 
76 


8692 
8751 
8808 


8698 
8756 
8814 


8704 
8762 
8820 


8710 
8768 
8825 


8716 
8774 
8831 


8722 
8779 
8837 


8727 8733 8739 
8785 8791 8797 
8842 8848 8854 


8745 
8802 
8859 


74 
75 
76 


77 
78 
79 


8865 
8921 
8976 


8871 
8927 
8982 


8876 
8932 
8987 


8882 
8938 
8993 


8887 
8943 
8998 


8893 
8949 
9004 


8899 
8954 
9009 


8904 
8960 
9015 


8910 
8965 
9020 


8915 
8971 
9025 


77 
78 
79 


80 


9031 


9036 


9042 


9047 


9053 


9058 


9063 


9069 


9074 


9079 


80 


81 
82 
83 


9085 
9138 
9191 


9090 
9143 
9196 


9096 
9149 
9201 


9101 
9154 
9206 


9106 
9159 
9212 


9112 
9165 
9217 


9117 
9170 
9222 


9122 
9175 
9227 


9128 
9180 
9232 


9133 
9186 
9238 


81 
82 
83 


84 
85 
86 


9243 
9294 
9345 


9248 
9299 
9350 


9253 

9304 
9355 


9258 
9309 
9360 


9263' 
9315 
9365 


9269 
9320 
9370 


9274 
9325 
9375 


9279 
9330 
9380 


9284 
9335 
9385 


9289 
9340 
9390 


84 
85 
86 


87 
88 
89 


9395 
9445 
9494 


9400 
9450 
9499 


9405 
9455 
9504 


9410 
9460 
9509 


9415 
9465 
9513 


9420 
9469 
9518 


9425 

9474 
9523 


9430 9435 
9479 9484 
9528 9533 


9440 
9489 
9538 


87 
88 
89 


90 


9542 


9547 


9552 


9557 


9562 


9566 


9571 


9576 


9581 


9586 


90 


91 
92 
93 


9590 
9638 
9685 


9595 
9643 
9689 


9600 
9647 
9694 


9605 
9652 
9699 


9609 
9657 
9703 


9614 
9661 
9708 


9619 9624 
9666 9671 
9713 9717 


9628 
9675 
9722 


9633 
9680 
9727 


91 
92 
93 


94 
95 
96 


9731 
9777 
9823 


9736 
9782 
9827 


9741 
9786 
9832 


9745 
9791 
9836 


9750 
9795 
9841 


9754 
9800 
9845 


9759 9764 
9805 9809 
9850 9854 


9768 
9814 
9859 


9773 
9818 
9863 


94 
95 
96 


97 
98 
99 


9868 
9912 
9956 


9872 
9917 
9961 


9877 
9921 
9965 


9881 
9926 
9969 


9886 
9930 
9974 


9890 
9934 
9978 


9894 
9939 
9983 


9899 
9943 
9987 


9903 
9948 
9991 


9908 
9952 
9996 


97 
98 
99 


100 


0000 


0004 


0009 


0013 


0017 


0022 


0026 


0030 


0035 


0039 


100 



170 



NATURAL TRIGONOMETRICAL FUNCTIONS. 



NATURAL TRIGONOMETRICAL FUNCTIONS. 



• 


~0 


Sine. 
.00000 


Co- 
vers. 


Cosec. 


Tang. 


Cotan. 


Se- 
cant. 


Ver. 

Sin. 


Cosine. 


90 







1 .0000 


Infinite 


.00000 i Infinite 


1 .0000 


.00000 


1.0000 







15 


.00436 




99564 


229.18 


.004361229.18 


1 .0000 


.00001 


.99999 




45 




30 


.00373 




99127 


114.59 


.00373 


114.59 


1 .0000 


.00004 


.99996 




30 




45 


.01309 




93691 


76.397 


.01309 


76.390 


1.0001 


.00009 


.99991 




15 


1 





.01745 




93255 


57.299 


.01745 


57.290 


1.0001 


.00015 


.99985 


89 







15 


.02181 




97819 


45.840 


.02182 


45.829 


1 .0002 


.00024 


.99976 




45 




30 


.02618 




97382 


38.202 


.02618 


38.188 


1 .0003 


.00034 


.99966 




30 




45 


.03054 




96946 


32.746 


.03055 


32.730 


1 .0005 


.00047 


.99953 




15 


2 





.03490 




96510 


28.654 


.03492 


28.636 


1.0006 


.00061 


.99939 


88 







15 


.03926 




96074 


25.471 


.03929 


25.452 


1 .0003 


.00077 


.99923 




45 




30 


.04362 




95638 


22.926 


.04366 


22.904 


1 .0009 


.00095 


.99905 




30 




45 


.04798 




95202 


20.843 


.04803 


20.819 


1.0011 


.00115 


.99885 




15 


3 





.05234 




94766 


19.107 


.05241 


19.031 


1.0014 


.00137 


.99863 


87 







15 


.05669 




94331 


17.639 


.05678 


17.611 


1.0016 


.00161 


.99839 




45 




30 


.06105 




93895 


16.380 


.06116 


16.350 


1.0019 


.00187 


.99813 




30 




45 


.06540 




93460 


15.290 


.06554 


15.257 


1.0021 


.00214 


.99786 




15 


4 





.06976 




93024 


14.336 


.06993 


14.301 


1.0024 


.00244 


.99756 


86 







15 


.07411 




92589 


13.494 


.07431 


13.457 


1 .0028 


.00275 


.99725 




45 




30 


.07846 




92154 


12.745 


.07870 


12.706 


1.0031 


.00308 


.99692 




30 




45 


.08281 




91719 


12.076 


.08309 


12.035 


1.0034 


.00343 


.99656 




15 


5 





.08716 




91284 


11.474 


.08740 


11.430 


1.0038 .00381 


.99619 


85 







15 


.09150 




90850 


10.929 


.09189 


10.883 


1.0042'. 00420 


.99580 




45 




30 


.09585 




90415 


10.433 


.09629 


10.385 


1.00461.00460 


.99540 




30 




45 


.10019 




89981 


9.9812 


. 1 0069 


9.9310 1.0051 


.00503 


.99497 




15 


6 





.10453 




89547 


9.5668 


.10510 


9.5 144i 1.0055 


.00548 


.99452 


84 







15 


.10887 




89113 


9.1855 


.10952 


9.1309,1.0060 


.00594 


.99406 




45 




30 


.11320 




88680 


8.8337 


.11393 


8.7769,1.0065 


.00643 


.99357 




30 




45 


.11754 




88246 


8.5079 


.11836 


8.4490 1.0070 


.00693 


.99307 




15 


1 





.12187 




87813 


8.2055 


.12278 


8.1443 1.0075 


.00745 


.99255 


83 







15 


.12620 




87380 


7.9240 


.12722 


7.8606 1.0081 


.00800 


.99200 




45 




30 


.13053 




86947 


7.6613 


.13165 


7.5958 


1.0086 


.00856 


.99144 




30 




45 


.13485 




86515 


7.4156 


.13609 


7.3479 


1.0092 


.00913 


.99086 




15 


8 





.13917 




86083 


7.1853 


.14054 


7.1154 


1 .0098 


.00973 


.99027 


82 







15 


.14349 




85651 


6.9690 


.14499 


6.8969! 1.0105 


.01035 


.98965 




45 




30 


.14781 




85219 


6.7655 


.14945 


6.6912 1.01 n 


.01098 


.98902 




30 




45 


.15212 




84788 


6.5736 


.15391 


6.4971 1.0118 


.01164 


.98836 




15 


9 





.15643 




84357 


6.3924 


.15838 


6.3138 1.0125 


.01231 


.93769 


81 







15 


.16074 




83926 


6.2211 


.16286 


6.1402 1.0132 


.01300 


.98700 




45 




30 


.16505 




83495 


6.0589 


.16734 


5.9758 1.0139 


.01371 


.98629 




30 




45 


.16935 




83065 


5.9049 


.17183 


5.819711.0147 


.01444 


.93556 




15 


10 





.17365 




82635 


5.7588 


.17633 


5.6713jl.0154 


.01519 


.98481 


80 







15 


.17794 




82206 


5.6198 


.18083 


5.5301il.0162 


.01596 


.98404 




45 




30 


.18224 




81776 


5.4874 


.18534 


5.3955^1.0170 .01675 


.98325 




30 




45 


.18652 




81348 


5.3612 


.18986 


5.2672 1.0179 .01755 


.98245 




15 


11 





.19081 




80919 


5.2408 


.19438 


5.1446|1.0187 


.01837 


.98163 


79 







15 


.19509 




80491 


5.1258 


.19891 


5.027311.0196 


.01921 


.98079 




45 




30 


.19937 




80063 


5.0158 


.20345 


4.915211.0205 


.02003 


.97992 




30 




45 


.20364 




79636 


4.9106 


.20800 


4.8077 K02 14 


.02095 


.97905 




15 


13 





.20791 




79209 


4.8097 


.21256 


4.7046 1.0223 


.02185 


.97815 


78 







15 


.21218 




78782 


4.7130 


.21712 


4.6057 


1.0233 


.02277 


.97723 




45 




30 


.21644 




78356 


4.6202 


.22169 


4.5107 


1.0243 


.02370 


.97630 




30 




45 


.22070 




77930 


4.5311 


.22628 


4.4194 


1.0253 


.02466 


.97534 




15 


13 





.22495 




77505 


4.4454 


.23087 


4.3315 1.0263 


.02563 


.97437 


77 







15 


.22920 




77080 


4.3630 


.23547 


4.2468,1.0273 


.02662 


.97338 




45 




30 


.23345 




76655 


4.2837 


.24008 


4.1653 1.0284 


.02763 


.97237 




30 




45 


.23769 




76231 


4.2072 


.24470 


4.0867 1.0295 


.02866 


.97134 




15 


14 





24192 




75808 


4.1336 


.24933 


4.0108 1.0306 


.02970 


.97030 


7G 







15 


.24615 




75385 


4.0625 


.25397 


3.9375 1.0317 


.03077 


.96923 




45 




30 


.25038 




74962 


3.9939 


.25862 


3.8667 1.0329 


.03185 


.96815 




30 




45 


.25460 




74540 


3.9277 


.26328 


3.7983 1.0341 


.03295 


.96705 




15 


15 





.25882 

Co- 
sine. 




74118 


3.8637 


.26795 


3.7320 1.0353 


03407 


.96593 


75 









Ver. 
Sin. 


Secant. 


Cotan 


Tang. .Cosec. 


Co- 
vers. 


Sine. 


M. 



From 75° to 90° read from bottom of table upwards. 



NATURAL TRIGONOMETRICAIi FUNCTIONS. 



171 



e 


M. 


Sine. 


Co- 
vers. 


Cosec 


Tang. 


Cotan. 


Secant. 


Ver. 

Sii. 


Cosine. 






15" 





.25882 


.74118 


3.8637 


.26795 


3.7320 


1.0353 


.U3407 


.96593 


75 


~ 




15 


.26303 


.73697 


3.8018 


.27263 


3.6680 


1.0365 


.03521 


.96479 




45 




30 


.26724 


.73276 


3.7420 


.27732 


3.6059 


1.0377 


.03637 


.96363 




30 




45 


.27144 


.72856 


3.6840 


.28203 


3.5457 


1.0390 


.03754 


.96246 




15 


16 





.27564 


.72436 


3.6280 


.28674 


3.4874 


1.0403 


.03874 


.96126 


74 







15 


.27983 


.72017 


3.5736 


.29147 


3.4308 


1.0416 


.03995 


.96005 




45 




30 


.28402 


.71598 


3.5209 


.29621 


3.3759 


1.0429 


.04118 


.95882 




30 




45 


.28820 


.71180 


3.4699 


.30096 


3.3226 


1 .0443 


.04243 


.95757 




15 


17 





.29237 


.70763,3.4203 


.30573 


3.2709 


1.0457 


.04370 


.95630 


73 







15 


.29654 


.703463.3722 


.31051 


3.2205 


1.0471 


.04498 


.95502 




45 




30 


.30070 


.69929 3.3255 


.31530 


3.1716 


1.0485 


.04628 


.95372 




30 




45 


.30486 


.69514 


3.2301 


.32010 


3.1240 


1 .0500 


.04760 


.95240 




15 


18 





.30902 


.69098 


3.2361 


.32492 


3.0777 


1.0515 


.04894 


.95106 


72 







15 


.31316 


.68684 


3.1932 


.32975 


3.0326 


1.0530 


.05030 


.94970 




45 




30 


.31730 


.68270 3.1515 


.33459 


2.9887 


1.0545 


.05168 


.94832 




30 




45 


.32144 


.67856 


3.1110 


.33945 


2.9459 


1 .0560 


.05307 


.94693 




15 


19 





.32557 


.67443 


3.0715 


.34433 


2.9042 


1.0576 


.05448 


.94552 


71 







15 


.32969 


.67031 


3.0331 


.34921 


2.8636 


1.0592 


.05591 


.94409 




45 




30 


.33381 


.66619 


2.9957 


.35412 


2.8239 


1 .0608 


.05736 


.94264 




30 




45 


.33792 


.66208 


2.9593 


.35904 


2.7852 


1 .0625 


.05882 


.94118 




15 


20 





.34202 


.65798 


2.9238 .36397 


2.7475 


1 .0642 


.06031 


.93969 


70 







15 


.34612 


.65388 


2.8892 


.36892 


2.7106 


1.0659 


.06181 


.93819 




45 




30 


.35021 


.64979 


2.8554 


.37388 


2.6746 


1.0676 


.06333 


.93667 




30 




45 


.35429 


.64571 


2.8225 


.37887 


2.6395 


1 .0694 


.06486 


.93514 




15 


21 





.35837 


.64163 


2.7904 


.38386 


2.6051 


1.0711 


.06642 


.93358 


69 







15 


.36244 


.63756 


2.7591 


.38883 


2.5715 


1.0729 


.06799 


.93201 




45 




30 


.36650 


.63350 


2.7235 


.39391 


2.5386 


1 .0743 


.06958 


.93042 




30 




45 


.37056 


.62944 


2.6986 


.39896 


2.5065 


1.0766 


.07119 


.92881 




15 


22 





.37461 


.62539 


2.6695 


.40403 


2.4751 


1.0785 


.07282 


.92718 


68 







15 


.37865 


.62135 


2.6410 


.40911 


2.4443 


1.0804 


.07446 


.92554 




45 




30 


.38268 


.61732 


2.6131 


.41421 


2.4142 


1.0824 


.07612 


.92388 




30 




45 


.38671 


.61329 


2.5859 


.41933 


2.3847 


1 .0844 


.07780 


.92220 




15 


23 





.39073 


.60927 


2.5593 


.42447 


2.3559 


1 .0864 


.07950 


.92050 


67 







15 


.39474 


.60526 


2.5333 


.42963 


2.3276 


1 .0834 


.08121 


.91879 




45 




30 


.39875 


.60125 


2.5078 


.43431 


2.2993 


1 .0904 


.08294 


.91706 




30 




45 


.40275 


.59725 


2.4829 


.44001 


2.2727 


1.0925 


.03469 


.91531 




15 


24 





.40674 


.59326 


2.4586 


.44523 


2.2460 


1.0946 


.08645 


.91355 


66 







15 


.41072 


.58928 


2.4348 


.45047 


2.2199 


1 .0968 


.03824 


.91176 




45 




30 


.41469 


.58531 


2.4114 


.45573 


2.1943 


1 .0989 


.09004 


.90996 




30 




45 


.41866 


58134 


2.3886 


.46101 


2.1692 


1.1011 


.09186 


.90814 




15 


25 





.42262 


57738 


2.3662 


.4663 1 


2.1445 


1.1034 


.09369 


.90631 


65 







15 


.42657 


.57343 


2.3443 


.47163 


2.1203 


1.1056 


.09554 


.90446 




45 




30 


.43051 


56949 


2.3228 


.47697 


2.0965 


M079 


.09741 


.90259 




30 




45 


.43445 


56555 


2.3018 


.48234 


2.0732 


1.1102 


.09930 


.90070 




15 


26 





.43837 


56163 


2.2812 


.48773 


2.0503 


1.1126 


.10121 


.89879 


64 







15 


.44229 


55771 


2.2610 


.49314 


2.0278 


1.1150 


.10313 


.89687 




45 




30 


.44620 


55380 


2.2412 


.49858 


2.0057 


1.1174 


.10507 


.89493 




30 




45 


.45010 


54990 


2.2217 


.50404 


1 .9840 


1.1198 


.10702 


.89298 




15 


27 





.45399 


54601 


2.2027 


.50952 


1 .9626 


1.1223 


.10899 


.89101 


63 







15 


.45787 


54213 


2.1840 


.51503 


1.9416 


1.1248 


. 1 1 098 


88902 




45 




30 


.46175 


.53825 


2.1657 


.52057 


1.9210 


1.1274 


. 1 1 299 


.88701 




30 




45 


.46561 


53439 


2.1477 


.52612 


1 .9007 


1.1300 


.11501 


.88499 




15 


28 





.46947 


.53053 


2.1300 


.53171 


1 .8807 


1.1326 


.11705 


.88295 


62 







15 


.47332 


.5266S 


2.1127 


.53732 


1.8611 


1.1352 


.11911 


.88089 




45 




30 


.47716 


.52284 


2.0957 


.54295 


1.8418 


1.1379 


.12118 


.87882 




30 




45 


.48099 


.51901 


2.0790 


.54862 


1.8228 


1.1406 


.12327 


.87673 




15 


29 





.48481 


.51519 


2.0627 


.55431 


1 .8040 


1.1433 


.12538 


.87462 


61 







15 


.48862 


.51138 


2.0466 


.56003 


1.7856 


1.1461 


.12750 


.87250 




45 




30 


.49242 


.50758 


2.0308 


.56577 


1.7675 


1 . 1 490 


.12964 


.87036 




30 




45 


.49622 


.50378 


2.0152 


.57155 


1.7496 


1.1518 


.13180 


.86820 




15 


30 





.50000 


.30000 


2.0000 


.57735 


1.7320 


1.1547 


.13397 


.86603 
Sine. 


60 


_0 






Co- 
sine. 


Ver. 
Sin. 


Se- 
cant. 


Co tan. 


Tang. 


Cosec. 


Co- 
vers. 


o 


M. 



From 60° to 75° read from bottom of table upwards. 



172 NATURAL TRIGONOMETRICAL FUNCTIONS. 



o 


M. 



Sine. 


Co- 
vers. 


Cosec. 


Tang. 


Co tan. 


Secant. 


Ver. 
Sin. 


Cosine 






80 


.50000 


.50000 


2.0000 


.57735 


1.7320 


1.1547 


.13397 


.86603 


GO 







15 


.50377 


.49623 


1 .9850 


.58318 


1.7147 


1.1576 


.13616 


.86384 




45 




30 


.50754 


.49246 


1.9703 


.58904 


1.6977 


1 . 1 606 


.13837 


.86163 




30 




45 


.51129 


.48871 


1.9558 


.59494 


1 .6808 


1.1636 


.14059 


.85941 




15 


31 





.51504 


.48496 


1.9416 


.60086 


1 .6643 


1 . 1 666 


.14283 


.85717 


59 







15 


.51877 


.48123 


1.9276 


.60681 


1.6479 


1.1697 


.14509 


.85491 




45 




30 


.52250 


.47750 


1.9139 


.61280 


1.6319 


1.1728 


.14736 


.85264 




30 




45 


.52621 


.47379 


1 .9004 


.61882 


1.6160 


1.1760 


. 1 4965 


.85035 




15 


32 





.52992 


.47008 


1.8871 


.62437 


1 .6003 


1.1792 


.15195 


.84805 


58 







15 


.53361 


.46639 


1 .8740 


.63095 


1.5849 


1.1824 


.15427 


.84573 




45 




30 


.53730 


.46270 


1.8612 


.63707 


1.5697 


1.1857 


.15661 


.84339 




30 




45 


.54097 


.45903 


1 .8485 


.64322 


1.5547 


1.1890 


.15896 


.84104 




15 


33 





.54464 


.45536 


1.8361 


.64941 


1.5399 


1.1924 


.16133 


.83867 


57 







15 


.54829 


.45171 


1.8238 


.65563 


1.5253 


1.1958 


.16371 


.83629 




45 




30 


.55194 


.44806 


1.8118 


.66188 


1.5108 


1.1992 


.16611 


.83389 




30 




45 


.55557 


.44443 


1.7999 


.66818 


1 .4966 


1 .2027 


.16853 


.83147 




15 


34 





.55919 


.44081 


1.7883 


.67451 


1.4326 


1 .2062 


.17096 


.82904 


56 







15 


.56280 


.43720 


1.7768 


.68087 


1.4687 


1.2098 


.17341 


.82659 




45 




30 


.56641 


.43359 


1.7655 


.68728 


1.4550 


1.2134 


.17587 


.82413 




30 




45 


.57000 


.43000 


1.7544 


.69372 


1.4415 


1.2171 


.17835 


.82165 




15 


35 





.57358 


.42642 


1.7434 


.70021 


1.4281 


1 .2208 


.18085 


.81915 


55 







15 


.57715 


.42285 


1.7327 


.70673 


1.4150 


1.2245 


.18336 


.81664 




45 




30 


.58070 


.41930 


1.7220 


.71329 


1.4019 


1.2283 


.18588 


.81412 




30 




45 


.58425 


.41575 


1.7116 


.71990 


1.3891 


1.2322 


.18843 


.81157 




15 


36 





.58779 


.41221 


1.7013 


.72654 


1.3764 


1.2361 


.19098 


.80902 


54 







15 


.59131 


.40869 


1.6912 


.73323 


1.3638 


1 .2400 


.19356 


.80644 




45 




30 


.59482 


.40518 


1.6812 


.73996 


1.3514 


1 .2440 


.19614 


.80386 




30 




45 


.59832 


.40168 


1.6713 


.74673 


1.3392 


1 .2480 


.19875 


.80125 




15 


37 





.60181 


.39819 


1.6616 


.75355 


1.3270 


1.2521 


.20136 


.79864 


53 







15 


.60529 


.39471 


1.6521 


.76042 


1.3151 


1.2563 


.20400 


.79600 




45 




30 


.60876 


.39124 


1.6427 


.76733 


1.3032 


1.2605 


.20665 


.79335 




30 




45 


.61222 


.38778 


1.6334 


.77428 


1.2915 


1 .2647 


.20931 


.79069 




15 


38 





.61566 


.38434 


1.6243 


.78129 


1 .2799 


1 .2690 


.21199 


.78801 


53 







15 


.61909 


.38091 


1.6153 


.78834 


1.2685 


1.2734 


.21468 


.78532 




45 




30 


.62251 


.37749 


1 .6064 


.79543 


1.2572 


1.2778 


.21739 


.78261 




30 




45 


.62592 


.37408 


1.5976 


.80258 


1 .2460 


1 2822 


.22012 


.77988 




15 


39 





.62932 


.37068 


1.5890 


.80978 


1.2349 


1 .2868 


.22285 


.77715 


51 







15 


.63271 


.36729 


1.5805 


.81703 


1.2239 


1.2913 


.22561 


.77439 




45 




30 


.63608 


.36392 


1.5721 


.82434 


1.2131 


1 .2960 


.22838 


.77162 




30 




45 


.63944 


.36056 


1.5639 


.83169 


1 .2024 


1.3007 


.23116 


.76884 




15 


40 





.64279 


.35721 


1.5557 


.83910 


1.1918 


1.3054 


.23396 


.76604 


50 







15 


.64612 


.35388 


1.5477 


.84656 


1.1812 


1.3102 


.23677 


.76323 




45 




30 


.64945 


.35055 


1.5398 


.85408 


1.1708 


1.3151 


.23959 


.76041 




30 




45 


.65276 


.34724 


1.5320 


.86165 


1 . 1 606 


1 .3200 


.24244 


.75756 




15 


41 





.65606 


.34394 


1.5242 


.86929 


1.1504 


1.3250 


.24529 


.75471 


49 







15 


.65935 


.34065 


1.5166 


.87698 


1.1403 


1.3301 


.24816 


.75184 




45 




30 


.66262 


.33738 


1.5092 


.88472 


1.1303 


1.3352 


.25104 


.74896 




30 




45 


.66588 


.33412 


1.5018 


.89253 


1.1204 


1.3404 


.25394 


.74606 




15 


43 





.66913 


.33087 


1 .4945 


.90040 


1.1106 


1.3456 


.25686 


.74314 


48 







15 


.67237 


.32763 


1.4873 


.90834 


1.1009 


1.3509 


.25978 


.74022 




45 




30 


.67559 


.32441 


1 .4802 


.91633 


1.0913 


1.3563 


.26272 


.73728 




30 




45 


.67880 


.32120 


1.4732 


.92439 


1.0818 


1.3618 


.26568 


.73432 




15 


43 





.68200 


.31800 


1 .4663 


.93251 


1.0724 


1.3673 


.26865 


.73135 


47 







15 


.68518 


.31482 


1.4595 


.94071 


1 .0630 


1.3729 


.27163 


.72837 




45 




30 


.68835 


.31165 


1.4527 


.94896 


1.0538 


1.3786 


.27463 


.72537 




30 




45 


.69151 


.30849 


1.4461 


.95729 


1 .0446 


1.3843 


.27764 


.72236 




15 


44 





.69466 


.30534 


1.4396 


.96569 


1.0355 


1 .3902 


.28066 


.71934 


46 







15 


.69779 


.30221 


1.4331 


.97416 


1 .0265 


1.3961 


.28370 


.71630 




45 




30 


.70091 


.29909 


1.4267 


.98270 


1.0176 


1 .4020 


.28675 


.71325 




30 




45 


.70401 


.29599 


1.4204 


.99131 


1 .0088 


1.4081 


.28981 


.71019 




15 


45 





.70711 


.29289 


1.4142 


1 .0000 


1 .0000 


1.4142 


.29289 


.70711 


45 









Cosine 


Ver. 

Sin. 


Se- 
cant. 


Cotan. 


Tang. 


Cosec. 


Co- 
vers. 


Sine. 


o 


M. 



From 45° to 60° read from bottom of table upwards. 



SPECIFIC GRAVITY. 



173 



MATERIALS. 

THE CHEMICAL ELE]>IENTS. 

Common Elements (43). 





Name. 


4J 

1^ 


11 


Name. 


1^ 


6^ 


Name. 


C a; 

1^ 


Al 


Aluminum 


27.1 


F 


Fluorine 


19. 


pd 


Palladium 


106.7 


Sb 


Antimony 


120.2 


Au 


Gold 


197.2 


p 


Phosphorus 


31. 


As 


Arsenic 


75.0 


H 


Hydrogen 


1.01 


pt 


Platinum 


195.2 


Ba 


Barium 


137.4 


I 


Iodine 


126.9 


K 


Potassium 


39.1 


Bi 


Bismuth 


208.0 


Ir 


Iridium 


193.1 


Si 


Silicon 


28.3 


B 


Boron 


ll.O 


Fe 


Iron 


55.84 


Ag 


Silver 


107.9 


Br 


Bromine 


79.9 


Pb 


Lead 


207.1 


Na 


Sodium 


23. 


Cd 


Cadmium 


112.4 


Li 


Lithium 


6.94 


Sr 


Strontium 


87.6 


Ca 


Calcium 


40.1 


Mg 


Magnesium 


24.34 


S 


Sulphur 


32.1 


C 


Carbon 


12. 


Mn 


Manganese 


54.9 


Sn 


Tin 


119. 


CI 


Chlorine 


35.5 


Hg 


Mercury 


200.6 


Ti 


Titanium 


48.1 


Cr 


Chromium 


52.0 


Ni 


Nickel 


58.7 


W 


Tungsten 


184.0 


Co 


Cobalt 


59. 


N 


Nitrogen 


14.01 


Va 


Vanadium 


51.0 


Cu 


Copper 


63.6 


O 


Oxygen 


16. 


Zn 


Zinc 


65.4 



The atomic weights of many of the elements vary in the decimal 
place as given by different authorities. The above are the most recent 
values referred to O = 16 and H = 1.008. When H is taken as 1, 
O = 15.879, and the other figures are diminished proportionately. 



Rare Elements (37). 



BerylUum, Be. 
Ca3sium, Cs. 
Cerium, Ce. 
Erbium, Er. 
Gallium, Ga. 
Germanium, Ge. 
Glucinum, G. 



Indiiun, In. 
Lanthanum, La. 
IMolybdenum, Mo. 
Niobium, Nb. 
Osmium, Os. 
Rhodium, R. 
Rubidiiun, Rb. 



Ruthenium, Ru. 
Samarium, Sm. 
Scandium, Sc. 
Selenium, Se. 
Tantalum, Ta. 
Tellurium, Te. 
Terbium, Tb. 



Thallium, Tl. 
Thorium, Th. 
Uranium, U. 
Ytterbium, Yr. 
Yttrium, Y. 
Zirconium, Zr. 



Elements recently discovered (1895-1900): Argon, A, 39.9; Krypton 
Kr, 81.8; Neon, Ne, 20.0; Xenon, X, 128.0; constituents of the atmos- 
phere, which contains about 1 per cent by volume of Argon, and very 
small quantities of the others. Helium, He, 4.0; Radium, Ra, 225.0; 
Gadolinium, Gd, 156.0; Neodymium, Nd, 143.6; Preesodymium, Pr, 
140.5; Thulium, Tm, 171.0. 



SPECIFIC GRAVITY. 

The specific gravity of a substance is its weight as compared with the 
weight of an equal bulk of pure water. In the metric system it is the 
weight in grammes per cubic centimeter. 

To find the specific gravity of a substance. 

W = weight of body in air ; w = weight of body submerged in water. 



Specific gravity = 



W 



W 



If the substance be lighter than the water, sink it by means of a 
heavier substance, and deduct the weight of the heavier substance. 

Specific gravity determinations are usually referred to the standard of 
the weight of water at 62° F., 62.355 lb. per cubic foot. Some experi- 



174 



MATERIALS. 



menters have used 60° F. as the standard, and others 32° and 39.1° F. 
There is no general agreement. 

Given sp. gr. referred to water at 39.1° F., to reduce it to the standard 
of 62° F. multiply it by 1.00112. 

Given sp. gr. referred to water at 62° F., to find w^eight per cubic foot 
multiply by 62.355. Given weight per cubic foot, to find sp. gr. multiply 
by 0.016037. Given sp. gr., to find weight per cubic inch multiply by 
0.036085. 

Weight and Specific Gravity of Metals. 





Specific Gravity. 
Range accord- 
ing to 
several 
Authorities. 


Specific Grav- 
ity. Approx. 
Mean Value, 

used in 
Calculation 
of Weight. 


Weight 

per 

Cubic 

Foot, 

lbs. 


Weight 

per 

Cubic 

Inch, 

lbs. 


Aluminum. » 


2.56 to 2.71 
6.66 to 6.86 
9.74 to 9.90 

7.8 to 8.6 

8.52 to 8.96 

8.6 to 8.7 

1.58 

5.0 

8.5 to 8.6 

19.245 to 19.361 

8.69 to 8.92 

22.38 to 23. 

6.85 to, 7.48 
7.4 to 7.9 

11.07 to 11.44 

7. to 8. 

1.69 to 1.75 

13.61 

13.58 

13.37 to 13.38 

8.279 to 8.93 

20.33 to 22.07 

0.865 
10.474 to 10.511 

0.97 
7.69* to 7.932t 
7.291 to 7.409 

5.3 
17. to 17.6 

6.86 to 7.20 


2.67 
6.76 
9.82 

8.60 
18.40 
]8.36 
[8.20 

8.853 

8.65 

1.58 

5.0 

8.55 
19.258 

8.853 
22.38 

7.218 

7.70 
11.38 

8. 

1.75 
13.61 
13.58 
13.38 

8.8 
21.5 

0.865 
10.505 

0.97 

7.854 

7.350 

5.3 
17.3 

7.00 


166.5 
421.6 
612.4 

536.3 
523.8 
521.3 
511.4 

552. 

539. 
98.5 
311.8 
533.1 

1200.9 
552. 

1396. 
450. 
480. 
709.7 
499. 
109. 
848,6 
846.8 
834.4 
548.7 

1347.0 
53.9 
655.1 
60.5 
489.6 
458.3 
330.5 

1078.7 
436.5 


0.0963 


Antimony 


0.2439 


Bismuth 


0.3544 


Brass: Copper + Zinc>| 

70 3ol. . 
60 40 
50 50^ 
Pirnr.. JCop., 95 to 801 
Bronzej^j^^ 5 to 20/ 

Cadmium. 


0.3103 
0.3031 
0.3017 
0.2959 

0.3195 
0.3121 


Calcium 


0.0570 


Chromium 


0.1804 


Cobalt 


0.3085 


Gold, pure 


6949 


Copper 


0.3195 


T -sr 

Indium 


8076 


Iron, Cast 


0.2604 


Iron, Wrought 

Lead 


0.2779 
0.4106 


Manganese .... 


2887 


Magnesium 


0.0641 


32° 

Mercury < 60° 

1212° 
Nickel 


0.4908 
0.4911 
0.4828 
0.3175 


Platinum 


0.7758 


Potassium 


0.0312 


Silver 


0.3791 


Sodium 


0.0350 


Steel 


0.2834 


Tin 


02652 


Titanium 


0.1913 


Tungsten 


0.6243 


Zinc 


0.2526 







* Hard and burned. 

t Very pure and soft. The sp. gr. decreases as the carbon is increased. 

In the first column of figures the lowest are usually those of cast metals, 
which are more or less porous; the highest are of metals finely rolled or 
drawn into wire. 

The weight of 1 cu. cm. of mercury at 0° C. is 1.3.59545 grams CThiessen). 
Taking atmosphere = 29.92 in. ol mercury at 32° F. = 14.6963 lb. per 
sq. in., 1 cu. in. of mercury = 0.49117 lb. Taking water at 0.036085 lb. 
per cu. in. at 62° F., the specific gravity of mercury is at 32° F. 13.611. 



SPECIFIC GRAVITY. 



1?5 



Specific Gravity of Liquids at 60=* F. 



Acid. Muriatic. 1 .200 

" Nitric 1.217 

" Sulphuric ,. 1.849 

Alcohol, pure 0.794 

95 percent 0.816 

50 percent... 0.934 

Ammonia, 27.9 per cent .. . 0.891 

Bromine. 2.97 

Carbon disulphide 1 .26 

Ether, Sulphuric 0.72 

Oil, Linseed,..., 0.93 



Oil, Olive..., 0.92 

•• Palm 0.97 

*• Petroleum 0.78 to 0.88 

" Rape... ...., 0.92 

*' Turpentine 0.86 

" Whale 0.92 

Tar 1. 

Vinegar 1 .08 

Water 1. 

Water,Sea ,., 1.026 to 1.03 



Compression of the following Fluids under a Pressure of 15 lbs. 
per Square Inch. 

Water 0.00004663 I Ether. . . , 0.000061 58 

Alcohol. , , 0.00002 1 6 | Mercury , 0.00000265 

The Hydrometer. 

The hydrometer is an instrument for determining the density of liquids. 
It is usually made of glass, and consists of three parts: (1) the upper 
part, a graduated stem or fine tube of uniform diameter; (2) a bulb, or 
enlargement of the tube, containing air; and (3) a small bulb at the 
bottom, containing shot or mercury which causes the instrument to float 
in a vertical position. The graduations are figures representing either 
specific gravities, or the numbers of an arbitrary scale, as in Baum^'s 
Twaddell's, Beck's, and other hydrometers. 

There is a tendency to discard all hydrometers with arbitrary scales and 
to use only those which read in terms of the specific gravity directly. 



Baume's Hydrometer and Specific Gravities Compared. 



FnrmiilfP /Heavy liquids, Sp. gr. = 
l^ormulse^Light hquids, Sp. gr. 



145 - 
140 ■ 



(145 - deg. Be.) 
(130 +deg. Be.) 



Degrees 
Baum^ 


Liquids 
Heavier 
than 
Water, 
Sp. Gr. 


Liquids 
Lighter 

than 
Water, 
Sp. Gr. 


Degrees 
Baume 


Liquids 
Heavier 

than 
Water, 
Sp. Gr 


Liquids 
Lighter 

than 
Water, 
Sp. Gr. 


Degrees 
Baum^ 


Liquids 
Heavier 

than 
Water, 
Sp. Gr. 


Liquids 
Lighter 

than 
Water, 
Sp. Gr. 


0.0 
1.0 
2.0 
3.0 
4.0 
5.0 
6.0 
7.0 
8.0 
9.0 
10.0 
11.0 
12.0 
13.0 
14.0 
15.0 
16.0 
17.0 


1.000 
1 007 
1.014 
1 021 
1.028 
1.036 
1.043 
1.051 
1.058 
1.066 
1.074 
1.082 
1.090 
1.099 
1.107 
1.115 
1.124 
1.133 
1 142 


■ Y.666" 
0.993 
0.986 
0.979 
0.972 
0.966 
0.959 
0.952 
0.946 


19.0 
20.0 
21.0 
22.0 
23.0 
24.0 
25.0 
26.0 
27.0 
28.Q 
29.0 
30.0 
31.0 
32.0 
33 
34.0 
35.0 
36.0 
37.0 


1.151 
1.160 
1.169 
1.179 
1.189 
1.198 
1.208 
1.219 
1.229 
1.239 
1.250 
1.261 
1.272 
1.283 
1.295 
1.306 
1.318 
1.330 
1.343 


0.940 
0.933 
0.927 
0.921 
0.915 
0.909 
0.903 
0.897 
0.892 
0.886 
0.881 
0.875 
0.870 
0.864 
0859 
0.854 
0.849 
0.843 
0.838 


38.0 
39.0 
40.0 
41 
42.0 
44.0 
46.0 
48.0 
50.0 
52.0 
54.0 
56.0 
58.0 
60.0 
65.0 
70.0 
75.0 


1.355 
1.368 
1.381 
1 394 
1 .408 
1.436 
1.465 
1.495 
1.526 
1.559 
1.593 
1.629 
1.667 
1.706 
1.813 
1.933 
2.071 


0.833 
0.828 
0.824 
0.819 
0.814 
0.805 
0.796 
0.787 
0.778 
0.769 
761 
0.753 
0.745 
0.737 
0.718 
0.700 
0.683 


18.0 

















176 



MATERIALS. 



Specific Gravity and Weight of Gases at Atmospheric ^Pressure 

and 3^r. 

(For other temperatures and pressures see Physical Properties of Gases.) 





Density, 


Density, 


Grammes 


Lbs. per 


Cubic Ft. 




Air = 1. 


H = I. 


per Litre. 


Cu. Ft. 


per Lb. 


Air , 


1 .0000 
1.1052 
0.0692 
0.9701 
0.9671 


14.444 
15.963 
1.000 
14.012 
n.968 


1.2931 
1.4291 
0.0895 
1.2544 
1.2505 


0.080728 

0.08921 

0.00559 

0.07831 

0.07807 


12 388 


Oxygen, 


1 1 209 


Hydroo"en, H 


178 931 


Nitrogen, N 


12 770 


Carbon monoxide, CO . 


12.810 


Carbon dioxide, CO2 . . 


1.5197 


21.950 


1 .9650 


0.12267 


8.152 


Methane,marsh-gas, CH4 


0.5530 


7.987 


0.7150 


0.04464 


22.429 


Ethylene, C2H4... 


0.9674 


13.973 


1.2510 


0.07809 


12.805 


Acetylene, C2H2 


0.8982 


12.973 


1.1614 


0.07251 


13.792 


Ammonia, NH3. , 


0.5889 


8.506 


0.7615 


0.04754 


21.036 


Water vapor, H2O . . . . 
Sulphur dioxide, SO2 . . 


C.6218 


8.981 


0.8041 


0.05020 


19.922 


2.213 


31.965 


2.862 


0.1787 


5.597 



Specific Gravity and Weight of Wood, 









- 








. 




Specific 




1^4 

^ )i 




Specific 








Gravity 








Gravity 








Avge- 






Avge. 




Alder 


0.56 to 0.80 


0.68 


42 


Hornbeam, . 


0.76 


0.76 


47 


Apple 


0.73 to 0.79 


0.76 


47 


Juniper .... 


0.56 


0.56 


35 


Ash 


0.60 to 0.84 


0.72 


45 


Larch. ..... 


0.56 


0.56 


35 


Bamboo .... 


0.31 to 0.40 


0.35 


22 


Lignum vita? 


0.65 to 1.33 


1.00 


62 


Beech 


0.62 to 0.85 


0.73 


46 


Linden . , . 


0.604 




37 


Birch 


0.56 to 0.74 


0.65 


41 


Locust 


0.728 




46 


Box 


0.91 to 1.33 


1.12 


70 


Mahogany. . 


0.56 to 1.06 


0.81 


51 


Cedar 


0.49 to 0.75 


0.62 


39 


Maple 


0.57 to 0.79 


0.68 


42 


Cherry 


0.61 to 0.72 


0.66 


41 


Mulberry. . . 


0.56 to 0.90 


0.73 


46 


Chestnut 


0.46 to 0.66 


0.56 


35 


Oak, Live . . 


0.96 to 1 .26 


1.11 


69 


Cork 


0.24 


0.24 


15 


Oak, White. 


69 to 0.86 


0.77 


48 


Cypress 


0.41 to 0.66 


053 


33 


Oak, Red . . 


0.73 to 0.75 


0.74 


46 


Dogwood . . 


0.76 


0.76 


47 


Pine, \Miite 


0.35 to 0.55 


0.45 


28 


Ebony 


1.13 to 1.33 


1.23 


76 


" Yellow 


0.46 to 0.76 


0.61 


38 


Elm 


0.55 to 0.78 


0.61 


3S 


Poplar 


0.38 to 0.58 


0.48 


30 


Fir , . . 


0.48 to 0.70 


0.59 


37 


Spruce 


0.40 to 0.50 


0.45 


28 


Gum 


0.84 to 1 .00 


0.92 


57 


Sycamore . . 


0.59 to 0.62 


0.60 


37 


Hackmatack 


0.59 


0.59 


37 


Teak 


0.66 to 0.98 


0.82 


51 


Hemlock. . . . 


0.36 to 0.41 


0.38 


24 


Walnut .... 


0.50 to 0.67 


0.58 


36 


Hickory . 


0.69 to 0.94 


0.77 


48 


Willow .... 


0.49 to 0.59 


0.54 


34 


Holly 


0.76 


0.76 


47 











PROPEKTIES OF THE USEFUL METALS. 



177 



Weight and Specific Gravity of Stones, Brick, Cement, etc. 
Water = 1.00.) 



(Pure 





Lb. per Cu. Ft. 


Sp. Gr. 


Ashes 


43 

87 
100 
112 
125 
135 

140 to 150 
136 
100 
112 

92 
115 

120 to 150 

120 to 155 

72 to 80 

90 to 110 

250 

156 to 172 
180 to 196 

160 to 170 

100 to 120 
130 to 150 
200 to 220 

55 to 57 

50 to 60 
140 to 185 
150 

160 to 180 
140 to 160 
140 to 180 
175 

90 to 100 
104 to 120 

72 

93 to 113 
165 

90 to 110 
118 to 129 
140 to 150 
170 to 180 
166 to 175 
135 to 200 
100 

110 to 120 
170 to 200 




Asphaltum 

Brick, Soft 


1.39 
1 .6 


" Common . . . . , 

" Hard 

" Pressed 

** Fire 


1.79 

2.0 

2.16 

2.24 to 2.4 


" Sand-lime 

Brickwork in mortar 


2.18 
1.6 


** cement 

Cement, American, natural 

Portland 

" " loose 


1.79 

2.8 to 3.2 

3.05 to 3. 15 


" " in barrel 




Clay 

Concrete 

Earth, loose 


1.92 to 2. 4 
1.92 to 2.48 
1.15 to 1.28 


ranSned 

Emery 

Glass 

" flint 

Gneiss i 


1.44 to 1.76 

4. 

2.5 to 2.75 

2.88to3.14 

2.56 to 2.72 


Granite \ 

Gravel • 


1.6 to 1 .92 


Gypsum 

Hornblende 

Ice 

Lime, quick, in bulk 

Limestone 

Magnesia, Carbonate 

Marble 

Masonry, dry rubble 


2.08 to 2.4 
3.2 to 3.52 
0.88 to 0.92 
0.8 to 0.96 
2.30 to 2.90 
2.4 

2.56 to 2.88 
2.24 to 2.56 


" dressed 

Mica 

Mortar 

Mud, soft flowing 


2.24 to 2.88 

2.80 

1 .44 to 1.6 

1 .67 to 1 .92 


Pitch 


1.15 

1 .50 to 1 .81 


Sand 

" wet 

Sandstone 


2.64 

1.44 to 1.76 
1.89 to 2. 07 
2.24 to 2.4 


Slate 

Soapstone 


2.72 to 2.88 
2.65 to 2.8 


Stone, various 

" crushed 


2.16to 3.4 


Tile 

Trap Rock 


1.76 to 1.92 
2.72 to3. 4 



PROPERTIES OF THE USEFUL METALS. 

Aluminum, Al. — Atomic weight 27.1. Specific gravity 2.6 to 2.7. 
The Ughtest of all the u.seful metals except magnesium. A soft, ductile, 
malleable metal, of a w^liite color, approaching silver, but with a bluish 
cast. Very non-corrosive. Tenacity about one-third that of wrought 
iron. Formerly a rare metal, but since 1890 its production and use 
have greatly increased on account of the discovery of cheap processes 
for reducing it from the ore. Melts at 1215° F. For further description 
see Aluminum, under Strength of Materials, page 380. 

Antimony (Stibium), Sb. — At. wt. 120.2 Sp. gr. 6.7 to 6.8. A 
brittle metal of a bluish-white color and highly crystaline or laminated 
structure. Melts at 842° F. Heated in the open air it bums with a 



178 3VIATEBIALS. 

bluish-white flame. Its chief use is for the manufacture of certain alloys, 
as type-metal (antimony 1, lead 4), britannia (antimony 1, tin 9), and 
various anti-friction metals (see Alloys). Cubical expansion by heat 
from 32° to 212° F., 0.0070. Specific heat 0.050. 

Bismuth, Bi. — At. wt. 208.5. Bismuth is of a peculiar light reddish 
color, highly crystalUne, and so brittle that it can readily be pulverized. 
It melts at 510° F., and boils at about 2300° F. Sp. gr. 9.823 at 54° F., 
and 10.055 just above the melting-point. Specific heat about 0.0301 at 
ordinary temperatures. Coefficient of cubical expansion from 32° to 
212°, 0.0040. Conductivity for heat about i/se and for electricity only 
about 1/80 of that of silver. Its tensile strength is about 6400 lbs. per 
square inch. Bismuth expands in cooling, and Tribe has shov/n that 
this expansion does not take place until after solidification. Bismuth is 
the most diamagnetic element known, a sphere of it being repelled by a 
magnet. 

Cadmium, Cd. — At. wt. 112.4. Sp. gr. 8.6 to 8.7. A bluish-white 
metal, lustrous, with a fibrous fracture. Melts below 500° F. and vola- 
tilizes at about 680° F. It is used as an ingredient in some fusible alloys 
with lead, tin, and bismuth. Cubical expansion from 32° to 212° F., 
0.0094. 

Copper, Cu. — At. wt. 63.6. Sp. gr. 8.81 to 8.95. Fuses at about 
1930° F. Distinguished from all other metals by its reddish color. Very 
ductile and malleable, and its tenacity is next to iron. Tensire strength 
20,000 to 30,000 lbs. per square inch. Heat conductivity 73.6% of that 
of silver, and superior to that of other metals. Electric conductivity 
equal to that of gold and silver. Expansion by heat from 32° to 212° F., 
0.0051 of its volume. Specific heat 0.093. (See Copper under Strength 
of Materials; also Alloys.) 

Gold (Aurum), Au. — At. wt. 197.2. Sp. gr., when 'pure and pressed 
in a die, 19.34. Melts at about 1915° F. The most malleable and duc- 
tile of all metals. One ounce Troy may be beaten so as to cover 160 sq. 
ft. of surface. The average thickness of gold-leaf is V282000 of an inch, 
or 100 sq. ft. per ounce. One grain may be drawn into a wire 500 ft. in 
length. The ductiUty is destroyed by the presence of V2000 part of lead, 
bismuth, or antimony. Gold is hardened by the addition of silver or of 
copper. U. S. gold coin is 90 parts gold and 10 parts alloy, which is 
chiefly copper with a little silver. By jewelers the flneness of gold is 
expressed in carats, pure gold being 24 carats, three-fourths fine 18 
carats, etc. 

Iridium, Ir. — Iridium is one of the rarer metals. It has a white 
lustre, resembling that of steel; its hardness is about equal to that of the 
ruby; in the cold it is quite brittle, but at white heat it is somewhat 
malleable. It is one of the heaviest of metals, having a specific gravity 
of 22.38. It is extremely infusible and almost absolutely inoxidizable. 

For uses of iridium, methods of manufacturing it, etc., see paper by 
W. L. Dudley on the "Iridium Industry," Trans. A. I. M. E., 1884. 

Iron (Ferrum),Fe. — At. wt. 55.9. Sp.gr.: Cast, 6.85 to 7.48; Wrought, 
7.4 to 7.9. Pure iron is extremely infusible, its melting point being above 
3000° F., but its fusibility increases with the addition of carbon, cast 
iron fusing about 2500° F. Conductivity for heat 11.9, and for electricity 
12 to 14.8, silver being 100. Expansion in bulk by heat: cast iron 
0.0033, and wrought iron 0.0035. from 32° to 212° F. Specific heat: 
cast iron 0.1298, wrought iron 0.il38, steel 0.1165. Cast iron exposed 
to continued heat becomes permanently expanded 1 1/2 to 3 per cent of its 
length. Grate-bars should therefore be aUowed about 4 per cent play. 
(For other properties see Iron and Steel under Strength of Materials.) 

Lead (Plumbum), Pb. — At. wt. 206.9. Sp. gr. 11.07 to 11.44 bv dif- 
ferent authorities. Melts at about 625° F., softens and becomes pasty 
at about 617° F. If broken by a sudden blow when just below the 
melting-point it is quite brittle and the fracture appears crystalline. 
Lead is very malleable and ductile, but its tenacity is such that it can 
be drawn into wire with great difficulty. Tensile strength, 1600 to 
2400 lbs. per square inch. Its elasticity is very low, and the metal 
flows under very slight strain. Lead dissolves to some extent in pure 
water, but water containing carbonates or sulphates forms over it a 
film of insoluble ^:L.lt which prevents further action. 



PROPERTIES OF THE USEFUL METALS. 179 

Magnesium, 3Ig. — At. wt. 24.36. Sp. gv. 1.69 to 1.75. Silver-white, 
brilliant, malleable, and ductile. It is one of the lightest of metals, 
weighing only about two thirds as much as aluminum. In the form of 
fiUngs, wire, or thin ribbons it is highly combustible, burning with a 
light of dazzling brilliancy, useful for signal-lights and for flash-lights 
for photographers. It is nearly non-corrosive, a thin film of carbonate 
of magnesia forming on exposure to dam.p air, which protects it from 
further corrosion. It may be alloyed with aluminum, 5 per cent Mg 
added to Al giving about as much increase of strength and hardness as 
10 per cent of copper. Cubical expansion by heat 0.0083, from 32° to 
212° F. Melts at 1200° F. Specific heat 0.25. 

Manganese, 3In. — At. wt. 55. Sp. gr. 7 to 8. The pure metal is not 
used in the arts, but alloys of manganese and iron, called spiegeleisen 
when containing below 25 per cent of manganese, and ferro-manganese 
when containing from 25 to 90 per cent, are used in the manufacture of 
steel. Metallic manganese, when alloyed with iron, oxidizes rapidly in 
the air, and its function in steel manufacture is to remove the oxygen 
from the bath of steel whether it exists as oxide of iron or as occluded 
gas. 

Mercury (Hydrargyrum), Hg. — At. wt. 199.8. A silver-w^hite metal, 
liquid at temperatures above — 39° F., and boils at 680° F. Unchange- 
able as gold, silver, and platinum in the atmosphere at ordinary tem- 
peratures, feut oxidizes to the red oxide when near its boiling-point. 
Sp. gr.: when liquid 13.58 to 13.59, when frozen 14.4 to 14.5. Easily 
tarnished by sulphur fumes, also by dust, from which it may be freed 
by straining through a cloth. No metal except iron or platinum should 
be allowed to touch mercury. The smallest portions of tin, lead, zinc, 
and even copper to a less extent, cause it to tarnish and lose its perfect 
liquidity. Coefficient of cubical expansion from 32° to 212° F. 0.0182; 
per deg. 0.000101. 

Nickel, Ni. — At. wt. 58.7. Sp. gr. 8.27 to 8.93. A silvery-white 
metal with a strong lustre, not tarnishing on exposure to the air. Duc- 
tile, hard, and as tenacious as iron. It is attracted to the magnet and 
may be made magnetic like iron. Nickel is very difficult of fusion, melt- 
ing at about 3000° F. Chiefly used in alloys with copper, as german- 
silver, nickel-silver, etc., and also in the manufacture of steel to increase 
its hardness and strength, also for nickel-plating. Cubical expansion 
from 32° to 212° F., 0.0038. Specific heat 0.109. 

Platinum, Pt. — At. wt. 194.8. A whitish steel-gray metal, malleable, 
very ductile, and as unalterable by ordinary agencies as gold. When 
fused and refined it is as soft as copper. Sp. gr. 21.15. It is fusible only 
by the oxyhydrogen blowpipe or in strong electric currents. When com- 
bined with iridium it forms an alloy of great hardness, which has been 
used for gun-vents and for standard weights and measures. The most 
important uses of platinum in the arts are for vessels for chemical labo- 
ratories and manufactories, and for the connecting wires in incandescent 
electric lamps and for electrical contact points. Cubical expansion from 
32° to 212° F., 0.0027, less than that of any other metal except the rare 
metals, and almost the same as glass. 

Silver (Argentum), Ag. — At. w^t. 107.9. Sp. gr. 10.1 to 11.1, accord- 
ing to condition and purity. It is the w^hitest of the metals, very malle- 
able and ductile, and in hardness intermediate between gold and copper. 
Melts at about 1750° F. Specific heat 0.056. Cubical expansion from 
32° to 212° F., 0.0058. As a conductor of electricity it is equal to copper. 
As a conductor of heat it is superior to all other metals. 

Tin (Stannum), Sn. — At. wt. 119. Sp. gr. 7.293. White, lustrous, 
soft, malleable, of little strength, tenacity about 3500 lbs. per square 
inch. Fuses at 442° F. Not sensibly volatile wiien melted at ordinary 
heats. Heat conductivitv 14.5, electric conductivity 12.4; silver being 
100 in each case. Expansion of volume bv heat 0.0069 from 32° to 212° F. 
Specific heat 0.055. Its chief uses are for coating of sheet-iron (called 
tin plate) and for making alloys with copper and other metals. 

Zinc, Zn.— At. wt. 65.4. Sp. gr. 7.14. Melts at 780° F. Volatilizes 
and burns in the air when melted, with bluish- white fumes of zinc oxide. 
It is ductile and malleable, but to a much less extent than copper, and 



180 



MATERIALS, 



its tenacity, about 5000 to 6000 lbs. per square inch, is about one tenth 
that of wrought iron. It is practically non-corrosive in the atmosphere, 
a thin film of carbonate of zinc forming upon it. Cubical expansion 
between 32° and 212° F., 0.0088. Specific heat 0.096. Electric conduc- 
tivity 29, heat conductivity 36, silver being 100. Its principal uses are 
for coating iron surfaces, called "galvanizing," and for making brass and 
other alloys. 

Table Showing the Order of 



Malleability. 


Ductility. 


Tenacity. 


Infusibility, 


Gold 


Platinum 


Iron 


Platinum 


Silver 


Silver 


Copper 


Iron 


Aluminum 


Iron 


Aluminum 


Copper 
Gold 


Copper 


Copper 


Platinum 


Tin 


Gold 


Silver 


Silver 


Lead 


Aluminum 


Zinc 


Aluminum 


Zinc 


Zinc 


Gold 


Zinc 


Platinum 


Tin 


Tin 


Lead 


Iron 


Lead 


Lead 


Tin 



MEASURES AND WEIGHTS OF VARIOUS MATERIALS 
(APPROXIMATE). 

Brickwork. — Brickwork, is estimated by the thousand, and for 
various thicknesses of wall runs as follov/s: 

8V4-in. wall, or 1 brick in thickness, 14 bricks per superficial foot. 
123/4 " " " 11/2" " *' 21 " 

17 " " " 2 " " " 28 " 

211/2 " " " 21/2 " " *' 35 •• 



An ordinary brick measures about 81/^X4 X 2 inches, which is equal 
to 66 cubic inches, or 26.2 bricks to a cubic foot. The average weight is 
4 1/2 lbs. 

Fuel. — A bushel of bituminous coal w^eighs 76 pounds and contains 
2688 cubic inches = 1.554 cubic feet. 29.47 bushels = 1 gross ton. 

One acre of bituminous coal contains 1600 tons of 2240 pounds per 
foot of thickness of coal worked. 15 to 25 per cent must be deducted for 
waste in mining. 

41 to 45 cubic feet bituminous coal when broken dowm = 1 ton, 2240 lbs. 

34 to 41 " " anthracite prepared for market ... =1 ton, 2240 lbs. 

123 ' ** of charcoal =1 ton, 2240 lbs. 

70.9 " " " coke =1 ton, 2240 lbs. 

1 cubic foot of anthracite coal = 55 to 66 lbs. 

I " " " bituminous coal = 50 to 55 lbs. 

1 " " Cumberland (semi-bituminous) coal = 53 lbs. 

I " " Cannel coal = 50.3 lbs. 

1 " " Charcoal (hardwood) = 18.5 lbs. 

1 '* " " (pine) =18 lbs. 

A bushel of coke weighs 40 pounds (35 to 42 pounds). 

A bushel of charcoal. — In 1881 the American Charcoal-Iron Work- 
ers' Association adopted for use in its official publications for the stand- 
ard bushel of charcoal 2748 cubic inches, or 20 pounds. A ton of char- 
coal is to be taken at 2000 pounds. This figure of 20 pounds to the 
bushel was taken as a fair average of different bushels used throughout 
the country, and it has since been established by law in some States. 

Cement. — Portland, per bbl. net, 376 lbs., per bag, net 94 lbs. 

Natural, per bbl. net, 282 lbs., per bag net 94 lbs. 

Lime. — A struck bushel 72 to 75 lbs. 

Grain. — A struck bushel of wheat = 60 lbs.; of corn = 56 lbs.; of 
oats = 30 lbs. 

Salt. — A struck bushel of salt, coarse, Syracuse, N. Y. = 56 lbs.; 
Tiirk's Island = 76 to 80 lbs. 



MEASURES AND WEIGHTS OF VARIOUS MATERIALS. 181 



Ores, Earths, etc. 

13 cubic feet of ordinary gold or silver ore, in mine = 1 ton = 2000 lbs. 

20 " " " broken quartz =1 ton = 2000 lbs. 

18 feet of gravel in bank =1 ton. 

27 cubic feet of gravel when dry =1 ton. 

25 " " " sand =1 ton. 

18 " " " earth in bank =1 ton. 

27 " " " earth when dry =1 ton. 

17 " " " clay =1 ton. 

Except where otherwise stated, a ton = 2240 lbs. 

WEIGHTS OF LOGS, LUMBER, ETC. 

Weight of Green Logs to Scale 1000 Feet, Board Measure. 

Yellow pine (Southern) 8,000 to lO.OOOlbs. 

Norway pine (Micliigan) 7,000 to 8,000 " 

nrui+^ r^4r,o ^TVT^r.v.^o.or.^ < off of stump 7,000 to 7,000 

White pme (Michigan) ^ ^^^ ^^ ^^^^^ r^ ^^QQ ^^ g qqO 

White pine (Pennsylvania), bark off 5,000 to 6,000 

Hemlock (Pennsylvania), bark off 6,000 to 7,000 

Four acres of water are required to store 1,000,000 feet of logs. 

Weight of 1000 Feet of Lumber, Board Measure. 

Yellow or Norway pine Dry, 3,000 lbs. Green, 5,000 lbs. 

White pine " 2,500 " " 4,000 " 

Weight of 1 Cord of Seasoned Wood, 128 Cu. Ft. per Cord, lbs. 

Hickory or sugar maple. . . . 4,500 f Poplar, chestnut or elm. . . 2,350 

White oak 3,850 j Pine (white or Norway). . . 2,000 

Beech, red oak or black oak . 3,250 J Hemlock bark, dry 2,200 

WEIGHT OF RODS, BARS, PLATES, TUBES, AND SPHERES 
OF DIFFERENT MATERIALS. 

Notation: b = breadth, t = tliickness, s = side of square, D = ex- 
ternal diameter, d = internal diameter, all in inches. 

Sectional areas: of square bars = 52; of flat bars = bt; of round rods 
= 0.7854 D2; of tubes = 0.7854 (D^ _ ^2) = 3.1416 (Dt -P). 

Volume of 1 foot in length: of square bars = 12^2; of flat bars = 12bt\ 
of round bars = 9.4248i)2; of tubes = 9.4248 (£>2 - ^2) = 37.699 
{Dt —t'), in cu. in. 

Weight per foot length = volume + w^eight per cubic inch of mate- 
rial. Weight of a sphere = diam.^ x 0.5236 X w^eight per cubic inch. 



Material. 



Cast iron 

Wrought iron 

Steel 

Copper & Bronze 1 
(copper and tin) J 

I3rassj35 2;inc... j 

Lead. 

Aluminum 

Glass 

Pine wood, dry . . . 







w a; • 




CO 




03 




>» 


. 




^ '^A 




3 
. 




£^0 




u-^ 


^•^J 


u gJ 


V, 4J 


^-^ 


^§.4 


%f 


%.^ 


=ge 


^^H 


-1. 


%r^^ 




^f§T3 




i^ 


r-^ 


^ oW 


r- 










62 X 


htx 






2)2 X 


7.21£ 


450. 


37.5 


31/8 


31/8 


.2604 


15-16 


2.454 


7.7 


450. 


40. 


31/3 


31/3 


.2779 


I. 


2.618 


7.854 


4S9.6 


40.8 


3.4 


3.4 


.2833 


1.02 


2.670 


8.855 


552. 


46. 


3.833 


3.833 


.3195 


1.15 


3.011 


8.393 


523.2 


43.6 


3.633 


3.633 


.3029 


1.09 


2.854 


11.33 


709,6 


59.1 


4.93 


4.93 


.4106 


1.48 


3.870 


2.67 


166.5 


13.9 


1.16 


1.16 


.0963 


0.347 


0.908 


2.62 


163.4 


13.6 


1.13 


1.13 


.0945 


0.34 


0.891 


0.481 


30.0 


2.5 


0.21 


0.21 


.0174 


1-16 


0.164 



.1363 
.1455 
.1484 

.1673 

.1586 

.2150 
.0504 
.0495 
.0091 



Weight per cylindrical in«, 
last col. -^12. 



1 in. long, = coeflacient of D^ jn next to 



182 MATERIALS. 

For tubes use the coeflacient of Z)2 jn next to last column, as for rods, 
and multiply it into (Z)2 - d^) ; or multiply it by 4 (Dt - t'^). 

For hollow spheres use the coefficient of D^ in the last column and 
multiply it into (1)3 — d^). 

For hexagons multiply the weight of square bars by 0.866 (short 
diam. of hexagon = side of square). For octagons multiply by 0.8284. 

COMMERCIAL SIZES OF MERCHANT IRON AND STEEL 

BARS. 

Steel Bars. 

Flats, Square Edge. — s/g to 3 in. wide, by any thickness from 
1/8 in. up to width; 3 to 5 in. wide by any thickness 1/4 to 3 in. 
inclusive; 5 to 7 in. wide, by any thickness, 1/4 to 2 in. inclusive. 

Flats, Band Edge. — Thicknesses are in B. W. G., s/g in. wide by 
No. 18 to No. 4. 7/16 in. by No. 19 to No. 4. 1/2 in. by No. 22 to No. 
4. 9/16 to 1 in. by No. 23 to No. 4. 1 i/ie to 2 in. by No. 22 to No, 4. 
21/16 to 3 in. by No. 21 to No. 1. 39/i6to 4 in. by No. 19 to No. 1. 
4 1/16 to 41/2 in. by No. 18 to No. 1. 49/i6 to 5 Vie in. by No. 17 to No. 1. 
51/8 to 6 3/4 in. by No. 16 to No. 1. 7 in., 7 1/4 in., 7 1/2 in., 7 5/8 in., 7 3/4 in., 
77/8 in., 8 in., 8 1/4 in., 8 1/2 in., 85/8 in., each by No. 14 to No. 1. 9 5/8 
in. by No. 12 to No. 1. 

Squares. — Widths across faces: 3/i6 to 2 in., advancing by 1/64 in. ; 
21/32 to 3 1/2 in., advancing by 1/32 in.; 3 9/i6 to 51/2 in., advancing by 
1/16 in. 

Round-cornered Squares. — 1/4 to 3/4 in., across faces, advancing 
by 1/64 in. 

Rounds. — Diameters: 7/32 to 13/4 in., inclusive, advancing by 1/64 
in.; 1 25/32 in. to 31.2 in. inclusive, advancing by 1/32; 3 9/i6 to 7 in., 
inclusive, advancing by Vie in. 

Half Rounds. — Diameters: 5/i6 to 7/8 in., inclusive, advancing by 
1/64 in. ; 15/16 to 1 3/4 in ., advancing by 1/16 in. ; 2 in. ; 2 1/2 in. ; 3 in. 

Hexagons. — Width across faces: 1/4 to 13/i6 in., inclusive, advanc- 
ing by 1/32 in.; 1 1/4 in. to 3 Vie in., advancing by 1/16 in. 

Iron Bars. 

Round. — V16 to 1 7/s5 in., advancing by V32 in.; 1 IV16 to 2 V4 in., advancing 
by V16 in.; 2 ^/g to 3 V4 in., advancing by Vs in.; 4 to 5 in., advancing by 
1/4 in. 

Squares. — Vie to Vs in.* advancing by 1/32 in.; n/ie in. to 1 in., advancing 
by V16 in.; 1 Vs in. to 2 V2 in., advancing by Vs in.; 2 V4 in. to 4 1/2 in., ad- 
vancing by 1/4 in. 

Half Rounds.— 3/8, Vie, V2, Vs, Wie, V4, Vs, 1, 1 Vs, 1 V4, 1 Vs, 1 V2, 
1 V4, 2 in. 

Ovals.— 1/2 X 1/4, 5/8 X 5/16, 3/4 X 3/8 and 7/8 X 7/i6 in. 

Half Ovals.— V2 X Vie, Vs X Vie, Vi X Vie, Vs X Vie, 1 X Vie, 
V4 X V4, Vs X V4, 1 X V4, 1 Vs X V4, 1 X Vie, 1 Vs X Vie, 1 V4 X Vie, 
1 X Vs, 1 Vs X ^8* 1 V4 X Vs, 1 V2 X Vs, 1 V4 X V2, 2 X Vs in. 

Flats.— V2 X Vie to Vs in.; Vs X Vie to V2 in.; V4 X Vie to Vs in.; 
Vs X Vie to V4 in.; 1 X Vie to Vs in.; 1 Vie X V4 to Vs in.; 1 Vs X Vie to 
1 in.; 1 V4 X Vie to 1 in.; 1 Vs X Vie to 1 Vs in.; 1 V2 X Vie to 1 1/4 in.; 

1 Vs X V4 to 1 V2 in.; 1 V4 X Vie to 1 V2 in.; 1 Vs X V4 to 1 V2 in.; 2 X V16 
to 1 V4 in.; 2 Vs X V4 to 1 V4 in.; 2 V4 X Vie to 2 in.; 2 Vs X V4 to 1 3/4 in.; 

2 V2 X Vie to 2 V4 in.; 2 Vs X V4 to 2 V4 in.; 2 V4 X Vie to 2 1/2 in.; 
2 7/8 X Vs to 1/2 in.; 2 Vs X Vs to 2 V4 in.; 3 X Vie to 2 V4 in.; 3 Vs X 1 V2 
to 2V8 in.; 3 V4 X V4 to 23/4 in.; 3 1/2 X Vu to 2 t/s in.; 3 3/4 x V4 to 3 in.; 
4 X V4 to 3 in.; 4 V4 X V4 to 2 in.; 4 1/2 X V4 to 2 V2 in.; 4 3/4 x V4 to 2 
in.; 5 X V4 to 2 3/4 in.; 5 V2 X V4 to 2 in.; 6 X V4 to 2 in.; 6 V2 X V4 to 
1 in.; 7 X 1/4 to 2 in.; 7 V2 X V4 to 1 in.; 8 X V4 to 2 in. 

Round Edge Flats.— 1 to 2 in. wide by 1/4 to 1 1/4 in. thick; 2 1/4 to 
4 V2 in. wide by s/g to 1 V4 in. thick. 



WEIGHT OF IRON AND STEEL SHEETS. 



183 



WEIGHT OF IRON AND STEEL SHEETS. 

Weights in Pounds per Square Foot. 

(For weights by the Decimal Gauge, see page 33.) 



Thickness by Birmingham 


Gauge. 


U.S. Standard Gauge, 1893. 
p. 32.) 


(See 


No. of 
Gauge. 


Thick- 
ness in 
Inches. 


Iron. 


Steel. 


No. of 
Gauge. 


Thick- 
ness, In. 
(Approx.) 


Iron. 


Steel. 


0000 


0.454 


18.16 


18.52 


0000000 


0.5 


20. 


20.40 


000 


.425 


17.00 


17.34 


000000 


0.4688 


18.75 


19.125 


00 


.38 


15.20 


15.50 


OUOOO 


0.4375 


17.50 


17.85 





.34 


13.60 


13.87 


0000 


0.4063 


16.25 


16.575 


1 


.3 


12.00 


12.24 


000 


0.375 


15. 


15.30 


2 


.284 


11.36 


11.59 


00 


0.3438 


13.75 


14.025 


3 


.259 


10.36 


10.57 





0.3125 


12.50 


12.75 


4 


.238 


9.52 


9.71 


1 


0.2813 


11.25 


11.475 


5 


.22 


8.80 


8.98 


2 


0.2656 


10.625 


10.837 


6 


.203 


8.12 


8.28 


3 


0.25 


10. 


10.20 


7 


.18 


7.20 


7.34 


4 


0.2344 


9.375 


9.562 


8 


.165 


6.60 


6.73 


5 


0.2188 


8.75 


8.923 


9 


.148 


5.92 


6.04 


6 


0.2031 


8.125 


8.287 


10 


.134 


5.36 


5.47 


7 


0.1875 


7.5 


7.65 


11 


.12 


4.80 


4.90 


8 


0.1719 


6.875 


7.012 


12 


.109 


4.36 


4.45 


9 


0.1563 


6.25 


6.375 


13 


.095 


3.80 


3.88 


10 


0.1405 


5.625 


5.737 


14 


.083 


3.32 


3.39 


11 


0.125 


5. 


5.10 


15 


.072 


2.88 


2.94 


12 


0.1094 


4.375 


4.462 


16 


.065 


2.60 


2.65 


13 


0.0938 


3.75 


3.825 


17 


.058 


2.32 


2.37 


14 


0.0781 


3.125 


3.187 


18 


.049 


1.96 


2.00 


15 


0.0703 


2.8125 


2.869 


19 


.042 


1.68 


1.71 


16 


0.0625 


2.5 


2.55 


20 


.035 


1.40 


1.43 


17 


0.0563 


2.25 


2.295 


21 


.032 


1.28 


1.31 


18 


0.05 


2. 


2.04 


22 


.028 


1.12 


1.14 


19 


0.0438 


1.75 


1.785 


23 


.025 


1.00 


1.02 


20 


0.0375 


1.50 


1.53 


24 


.022 


.88 


.898 


21 


0.0344 


1.375 


1.402 


25 


.02 


.80 


.816 


22 


0.0312 


1.25 


1.275 


26 


.018 


.72 


.734 


23 


0.0281 


1.125 


1.147 


27 


.016 


.64 


.653 


24 


0.025 


1 


1.02 


28 


.014 


.56 


.571 


23 


0.0219 


o:875 


0.892 


29 


.013 


.52 


.530 


26 


0.0188 


0.75 


0.765 


30 


.012 


.48 


.490 


27 


0.0172 


0.6875 


0.701 


31 


.01 


.40 


.408 


28 


0.0156 


0.625 


0.637 


32 


.009 


.36 


.367 


29 


0.0141 


0.5625 


0.574 


33 


.008 


.32 


.326 


30 


0.0125 


0.5 


0.51 


34 


.007 


.28 


.286 


31 


0.0109 


0.4375 


0.446 


35 


.005 


.20 


.204 


32 


0.0102 


0.40625 


0.414 


36 


.004 


.16 


.163 


33 


0.0094 


0.375 


0.382 










34 


0.0086 


0.34375 


0.351 










35 


0.0078 


0.3125 


0.319 










36 


0.0070 


0.28125 


0.287 










37 


0.0066 


0.26562 


0.271 










38 


0.0063 


0.25 


0.255 



Iron. Steel. 

Specific gravity 7.7 7.854 

Weight per cubic foot 480. 489.6 

Weight per cubic inch 0.2778 0.2833 

As there are many gauges in use differing from each other, and even the 
thicknesses of a certain specified gauge, as the Birmingham, are not assumed 
the same by all manufacturers, orders for sheets and wires should always 
state the weight per square foot, or the thickness in thousandths of an inch. 



184 



MATERIALS. 



WEIGHTS OF SQUARE AND ROUND BARS OF WROUGHT 
IRON IN POUNDS PER LINEAL FOOT. 

Iron weighing 480 lb. per cubic foot. For steel add 2 per cent. 



ill 


m 


tof 
Bar 
ong. 


hi 


tof 
Bar 
ong. 


tof 
Bar 
ong. 




tof 
Bar 
.ong. 


tof 
Bar 
ong. 




*53 S;*^ 


w 


c a « 






^.-^ 


0) zi-*^ 


|b.s 


^i- 


^1- 


|Q.2 


^^^ 


^S^ 


|a.s 


■^i^ 


>.s^ 









11/16 


24.08 


18.91 


3/8 


96.30 


75.64 


Vl6 


0.013 


0.010 


3/4 


25.21 


19.80 


7/16 


98.55 


77.40 


1/8 


.052 


.041 


^3/16 


26.37 


20.71 


1 ' 

1/2 


100.8 


79.19 


3/16 


.117 


.092 


7/8 


27.55 


21.64 


/I6 


103.1 


81.00 


1/4 


.208 


.164 


15/16 


28.76 


22.59 


5/8 


105.5 


82.83 


5/16 


.326 


.256 


3 


30.00 


23.56 


11/16 


107.8 


84.69 


3/8 


.469 


.368 


1/16 


31.26 


24.55 


3/4 


110.2 


86.56 


7/16 


.638 


.501 


1/8 


32.55 


25.57 


13/16 


112.6 


88.45 


72 


.833 


.654 


3/16 


33.87 


26.60 


7/8 


115.1 


90.36 


9/16 


1.055 


.828 


1/4 


35.21 


27.65 


15/16 


117.5 


92.29 


5/8 


1.302 


1.023 


5/16 


36.58 


28.73 


6 


120.0 


94.25 


11/16 


1.576 


1.237 


3/8 


37.97 


29.82 


1/8 


125.1 


98.22 


3/4 


1.875 


1.473 


7/16 


39.39 


30.94 


1/4 


130.2 


102.3 


13/16 


2.201 


1.728 


1/2 


40.83 


32.07 


3/8 


135.5 


106.4 


7/8 


2.552 


2.004 


9/16 


42.30 


33.23 


1/2 


140.8 


110.6 


15/16 


2.930 


2.301 


5/8 


43.80 


34.40 


5/8 


146.3 


114.9 


1 


3.333 


2.618 


11/16 


45.33 


35.60 


3/4 


151.9 


119.3 


1/16 


3.763 


2.955 


3/4 


46.88 


36.82 


7/8 


157.6 


123.7 


1/8 


4.219 


3.313 


13/16 


48.45 


38.05 


7 


163.3 


128.3 


3/16 


4.701 


3.692 


7/8 


50.05 


39.31 


1/8 


169.2 


132.9 


1/4 


5.208 


4.091 


15/16 


51.68 


40.59 


1/4 


175.2 


137.6 


5/16 


5.742 


4.510 


4 


53.33 


41.89 


3/8 


181.3 


142.4 


3/8 


6.302 


4.950 


1/16 


55.01 


43.21 


1/2 


187.5 


147.3 


7/16 


6.888 


5.410 


1/8 


56.72 


44.55 


5/8 


193.8 


152.2 


1/2 


7.500 


5.890 


3/16 


58.45 


45.91 


3/4 


200.2 


157.2 


9/16 


8.138 


6.392 


1/4 


60.21 


47.29 


7/8 


206.7 


162.4 


5/8 


8.802 


6.913 


5/l6 


61.99 


48.69 


8 


213.3 


167.6 


11/16 


9.492 


7.455 


3/8 


63.80 


50.11 


1/4 


226.9 


178.2 


3/4 


10.21 


8.018 


7/16 


65.64 


51.55 


1/9 


240.8 


189.2 


13/16 


10.95 


8.601 


1/2 


67.50 


53.01 


3/4 


255.2 


200.4 


7/8 


11.72 


9.204 


9/16 


69.39 


54.50 


9 


270.0 


212.1 


15/16 


12.51 


9.828 


5/8 


71.30 


56.00 


1/4 


285.2 


224.0 


2 


13.33 


10.47 


11/16 


73.24 


57.52 


1/2 


300.8 


236.3 


1/16 


14.18 


11.14 


3/4 


75.21 


59.07 


3/4 


316.9 


248.9 


1/8 


15.05 


11.82 


13/16 


77.20 


60.63 


10 


333.3 


261.8 


3/16 


15.95 


12.53 


7/8 


79.22 


62.22 


1/4 


350.2 


275.1 


1/4 


16.88 


13.25 


15/16 


81.26 


63.82 


1/2 


367.5 


288.6 


5/16 


17.83 


14.00 


5 


83.33 


65.45 


3/4 


385.2 


302.5 


?(« 


18.80 


14.77 


1/16 


85.43 


67.10 


11 


403.3 


3168 


7/16 


19.80 


15.55 


1^8 


87.55 


68.76 


1/4 


421.9 


331.3 


1/2 


20.83 


16.36 


3/16 


89.70 


70.45 


1/2 


440.8 


346.2 


9/16 


21.89 


17.19 


1/4 


91.88 


72.16 


3/4 


460.2 


361.4 


5/8 


22.97 


18.04 


5/16 


94.08 


73.89 


12 


480. 


377. 



WEIGHT OF STEEL BARS. 



185 



WEIGHT 


OF SQUARE 


AND ROUND 


STEEL BARS 


PER LINEAL 




FOOT. (Steel Weighing 489.6 lb. 


per cu. ft.) 




^ »H o5 

S ?i <^ 

III 

'.SQ.S 


Weight of 
Square Bar 
1 Ft. Long. 


1 Weight of 
Round Bar 
1 Ft. Long. 


^ ^ en 

ill 
lis 


Weight of 

Square Bar 

I 1 Ft. Long. 


' Weight of 
Round Bar 
I Ft. Long. 


ill 


Weight of 
Square Bar 
1 Ft. Long. 


Weight of 
Round Bar 
1 Ft. Long. 









11/16 


24.56 


19.29 


3/8 


98.23 


77.15 


1/16 


0.013 


0.010 


3/4 


25.71 


20.20 


7/16 


100.5 


78.95 


1/8 


.053 


.042 


13/16 


26.90 


21.12 


1/2 


102.8 


80.77 


3/16 


.119 


.094 


7/8 


28.10 


22.07 


9/16 


105.2 


82.62 


1/4 


.212 


.167 


15/16 


29.34 


23.03 


5/8 


107.6 


84.49 


5/16 


.333 


.261 


3 


30.60 


24.03 


■ 11/16 


110.0 


86.38 


3/8 


.478 


.375 


1/16 


31.89 


25.04 


3/4 


112.4 


88.29 


7/16 


.651 


.511 


1/8 


33.20 


26.08 


13/16 


114.9 


90.22 


1/2 


.850 


.667 


3/16 


34.55 


27.13 


7/8 


117.4 


92.17 


9/16 


1.076 


.845 


1/4 


35.91 


28.20 


15/16 


119.9 


94.14 


5/8 


1.328 


1.043 


5/16 


37.31 


29.30 


6 


122.4 


96.14 


n/i6 


1.608 


1.262 


3/8 


38.73 


30.42 


1/8 


127.6 


100.2 


3/4 


1.913 


1.502 


7/l6 


40.18 


31.56 


1/4 


132.8 


104.3 


13/16 


2.245 


1.763 


1/2 


41.65 


32.71 


3/8 


138.2 


108.5 


7/8 


2.603 


2.044 


9/16 


43.15 


33.89 


1/2 


143.6 


112.8 


15/16 


2.989 


2.347 


5/8 


44.68 


35.09 


5/8 


149.2 


117.2 


1 


3.400 


2.670 


11/16 


46.24 


36.31 


3/4 


154.9 


121.7 


1/16 


3.838 


3.014 


3/4 


47.82 


37.56 


7/8 


160.8 


126.2 


1/8 


4.303 


3.379 


13/16 


49.42 


38.81 


7 


166.6 


130.9 


3/16 


4.795 


3.766 


7/8* 


51.05 


40.10 


1/8 


172.6 


135.6 


1/4 


5.312 


4.173 


15/16 


52.71 


41 .40 


1/4 


178.7 


140.4 


5/16 


5.857 


4.600 


4 


54.40 


42.73 


3/8 


184.9 


145.2 


3/8 


6.428 


5.049 


1/16 


56.11 


44.07 


1/2 


191.3 


150.2 


7/16 


7.026 


5.518 


1/8 


57.85 


45.44 


5/8 


197.7 


155.2 


1/2 


7.650 


6.008 


3/16 


59.62 


46.83 


3/4 


204.2 


159.3 


9/16 


8.301 


6.520 


1/4 


61 .41 


48.24 


7/8 


210.8 


165.6 


5/8 


8.978 


7.051 


5/16 


63.23 


49.66 


8 


217.6 


171.0 


11/16 


9.682 


7.604 


3/8 


65.08 


51.11 


1/4 


231.4 


181.8 


3/4 


10.41 


8.178 


7/16 


66.95 


52.58 


1/2 


245.6 


193.0 


13/16 


11.17 


8.773 


1/2 


68.85 


54.07 


3/4 


260.3 


204.4 


7/8 


11.95 


9.388 


9/16 


70.78 


55.59 


9 


275.4 


216.3 


15/16 


12.76 


10.02 


5/8 


72.73 


57.12 


1/4 


290.9 


228.5 


2 


13.60 


10.68 


11/16 


74.70 


58.67 


1/2 


306.8 


241.0 


1/16 


14.46 


11.36 


3/4 


76.71 


60.25 


3/4 


323.2 


253.9 


1/8 


15.35 


12.06 


13/16 


78.74 


61.84 


10 


340.0 


267.0 


3/16 


16.27 


12.78 
13.52 


7/8 


80.80 


63.46 


1/4 


357.2 


^80.6 


1/4 


17.22 


15/16 


82.89 


65.10 


1/2 


374.9 


294.4 


5/16 


18.19 


14.28 


5 


85.00 


66.76 


3/4 


392.9 


308.6 


3/8 


19.18 


15.07 


1/16 


87.14 


68.44- 


11 


411.4 


323.1 


7/16 


20.20 


15.86 


1/8 


89.30 


70.14 


1/4 


430.3 


337.9 


1/2 


21.25 


16.69 


3/16 


91.49 


71.86 


1/2 


449.6 


353.1 


9/16 


22.33 


17.53 


1/4 


93 72 


73.60 


3/4 


469.4 


368.6 


5/8 


23.43 


18.40 


5/16 


95.96 


75.37 


12 


489.6 


384.5 



Weight of Fillets. 



Ra- 


Area, 
Sq. In. 


^ Weight per In., Lb. 


Ra- 
dius, 
In. 


Area, 
Sq. In. 


Weight per In., Lb. 


dius, 
In. 


Cast 
Iron. 


Steel. 


Brass. 


Cast 
Iron. 


Steel. 


Brass. 


1/4 

3/8 

i 7/16 

1/2 


0.0134 
.0209 
.0302 
.0411 
.0536 
.0679 
.0834 
.1014 
.1207 


0.0035 
.0054 
.0078 
.0107 
.0140 
.0177 
.0218 
.0264 
.0315 


0.0038 
.0059 
.0085 
.0116 
.0152 
.0192 
.0237 
.0287 
.0342 


0.0040 
.0061 
.0088 
.0120 
.0157 
.0200 
.0244 
.0300 
.0352 


13/16 
7/8 

15/16 
1 

1 1/8 
1 1/4 
1 3/8 
1 1/2 
15/8 


0.1416 
.1634 
.1886 
.2146 
.2716 
.3353 
.4057 
.4828 
.5668 


0.0369 
.0428 
.0491 
.0559 
.0709 
.0874 
.0920 
.1259 
.1479 


0.0401 
.0465 
.0534 
.0608 
.0771 
.0950 
.1000 
.1368 
.1608 


0.0414 
.0479 
.0550 
.0626 
.0794 
.0979 
.1030 
.1410 
.1657 



Continued on next page. 



186 



MATERIALS. 



Weights per Lineal Incli of Round, Square and Hexagon Steel. 

Weight of 1 cu. in. = 0.2836 lb. Weight of 1 cu. ft. = 490 lb. 



Thick- 








Thick- 








ness or 
Diam- 


Round. 


Square. 


Hexagon. 


ness or 
Diam- 


Round. 


Square. 


Hexagon. 


eter. 








eter. 








1/32 


0.0002 


0.0003 


0.0002 


17/8 


0.7831 


0.9970 


0.8635 


1/16 


.0009 


.0011 


.0010 


1 15/ 


.8361 


1.0646 


.9220 


3/32 


.0020 


.0025 


.0022 


2 


.8910 


1.1342 


.9825 


1/8 


.0035 


.0044 


.0038 


2 1/16 


.9475 


1 .2064 


1.0448 


5/32 


.0054 


.0069 


.0060 


2 1/8 


1.0058 


1.2806 


1.1091 


3/16 


.0078 


.0101 


.0086 


2 3/16 


1 .0658 


1.3570 


1.1753 


7/32 


.0107 


.0136 


.0118 


2 1/4 


1.1276 


1.4357 


1.2434 


1/4 


.0139 


.0177 


.0154 


2 5/16 


1.1911 


1.5165 


1.3135 


9/32 


.0176 


.0224 


.0194 


2 3/8 


1.2564 


1 .6569 


1 .3854 


5/16 


.0218 


.0277 


.0240 


2 7/16 


1 .3234 


1 .6849 


1 .4593 


11/32 


.0263 


.0335 


.0290 


2 1/2 


1.3921 


1.7724 


1.5351 


3/8 


.0313 


.0405 


.0345 


2 5/8 


1.5348 


1.9541 


1.6924 


13/32 


.0368 


.0466 


.0405 


2 3/4 


1 .6845 


2.1446 


1 .8574 


7/16 


.0426 


.0543 


.0470 


2 7/8 


1.8411 


2.3441 


2.0304 


15/32 


.0489 


.0623 


.0540 


3 


2.0046 


2.5548 


2.2105 


1/2 


.0557 


.0709 


.0614 


3 1/8 


2.1752 


2.7719 


2.3986 


17/32 


.0629 


.0800 


.0693 


3 1/4 


2.3527 


2.9954 


2.5918 


9/16 


.0705 


.0897 


.0777 


3 3/8 


2.5371 


3.2303 


2J977 


19/32 


.0785 


.1036 


.0866 


3 1/2 


2.7286 


3.4740 


3.0083 


5/8 


.0870 


.1108 


.0959 


3 5/8 


2.9269 


3.7265 


3.2275 


21/32 


.0959 


.1221 


.1058 


3 3/4 


3.1323 


3.9880 


3.4539 


11/16 


.1053 


.1340 


.1161 


3 7/^ 


3.3446 


4.2582 


3.6880 


23/32 


.1151 


.1465 


.1270 


4 


3.5638 


4.5374 


3.9298 


3/4 


.1253 


.1622 


.1382 


4 1/8 


3.7900 


4.8254 


4.1792 


25/32 


.1359 


.1732 


.1499 


4 1/4 


4.0232 


5.1223 


AA36A 


13/16 


.1470 


.1872 


.1620 


4 3/8 


4.2634 


5.4280 


4.7011 


27/32 


.1586 


.2019 


.1749 


4 1/2 


4.5105 


5.7426 


4.9736 


7/8 


.1705 


.2171 


.1880 


4 5/8 


4.7645 


6.0662 


5.2538 


29/32 


.1829 


.2329 


.2015 


4 3/4 


5.0255 


6.6276 


5.5416 


15/16 


.1958 


.2492 


.2159 


4 7/8 


5.2935 


6.7397 


5.8371 


31/32 


.2090 


.2661 


.2305 


5 


5.5685 


7.0897 


6.1403 




.2227 


.2836 


.2456 


5 1/8 


5.8504 


7.4496 


6.4511 


1 1/16 


.2515 


.3201 


.2773 


5 1/4 


6.1392 


7.8164 


6.7697 


11/8 


.2819 


.3589 


.3109 


5 3/8 


6.4351 


8.1930 


7.0959 


13/16 


.3141 


.4142 


.3464 


5 1/2 


6.7379 


8.5786 


7.4298 


1 1/4 


.3480 


.4431 


.3838 


5 5/8 


7.0476 


8.9729 


7.7713 


15/16 


.3837 


.4885 


.4231 


5 3/4 


7.3643 


9.3762 


8.1214 


13/8. 


.4211 


.5362 


.4643 


5 7/8 


7.6880 


9.7883 


8.4774 


1 7/16 


.4603 


.5860 


.5076 


6 


8.0186 


10.2192 


8.8420 


1 1/2 


.5012 


.6487 


.5526 


6 1/4 


8.7007 


11.0877 


9.5943 


1 9/16 


.5438 


.6930 


.5996 


61/2 


9.4107 


11 .9817 


10.3673 


15/8 


.5882 


.7489 


.6480 


6 3/4 


10.1485 


12.9211 


1 1 . 1 908 


1 11/16 


.6343 


.8076 


.6994 


7 


10.9142 


13.8960 


12.0351 


13/4 


.6821 


.8685 


.7521 


7 1/2 


12.5291 


15.9520 


13.8158 


1 13/16 


.7317 


.9316 


.8069 


8 


14.2553 


18.1497 


15.7192 





Weight of YiWeU,— Continued from 


page 185. 




Ra- 


Area, 
Sq. In. 


Weight per In., Lb. 


Ra- 
dius, 
In. 


Area, 
Sq. In. 


Weight per In., Lb. 


dius, 
In. 


Cast 
Iron. 


Steel. 


Brass. 


Cast 
Iron. 


Steel. 


Brass. 


13/4 


0.6572 


0.1713 


0.1862 


0.1920 


2 7/8 


1.774 


0.4621 


0.5022 


0.5017 


17/8 


.7545 


.1970 


.2137 


.2202 


3 


1.931 


.4950 


.5471 


.5635 


2 


.8585 


.2237 


.2431 


.2504 


3 1/4 


2.267 


.5903 


.6417 


.6609 


21/8 


.9692 


.2502 


.2743 


.2826 


3 1/2 


2.629 


.6926 i .7438 


.7661 


21A 


1.086 


.2832 


.3079 


.3172 


3 3/4 


3.018 


.7873 i .8523 


.8817 


2 3/8 


1.210 


.3155 


.3429 


.3532 


4 


3.434 


.8933 


.9709 


1.000 


21/2 


1.341 


.3496 


.3800 


.3914 


4 1/4 


3.876 


1.008 


1.096 


1.130 


2 5/8 


1.478 


.3857 


.4192 


.4317 


4 1/2 


4.346 


1.132 


1.231 


1.270 


2 3/4 


1.623 


.4222 


.4589 


.4727 


4 3/4 


4.842 


1.261 


1.371 


1.421 



WEIGHT OF PLATE IRON. 



187 



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,?w — ^^^rn^ir^insorvcoCT^OO — r^r^i"^in\oooo—- mmNOXOC^mm. r^oOO 
u^ t>» O^ — m in r>, o^' — c^' in r-»* O cs 'f" sd oo O r^ O O in O^ en r^ — in c -^ co fs\o O m 
cS(Nr^jfnmmmfn"^'^"^"^'-nininininvONO^r^r>r>.coooo^0^ooO' cn(S 



OoOi'^eAOoOint^OoOinfnOcOinmOaOinO'nCinOinOmcmO 

in en f*^, — ; q 00 f>. sO in en es — o oo r>. vO m en cs O r>. in. fs o r>. m «s> q r*. inm q oo m 

<N -^ sO oo O — m in pn o— * m in o oo O <N ■^' vO O en r>. — m oo (N vO o en h-.— vn oo eN 
rslcNeSfvicnenenenencn'^'^'^-'T'^ininininvOvOvOr^i^t^oOQOOO^O^OOO — 



O •— en u^ O 00 O -- rn' in O ® O —•' e^' in\o' 00 o" en sd O e^ vO O en \0 O en sO O en vO O 
^r^ir^«Sfs|cNcnenenenmen'^-^-^'<r"<T"^inininvO^OvOr^i^r^oooooCC^O^O^O 

§ ^ - 7 

H t_. O vO <N oo en Oin — rsmoo "^OOrS oOen O^ in rs.00 Oe^eninrnoOO — enin vOoO O 

M 4) fQ in^-^oOenrvr^rN — sCOinO"^O^enooesr>.vOinin-^encs— qqc^oOf^^min 

- ^ '^ ^'odo — en Vo^<c^ Of^'enu^xdr>.*a^ oVien'vC (>e^*inoo" — ■^"t^or^ 

e^rvjrsi^rgrvirvicnenenenenenen'^'^f^-^'^inininsO^^i^t^t^r^QOoOQO 



8nOn>Ouno^nOinOinOinOinOinOOOOOOOOOOOOOOqO 
_ rvj in ^_ q r^ in r>. o eN in r^ O ^l in r>i O cs in o in O in q in q in q in q in q in q 

in vO f^ 30 O* — ' 's)' ^rs" in" sO' r>' o6 o — ' ni en in'sO t^ O r<i in r>! o M in" r^* O <N m r^ O rj in 
— — (Nr^jrv|'s)csj?sjrs!rv]-^-<>cnr^. enenen^-^-^-^ininmin^OO vCl->0 r*. r>. r>. 



'>r^ent>.— ^n(:^fncne^^oo■^coenr^ — lnenev^o(:^r^ln^f^^OG0r^lnenf^O 

m in sO \0 r>» r>. r^ 00 00 O^ o O O O ■ c^ esi en "^ m m -O r^ oO ^ q q — _ f^ en ^ m 

(sj en ■^' in" nO' r-N* ro O^ O — 'N en" m" vO r>." oO c> o --" e^* m' r>i O^' — en" in r>.' O «S "^ vO oo O M 
— rsir^rsifse^fsrvjesmenenenenenen ^•^■^Trininininun>c>vo 



|Oenr:jOenrsOenr>.Ornr>Oenr^Oent^Ot^enOf^:nOr>jenOt>.enOr>.enO 
O-o sOinen — OoOsOinm — ooo^Olnen — OOenOOenoqenqqenq^. enq 
O o — • <^' <^' ^' mm* vO' r>." oo" o* O O — ' ni en" '^' m! vd od o" — en" m" vd cd o" -- en m vO on o 
rvifvieNesc^(N<N(Nrs»- - — — — — ^.»^ 



i^nenenen-^-^-^"^"^"^''^ 



■D enmooOenmr^OenmooO<NmooOenmomOmomomOinOmOmO 
n — 1^_ en O O r^ 00 m — r>i fn O O M oo m — t>. O rJ m r>. q rvJ m r^ q CvJ m r>. q fs m 

>i GO od o" O o" — — " (SJ en" en" ^ m" m' xd ^d r^' oO QC" O --Vi r^v" m" vd r-^ oc O -- na en m O t^ 
— . — , — ,— .— r^(vj(vi(viesmr^c^encnenmencncn 



Ocqenmr^aoOrvjenmr>.oooeSenmt^ooOenr>.Oent^Oent^Ornr>«Oenr^O 
q "^^ 00 Cvl O q m_ O en r->. — m O "^ 00 c^ O O m e — O oq ^^ i^. en — O oO ^O m en ^_ q 



.^ ^^ nj r^ en en en" en en ^f Tj'" tt" tt vn in in in in vO O O rN r^ 1^ CO CO O^ O^ O O O •— •— nj nj 



fvjcn'^«i^>0r^o0<>0 — rgen'<rmv£>r>^QOc>Or^"^>OQOOr<»"*>0«OfN"n-0«0 
— — — — — — — f^^^^c^^«s^^^^^^^(^J^^<s«nf<^cncn«<^'^"n•^"^"^«i^l'^»'^•'^^'^'0 



188 



MATERIALS. 



*—'—*—'-''' '^* •-' '^' '^' -^' — ■ (s cW -"T in sd t^ oo O^* O — * ri rW •^" iX -o' r^' oo o^' O — 

— — — — '— — '— — CNl(N(N<N(N(Nl<N(NtN(Nc^fA 



CO 



O — CNfO'^msOrNQOO^O'- 



oOt^sO-^cA'— OQ0t>im-nT<^'— OQ0^Nlf^■<^Csi— O^oOvOm'^rq— O^QO^OincA 
00 r^ o in TT (^ rsj o 0^_ 00 r>._ vo in TT csj — o O^ 00 i^ in -^^ cA ^ 
O •— ' Cs) cW V in sO r>»' t>.' 00 O^ O — cni* m' V m' m* vO r>! oo* o' O — ' CN m' c<^' V m' \o" h>." oo 
'—'—'—'—'—'— — — — — — CNjcNfsjcsjfvicsrgrNicscN 



f<^r>.Oc<^t>.Oc<^^>lOcr^^>.Or*^t>>Or'^r^Oc<^r>.Of<^^>lOf^^NOc^r>.Of<^^>. 
oO^vOmcA — OoOOinc*^'— OoOvOinco — OoO'Ovnr<^ — OQOvOinr<^ — Ooo^O 

O — " rq cK "^' in in vO i^* oo O^' O O — " Cvj' rW V m' m' sO* rs* oo* O^' o" O — (N cW '^' m* in so" 



oovO"^fA — 0^r^inr<^ — o^QOvO"^(NOoovO"^m — o^r>.inf<^ — o^oOvO'^eNO 

rsinm'— 0^\0"^(NOQ0»n, r<^.— Osi^mrNOoONO'^'— Or>inc<^O00\0'^(SO 

O --' csi cA cW ■^" in \0 1^' r^" oc' <> o O — rs cW n-' ■^* m' \0 r>.' r>.' oo* O* O — ' — ' (N cW tt m* 

' — — — — — — — (NCNc^cNCNcsr^ 



t>,lnc<^ — O^NO"^<NO^t^inc<^OoOvOf<^ — O^vO-^^NOr^inr^OoONO-*- Otv. 

vOfnOl^coOt>.Trot>>'^ — 00"^ — oom — 00in(Sia\in(SO^vO(NO^sOf<^a^vO 

O — CNJ (N cA n- "^' in \0 ^O t^' 00 00 O^" O O — eg rsj' rW "^' ^" m' vo" o' tv," co* oo' O^' O O — 

— — ' — ' ' ' (NCNCS 



O — — r^r^cA-<l-tninvOvOt>.ooooc^OO — — (sir<^f<^"^ininvOsor->.QOoOOO 



O — — cS(NJc0T5-Trininv0N0t>.00Q00^0^OO — <NCSlrr\fr\rj-'^mvO^Or^r^0C 



O — — c\jcscAc<\-^'^ininNO'Ot->.^NOOooo^O^OO'— »— r^c<>cn'^"^ininsONO 



• ;<>Q0 

^ vOc^ — OO-^- OOinr^O^vOc^O^vOr^Or^"^- OO"^ — 00incvJO^v0ma>vOroO 
^ •^0\T^-ooc<^oocs^NC^^^o — vOOinoino^'^o^r<^oom^N(Sr>.'— nO- tnomo 
O * — — (si o4 rK cK ^" •^' in in sO o" r>." r>.' r>.' co' oo O^ O^ o o — — ' (N cn* co cW ■^' '^' m" 



— r«Mnr>ooor<jr<Mnr>.ooOfSfnvni>»ooo<Sf^. inh>ooor<ir<Mnt^or)0<Srr, 
■^_ 00 r^_^ >0 O in (> rn 1^ — in O "^ CO OsJ vO O u^ O^ c^ ^> — in O "^_ <© <N ^_ O in On rr, 
O ' — — c^'cNicvJcKcKn-'n-'inu'^'insO o r^'r>.'r^'oO oo'(^^ — <n r^i r^^f^ 



ino^ 

vOf^ONvOfNONinrqcoin — 00"^Oi^mO\Orr>0NN0r^0^in — 00"^ — t^-^or^ 
cA ^N O Tf GO — in c> r>4 \0 O en r^ — -^ CO Csi u^ o^ fv) sO O c<^ r-> — -^ 00 C-) in <> ^r^ v^^ 
O — — — cvj csj (Nj m' cW ■^' '^' •«^' in in in vO \0 vO r>« r> 00 00 00 O^ O^ O^ O O o 



r<Mn 00 

— (NjmmvOooo^O- m'^invOooo^O — f^'^mvOooc^O — (^"^mvOooo^o 

r^^vOO'C-au^oO'— inoo— •■^t^OrO^OOfnOONfNinQO'— inoO"— ■^r>.Or<>i^qo 

— — — cs cnI cn* en ^'^ en '^' ■^" -"T in in in in ^o O O t>«. r>. tv, oo oo oo O^ O^ O^ O 



O 

^0(NcO'*0^0r^JoO"^0^0^<^ONln — t>.mONin — r>.^<^O^ln — h».roON»n — rscn 
r^int>.OrninooOcnsOcO'— rnvOO^"— "^NOON(S■^^>«0^p^ln^>0(NlncoOf<^ 
O — — — — (s ?Nf csf CN cW cW cK cW ■^' ■^* "^ "^ iW in in in O vO vO t>. r>. t~> t^ 00 oc 



f^)"^OcoorviTtvocoocNiu^t^O^--rninr>«0^— ■fninr>o<N'«rNOco_OfN 
* — — — — — rvj rsi (N rg Csj en en" en" en en '^* ■<*■ "^' ■^" in in in in in vO ^O^ 






* 00 tH-^ t-H 00 r 



^^ ^~-eo ^-~liO 



WEIGHTS OF FLAT WROUGHT IRON. 



189 



■5 

i 


5** 


<^''^''-'2 j:?"::: t:^'^'^ jq ?^ ^ ?? 1^ P^ ? 5^ S 1?; S S ^ ic: § 


H 
H 


ri S « -- ^ r^ O c<^ <5 a^_ csl u^ t^_ O en ^, <N 00/^_ O »n •- t^ c<^ 
fsi V NO o' — ' f^' <> 00 O <N u->' r^' o^' (S ^' vd — ' in o m' o' t" oo rW 


h 


oo r^ in c*^ (N O 00 r^ u-N r*^ f;<l O 00 r^ in r^ O t-; r;^ O c^ rn O r;; 
O ^ Cs| c<^ -^ u^ u^ O r^ 00 C> O O — rsi_ cr\ in_ nO 00 O -- CO in vO 
tsi ■«•* vo oo o' CN "^" ^' 00 O (vj in r> o^ — en r>. — in o "^ 00 cnJ \d 
^^^i:.^-- — ^cscNrsirqcMcncncA-f^inininvOvO 


s; 


ooinmOoommOooinmOooinrnOinOinoinoino 

00 1>. vS in cA cs —, q 00^ t>>. vO, in_ m^ cs — q t-. m (n o r> m csj q 

»-*cninr>»*0^*--*cnin vO 00 o* (Nf Vo odo m'l^ — moccNvOO 

^ ^^- — (N (N cs CN cvj en en en ^ ^ "^ in in vo 


5) 


t>.xr — oomenor^^'l- — aOin(NCh^OenoOeSOO'^oOent^ 

r>. in en q oq vO ^_ — (> r>>. ^_ es q r>, m m_ oo_ ■<»•_ a m q in — sO 

— * en in t>.' oo' O eNi' T* m* r^' o^" — m" V so' co* — * m' cr' co vd <> m vd 

— — — (SrqcMr-aeNenenen^'^'^inin 


k * 

00 


i>.mot>scnOr^f<^or^enOr^enOt^Oenr^Oenr^Oen 
nO en q vo en q ^o en_ q vO_ m_ q xO_ en_ q o q en q o_ cn_ q q en 

— 'eninvdodo— en'in'vdoo'o — en'in vdo'cn vO'o en vdo en 
(vicNCvieNCNcnenen^^'^inin 




^Oeno^in — oO"^OvOenOMn — oo-^OeninooOf<MnQOO 
in -- q <vi q m_ q in q q — t>n en q ^ q — es en m q t^ q q 

^ en ■^' \d r>.' o^" O p^' n-* m' hs" od O — ' m' m" od — -^ i^ O en vd O 
— — — — — — escNCvlc^r^jrnenen'^'^'^in 




vOrqoOenOin- t^enoo^OvOcvloOeninr^oCOe^eninr^j 

"^^qen q<N t^ (SI vO — in o in a> ^ 00 en es — o o o qr^ q 

— * cs '^' in r>>' od O — en -^^ <> r>J od O — en vd o* rg m" r>.' o en' <> 

— — 1 fv^cNCNrqeNenenen^^'^ 


ft* 


— — rvlenen^-nnvOvOr^oooooao — en'^tmsooooo 

"^^ q rg q q ^^ q r<i q q '^i-^ q (n q q q en — q r>. q en — q 

•— * (si ■^' in rs od O^ — rq ■^* m" ^d od O^' — evj in cd O en vd O^' es m' 

— — — — — — — csjcsjeNjeNcncnencn'^T 


^ 

O 


m — vOr^rsrnooeno^OinovO- t^ooooao — rsjcnen 

t<^ IN. q ^^ r>. — -"T q — q q es q q q q q q r>, q ?n q q q 

^ c^' -"T in nO od 0^' O esi en '^' <> t^ od O — ■^' r^' O^' rs m' r>i* o rn 

— — — — — — — csiCNCNCNCSenenen'^'^ 


CO 


OO — >-' r4rvi(N(Nenenenmen'<r'^inininvOsDt>^ 

en q q «N q q — 't; r^^ q r<s, vo_ q <n m oo_ rj-_ q q rv^ q ^t- q q 

— ' csf en in" vd r>.' a\* o' — en ■^* m' vd od Ov' O en vd oo' — en vd O^' — 

— — — — — — — — fsjCNCvjesienenenen"^ 




inoinoinoinoinoinomoinooooooooo 

rq in r>. o es in r>. q cn) q r^ q rq q r> q in o m o m o m o 

— cs en in vd t>.' od o" — eN en m' vd tv.' od o* es m* r^," o" es in rs' o* 

' ' ' (NCSCMCSenenenenT 


W3 


OOOvOvOvOvO^oocooooooot^itvr^r^sOvOininin'^'^m 

CN^inr>Ov — rninr>>av — cnqr^Ov — qovcnr> — inoven 

— cs en '^* in tv.* od a o" — en ^* m* vd r^* Ov* — en vo" od — en m' od 

— — — — — — — — r4rvicvirsifnenenen 


ft* 


tnav"^aOenoOrvir>« — voOino-^Ovenenrvj — oOvQOoot^ 

— (S ■^q^N qq — en -^qr^ qq— en qov es m r^ o en vO 

— cm" en '^" m' nO od O^* o" — es* en f " vo' r>.' od o' (ni' m' r>.* o' evf '^' vd 

— — — ' — — CvjestNCNrMmenen 


10 


OOvcooot^NvOvOin-^Tj-menr^ OOvcovOin'<ren — o 

O — CM qn- in qr>N oo ov o — eN q^ qqoo o <n ^ vo oo o 

— * CM m* '^" in* vd r>." od o* o" cm" en" '*" m' vd t>>.' c>" — tj-' vd oo' o cm m" 

— — — — — — — — CMCMCMCMenenen 


^^* 


^oomr^ — inovencocMvOO^ooenr>.inm(MOaot^«nfn 
q q — — CM (N CM q q ^_ -^^ q q q q q t-> q q o q — cm q 
— CM en -^ in vd r>* od Ov' o' — cm" eA -^ in vd od o" rg" m' hs' o* — rn 

— — — — CMCMCMfSCMencn 


o 










0) 

Q 0) 



190 



MATERIALS. 



WEIGHTS OF STEEL BLOOMS. 

Soft steel. 1 cubic inch = 0.284 lb. 1 cubic foot =» 490.76 lbs. 



Size, 
Inches 



Lengths. 



12 X6 

X^ 

X4 
n X6 

X5 
X4 

10 X8 
X7 
X6 
X5 
X4 
X3 

9 X8 

X7 
X6 
X5 
X4 
X3 

8 X8 

X7 
X6 
X5 
X4 

X3 

7 X7 
X6 
X5 
X4 
X3 

61/2 X 61/2 
X4 

6 X6 
X5 
X4 
X3 

51/2X51/2 
X4 

5 X5 
X4 

41/2X41/2 
X4 

4 X4 
X31/2 
X3 

31/2X31/2 

X3 
3 X3 



20.^3 
17.04 
13.63 
18.75 
15.62 
12.50 

22.72 
19.88 
17.04 
14.20 
11.36 
8.52 

20.45 
17.89 
15.34 
12.78 
10.22 
7.66 

18.18 
15.9 
13.63 
11.36 
9.09 
6.82 

13.92 

11.93 

9.94 

7.95 

5.96 

12 
7.38 

10.22 
8.52 
6.82 
5.11 

8.59 
6.25 
7.10 
5.68 

5.75 
5.11 
4.54 
3.97 
3.40 

3.48 
2.98 
2.56 



123 
102 
82 
113 
94 
75 

136 
120 
102 
85 
68 
51 

123 
107 
92 
77 
61 
46 

109 
95 

82 
68 
55 
41 

83 

72 
60 
48 



13" 



245 
204 
164 
225 
183 
150 

273 
239 
204 
170 
136 
102 

245 
215 
184 
153 
123 
92 

218 
191 
164 
136 
109 
82 

167 
143 
119 
96 



30 

72 


U 
144 


44 


89 


61 


123 


51 


102 


41 


82 


31 


61 


52 


103 


37 


75 


43 


85 


34 


68 


35 


69 


31 


61 


27 


55 


24 


48 


20 


41 


21 


42 


18 


36 


15 


31 



18'' 


34" 


30" 


36" 

736 


43" 


48" 

982 


54" 


60" 


36S 


491 


613 


859 


1104 


122/ 


307 


409 


511 


613 


716 


818 


920 


1022 


245 


327 


409 


491 


573 


654 


736 


818 


338 


450 


563 


675 


788 


900 


1013 


1125 


231 


375 


469 


562 


656 


750 


843 


937 


225 


300 


375 


450 


525 


600 


675 


750 


409 


545 


682 


818 


954 


1091 


1227 


1363 


353 


477 


596 


715 


835 


955 


1074 


1193 


307 


409 


511 


613 


716 


818 


920 


1022 


256 


341 


426 


511 


596 


682 


767 


852 


205 


273 


341 


409 


477 


546 


614 


682 


153 


204 


255 


306 


358 


409 


460 


511 


363 


491 


'613 


736 


859 


982 


1104 


1227 


322 


430 


537 


644 


751 


859 


966 


1073 


276 


368 


460 


552 


644 


736 


828 


920 


230 


307 


383 


460 


537 


614 


690 


767 


184 


245 


307 


368 


429 


490 


552 


613 


138 


184 


230 


276 


322 


368 


414 


460 


327 


436 


545 


655 


764 


873 


982 


1091 


286 


382 


477 


572 


668 


763 


859 


954 


245 


327 


409 


491 


573 


654 


736 


818 


205 


273 


341 


409 


477 


546 


614 


682 


164 


218 


273 


327 


382 


436 


491 


545 


123 


164 


204 


245 


286 


327 


368 


409 


251 


334 


418 


501 


585 


668 


752 


835 


215 


286 


358 


430 


501 


573 


644 


716 


179 


7.38 


298 


358 


417 


477 


536 


596 


143 


191 


239 


286 


334 


382 


429 


477 


107 


143 


179 


214 


250 


286 


322 


358 


216 


288 


360 


432 


504 


576 


648 


720 


133 


177 


221 


266 


310 


354 


399 


443 


184 


245 


307 


368 


429 


490 


551 


613 


153 


204 


255 


307 


358 


409 


460 


511 


123 


164 


204 


245 


286 


327 


368 


409 


92 


123 


153 


184 


214 


245 


276 


307 


155 


206 


258 


309 


361 


412 


464 


515 


112 


150 


188 


225 


262 


300 


337 


375 


128 


170 


213 


256 


298 


341 


383 


426 


102 


136 


170 


205 


239 


273 


307 


341 


104 


138 


173 


207 


242 


276 


311 


345 


92 


123 


153 


184 


215 


246 


276 


307 


82 


109 


136 


164 


191 


218 


246 


272 


72 


96 


119 


143 


167 


181 


215 


238 


61 


82 


102 


122 


143 


163 


184 


204 


63 


84 


104 


125 


146 


167 


188 


209 


54 


72 


89 


107 


125 


143 


161 


179 


46 


61 


77 


92 


108 


123 


138 


154 



ROOFING MATERIALS AND ROOF CONSTRUCTION. 191 

ROOFING MATERIALS AND ROOF CONSTRUCTION. 

Approximate Weight of Roofing Materials. 

(American Sheet & Tin Plate Co.) 



Material. 



Corrugated galvanized iron, No. 20, unboarded 

Copper, 1 6 oz. standing seam 

Felt and asphalt, without sheathing 

Glass, 1/8 in. thick 

Hemlock sheathing, 1 in. thick 

Lead, about 1/ g in. thick 

Lath and plaster ceiling (ordinary) 

Mackite, 1 in. thick, with plaster 

Neponset roofing, felt, 2 layers 

Spruce sheathing, 1 in. thick 

Slate, 3/i6 in. thick, 3 in. double lap 

Slate, 1/8 in. thick, 3 in. double lap 

Shingles, 6 in. X 18 in., I/3 to weather 

Skylight of glass, 3/i6 to I/2 in., including frame 

Slag roof, 4-ply 

Terne plate, IC, without sheathing 

Terne plate, IX, without sheathing ; . . . 

Tiles (plain), 10 I/2 in. X 6 I/4 in. X Vs in. — 5 1/4 in. to weather 

Tiles (Spanish), 14 I/2 in. X 10 I/2 in.— 7 I/4 in. to weather 

White pine sheathing, 1 in. thick 

Yellow pine sheathing, 1 in. thick 



Lb. per 


sq. ft. 


21/4 


I 1/4 


2 


13/4 


2 


6 to 8 


6 to 8 


10 


1/2 


21/2 


6 3/4 


41/2 


2 


4 to 10 


4 


1/2 


5/8 


18 


8 1/2 


21/2 


4 



Snow and Wind Loads on Roofs. 

In designing roofs, in addition to the weight of roofing material to 
be supported, recognition must be given to possible snow and wind loads. 

In snowy localities the minimum snow load per horizontal sq. ft. of 
roof should be considered as 25 lb. for slopes up to 20 degrees. For 
each degree increase in slope up to 45 degrees, this load may be reduced 
1 lb. Above 45-degree slope no snow load need be considered. In 
especially severe climates these allowances should be increased in ac- 
cordance with actual conditions. 

The w'ind load is the pressure normal to the surface of the roof pro- 
duced by a wind blowing horizontally. The wind pressure against a 
vertical plane as determined by the U.S. Signal Service at Mt. Wash- 
ington, N. H., is for various velocities of wind: 

Velocity, miles per hr 10 

Pressure, lb. per sq. ft 0.4 

The pressure on a flat surface is twice that on a cylindrical surface 
of the same projected area. For further information regarding wind 
pressure, see page 626. As the slope of the roof increases, the greater 
becomes the wind pressure on it. The pressure normal to the surface 
of roofs of different slopes exerted by a wind velocity of 100 miles per 
hour (40 lb. per sq. ft. on a vertical plane) is 



20 30 40 


50 


60 


80 


100 


1.6 3.6 6.4 


10.0 


14.4 


25.6 


40.0 



Rise. in. per ft. . 
Angle wdth 

horizontal. . . 
Pitch (Rise ^ 

Span) 

W^ind pressure. . 



12 



16 



18 



24 



18° 26' 26° 34' 33° 41' 45° 0' 53° 8' 56° 19' 63° 26' 



1/6 

16.8 



i / 4 

23.7 



1/3 
29.1 



1/2 
36.1 



2'3 

38.7 



39.3 



1 
40.0 



Roof Construction. (N. G. Taylor Co., Philadelphia.) — Roofs with 
less than I/3 pitch are made with flat seams, and should preferably be 
covered with 14 X 20 in. sheets, rather than with 20 X 28-in. sheets, as 
the larger number of seams tend to stiffen the surface and prevent 
buckles. For a flat seam roof the edges of the sheets are turned 1/2 in., 
locked together and soldered. The sheets are fastened to the sheath- 



192 



MATERIALS. 



ing boards by cleats 8 in. apart and locked in the seams. Two 1-in 
barbed and tinned nails are driven in each cleat. Steep tin roofs 
should be made with standing seams and from 28 X 20-in. sheets. The 
sheets are first single or double seamed and soldered together in a long 
strip reaching from eave to ridge. The sloping seams are composed 
of two "upstands" interlocked at the upper edge and held to the sheath- 
ing boards by cleats. No solder is used in standing seams as a rule 
In soldering tin roofs, only a good rosin flux should be used. The use 
of acid must be carefully avoided. 

Roof Paints.— The American Sheet and Tin Plate Co. recommends 
for painting metal work and tin roofs metalhc brown, Venetian red, or 
red oxide paint, ground in pure linseed oil. The paint should be 
rubbed well in, and should not be spread thin. See also Preservative 
Coatings, page 471. 

Tin Plates are made of soft sheet steel coated with tin, and are 
called in the trade "coke" or "charcoal" plates according to the weight 
of coating. These terms have survived from the time when the highest 
quahty of plate was made from charcoal-iron, while the lower grades 
were made from coke-iron. Consequently, plates to-day with the 
lighter coatings are known as coke-plates, and are used for tin cans, etc. 
The various grades of charcoal-plates are designated by the letters A to 
AAAAA, the latter having the heaviest coating and the highest polish. 
There is one other brand made with a heavier coating than 5A, which is 
especially adapted for nickel-plating. The unit of value and measure- 
ment of tin plates is the "base-box," which will hold 112 sheets of 
14 X 20 in. plate, or 31360 sq. in. of any size. Plates lighter than 65 lb. 
per base-box (No. 36 gage) are known as taggers tin. 



Weiglits of Standard Galvanized Sheets. 

(American Sheet & Tin Plate Co.) 





^il 


^i^ 




oii 


^^ 




fnii 


&^ 




fc±i 


fi^li 


6 


a*^ 


^ . 


6 


qt: 


a^ 


o 


ft^ 


ft*^ 


a> 


^ . 


ft^ 




S- 


5- 


O 


§S 


d- 


O 


6^ 


5» 


O 


6^ 


d- 


8 


112.5 


7.031 


15 


47.5 


2.969 


22 


22.5 


1.406 


29 


11.5 


0.719 


9 


102.5 


6.406 


16 


42.5 


2.656 


23 


20.5 


1.281 


30 


10.5 


.656 


10 


92.5 


5.781 


17 


38.5 


2.406 


24 


18.5 


1.156 


31 


9.5 


.594 


11 


82.5 


5.156 


18 


34.5 


2.156 


25 


16.5 


1.031 


32 


9.0 


.563 


12 


72.5 


4.531 


19 


30.5 


1.906 


26 


14.5 


0.906 


33 


8.5 


.531 


13 


62.5 


3.906 


20 


26.5 


1.656 


27 


13.5 


.844 


34 


8.0 


.500 


14 


52.5 


3.281 


21 


24.5 


1.531 


28 


12.5 


.781 















Standard Weiglits and Gages of Tin Plate. . 

(American Sheet & Tin Plate Co., Pittsburgh.) 





6 




g.s 




6 


a4 


^l 




6 


a* 


gfi 


73 1: 


4. :z; 

^ Q) O 


M 


Wo 

°x 


^i 


^ 0) 0) 


2S 

°x 


0) S 
T3 C 




l^. 


?; 


i- 


1^^ 




i-^ 




^^6 


i^ 


pa 


t- 


^O 


i^ 


i^i 


55 1b. 


38 


0.252 


55 


lOOlb. 


301/, 


0.459 


100 


3XL 


26 


0.771 


168 


60 " 


37 


.275 


60 


IC 


30 


.491 


107 


DX 


26 


.826 


180 


65 " 


36 


.298 


65 


1181b. 


29 


.542 


118 


4X 


25 


.895 


195 


70 " 


35 


.321 


70 


IX 


28 


.619 


135 


4XL 


25 


.863 


188 


75 " 


34 


.344 


75 


IXL 


28 


.588 


128 


D2X 


24 


.964 


210 


80 " 


33 


.367 


80 


DC 


28 


.638 


139 


D3X 


23 


1.102 


240 


85 " 


32 


.390 


85 


2X 


27 


.711 


155 


D4X 


22 


1.239 


270 


90 " 


31 
31 


.413 
.436 


90 
95 


2XL 
3X 


27 
26 


.679 
.803 


148 
175 










95 " 











TIN AND TERNE PLATES. 



193 



Sizes and Net Weight per Box of 100 lb. (0.459 lb. per sq. ft.) 
Tin Plates. 



Size of 
Sheets. 



Sheets 
per 


Weight 
per 


Size of 
Sheets. 


Sheets 
per 


Weight 
per 


Box. 


Box. 


Box. 


Box. 


225 


100 


15X15 


225 


161 


112 


100 


16X16 


225 


183 


112 


200 


17X17 


225 


206 


225 


143 


18X18 


112 


116 


225 


172 


19X19 


112 


129 


225 


189 


20X20 


112 


143 


225 


103 


21 X21 


112 


158 


112 


103 


22X22 


112 


172 


225 


121 


23X23 


112 


189 


112 


121 


24X24 


112 


204 


225 


140 


26X26 


112 


241 


112 


140 


16X20 


112 


114 



Size of 
Sheets. 



Weight 
per 
Box. 



10 X14 
14 X20 
20 X28 

10 X20 

11 X22 
1 1 1/2 X23 



12 
12 
13 
13 
14 
14 



X12 
X24 
X13 
X26 
X14 
X28 



14 X31 

111/4X223/4 
131/4X173/4 
131/4X191/4 
131/2X191/2 
131/2X193/ 



XI 83/. 

XI91/. 

X21 

X22 

X221A 



151/2X23 



155 

91 
84 
91 
94 
95 
103 
103 
105 
110 
111 
127 



For weight per box of other than 100-lb. plates multiply by the 
figures in the column "AVeight per Box" in the preceding table, and 
divide by 100. Thus for IX plates 20 X 28 in« 200 X 135 h- 100 = 270. 

Sheets Required for Tin Roofing. 

(American Sheet & Tin Plate Co., 1914.) 





Sheets 




Sheets 




Sheets 




Sheets 




Sheets 


£ 


Required. 


+^ 


Required 


-t-j 


Required. 


xn 


Required. 


^ 


Required. 


6" 




C^OO 




0) 




in 


1^ 


CO 00 


1^ 
^0 






So 


6_: 





"^x 


• tN 




D0<^ 


•(N 




rTj ^ 


•rs) 




r/)^ 


•CN 




zn^ 


• r^ 




■«x 





2x 


'^X 




::x 


•^x 




::x 


■fix 





^x 


■^x 




c«^ 


c3o 





rt 


c5o 





rt-^ 


So 





(SjTT 


c3o 





OStT- 


rto 


'A 


s- 


■en 


:z; 


E- 


Ul 


Z 


E- 


CO 


640 


fe- 


Ul 


% 


s 


Ul 


100 


59 


31 


280 


164 


86 


460 


269 


141 


374 


197 


820 


479 


152 


no 


65 


34 


290 


170 


89 


470 


275 


144 


650 


379 


200 


830 


484 


255 


120 


70 


37 


300 


175 


92 


480 


280 


148 


660 


385 


203 


840 


490 


258 


130 


76 


40 


310 


181 


95 


490 


286 


151 


670 


391 


206 


850 


496 


261 


140 


82 


43 


320 


187 


99 


500 


292 


154 


680 


397 


209 


860 


502 


264 


150 


88 


46 


330 


193 


102 


510 


298 


157 


690 


403 


212 


870 


508 


267 


160 


94 


50 


340 


199 


105 


520 


304 


160 


700 


409 


215 


880 


514 


270 


170 


100 


53 


350 


205 


108 


530 


309 


163 


710 


414 


218 


890 


519 


273 


180 


105 


56 


360 


210 


111 


540 


315 


166 


720 


420 


221 


900 


525 


276 


190 


111 


59 


370 


216 


114 


550 


321 


169 


730 


426 


224 


910 


531 


279 


200 


117 


62 


380 


222 


117 


560 


327 


172 


740 


432 


227 


920 


537 


282 


210 


123 


65 


390 


228 


120 


570 


333 


175 


750 


438 


230 


930 


543 


285 


220 


129 


68 


400 


234 


123 


580 


339 


178 


760 


444 


233 


940 


549 


288 


230 


135 


71 


410 


240 


126 


590 


344 


181 


770 


449 


236 


950 


554 


291 


240 


140 


74 


420 


745 


129 


600 


350 


1^4 


780 


455 


239 


960 


560 


295 


250 


146 


77 


430 


251 


132 


610 


356 


187 


790 


461 


243 


970 


566 


298 


260 


152 


80 


440 


257 


135 


620 


362 


190 


800 


467 


246 


980 


572 


301 


270 


158 


83 


450 


263 


138 


630 


368 


. 194 


810 


473 


249 


990 1 578 


304 



Terne Plates, or Roofing Tin, are coated with an alloy of tin and lead. 
In the "U. S. Eagle, N.M." brand the alloy is 32% tin, 68% lead. 
The weight per 112 sheets of this brand before and after coating is as 
follows : 

IC 14 X 20 IC 20 X 28 IX 14 X 20 IX 20 X 28 
Black plates. . . 95 to 100 lb. 190 to 200 lb. 125 to 130 lb. 250 to 260 lb. 
After coating. . . 1 15 to 120 230 to 240 145 to 150 290 to 300 

Terne plates are made in two thicknesses: IC, in which the iron body 
weighs about 50 lb. per 100 sq. ft., and IX, in which it weighs 62 1/2 lb. 
per 100 sq. ft. The IC grade is preferred for roofing, while the IX 



194 



MATERIALS. 



grade is used for spouts, valleys, gutters, and flashings. The standard 
weight of 14 X 20 in. IC plates is 107 lb. per base-box, and of 14 X 20- 
in. IX plate 135 lb. 

Long terne sheets are made in gages, Nos. 14 to 32, from 10 to 40 in. 
wide and up to 120 in. long. They are made in five grades with coat- 
ings of 8, 12, 15, 20, and 25 lb. 

A box of 112 sheets 14 X 20 in. will cover approximately 192 sq. ft. 
of roof, flat seam, or 583 sheets 1000 sq. ft. For standing seam roofing 
a sheet 20 X 28 in. will cover 475 sq. in., or 303 sheets 1000 sq. ft. A 
box of 112 sheets 20 X 28 in. will cover approximately 366 sq. ft. 

The common sizes of tin plates are 10 X 14 in. and multiples of that 
measure. The sizes most generaUy used are 14 X 20 and 20 X 28 in. 



Specifications for Tin and 


Terne Plate. 


^Penna. 


R.R., 1903.) 




Material Desired. 


Rejected if less than 




Tin 
Plate. 


No. 1 
Terne. 


No. 2 
Terne. 


Tin 
Plate. 


No. 1 

Terne. 


No. 2 
Terne. 


Coating: 

Tin, per cent . 


100 



0.023 

0.496 
.625 
.716 
.808 
.900 


26 

74 

0.046 

0.519 
.648 
.739 
.831 
.923 


16 

84 

0.023 

0.496 
.625 
.716 
.808 
.900 








Lead, per cent 

Amount per sq. ft., lb. . 
Weight, lb. per sq. ft. of 
Grade IC 








0.0183 

0.468 
.590 
.676 
.763 
.850 


0.0413 

0.490 
.612 
.699 
.787 
.874 


0.083 
0.468 


Grade IX 


.590 


Grade IXX 


.676 


Grade IXXX 


.763 


Grade IXXXX 


.850 



Each sheet in a shipment of tin or terne plate must (1) be cut as 
nearly exact to size ordered as possible; (2) must be rectangular, flat, 
and free from flaws; (3) must double seam successfully under reason- 
able treatment ; (4) must show a smooth edge with no sign of fracture 
when bent through an angle of 180 degrees and flattened down with a 
wooden mallet; (5) must be so nearly Uke every other sheet in the ship- 
ment, both in thickness and in uniformity and amount of coating, that 
no diflaculty will arise in the shops due to varying thickness of sheets. 

Corrugated Sheets.— Weight per 100 Sq. Ft., Lb. 

(American Sheet & Tin Plate Co., Pittsburgh, 1914.) 



Corruga- 
tions. 


5/8 in. 


1 1/4 in. 


2 in. 


2 1/2 in.* 
26 in. 


2 1/2 in.f 
27 1/2 in. 


3 in. 


5 in. 








wide. 


wide. 






U. S. Std. 


V) 


i 


'S 


i 


'^ 


fl 


V, 


fi 


'^ 


c 


'^ 


fl 


1? 


fi 


Sheet 
Metal 


*3 


'rt N 


■3 


Is 


'3 




^ 

3 




'3 


'3 N 


*5 




'3 


^0 

13 N 


Gage. 


Ph 


o 


Ph 





P^ 





PL| 





PL, 





Ph 





fu . 





29 




81 




81 




77 




77 




78 




77 




77 


28 


71 


88 


7i 


88 


68 


84 


68 


84 


69 


85 


68 


84 


68 


84 


27 


78 


95 


78 


95 


75 


91 


75 


91 


76 


92 


75 


91 


75 


91 


26 


85 


102 


85 


102 


82 


98 


82 


98 


83 


99 


82 


98 


81 


97 


25 


99 


116 


99 


116 


95 


111 


95 


111 


97 


113 


95 


111 


95 


111 


24 


113 


130 


113 


130 


109 


125 


109 


125 


110 


126 


109 


125 


108 


124 


23 






127 
141 
155 


144 
158 
172 


122 
136 
149 


138 
151 
165 


122 
136 
149 


138 
151 
165 


124 
137 
151 


140 
153 
167 


122 
136 
149 


138 
151 
165 


122 
135 
148 


137 


22 






151 


21 






164 


20 






169 


186 


163 


178 


163 


178 


165 


181 


163 


178 


162 


178 


18 










216 
270 


232 
286 


216 
270 
338 
472 
607 


232 
286 
353 
488 
623 


219 
274 
342 
478 
615 


235 
290 


216 

770 


232 
286 
353 
488 


215 
269 
336 
470 


?31 


16 










785 


14 










358 338 
494 472 


35? 


12 














486 


10 














631 







* Siding. t Roofing, 



SLATE. 



195 



Covering width of plates, lapped one corrugation. 24 in. Standard 
lengths, 5, 6, 7, 8, 9, and 10 ft.: maximum length, 12 ft. 

Ordinary corrugated sheets should have a lap of 1 1/2 or 2 corrugations 
side-lap for roofing in order to secure water-tight side seams ; if the roof 
is rather steep 1 1/2 corrugations will answer. Some manufacturers 
make a special high-edge corrugation on sides of sheets, and thereby are 
enabled to secure a water-proof side-lap with one corrugation only, thus 
saving from 6% to 12% of material to cover a given area. 

No. 28 gage corrugated iron is generally used for applying to wooden 
buildings; but for applying to iron framework No. 24 gage or heavier 
should be adopted. 

Galvanizing sheet iron adds about 21/2 oz. to its weight per square 
foot. 

Slate. 

Slate in roofs is measured by the square, 1 square being equal to 100 
superficial square feet. In measuring, the width of the eaves is allowed 
at the widest part. Hips, valleys, and cuttings are measured Uneally 
and 6 in. extra is allowed. The thickness of slate for roofing varies 
usually from 1 /g to 3/15 in. The weight varies, when lapped, from 
41/2 to 6 3/4 lb. per sq. ft. The laps range from 2 to 4 in., 3 in. being 
the standard. As slate is usually laid, the number of square feet of roof 
covered by one slate is w (Z — 3) -=- 288, w and I being the width and 
length respectively of the slate in inches. 

Number and Superficial Area of Slate for One Square of Roof. - 



Size, 
In. 


No. 


Area, 
Sq. 
Ft. 


Size, 
In. 


No. 


Area, 
Sq. 
Ft. 


Size, 
In. 


No. 

per 

Sq. 


Area, 
Sq. 
Ft. 


Size, 
In. 


No. 


Area, 

Sq. 
Ft. 


6X12 
7X12 
8X12 
9X12 
7X14 
8X14 


533 
457 

400 
355 
374 
327 
291 


267 
'254' 


10X14 
8X16 
9X16 

10X16 
9X18 

10X18 

12X18 


261 
277 
246 
221 
213 
192 
160 


'246' 

'240' 
■246' 


10X20 
11X20 
12X20 
14X20 
16X20 
12X22 
14X22 


169 
154 
141 
121 
137 
126 
108 


235 
23i 


12X24 
14X24 
16X24 
14X26 
16X26 


114 
98 
86 
89 
78 


228 
'225' 


9X14 









Weight of Slate, in Pounds, for One Square of Roof. 

(1 cu. ft. slate = 175 lb.) 



Length 

of 

Slate, In. 


Thickness of Slate, Inch. 


Vs 


V16 


V4 


Vs 


V2 


5/8 


Vi 


1 


12 


483 


724 


967 


1450 


1936 


2419 


2902 


3872 


14 


460 


688 


920 


1379 


1842 


2301 


2760 


3683 


16 


445 


667 


890 


1336 


1784 


2229 


2670 


3567 


18 


434 


650 


869 


1303 


1740 


2174 


2607 


3480 


20 


425 


637 


851 


1276 


1704 


2129 


2553 


3408 


22 


418 


626 


836 


1254 


1675 


2093 


2508 


3350 


24 


412 


617 


825 


1238 


1653 


2066 


2478 


3306 


26 


407 


610 


815 


1222 


1631 


2039 


2445 


3263 



Corrugated Arches. 

For corrugated curved sheets for floor and ceiling construction in 
fireproof buildings. No. 16, 18, or 20 gage iron is commonly used, and 
sheets may be curved from 4 to 10 in. rise — the higher the rise the 
stronger the arch. By a series of tests it has been demonstrated that 
corrugated arches give the most satisfactory results with a base length 
not exceeding 6 ft., and 5 ft. or even less is preferable where great 
strength is required. These corrugated arches are made with 1 1/4 X 3/8, 



196 MATERIALS. 

2 1/2 X V2, 3 X 3/4, and 5 X 7/8 in. corrugations, and in the same width 
of sheet as above mentioned. 

Terra-Cotta. 

Porous terra-cotta roofing 3 in. thick weighs 16 lb. per square foot and 
2 in. thick 12 lb. per square foot. 

Ceiling made of the same material 2 in. thick weighs 11 lb. per square 
foot. 

Tiles. 

Flat tiles 6 1/4 X 10 1/2 X s/g in. weigh from 1480 to 1850 lb. per square 
of roof (100 square feet), the lap being one-half the length of the tile. 

Tiles with grooves and fillets weigh from 740 to 925 lb. per square of 
roof. 

Pan-tiles 14 1/2 X 10 1/2 laid 10 in. to the weather weigh 850 lb. per 
square. 

Pine Sliingles. 

The figures below give the weight of shingles required to cover one 
square of a common gable roof. For hip roofs add 5 per cent. 

Inches exposed to weather 4 41/2 5 51/2 6 

No. of shingles per square of roof 900 800 720 655 600 

Weight of shingles per square, lb 216 192 173 157 144 

Slcylight Glass Required for One Square of Roof. 

Dimensions, in 12 X 48 15 X 60 20 X 100 94 X 156 

Thickness, m 3/i6 1/4 a/g 1/2 

Area, sq. ft 3.997 6.246 13.880 101.768 

Weight per square, lb 250 350 500 700 

No allowance has been made in the above figures for lap. If ordinary 
window-glass is used, single thick glass (about i/ie inch) will weigh about 
82 lb. per square, and double thick glass (about i/g inch) Avill weigh 
•about 164 lb. per square, no allowance being made for lap. A box of 
ordinary window-glass contains as nearly 50 square feet as the size of 
the panes will admit. Panes of any size are made to order by the 
manufacturers, but a great variety of sizes are usually kept in stock, 
ranging from 6X8 inches to 36' X 60 mches. 

THICKNESS OF CAST-mON WATER-PIPES. 

P. H. Baermann, in a paper read before the Engineers' Club of Phila- 
delphia in 1882, gave twenty different formula3 for determining the 
thickness of cast-iron pipes under pressure. The formulae are of three 
classes : 

1. Depending upon the diameter only. 

2. Those depending upon the diameter and head and which add a 
constant. 

3. Those depending upon the diameter and head contain an additive 
or sub tractive term depending upon the diameter, and add a constant. 

The more modern formulae are of the third class, and are as follows: 

t = 0.00008/irf+ 0.01^7+ 0.36 Shedd, No. 1. 

t = O.OOOOQhd + 0.0133f/ + 0.296 Warren Foundry, No. 2. 

t = 0.0()0().58^rf + 0.0152rf + 0.312 Francis, No. 3. 

t = 0.00()048^f/ + 0.013rf + 0.32 Dupuit, No. 4. 

t = 0.00004/irf + 0.1 ^JJ+ 0.15 Box, No. 5. 

t = 0.000135/irf + 0.4 - O.OOlld Whitman, No. 6. 

t = 0.00006 (/I + 230) d + 0.333 - 0.0033rf Fanning, No. 7. 

t = O.OOOldhd -h 0.25 - 0.0052d Meggs, No. 8. 

In which t = thickness in inches, h = head in feet, d = diameter in 
inches. For h = 100 ft., and rf = 10 in., formulae Nos. 1 to 7 inclusive 
give to from 0.49 to 0.54 in., but No. 8 gives only 0.35 in. Fanning's 
formula, now (190S) in most common use, gives 0.50 in. 

Rankine (Civil Engineering), p. 721, says: "Cast-iron pipes should be 
made of a soft and tough quaUty of iron. Great attention should be paid 



THICKNESS OF CAST-IRON WATER-PIPES. 



197 



to molding them correctly, so that the thickness may be exactly uniform 
all round. Each pipe should be tested for air-bubbles and flaws by ring- 
ing it with a hammer, and for strength by exposing it to double the 
intended greatest working pressure." The rule for computing the thick- 
ness of a pipe to resist a given working pressure is t = rp/f , where r is 
the radius in inches, p the pressure in pounds per square inch, and /the 
tensile strength of the iron per square inch. When / = 18,000. and a 
factor of safety of 5 is used, the above expressed in terms of d and h 
becomes t = 0.5dx 0.433/1 ^ 3600 = 0.00006rf/i. 

"There are hmitations, however, arising from difficulties in casting, 
and by the strain produced by shocks, which cause the thickness to be . 
made greater than that given by the above formula." (See also Burst- 
ing Strength of Cast-iron Cylinders, under " Cast Iron.") 

The most common defect of cast-iron pipes is due to the ' ' shifting of 
the core," which causes one side of the pipe to be thinner than the other. 
Unless the pipe is made of very soft iron the thin side is apt to be chilled 
in casting, causing it to become brittle and it may contain blow-holes 
and " cold-shots." This defect should be guarded against by inspection 
of every pipe for uniformity of thickness. 



Standard Thicknesses and Weights of Cast-Iron Pipe. 

(U. S. Cast Iron Pipe & Foundry Co., 1915.) 







Class A. 




Class B 






Class C 


. 


Class D. 


'% 2 


100 Ft. Head. 


200 Ft. Head. 


300 Ft. Head. 


400 Ft. Head. 




43 Lb. Pressure, 


86 Lb. Pressure. 


130 Lb. Pressure. 


173 Lb. Pressure 


13 d 


H 


Pounds per 




Pounds per 


|4 


Pounds per 




Pounds per 


l5 


Ft. 


L'gth. 


Ft. 


L'gth. 


Ft. 


L'gth. 


Ft. 


Lgth. 


3 


0.39 


14.5 


175 


0.42 


16.2 


194 


0.45 


17.1 


205 


0.48J 18.0 


216 


4 


.42 


20.0 


240 


.45 


21.7 


260 


.48 


23.3 


280 


.521 25.0 


300 


6 


.44 


30.8 


370 


.48 


33.3 


400 


.51 


35.8 


430 


.551 38.3 


460 


8 


.46 


42.9 


515 


.51 


47.5 


570 


.56 


52.1 


625 


.60 55.8 


670 


10 


.50 


57.1 


685 


.57 


63.8 


765 


.62 


70.8 


850 


.68; 76.7 


920 


12 


.54 


72.5 


870 


.62 


82.1 


985 


.68 


91.7 


1100 


.75 


100.0 


1200 


14 


.57 


89.6 


1075 


.66 


102.5 


1230 


.74 


116.7 


1400 


.82 


129.2 


1550 


16 


.60 


108.3 


1300 


.70 


125.0 


1500 


.80 


143.8 


1725 


.89 


158.3 


1900 


18 


.64 


129.2 


1550 


.75 


150.0 


1800 


.87 


175.0 


2100 


.96 


191.7 


2300 


20 


.67 


150.0 


1800 


.80 


175.0 


2100 


.92 


208.3 


2500 


1.03 


229.2 


2750 


24 


.76 


204.2 


2450 


.89 


233.3 


2800 


1.04 


279.2 


3350 


1.16 


306.7 


3680 


30 


.88 


291.7 


3500 


1.03 


333.3 


4000 


1.20 


400.0 


4800 


1.37 


450.0 


5400 


36 


.99 


391.7 


4700 


1.15 


454.2 


5450 


1.36 


545.8 


6550 


1.58 625.0 


7500 


42 


1.10 


512.5 


6150 


1.28 


591.7 


7100 


1.54 


716.7 


8600 


1.78 825.0 


9900 


48 


1.26 


666.7 


8000 


1.42 


750.0 


9000 


1.71 


908.3 


10900 


1.96 1050.0 


12600 


54 


1.35 


800.0 


9600 


1.55 


933.3 


11200 


1.90 


1141.7 


13700 


2.23 1341.7 


16100 


60 


1.39 


916.7 


11000 


1.67 


1104.2 


13250 


2.00 


1341.7 


16100 


2.38 1583.3119000 


72 


1.62 


1281.9 


15380 


1.95 


1547.3 


18570 


2.39 


1904.3 


22850 


1 


84 


1.72 


1635.8 


19630 


2.22 


2104.1 


25250 








:: ::;; 1 ::: 



The above weights are per length to lay 12 feet, including standard 
sockets; proportionate allowance to be made for any variation. 

Weight of Underground Pipes. (Adopted by the Natl. Fire Pro- 
tection Association, 1913.) Weights are not to be less than those 
specified when the normal pressures do not exceed 125 lb. per sq. in. 
When the normal pressures are in excess of 125 lb. heavier pipes should 
be used. The weights given include sockets. 

Pipe, in 4 

Weights per foot, lb 23 



6 


8 


10 


12 


14 


16 


35.8 


52.1 


70.8 


91.7 


116.7 


143.8 



198 



MATERIALS. 



Standard Thicknesses and Weights of Cast Iron Pipe. 
For Fire Lines and High-Pressure Service. 

(U. S. Cast Iron Pipe & Foundry Co., 1915.) 



Inside 
In. 


Class E. 




Class F. 


Class G. 


Class H. 


500 ft. Head. 


600 ft. Head. 


700 ft. Head. 


800 ft. Head. 


217-lb. Pressure. 


260-1 b. Pressure. 


304"lb. Pressure. 


347-lb. Pressure. 


1.1 


^^ 


Lb. per 


,^^ 


Lb. per 


i^ 


Lb. per 


1 d 


Lb. per 


6Q 


" u7 




o ^ 




.2 ./- 




.^ rn 




o" 


■■d '^ 




S w 






i ^ 






jd ^ 




iz; 


HS 


Ft. 


Lgth. 


HS 


Ft. 


Lgth. H S 


Ft. 


Lgth. 


HS 


Ft. 


Lgth. 


6 


0.58 


42.5 


510 


0.61 


44.3 


531 0.65 


48.1 


577 


0.69 


50.5 


606 


8 


.66 


60.9 


731 


.71 


66.8 


802 


.75 


72.3 


868 


.80 


76.1 


913 


10 


.74 


86.9 


1043 


.80 


92.8 


1114 


.86 


101.4 


1217 


.92 


107.3 


1288 


12 


.821 114.6 


1375 


.89 


122.8 


1474 


.97 


136.2 


1634 


1.04 


144.4 


1733 


14 


.90| 145.6 


1747 


.99 


158.8 


1905 


1.07 


175.1 


2101 


1.16 


187.5 


2250 


16 


.98 


180.7 


2168 11.08 


196.5 


2358 


1.18! 218.0 


2616 


1.27 


233.8 


2805 


18 


1.07 


221.8 


2662 1.17 


239.3 


2872 


1.281 268.2 


3218 


1.39 


287.8 


3453 


20 


1.15 


265.8 


3190 1.27 


287.3 


3448 


1.39 


321.8 


3862 


1.51 


345.8 


4149 


24 


1.31 


359.1 


4309 1.45 


392.3 


4707 


1.75 


479.8 


5758 


1.88 


510.6 


6127 


30 


1.55 
1 80 


530.9 
738.1 


6371 1.73 
8857 2.02 


588.8 
821.0 


7065 
9852 














36 































All lengths to lay 12 ft. Weights are approximate; those per foot 
include allowance for bell; those per length include bell. Propor- 
tionate allowance is to be made for variations from standard length. 



Standard and Heavy Cast Iron Bel! and Spigot Gas Pipe. 
Weights and Dimensions. 

(U. S. Cast Iron Pipe & Foundry Co., 1914.) 





Actual Out- 


Thickness, 


Dia. of Sock- 


d 


Weight per 


Weight per 


— fl 


side Dia., In. 


In. 


ets, 


In. 


•Si 


Foot, Lb. 


Length, Lb. 






>> 

> 


V 


e!5 




>> 

> 


St3 




i^ 


e3 


1^ 
























^- 


ffl 


m ^ 


w 


^'^ 


w 


qW 


^^ 


w 


Xfl ^ 


w 


4 


4.80 5.00 


0.40 


0.42 


5.80 


5.80 


4.00 


19.33 


20.0 


Til 


240 


6 


6.90 7.10 


.43 


.47 


7.90 


7.90 


4.00 


30.25 


32.8 


363 


394 


8 


9.05 9.05 


.45 


.49 


10.05 


9.85 


4.00 


42.08 


45.3 


505 


544 


10 


11 .10 11 .10 


.49 


.51 


12.10 


11.90 


4.00 


55.91 


58.7 


671 


703 


12 


13.20 13.20 


.54 


.57 


14.20 


14.00 


4.50 


73.83 


76.1 


886 


913 


16 117.40 1/.40 


.62 


.65 


18.40 


18.40 


4.50 


112.58 


117.2 


1351 


1406 


20 121.60 21 .60 


.6G 


.75 


22.85 


22.60 


4.50 


153.83 


166.7 


1846 


2000 


24 25.80| 25.80 


.76 


.82 


27.05 


26.80 


5.00 206.41 


224.0 


2477 


2683 


30 31.74 32.00 


.85 


1.00 


32.99 


33.00 


5.00 284.00323.9 


3408 


3887 


36 37.96 38.30 


.95 


1.05 


39.21 


39.30 


5.00 


379.25 442.7 


4551 


5312 


42 44.20 44.50 


1 .07 


1 .26 


45.45 


45.50 


5.00 


497.66581.3 


5972 


6975 


48 50.50 50.80 


1 .26 


1.38 


51.75 


51 .80 


5.00 


663.50 739.6 


7962 


8873 



The Standard pipe listed above conforms to the standard adopted by 
the American Gas Institute in 1911. The heavy pipe given is not in- 
cluded in the A. G. I. standards but is used by many gas engineers for 
service under paved streets with heavy traffic, or where subsoil condi- 
tions make the heavier pipe desirable. Pipes are made to lay 12 ft. 
length. Weights per foot include bell and bead. Length of bead = 
0.75 in. for 4- and 6-in. pipe; 1.00 in. for 8- to48-in. pipe. Thickness of 
bead = 0.19 in. for 4- and 6-in. pipe; 0.25-in. for 8- to 48-in. pipe. 



LEAD REQUIRED FOR CAST IRON PIPE JOINTS. 199 

Standard Flanged Cast Iron Pipe for Gas. 

(United Cast Iron Pipe & Foundry Co., 1914, Am. Gas. Inst. Std., 1913.) 



Nomi- 
nal 

Diam. 
In. 

4~ 

6 

8 
10 
12 
16 
20 
24 
30 
36 
42 
48 



Thick- 


Flange 


ness, 


Diam., 


In. 


In. 


0.40 


9.00 


.43 


11 .00 


.45 


13.00 


.49 


16.00 ; 


.54 


18.00 1 


.62 


22.50 ! 


.68 


27.00 


.76 


31 .00 


.85 


37.50 


.95 


44.00 


1.07 


50.75 


1.26 


57.00 



Flange i 
Thick- 
ness, 
In. 



Bolt 

Circle 

Diam., 

In. 



0.72 

.72 

.75 

.86 

.875 

1 .00 

1 .00 

1 .125 

1 .25 

1 .375 

1.56 

1.75 



7.125 
9.125 
11 .125 
13.75 
15.75 
20.00 
24.50 
28.50 
35.00 
41.25 
47.75 
54.00 



Bolts 


No. 


Size, 
In. 


4 


0.625 


4 


.625 


8 


.625 


8 


.625 


8 


.625 


12 


.75 


16 


.75 


16 


.75 


20 


.875 


24 


.875 


28 


1.00 


32 


1.00 



Wgt. 

Single 

Flange, 

Lb. 



Approx. Wgt., 
Lb. 

Foot. I Lgth. 



8.19 

10.46 

12.65 

22.53 

25.96 

39.68 

51 .10 

65.00 

96.70 

132.26 

186.83 

235.23 



18.62) 

29.01, 

40.05 

54.71 

71 .34 

108.61 

147.95 

197. 38| 

273.45 

366. 67 1 

483.48' 

647.36' 



223 

348 

481 

656 

856 

1303 

1775 

2369 

3281 

4400 

5802 

7768 



Pipe is made in 12-ft. lengths, and faced Vi6 in. snort for gaskets. 
Weight per foot includes flanges. Flanges are Am. Gas. Inst., and are 
different from the " American 1914" standard for water and steam pipe. 
Pipes heavier than above may be made by reducing internal diameters. 



Threaded Cast Iron Pipe. 

(U. S. Cast Iron Pipe & Foundry Co., 1914.) 



Nominal diam., in 

Actual outside diam., in. 
Thickness, in., Class B . . 
Wt. per foot. Class B . . . 
Thickness, in., Class D . . 
Wt. per foot. Class D . . . 



3 


4 


6 


8 


10 


3.96 


5.00 


7.10 


9.30 


11.40 


0.42 


0.45 


0.48 


0.51 


0.57 


14.6 


20.1 


31.2 


43.9 


60.5 


0.48 


0.52 


0.55 


0.60 


0.68 


16.4 


22.8 


35.3 


51.2 


71.4 



12 
13.50 

0.62 
78.9 

0.75 
93.7 



Quantity of Lead Required for Cast Iron Pipe Bell and Spigot Joints. 

(U. S. Cast Iron Pipe & Foundry Co., 1914.) 



8 


Depth of Joint 


1 
Id 

s 


Depth of Joint 




2 In. 1 2 1/4 In. 1 2 1/2 In. 1 Solid. 


2 In. 1 21/4 In. 1 21/2 In. Solid. 


.5 1-1 

G 


Approx. Weight of Lead in Joint. — Lb. 


Approx. Weight of Lead in Joint.— Lb. 


3 


6.00 


6.50 


7.00 


10.25 


24 


44.00 


48.00 


52.50 


95.00 


4 


7.50 


8.00 


8.75 


13.00 


30 


54.25 


59.50 


64.75 


117.50 


6 


10.25 


11.25 


12.25 


18.00 


36 


64.75 


71 .00 


77.25 


140.25 


8 


13.25 


14.50 


15.75 


23.00 


42 


75.25 


78.75 


85.50 


155.25 


10 


16.00 


17.50 


19.00 


31.00 


48 


85.50 


94.00 


102.25 


202.25 


12 


19.00 


20.50 


22.50 


36.50 


54 


97.60 


107.10 


li6.60 


238.60 


14 


22.00 


24.00 


26.00 


38.50 


60 


108.30 


118.80 


129.50 


255.50 


16 


30.00 


33.00 


35.75 


64.75 


72 


128.00 


140.50 


153.00 


302.50 


18 


33.80 


36.90 


40.00 


72.00 


84 


147.00 


161.50 


175.60 


348.00 


20- 


37.00 


40.50 


44.00 


80.00 













The above table gives the calculated weight of lead required for pipe 
joints both with and without gasket. Weight of lead taken at 0.41 
lb. per cu. in. Allowance has been made for lead to project beyond the 
face of the bell for calking. Pipe specifications allow lead space to vary 
from those given in tables, hence the weights of lead may vary ap- 
proximately 1 1 to 16 per qent from those given above. 



200 



MATERIALS 



Cast-iron Pipe Columns, Weight and Safe Loads, Pounds. 

(U. S. Cast Iron Pipe and Foundry Co., 1914.) 





ength. 


4-Inch Pipe. 


6-Inch Pipe. 


8-Inch Pipe. 


10-Inch Pipe. 




Wgt. 


Load. 


Wgt. 


Load. 


Wgt. 


Load. 


Wgt. 


- Load. 


6 ft. in. 


160 


56070 


245 


100100 


359 


164410 


428 


224200 


6 


6 


171 


54130 


262 


98310 


385 


162400 


464 


222300 


7 





183 


52190 


280 


96270 


410 


160350 


500 


220300 


7 


6 


194 


50250 


298 


94100 


436 


158200 


535 


218300 


8 





206 


48320 


316 


92040 


462 


156000 


571 


216200 


8 


6 


217 


46440 


333 


89820 


487 


153600 


607 


213900 


9 





229 


44590 


351 


87620 


513 


151200 


643 


211600 


9 


6 


240 


42800 


368 


85450 


539 


148760 


678 


209300 


10 





251 


41050 


386 


83260 


564 


1 46260 


714 


206900 


10 


6 


262 


39360 


404 


81040 


590 


143700 


750 


204500 


11 





274 


37730 


421 


78840 


615 


141160 


785 


202200 


11 


6 


285 


36160 


439 


76700 


642 


138570 


821 


1 99800 


12 





297 


34670 


457 


74580 


667 


135920 


857 


197400 


12 


6 


308 


33220 


474 


71600 


692 


133340 


893 


195000 


Base and Top 


Castir 


igs. 












Ins. 


square 




10 


1 


2 




14 


16 


Wt., 


lbs. 




65 


1 


00 




45 


200 



Add weight of base and top castings for complete weight of column. 
Loads are based on Gordon's formula, with a factor of safety of 8. 



Weight of Open End Cast-Iron Cylinders. 

Cast iron = 450 lbs. per cubic foot. 
Pounds per Lineal Foot. 





Thick. 


Wgt. 




Thick. 


Wgt. 




Thick. 


Wgt. 




Thick. 


Wgt. 


Bore. 


of 


per 


Bore. 


of 


per 


Bore. 


of 


per 


Bore. 


of 


per 




Metal. 


Foot. 




Metal. 


Foot. 




Metal. 


Foot. 




Metal. 


Foot. 


In. 


In. 


Lb. 


In. 


In. 


Lb. 


In. 


In. 


Lb. 


In. 


In. 


Lb. 


4 


3/8 


16.1 


11 


1/^ 


56.5 


17 


7/8 


153.6 


24 


7/8 


213.7 




V:^ 


22.1 




5/8 


71.3 


18 


5/8 


114.3 




1 


245.4 




5/8 


28.4 




3/4 


86.5 




3/4 


138.1 


26 


3/4 


197.0 


5 


3/8 


19.8 


12 


1/2 


61.4 




7/8 


162.1 




7/8 


230.9 




1/? 


27.0 




5/8 


77.5 


19 


5/s 


120.4 




1 


265.1 




5/« 


34.4 




3/4 


93.9 




3/4 


145.4 


28 


3/4 


211.7 


6 


3/8 


23.5 


13 


1/^ 


66.3 




7/8 


170.7 




7/8 


248.1 




1/^ 


31.9 




6/8 


83.6 


20 


5/8 


126.6 




1 


284.7 




5/8 


40.7 




3/4 


101.2 




3/4 


152.8 


30 


7/8 


265.2 


7 


3/8 


27.2 


14 


1/2 


71.2 




7/8 


179.3 




1 


304.3 




1/2 


36.8 




5/8 


89 7 


21 


5/8 


132.7 




11/8 


343.7 




5/8 


46.8 




3/4 


108.6 




3/4 


160.1 


32 


7/8 


282.4 


8 


3/8 


30.8 


15 


5/8 


95 9 




7/8 


187.9 




1 


324.0 




1/2 


41.7 




3/4 


116.0 


22 


5/8 


138.8 




11/8 


365.8 




5/8 


52.9 




7/8 


136.4 




3/4 


167.5 


34 


7/8 


299.6 


9 


1/2 


46.6 


16 


5/8 


102.0 




7/8 


196.5 




1 


343.7 




5/8 


59.1 




3/4 


123 3 


23 


3/4 


174.9 




11/8 


388.0 




3/4 


71.8 




7/8 


145.0 




7/8 


205.1 


36 


7/8 


316.6 


10 


1/^ 


51.5 


17 


5/8 


108.2 




1 


235.6 




1 


363.1 




5/8 


65.2 




3/4 


130.7 


24 


3/4 


182.2 




11/S 


410.0 




3/4 


79 2 





















The weight of two flanges may be reckoned = weight of one foot. 



WELDED PIPE. 



201 



WROUGHT-IRON (OR STEEL) WELDED PIPE. 

For discussion of the Briggs Standard of Wrought-iron Pipe Dimen- 
sions, see Report of the Committee of the A. S. M. E. in "Standard 
Pipe and Pipe Threads," 1886. Trans., Vol. VIII, p. 29. The diameter 
of the bottom of the thread is derived from the formula D — 

(0.05D + 1.9) X -, in which D = outside diameter of the tubes, and n 

n 
the number of threads to the inch. The diameter of the top of the 

thread is derived from the formula 0.8 - X 2 + c?, or 1.6 — he?, in which 

n n 

d is the diameter at the bottom of the thread at the end of the pipe. 
The sizes for the diameters at the bottom and top of the thread at the 
end of the pipe are as follows : 

Standard Pipe Threads. 





Nom- 


r^'^ 


Diam. Diam. 




Nom- 


rr.-^ 


Diam. 


Diam. 




inal 


^^ 


of Pipe of Pipe 




inal 


'^ fl 


of Pipe 


of Pipe 


Size. 


Ex- 


%^ 


at Root; at Top 


Size. 


Ex- 


<1^ V 


at Root 


at Top 




ternal 


!b, 9. 


of 1 of 




ternal 


^fe 


of 


of 




Diam. 


H^ 


Thread. 


Thread. 




Diam. 


H^ 


Thread. 


Thread. 


1/8 


0.405 


27 


0.3339 


0.3931 


5 


5.563 


8 


5.2907 


5.4907 


1/4 


.540 


\% 


.4329 


.5218 


6 


6.625 


8 


6.3460 


6.5460 


3/8 


.675 


18 


.5676 


.6565 


7 


7.625 


8 


7.3398 7.5398 


1/2 


.840 


14 


.7013 


.8156 


8 


8.625 


8 


8.33361 8.5336 


3/4 


1.050 


14 


.9105 


1 .0248 


9 


9.625 


8 


9.3273i 9.5273 


1 


1.315 


111/7 


1.1440 


1.2832 


10 


10.750 


8 


10.4453 10.6453 


11/4 


1.660 111 2 


1 .4876; 1 .6267 


11 


11 .750 


8 


11 .4390 11 .6390 


n/2 


1 .900 111/2 


1.7265 


1 .8657 


12 


12.750 


8 


12.4328; 12.6328 


2 


2.375 111/2 


2.1995 


2.3386 


13 


14.000 


8 


13.6750 13.8750 


21/2 


2.875 8 


2.6195 


2.8195 


14 


15.000 


8 


14.6688 14.8688 


3 


3.500 8 


3.2406 3.4406 


15 


16.000 


8 


15.6625 15.8625 


31/2 


4.000 8 


3. 73751 3.9375 


17 0.D. 


17.000 


8 


16.6563116.8563 


4 


4.500 8 


4.2343! 4.4343 


18 0.D. 


18.000 


8 


17.6500 17.8500 


41/2 


5.000 8 


4.73131 4.9313 


20 O.D. 


20.000 


8 


19.6375119.8375 



Tap Drills for Pipe Taps (Briggs' Standard) . 



Size of 
Tap, 
In. 



Size of 

Drill, 

In. 



Size of 
Tap, 
In. 



Size of 

Drill, 

In. 



Size of 
Tap, 
In. 



Size of 

Drill, 

In. 



Size of 
Tap, 
In. 



Size of 

Drill, 

In. 



1/8 
1/4 
3/8 
1/2 



21/64 
29/64 
19/32 
23/32 



3/4 
I 

1 1/4 

I 1/2 



lVl6 
1 3/16 
1 15/32 
1 23/32 



2 

21/2 

3 

31/2 



2 3/16 
211/16 

3 5/16 
313/16 



4 

41/2 

5 

6 



4 3/16 
411/16 

5 1/4 
615/16 



Ha\ing the taper, length of full-threaded portion, and the sizes at 
bottom and top of tlu-ead at the end of the pipe, as given in the table, 
taps and dies can be made to secure these points correctly, the length 
of the imperfect threaded portions on the pipe, and the length the tap 
is run Into the fittings beyond the point at which the size is as given, or. 
in other words, beyond the end of the pipe, having no effect upon the 
standard. The angle of the thread is 60°, and it is slightly rounded off 
at top and bottom, so that, instead of its depth being 0.866 its pitch, as 
is the case with a full Y-thread, it is 4/5 the pitch, or equal to 0.8 -^ n, n 
being the number of threads per inch. 

Taper of conical tube ends, 1 in 32 to axis of tube = M inch to the 
foot total taper. 

The thread is perfect for a distance (L) from the end of the pipe, ex- 
pressed by the rule, L = (0.8 D + 4.8) -i-n; where D = outside diameter 



202 



MATERIALS. 



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WELDED PIPE. 



203 



in inches. Then come two threads, perfect at the root or bottom, 
but imperfect at the top, and then come three or four threads imperfect 
at both top and bottom. These last do not enter into tlie joint at all, 
but are incident to the process of cutting the threads. The thickness 
of the pipe under the root of the thread at the end of the pipe = 0.0175 
D + 0.025 in. 

Briggs' standard gages are made by Pratt & Whitney Co., Hartford, 
Conn. 

Standard Welded Pipe. — The permissible variation in weights is 5% 
above and 5% below those given in the table on the opposite page. 
Pipe is furnished with threads and couplings, and in random lengths 
unless otherwise ordered. Weights are figured on the basis of one 
cubic inch of steel weighing 0.2833 lb., and the weight per foot with 
threads and couplings is based on a length of 20 feet, including the 
coupling, but shipping lengths of small sizes will usually average less 
than 20 feet. Taper of threads is % inch diameter per foot length for 
all sizes. The weight of water contained in one lineal foot is based 
on a weight of 62.425 pounds per cubic foot, wliich is the weight at its 
maximum density (39.1° F.) 

The steel used for lap-welded pipe has the following average analysis 
and physical properties: 

El. Tens. Elong. 
C Mn S P Lim. Str. in 8 in. 

Bessemer 0.07 0.30 0.045 0.100 36,000 58,000 22% 

Open-hearth 0.09 0.40 0.035 0.025 33,000 53,000 25% 



Extra Strong Pipe. (National Tube Company, 1915) 





Diameter. 


^ 


fa ^ 
(D g 


Circum- 
ference. 


Transverse Area. 


Length of 
Pipe per 
Sq. Foot. 


1^£ 

o «o 
















. 


0) 


OJ 


i 


^1 


r 






lis 






i-i 

1— 1 


3 






cOO 




In. 


In. 


In. 


Lb. 


In. 


In. 


Sq.In. 


Sq. In. 


Sq.In 


Ft. 


Ft. 


Ft. 


1/8 


0.405 


0.215 


.095 


0.314 


1.272 


0.675 


0.129 


0.036 


0.093 9.431 


17.766 


3966.393 


1/4 


.540 


.302 


.119 


.535 


1.696' .949 


.229 


.072 


.157 7.073 


12.648 


2010.290 


3/8 


.675 


.423 


.126 


.7381 2.121 1.329 


.358 


.141 


.217 5.658 


9.030 


1024.689 


1/^ 


.840 


.546 


.147 


1.087 


2.639 


1.715 


.554 


.234 


.320 4.547 


6.995 


615.017 


3/4 


1.050 


.742 


.154 


1.473 


3.299 


2.331 


.866 


.433 


.433 3.637 


5.147 


333.016 


1 


1.315 


.957 


.179 


2.171 


4.131 


3.007 


1.358 


.719 


.63912.904 


3.991 


200.193 


11/4 


1.660 


1.278 


.191 


2.996 


5.215 


4.015 


2.164 


1.283 


.88112.301 


2.988 


112.256 


11/2 


1 900 


1 500 


.200 


3.631 


5.969 


4.712 


2.835 


1.767; 1.068 2.010 


2.546 


8L487 


2 


2.375 


1.939 


.218 


5.022 


7.461 


6.092 


4.430 


2.953! 1.477! 1.608 


1.969 


48.766 


21/2 


2.875 


2.323 


.276 7.661 


9.032 


7.298 


6.492 


4.238 


2.25411.328 


1.644 


33.976 


3 


3.500 


2.900 


.300 10.252 


10.996 


9.111 


9.621 


6.605 


3.01611.091 


1.317 


21.801 


31/2 


4.000 


3.364 


.318 12.505 12.566 10.568 


12.566 


8.888 


3. 678! 0.954 


1.135 


16.202 


4 


4.500 


3.826'.337 14.983 14.137 12.020 


15.904 


11.497 


4.407 


.848 


0.998 


12.525 


41/2 


5.000 


4.290 .355 17.611 15.708113.477 


19.635 


14.455 


5.180 


.763 


.890 


9.962 


3 


5.563 


4.8 1 3 :.375 20.778 17.477t 15.120 


24.306 


18.194 


6.112 


.686 


.793 


7.915 


6 


6.625 


5.761 .432 23.573 20.813 18.099 


34.472 


26.067 


8.405 


.576 


.663 


5.524 


7 


7.625 


6.625 .500 33.043 23.955 20.813 


45.664 


34.472 11.192 


.500 


.576 


4.177 


8 


8.625 


7.625 .500 43.388 27.096 23.955 


58.426 


45.663 12.763 


.442 


.500 


3.154 


9 


9.025 


8.625 


.500 43.728 30.238 27.095 


72.760 


58.426 14.334 


.396 


.442 


2.465 


10 


10.750 


9.750 


.500 54.735 33.772,30.631 


90.763 


74.662! 16.101 


.355 


.391 


1.929 


11 


11.750 


10.750 


.500 60.075 36.914 33.772 


108.434 


90.763: 17.671 


.325 


.355 


1.587 


12 


12.750 


11.7^^0 .500 65.415 40.055 36.914 


127.676 


108.434 19.242 


.299 


.325 


1.328 


13 


14.000 


13.000 .500 72.091 43.982 40.841 


153.938 


132.732 21.206 


.272 


.293 


1.085 


14 


15.000 


14.000 .500 77.431 47.124 43.982 


176.715 


153.938 22.777 


.254 


.272 


0.935 


15 


16.000 


15.000 


.500 


82.771 


50.265 


47.124 


201.062 


176.715 


24.347 


.238 


.254 


.815 



The permissible variation in weight is 5% above and 5% below. 
Furnished with plain ends and in random lengths unless otherwise 
ordered. 



204 MATERIALS. 

Double Extra Strong Pipe. (National Tube Company, 1915.) 









^rA-\ ^. _.. 




Length of 


2 W)4J 




Diameter. 


0) 


fiH fl ' ference. 


Transverse Area. 


Pipe per 
Sq. Foot. 


fas 














0"^ 

r 


|i3 i-i 


1 




ii 




In. 


In. 


In. Lb. 


In. 


In. 


Sq.In Sq.In Sq.In 


Ft. Ft. 


Feet. 


ih 


0.840 


0.252 


0.294 1.714' 2.639 


0.792 


0.554 0.050 0.504 


4.547i 15.157 


2887.165 


3/4 


I.O7O 


.434 


.308! 2.440 3.299' 1.363 


.866 .148' .718 


3.637 


8.801 


973.404 


1 


1.315 


.599 


.358 


3.659 4.1311 1.882 


1.358 .282 1.076 


2.904 


6.376 


510.998 


11 /<1 


1.660 


.896 


.382 


5.214 5.215 2.815 


2.164 .6301 1.534 


2.301 


4.263 


228.379 


n/o 


1.900 


1.100 


.400 


6.408 5.969 3.456 


2.835 .9501 1.885 


2.010 


3.472 


151.526 


? ' ■ 


7.375 


1.503 


.436 


9.029 7.461 4.722 


4.4301 1.774! 2.656 


1.608 


2.541 


81.162 


?l/o 


2.875 


1.771 


.552 13.695 9.032! 5.564 


6.492 2.464! 4.028 


1.328 


2.156 


58.457 


^ 


3.500 


2.300 


.600 18.583 10.996 7.226 


9.621 ! 4.155 


5.466 


1.091 


1.660 


34.659 


31/9 


4.000 


2.728 


.636 22.850 12.5b6l 8.570 


12.5661 5.845 


6.721 


0.954 


1.400 


24.637 


4 


4,500 


3.152 


.67427.541 14.1371 9.902 


15.904 7.803 


8.101 


.848 


1.211 


18.454 


41/9 


5.000 


3.580 


.710 32.530 15.708' 11.247 


19.635 10.066 


9.569 


.763 


1.066 


14.306 


5 


5.563 


4.063 


.750 38.552 17.477:12.764 


24.306 12.966 


11.340 


.686 


0.940 


11.107 


6 


6.675 


4.897 


.864 53.160 20.813 15.384 


34.472 18.835 


15.637 


.576 


.780 


7.646 


7 


7.625 


5.875 


.875 63.079 23.955 18.457 


45.664 27.109 


18.555 


.500 


.650 


5.312 


8 


8.625 


6.875 


.875 72.424 27 .096121. 598 


58.426i37.122 


21.304 


.442 


.555 


3.879 



The permissible variation in weight is 10% above and 10% below. 
Furnished with plain ends and in random lengths unless otherwise 
ordered. 

Standard Boiler Tubes and Flues — Lap- Welded. 

(National Tube Company, 1915.) 



Diameter. 


i 




Circum- 
ference. 


Transverse Area. 


Length of Tube 
per Sq. Foot. 








5 




H 


id 

St 


1^ 




1 


Xu 


-"1 






in. 


In. 


In. 


Lb. 


In. 


In. 


Sq.In. 


Sq.In. Sq.In 


Ft. 


Ft. 


Ft. 


Ft. 


•13/4 


1.560 


0.095 


1.679 


5.498 


4.901 


2.405 


1.911 


.494 


2.182,2.448 


2.315 


75.340 


2 


I.81O 


.095 


1.932 


6.283 


5.686 


3.142 


2.573 


.569 


1.909 2.110 


2.010 


55.965 


2i/4 


2.O0O 


.095 


2.186 


7.0o9 


6.472 


3.976 


3.333 


.643! 1.697! 1.854 


1.775 


43.205 


21/? 


2.232 


.109 


2.783 


7.854 


7.1b9 


4.909 


4.090 


.819 1.527*1.673 


1.600 


35.208 


23/4 


2.532 


.109 


3.074 


8.639 


7.955 


5.940 


5.036 


.904 1 .388 1 .508 


1.448 28.599 


3 


2.782 


.109 


3.365 


9.425 


8.740 


7.0t)9 


6.079 


.990 1 .273 


1 .373 


1.323 23.690 


31/4 


3.010 


.120 


4.011 


10.210 


9.456 


8.296 


7.116 


1.180! 1.175 


1.269 


1.222 20.237 


31/1^ 


3.260 


.120 


4.331 


10.996 


10.242 


9.621 


8.347 


1.274 1.091 


1.171 


1.131 


17.252 


33/4 


3.510 


.120 


4.652 


11.781 


1 1 .027 


1 1 .045 


9.677 


1.368 1.018 


1.088 


1.053 


14.882 


4 


3.732 


.134 


5.532 


12.5o6 


11.724 


12.5ob 


10.939 


1.627 


0.954! 1.023 


0.989 


13.164 


41/?, 


4.232 


.134 


6.2t8 


14.137 


13.295 


15.904 


I4.O06 


1.838 


.848 0.902 


.875 


10.237 


5 


4.704 


.H8 


7. 6o9 15.708 


14.778 


19.035 


17.379 


2.256 


.763 


.812 


.787 


8.286 


6 


5.670 


.165 


10.282 18.850 


17.813 


28.274 


25.249 


3.025 


.636 


.673 


.655 


5.703 


7 


6.670 


.165 


12.044 21.991 


20.954 


38.485 


34.942 


3.543 


.545 


.572 


.559 


4.121 


8 


7.670 


165 


13.807 25.133 


24.096 


50.265 


46.204 


4.061 


.477 


.498 


.487 


3.117 


9 


8.640 


.180 


16.955 28.274 


27.143 


63.617 


58.629 


4.988 


.424 


.442 


.433 


2.456 


1U 


9.594 


.203 


21.240 31.416130.140 


78.540 


72.292 


6.248 


.381 


.398 


.390 


1.992 


II 


10.560 


.220 25.329 34.5^8133.175 


95.033 


87.582 


7.451 


.347 


.361 


.354 


1.644 


12 


1 1 .542 


.229 28.788 37.699 36.2o0' 113.097 


104.629 


8.468 


.318 


.330 


.324 


1.376 


13 


12.524 


.238 32.439 40.841 39. 3't5 132.732 


123.190 


9.542 


.293 


.304 


.299 


1.169 


14 


13.504 


.2^8 36.424 43.982 42.424 153.938 


143.224 


10.714 


.272 


.282 


.277 


1.005 


13 


14.482 


.259^.775 47.124 45.497.176.715 


164.721 


11.994 


.254 


.263 


.259 


0.874 


16 


15.460 


.270 


45.359 


50.265 


48.509 


201.062 


187.719 


13.343 


.238 


.247 


.242 


.767 



LAP-WELDED STEEL PIPE. 



205 



Weights and Bursting Strength oif Lap-Welded Steel Pipe. 

(American Spiral Pipe Works, Chicago, 1911.) 

20-Ft. Lengths, Plain Ends without Connections. Thicknesses in 
U. S. Standard Gage or Inches. Bursting Strength in Lb. per Sq. In. 
Internal Pressure. 



.3 


Is 


3 


.5 a» 

m 4J 


5 


i 






03 

5 ^ 

T3 fl 


i 

Is 






T 

l-H 




r 






s 

H 


r 




•53^ 
1— t 


g" 


r 




12 


10G 


19.3 


1172 


28 


3/4 


244 


2678 


42 


1/4 


119 


595 




3/16 


25.8 


1562 


" 


1 


329 


3570 


" 


1/2 


239 


1190 


** 


1/4 


34.6 


2083 


" 


11/4 


416 


4462 


'* 


3/4 


362 


1784 


14 


10G 


22.4 


1005 


30 


3/16 


64 


625 


" 


1 


486 


2380 




1/4 


40.2 


1785 


" 


1/4 


85 


833 


" 


11/4 


612 


2976 


" 


3/8 


61.0 


2678 


" 


1/2 


172 


1666 


44 


1/4 


124 


568 


'* 


1/2 


82.0 


3568 


" 


3/4 


261 


2500 


" 


1/2 


250 


1136 


16 


lOG 


25.6 


879 


" 


1 


352 


3328 


" 


3/4 


378 


1705 


** 


1/4 


45.8 


1562 


" 


I 1/4 


444 


4160 


** 


1 


508 


2277 


" 


3/8 


69.4 


2344 


32 


3/16 


68 


586 


" 


11/4 


640 


2840 


" 


1/2 


93.5 


3124 


" 


1/4 


91 


781 


48 


1/4 


135 


520 


(( 


5/8 


118.0 


3904 


" 


1/2 


183 


1562 


" 


1/2 


273 


1040 


18 


10G 


28.7 


781 


** 


3/4 


278 


2344 


** 


3/4 


412 


1562 


" 


1/4 


51.4 


1388 


" 


1 


374 


3125 


" 


1 


553 


2080 


" 


3/8 


77.8 


2082 


" 


11/4 


472 


3906 


" 


11/4 


696 


2604 


" 


1/2 


104.7 


2776 


34 


3/16 


72 


551 


50 


1/4 


141 


500 


" 


Vs 


132.0 


3472 


** 


1/4 


96 


735 


** 


1/2 


284 


1000 


20 


10G 


31.9 


703 


** 


1/2 


194 


1470 


" 


3/4 


429 


1500 


" 


1/4 


57.0 


1250 


" 


3/4 


294 


2206 


f 


1 


576 


2000 


t< 


1/2 


116.2 


2500 


" 


1 


396 


2942 


" 


11/4 


724 


2500 


** 


3/4 


177.0 


3736 


'< 


11/t 


500 


3678 


54 


1/4 


152 


463 


22 


10G 


35.0 


639 


36 


3/16 


76 


520 


" 


1/2 


306 


926 


" 


1/4 


62.6 


1136 


" 


1/4 


102 


694 


" 


3/4 


462 


1390 


" 


1/2 


127.0 


2272 


*' 


1/2 


206 


1388 


" 


1 


620 


1852 


" 


3/4 


194.0 


3410 


" 


3/4 


311 


2080 


" 


11/4 


780 


2315 


" 


1 


262.0 


4555 


" 


1 


419 


2776 


60 


1/4 


169 


416 


24 


lOG 


38.0 


586 


" 


11/4 


528 


3472 


" 


1/2 


340 


832 


** 


1/4 


68.0 


1041 


38 


3/16 


80 


493 


" 


3/4 


513 


1250 


" 


1/2 


138.0 


2082 


" 


1/4 


107 


658 


*' 


1 


688 


1664 


" 


3/4 


210.0 


3124 


" 


1/2 


217 


1316 


'* 


11/4 


864 


2080 


" 


1 


284.0 


4160 


'* 


3/4 


328 


1972 


66 


1/4 


186 


379 


26 


3/16 


55.0 


721 


" 


1 


441 


2632 


*< 


1/2 


374 


758 


" 


1/4 


74.0 


961 


" 


11/4 


556 


3288 


" 


3/4 


563 


1132 


" 


1/2 


150.0 


1922 


40 


3/16 


84 


467 


" 


1 


755 


1516 


" 


3/4 


227.0 


2885 


" 


1/4 


113 


625 


'* 


11/4 


948 


1892 


<* 


1 


307.0 


3847 


" 


1/2 


228 


1250 


72 


1/4 


203 


347 


" 


11/4 


388.0 


4809 


" 


3/4 


345 


1868 


** 


1/2 


407 


694 


28 


3/16 


60.0 


669 


" 


1 


464 


2500 


" 


3/4 


614 


1040 


" 


1/4 


80.0 


892 


" 


11/4 


584 


3124 


" 


1 


822 


1388 


*' 


1/2 


161.0 


1784 


42 


3/16 


89 


446 


** 


11/4 


1032 


1736 



For dimensions of extra heavy rolled steel flanges for above pipe, 
see table page 211. 

Square Pipe, external size, 7/8, 1, II/4, II/2, m/ie, 2, 21/2, 3 in. 

Rectangular Pipe, external size, 1 1/4 X 1, 1 1/2 X 1 1/4, 2X1 1/4, 
2X1 1/2, 21/2X1 1/2, 3X2. 

Two or more thicknesses of each size. 

Pipe Specialties. — Hand railings and their fittings; ladders with flat 
or round pipe bars and runners; seamless cylinders, with flat, domed, 
disked, or necked ends; special shapes for automobiles, to replace drop 
forgings; tapered tubes, and other specialties are illustrated in National 
Tube Co.'s Book of Standards. 



206 



MATERIALS. 



Special Sizes of Lap-welded Pipe — Boston Casing. (National Tube Co.) 



1^ 






si 
1'^ 




II 


1^ 


|q 




1^ 


1.2 




2 


21/4 


0.100 


41/2 


4 3/4 


0.145 


55/8 


6 


0.224 


81/4 


85/8 


0.217 


21/4 


21/2 


.108 


41/2 


43/4 


.193 


55/8 


6 


.275 


81/4 


85/8 


.264 


21/2 


23/4 


.113 


43/4 


5 


.152 


6 1/4 


6 5/8 


.169 


8 5/8 


9 


.196 


2 3/4 


3 


.116 


5 


51/4 


.153 


6 1/4 


6 5/8 


.185 


95/8 


10 


.209 


3 


31/4 


.120 


5 


51/4 


.182 


6 5/8 


7 


.174 


10 5/8 


11 


.224 


3 1/4 


31/2 


.125 


5 


51/4 


.182 


6 5/8 


7 


.231 


115/8 


12 


.243 


31/2 


33/4 


.129 


5 


51/4 


.241 


71/4 


75/8 


.181 


121/2 


13 


.259 


33/4 


4 


.134 


5 


51/4 


.301 


75/8 


8 


.186 


131/2 


14 


.276 


4 


41/4 


.138 


53/16 


51/2 


.154 


75/8 


8 


.236 


141/2 


15 


.291 


41/4 


41/2 


.142 


55/8 


6 


.164 


81/4 


85/8 


.188 


151/2 


16 


.302 


41/4 


41/2 


.205 


55/8 


6 


.190 















Other sizes of lap- welded pipe: Inserted Joint Casing, external 
diameters same as Boston Casing, with the least thickness. The 5 5/8 
casing is made 0. 164 and 0. 190 in. thick. California Diamond X Casing, 
sizes 5 5/8 to 15 1/2, all heavier than Boston. Oil Well Tubing, II/4 to 4 in. ; 
Bedstead Tubing, 3/8 to 3 in. ; Flush Joint Tubing, 3 to 18 in. ; AUison 
Vanishing Thread Tubing, 2 to 8 in., ends upset, II/4 to 8 in., ends not 
upset; Special Rotary Pipe, 2 1/2 to 6 in.; South Penn Casing, 5 3/i6 to 
12 1/2 in. ; Reamed and Drifted Pipe, 2 to 6 in. ; Air-hne Pipe, 1 1/2 to 6 in. ; 
Drill Pipe, 4 to 6 in.; Dry-kiln Pipe, 1 and II/4 in.; Tuyere Pipe, 1 and 
11/4 in. 

TUBULAR ELECTRIC LEVE POLES. 

For railway work the poles most used are 30 ft. long, and are com- 
posed of 7-in., 6-in., and 5-in. pipe. Anchor poles are usually 8-in., 
7-in., and 6-in., but often they are made of larger pipe. Full directions 
for designing such poles are given in the National Tube Co.'s Book of 
Standards, which contains 38 pages of tables of dimensions, load, de- 
flection, etc., of poles of different sizes and weights. 

PROTECTIVE COATINGS FOR PIPE. 

(1) Galvanizing — The pipe cleaned from scale and rust by pickling 
in warm dilute sulphuric acid, washed, immersed in an alkaline bath, 
dried and immersed in molten zinc. (2) Bituminous Coating — The 
cleaned, dried and warmed pipe is dipped in a bath of refined coal tar 
pitch, free from water and the lighter oils, at a temperature not below 
212°, and then baked. (3) ''National Coating." — The bituminous 
coated pipe, after baking is wrapped with a strip of fabric saturated 
with the hot compound, the edges of the fabric overlapping. 

VALVES AND FITTINGS. 

(From Information Furnished by National Tube Co., 1915.) 

Wrought pipe is usually connected in one of three ways, screwed, 
flanged or leaded joints. 

Screwed. — Pipe in sizes from i/s in. to 15 in. inclusive is regularly 
threaded on the ends, and is connected by means of threaded couplings. 

Flanged. — Pipe in sizes II/4 inches and larger is frequently connected 
by drilled flanges bolted together, the joint being made by a gasket 
between the flange faces. 

Flanges are attached to the pipe in a variety of ways. The most 
common method for sizes of pipe from I1/4 in. to 15 in. inclusive 
is by screwing them on the pipe. Many prefer peened flanges for 
pipe larger than 6 in. The peened flange is shrunk on the end of 
the pipe, and the latter is then peened over or expa^nded into a recess 
in the flange face. Steel flanges are also welded to pipe and loose 
flanges are used by flanging over the pipe ends. When no method 
of attaching is stated, screwed flanges are always furnished. 



VALVES AND FITTINGS. 207 

Working Pressures. — All valves and fittings are classified, as a rule, 
under five general headings, representing the working pressures for 
which they are suitable, as follows: Low Pressure, up to 25 pounds 
per square inch. Standard, up to 125 pounds per square inch. Medium 
Pressure, from 125 pounds to 175 pounds per square inch. Extra 
Heavy, from 175 pounds to 250 pounds per square inch. Hydraulic, 
for high pressure water up to 800 pounds per square inch. 

The following table gives the names of different valves and fittings, 
the material of which they are made, and the regular sizes manu- 
factured for the different pressures {L, low; S, standard; M, medium; 
E, extra heavy; H, hydrauUc): 

SCREWED FITTINGS. 

Malleable Iron S, E, H, sizes l/s to 8 in. 

Cast Iron S, E, " 1/4 to 12 in. 

FLANGED FITTINGS. 

Cast Iron L. S, E, H, sizes 2 in. and larger. 

GATE VALVES. 

Brass L S M E H up to 3 in. 

Iron Body, sizes. . 12 to 48 2 to 30 2 to 18 1 1/4 to 24 1 1/2 to 12 in. 

GLOBE AND ANGLE VALVES. 

Brass S, i/s to 4; M, 1/4 to 3; E, 1/2 to 3; H, I/2 to 2 

Iron Body *S, 2 to 12; E,2 to 12 

CHECK VALVES. 

Brass S, M, E, H, sizes i/s to 3 in. 

Iron Body L, S, M, E, H, " 2 to 12 in. 

COCKS, STEAM AND GAS. 

Brass sizes 1/4 to 3 in. 

Iron Body ** 1/2 to 3 in. 

Nipples. — Nipples are made in all sizes from i/g in. to 12 in. in- 
clusive, in all lengths, either black or galvanized, and regular right- 
hand or right- and left-hand threads. (For table of nipples see National 
Tube Co.'s Book of Standards.) Long screws or tank nipples are made 
of extra heavy pipe because there is less danger of crushing or splitting 
them when screwing up. 

Screwed Fittings — Malleable Iron. — Standard Malleable Iron Fittings 
are made both plain and beaded. The former are generally used for 
low pressure gas and water, as in house plumbing and railing work. The 
beaded is the standard steam, air, gas, or oil fitting. Beaded fittings, 
in sizes 4 in. and smaller, are made in nearly every useful combination of 
openings. Sizes larger than 4 in. are not usually made reducing except 
by means of bushing. Extra heavy and hydrauhc malleable iron 
fittings are flat bead, or banded. 

Screwed Fittings — Cast Iron. — ^It is not considered good practice to 
use screwed cast-iron fittings of any kind in sizes larger than 6 in. 

Flanged Fittings. — The flanges of the low pressiu'e and standard are 
the same with the exception of the flange thickness, which is less on the 
low pressure. These flanges are knowTi as the American Standard. 
(See pp. 209, 210.) 

There is no recognized standard for flanges in hydraulic work. 

Unions. — Unions are usually classified under two headings, Nut unions 
and Flange unions. Nut unions are commonly used in sizes 2 in. and 
smaller, and flange unions in sizes larger than 2 in. However, many 
manufacturers make nut unions as large as 4 in. and flange unions 
smaller than 2 in. 

Nut unions are made in malleable iron, bra.ss, and malleable iron, 
and ail brass. The all malleable iron union (lip union) is the standard 
malleable iron union of the trade and requires a gasket. The brass 
and malleable iron union is a better union, because no gasket is re- 
quired and there is no possibiUty of the parts rusting together. The 
pipe end of this union which carries an external thread, called the 



208 MATERIALS. / 

thread end, upon which'the nut or ring screws, is made of brass, and the 
other pipe end (called the bottom) and nut ring are made of malleable 
iron. The seat formed by the brass and iron pipe ends, when brought 
together, is truly spherical and the harder iron is sure to make a perfect 
joint with the softer brass. 

All-brass unions are made with a spherical or conical seat, no gaskets 
being required. The finished all-brass union is often used where showy 
work is desired, such as oil piping for engines, etc. 

Flange unions are made of malleable iron, malleable iron and brass, 
cast iron, and cast iron and brass. 

The type of flange union recommended for standard work is made 
with a brass to iron non-corrosive ball joint seat which requires no 
gasket to make a tight joint even when the pipe alignment is imperfect. 
The flange is loose on the collar, so that the bolts match the holes in 
any position. 

Valves arid Cocks. — The most common means for regulating the flow 
of fluids in pipes is by means of valves and cocks, valves being pre- 
ferred because of the easier operation and greater reliability. The 
common types of valves are straightway or gate, globe, and angle. A 
globe valve offers more resistance to the flow of any fluid than the 
straightway valve. 

Globe and Angle Valves. — Many manufacturers make a globe and 
angle valve known as light standard or competition valve, but it is 
not recommended for any work except the lowest pressiu'es, or where 
the valve will not be often opened or closed. 

CocA:5.— Among the modern types of cocks is one made with iron 
body and brass plug. This cock has an inverted plug with a spring 
at the bottom constantly pressing the plug against the seat, which 
reseats the plug if it should stick. These cocks are tested to 250 lb. 
cold-water pressure, and 125 lb. compressed-air pressure imder water, 
and are recommended for 125 lb. working pressure. 

Blast Furnace Fittings. — Tuyere cocks and tuyere unions used in 
blast furnace piping are ahvays made of brass on account of ease in 
disconnecting, greater reliability of metal and resistance to corrosion 
from the impurities in the water, such as sulphuric acid. 

STANDARD PIPE FLANGES (CAST IRON). 

The following tables showing dimensions of standard pipe flanges 
were adopted by the American Society of INIechanical Engineers, the 
Master Steam and Hot Water Fitters' Association, and a committee 
representing the manufacturers of pipe fittings. They represent a 
compromise between the standards adopted by the American Society of 
Mechanical Engineers and the Master Steam and Hot Water Fitters* 
Association in 1912, known as the 1912 U. S. Standard, and the stand- 
ards adopted by a conference of manufactiu-ers in July, 1912, known 
as the Manufacturers' standard. The new stand^irds, given in the 
tables, are called the American Standard, and became effective Jan. 1, 
1914. The table of flanges for extra heavy fittings is for working 
pressures up to 250 lb. per sq. in. The table for ordinary fittings is for 
working pressures up to 125 lb. per sq. in. In the tables, the values of 

stresses in pipe walls were calculated from the formula S= — 7—' 

where p = working pressure, lb. per sq. in., t = thickness of pipe, 
in., and r = radius of pipe, in. The highest stress was found to be 
2000 lb. per sq. in. on the 250-lb., 46- and 48-in. pipe walls, giving a 
factor of safety of about 10. The desirable thickness of pipe (Col. 2) 

is calculated from the formula T = f^^^ D + 0.3331 1 - j^) |l-2. 

where p = pressure, lb., per sq. in., 3 = 1800, and d = diameter 
of pipe. The minimum thickness in even fractions of an inch is given 
in Col. 3. The following approximate formulae were also used for 
ordinary fittings: Diam. of bolt circles = 1.10 d +3. Flange thick- 
ness (for pipe diameters 26 to 100 in. inclusive) = 0.0315 d + 1.25. 
For extra heavy fittings the formuh« are: Bolt circle = 1.171 d 4-3.75; 
Flange thickness = 0.0546 d -h 1.375 (for sizes 10 to 48 in. inclusiye). 



American Standard Cast Iron Pipe Flanges for Pressures up to 

125 Lb. per Sq. In. (All Dimensions in Inches.) 



209 



Pipe 


^^ 


Flanges. 




Bolts. 






u 
o 


Thickness 




s 




'0 

it 


1 
'on 


1 


5 


> ^ 




0) 



on 


See Fig. 75, 
p. 210 


^ 


i4 


•si 




5 


A 


B 


C 


1 


0.43 


7/16 


143 


4 


7/16 


|l/2 


3 


"4 


7/16 


0.093 


264 


9/16 


2:12 


0.91 


VJ] 


11/4 


0.44 


7/16 


178 


41/2 


1/2 


15/8 


33/8 


4 


7/16 


0.093 


412 


9/16 


2.38 


0.91 


1.47 


11/2 


0.45 


7/16 


214 


5 


9/16 


13/4 


37/8 


4 


1/2 


0.126 


438 


5/8 


2.73 


1.00 


1.73 


2 


0.46 


7/16 286 


6 


5/8 


2 


43/4 


4 


6/8 


0.202 


486 


3/4 


3.351 


1.21' 


2.14 


21/2 


0.48 


7/16 357 


7 


11/16 


21/4 


51/2 


4 


5/8 


0.202 


750 


3/4 


3.88 


1.21 


2.67 


3 


0.50 


7/16 428 


71/2 


3/4 


21/4 


6 


4 


5/8 


0.202 


1093 


3/4 


4.23 


I.21I 


3.02 


31/2 


0.52 7/161 500 


81/2 


13/16 


21/2 


7 


4 


5/8 


0.202 


1488 


3/4 


4.94 


1.211 


3.73 


4 


0.53 


1/2 


500 


9 


15/16 


21/2 


71/2 


8 


5/8 


0.202 


972 


3/4 


2.87 


1.21, 


1.56 


41/2 


0.55 


1/2 


562 


91/4 


15/16 


23/8 


73/4 


8 


3/4 


0.302 


823 


7/8 


2.96 


1.44 


1.52 


5 


0.56 


1/2 


625 


10 


15/16 


21/2 


81/2 


8 


3/4 


0.302 


1016 


7/8 


3.25 


1.44 


1.81 


6 


0.60 


9/16 


667 11 


1 


21/2 


91/2 


8 


3/4 


0.302 


1463 


7/8 


3.63 


1.44 


2.19 


7 


0.63 


V8 


700 12 1/2' 1 1/16 


2 3/4 


103/4 


8 


3/4 


0.302 


1991 


7/8 


4.11 


1.44 1 


2.67 


8 


0.66 


5/8 


800 131/2 


1 1/8 


2 3/4 


113/4 


8 


3/4 


0.302 


2600 


7/8 


4.50 


1.44' 


3.06 


9 


0.70 


11/16 818 15 


1 1/8 


3 


131/4 


12 


3/4 


0.302 


2194 


7/8 


3.43 


1.44 


1.99 


10 


0.73 


3/4 


833 16 


1 3/16 


3 


141/4 


12 


7/8 


0.420 


1948 


1 


3.69 


1.66 


2.03 


12 


0.80 


13/16 


923 19 


1 1/4 


31/2 17 


12 


7/8 


0.420 


2805 


1 


4.40 


1.66 


2.74 


14 


0.86 


7/8 


1000! 21 


1 3/8 


31/2 18 3/4 


12 


1 


0.550 


2915 


1 1/8 


4.86 


1.88 


2.98 


15 


0.90 


7/8 


1072 


221/4 


1 3/8 


3 5/81 20 


16 


1 


0.550 


2510 


11/8 


3.90 


1.88 


2.02 


16 


0.93 


1 


1000 


231/2 


1 7/16 


3 3/4J 21 1/4 


16 


1 


0.550 


2856 


11/8 


4.14 


1.88 


2.26 


18 


1. 00 


1 1/16 


1059 


25 


1 9/16 


31/9I 22 3/4 


16 


1 1/8 


0.694 


2865 


11/4 


4.44 


2.09 


2.35 


20 


1.07 


1 1/8 


nil 


271/2 


1 11/16 


33/i, 25 


20 


1 1/8 


0.694 


2829 


11/4 


3.91 


2.09 


1.82 


22 


1.13 


1 3/16 


1158 291/2 


113/16 3 3/41 271/4 


20 


11/4 


0.893 


2660 


13/8 


4.26 


2.31 


1.95 


24 


1.20 


1 1/4 1200 32 


1 7/8 


4 1 291/2 


20 


1 1/1 


0.893 


3166 


13/8 


4.62 2.31 


2.31 


26 


1.27 


1 5/16 ! 1238 


341/4 


2 


41/8 313/4 


24 


1 1/4 


0.893 


3096 


13/8 


4.14 2.31 


1.83 


28 


1.33 


1 3/8 11273 


361/2 


2 I/16 


41/4 34 


28 


1 1/4 


0.893 


3078 


13/8 


3.81 2.31 


1.50 


30 


1.40 


1 7/16' 1304 


38 3/4 


2 1/8 


43/8, 36 


28 


13/8 


1.057 


2985 


11/2 


4.03 2.53 


1.50 


32 


1.47 


1 1/2 11333 


413/4 


2 1/4 


47/8 


381/2 


28 


1 1/2 


1.294 


2775 


15/8 


4.31 2.75 


1.56 


34 


1.54 


1 9/16 1360 433/4I2 5/16 


4 7/8 


401/2 


32 


11/2 


1.294 


2741 


15/8 


3.972.75 


1.22 


36 


1.60 


1 5/8 11385 46 !2 3/8 


5 


42 3/4 


32 


1 1/2 


1.294 


3073 


15/8 


4.19:2.75 


1.44 


38 


1.67 


111/1611407 


48 3/4 2 3/8 


5 3/8 451/4 


32 


1 5/8 


1.515 


2924 


13/4 


4.432.96 


1.47 


40 


1.73 


1 3/4 J1428 


503/4 2 1/2 


5 3/8! 471/4 


36 


15/8 


1.515 


2880 


13/1 


4.1112.96 


1.15 


42 


1.82 


113/16 1448 


53 2 5/8 


51/21 491/2 


36 


15/8 


1.515 


3175 


13/4 


4.31 


2.96 


1.35 


44 


1.87 


1 7/8 1467 


55 1/4' 2 5/8 


5 5/8 513/4 


40 


1 5/8 


1.515 


3136 


13/4 


4.06 


2.96 


1.10 


46 


1.94 


115/16 1484 


57 1/4 2 11/16 


5 5/8' 533/4 


40 


15/8 


1.515 


3428 


13/4 


4.22 


2.96 


1.26 


48 


2.00 


2 1500 


591/22 3/4 


53/4, 56 


44 


15/8 


1.515 


3393 


13/4 


3.9812.96 


1.02 


50 


2.07 


2 1/16 1515' 613/4 2 3/4 


57/8 


581/4 


44 


13/4 


1 .746 


3195 


17/8 


4.14 


3.19 


0.95 


52 


2.14 


2 1/8 1530 64 2 7/8 


6 


60 1/2 


44 


13/4 


1.746 


3456 


17/8 


4.30 


3.19 


1.11 


54 


2.20 


2 3/16 1543 661/4 3 


61/8 


62 3/4 


44 


13/4 


1.746 


3726 


17/8 


4.45 


3.19 


1.26 


56 


2.27 


21/4 


1555 68 3/4 3 


63/8 


65 


148 


13/4 


1.746 


3674 


17/8 


4.263.19 


1.07 


58 


2.34 


2 5/16 


1567i 71 


3 1/8 


6 1/2 


671/4 


!48 


13/4 


1.746 


3941 


17/8 


4.40 3.19 


1.21 


60 


2.41 


2 7/16 


15381 73 


3 1/8 


6 1/2 


691/4 


52 


13/4 


1.746 


3892 


17/8 


4.1913.19 


1.00 


62 


2.47 


2 1/2 


1550| 753/4 


3 1/4 


6 7/8 


713/4 


52 


17/8 


2.051 


3538 


2 


4.343.41 


0.93 


64 


2.54 


2 9/16 


156l' 78 


3 1/4 


7 


74 


52 


17/8 


2.051 


3770 


2 


4.48i3.41 


1.07 


66 


2.61 


2 5/8 11572 80 


3 3/8 


7 


76 


52 


17/8 


2.051 


J4010 


2 


4.603.41 


1.19 


68 


2.68 


211/16 1582 821/4 


3 3/8 


71/8 


781/4 


56 


17/8 


2.051 


3952 


2 


4.38i3.41 


0.97 


70 


2.74 


2 3/4 11591 841/2 


3 1/2 


71/4 


80 1/2 


56 


17/8 


2.051 


4188 


2 


4.5113.41 


1.10 


72 


2.81 


213/16:1600! 86 1/2 


3 1/2 


71/4 


821/2 


160 


1 7/8 


2.051 


4136 


2 


4.333.41 


10.92 


74 


2.88 


2 7/8 il609 881/2 


3 5/8 


71/4 


841/2 


60 


1 7/8 


2.051 


4368 


2 


4.4413.41 


!l.03 


76 


2.94 


215/16 1617: 903/4 


3 5/8 


73/8 


861/2 


60 


1 7/8 


2.051 


4608 


2 


4.5413.41 


11.13 


78 


3.01 


3 11625 93 


3 3/4 


71/2 


88 3/4 


60 


2 


2.302 


4325 


2 1/g 


4.6613.63 


1.03 


80 


3.08 


3 1/16! 1633 951/4 


3 3/4 


75/8 


91 


[60 


2 


2.302 


4549 


21/fe 


4.78 3.63 


1.15 


82 


3.15 


31/8 '1640 


971/2 


3 7/8 


73/4 


931/4 


60 


2 


2.302 


4779 


2 1/s 


4.90 3.63 


1.27 


84 


3.21 


3 3/16' 1647 


993/4 


3 7/8 


77/8 


951/2 


,64 


2 


2.302 


4702 


2l/t 


4.68 3.63 


1.05 


86 


3.28 '3 1/4 1653 


102 


4 


8 


973/4 


64 


2 


2.302 


4928 


2 1/8 


4.79 3.63 


1.16 


88 


3.35 i3 5/i6il660 


1041/4 


'4 


81/8 


100 


168 


2 


2.302 


4857 


2 1/s 


4.60 3.63 


0.97 


90 


3.41 3 3/8 


1667 


106 1/2 


4 1/8 


81/4 


1021/4 


'68 


21/8 


2.648 


4416 


2 1/4 


4.71 3.83 


0.88 


92 


3.48 3 1/2 


1643 


108 3/4 


:4 1/8 


|83/8 


1041/2 


68 


21/8 


2.648 


4615 


2 1/4 


4.81 3.83 


0.98 


94 


3.55 13 9/16 


1649 


111 


4 1/4 


181/2 


1061/4 


68 


21/8 


2.648 


4817 


21/4 


4.89 3.83 


1.06 


96 


3.62 i3 5/8 


1655 


1131/4 


4 1/4 


18 5/8 


108 1/2 


|68 


21/4 


3.023 


4401 


2 3/8 


4.99 4.06 


0.93 


98 


3.68 1311/16 


1661 


1151/2 


4 3/8 


8 3/4 


1103/4 


'68 


21/4 


3.023 


4587 


2 3/8 


5.09 4.06 


1.03 


100 


3.75 i3 3/4 


1667 


117 3/4 


!4 3/8 


18 7/8 


113 


|68 


21/4 


3.023 


4776 


2 3/8 


5.20I4.O6 


I1.I4 



210 



MATERIALS. 



The last three columns of the table refer to the sketch Fig. 75, and show 
the distances between bolt holes, the maximum 
space occupied by the nuts and the minimum 
, space between adjacent nuts, all measured on 
/— K '/"'~\i ^^^ chord. Bolt holes are to straddle the center 
/- j \ — ^--t— V li^i^' ^^^ ^1*6 ^o t>6 Vs in. larger in diameter than 
VlyUe^Viy the bolts. Standard weight fittings and flanges 
are to be plain faced, but extra heavy fittings and 
flanges are to have a raised surface i/ie in. high 
inside of bolt holes for gaskets. Square head bolts 
with hexagonal nuts are recommended, but for 
bolts 1 5/8 in. diameter and larger, studs with a nut 
on each end may be substituted. Flanges are to 
be spot bored for nuts for sizes 32 in. to 100 in. inclusive. For super- 
heated steam, steel flanges, fittings and valves are recommended. 




Fig. 75. 



American Standard Extra Heavy Cast Iron Pipe Flanges 
For Pressures up to 250 Lb. per Sq. In. (All Dimensions in Inches.) 



Pipe jS,^ 

£^ 

Thickness - cr 



Flanges. 



^S 



1 

HA 

11/2 

2 

21/2 
3 

31/2 

4 

41/2 

5 
6 

7 

8 

9 
10 
12 
14 
15 
16 
18 
20 
22 
24 
26 
28 
30 
32 
34 
36 
38 
40 
42 
44 
46 
48 



S2 



0.451 
0.47 
0.49 
0.51 
0.53 
0.56' 
0.59 
0.61! 
0.64 
0.67 
0.72 
0.78 
0.83 
0.89 
0.94 
1.05 
1.16 
1.21 
1.27 
1.37 
1.48 



1/2 
1/2 
1/2 
1/2 
9/16 
9/16 
9/16 
5/8 
5/8 
11/16 
3/4 
13/16 
13/16 
7/8 
15/16 

1 

1 1/8 

13/16 

11/4 

13/8 

11/2 



1.591 19/16 
1 .70 1 5/8 



1 13/16 

17/8 
2.02 2 

2.13 2 1/8 1 
2.24 21/4 
2.35 2 3/8 
2.46 2 7/16 

2.56'2 9/16 
2.67 211/16 
2.78 2 13/16 
2.89 2 7/8 
3.003 



Wh^ 



250 
312 
375 
500 

555| 
667 
778 



41/2 

5 

6 

61/2 

71/2 

81/4 

9 






11/16 
3/4 

13/16 
7/8 



800! 10 
900 101/2 
909jll 

100o'l2l/2 
10/7 14 
1230 15 
1285 161/4 
1333jl7i/2 
1500 201/2 
1555 23 
1579 24 1/2 
1600 25 1/2 
1636|28 

1666'30l/2 
1760 33 
1846 36 
1793 381/4 
1866,40 3/4 

1875 43 
1882 451/4 
1889 471/2 
1894 50 
1948 52 1/4 

1953 541/2 
1953 57 
1955 591/1 
2000 61 1/2 
2000 65 



13/4 

17/8 
21/4 
21/4 
21/2 
2 5/8 
2 3/4 



11/8 
13/16 
1 1/4 
1 5/13 
1 3/8 
1 7/16 

1 1/2 
15/8 
13/4 
17/8 

2 

21/8 

2 3/16 
21/4 
2 3/8 

21/2 
2 5/8 
2 3/4 
2 13/16 

2 15/16 

3 

31/8 

3 1/4 
3 3/8 
3 7/16 7 1/8 

3 9/16 71/4 
311/16 7 1/2 

3 3/4 7 5/8! 

3 7/8 !7 3/4! 

4 I8I/2! 



^S 



PQ^ 



3 
3 

3. 

31/4 
31/2! 

31/2: 
35/8 

3 3/4| 

41/4 
41/2^ 
43/4' 
43/4 

5 I 

51/4' 
51/4 
53/4 

61/8 
63/8 

6 1/2' 

6 5/8; 

6 3/4! 



31/4 

33/4 

41/2 

5 

57/8 

6 5/8 
71/4 
77/8 
81/2 

91/4 

10 5/8 
117 
13 
14 

151/4 



Bolts. 



173/4 16 
20i/4i20 



21 1/2 
221/2 
243/4 

27 

291/4 
32 

341/2 
37 

391/4 
41 1/2 
431/2 
46 
48 

501/4, 
52 3/4 36 



55 

571/4 

60 3/4 



Q^ 












m' 



1/2 10. 126 389 
1/20.126 609 
5/8 0.202 547 
5/80.2021 972 
3/4 0.30211016 

3/4 '0.302! 731 
3/4 0.302 995 
3/1 0.302 1300 
3/1 0.302 1646 
3/4^0.302,2032 
3/4 0.302' 1950 
7/8 0.420 1909 1 
7/8 0.420 2493 1 
0.550 2410 1 
0.550,2231.1 






See Fig. 75, 
p. 210. 



1/80.694 
1/8 0.694 
1/40.893 
1/4 0.893 
1/10.893 

3/8' 1.057 
1/2 1.295 
5/8 1.515 
5/8 1.515 
5/8 1.515 

3/4' 1.746 

7/8 2.051 

7/8 2.051 

7/8 2.051 

7/8 2.051 

7/82.051 

7/8 2.051 

1 2.302 

2.302 

!2.302! 



2546M 
2773 1 
2473 1 
2814 1 
2968 1 
3096 1 
3058 1 
3110 1 
3126 I 
3629,1 
36l5'l 
3501 2 
3952 2 
3877 2 
4320 2 

4255 '2 
4691 2 
4587 2 
4512:2 
49132 



5/8 2.29 
5/812.65 
3/4|3.17 

3/43.53 

7/8 4.15 
7/8'2.53 
7/8' 2.77 
7/83.01 
7/8i3.25 
7/8,3.53 
7/8'2.75 
13.07 
!3.36 
1/8:3.62 
i/8!2.97 
i/4'3.46 
1/43.17 
3/8 3.36 

3/8 3.52: 

3/8,3.23| 
I/23.52I 
5/8 3.81 

3/4:4.18 
3/43.86 

3/4|4.14 

7/8'4.38 
14.64 
i4.87 
4.50 
4.701 



B I C 

LOO 1^29 
1 .00 1 .65 
1.21 1.96 
1.21 2.32 
1.44,2.71 
1.44 1.09 
1 .44 1 .33 
1.44 1.57 
1.44 1.81 
1.44,2.09 
1.441.31 
1.66 1.41 
1.66 1.70 
1.88 1.74 
1.88,1.09 
2.091.37 
2.09 1.08 
2.31 1.05 
2.31 1.21 
2.31,0.92 
2.53'o.99 
2.75 1.06 

2 96 1 .22 
2.960.9J 
2.96 1.18 
3.191.19 

3 41 1.26 
3.41 1.46 
3.41 1.09 
3.41,1.29 

4.38'3.41 0.97 
4.59 3.41 1.18 
1/8 4.79 3.63 1.16 
1/8 4.49,3.63 0.86 
1/8 4.76-3.63 1.13 



* Thickness of flange given in table includes raised face. 



FORGED AND ROLLED STEEL FLANGES. 



211 



Forged Steel Flanges for Riveted Pipe. 

Riveted Pipe Manufacturers' Standard.* 



_^ 




m c5 






^ 
.«'« 


- ^ 




m bfl 






0) 


a fi 




2^ c 






0.3 


a c 




^ C 






of"^ 


11 


55 


go 


oi2 


'Si 

Ml 


.2 o 






£-2 
go 


« 


oi 
Ml 




3 


6 


5/16 .... 


4 


7/16 


4 3/4 


16 


211/4 


5/8 3/4 


12 


1/^ 


191/4 


4 


7 


5/lo 9/16 


8 


7/16 


5 15/16 


18 


231/4 


5/8 3/4 


16 


5/8 


211/4 


5 


8 


5/16 9/16 


« 


7/16 


6 15/16 


20 


251/4 


5/8 7/8 


16 


5/8 


231/8 


6 


9 


3/8 9/16 


8 


1/2 


7 7/8 


22 


281/4 


11/16 7/8 


16 


5/8 


26 


7 


10 


3/8 9/16 


8 


1/2 


9 


24 


30 


11/16 7/8 


16 


5/8 


273/4 


8 


II 


3/8 5/8 


8 


1/2 


10 


26 


32 


.... 1 


24 


3/4 


293/4 


9 


13 


3/8 5/8 


8 


1/2 


II 1/4 


28 


34 




1 


28 


3/4 


313/4 


10 


14 


3/8 11/16 


8 


1/2 


121/4 


30 


36 




1 


28 


3/4 


333/4 


11 


13 


7/16 .... 


12 


1/2 


13 3/8 


32 


38 






28 


3/4 


353/4 


12 


16 


7/16 3/4 


12 


1/2 


14 1/4 


34 


40 






28 


3/4 


373/4 


13 


17 


7/16 .... 


12 


1/2 


15 1/4 


36 


42 




11/8 


32 


3/4 


393/4 


14 


18 


7/16 3/4 


12 


1/2 


16 1/4 


40 


46 




11/8 


32 


3/4 


433/4 


15 


19 


9/15 3/4 12 1 1/2 1 


17 7/16 42 


48 




H/sl 


36 


3/4 


453/4 



* Flanges for riveted pipe are also made with the outside diameter and 
the drilling dimensions the same as those of the A. S. M. E. standard 
(page 209), and with the thickness as given in the second column of fig- 
ures under "Thickness of Flange" in the above table. 

Curved Forged Steel Flanges are also made for boilers and tanks, 
See catalogue of American Spiral Pipe Works, Chicago. 



Forged and Rolled Steel Flanges. 

Dimensions in Inches. (American Spiral Pipe Works, 1913.) 




r< A 


^ 












1 


Standard Companion Flanges. 


Standard Shrink Flanges, 






II 






.11 






i 

^3 


15 fl 


. 




^ 





< 


H 


Q 


Q 


z; 





w 


H 


Q 


Q 




A 


B 


C 


D 


E 




A 


B 


C 


D 


E 


I 





21,8 


5/8 


1 


^1/8 


4 


9 


^3/8 


15/16 


2 3/ 16 


33/4 


21/? 


7 


21/2 


11 16 


11/16 


35/8 


41/? 


91/4 


47/8 


I'Vlfi 


21/4 


61/8 


3 


71/0 


31/8 


a/4 


11/8 


45/6 


i> 


10 


57/16 


IV16 


25/16 


6 7/8 


31/7 


«!/? 


35,8 


13 6 


13/16 


47/8 


6 


11 


61/? 


1 


27/16 


7 7/8 


4 


9 


41/8 


15/16 


13/6 


!>3/8 


7 


121/2 


71/? 


11/16 


21/2 


9 


41/? 


91/4 


45/8 


IVI6 


11/4 


313/16 


8 


131/2 


8 1/2 


11/8 


25/8 


10 


5 


10 


51/8 


15/16 


15/-6 


67/16 


9 


15 


91/. 


1 1/8 


23/4 


llVs 


6 


11 


63/6 


1 


17/-6 


^y/16 


10 


15 


105/8 


13/,6 


3 


121/4 


7 


121/^ 


73/6 


11/16 


li/:> 


85/8 


12 


19 


125/8 


11/4 


33/s 


141/2 


8 


131/? 


83/6 


11/8 


158 


911/6 


14 


21 


13 7/8 


13/8 


33/8 


157/8 


9 


15 


93/6 


11/8 


13/4 


105/8 


15 


221/4 


147/8 


13/8 


31/? 


167/8 


10 


16 


105/6 


13/16 


17/8 


1115/6 


16 


231/2 


15 7/8 


17/6 


35/8 


18 


12 


19 


125/6 


11/4 


21/16 


1418 


18 


25 


177/8 


1«/1R 


37/8 


201/8 


14 


21 


131/2 


13/8 


23/.6 


157/;6 


20 


271/2 


197/8 


111/16 


41/8 


221/4 



212 MATERIALS. 

Forged and Rolled Steel Flanges. — Continued. 
Extra Heavy Companion Flanges. 



3fi 


M.2 


B 


ii 


1:^ ^ 




1^ 


W.2 




^A 








"SQ 


oQ 


2 c 


^W 


.2W 


^Q 


SQ 


A fl 


^W 


.sa 


is 


O 


m 


H 


Q 


Q 


'A^ 


O 


m 


H 


Q 


Q 


Z'^ 


A 


B 


c 


D 


E 




A 


B 


C 


D 


E 


2 


61/2 


21/8 


7/8 


3/8 


3 3/8 


7 


14 


7 3/16 


1 5/16 


2 1/16 


91/8 


21/2 


71/2 


21/2 


1 


17/16 


4 1/16 


8 


15 


8 3/16 


13/8 


2 3/16 


101/8 


3 


81/4 


31/8 


1 


1 9/16 


4 11/16 


9 


16 


9 3/16 


1 V/16 


2 1/4 


113/16 


31/2 


9 


3 5/8 


11/8 


15/8 


5 5/16 


10 


171/2 


10 5/16 1 1/2 


2 3/8 


12 9/16 


4 


10 


41/8 


11/8 


13/4 


5 13/16 


12 


20 


12 5/16: 15/8 


2 9/16 


14 5/8 


41/2 


101/2 


4 5/8 


n/4 


1 13/lfi 


6 1/4 


14 


221/2 


131/2 13/i 


2 11/16 


15 13/16 


5 


11 


51/8 


11/4 


1 7/8 


6 13/16 


13 


231/2 


141/2 I 13/16 


213/16 


17 3/16 


6 


121/2 


6 3/iol 1 1/4 


2 


7 7/8 


16 


25 


151/2 17/8 


3 1/16 


181/4 



^a— 



Extra Heavy High Hub Flanges. 



Size. 


A 


B 


C 


D 


E 


Size. 


A 


B 


c 


D 


E 


4 


10 


4 3/8 


11/8 


31/8 


5 3/4 


18 


27 


17 7/8 


2 


5 


203/4 


41/2 


101/2 


4 7/8 


11/4 


31/4 


61/4 


20 


291/2 


197/8 


21/4 


5 1/2 


221/2 


5 


11 


5 7/16 


11/4 


31/4 


7 


22 


31 1/2 




21/4 


51/2 


24 3/4 


6 


121/2 


61/2 


11/+ 


31/4 


7 15/16 


24 


34 




2 7/16 


61/4 


27 


7 


14 


71/2 


15/16 


3 3/8 


91/8 


30 


40 




2 7/16 


61/4 


33 


8 


15 


81/2 


13/8 


31/2 


10 5/10 


36 


46 




2 7/16 


61/4 


39 


9 


16 


91/2 


1 7/16 


3 5/8 


113/8 


42 


52 




2 7/16 


61/4 


45 


10 


17 V^ 


10 5/8 


11/2 


3 3/4 


12 5/8 


48 


581/4 




2 7/16 


61/2 


511/4 


11 


18 3/4 


115/8 


19/16 


3 7/8 


13 5/8 


54 


641/2 




2 7/16 


61/2 


57 1/4 


12 


20 


12 5/8 


15/8 


4 


14 3/4 


60 


70 3/s 




2 7/16 


61/2 


63 3/8 


14 


221/2 


13 7/8 


13/4 


4 3/8 


16 3/16 


66 


77 




2 7/16 


71/2 


691/2 


15 


23 1/2 


14 7/8 


1 13/16 


41/2 


171/4 


72 


831/8 




2 7/16 


71/2 


75 5/8 


16 


25 


15V/8 


17/8 


4 3/4 


181/2 















The Rockwood Pipe Joint. — The system of flanged joints now in 
common use for high pressures, made by slipping a flange over the pipe, 
expanding the end of the pipe by rolling or peening, and then facing it in 
a lathe, so that when the flanges of two pipes are bolted together the 
bearing of the joint is on the ends of the pipes themselves and not on the 
flanges, was patented by George I. Rockwood, April 5, 1897, No. 580,058, 
and first described in Eng. Rec, July 20, 1895. The joint as made by- 
different manufacturers is known by various trade names, as Walmanco, 
Van Stone, etc. 

Matheson Joint and Converse Lock-joint Pipe. — Sizes, external 
diameters 2 to 20 in., 22, 24, 26, 28, and 30 in. Kimberley Joint Pipe, 
6 to 30 in. These pipes are considerably lighter than standard pipe. 
The Converse and Kimberley joints are made with special forms of ex- 
ternal hubs, filled and calked with lead. The Matheson joint is also 
a lead-packed joint, but the bell or socket is made by expanding one of 
the pipes, the end being reinforced by a steel band. The lead required 
per joint is less than for other lead- joint pipes of the same diameter. 



PIPE FITTINGS. 

Dimensions of Standard Cast-iron Flanged Pipe Fittings, for Pres- 
sures up to 15>5 Lb. per Sq. In. (Adopted March 20, 1914, by a 
joint committee of manufacturers and of the Am. Soc. M. E.) 
Dimensions in the tables, pages 213 and 214, refer to corresponding 
letters on the sketches on page 215. For dimensions of flanges 
and bolts see Table of Standard Flanges, pages 209 and 210. 



213 



Standard Cast Iron Flanged Pipe Fittings for Pressures up to 125 lb. 






per Sq. ] 


[n. (see sketches p. 215.) 




Size. 


Tees, 
and 


Crosses 
Ells. 


Long 

Radius 

Ells. 


45 

degree 

Ells. 


Laterals. 


Re- 
ducers. 


Min. 
Thick- 
ness of 
Metal. 




A-A 


A 


B 


C 


D 


E 


F 


G 




! 


7 


3 1/2 


5 


13/4 


71/2 


53/4 


13/4 




V16 


I 1/4 


71/2 


3 3/4 


51/2 


2 


8 


6 1/4 


13/4 




7/16 


1 1/2 


8 


4 


6 


21/4 


9 


7 


2 




7/16 


2 


9 


4 1/2 


6 1/2 


21/2 


101/2 


8 


21/2 




7/I6 


21/2 


10 


5 


7 


3 


12 


91/2 


21/2 




7/16 


3 


n 


5 1/2 


73/4 


3 


13 


10 


3 


' 6 " 


7/16 


31/2 


12 


6 


8 1/2 


31/2 


141/2 


111/2 


3 


61/2 


7/16 


4 


13 


61/2 


9 


4 


15 


12 


3 


7 


1/2 


41/2 


14 


7 


91/2 


4 


15 1/2 


121/2 


3 


71/2 


1/2 


5 


15 


71/2 


101/4 


41/2 


17 


13 1/2 


31/2 


8 


1/2 


6 


16 


8 


111/2 


5 


18 


141/2 


31/2 


9 


9/I6 


7 


17 


8 1/2 


12 3/4 


51/2 


201/2 


16 1/2 


4 


10 


5/8 


8 


18 


9 


14 


51/2 


22 


17 1/2 


41/2 


11 


5/8 


9 


20 


10 


15 1/4 


6 


24 


191/2 


41/2 


111/2 


11/16 


10 


22 


11 


16 1/2 


6 1/2 


25 1/2 


201/2 


5 


12 


3/4 


12 


24 


12 


19 


71/2 


30 


241/2 


51/2 


14 


13/16 


14 


-28 


14 


21 1/2 


71/2 


33 


n 


6 


16 


7/8 


15 


29 


14 1/2 


22 3/4 


8 


341/2 


281/2 


6 


17 


7/8 


16 


30 


15 


24 


8 


361/2 


30 


6 1/2 


18 


1 


18 


33 


16 1/2 


26 1/2 


8 1/2 


39 


32 


7 


19 


1 I/16 


20 


36 


18 


29 


91/2 


43 


35 


8 


20 


1 1/8 


22 


40 


20 


311/2 


10 


46 


371/2 


8 1/2 


22 


13/16 


24 


44 


22 


34 


11 


491/2 


401/2 


9 


24 


11/4 


26 


46 


23 


361/2 


13 


53 


44 


9 


26 


1 5/16 


28 


48 


24 


39 


14 


56 


461/2 


91/2 


28 


1 V8 


30 


50 


25 


411/2 


15 


59 


49 


10 


30 


1 7/16 


32 


52 


26 


44 


16 








32 


1 1/2 


34 


54 


27 


461/2 


17 










34 


19/16 


36 


56 


28 


49 


18 










36 


1 5/8 


38 


58 


29 


511/2 


19 










38 


1 11/16 


40 


60 


30 


54 


20 










40 


13/4 


42 


62 


31 


561/2 


21 










42 


1 13/16 


44 


64 


32 


59 


22 











44 


1 7/8 


46 


66 


33 


61 1/2 


23 










46 


1 15/16 


48 


68 


34 


64 


24 










48 


2 


50 


70 


35 


66 1/2 


25 











50 


2 1/16 


52 


74 


37 


69 


26 










52 


2 1/8 


54 


78 


39 


71 1/2 


27 










54 


2 3/16 


56 


82 


41 


74 


28 










56 


21/4 


58 


84 


42 


761/2 


29 










58 


2 5/16 


60 


88 


44 


79 


30 










60 


2 7/16 


62 


90 


45 


81 1/2 


31 










62 


21/2 


64 


94 


47 


84 


32 










64 


2 9/16 


66 


96 


48 


861/2 


33 










66 


2 5/8 


68 


100 


50 


89 


34 










68 


2 11/16 


70 


102 


51 


91 1/2 


35 










70 


2 3/4 


72 


106 


53 


94 


36 











72 


2 13/16 

2 7/8 


74 


108 


54 


961/2 


37 











74 


76 


112 


56 


99 


38 










76 


2 15/16 


78 


116 


58 


101 1/2 


39 










78 


3 


80 


118 


59 


104 


40 










80 


31/16 


82 


120 


60 


106 1/2 


41 










82 


31/8 


84 


124 


62 


109 


42 










84 


3 3/16 


86 


126 


63 


1111/2 


43 










86 


31/4 


88 


130 


65 


114 


44 










88 


3 5/16 


90 


134 


67 


116 1/2 


45 










90 


3 3/8 


92 


136 


68 


119 


46 










92 


31/2 


94 


138 


69 


121 1/2 


47 










94 


3 9/16 


96 


142 


71 


124 


48 










96 


35/8 


98 


146 


73 


1261/2 


49 










98 


3 11/16 


100 


148 


74 


129 


50 










100 


3 3/4 



214 



MATERIALS. 



Dimensions of American Standard Flanged Reducing Fittings. Short 
Body Pattern. (All Dimensions in Inches.) 

Long body patterns are used when outlets are larger than those in 
table, and have the same dimensions as straight size fittings. All re- 
ducing fittings from 1 to 16 in. inclusive have same dimensions as 
straight size fittings. The dimensions of reducing fittings are always 
regulated by the reduction of the outlet. 





Tees, Ells, Crosses. 


Laterals. 




Tees, Ells, 
and Crosses. 




%% 






s 


% 








%i 










. 3 






Xfl 


43 










xfiT^ 
. 3 








s 


^o 








O 








S 


^o 








Xfl 


^'o 


AA 


A 


B % 


"S I 


) E 


F 


2 


H 


xn 


S'S 


AA 


A 


B 


18 


12 


26 


13 


15 1/2 


9 . 


26' 25 


1 


7 1/9 


60 


40 


66 


33 


41 


20 


14 


28 


14 


17 1 


. 


28 27 


1 


29 1/2 


62 


40 


66 


33 42 


22 


15 


28 


14 


18 1 


. 


29 28 1/2 


V? 


31 1/2 


64 


42 


68 


34 44 


24 


16 


30 


15 


19 1 


2 : 


J2 31 1/2 


1/9 


34 1/2 


66 


44 


70 


35 45 


26 


18 


32 


16 


20 1 


2 : 


J5 35 





38 


68 


44 


70 


35 46 


28 


18 


32 


16 


21 1 


4 : 


J7i 37 





40 


70 


46 


74 


37 47 


30 


20 


36 


18 


23 1 


5 : 


J9 39 





42 


72 


48 


80 


40 48 


32 


20 


36 


18 


24 














74 


48 


80 


40 49 


34 


22 


38 


19 


25 
















76 


50 


84 


42 50 


36 


24 


40 


20 


26 
















78 


52 


86 


43 i 52 


38 


24 


40 


20 


28 
















80 


52 


86 


43 53 


40 


26 


44 


22 


29 
















82 


54 


88 


44; 54 


42 


28 


46 


23 


30 
















84 


56 


94 


47| 56 


44 


28 


46 


23 


31 
















86 


56 


94 


47 57 


46 


30 


48 


24 


33 
















88 


58 


96 


48! 58 


48 


32 


52 


26 


34 
















90 


60 


100 


50 61 


50 


32 


52 


26 


35 
















92 


60 


100 


50 62 


52 


34 


54 


27 


36 
















94 


62 


104 


52 63 


54 


36 


58 


29 


37 
















96 


64 


106 


53 64 


56 


36 


58 


29 


39 
















98 


64 


106 


53 65 


58 


38 


62 


31 


40 
















100 


66 


110 


55 67 



Extra Heavy American Standard Flanged Reducing Fittings. 
Body Pattern. (AH Dimensions in Inches.) 



Short 





Tees, Ells and Crosses. 




Laterals. 






Tees, Ells and Crosses. 




ii 






Mi 














i 


iS 






iB 








i 


iS 








w 


^•5 


AA A 


K 


§-3 D 


E 


F 


H 


xn '^ O 


AA 


A 


K 


18 


12 


28 14 


17 


9 34 


31 


3 


32 1/9 


34 22 


44 


22 


28 


20 


14 


31 15 1/2 


18 1/2 


10 


37 34 


3 


36 


36 24 


47 23 1/2 


29 1/2 


22 


15 


33 16 1/2 


20 


10 


40 


37 


3 39 


38 24 


47 23 1/2 


301/2 


24 


16 


34! 17 


21 l/o 


12 


44 


41 


3 


43 


40 26 


50 25 


31 1/2 


26 


18 


38 19 


23 












42 28 


53 26 1/2 


33 1/2 


28 


18 


38 19 


24 












44 28 


53 26 1/2 


34 1/2 


30 


20 


411 201/2 


25 1/2 












46 30 


55 27 1/2 


35 1/2 


32 


20 


411 20 1/2 


26 1/2 












48 32 


58 29 


37 1/2 



Standard Brass Flanges as adopted Sept. 17, 1913, by the Committee 
of manufacturers on the standardization of Valves and Fittings, to be- 
come effective Jan. 1. 1914 are listed on page 215. The bolt holes for 
these flanges are to be drilled i/ir, in. greater than the bolt diameter for 
sizes 2 in. and smaller, and Vs in. greater than the bolt diameter for 
sizes 2 1/2 in. and larger. The flanges have smooth, plain faces, and when 
coupled to extra heavy iron flanges, the latter should have the raised 
surface faced off. 



STANDAKD BRASS FLANGES. 



215 




Lateral 



V-K- 



f'-M 



4-' 



Tee 




STRAIGHT SIZE FITriNGS. 



Single Sweep Single Sweep 
Tee Tee 






K->-^K- 



Cr.oss 



Cross 




Eaterals 
REDUCING FITTINGS. 




Reducers 



The dimensions on these sketches refer to the corresponding letters 
in the tables of flanged fittings, pages 213 and 214, and also to the 
reference letters in the tables of screwed fittings, page 216. 









Standard Brass Flanges. 










Standard — For Pressures 


up 


Extra Heavy — For Pressures 






to 125 Lb. 






up to 250 Lb. 




Size, 
In. 


Diam., 
In. 


Thick- 
ness, 
In. 


Bolt 

Circle , 

In. 


No. 

of 
Bolts. 


Size 

of 

Bolts, 

In. 


Diam., 
In. 


Thick- 
ness, 
In. 


Bolt 

Circle , 

In. 


No. 

of 

Bolts. 


Size 

of 

Bolts, 

In. 


V4&V8 


2 1/2 


9/32 


1 11/16 




3/8 


3 


3/8 


2 


4 


V16 


V2 


3 


V16 


2 1/8 




3/8 


31/2 


13/32 


2 3/8 


4 


Vifi 


3/4 


31/2 


11/32 


21/2 




3/8 


4 


Vl6 


2V8 


4 


1/2 


1 


4 


3/8 


3 




'/ifi 


41/2 


1/2 


31/4 


4 


v^ 


1 V4 


41/2 


IV32 


33/8 




Vifi 


5 


11/32 


33/4 


4 


Vi^ 


1 V2 


5 


V16 


3 '/h 




v. 


6 


V16 


41/2 


4 


Vr 


2 


6 


1/2 


43/4 




V8 


6 1/2 


Vs 


5 


4 


V8 


2 1/2 


7 


V16 


51/. 




V8 


71/2 


IV 16 


57/8 


4 


3/4 


3 


71/2 


Vs 


6 




V8 


8 1/4 


3/4 


6V8 


8 


3/4 


31/2 


8 1/2 


lVi6 


7 




V8 


9 


13/16 


71/4 


8 


3/4 


4 


9 


II/16 


71/2 


8 


V8 


10 


V8 


77/8 


8 


3/^ 


41/2 


9V4 


23/32 


73/4 


8 


3/4 


101/2 


Vh 


8 1/2 


8 


3/4 


5 


10 


V4 


8 1/2 


8 


3/4 


11 


1V16 


91/4 


8 


3/4 


6 


It 


IV16 


91/. 


8 


3/4 


121/2 


1 


10 5/8 


12 


% 


7 


121/9 


V8 


10 3/4 


8 


3/4 


14 


1 V16 


11 Vs 


12 


8 


131/2 


IV16 


113/4 


8 


3/4 


15 


11/8 


13 


12 


'Vp, 


9 


15 


IV16 


131/4 


12 


3/4 


16 1/4 


1 i/s 


14 


12 


1 


10 


16 


1 


141/4 


12 


V8 


171/2 


13/16 


151/4 


16 


1 


12 


19 


1 V16 


17 


12 


Vs 


20 1/2 


IV4 


173/4 


16 


IVs 



216 



MATERIALS. 



Dimensions of Screwed Cast Iron and Malleable Pipe Fittings, For 
Steam and Water. (Crane Co., Chicago, 1914.) 

R = regular fitting; E.H. = extra heavy fitting. For meaning of 
dimensions see sketches p. 215. Dimensions in inches. 



Sig. Tee, Cross, Ell. 


Long 
Rad. 
Ell. 


45 Deg. Ell. 


Lateral. 


Reducer.* 


Dimension. A 


B 


C 


D 


E 


G 


Size, 
Ins. 


Cast Iron, 


MaU. 


Mall. 


Cast Iron. 


Mall. 


C. L 


C.I. 


C.I. 


Mall. 


1/4 
3/8 
1/2 
3/4 

1 

1 1/4 

1 1/2 

2 1/2 

3 1/2 

4 

6 

7 

8 

9 
10 
12 


R. 

13/16 
15/16 

11/8 

15/16 

17/16 

13/4 

1 15/16 

21/4 

211/16 

31/8 

3 7/16 
33/4 
41/16 

4 7/16 
51/8 
513/16 
61/2 

7 3/16 
7 7/8 
91/4 


E.H. 

2 

21/4 
2 9/16 

3 

31/2 

41/8 

411/16 

51/8 

51/2 

61/8 

71/4 

81/8 

91/8 

livV 

13 3/8 


E.H. 

11/16 

11/4 

11/2 

13/4 

2 

21/4 

21/2 

3 

31/2 
41/8 

4 5/8 
51/8 

5 5/8 
61/4 
71/4 


E.H. 

21/2 
3 

31/2 

4 

4 3/4 
51/2 
61/4 

7 

7 3/4 
81/2 
91/2 


R. 

3/4 

13/16 

7/8 
1 

11/8 
15/16 
17/16 
1 11/16 

1 15/16 

2 3/16 
2 3/8 

2 5/8 
213/16 
31/16 

3 7/16 
3 7/8 
41/4 
411/16 
5 3/16 

6 


E.H. 

13/8" 

11/2 

15/8 

1 15/16 
21/4 
21/2 

2 9/16 

2 3/4 
3 

3 5/16 

3 3/4 
4 

4 3/4 

4'7/8 ■ 
51/2 


E.H. 

3/4 

,Vs 

11/8 
15/16 
11/2 

1 11/16 
2 

21/4 
21/2 

2 5/8 

2 13/16 


R. 

2'l/2' ' 
3 

31/2 
41/4 

4 7/8 

5 3/4 
61/4 

7 7/8 

8 7/8 

9 3/4 
115/8 
115/8 
13 7/16 
151/4 
1615/16 
2011/16 
2011/16 
241/8 


R. 

i7/8' 

21/4 

2 3/4 

31/4 

313/16 

41/2 

5 3/16 
61/8 

6 7/8 

7 5/8 
91/4 

91/1 

10 3/4 
121/4 
13 5/8 
16 3/4 
16 3/4 
19 5/8 


R. 

2"i/8 ■ 

21/4 
2 7/16 

2 11/16 
215/16 
31/8 

3 3/8 
3 5/8 

3 7/8 

4 3/8 

4 13/16 
51/4 

5 11/16 

6 3/16 
71/8 


E. H. 

ri"i/i6 

2 

23/8 
2 11/16 
2 3/16 



* The reducers are for reducing from the size of pipe given to the 
next smaller size. In addition, malleable reducers are listed for 1}4 X 
1/^, 1 H X 1, 1 3^ X H, 2 X 1, 2 X H- The dimension G given in the 
table is the same for these special fittings as for the regular fittings 
given above. 

Strength of Pipe Fittings. — To determine the actual bursting strength 
of cast iron fittings, and also to determine the influence of form upon 
the strength, Crane Co. conducted experiments in which flanged 
fittings of different sizes and forms were tested to destruction by inter- 
nal pressure. The experiments showed that the strength of ells is 
practically the same, regardless of degree, or whether the ell is straight 
or reducing sizes. Fittings of the same general shape as the tee or 
cross are of nearly the same strength, and relatively of about two-thirds 
the strength of an ell. The straight lateral has about one- third the 
strength of the ell. The following average figures of bursting strength 
of extra heavy tees and ells are condensed from the company's 1914 
catalogue : 

Size of fitting, ins., 6 8 10 12 14 16 18 20 24 

Thickness of metal, in. 3/4 i3/i6 i5/i6 1 li/8 Wie li/4 15/i6 II/2 

Tees, Ferro-steel: 
Burst at, lb. per sq. in. 2733 2250 2160 2033 1825 1700 1450 1275 1300 

Tees, Cast Iron: 
Burstat,lb.persq.in.l687 1350 1306 1380 1100 1025 600 750 700 

Ells, Ferro-steel: 
Burstat,lb.persq.in.3266 2725 2350 2133 

Ells, Cast Iron: 
Burstat,lb.persq.in.2275 1625 1541 1275 1075 1250 



STANBARD STRAIGHT-WAY GATE VALVES. 



217 



1/2 3/4 1 11/4 


11/2 2 21/2 


3 


1/2 1/2 9/16 5/8 


5/8 11/16 15/16 


1 



Length of Thread on Pipe that should be screwed into fittings to 
make a tight joint is given by Crane Co. as follows: 

Size of pipe, in l/g I/4 ^/g 

Length of thread, in. 1/4 S/g S/g 

Size of pipe, in 31/2 4 41/2 5 6 7 8 9 10 12 

Length of thread, in, 11/16 II/16 11/8 Wie II/4 11/4 15/i6 13/8 11/2 15/8 

VALVES. 

Dimensions of Standard Globe, Angle and Cross Valves. 

(Crane Co., 1914.) 
Iron Body, Brass Trimmings, with Yoke. 
Dimensions in Inches: B, face to face, flanged; B/2, center to face, 
flanged (Angle and Cross Valves) ; C, diameter of flanges; D, thickness 
of flanges; S, center to top of stem, open; O, diameter of wheel. 



B 


B/2 


C 


D 


8 


4 


6 


5/8 


81/2 


41/4 


7 


11/16 


91/2 


43/4 


71/2 


3/4 


101/2 


51/4 


81/2 


13/16 


11 


^1/2 


9 


15/16 


12 


6 


91/4 


15/16 


13 


6 1/2 


10 


15/16 


14 


7 


11 


1 



o 



103/41 
111/4I 
123/4! 

13 

151/4 

151/4 

171/4110 

19 il2 



6 1/2 
61/2 

71/2 
71/2 
9 
9 



Size.' B 



B/2 



81/2 
10 
12 
14 
15 
16 



121/2 

131/2 

16 

19 

21 

221/4 



D 



S O 



1 1/16:201/2 14 
1 1/8 23 3/4! 16 
13/16128 1 18 



11/4 

13/8 
13/8 



23 1/2; 17/16 



34 20 

38 1/2 24 
38 1/2 24 
41 1/2 27 

I 



Standard Straight- Way Gate Valves. 

Iron Body. Brass Trimmings. 



(Crane Co., 1914.) 
Wedge Gate. 



Dimensions in Inches: A, nominal size; B, face to face, flanged; C, 
diam. of flanges; D, thickness of flanges; K, end to end, screwed; N, 
center to top of non-rising stem; O, diam. of wheel; S, center to top of 
rising stem, open; Y, center to outside of by-pass; P, size of by-pass; 
X, nmnber of turns to open. 



A 


B 


C 


D 


K 


N 





S 


Y 


P 


X 


2 


7 


6 


5/8 


5 7/16 


113/4 


61/2 


141/2 






7 


21/2 


71/2 


7 


11/16 


57/8 


12 3/4 


61/2 


16 






8 


3 


8 


71/2 


3/4 


61/8 


141/4 


71/2 


19 






101/4 


31/2 


81/2 


81/2 


13/16 


61/2 


151/4 


71/2 


211/4 






101/8 


4 


9 


9 


15/16 


6 7/8 


161/i 


9 


24 






8 3/4 


41/2 


91/2 


91/4 


15/16 


71/8 


175/8 


9 


251/2 






9 


5 


10 


10 


15/16 


73/8 


19 


10 


281/2 






11 


6 


101/2 


11 


1 


73/4 


20 3/4 


12 


313/4 






12 5/8 


7 


11 


121/2 


11/16 


81/4 


23 


12 


371/4 






151/4 


8 


111/2 


13 1/2 


11/8 


8 3/4 


26 


14 


41 






16 


9 


12 


15 


1 1/8 


91/4 


28 


14 


443/4 






18 3/4 


10 


13 


16 


13/16 


97/8 


301/4 


16 


50 






201/2 


12 


14 


19 


11/4 


115/8 


351/4 


18 


571/4 






241/8 


14 


15 


21 


13/8 




391/4 


20 


66 3/4 


191/2 




281/4 


15 


15 


221/4 


13/8 




411/8 


20 


69 3/4 


21 




311/2 


16 


16 


231/2 


17/16 




441/4 


22 


751/4 


23 3/4 




331/4 


18 


17 


25 


19/16 




48 3/1 


24 


86 


24 3/4 


3 


351/2 


20 


18 


271/2 


1 11/16 




521/2 


24 


91 


27 3/4 




421/4 


22 


19 


291/2 


1 13/16 




551/2 


27 


100 


29 




46 


24 


20 


32 


1 7/8 




62 


30 


109 


301/2 




50 


26 


23 


341/4 


2 




65 7/8 


30 


1171/2 


32 




65 


28 


26 


361/2 


2 1/16 




70 


36 


125 


33 




80 


30 


30 


38 3/4 


2 1/8 




751/2 


36 


133 


34 




921/2 


36 


36 


453/4 


2 3/8 




83 




158 1/2 


39 


6 


108 



218 



MATERIALS. 



Extra Heavy Straight-Way Gate Valves. 

Ferro-steel. Hard Metal Seats. Wedge Gate. (For meaning of letters, seep. 217.) 



A 


B 


K 


C 


D 


N 


S 





P 


Y 


X 


U/4 


61/2 


51/2 


5 


3/4 


8 3/4 


10 5/8 


5 






12 


11/2 


71/2 


61/4 


6 


13/16 


9 5/8 


121/4 


51/2 






11 


2 


81/2 


7 


61/2 


7/8 


10 1/:^ 


13 3/4 


61/2 






14 


21/2 


91/2 


8 


71/2 


1 


12 7/8 


16 


71/2 






15 


3 


111/8 


9 


81/4 


11/8 


14 5/8 


191/2 


9 






14 


31/2 


117/8 


10 


9 


13/16 


151/2 


22 


10 






16 


4 


12 


11 


10 


11/4 


17 3/4 


241/2 


12 






18 


41/2 


131/4 


121/4 


101/2 


15/18 


18 3/4 


27 


12 






21 


5 


15 


131/2 


11 


13/8 


201/4 


29 3/4 


14 






23 


6 


15 7/8 


15 7/8 


121/2 


17/13 


23 


341/8 


16 


11/4 


13 


28 


7 


161/4 


161/4 


14 


11/2 


24 3/4 


38 


18 


11/4 


141/8 


30 


8 


161/2 


161/2 


15 


15/8 


28 3/4 


42 3/4 


20 


11/2 


15 7/8 


34 


9 


17 


17 


161/4 


13/4 


301/2 


47 


20 


11/2 


163/8 


40 


10 


18 


18 


171/2 


17/8 


33 3/4 


52 3/4 


22 


11/2 


16 7/8 


39 


12 


19 3/4 




201/2 


2 


371/4 


60 


24 


2 


19 7/8 


46 


14 


221/2 




23 


21/8 


42 3/4 


67 3/4 


24 


2 


20 5/8 


52 


15 


221/2 




241/2 


2 3/16 


42 3/4 


67 3/4 


24 


2 


20 5/8 


52 


16 


24 




251/2 


21/4 




751/4 


27 


3 


251/4 


60 


18 


26 




28 


2 3/8 




821/4 


30 


3 


261/^ 


67 


20 


28 




301/2 


21/2 




91 1/2 


30 


4 


301/2 


74 


22 


291/2 




33 


2 5/8 




101 


36 


4 


321/4 


82 


24 


31 




36 


2 3/4 




109 


36 


4 


33 


88 



For dimensions of IVIedium Valves and Extra Heavy Hydraulic 
Valves, see Crane Company's catalogue. 

NATIONAL STANDARD HOSE COPULINGS 

Adopted by the National Board of Fire Underwriters, American 
Waterworks Association, New England Waterworks Association, Na- 
tional Firemen's Association, National Fire Protection Association. 



Dimensions in Inches. 




^^SM} 



It- 



A, 
B, 
C, 
D 
E. 
N 
F. 
G 



21/2 


3 


31/2 


41/2 


V4 


V4 


1/4 


1/4 


3Vl6 


35/8 


41/4 


53/4 


2.8715 


3.3763 


4.0013 


5.3970 


1 


11/8 


11/8 


1 3/8 


71/2 


6 


6 


4 


7/8 


1 


1 


1 1/4 


3.0925 


3.6550 


4.28 


5.80 



The threads to be of the 60° V. pattern with 0.01 in. cut off the top 
of thread and 0.01 in. left in the bottom of the 2 H-in., 3-in., and 3 H-in. 
couplings, and 0.02 in. in Uke manner for the 4 H-in. couplings. 

A = inside diameter of hose couplings, N = number of threads per 
inch. 

WOODEN STAVE PIPE. 

Pipes made of wooden staves, banded with stsel hoops, are made by 
the Excelsior Wooden Pipe Co., San Francisco, in sizes from 10 inches to 
10 fe(^t in diameter, and are extensively used for long-distance piping, 
especially in the Western States. The hoops are made of steel rods with 
ups(;t and threaded ends. When buried below the hydraulic grade line 
and k(;pt full of water, these pipes are practically indestructible. For 
the economic design and use of stave pipe see paper by A. L. Adams, 
Trans. A. S. C. E., vol. xli. 



RIVETED HYDRAULIC PIPE. 



219 



Weight and Strength of Riveted Hydraulic Pipe. 

(Pelton Water Wheel, San Francisco, 1915.) 



Thic 


kness. 


4 in 


5-in. 


6-in. 


7 m 


8-in. 


Gauge. 


in. 








*s 


\V 


.S 


W 


S 


W 


*s 


n 


S 


W 


18 


D.050 


555 


2.8 


444 


3.5 


370 


4.1 


317 


4.7 


277 


5.3 


16 


.062 


693 


3.7 


555 


4.4 


462 


5.2 


396 


5.9 


346 


6.7 


14 


078 


866 


4.4 


693 


5.5 


578 


6.4 


495 


7.3 


433 


8.2 


12 


.109 
.140 










80a 


8.8 


693 


10.0 


606 
777 


11 5 


10 












14.5 




9-in. 


10-in. 


11 -in. 


12-in. 


14-in. 


16 


0.0o2 


30d 


7.5 


277 


8.3 


252 


9.0 


231 


9.9 


198 


11.4 


14 


.078 


385 


9.2 


346 


10.2 


314 


11.0 


289 


12.2 


248 


14.0 


12 


.109 


539 


12.6 


485 


14.2 


439 


15.2 


404 


16.7 


346 


19.2 


10 


.140 


693 


16.4 


623 


18.0 


565 


19.3 


519 


21.0 


445 


24.2 


8 


.171 
3/16 






761 

832 


21.5 
23.5 


693 
757 


23.5 
25.5 


635 
693 


25.6 
27.7 


543 
594 


29.5 








31.9 












15-in. 


16-in. 


18-in. 


20-in. 


22-in. 


16 


0.062 


185 


12.0 


l^^ 


12.8 


154 


14.5 


139 


16.0 


126 


17.7 


14 


.078 


231 


14.0 


^17 


16.0 


193 


17.8 


173 


19.6 


157 


21.2 


12 


.109 


323 


20.3 


303 


21.5 


270 


24.4 


242 


27.3 


220 


29.2 


10 


.140 


415 


25.7 


388 


27.3 


346 


30.7 


311 


34.5 


283 


37.1 


8 


.171 


507 


30.4 


475 


33.3 


422 


38.4 


380 


41.5 


346 


45.2 




3/16 


555 


34.0 


520 


36.0 


462 


40.5 


416 


45.0 


378 


49.0 




1/4 


739 


45.5 


693 


48.2 


616 


54.1 


555 


59.6 


505 


65.5 




5/16 
3/8 

7/16 






866 


60.6 


770 
924 


67.7 
81.3 


693 
831 
970 


74.6 
89.5 
105.0 


631 
757 
883 


81.5 








98.0 













114.5 




24-in. 


26-in. 


30-in. 


36-in. 


42-in. 


14 


0.078 


144 


23.7 


133 


25.5 














12 


.109 


202 


32.5 


186 


34.5 


162 


39.5 


134 


47.7 






10 


.140 


259 


40.5 


239 


43.7 


208 


50.3 


173 


60.0 


148 


69.5 


8 


.171 


317 


49.2 


293 


53.0 


254 


60.5 


211 


75.0 


181 


84.7 




3/16 


346 


53.0 


320 


57.5 


277 


65.5 


231 


79.0 


198 


91.5 




1/4 


462 


71.0 


427 


76.5 


370 


87.5 


308 


105.5 


264 


122.0 




5/16 


578 


88.5 


533 


95.5 


462 


109.0 


385 


130.0 


330 


151.0 




3/8 


693 


106.0 


640 


114.5 


555 


130.5 


462 


156.0 


396 


180.5 




7/:6 


808 


124.5 


747 


134.0 


647 


151.5 


539 


182.5 


462 


211.0 




1/2 


924 


142.0 


854 


153.0 


739 


174.5 


616 


207.0 


528 


240.5 




5/8 
3/4 
7/8 






1066 


191.0 


924 
1108 


220.0 
264.0 


770 
924 
1078 


260.0 
312.5 
366.0 


660 
792 
924 


302.0 








361.5 












424.0 




48-in. 


54-in. 


60-in. 


66-in. 


72-in. 


8 


0.171 


158 


98.0 


141 


110.0 


127 


121.0 












3/16 


173 


106.0 


154 


119.0 


139 


131.0 


127 


144.5 


115 


158.0 




1/4 


231 


142.0 


205 


159.0 


185 


175.0 


168 


193.0 


154 


211.0 




5/16 


289 


177.0 


256 


198.0 


23! 


218.0 


210 


239.0 


193 


260.0 




3/8 


346 


212.0 


308 


237.0 


277 


261.0 


252 


286.5 


231 


312.0 




7/16 


404 


249.0 


359 


277.5 


323 


303.0 


294 


334.0 


270 


365.0 




1/2 


462 


284.0 


411 


316.5 


370 


349.0 


336 


382.0 


308 


414 




5/8 


578 


354.0 


513 


399.5 


462 


440.0 


420 


480.0 


385 


520.0 




3/4 


693 


430.0 


616 


479.5 


555 


528.0 


504 


577.5 


462 


624.0 




7/8 


808 


505.0 


719 


563.5 


647 


620.0 


588 


677.0 


539 


732.0 




1 


924 


582.0 


822 


647.5 


739 


712.0 


672 


777.5 


616 


840.0 



Pipe made of sheet steel plate, ultimate tensile strength 55,000 lbs. per 
sq.in., double-riveted longitudinal joints and single-riveted circular joints. 
Strength of longitudinal joints, 70%. Strain by safe pressure, 1/4 of ulti- 
mate strength. 



220 



MATERIALS. 



Riveted Iron Pipe. 

(Abendroth & Root Mfg. Co.) 

Sheets punched and rolled, ready for riveting, are packed in con- 
venient form for shipment. The following table shows the iron and 
rivets required for punched and formed sheets. 



Number Square Feet of 
Iron Required to Make 
100 Lineal Feet Punched 
and Formed Sheets 
when put Together. 


Approximate No. of 
Rivets 1 Inch apart 
Required for 100 
Lineal Feet Punched 
and Formed Sheets. 


Number Square Feet of 
Iron Required to Make 
100 Lineal Feet Punched 
and Formed Sheets 
when put Together. 


Approximate No. of 
Rivets 1 Inch apart 
Required for 100 
Lineal Feet Punched 
and Formed Sheets. 


Diam- 
eter in 
Inches. 


Width 
of Lap 

in 
Inches. 


Square 
Feet. 


Diam- 
eter in 
Inches. 


Width 
of Lap 

in 
Inches. 


Square 
Feet. 


8 
9 
10 

n 

12 
13 


1 
1 

11/2 
11/2 
11/2 
11/2 
11/2 
11/2 
11/2 
11/2 
11/9. 


90 
116 
150 
178 
206 
234 
258 
289 
314 
343 
369 


1600 
1700 
1800 
1900 
2000 
2200 
2300 
2400 
2500 
2600 
2700 


14 
15 
16 
18 
20 
22 
24 
26 
28 
30 
36 


11/2 

11/2 
11/2 
11/2 
11/2 
11/2 
11/2 
11/2 
11/2 
11/2 
11/2 


397 
423 
452 
506 
562 
617 
670 
725 
779 
836 
998 


2800 
2900 
3000 
3200 
3500 
3700 
3900 
4100 
4400 
4600 
5200 



Spiral Riveted Pipe. 

Approximate Bursting Strength. Pounds per Square Inch. 
(American Spiral Pipe Works, Chicago, 1915.) 



Inside 






Thickness.— L 


I. S. Standard Gauge. 






Diam. 
Inches. 


















No.20. 


No. 18. 


No. 16. 


No. 14. 


No. 12. 


No. 10. 


No. 8. 


No. 6. 


No. 3 
(1/4"). 


3 


1500 


2000 
















4 


1125 


1500 


1875 














5 


900 


1200 


1500 














6 




1000 


1250 


1560 


2170 










7 




860 


1070 


1340 


1860 










8 




750 


935 


1170 


1640 










9 






835 


1045 


1460 










10 






750 


935 


1310 










11 






680 


850 


1200 










12 






625 


780 


1080 


1410 








13 






575 


720 


1010 


1295 








14 






535 


670 


940 


1210 








15 








625 


875 


1125 








16 








585 


820 


1050 


1290 


1520 


1880 


18 








520 


730 


940 


1140 


1360 


1660 


20 








470 


660 


840 


1030 


1220 


1500 


22 








425 


595 


765 


940 


1108 


1364 


24 








390 


540 


705 


820 


1015 


1250 


26 










505 


650 


795 


935 


1154 


28 










470 


605 


735 


870 


1071 


30 










435 


560 


685 


810 


1000 


32 










410 


525 


645 


760 


940 


34 










380 


490 


600 


715 


880 


36 










365 


470 


570 


680 


830 


40 










330 


420 


515 


610 


750 



BENT AND COILED PIPES. 

Weight per Sq. Ft. of Sheet Steel for Riveted Pipe. 

(American Spiral Pipe Works, Chicago, 1915.) 



221 



Thick- 
ness 
B.W.G. 


Thick- 
ness, 
In. 


Weight 
in Lb., 
Black. 


Weight 
in Lb., 
Galvan- 
ized. 


Thickness 
B.W.G. 


Thick- 
ness, 
In. 


Weight 
in Lb., 
Black. 


Weight 
in Lb., 
Galvan- 
ized. 


26 
24 
22 
20 


0.018 
.022 
.028 
.035 


0.7344 
0.8976 
1.1424 
1.428 


0.8844 
1.0476 
1.2924 
1.578 


18 
16 
14 
12 


0.049 
.065 
.083 
.109 


1.9992 
2.652 
3.3864 
4.4472 


2.1492 
2.802 
3.5364 
4.5972 



Weights based on steel of 489.6 lb. per cu. ft. Weights of galvanized 
sheets based on an addition of 0.075 lb. per sq. ft. of surface. 

BENT AND COILED PIPES. 

(National Pipe Bending Co., New Haven, Conn.) 
Coils and Bends of Iron and Steel Pipe. 



Size of pipe Riches 

Least outside diameter 
of coil Inches 


1/4 
2 


3/8 
21/2 


V2 
31/2 


3/4 
41/2 


1 
6 


11/4 

8 


11/2 

12 


2 
16 


2V2 
24 


3 

32 


Size of pipe Inches 

Least outside diameter 
of coil Inches 


31/2 
40 


4 

48 


41/2 
52 


5 

58 


6 

66 


7 
80 


8 
92 


9 

105 


10 
130 


12 
156 



Lengths continuous welded up to 3-in. pipe or coupled as desired. 

90° Bends in Iron or Steel Pipe. 

(Whitlock Coil Pipe Co., Hartford, Conn.) 



Size pipe, I.D 


3 
12 

3 
15 


,33 V. 

31/9 

161/5 


4 
15 

31/2 

181/2 


4 
21 


5 

20 

4 

24 


6 

23 

4 
27 


7 


8 
30 

5 
35 


9 

36 

5 

41 


10 

42 

6 

48 


1? 


Radius of bend 


26 

5 

31 


48 


End 


6 


Center to face 


54 






Size pipe, O.D 


14 

60 

7 

67 


16 
70 

7 
77 


18 

80 

7 

87 


20 

90 

8 

98 


22 

100 

8 

108 


24 

no 

8 
118 


26 
120 

10 
130 


28 
140 

10 
150 


30 


Radius of bend 


160 


End 


10 


Center to face 


170 














1 





The radii given are for the center of the pipe. "End" means the 
length of straight pipe, in addition to the 90° bend, at each end of the 
pipe. "Center to face" means the perpendicular distance from the 
center of one end of the bent pipe to a plane passing across the other end. 
The dimensions given are the minimums recommended. Larger radii 
than are shown are recommended for flexibiUty and lesser friction. 

Flexibility of Pipe Bends. (Valve World, Feb., 1906.)— So far as 
can be ascertained, no thorough attempt has ever been made to de- 
termine the maximum amount of expansion which a U-loop, or quarter 
bend, would take up in a straight run of pipe having both ends anchored. 
The Crane Company has adopted five diameters of the pipe as a stand- 
ard radius, which comes nearer than any other to suiting average re- 



222 



MATERIALS. 



quirements, and at the same time produces a symmetrical article. Bends 
shorter than tliis can be made, but they are extremely stiff, tend to 
buckle in bending, and the metal in the outer wall is stretched beyond 
a desirable point. 

In 1905 the Crane Company made a few experiments with 8-inch U 
and quarter bends to ascertain the amount of expansion they would take 
up. The U-bend was made of steel pipe 0.32 inch thick, weighing 28 
lbs. per foot, with extra heavy cast-iron flanges screwed on and refaced. 
It was connected by elbows to two straight pipes, N, 67 ft., 5. 82 ft., 
which were firmly anchored at their outer ends. Steam was then let 
into the pipes with results as follows: 
80 lb. Expansion, Total 1 7/8 in. Flange broke. 

50 1b. Expansion, iV, Vg.S, H/s. Total 2 in. 
100 lb. Expansion, N, IZ u, S, II/2 . Total 2ii/i6in. 
150 lb. Expansion, i\^, H g , 5, IT/g . Total 3 in. 
2001b. Expansion, iV, 11/2. 5, 17/8 . Total 3 3/8 in. Flange broke 

at 208 lbs. 

Quarter bend, full weight pipe. Straight pipe 148 ft., one end. 80 
lbs. Total expansion, 13/8. Flange leaked. 

Quarter bend, extra heavy pipe. Expanded 7/8 in. when a flange 
broke. Replaced with a new flange, which broke when the expansion 
was 1}4 in. 

Wrought Pipe Bends. (National Tube Co.). — The following are 
given as the advisable (R) and the least allowable (Ri) radii in inches 
to which pipe should be bent: 



Size. 


R. 


Ri. 


Size. 


R. 


Ri. 


Size. 


R. 


Ri. 


Size. 


R. 


Ri. 


Size. 


R. 


Ri. 


2V? 


15 


10 


41/0 


27 


18 


8 


48 


32 


12 


72 


48 


180.D. 


125 


90 


3 


18 


12 


5 


30 


20 


9 


54 


36 


13 


84 


60 


20O.D. 


150 


120 


3V? 


21 


14 


6 


36 


24 


10 


60 


40 


14 


90 


68 


22 0.D. 


165 


132 


4 


24 


16 


7 


42 


28 


11 


66 


44 


15 


100 


76 


^4 0.D. 


180 


144 



Bends of 12-in. pipe and smaller to be of full weight pipe; 14 to 16 
in. outside diameter, not less than 3/8 in. tliick; 18 in. and larger, not 
less than 7/iq to 1/2 in. thick. With welded flanges there must be a 
short straight length of pipe, preferably equal to two diameters of the 
pipe, between the flange and the bend. m 

Coils and Bends of Drawn Brass and Copper Tubing. 



Size of tube, outside diameter. .Inches 
Least outside diameter of coil. .Inches 


:'' 


3/8 
11/2 


^1/2 


5/8 
21/2 


3/4 
3 


1 
4 


11/4 
6 


13/8 
7 


Size of tube, outside diameter. .Inches 
Least outside diameter of coil. .Inches 


11/2 

8 


15/8 
9 


13/4 

10 


2 
12 


21/4 

14 


23/8 
16 


21/2 
18 


23/4 
20 



Lengths continuous brazed, soldered, or coupled as desired. 

SEAMLESS TUBES. 

Locomotive Boiler Tubes, Seamless. — Diameters, external, 1 1/2, 1V4, 
17/8, 2, 21/4, 21/2, and 3 in. 

N^inc thicknesses of 

each size, inch. .. . 095 .109 .110 .120 .125 .134 .135 .148 .150 
Birmingham wire 

gage 13 12 ... 11 ... 10 ... 9 ... 

Shelby Seamless Steel Tubes are made of three classes of open- 
hearth steel: 0.17 C (0.14 to 0.19%); 0.35 C (0.30 to 0.40%); and 
31/2% nickel (0.20 to 0.30 C, 3 to 4%, nickel). In all, manganese is 
from 0.40 to 0.60%,; sulphur, 0.015 to 0.040; phosphorus, 0.010 to 
0.035%. Hot finished tubes are not given any heat treatment after 




COLD-DRAWN SEAMLESS STEEL TUBES. 



223 





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224 



MATERIALS. 



leaving the hot mills, 
treated after drawing, 
as follows: 



Cold-drawn tubes are annealed before and heat- 
The physical properties of finished material are 



Temper 


Tensile 
Strength. 


Elastic 
Limit. 


Elong. in 
8 In., %. 




S, unannealed . . . 
T, finish anneal . . 


65.000 to 80,000 


60,000 to 70,000 


3 to 7 


0.17 C 


60,000 to 75,000 


50.000 to 65,000 


10 to 16 


W, soft anneal . . . 
Y, retort anneal . 


47,000 to 55.000 


27,000 to 35,000 


28 to 33 




45.000 to 52,000 


22.000 to 28,000 


30 to 40 




S, unannealed. . . 


85,000 to 100.000 


75,000 to 90.000 


Low 


0.35 C 


-< T, finish anneal . . 


80.000 to 95.000 


70.000 to 85.000 


12 to 18 




U, med. anneal . . 


65.000 to 80.000 


50.000 to 60.000 


20 to 30 


V 


( S, unannealed . . . 


95.000 to 110.000 


85.000 to 100.000 


10 to 18 in 2'' 


31/2% Ni. 


W, finish anneal . . 


85.000 to 105.000 


75,000 to 90,000 


15 to 25 in 2" 




U, med. anneal . . 


70.000 to 85,000 


45,000 to 60,000 


40 to 50 in 2" 



The 0.17 C tube is also fiunished in intermediate tempers. U, V, 
and X, between T and Y, and special treatments are given to order. 

In estimating the effective steam-heating or boiler surface of tubes. 
the surface in contact with air or gases of combustion (whether internal 
or external to the tubes) is to be taken. 

For heating liquids by steam, superheating steam, or transferring heat 
from one liquid or gas to another, the mean surface of the tubes is to be 
taken. 

Outside Area of Tubes. 

To find the square feet of surface, S, in a tube of a given length, L, in 
feet, and diameter, d, in inches, multiply the length in feet by the diam- 
eter in inches and by 0.2618. Or, S = ^'^^^^^^ =0.2618 dL. For the 

diameters in the table below, multiply the length in feet by the figures 
given opposite the diameter. 



Area of Tubes per Lineal Foot. 



Diam. 


Area, 


Dia. 


Area, 


Dia. 


Area, 


Dia. 


Area, 


Dia. 


Area, 


Dia. 


Area, 


In. 


Sq. Ft. 


In. 


Sq. Ft. 


In. 


Sq. Ft. 


In. 


Sq. Ft. 


In. 


Sq. Ft. 


In. 


Sq. Ft. 


1/4 


0.0654 


11/4 


0.3272 


21/4 


0.5890 


31/4 


0.8508 


5 


1.3090 


9 


2.3562 


1/2 


.1309 


11/9 


.3927 


2ih 


.6545 


31/0 


.9163 


6 ,1.5708 


10 2.6180 


3/4 


.1963 


13/4 


.4581 


23/4 


.7199 


3 3/4 


.9817 


7 


1 .8326 


11 


2.8798 


1 


.2618 


2 


.5236 


3 


.7854 


4 


1 .0472 


8 


2.0944 


12 


3.1416 



Seamless Brass and Copper Tube, Iron Pipe Sizes. 



Nominal 


Diam., In. 


Wt. per Ft., 
Lb. 


Nominal 
Size, 
In. 


Diam 


., In. 


Wt. per Ft., 
Lb. 


Size, 
In. 


Out- 
side. 
0.405 
.540 
.675 
.840 
1.050 
1.315 
1.660 
1.900 
2.375 
2.875 


In- 
side. 
0.281 
.375 
.494 
.625 
.822 
1.0t>2 
1.3t)8 
1.600 
2.062 
2.500 


Brass 


Cop- 
per. 
0.259 
.459 
.644 
.958 
r.298 
1.829 
2.698 
3.193 
4.224 
6.130 


Out- 
side. 
3.500 
4.000 
4.500 
5.000 
5.563 
6.625 
7.625 
8.625 
9.625 
10.750 


In- 
side. 
3.062 
3.500 
4.000 
4.500 
5.062 
6.125 
7.062 
8.O0O 
8.937 
10.019 


Brass 


Cop- 
per. 


1/8 
1/4 
3/8 
1/2 
3/4 

1 

11/4 

u/. 

21/2 


0.246 

.437 

.612 

.911 

1.235 

1.7^0 

2.557 

3.037 

4.017 

5.830 


3 

31/2 
4 

41/2 

6 
7 
8 
9 
10 


8.314 
10.85 
12.29 
13.74 
15.40 
18.44 
23.92 
30.05 
36.94 
43.91 


8.741 
11.41 
12.93 
14.44 
16.19 
19.39 
25.15 
31.60 
38.84 
46.17 



SEAMLESS BRASS TUBES. 



229 



Weight per Foot of Seamless Brass Tubes. 

(Condensed from Manufacturers' Standard Tables, 1915.) 



A.W.G. 


2 


4 


6 


8 


' 10 


1 12 


14 


16 


18 


20 


22 


24 


Wall.* 


0.2576 


0.2043 


0.162C 


0.1285 


0.1019 


.0808 


.0641 


.0508 .0403 


.0320 


.0253 


.0201 


Diam.f 

1/8 
















0.044 0.039 


0.034 


0.029 


0.024 


3/16 














0:692 


.080' .069 


.058 


.048 


.039 


1/4 










6:17510.158 


.138 


.117, .098 


.081 


.066 


.053 


5/16 










.248 .217 


.184 


.154: .127 


.104 


.084 


.068 


3/8 








6:376 


.322' .275 


.231 


.191 


.156 


.127 


.103 


.083 


1/2 






6:634 


.562 


.469 .392 


.323 


.264 


.214' .173 


.139 


.112 


5/8 


i.io 


6:994 


.868 


.748 


.617 


.509 


.416 


.338 


.273| .219 


.176 


.141 


3/4 


1.47 


1.29 


1.10 


.934 


.764 


.626 


.509 


.411 


.331 .266i .213 


.170 


7/8 


1.84 


1.59 


1.34 


1.12 


.911 


.743 


.601 


.485' .389 .312 


.249 


.199 


1 


2.21 


1.88 


1.57 


1.31 


1.06 


.859 


.694 


.558; .448 


.358 


.286 


.228 


11/8 


2.59 


2.18 


1.81 


1.49 


1.21 


.976 


.787 


.632! .506 


.404 


.322 


.257 


11/4 


2.96 


2.47 


2.04 


1.68 


1.35 


1.09 


.879 


.705 .564 


.450 


.359 


.286 


13/8 


3.33 


2.77 


2.27^ 


1.86 


1.50 1.21 


.972 


.779 .622 


.497 


.396 


.315 


1 1/2 


3.70 


3.06 


2.51 


2.05 


1.65 1.33 


1.06 


.852 .681 


.543! .432 


.344 


13/4 


4.45 


3.65 


2.98 


2.42 


1.94 1.56 


1.25 


.999 .797 


.6351 .506 


.402 


2 


5.19 


4.24 


3.45 


2.79 


2.24 1.79 


1.44 


1.15 


.914 


.728 .579 


.460 


21/4 


5.94 


4.84 


3.91 


3.16 


2.53 2.03 


1.62 


1.29 


1.03 


.820! .652 


.519 


21/2 


6.68 


5.43 


4.38 


3.54 


2.83 i2.26 


1.81 


1.44 


1.15 


.9!3i .722 


.577 


2 3/4 


7.43 


6.02 


4.85 


3.91 


3.12 12.50 


1.99 


1.59 


1.26 


1.01 


.799 


.635 


3 


8.17 


6.61 


5.32 


4.28 


3.42 2.73 


2.18 


1.73 


1.38 


1.10 


.872 


.693 


31/4 


8.92 


7.20 


5.79 


4.65 


3.71 


2.96 


2.36 


1.88 


1.50 


1.19 


.946 


.751 


31/2 


9.66 


7.79 


6.26 


5.02 


4.01 


3.20 


2.55 


2.03 


1.61 


1.28 11.02 


.809 


3 3/4 


10.4 


8.38 


6.73 


5.39 


4.30 


3.43 


2.73 


2.18 


1.73 


1.37 1I.O9 


.867 


4 


11.2 


8.97 


7.19 


5.77 


4.60 J3.66 


2.92 


2.32 


1.85 


1.47 


1.17 


.926 


41/4 


11.9 


9.56 


7.66 


6.14 


4.89 3.90 


3.10 


2.47 


1.96 


1.56 


1.24 


.984 


41/2 


12.6 


10.2 


8.13 


6.51 


5.19 '4.13 


3.29 


2.62 2.08 


1.65 


1.31 


1.04 


4 3/4 


13.4 


10.7 


8.60 


6.83 


5.48 


4.37 


3.47 


2.76 ,2.20 


1.74 


1.39 


1.10 


5 


14.1 


11.3 


9.07 


7.25 


5.78 


4.60 


3.66 


2.91 2.31 


1.84 


1.46 


1.16 


51/4 


14.9 


11.9 


9.54 


7.62 


6.07 


4.83 


3.85 


3.06 2.43 


1.93 






51/2 


15.6 


12.5 


10.0 


8.00 


6.36 


5.07 


4.03 


3.20 i2.55 


2.02 








5 3/4 


16.4 


13.1 


10.5 


8.37 


6.66 


5.30 


4.22 


3.35 :2.66 


2.1 










6 


17.1 


13.7 


10.9 


8.74 


6.95 


5.53 


4.40 


3.50 2.78 


2.2 










61/4 


17.9 


14.3 


11.4 


9.11 


7.25 15.77 


4.59 


3.65 2.90 1 .. 










61/2 


18.6 


14.9 


11.9 


9.48 


7.54 ;6.00 


4.77 


3.79 3.0 














6 3/4 


19.4 


15.5 


12.3 


9.85 


7.84 '6.24 


4.96 


3.94 


_ 














7 


20.1 


16.1 


12.8 


10.2 


8.13 6.47 


5.14 


4.09 


. . 














71/4 


20.8 


16.7 


13.3 


10.6 


8.43 16.70 


5.33 


4.23 
















71/2 


21.6 


17.2 


13.8 


11.0 


8.72 '6.94 


5.51 


4.38 
















7 3/4 


22.3 


17.8 


14.2 


11.3 


9.02 17.17 


5.70 


4.53 
















8 


23.1 


18.4 


14.7 


11.7 


9.31 7.40 


5.88 


4.67 
















81/4 


23.8 


19 


15.2 


12.1 


9.61 7.64 


6.07 


4.82 
















81/2 


24.6 


19.6 


15.6 


12.5 


9.90 7.87 


6.25 


4.97 
















8 3/-4 


25.3 


20.2 


16.1 


12.8 


10.2 8.11 


6.44 


5.12 
















9 


26.1 


20.8 


16.6 


13.2 


10.5 8.34 


6.63 


5.26 
















91/4 


26.8 


21.4 


17.0 


13.6 


10.8 8.57 


6.81 


5.41 
















91/2 


27.6 


22.0 


17.5 


13.9 


11.1 8.81 


7.00 


5.56 
















9 3/4 


28.3 


22.6 


18.0 


14.3 


11.4 9.04 1 


7.18 


5.70 
















10 


29.0 


23.2 


18.4 


14.7 


11.7 1 


9.27 i 


7.37 


5.85 

















* Thickness in inches. f Outside diameter, inches. 

Seamless brass tubes are made from ^^ in. to 1 in. outside diameter, 
varying by 1/16 in., and from 1 Y^ in. to 10 in. outside diameter, varying by 
y?, in., and in all gages from No. 2 to No. 24 A. W. G. witmn the hmiis 
of the above table. To determine the weight per foot of a tube of a 
given inside diameter, add to the weights given above the weights given 
below, under the corresponding gage numbers. 

A.W.G. 2 4 6 8 10 12 14 16 18 20 22 24 26 

Lb.perft. 1.54 .966 .607 .382 .240 .151 .095 .060 .038 .024 .015 .009 .0059 

For copper tubing add 5 % to the weights given above. 



226 



MATERIALS. 



Aluminum Tubing is made in sizes from H to 2 m. diam., advanc- 
^n^hv i/A^ch ancl from 2 to 6 in. diam., advancing by^ m.. m 
l.^nH^P^l'^t an thiXnesse^^^^ No. 24 to No. 1 B.W.G. Alummum 

SSet midi in ^zef tfcorr^^^^ with iron-pipe fittings ranging m 
H amete? from 1 8 to 4 in. Aluminum pipe fittings are made m prac- 
Sv all standard pipe sizes. Details of .sizes,, weights, strength 
etc of these tubes, pipes, and fittings are given m the pamphlets of 
the'Aluminum Co. of America, Pittsburgh. 

Lead and Tin-Lined Lead Pipe. 

(United Lead Company, New York, 1915.) 



In- 



Dia., 
In. 



Let- 
ter. 



7/16 
7/16 
1/2 
1/2 
1/2 
1/2 
1/2 
1/2 
1/2 
1/2 
1/2 
5/8 
5/8 
6/8 
6/8 
6/8 



D 

C 

B 

A 

AA 
AAA 



E 
D 
C 
B 

Spec'l 

A 

AA 

Spec'l 

AAA 

E 

D 

C 

B 

A 



Weight 
per Ft. 



10 oz. 
12 

1 lb. 

1 1/4 " 
1 1/2 " 
1 3/4 " 



lb. 



12 

1 

1 1/4 " 
1 1/2 " 
1 3/4 " 
2 

21/2 " 

3 

3/4 " 
1 
1 1/2 " 

2 

21/2 " 



In- 
side Let- 
Dia., ter. 
In. 



1 

1 

1 1/4 

1 1/4 

1 1/4 

1 1/4 

1 1/4 



AA 
AAA 

E 

D 

C 
5pec'l 

B 

A 

AA 
AAA 

E 

D 

C 

B 

A 

AA 
AAA 

E 

D 

C 

B 

A 



Weight k 
per Ft. .J< 



2 3/4 lb. 

31/2 " 

1 

1 1/4 " 

1 3/4 " 

2 

2 1/4 " 

3 

31/2 " 

4 3/4 " 

1 1/2 " 
2 

21/2 " 

3 1/4 " 

4 

4 3/4 " 
6 

2 

21/2 " 
3 

3 3/4 " 

4 3/4 " 



In- 
side 
Dia. 
In. 



Let- 
ter. 



1 1/4 

1 1/4 
1 1/2 
1 1/2 
I 1/2 
1 1/2 
1 1/2 
1 1/2 
1 1/2 
1 3/4 
13/4 
13/4 
1 3/4 
1 3/4 
13/4 

2 
2 
2 
2 
2 
2 



AA 
AAA 

E 

D 

C 

B 

A 

AA 
AAA 

D 

C 

B 

A 

AA 
AAA 

D 

C 

B 

A 

AA 
AAA 



Weight 
per Ft. 



5 3/4 lb. 

6 3/4 " 
3 

31/2 " 

4 1/4 ;; 

61/2 " 

7 1/2 " 

8 1/2 " 

4 
5 
6 
7 

81/2 " 
10 

4 3/4 " 

6 

7 

8 

9 
113/4 " 



25 
28 
12 
14 
16 
19 
24 
27 
30 
14 
17 
20 
23 
27 
31 
14 
18 
21 
23 
26 
33 



Weight of lead is taken 0.4106 lb. per cu. in , The safe working 
strength of lead is about Y^ the elastic hmit, or 22.5 lb. per sq. in. 

To find the thickness of lead pipe required when the head of 
water is given. (Chadwick Lead Works.) . ^^^^^a ^Yr>rP<5<5Pd 

Rule.— Multiply the head in feet by size of pipe wanted e^^^^^^ 
rtppimallv and divide bv 750; the quotient will be the thickness re- 
qSrS in onihuAd^^^^^^ of an inch.^ Thus the thickness of a half-mch 
pipe for a head of 25 feet will be 

25 X 0.50 -^ 750 = 0.16 inch. 

Weight of Lead Pipe Which Should Be Used for a Given 
Head of Water (United Lead Co., New York, 1915.) 



Head or 

Number 

of Feet 

Fall. 



30 ft. 

50 ft. 

75 ft. 
100 ft. 
150 ft. 
200 ft. 



Pres- 
sure 
per sq. 
inch. 



131b. 
221b. 
32 1b. 
44 1b. 
65 1b. 
87 1b. 



Caliber and Weight per Foot. 



Letter. 



D 
C 
B 
A 

AA 
AAA 



10 oz. 

12 oz. 
1 lb. 
11/4 lb, 
1 1/2 lb, 
1 3/4 lb. 



1/2 in. 1 5/8 in. 



3/4 lb. 
1 lb. 
1 1/4 lb. 

1 3/4 lb. 

2 lb. 

3 lb. 



1 lb. 

1 1/2 lb. 

2 lb. 
2 1/2 lb. 

2 3/4 lb, 

3 1/2 lb. 



3/4 in. 



1 1/4 lb, 

1 3/4 lb, 

2 1/4 lb 

3 lb. 

3 1/2 lb. 

4 3/4 lb. 



I in. 



2 lb. 

2 1/2 lb. 

3 1/4 lb. 

4 lb. 
4 3/4 lb. 
6 lb. 



11/4 in. 



2 1/2 lb. 

3 lb. 

3 3/4 lb. 

4 3/4 lb. 

5 3/4 lb. 
6 3/4 lb. 



LEAD AND TIN-LINED PIPE. 



227 



1 1/2 in., 2 and 3 pounds per foot. 

2 "3 and 4 pounds per foot. 

3 "3 1/2, 3, and 6 pounds per foot. 
3 1/2 " 4 pounds per foot. 



Lead Waste-Pipe. 



4 in., 5, 6, and 8 pounds per foot. 
41/2 " 6 and 8 pounds per foot. 

5 " 8, 10, and 12 pounds per foot. 

6 "12 pounds per foot. 



Tin-Lined and Lead-Lined Iron Pipe. 

(United Lead Co., New York, 1915.) 





Wt. per ft., lb. 




Wt. per ft., lb. 




Wt. per ft., lb. 




Wt. per 


Size, 
Tn. 




Size, 
In. 




Size, 
In. 




Size, 
In. 


ft., lb. 
Lead 


Lead Tin 


Lead Tin 


Lead Tin 




Lined. Lined. 




Lined, j Lined. 




Lined. , Lined. 




Lined. 


1/9 


1 3/8 1 


2 


6 1/8 


51/4 


41/2 


18 


16 


9 


66 


3/4 


1 5/8 


13/8 


21/2 


8 1/2 


71/2 


5 


21 1/2 


26 1/10 


10 


75 


1 


21/2 


21/4 


3 


111/2 


101/6 


6 


29 3/4 


19 1/6 


12 


88 


1 1/4 


31/2 


3 


31/?, 


14 1/2 


12 8/10 


7 


36 








1 1/2 


43/8 


33/4 


4 


15 2/3 


14 1/6 


8 


47 









Block Tin Pipe and Tubing. 



Diam., In. 


Thick- 


Wt. 

per 
ft., 


Diam., In. 


Thick- 


Wt. 


Diam., In. 


Thick- 


Wt. 


In- 


Out- 


ness, 


In- 


Out- 


ness, 


In- 


Out- 


ness. 


Z 


side. 


side. 


in. 


oz. 


side. 


side. 


in. 


oz. 


side. 


side. 


in. 


oz. 


Tubing. 






Pipe. 






Pipe. 






1/8 


0.25 


0.052 


1.9 


3/8 


0.495 


0.06 


4 


5/8 


0.800 


0.037 


10 


1/8 


.202 


.0385 


1 


3/8 


.503 


.064 


41/2 


5/8 


.831 


.103 


12 


3/I6 


.292 


.053 


2 


3/8 


.515 


.07 


5 


3/4 


.901 


.076 


10 


3/16 


.331 


.072 


3 


3/8 


.539 


.082 


6 


3/4 


.928 


.089 


12 


3/lfi 


.367 


.09 


4 


3/8 


.561 


.093 


7 


1 


1.172 


.086 


15 


1/4 


.388 


.069 


31/2 


3/8 


.584 


.104 


8 


1 


1 .204 


.102 


18 


Pipe. 






1/-? 


.632 


.066 


6 


1 1/4 


1.436 


.093 


20 






ho, 


.670 


.085 


8 


1 1/4 


1.471 


.110 


24 


1/4 


.400 


.075 


4 


1/^ 


.707 


.103 


10 


1 I/? 


1.746 


.123 


32 


1/4 


.433 


.091 


5 


1/^ 


.741 


.120 


12 


1 1/9 


1.802 


.151 


40 


V16 


.444 


.066 


4 


5/8 


.735 


.055 


6 


2 


2.236 


.118 


40 


7/16 


.562 


.065 


5 


5/8 


.768 


.071 


8 


2 


2.280 


.140 


48 



Weight of tin taken as 0.2652 lb. per cubic inch. 



Weight Per Foot of Brass- and Copper-Lined Iron Pipe. 

(United Lead Co., New York, 1915.) 







V 






T3 






73 






'V 




^3 



s 




-S 


S 







S 




-2 


§ 






ij 




.2 


v3 




fl 


►J 




c 


J 










41 


41 

$6 


02 


41 


41 

^0 






41 
^0 


1/2 


1 


1 


11/4 


2 2/z 22/3 


21/0 


6 7/10 


6 3/4 


5 


191/2 


19 3/4 


//4 


13/8 


13/8 


1 1/2 


3 1/4 3 1/4 


3 


8 3/4 


88/10 


6 


251/4 


25 6/10 


1 


2 


2 


2 


41/3, 43/8 


4 


12 6/10 


12 7/10 


8 


38 


381/2 



228 



MATERIALS. 



Lead -Lined pipe is particularly adapted for use in contact with acids, 
mine water, salt water, or any liquid which has a corrosive action on 
iron pipe. 

Lead Covered iron pipe for use in bleacheries, etc., where steam 
passes tlirough the pipe and the exterior is in contact with acid or cor- 
rosive solutions is made in commercial sizes of H. M. 1, IM. IH. 2 
and 3 inches. 

Brass and Copper Pipes, Lined with Tin or Lead, are made in com- 
mercial sizes of 3^, H, 1, 1 M, 1 H, and 2 inches. 

Sheet Lead is rolled to any weight per sq. ft. from 1 to 7 lb. in any 
width up to 11 ft. 6 in., and from 8 lb. up, 12 ft. wide. A square foot of 
rolled sheet lead 1 in. thick weighs approximately 59 3^ lb. 

Approximate Weight of Sheet Zinc. 

(Aluminum Co. of America, 1914.) 





^\n 






fn ' 








5^-Q 




W M* 


^ ^ 

O}'^ 


o 


oj a> 


^.1-; 


o 


o o 


il,h3 


o 


QJ o 


^.1-) 


o 


2 '^ 


i- J 


Z 


^■§ 


4> .. 


:z; 


.^w 


a3 . 


Z 


^ O 


•n,J 


Z 


&^ 


K r 




.^ ^ 


^£ 


u 


15^ 


,.•£ 




SJ c 
•^^-^ 


^£ 






,^£ 


N 


H 


i^ 


N 


H 


i^ 


N 


H 


^ 


N 


H 


i^ 


1 


0.002 


0.075 


8 


0.016 


0.60 


15 


0.040 


1.50 


22 


0.090 


3.37 


2 


.004 


.15 


9 


.018 


.67 


16 


.045 


1.68 


23 


.100 


3.75 


3 


.006 


.225 


10 


.020 


.75 


i7 


.050 


1.87 


24 


.125 


4.70 


4 


.008 


.30 


11 


.024 


.90 


18 


.055 


2.06 


25 


.250 


9.40 


5 


.010 


.37 


12 


.028 


1.05 


19 


.060 


2.25 


26 


.375 


14.10 


6 


.012 


.45 


13 


.032 


1.20 


20 


.070 


2.62 


27 


.500 


18.80 


7 


.014 


.52 


14 


.034 


1.35 


21 


.080 


3.00 


28 


1.000 


37.60 



Weight of Sheet or Bar Brass. 

(Compiled from Manufacturers' Standard Tables.) 



i 

2 o 


M 

d* 






c3 


d* 


.J 




(A 


it 

6' 


o 


«3 




mU^ 


03 


T? . 


fl ^ 


w72 


<A . 


T3 . 




mC/2 


<a . 


t3 . 




•^ ft 

m 








%l 

m 


d*— 


§£ 
1- 




la 




§£ 


In. 




Lb. 


Lb. 


In. 




Lb. 


Lb. 


In. 




Lb. 


Lb. 


1/16 


2.77 


0.014 


0.011 


3/4 


33,21 


2.075 


1.630 


17/16 


63.66 


7.623 


5.987 


1/8 


5.54 


.058 


.045 


13/lB 


35.98 


2.435 


1.913 


11/2 


66.42 


8,300 


6.519 


Vl6 


8.30 


.130 


.102 


7/8 


38.75 


2.824 


2.218 


19/16 


69.19 


9,006 


7.073 


1/4 


11.07 


.231 


.181 


15/lfi 


41.51 


3.242 


2.546 


15/8 


71.96 


9,741 


7.651 


5/16 


13.84 


.360 


.283 


1 


44.28 


3.689 


2.897 


1 11/16 


74.73 


10.50 


8.250 


3/8 


16.61 


.519 


.407 


'1/16 


47.05, 


4.164 


3.271 


13/4 


77.49 


11.30 


8.873 


V/16 


19.37 


.706 


.555 


11/8 


49.82 


4.669 


3.667 


1 13/16 


80.26 12 12 


9 518 


1/2 


22.14 


.922 


.724 


13/16 


52.59 


5.202 


4.086 


17/8 


83.03 12,97 


10.19 


y/16 


24.91 


1.167 


.917 


11/4 


55.35 


5.764 


4.527 


1 15/16 


85.80 13.85 


10,88 


V8 


27.68 


1.441 


1.132 


15/16 


58.12 


6.355 4.991 


2 


88.56 14.76 


11.59 


11/16 


30.44 


1.744 


1.369 


13/8 


60.89 


6.974 5.478 




1 





WEIGHT OF*COPPER AND BRASS WIRE AND PLATES. 229 



^1 


« 


lA — t^ O^ vO 00 lA O^ c^ — u*\ <N vO ^ C^ vO '^ <^ — 

.0(NO^o<Nmooooomm(Nc^o^co — t^LnsOON »r>"^ 
rOvO<NO^O^a^O<NiAO^'^OMn'— r^-^rsjO^rN^u-Ncn • • 
J «N — Ov CO r^ r>. sD lA Tj- TT (X^ f<^ c<> (N <N <N — — — — 00 — 


O u^ 


a) 

1 


lAI^OfN (N — — C^OOOOOOMA — u-\Tj-m § 
.oOf^mOoooot^Ln — -^cf^oor^ — C^ — vOcoic^un onvD 

>JJf<^ — OOoOt^vOintn'=r'^cor<^<NfN«N<N — — — oqu^ 


~'-o :;; 






<N<N<NO<N0^ — 
^ — ir^-«i- — m\0 — -^moOO — f^ov^ nO 
• rj- ^ CO tS- f^ (N O O in O^ Ov <N ^ Tj- O (N r^ wn u-^ CO ^ <N 
-^ f<^ in vO '^ <N <r^ 00 vO vO 00 <N 00 -^ — 0^ r^ in 'r cA fsi • • 

(Jf^co^ — a^f^'^^f^<^<^-= oooooo coco 


cs — »- — Q m 


i 

Oh 
O 
O 


f<^ vo 00 m CO sO o 
OOr^M^ — \OinLnOMninrN.o vO^*0^ O 
• mc>.T}--^'— OO-^ -^ '^ — — — ommot^mtN O^vO 
-" in ■«}- Tj- <N r^ r^ — 00 00 O -^ O m rsi o^ r>. \0 -^ f^ <N • • 
h^l 'sf OMTN (N OM>. sO -^ r^ f<^ <N — OOOOOO COm 


<N — — — O m 


O • 


rsjr^ — OOOm — r^inc0OO'^'^Of<^tn — '^ • • 

vO^t^OOTt-a^-^tnrsirsiinoOO — OmvOc^-^ -if 

•■^mm — o^a>> — vO(NOO^c^Of<^sOO -^OMn— -^ 

'tr co>J^fsjOt^in-^rsj — Oooi^r^NOLninTj-cnmm •« 

^'(N(NrslfN -OOOOOOOOOO --^ 

^OOOOOOOOOOOOOOOOOOOO >,-g 


O '^o 

2fe 


11 


— <N(^T}-vAv0t^00a^O — fSfn^ln^OI^OOO^O -SM 


(D O 

II 




r>.r^ino^Ot^<Noocor>«cor^ — ''i-ina^m 
h^T^-mo^ — — vO■^m^^ooo^^O — — r^oo^f^(N^nOcooO'— 
•f<^— — c^oo-^— OO— cf^NOOmom— oomtNOr^m'^ 


JOoOvOrrtN — Oa'OOr^vOinm'^'«}-(^mfNfS(N<N'— •— •— 




O^r^ — O^oOr^f^ — — — t>»fN(^u^NO — 0^ 

OvOO^^O^f^<Ninrs>Ot>^'rO^ — 0'^fn^O'^ln0^sD^Or^ 

^f'^0^00C)fna^v0T^•TJ-ln^£)0^<Nt^<Nt^(r^0^s0cnOc0s0'^ 


h5 — cOvOi^f*^ — Oa^cOr>.vOlnu-^^r}■f^^f<^<N<N<N<N — »- — 


li 
El 

|8 


pq 


m — — 0^ — CO 

f^f^^COvOfN — <N — (NcncO'^Or^'-'^ 

.vO-^rfO'— (N'Ofnf^sOOMnt^0^r^ooo^oocn'^O^vOr>.a^ 


jO^fAr^-^ — — '— 0«J^in0^f^r^C^cnoO"^ — O^t^vn-^priCN 
"OOOCOO■^O^ln<NO^t^tn-<1■^^<N<N — — — 
vO'^f'^cOfN — — — 


i 
6 


OM^t^<NT}-vO 

^n0^f^c0^^na^O'^^0^^^o<NO0^ 

/jtNunc^ooNO — ininc<^inoo\0-:^o^f^'>C"^°C)cofNa^o^o 


k1 — CO^f^0^c<^ — O^vDOO^c^OO^— -^OMnCNO^t^NO-^C^^m 
rj-oo — inOmcNOr^sDinc^c^CN — — — 
>Oin^m<NfN — — — 


II 

U CO 


(NOO— ^OOOt-^rAO — 
.OrrOvOO(r^<N — ^rgooa^f<^0^'^O^Oco^<NlnOO^\0 

r20vOaOoOms0^c<^0^0(NTJ-TfOO^:^COO^OOcO(N^noOO^ 
7lOC^'^TJ■o^^^O^•^ — <N-^oO"^ — OO — TS-^>.OmOln — 
r^oo\OfNoOlnr^^OoovOn•<N— oo^oor^sOmmTfTrmfO 
115 -^ -^pr^roCNCNrs) (N — — — — — — OOOOOOOOOO 

d 






0000 — <SC^'«»'iAsOt^OOO^O — rSfi^TMnvOr^OOO^O 



230 



MATERIALS. 



Weight of Aluminum Plates. (Brown & Sharpe Gage.) 
(Aliiminum Co. of America, 1914.) 





Thick- 






Thick- 






Thick- 




Gage. 


ness, 
In. 


It 


Gage. 


ness, 
In. 


Wgt., 
Lb. 


Gage. 


ness, 
In. 


^L^' 


0000 


0.46000 


6.406 


12 


0.080808 


1.126 


27 


0.014195 


0.1976 


000 


.40964 


5.704 


13 


.071961 


1.002 


28 


.012641 


.1760 


00 


.36480 


5.080 


14 


.064084 


.8924 


29 


.011257 


.1567 





.32486 


4.524 


15 


.057068 


.7946 


30 


.010025 


.1396 


] 


.28930 


4.029 


16 


.050820 


.7078 


31 


.008928 


.1244 


2 


.25763 


3.588 


17 


.045257 


.6302 


32 


.007950 


.1107 


3 


.22942 


3.195 


18 


.040303 


.5612 


33 


.007080 


.09854 


4 


.20431 


2.845 


19 


.035890 


.4998 


34 


.006304 


.08778 


5 


.18194 


2.534 


20 


.031961 


.4450 


35 


.005614 


.07817 


6 


.16202 


2.256 


21 


.028462 


.3964 


36 


.005000 


.06962 


7 


.14428 


2.009 


22 


.025347 


.3530 


37 


.004453 


.06201 


8 


.12849 


1.789 


23 


.022571 


.3143 


38 


.003965 


.05521 


9 


.11443 


1.594 


24 


.020100 


.2798 


39 


.003531 


.04917 


10 


.10189 


1.418 


25 


.017900 


.2492 


40 


.003144 


.04378 


11 


.090742 


1.264 


26 


.015940 


.2219 









Weiglit of Sheet or Bar Aluminum (Sp. Gr. 2.68). 
(Aluminiun Co. of America, 1914.) 



i1 


a* 






0) t-i 


1-1 . 


to 


52 bi 

pq o 


c<3 

^ o 




bjo 






la 


c4 . 










Is: 




ll 


C3 


Is 


In. 




Lb. 


Lb. 


In. 




Lb. 


Lb. 


In. 




Lb. 


Lb. 


1/16 


0.8690.004 


0.003 


3/4 


10.436 0.652 


0.516 


17/16 


20.002 


2.396 


1.882 


1/8 


1.739 .018 


.014 


13/16 11.306 .766 


.601 


11/2 


20.872 


2.609 


2.049 


3/16 


2.609 .041 


.032 


7/8 12.175! .888 


.697 


I 9/16 


21.741 


2.831 


2.223 


1/4 


3.4791 .072 


.057 


15/16 13.045 1.019 


.800 


15/8 


22.611 


3.062 


2.405 


5/16 


4.348 .114 


.089 


1 113.9151.159 


.911 


1 11/16 


23.481 


3.302 


2.593 


3/8 


5.218 .163 


.128 


11/16 14.784 1.309 


1.028 


13/4 


24.350 


3.550 


2.7£9 


7/16 


6.088 .222 


.174 


I 1/8 15.654 1.467 


1.152 


1 13/16 


25.250 


3.810 


2.992 


1/2 


6.958 .290 


.227 


13/16 16.524 1.635 


1.284 


17/8 


26.090 


4.075 


3.202 


9/16 


7.827 .367 


.288 


11/i 17.934 1.812 


1.423 


1 15/16 


26.960 


4.352 


3.417 


5/8 


8.6971 .453 


.356 


15/16 18.263 1.997 


1.569 


2 


27.829 


4.638 


3.642 


11/16 


9.567 


.548 


.430 


13/8 


19.133 


2.192 


1.722 











For further particulars regarding aluminum see pp. 380-383; 396-401. 

Weight Per Foot of Copper Rods, Pounds. 

(From tables of manufacturers, 1914.) 



In. 


Round. 


^Square. 


In. 


Round. 


Square. 


In. 


Round. 


Square. 


1/8 


0.04735 


0.06028 


1 1/8 


3.835 


4.882 


2 1/8 


13.68 


17.41 


1/4 


.1894 


.2411 


11/4 


4.735 


6.028 


2 1/4 


15.34 


19.53 


3/8 


.4261 


.5424 


1 3/8 


5.729 


7.293 


2 3/8 


17.09 


21.76 


1/2 


.7576 


.9644 


1 1/2 


6.818 


8.679 


2 1/2 


18.94 


24.11 


5/8 


1.184 


1.507 


1 5/8 


8.002 


10.19 


2 5/8 


20.88 


26.58 


3/4 


1.705 


2.170 


1 3/4 


9.281 


11.81 


2 3/4 


22.92 


29.18 


7/8 


2.320 


2.953 


I 7/8 


10.65 


13.56 


2 7/8 


25.05 


31.89 


1 


3.030 


3.857 


2 


12.12 


15.53 


3 


27.27 


34.71 



For weight of octagon rod. multiply the weight of round rod by 1.084. 
For weight of hexagon rod, multiply the weight of round rod by 1.12. 



SCREW THREADS. 



231 



SCREW THREADS. 

Sellers or U. S. Standard. 

The system of screw threads devised by AViHiam Sellers and recom- 
mended for adoption by a committee of the Franklin Institute in 1864 
is now in general use in the United States and is known as the U. S. 
standard. The angle of the thread is 60 deg. The thread is flat- 
tened at the top, the width of flat being one-eighth the pitch. The 
bottom of the thread is filled in, the width of flat at the bottom also 
being one-eighth the pitch. The wearing surface of the thread is thus 
three-quarters the pitch. 

Diam. at root of thread = diam. of bolt— (1.299 ~ No. of threads 
per in.). 

For a sharp Y thread, with an angle of 60 deg. the formula is 
Diam. at root of thread = diam. of bolt — (1.733 -J- No. of threads per in.). 

The rules for dimensioning nuts and heads given in the Franklin 
Institute report are: 

Let d = diameter of bolt, D = short diameter of rough nut or head, 

(Continued on page 232.) 



Dimensions of Screw-Threads, Sellers or U. S 


. Standard. 




Bolts and Threads. 


Nuts and 
Heads 


Bolt 


3 


'V 


4J 




^ 


■jj> 


& 


+^ fl 


.^ . 






s 




i 


«4-( a> 





pq s 


^M 


SI 


i§ 




Z 
^ 




o 


m 


°^ 





o^S 


0^ 1 


" M 


og" 


S2 


S 




i 














§1 


70 


•^ 

2 


^ 
u 

3 


5 


H 


p 


^HHHH 


< 


m 


^ 


hj 


H 


H 


In. 




In. 


In. 






In. 


In. 


In. 


In. 


In. 


1/4 


20 


0.185 


0.0062 


0.049 


0.027 


1/2 


0.578 


0.707 


1/4 


V4 


5/16 


18 


.240 


.0069 


.077 


.045 


19/32 


.686 


.840 


5/16 


1V64 


3/8 


16 


.294 


.0078 


.110 


.068 


11/16 


.794 


.972 


3/8 


IV32 


7/16 


14 


.345 


.0089 


.150 


.093 


25/32 


.902 


1.105 


7/16 


2^64 


1/2 


13 


.400 


.0096 


.196 


.126 


7/8 


1.011 


1.237 


1/2 


V16 


9/16 


12 


.454 


.0104 


.249 


.162 


31/32 


1.119 


1.370 


9/16 


3V64 


5/8 


11 


.507 


.0113 


.307 


.202 


1 I/I6 


1.227 


1.502 


5/8 


IV32 


3/4 


10 


.620 


.0125 


.442 


.302 


11/4 


1.444 


1.768 


3/1 


Vs 


7/8 


9 


.731 


.0139 


.601 


.420 


1 7/16 


1.660 


2.033 


V8 


23/32 


1 


8 


.837 


.0156 


.785 


.550 


1 5/8 


1.877 


2.298 


1 


13/16 


11/8 


7 


.939 


.0178 


.994 


.694 


1 IV16 


2.093 


2.563 


1 1/8 


29/32 


11/4 


7 


1.065 


.0178 


1.227 


.891 


2 


2.310 


2.828 


1 1/4 


1 


13/8 


6 


1.160 


.0208 


1.485 


1.057 


23/16 


2.527 


3.093 


1 3/8 1 V32 


11/2 


6 


1.284 


.0208 


1.767 


1.295 


2 3/8 


2.743 


3.358 


1 1/2 1 V16 


15/8 


51/2 


1.389 


.0227 


2.074 


1.515 


2 9/16 


2.960 


3.623 


15/8 1 9/32 


13/4 


5 


1.491 


.0250 


2.405 


1.746 


2 3/4 


3.176 


3.889 


13/4 ,13/8 


17/8 


5 


1.616 


.0250 


2.761 


2.051 


2 15/16 


3.393 


4.154 


1 7/8 , 1 15/32 


2 


41/2 


1.712 


.0278 


3.142 


2.302 


31/8 


3.609 


4.419 


2 jlVie 


21/4 


41/2 


1.962 


.0278 


3.976 


3.023 


31/2 


4.043 


4.949 


2 1/4|1 3/4 


21/2 


4 ■ 


2.176 


.0312 


4.909 


3.719 


37/8 


4.476 


5.479 


21/2 ,1 lVl6 


23/4 


4 


2.426 


.0312 


5.940 


4.622 


41/4 


4.909 


6.010 


2 3/4 21/8 


3 


31/2 


2.629 


.0357 


7.069 


5.428 


45/8 


5.342 


6.540 


3 2Vi6 


31/4 


31/2 


2.879 


.0357 


8.296 


6.510 


5 


5.775 


7.070 


31/421/2 


31/2 


31/4 


3.100 


.0384 


9.621 


7.548 


53/8 


6.208 


7.600 


31/21211/16 


3 3/4 


3 


3.317 


.0417 


11.045 


8.641 


53/4 


6.641 


8.131 


33/4 2 7/3 


4 


3 


3.567 


.0417 


12.566 


9.993 


6 1/8 


7.074 


8.661 


4 |3 V16 


41/4 


2 7/8 


3.798 


.0435 


14.186 


11.328 


6 1/2 


7.508 


9.191 


4 1/4 3 1/4 


41/2 


2 3/4 


4.028 


.0454 


15.904 


12.743 


6 7/8 


7.941 


9.721 


4 1/2 3 7/16 


4 3/4 


2 5/8 


4.256 


.0476 


17.721 


14.250 


71/4 


8.374 


10.252 


43/4 35/8 


5 


21/2 


4.480 


.0500 


19.635 


15.763 


75/8 


8.807 


10.782 


5 i 3 13/16 


51/4 


21/2 


4.730 


.0500 


21.648 


17.572 


8 


9.240 


11.312 


51/44 


51/2 


2 3/8 


4.953 


.0526 


23.758 


19.267 


8 3/8 


9.673 


11.842 


51/2 4Vi6 


5 3/4 


2 3/8 


5.203 


.0526 


25.967 


21.262 


8 3/4 


10.106 


12.373 


53/4 43/8 


6 


21/4 


5.423 


.0555 


28.274 


23.098 


91/8 


10.539 


12.903 


6 49/16 



232 



MATERIALS. 



Di= short diameter of finished nut or head; T = thickness of rough 
nut; Ti = thickness of finished nut; t = thickness of rough head, ti 
thickness of finished head; D = 1.5 d + i/s; £>i = 1.5 rf + i/ie; T = d; 
Ti = d- i/ie; t = y2D; ti = i/2d- i/i6. 

The dimensions given by the above formulae for nuts and heads are 
not generally accepted by the makers of nuts and bolts. The general 
practice is to make the rough and finished nuts of the same dimensions, 
otherwise difterent wrenches would be required for the same size of 
nut. The dimensions of nuts and bolt heads given in the above table 
are those adopted by the Upson Nut Co., Hoopes and Townsend, and 
the U. S. Navy, and agree with the formulae D = 1.5 d-{- i/s, T = Ti = 
d,t = ti = 1/2 D. 





Screw-Threads, Whitworth (English) Standard. 




Q 


i 


Q 


1 


s 

1 


i 


1 


i 


s 


i 


1/4 


20 


5/8 


11 


8 


13/4 


5 


3 


31/2 


5/16 


18 


11/16 


11 


11/8 


7 


17/8 


41/2 


31/4 


31/4 


3/8 


16 


3/4 


10 


11/4 


y 


2 


41/2 


31/2 


31/4 


7/16 


14 


13/16 


10 


13/8 


6 


21/4 


4 


33/4 


3 


1/2 


12 


7/8 


9 


11/2 


6 


21/2 


4 


4 


3 


e/16 


.2 


15/16 


9 


15/8 


5 


23/4 


31/2 







In the Whitworth or EngHsh system the angle of the thread is 55 
degrees, and the point and root of the thread are rounded to a radius of 
0.1373 X pitch. The depth of the thread is 0.6403 X pitch. 



International Standard Thread (Metric System). 

The form of thread is the same as the U. S. Standard. P = pitch, 
= 1 — No. of threads per millimeter. 



Diam., mm. 6 7 8 9 10 11 12 

Pitch, mm. 1.0 1.0 1.25 1.25 1.5 1.5 1.75 

Diam., mm. 30 33 36 39 42 45 48 52 

Pitch, mm. 3.5 3.5 4. 4. 4.5 4.5 5. 5. 



14 16 18 20 22 24 27 

2. 2. 2.5 2.5 2.5 3. 3. 

56 60 64 68 72 76 80 

5.5 5.5 6. 6. 6.5 6.5 7. 



British Association Standard Thread. 

The angle between the threads is 47 H°. The depth of the thread is 
0.6 X the pitch. The tops and bottoms of the threads are rounded with 
a radius of 2/11 of the pitch. 

Number 1 2 4 5 5 6 

Diameter, mm 6.0 5.3 4.7 4.1 3.64 3.2 2.8 

Pitch, mm 1.00 0.90 0.81 0.73 0.66 0.59 0.53 

Number 7 8 9 10 12 14 19 

Diameter, mm 2.5 2.2 1.9 1.7 1.3 1.0 0.79 

Pitch, mm 0.48 0.43 0.39 0.35 0.28 0.23 0.19 



Limit Gages for Iron for Screw-Threads. 

In adopting the Sellers, or Franklin Institute, or United States Stand- 
ard, as it is variously called, a difficulty arose from the fact that it is 
the habit of iron manufacturers to make iron over-size, and as there are 
no over-size screws in the Sellers system, if iron is too large it is necessary 
to cut it away with the dies. So great is this difficulty, that the practice 
of making taps and dies over-size has become very general. If the 
Sellers system is adopted it is essential that iron should be obtained of 
the correct size, or very nearly so. Of course no high degree of precision 
is possible in rolling iron, and when exact sizes were demanded, the ques- 
tion arose how much allowable variation there should be from the true 
size. It was proposed to make limit-gages for inspecting iron with two 
openings, one larger and the other smaller than the standard size, and 



SCREW THREADS. 



233 



then specify that the iron should enter the large end and not enter the 
small one. The following table of dimensions for the limit-gages was 
adopted by the Master Car-Builders' Association in 1883. 



o 



1/4 
5/16 
3/8 
7/16 
1/2 
9/16 



a;0 



0.2550 
0.3180 
0.3810 
0.4440 
0.5070 
0.5700 






0.2450 
0.3070 
0.3690 
0.4310 
0.4930 
0.5550 



O.OIOI 
0.011 
0.012 
0.013 
0.014 
0.015 



0) C 

5/8 
3/4 



1 

11/8 
11/4 



0)0 
530 



0.6330 
0.7585 
0.8840 
! .0095 
1.1350 



m 

0.6170 
0.7415 
0.8660 
0.9905 



61 



0.01 
0.017 
0.01 
0.01 
1.1150,0.020 
I .260511 .239510.021 



w 






81 






8 

§ 

a> 

to 

s 



3/8 1 .3860 I .364010.022 
II/2I1 .5115 1 .4885 0.023 

5/8 1 .6370 1 .6130,0.024 
13/4 1 .762511. 7375 0.025 
17/8 1 .88801 1.86201 0.026 



Caliper gages with the above dimensions, and standard reference 
gages for testing them, are made by the Pratt & Whitney Co., Hartford. 

Automobile Screws and Nuts. — The Society of Automobile Engi- 
neers (1912) adopted standard specifications for hexagon head screws, 
castle and plain nuts known as the A.L.A.M. standard. Material to 
be steel, elastic limit not less than 60,000 lbs. per sq. in., tensile strength 
not less than 100,000 lbs. per sq. in. U. S. Standard thread is used, the 
threaded portion of screws being 1 3^ times the diameter. The castle 
nut has a boss on the upper siu'face with six slots for a locking pin 
through the bolt. 



Standard Automobile Screws, Castle and Plain Nuts. 

All dimensions in inches. P = pitch, or number of threads per inch. 
d = diam. of cotter pin. P -h 8 = flat top of thread. The body 
diam. of screws is 0.001 in. less than nominal diam., with a plus 
tolerance of zero and a minus tolerance of 0.002 in. The top shall be 
between 0.003 in. and 0.003 in. large. 





D 


P 


B 


Ai 


H 


K 


I 


A 


c 


E 


d 


1/4 


28 


7/16 


7/32 


3/16 


I/16 


3/32 


9/32 




5/64 


1/16 


5/16 


24 


1/2 


17/64 


15/64 


I/16 


7/64 


21/64 


3/.32 


5/64 


1/16 


V8 


24 


9/16 


21/64 


9/32 


3/32 


1/8 


13/32 


1/8 


1/8 


3/32 


V/16 


20 


5/8 


3/8 


21/64 


3/32 


1/8 


29/64 


1/8 


1/8 


3/32 


1/2 


20 


3/4 


7/18 


3/8 


3/32 


1/8 


9/16 


3/16 


1/8 


3/32 


y/16 


18 


7/8 


31/64 


27/64 


3/32 


1/8 


39/64 


3/16 


5/32 


1/8 


5/8 


18 


15/16 


35/64 


15/32 


3/32 


1/8 


23/32 


1/4 


5/32 


1/8 


11/16 


16 


1 


19/32 


33/64 


3/32 


1/8 


49/64 


1/4 


5/32 


1/8 


3/4 


16 


11/16 


21/32 


9/16 


3/32 


1/8 


13/16 


1/4 


5/.32 


1/8 


,V/8 


14 


11/4 


49/0 


21/32 


3/32 


1/8 


29/32 


1/4 


5/32 


1/8 


1 


14 


1 7/16 


7/8 


3/4 


3/32 


1/8 


1 


1/4 


5/32 


1/8 


11/8 


12 


15/8 


63/64 


27/32 


5/32 


7/32 


15/32 


5/16 


7/32 


11/64 


11/4 


12 


1 13/16 


13/32 


15/16 


5/32 


7/32 


11/4 


5/16 


7/32 


11/64 


i^/8 


12 


2 


1 13/64 


11/32 


3/16 


1/4 


1 13/32 


3/8 


1/4 


13/64 


11/2 


12 


23/16 


15/16 


U/S 


3/16 


1/4 


11/2 


3/8 


1/4 


13/64 



234 



MATERIALS. 



The Acme Screw Thread. 

The Acme Thread is an adaptation of the commonly used style of worm 
thread and is intended to take the place of the square thread. It is a 
little shallower than the worm thread, but the same depth as the square 
thread and much stronger than the latter. The angle of the thread is 29*^, 

The various parts of the Acme Thread are obtained as follows: 

Width of point of tool for screw or tap thread = 
(0.3707 -i- No. of Threads per in.) - 0.0052. 

Width of screw or nut thread = 0.3707 -^ No. of Threads per in. 

Diam. of Tap = Diam. of Screw + 0.020. 

""sSew alZot } = Diam. of Sere. -^—^^^±-^--^_ + 0.020. 

Depth of Thread = -j 1 ^ (2 X No. of Threads per in.) j- + 0.010. 

The angle of the thread is 29 deg. 

MACHINE SCUEWS.— A. S.M.E. Standard. 

The American Society of Mechanical Engineers (1907) received a report 
on standard machine screws from its committee on that subject. The 
included angle of the thread is 60 degrees and a flat is made at the top 
and bottom of the thread of one-eighth of the pitch for the basic diameter. 
A uniform increment of 0.013 inch exists between all sizes from to 10 
and 0.026 inch in the remaining sizes. The pitches are a function of the 
diameter as expressed by the formula 

Threads per inch = ^^^^^ • 

The minimum tap conforms to the basic standard in all respects except 
diameter. The difference between the minimum tap and the maximum 
screw provides an allowance for error in pitch and for wear of the tap in 
service. 

A. S. M. E. Standard Machine Screws. 
(Corbin Screw Corporation.) 



Size. 


Outside Diameters. 


Pitch Diameters. 


Root Diameters. 


No. 


Out. 
Dia. 

and 


Mini- 


Maxi- 


Dif- 
fer- 


Mini- 


Maxi- 


Dif- 
fer- 


Mini- 


Maxi- 


Dif- 
fer- 




Thds. 


mum. 


mum. 




mum. 


mum. 




mum.. 


mum. 










ence. 






ence. 






ence, 




per In. 























0.060-80 


0.0572 


0.060 


0.0028 


0.0505 


0.0519 


0.0014 


0.0410 


0.0438 


0.0028 


1 


.073-72 


.070 


.073 


.003 


.0625 


.064 


.0015 


.052 


.055 


.0030 


2 


.086-64 


.0828 


.086 


.0032 


.0743 


.0759 


.0016 


.0624 


.0657 


.0033 


3 


.099-56 


.0955 


.099 


.0035 


.0857 


.0874 


.0017 


.0721 


.0758 


.0037 


4 


.112-48 


.1082 


.112 


.0038 


.0966 


.0985 


.0019 


.0807 


.0849 


.0042 


5 


.125-44 


.1210 


.125 


.0040 


.1082 


.1102 


.0020 


.0910 


.0955 


.0045 


6 


.138-40 


.1338 


.138 


.0042 


.1197 


.1218 


.0021 


.1007 


.1055 


.0048 


7 


.151-36 


.1466 


.151 


.0044 


.1308 


.1330 


.0022 


.1097 


.1M9 


.0052 


8 


.164-36 


.1596 


.164 


.0044 


.1438 


.146 


.0022 


.1227 


.1279 


.0052 


9 


.177-32 


.1723 


.177 


.0047 


.1544 


.1567 


.0023 


.1307 


.1364 


.0057 


10 


.190-30 


.1852 


.190 


.0048 


.166 


.1684 


.0024 


.1407 


.1467 


.0060 


12 


.216-28 


.2111 


' .216 


.0049 


.1904 


.1928 


.0024 


.1633 


.1696 


.0063 


14 


.242-24 


.2368 


.242 


.0052 


.2123 


.2149 


.0026 


.1808 


.1879 


.0071 


16 


.268-22 


.2626 


.268 


.0054 


.2358 


.2385 


.0027 


.2014 


.209 


.0076 


18 


.294-20 


.2884 


.294 


.0056 


.2587 


.2615 


.0028 


.2208 


.229 


.0082 


20 


.320-20 


.3144 


.320 


.0056 


.2847 


.2875 


.0028 


.2468 


.255 


.0082 


22 


.346-18 


.3402 


.346 


.0058 


.3070 


.3099 


.0029 


.2649 


.2738 


.0089 


24 


.372-16 


.366 


.372 


.0060 


.3284 


.3314 


.0030 


.281 


.2908 


.0098 


26 


.398-16 


.392 


.398 


.0060 


.3544 


.3574 


.0030 


.307 


.3168 


.0098 


28 


.424-14 


.4178 


.424 


.0062 


.3745 


.3776 


.0031 


.3204 


.3312 


.0108 


30 


.450-14 


.4438 


.450 


.0062 


.4005 


.4036 


.0051 


.3464 


.3572 


.0108 



A. S. M. E. STANDARD TAPS. 



235 



A. S. M. E. Special Screws. 

(All Dimensions in Inches.) 



New. Outside Diameters. Pitch Diameters. Root Diameters. 



0}d Outside 
No. Diam. and 
j Threads 
I per In. 



Mini- j Maxi- 
mum. Imum. 



Dif- 
fer- 



Mini- Maxi- 
mum, mum. 



Dif- 
fer- 
ence. 



Mini- Maxi-j 



Dif- 



mum.'mum. 



i fer- 
ence. 



1 


0.073-64 


0.0698 


0.073 0.0032 0.0613 0.0629 


0.0016 0.0494 0.0527 0.0033 


2 


.086 -56 


.0825 


.086 


.0035 j 


.0727 


.0744 


.0017 


.0591 


.0628 


.0037 


S 


.099-48 


.0952 


.099 


.0038 


.0836 


.0855 


.0019 


.0677 


.0719 


.0042 


4 


.112-40 


.1078 


.112 


.004/' 


.0937 


.0958 


.00211 


.0747 


.0795 


.0048 




36 


.1076 


.112 


.0044 


.0918 


.0940 


.0022 


.0707 


.0759 


.0052 


5 


.125-40 


.1208 


.125 


.0042 


.1067 


.1088 


.0021 


.0877 


.0925 


.0048 




36 


.1206 


.125 


.0044 


.1048 


.1070 


.0022 


.0837 


.0889 


.0052 


6 


.138-36 


.1336 


.138 


.0044 


.1178 


.1200 


.0022 


.0967 


.1019 


.0052 




32 


.1333 


.138 


.0047 


.1154 


.1177 


.0023 


.0917 


.0974 


.0057 


7 


.131-32 


.1463 


.151 


.0047 


.1284 


.1307 


.0023 


.1047 


.1104 


.0057 




30 


.1462 


.151 


.0048 


.1270 


.1294 


.0024 


.1017 


.1077 


.0060 


8 


.164-32 


.1593 


.164 


.0047 


.1414 


.1437 


.0023 


.1177 


.1234 


.0057 




30 


.1592 


.164 


.0048 


.1400 


.1424 


.0024 


.1147 


.1207 


.0060 


9 


.177-30 


.1722 


.177 


.0048 


.1529 


.1553 


.0024 


.1277 


.1337 


.0060 




24 


.1718 


.177 


.0052 


.1473 


.1499 


.0026 


.1158 


.1229 


.0071 


10 


.190-32 


.1853 


.190 


.0047 


.1674 


.1697 


.0023 


.1437 


.1494 


.0057 




24 


.1848 


.190 


.0052 


.1603 


.1629 


.0026 


.1288 


.1359 


.0071 


12 


.216-24 


.2108 


.216 


.0052 


.1863 


.1889 


.0026 


.1548 


.1619 


.007 r 


14 


.242-20 


.2364 


.242 


.0056 


.2067 


.2095 


.0028 


.1688 


.1770 


.0082 


16 


.268-20 


.2624 


.268 


.0056 


.2327 


.2355 


.0028 


.1948 


.2030 


.0082 


18 


.294-18 


.2882 


.294 


.0058 


.2550 


.2579 


.0029 


.2129 


.2218 


.0089 


20 


.320-18 


.3142 


.320 


.0058 


.2810 


.2839 


.0029 


.2389 


.2478 


.0089 


22 


.346-16 


.3400 


.346 


.0060 


.3024 


.3054 


.0030 


.2550 


.2648 


.0098 


24 


.372-18 


.3662 


.372 


.0058 


.3330 


.3359 


.0029, 


.2909 


.2998 


.0089 


26 


.398-14 


.3918 


.398 


.0062 


.3485 


.3516 


.0031' 


.2944 


.3052 


.0108 


28 


.424-16 


.4180 


.424 


.0060 


.3804 


.3834 


.0030 


.3330 


.3428 


.0098 


30 


.450-16 


.4440 


.450 


.0060 


.4064 


.4094 


.0030i 


.3590 


. .3688 


.0098 









A. 


S. M. 


E. Standard Taps. 












(Corbin Screw Corporation 


) 








Size. 


Outside Diameters. 


Pitch Diameters. 


Root Diameters. 


7S ^ 




Out. Dia. 

and 

Thds. 

per In. 


Mini- 


Maxi- 


Dif- 


Mini- 


Maxi- 


Dif- 


Mini- 


Maxi- 


Dif- 


Qi 


No. 


mum, 
In. 


mum, 
In. 


fer- 
ence. 


mum, 
In. 


mum, 
In. 


fer- 
ence. 


mum, 
In. 


mum, 
In. 


fer- 
ence. 


a.5 


0.060-80 


0.0609 


0.0632 


0.0023 


0.0528 


0.0538 


0.0010 


0.0447 


0.0466 


0.0019 


0.0465 


1 .073-72 


.0740 


.0765 


.0025 


.0650 


.0660 


.0010 


.0560 


.0580 


.0020 


.0595 


2 i .086-64 


.0871 


.0898 


.0027 


.0770 


.0781 


.0011 


.0668 


.0o89 


.0021 


.0700 


3 1 .099-56 


.1002 


.1033 


.0031 


.0886 


.0897 


.0011 


.0770 


.0793 


.0023 


.0785 


4 ; .112-48 


.1133 


.1168 


.0035 


.0998 


.1010 


.0012 


.0862 


.0887 


.0025 


.0890 


5 1 .125-44 


.1263 


.1301 


.0038 


.1116 


.1129 


.0013 


.0968 


.0995 


.0027 


.0995 


6 


.138-40 


.1394 


.1435 


.0041 


.1232 


.1246 


.0014 


.1069 


.1097 


.0028 


.1100 


7 


.151-36 


.1525 


.1569 


.0044 


.1345 


.1359 


.0014 


.1164 


.1193 


.0029 


.1200 


8 


.164-36 


.1655 


.1699 


.0044 


.1475 


.1489 


.0014 


.1294 


.1323 


.0029 


.1360 


9 


.177-32 


.1786 


.1835 


.0049 


.1583 


.1598 


.0015 


.1380 


.1411 


.0031 


.1405 


10 .190-30 


.1916 


.1968 


.0052 


.1700 


.1716 


.0016 


.1483 


.1515 


.0032 


.1520 


12 .216-23 


.2176 


.2232 


.0056 


.1944 


.1%1 


.0017 


.1712 


.1745 


.0033 


.1730 


14 \ .242-24 


.2438 


.2503 


.0062 


.2167 


.2184 


.0017 


.1896 


.1931 


.0035 


.1935 


16 : .268-22 


.2698 


.2765 


.0067 


.2403 


.2421 


.0018 


.2108 


.2144 


.0036 


.2130 


18 .294-20 


.2959 


.3031 


.0072 


.2634 


.2652 


.0018 


.2309 


.2346 


.0037 


.2340 


20 ! .320-20 


.3219 


.3291 


.0072 


.2894 


.2912 


.0018 


.2569 


.2606 


.0037 


.2610 


22 i .346-18 


.3479 


.3559 


.0080 


.3118 


.3138 


.0020 


.2737 


.2796 


.0039 


.2810 


24 1 .372-16 


.374 


.3828 


.0088 


.3334 


.3354 


.0020 


.2928 


.2968 


.0040 


.2968 


26 .398-16 


.400 


.4088 


.0088 


.3594 


.3614 


.0020 


.3188 


.3228 


.0040 


.3230 


28 .424-14 


.4261 


.4359 


.0098 


.3797 


.3818 


.0021 


.3333 


.3374 


. 00-^1 


.3390 


30 I .450-14 


.4521 


- .4619 


.0098 


.4057 


.4078 


.0021 


.3593 


.3634 


.0041 


.3680 



236 



MATERIALS. 



A. S. M. £. Special Taps. 

(Corbin Screw Corporation.) 



Size. 


Outside Diameters. 


Pitch Diameters. 


Root Diameters. 






Out. Dia. 
and 


Min., 


Max., 


Dif- 
fer- 


Min., 


Max., 


Dif- 
fer- 


Min., 


Max., 


Dif- 
fer- 




No 


Thds. 


In. 


In. 


In. 


In. 


In. 


In. 




per In. 






ence. 






ence. 


0.0538 




ence. 


1 


0.073-64 


0.0741 


0.0768 


0.0027' 0.0640 


0.0651 


0.0011 


0.0559 


0.0021 


0.0550 


2 


.086-56 


.0872 


.0903 


.0031 


.0756 


.0767 


.0011 


.0640 


.0663 


.0023 


.0670 


3 


.099-48 


.1003 


.1038 


.0035 


.0868 


.0880 


.0012 


.0732 


.0757 


.0025 


.0760 


4 


.112-40 


.1134 


.1175 


.0041 


.0972 


.0986 


.0014 


.0809 


.0837 


.0028 


.0820 




36 


.1135 


.1179 


.0044 


.0955 


.0969 


.0014 


.0774 


.0803 


.0029 


.0810 


5 


.125-40 


.1264 


.1305 


.0041 


.1102 


.1116 


.0014 


.0939 


.0967 


.0028 


.0980 




36 


.12o5 


.1309 


.0044 


.1085 


.1099 


.0014 


.0904 


.0933 


.0029 


.0935 


6 


.138-36 


.139!) 


.14:>V 


.Ou44 


.1215 


.1229 


.0014 


.1034 


.1003 


.0029 


.1065 




32 


.1390 


.14^5 


.00^9 


.1193 


.12u8 


.0015 


.0990 


.1021 


.0031 


.1015 


7 


.151-32 


.1526 


.1575 


.0049 


.1323 


.1338 


.0015 


.1120 


.1151 


.0031 


.1160 




30 


.1526 


.1578 


.0052 


.1310 


.1326 


.0016 


.1093 


.1125 


.0032 


.1130 


8 


.164-32 


.1656 


.1705 


.0049 


.1453 


.1468 


.0015 


.1250 


.1281 


.0031 


.1285 




30 


.1656 


.1708 


.0052 


.1440 


.1456 


.0016 


.1223 


.1255 


.0032 


.1285 


9 


.177-30 


.1786 


.1838 


.0052 


.1569 


.1585 


.0016 


.1353 


.1385 


.0032 


.1405 




24 


.1788 


.1850 


.0062 


.1517 


.1534 


.0017 


.1247 


.1282 


.0035 


.1285 


10 


.190-32 


.1916 


.1965 


.0049 


.1713 


.1728 


.0015 


.1510 


.1541 


.0031 


.1540 




24 


.1918 


.1980 


.0062 


.1647 


.1664 


.0017 


.1377 


.1412 


.0035 


.1405 


12 


.216-24 


.2178 


.2240 


.00t)2 


.1907 


.1924 


.0017 


.1637 


.1672 


.0035 


.1660 


14 


.242-20 


.2439 


.2511 


.0072 


.2114 


.2132 


.0018 


.1789 


.1826 


.0037 


.1820 


16 


.268-20 


.2699 


.2771 


.0072 


.2374 


.2392 


.0018 


.2049 


.2086 


.0037 


.2090 


18 


.294-18 


.2959 


.3039 


.0080 


.2598 


.2618 


.0020 


.2237 


.2276 


.0039 


.2280 


20 


.320-18 


.3219 


.3299 


.0080 


.2858 


.2878 


.0020 


.2497 


.2536 


.0039 


.2570 


22 


.346-16 


.3480 


.3568 


.0088 


.3074 


.3094 


.0020 


.2668 


.2708 


.0040 


.2720 


24 


.372-18 


.3739 


.3819 


.0080 


.3378 


.3398 


.0020 


.3017 


.3056 


.0039 


.3125 


26 


.398-14 


.4u01 


.4099 


.0098 


.3537 


.3558 


.0021 


.3073 


.3114 


.0041 


.3125 


28 


.424-16 


.42o0 


.4348 


.0088 


.3854 


.3874 


.0020 


.3448 


.3488 


.0040 


.3480 


30 


.450-16 


.4520 


.4o0o 


.0008 


.4114 


.4134 


.0020 


.3708 


.3748 


.0040 


.3770 



Wood Screws. 

Two systems of wood screw threads are in common use, that of the 
American Screw Co. and that of the Asa I. Cook Co. They are alike 
as to diameters but differ in the number of threads per inch. 







Threads 






Threads 






Threads 




Diam., 
In. 


per In. 


No. 


Diam., 
In. 


per In. 


No. 


Diam., 
In. 


per In. 


No. 


^ 1 

<72 


^00 


5 a> 
<V1 


|00 


c So 


|oo 





0.058 


32 


30 


11 


0.203 


12 


12.5 


22 


0.347 


7 


7.5 


1 


.071 


28 


28 


12 


.216 


11 


12 


23 


.361 


7 




2 


.084 


26 


26 


13 


.229 


11 


11 


24 


.374 


7 


7 


3 


.097 


24 


24 


14 


.242 


10 


10 


25 


.387 


7 




4 


.110 


22 


22 


15 


:¥i 


10 


9.5 


26 


.400 


6 


6.5 


5 


.124 


20 


20 


16 


9 


9 


27 


.413 


6 




6 


.137 


18 


18 


17 


.282 


9 


8.5 


28 


.426 


6 


6.5 


y 


.150 


16 


17 


18 


.295 


8 


8 


29 


.439 


6 




8 


.163 


15 


15 


19 


.308 


8 




30 


.453 


6 


6 


9 


.176 
.189 


14 
13 


14 
13 


20 
21 


.321 
.334 


8 
8 


7.5 










10 











STANDARD STUDS. 



237 



Dimensions of Macliine Screw Heads, A. S. M. E. Standard 




FLAT HEAD. ROUND HEAD.* OVAL FILLISTER FLAT FILLIS- 

(1) (2) HEAD. TER HEAD. 

(3) (4) 

* Form of head is semi-elliptical in axial cross section. 



Dimensions 



A = Diam. of Body. D = Width of Slot = 0.173 A + 
B = Diam. of J (1) 
Head and rad. >-2A -0.008 

of oval (3). ) 
C = Height of) A -0.008 

Head or Side V 1.739 

of Head (3).i 
E = Depth of Slot. H O 
F = Height of ) 

Head (3). t 



(2) 
1.85A -0.005 



0.7A 
HC +0.01 



(3) 
1.64A -0.009 



0.66A -0.002 

HF 
0.134B +C 



0.015. 

(4) 
1.64A -0.009 



0.66A -0.002 

'AC 



A 


B 


B 


B 


C 


C 


C 


D 


E 


E 


E 


E 


F 


(1) 


(2) 


(3,4) 


(1) 


(2) 


(3,4) 


(1) 


(2) 


(3) 


(4) 


(3) 


0,060 


0.112 


0.106 


0.0894 


0.030 


0.042 


0.0376 


0.025 


0.010 


0,031 


0.025 


019 


0.0496 


.073 


.138 


.130 


.1107 


.037 


.051 


.0461 


.028 


.012 


.035 


.030 


.023 


.O0O9 


.086 


.164 


.154 


.1320 


.045 


.060 


.0548 


.030 


.015 


.040 
,044 


.036 


.027 


.0725 


.099 


.190 


.178 


.1530 


.052 


.069 


.0633 


.032 


.017 


.042 


.032 


.0838 


.112 


.216 


.202 


.1747 


.060 


.078 


.0719 


.034 


.020 


.049 


.048 


.036 


.0953 


.125 


.242 


.226 


.1960 


.067 


.087 


.0805 


.037 


.022 


,053 


,053 


.040 


.1068 


.138 


.268 


.250 


.2170 


.075 


.097 


.0890 


.039 


.025 


,058 


059 


.044 


.1180 


.151 


.294 


.274 


.2386 


.082 


.106 


.0976 


.041 


.027 


.063 


.065 


.049 


.1296 


.164 


.320 


.298 


.2599 


.090 


.115 


.1062 


.043 


.030 


.067 


.071 


.053 


.1410 


.177 


.346 


. 322 


. 2813 


.097 


.124 


.1148 


.046 


.032 


.072 


.076 


.057 


.1524 


.190 


.372 


.346 


.3026 


.105 


.133 


.1234 


.048 


.035 


.076 


.082 


.062 


.1639 


.216 


.424 


.394 


.3452 


.120 


.151 


.1405 


.052 


.040 


.085 


.093 


.070 


.1868 


.242 


.476 


.443 


.3879 


.135 


.169 


.1577 


.057 


.045 


.094 


.105 


.079 


.2097 


.268 


.528 


.491 


.4305 


.150 


.188 


.1748 


.061 


.050 


.104 


.116 


.087 


.2325 


.294 


.580 


.539 


.4731 


.164 


.206 


.1920 


.066 


.055 


.113 


.128 


.096 


.2554 


.320 


.632 


.587 


.5158 


.179 


.224 


.2092 


.070 


.060 


.122 


.104 


.104 


.2783 


.346 


.684 


.635 


.5584 


.194 


.242 


.2263 


.075 


.065 


.131 


.150 


.113 


.3011 


.372 


.736 


.683 


.6010 


.209 


.260 


.2435 


.079 


.070 


.140 


.162 


.122 


.3240 


.398 


.788 


.731 


.6437 


.224 


.279 


.2606 


.084 


.075 


.149 


.173 


.130 


.3469 


.424 


.840 


.779 


.6863 


.239 


.297 


.2778 


.088 


.080 


.158 


.185 


.139 


.3698 


.450 


.892 


.827 


.7290 


.254 


.315 


.2950 


.093 


.085 


.167 


.196 


.147 


.3927 



Standard Studs.— The Upson Nut Co., Cleveland, gives (1914) the 
following formulae for the dimensions of standard stud bolts with 
either V or U. S. Standard threads: A = diam. of stud; B = 
length of short thread ; C = length of unthreaded portion ; D = length 
of long thread; E = total length of stud, all in inches. B = A -{- H; 
C = A; D = E- {B-\-C). 



238 



MATERIALS. 



Dimensions of Standard Set and Cap-Screws. 

Compiled from tables of leading manufacturers. All dimensions 
in inches. D = short diam. of head, square and hex. heads, or diam. 
of round head; L = maximum length, I = minimum length under head; 
U, i, maximum and minimum length over all; H = length of head. 



Diam. of Screws . . . 
Threads per In 


Vs 
40 


Vl6 

24 


V4 

20 


Vl6 

18 

-;" 

V2 


Vs 
16 

Vs 

V2 


Vl6 

14 

V. 
Vs 

V4 


or 13 

Vs 
Vs 

1/2 

4 

V4 


Vl6 
12 

> 

V4 

lVl6 
Vl6 

4 

V^16 
13/16 

Vie 
6 
1 

1 
3 

11/2 
lVl6 

11/4 

Vs 


Vs 

11 

Vs 

4V2 

V4 

V4 

Vs 

41/2 
1 

Vs 

Vs 

41/2 

1 

Vs 

%^ 

11/4 
IVs 

13/4 
1 

3 

11/2 

1V16 


V4 

10 

v7 

43/4 

1 

Vs 

V4 

43/4 

1V4 

1 

V4 

43/4 

1V4 

1 

V4 

6 

11/2 

nu 

2 

11/4 

13/4 

Vs 


Vs 
9 

11/4 

IVs 

11/2 

IVs 

'// 

11/2 
IVs 

? 

IV4 


1 

8 

\ 

11/2 

11/4 
1 
5 

13/4 

11/4 
1 

5 

13/4 
.V4 

6 
2 


11/8 

7 

13/4 
13/s 

IVs 
2 

IVs 
li/s 

2 


11/4 
7 


Sq Head |£ 






V2 


'Y^ 






Set-Screws. ]{ 






2 


[D 






Vs 

3/4 


Vl6 
V4 


V2 

Vs 

V4 


11/2 
11/4 


Sq. Head f H 
Cap-Screws. 1 L 














2 


[D 






Vl6 
V4 

Vs 

V4 
3V2 

V4 
1V32 

2 1/4 
V4 


V4 
Vl6 

?/• 

Vs 

2V4 
V4 
Vl6 

21/2 
V4 

11/32 


Vs 

V4 
Vl6 

Vs 
4 

V4 
3/4 

V4 
5/8 
2V4 
V4 

Vl6 


Vs 
%^^ 

V4 

Vs 

Vl6 
4V4 
V4 
13/16 

1 
3A 

V4 
V2 


3/4 

V4 
1/2 

6 

3/4 
1V4 

1 

Vl6 


11/2 


Hexagon rr 






Head < j 






Cap-Screws, i ^ 






2 


Round and [ D 


Vl6 

Vs 

V4 


Vl6 

3 1/4 
V4 




Filister H 






Head 1 L 

Cap-Screws. [ I 








V4 
1V4 
V4 


3/s 

V4 






Flat Head I Y, 










Cap-Screws. \ y 










Button-Head f? 


V32 
1V4 

V4 


V4 


Vl6 
21/4 
V4 


















Cap-Screws. > 


.... 








Socket Set-Screws, 
Length. . 


' 


11/4 

















Threads are U. S. Standard. On all cap-screws of 1 in. and less in 
diam. and 4 in. long and under, threads are cut M of the length of body; 
longer than 4 in. threads are cut' 3^ of the length of body. Lengths 
advance by K in- from minimum to maximum. 



Oval Head Rivets — -Approximate Number in One Pound 

(Garland Nut & Rivet Co., Pittsburgh.) 



Diam. 


V16 


3/8 


V16 


1/4 


3/16 


V8 


Diam. 


V16 


3/8 


V16 


V4 


3/16 


V8 


Length 












Leneth 














V4 








123 


262 1630 


1 Vs 


IOV2 


16 


23 


40 


71 


166 


3/8 






56 il02 


210 500 


13/8 


10 


15 


21 


36 


68 


160 


1/2 


21 


34 


49 


90 


177 1415 


1 V8 


91/2 


14 V2 


20 


35 


62 


145 


V8 


19 


30 


45 


78 


150 350 


2 


9 


14 


18 


32 


60 


140 


3/4 


17 


27 


39 


70 


132 300 


2V4 


8V2 


13 


16 


29 


55 




7/8 


16 


24 


35 


62 


110 1280 


21/2 


8 


12 


15 


27 


48 




1 . 


15 


22 


33 


56 


100 


250 


2 3/4 


7V2 


11 


14 


25 


44 




n/8 


14 


21 


31 


50 


96 




3 • 


7 


10 


13 


23 


42 




1 1/4 13 


20 


27 


46 


88 


205 


31/2 


6 


9 


12 


20 






1 3/8 12 


18 


26 


44 


80 




4 




8 




18 






n/2 i 11 


17 


24 


42 


77 1178 















Small rivets are made to fit holes of their rated size; the actual diameter 
may vary slightly from the decimals given below: 

Size , 3/32 7/64 Vs 9/64 

Approx. diam 094 .109 125 .140 

Size 7/32 V4 9/32 



Approx. diam. 



5/32 1V64 3/ic 
155 .170 .185 
5/16 3/8 7/18 



.215 ,245 .275 .305 .365 .425 



WEIGHT OF RIVETS. 



239 



Weight of 100 Cone Head Rivets. 

(Hoopes & Townsend, Philadelphia, 1914.) 



L'gth 
Under 


Scant Diameter, In. 


Head 
In. 


1/2 


Vl6 


Vs 


11/16 


V4 


lVl6 


7/8 


1 


IVs* 


11/4* 


3/4 


8.6 


11.9 


15.5 
















7/8 


9.3 


12.7 


16.5 
















1 


9.9 


13.6 


17.6 


22.4 


28.1 


34.5 










1 1/8 


10.6 


14.4 


18.6 


23.6 


29.6 


36.3 










n/4 


11.2 


15.2 


19.6 


24.9 


31.1 


38.1 


46 


65 






13/8 


11 .9 


16.1 


20.7 


26.1 


32.6 


39.8 


48 


68 


93 




U/2 


12.5 


16.9 


21 .7 


27.4 


34.1 


41.6 


50 


70 


96 


i27 


15/8 


13.2 


17.7 


22.7 


28.6 


35.6 


43.4 


52 


73 


100 


132 


13/4 


13.8 


18.6 


23.8 


29.9 


37.1 


45.1 


54 


76 


103 


136 


17/8 


14.5 


19.4 


24.8 


31.1 


38.6 


46.9 


56 


78 


107 


140 


2 


15.1 


20.2 


25.8 


32.4 


40.1 


48.7 


58 


81 


110 


145 


21/8 


15.8 


21.0 


26.9 


33.7 


41 .6 


50.5 


60 


84 


114 


149 


21/4 


16.4 


21.9 


27.9 


34.9 


43.1 


52.2 


62 


87 


117 


153 


2 3/8 


17.1 


22.7 


28.9 


36.2 


44.6 


54.0 


64 


89 


121 


158 


21/2 


17.8 


23.5 


30.0 


37.4 


46.1 


55.8 


66 


92 


124 


162 


2 5/8 


18.4 


24.4 


31.0 


38.7 


47.6 


57.5 


68 


95 


128 


166 


2 3/4 


19.1 


25.2 


32.0 


39.9 


49.1 


59.3 


70 


97 


132 


171 


2 7/8 


19.7 


26.0 


33.1 


41.2 


50.6 


61.1 


72 


100 


135 


175 


3 


20.4 


26.9 


34.1 


42.5 


52.1 


62.8 


74 


103 


139 


179 


31/4 


21.7 


28.5 


36.2 


45.0 


55.1 


66.4 


78 


108 


146 


188 


31/2 


22.9 


30.2 


38.2 


47.5 


58.1 


69.9 


83 


114 


153 


197 


33/4 


24.3 


31.9 


40.3 


50.0 


61.1 


73.4 


87 


119 


160 


205 


4 


25.6 


33.5 


42.4 


52.5 


64.1 


77.0 


91 


124 


167 


214 


41/4 


26.9 


35.2 


44.4 


55.0 


67.1 


80.5 


95 


130 


174 


223 


41/2 


28.2 


36.9 


46.5 


57.5 


70.1 


84.0 


99 


135 


181 


232 


4 3/4 


29.5 


38.5 


48.6 


60.0 


73.1 


87.6 


103 


141 


188 


240 


5 


30.8 


40.2 


50.6 


62.6 


76.1 


91.1 


107 


146 


195 


249 


51/4 


32.1 


41.9 


52.7 


65.1 


79.1 


94.6 


111 


151 


202 


258 


51/2 


33.4 


43.5 


54.8 


67.6 


82.1 


98.2 


115 


157 


209 


266 


5 3/4 


34.7 


45.2 


56.8 


70.1 


85.1 


101.7 


120 


162 


216 


275 


6 


36.0 


46.8 


58.9 


72.6 


88.1 


105.2 


124 


167 


223 


284 


61/2 


38.7 


50.2 


63.0 


77.6 


94.1 


112.3 


132 


178 


237 


301 


7 


41.3 


53.5 


67.2 


82.7 


100.2 


119.4 


140 


189 


251 


319 


Wgt. 














■ 








of 


4.7 


6.9 


9.3 


12.3 


16.1 


20.4 


26 


38 


54 


75 


Hds. 























* All Rivets larger than one inch are made to exact diameter. 

Tinners' Rivets. Flat Heads. (Garland Nut & Rivet Co.) 



r 


^ 


fe . 


^ 


M 


ti 




^ 


0) . 




rG 


^. . 






ao 
■4J0 


1 cj 

.Si— ( 




g- 


id 

5^ 






id 

5"^ 




ag 


0.070 


1/8 


4 oz. 


0.115 


13/64 


1 lb. 


0.160 


5/16 


3 lbs. 


0.225 


7/16 


8 


.080 


9/64 


6 


.120 


7/32 


1 1/4 


.163 


21/64 


31/2 


.230 


29/64 


9 


.090 


5/32 


8 


.125 


15/64 


1 1/2 


.173 


11/32 


4 


.233 


15/32 


10 


.094 


11/64 


10 


.133 


1/4 


1 3/4 


.185 


3/8 


5 


.253 


1/2 


12 


.101 


3/16 


12 


.140 


17/64 


2 


.200 


25/64 


6 


.275 


33/64 


14 


.109 


3/16 


14 


.147 


9/32 


21/2 


.215 


13/32 


7 


.293 


17/32 


16 



240 



MATERIALS. 



Shearing Value, Area of Rivets, and Bearing Value of Riveted Plates. 

Shearing Value = Area of Rivet X Allowable Shearing Stress Per Sq. In. 
Bearing Value = Diameter of Rivet X Thickness of Plate X Allowable 
Bearing Stress Per Square Inch. 



Di- 
am. 
of 


Area, 
Sq. 
In. 


Single 
Shear 

6,000 
Lbs. 

Sq.In. 


Double 
Shear 
6,000 

Lbs. 
Sq.In. 

2356 
3682 
5301 
7216 
9425 


Bearing Value for Different Thicknesses of Plate 
in Inches at 12,000 Lb. per Square Inch. 


Riv- 
et. 
In. 


In. 


Vl6 

In. 


Vs Vl6 V2 

In. In. In. 


In. 


V4 

In. 


;/8 

In. 


In. 


1/2 
5/8 


0.1964 
0.3068 
0.4418 
0.6013 
0.7854 


1178 
1841 
2651 
3608 
4712 


1500 
1875 


1875 
2344 
2813 


2250 2625 3000 .... 
2813 328)1 3750 4688 


6750 
7875 


9188 
10500 




3/4 


2250 
2625 
3000 


3375 
3938 


3933; 4500( 5625 
4594! 5250 6563 




7/8 


3281 
3750 




1 


45001 52501 6000 


7500 


90001 


12000 



Di- 

am. 
of 
Riv- 
et, 
In. 



1/2 
5/8 
3/4 



Area, 
Sq. 
In. 



0.1964 
0.3068 
0.4418 



Single 
Shear 
7,500 

Lbs. 

Sq. 

In. 



1473 
2301 
3313 
7/8 0.6013' 4510 
1 0.7854 5891 



Double 
Shear 
7,500 
Lbs. 

Sq. 

In. 



Bearing Value for Different Thicknesses of Plate 
in Inches at 1 5,000 Lbs. per Square Inch. 




Di- 
am. 
of 
Riv- 
et, 
In. 



1/2 
5/8 
3/4 

7/8 



Area, 
Sq. 
In. 



0.1964 
0.3068 
0.4418 
0.6013 
0.7854 



Single 
Shear 
10,000 
Lbs. 

Sq. 

In. 



1964 
3068 
4418 
6013 
7854 



Double 

Shear 

10,000 

Lbs. 

Sq. 

In. 



3927 
6136 
8836 



Bearing Value for Different Thicknesses of Plate 
in Inches at 20,000 Lbs. per Square Inch. 



1/4 

In. 



2500 
3125 



Vl6 

In. 



3125 
3906 
4688 



Vl6 

In. 



3750 4375 



3750 
12026 4375 5469 
15708 5000 62501 750618750 



5469 i6563 
|6250|7500 



4688 5469 
5625 6563 
7656 



In. 



Vs 
In. 



5000 
6250 7813 
7500 l 9375 



In. 



11250 
10938 |13125 
125001 15000 



Vs 
In. 



1 
In. 



15313 .... 
17500 20000 



Dia. 
of 


Area 

in 

Square 

Inches. 

0.0274 
0.0491 
0.0764 

0.0924 
0.1104 
0.1499 


6,000 Lbs. 
per Sq. In. 


Bearing Value for Different Thicknesses of Plate 
in Inches at 1 2,000 Lb. per Square Inch. 


Riv- 
et. 


Single 
Shear 


Double 
Shear. 


1/8 

In. 


;/i6 

In. 


In. 


Vl6 

In. 


11/32 

In. 


Vs 
In. 


't 


3/16 


164 
295 
458 
554 
662 
899 


328 
589 
917 
1109 
1325 
1799 


281 
375 
468 

515 
563 
656 


422 


750 
938 


ii72 
1289 
1406 


1418 
1547 


i687 
1969 




1/4 
5/16 


563 
703 




11/32 

3/8 


773 
844 
984 


1031 
1125 




7/16 


1313 


1640 


1 1804 


2297 



All bearing values above or to right of zigzag lines are greater than 
double shear. Values between upper and lower zigzag lines are less 
than double and greater than single shear. Values below and to left 
of lower zigzag lines are less than single shear. 



WEIGHT OF LAG SCREWS 



241 



LENGTH OF RIVETS REQUIRED FOR VARIOUS GRIPS 

(American Bridge Co. Standard — Dimensions in Inches.) 

pcdja (t=^ (}=:ii fczalq 

r< ^Length — ^-j ^•^- Length— >^ h— Length— >i "« ^Length >* 



Grip 




Diameter, 


In. 




Grip 
b 


Diameter, In. 


a 


1/2 


5/8 


3/4 


7/8 


I 


1/2 


5/8 


3/4 _ 


7/8 


1 


1/2 


! 1/? 


13/4 


I 7/8 


2 


2 1/8 


1/2 


I 1/8 


11/4 


11/4 


13/8 


13/8 


5/8 


15/s 


17/8 


2 


2 1/8 


2 1/4 


5/8 


11/4 


13/8 


1 3/8 


1 1/2 


1 1/2 


3/4 


1 V4 


2 


2 1/8 


2 1/4 


2 3/8 


3/4 


1 3/8 


1 1/2 


1 1/2 


1 5/8 


15/8 


7/8 


1 7/8 


2 1/8 


2 1/4 


2 3/8 


2 1/2 


7/8 


1 1/2 


1 5/8 


1 5/8 


13/4 


13/4 


1 


2 


2 1/4 


2 3/8 


2 1/? 


2 5/8 




15/8 


13/4 


13/4 


17/8 


17/8 


1/4 


2 1/4 


2 1/2 


2 5/8 


2 3/4 


2 7/8 


1/4 


1 7/8 


2 


2 


2 1/8 


2 1/8 


1/2 


2 5/8 


2 7/8 


3 


3 1/8 


3 1/4 


1/2 


2 1/8 


2 1/4 


2 3/8 


2 3/8 


2 1/2 


3/4 


3 


3 1/4 


3 3/8 


3 1/? 


3 5/8 


3/4 


2 1/? 


2 5/8 


2 3/4 


2 3/4 


2 7/8 


2 


3 1/4 


3 1/2 


3 5/8 


3 3/4 


3 7/8 


2 


2 3/4 


2 7/8 


3 


3 


3 1/8 


1/4 


3 1/^, 


3 3/4 


3 7/8 


4 , 


4 1/8 


1/4 


3 


3 1/8 


3 1/4 


3 1/4 


3 3/8 


1/2 


3 3/4 


4 


4 1/8 


4 1/4 


4 3/8 


1/2 


3 1/4 


3 3/8 


3 1/2 


3 1/2 


3 5/8 


3/4 


4 


4 1/4 


4 3/8 


4 1/? 


4 5/8 


3/4 


3 1/2 


3 5/8 


3 3/4 


3 3/4 


3 7/8 


3 


4 3/8 


4 5/8 


4 3/4 


4 7/8 


5 


3 


3 7/8 


4 


4 


4 1/8 


4 1/4 


1/4 


4 5/8 


4 7/8 


5 


5 1/8 


5 1/4 


1/4 


4 1/8 


4 1/4 


4 1/4 


4 3/8 


4 1/2 


1/^ 


4 7/8 


5 1/8 


5 1/4 


5 3/8 


5 1/2 


1/2 


4 3/8 


4 1/2 


4 1/2 


4 5/8 


4 3/4 


3/4 


5 1/8 


5 3/8 


5 1/? 


5 5/8 


5 3/4 


3/4 


4 5/8 


4 3/4 


4 3/4 


4 7/8 


5 


4 


5 3/8 


5 5/8 


5 3/4 


5 7/8 


6 


4 


4 7/8 


5 


5 


5 1/8 


5 1/4 


1/4 


5 3/4 


6 


6 1/8 


6 1/4 


6 3/8 


1/4 


5 1/4 


5 3/8 


5 3/8 


5 1/? 


5 5/8 


1/2 


61/8 


6 3/8 


6 1/? 


6 5/8 


6 3/4 


1/2 


5 5/8 


5 3/4 


5 3/4 


5 3/4 


5 7/8 


3/4 


6 3/8 


6 5/8 


6 3/4 


6 7/8 


7 


3/4 


5 7/8 


6 


6 


6 


61/8 


5 


6 5/8 


6 7/8 


7 


■/1/8 


/1/4 


5 


6 1/8 


6 1/4 


6 1/4 


6 1/4 


6 3/8 







Weight of 100 Lag Screws. 

(Hoopes & Townsend, Philadelphia, 1914.) 








Diameter, Inches. 




V16 


Vs 


7/l6 


1/2 


Vl6 


Vs 


3/4 


7/8 


1 


1 Vs 


1 1/4 


in. 

IV2 


lb. 
4.2 
4.7 
5.2 
5.7 
6.2 
7.2 
8.2 
9.2 
10.2 
11.3 
12.4 
13.5 


lb. 
6.5 
7.1 
7.7 
8.4 
9.2 
10.6 
12.0 
13.5 
15.0 
16.5 
18.0 
19.5 


lb. 

9.2 
10. 
10.9 
11.8 
12.7 
14.6 
16.6 
18.8 
20.7 
22.8 
24.9 
27.0 
31.1 
35.2 


lb. 

13.0 
13.8 
14.9 
16.1 
17.4 
19.0 
21.5 
24.0 
26.5 
29.0 
31.5 
34.0 
39.0 
44.0 
49.0 
54.0 


lb. 


lb. 


lb. 


lb. 


lb. 


lb. 


lb. 


13/4 
















7'' 


23.0 
24.5 
26.0 
29.2 
32.5 
35.9 
39.3 
42.7 
46.1 
49.5 
56.3 
63.1 
69.9 
76.7 
83.5 
90.5 


24.8 

27.3 

29.0 

32.9 

36.9 

41.0 

44.9 

48.8 

52.7 

56.6 

64.5 

72.5 

80.5 

88.5 

96.5 

104.5 

112.5 

121.0 

129.5 

138.0 












•§ 2 1/2 












43.0 
48.3 
53.8 
59.6 
65.5 
71.5 
77.5 
83.5 
95.5 
107 6 










31/2 


75.0 
78.5 
82.0 
86.0 
90.0 
98.0 
106.0 
122.5 
HQ 








90 
99 
108 
118 
128 
138 
158 
178 
198 
219 
240 
261 
282 
304 
326 
348 






■S 4 






rt 41/2 






« 51/2 

0) 6 
'? 7 


150 
163 
176 
203 
230 
257 
284 
311 
338 
365 
393 
421 
449 


240' 
270 








300 






119.8 155.5 


332 








131.0 
143.1 
155.4 
167.6 
179.8 
192.0 
204.0 


172.0 
188.5 
205.0 
221.5 
238.0 
255.0 
272.0 


365 


S'l 








395 


^12 










425 


13 










459 


14 












493 


15 












527 


16 












562 
















Thds. 
per in. 


10 


7 


7 


6 


5 


5 


41/2 


41/2 


3 


3 


3 



242 



MATERIALS 



Approximate Weight of Macliine Bolts per 100, Square Heads and 
Square Nuts. (Hoopes & Townsend, Philadelphia, 1914.) 



Length Under 


Diameter. 


Head to 
Point, In. 


1/4 


3/8 


Vlfi 


1/2 


9/16 


V8 1 3/4 


7/8 


1 


11/4 


11/2 


13/4 


2 


In. 


In. 


In. 


In. 


In. 


In. I In. 


in. 


In. 


in. 


in. 


in. 


in. 


11/4 
11/2 
2 


3.1 

48 
5S 


8.4 
9.2 
10.8 
12.3 
13,8 


12.5 
13.6 
15.7 
17.8 
19.9 


17.7 


74,3 


30.7 50.4 

32.8 53.5 












19.1 26.0 














21. 8i 29.5 37.1 59.7 


89.4 125.7 










21/2 

3 


24.6! 33.0' 41.4 65.91 97.3 136.8 


246.3 
263.5 








27.41 36.5 


45.7 72.1 105.7 147.8 


470 






31/2 

4 


6.2 
69 


15.3 
16.9 


21.8 
24.0 


29.8' 40.0 


50.0 78.3 114.2 158.9 
54.4 84.5 122.6 169.9 


280.8 495 
298.1 520 






32.6 


43.5 


720 




41/2 


7.5 


18.4 


26 1 


35.4 


46.7 


58.3 90.3 


no .5 179.4 


314.1 545 


753 




5 


8.7 


19.9 


28.2 i 


38.1 


50.2 


62.6 96.5 


138.9 190.4 


331.4 570 


786 


1180 


51/2 


8.9 


21.5 


30,3; 


40.9 


53.7 


66.9; 102.7 147.4 201.5 


348.6 595 


820 


1225 


6 


9.6 


23.0 


32.4 


43.7 


57.2 


71.3 108.9 155.8 212.5 


365.9 620 


854 


1270 


61/2 


10.3 


24.6 


34.5 


46.4 


60.7 


75.6 115.1 164.3 223.6 


383.1 645 


888 


1315 


7 


11.0 


26.1 


36.6 


49.2 


64.2 


79.9 121.3 172.7 234.6 


400.4 670 


922 


1360 


71/2 


11.7 


27.7; 38.8 


51.9 


67.6 


84.2 127.6 181.2 245.6 


417.7 695 


956 


1405 


8 


17,4 


29. 2 1 40.9 


54.7 


71.1 88.5 133.8 189.6 256.7 


434.9 725 


990 


1450 


9 


13.7 


32.4 44.9 


60.0 77.8 96.8 145.7 205.9 278.0 


468.2; 775 


1058 


1540 


10 


15.1 


35.5 


49.1 


65.5 84.8 105.4 158.2 222.8 300.0 


502.7' 825 


1126 


1630 


11 


16.5 


38.6 


53.4 


71.0 91.8 114.1 170.6239.8322.2 


537.3 875 


1194 


1720 


' 12 


17.9 


41.7 


57.6 


76.5 98.8 122.7 183.0 256.7 344.3 


571.81 925 


1262 


1810 


13 


19.3 


44.8 61.8 


82.0 105.5il31.0 195.4 


273.6 366.3 


606.3 975 


1330 


1900 


14 


20.6 


47 .9i 66.0 


87.6 112.5:139.6 207.9 


290.5 388.4 


640.8 1025 


1398 


1990 


15 


22.0 


51.0; 70.3 


93.1 119.5 148.2 220.3 


307.4 410.5 


675.3,1075 


1468 


2080 


16 


23.4 


54.1 


74.5 


98.6 126.4 156.9232.7 


324.3 432.6 


709.811125 


1536 


2170 


17 


24.8 


57.2 


78.7 104.1; 133.4 165.5 245.1 


341 .2 454.7 


744.3; 1175 


1604 


2260 


18 


26.2 


60.3 


82.9 109.7 140.4 174.1 257.6 358.1 476.8 


778.9; 1225 


1672 


2350 


20 


28.9 


66.5 


91 .4 120.7 154.4 191 .4 282.4 392.0 521 .0 


847.9 1325 


1808 


2530 


22 


31.7 


72.7 


99.9 131.7 168.4:203.6 307 .3S425 .8 565.1 


916.9 1425 


1944 


2710 


24 


34.4 


78.9 


108.3 142.8 182.4 225.9 332.1 


459.6 609.3 


986.0 1525 


2080 


2890 


26 


37.2 


85.2 


116.8 153.8 196.3 243.1 357.0 


493.4 653.5 


1055.0 1625 


2216 


3070 


28 


40.0 


91.41125.2 164.9 210.3 260.4 381.8 


527.3 697.7 


1124.0 1725 


2352 


3250 


30 


42.7 


97.6 


133.7 


175.9 


224.3 


277.7 406.7 


561.1 


741.9 


1193.0 1825 


2488 


3450 











Weight per 1 00 Nuts. 






Square 
Hexagon 


0.7 
0.6 


2.5 
2.1 


3.9 
3.2 


5.7 8.1 9.91 16.8 26.9 40.1 

4.8 6.7 8.3 14.0 22.3 33.4 


77.8 
64.0 


162 257 381 
134 207 307 


Diff. 


0.1 


0.4 


0.7 


0.9 1.4 1.6 2.8 4.6 6.7 


13.8 


28 50 74 











Weight of 100 Heads. 








Square 
Hexagon 


0.8 
0.7 

0.1 


2.4 
2.2 


4.0 
3.5 


5.9 
5.3 


8.8l 11.41 20.0 31.4 44.91 
7.9| 10.3 17.0| 28.2 39.4 


90.9; 144 
83.9 132 


231 
215 


345 
302 


Diff. 


0.2 


0.5 


0.6 


0.9 1.1 ' 3.0 3.2 5.5 


7.0 12 


16 


43 



Subtract 



For Weight of Bolts with Hex. Heads and Hex. Nuts. 

I 0.2 I 0.6| 1.2| 1.5| 2.3| 2.7| 5.81 7.8| 12.2| 20 8| 40| 66[ 117 



Sizes of Cast Washers. (Up.son Nut Co., 


Cleveland, 1914.) 


Diam. 


Hole. 


Thick. 


Bolt. 


Weight. 
Lbs. 


Diam. 


Hole. 


Thick. 


Bolt. 


Weight. 
Lbs. 


In. 
21/4 
23/4 

31/2 


In. 

5/8 

3/4 
7/8 
1 


In. 

11/16 
3/4 

13/10 

7,'8 


In. 

1/2 
5/8 

3/4 
7/8 


1/2 

5/8 

3/4 

11/4 


In. 

4 
41/2 

6 


In. 

u/s 

11/4 
13/8 
13/4 


In. 
15/16 

11/8 
11/4 


In. 

1 

11/8 

11/4 

11/2 


15/8 

5 



WROUGHT WASHERS. 



243 



Weight and Dimensions of Hanger Bolts. 

(Hoopes & Townsend, Philadelphia, 1914.) 

One end cut with deep wood screw thread, the other fitted with a 
standard cold punched, chamfered and trimmed square nut. 



Diameter, In. 


V2 


5/8 


V4 


Vs 


1 ' 


11/8 


11/4 


13/8 


|M/2 


Length Over All, In. 






Approximate Weight per 


100. 






4 


24 
34 
44 
54 




















6 


53 
67 
81 
95 


80 
97 
114 
134 
154 


106 
138 
166 
196 
226 
256 












8 


174 
217 
259 
295 
329 


257 
299 
332 
374 
417 


301 
351 
401 
451 
501 






10 
12 
14 


456 
511 
566 
621 


532 
597 
677 


16 






747 












Threads per inch: 

Nut end 

Screw end 


13 
6 


11 

5 


10 

41/2 


9 

41/2 


8 
3 


7 

3 


7 

3 


6 

21/2 


6 

21/2 



Turnbucldes. 

(Cleveland City Forge and Iron Co.) 
Standard sizes made with right and left threads. D = outside diameter 




Fig. 76., 

of screw, A = length in clear between heads = 6 ins. for all sizes, 
B = length of tapped heads = 1 1/2 D nearly. C = 6 ins. + 3 D nearly. 



Wrought Washers, Manufacturers' Standard. 

(Upson Nut Co., Cleveland, 1914.) 







«d 




rO 


M 






^^ 




rO 


S.3 


g 


qJ 


1^ 




h5 


bog 


S 





^i 


+5 




m 


.s 





•rW 





— 


^'~ 


.2 





•riW 





6 — 


(U- 


Q 


W 


Eh 


W 


Z 


^ 


Q 


W 


H 


m 


Z 


\^ 


In. 


in. 


No. 


In. 






In. 


In. 


No 


In. 






9/16 


1/4 


18 


3/16 


39400 


2.53 


21/2 


1 1/16 


8 


. 1 


568 


176 


3/4 


5/16 


16 


1/4 


15600 


6.4 


2 3/4 


11/4 


8 


11/8 


473 


211 


7/8 


3/8 


16 


5/16 


11250 


8.8 


3 


13/8 


8 


11/4 


364 


261 


1 


7/16 


14 


3/8 


6800 


14.7 


31/4 


11/2 




13/8 


275 


364 


11/4 


1/2 


14 


7/16 


4300 


21. 


31/2 


15/8 




11/2 


256 


390 


13/8 


9/16 


12 


ih. 


2600 


38.4 


33/4 


13/4 




15/8 


220 


454 


11/2 


5/8 


12 


9/lfi 


2250 


44.4 


4 


17/8 




13/4 


197 


508 


13/4 


11/16 


10 


5/8 


1300 


77. 


41/4 


2 




17/8 


174 


575 


2 


13/16 


9 


3/4 


900 


111. 


41/2 


21/8 




2 


160 


625 


21/4 


15/16 


8 


7/8 


782 


153. 


43/4 


2 3/8 

2 5/8 


4 


21/4 

21/2 


122 
106 


820 
943 



244 



MATERIALS. 



Trark Bolts and V. S. Standard Hexagon Nuts, Sizes and Weights for 
Different Weights of BaU. (Upson Nut Co., Clevela nd, 1914.) 



O 



5 



o 
6 



^ o 



(/2 I " 

Rails 70 to 1 OOib. per Yard 



X 5 1 5/8 

X 4 3/4 1 5/8 
X 4 1/2 I 5/8 
X41/4|15/8 
X 4 15/8 

X 3 3/4 1 5/8 
X 3 1/2' 1 5/8 
X 3 1/4: 15/8 
X 3 15/8 
7/8 X 5 1/2 1 7/18 
7/8X51/4 17/18 
7/8X5 17/16 
7/8 X 4 3/4! 1 7/16 
7/8X41/2117/16 
7/8X41/4 17/16 
7/8X4 1 1 7/16 



110 
115 
120 
125 
130 
135 
140 
145 
150 
143 
148 
153 
158 
163 
168 
173 



13. 0| 

12 

11.8 

11 

10.8 

10 

10.0 
9 
9 
9 

9.5 
9.2 
8.9 
8.6 
8.4 
8.1 



i 
2 

0) 

m 



3 

s 



3 

^^ 

6 






Rails 45 to 85 lb. per Yard, 



{Continued) 



3/4 X 5 1/2' 1 1/4 

3/4 X 5 1/4 1 1/4 



Rails 45 to 85 lb. per Yard. 



7/8X3 7/8! 17/161 178 
7/8X3 3/4 17/16! 183 



7/8 X 3 1/2 
7/8 X 3 1/4 
7/8X3 
3/4 X 5 3/4 



1 7/l6| 
1 7/16 
1 7/16 
1 1/4 



3/4X5 

3/4 X 4 3/4 

3/4 X 4 1/2 
3/4 X 4 1/4 
3/4 X 4 1/8 
3/4X4 
3/4 X 3 7/8 



11/4 
1 1/4 
11/4 
11/4 
11/4 
11/4 
1 1/4 



205 
210 
215 
220 
225 
230 
235 
240 
247 
254 



3/4X3 3/4,11/4 -. 

3/4X3 5/8' 11/4 257 

3/4X3 1/2,11/4 260 

3/4X31/4 11/4 266 

3/4X3 11/4 283 



6.8 
6.7 
6.6 
6.4 
6.3 
6.2 
6.1 
6.0 
5.8 
5.7 
5.6 
5 5 
5 3 
5.0 



s 

0) 







m 


rj . 


-tf 


t-, rs -^^ 


3 
2 


6 §.S 




fM Ml «:?H9 










CM 


*■§ 


s 




a^ 


5 


d 





Rails 20 to 301b. per Yard. 



5/8 X 2 1/4 

",-X2 
1/2X3 

1/2X2 3/4 

1/2 X 2 1/2 
1/2 X 2 1/4 
1/2X2 



Rails 30 to 40 lb. per Yard, 



7.9 

7.7 

7.5 

7.3 

7 

7.0 



3/4X2 3/4 11/4 

3/4 X 2 1/2 1 1/4 



5/8 X 3 1/2 
5/8 X 3 1/4 
5/8 X 3 
5/8 X 2 3/4 
5/8 X 2 1/2 



11/16 
1 1/16 
11/16 
11/16 
11/16 



300 
317 
375 
392 
410 
435 
465 



4.7 
4.4 
3.8 
3.6 
3.4 
3.2 
3 



1 1/16 
1 1/16 

7/8 
7/8 
7/8 
7/8 
7/8 



495 
525 
715 
737 

760 
800 
820 



2.8 

2.7 

2. 

1.9 

1.9 

1.8 

1.7 



Rails 12 to 161b. per Yd. 



1/2 X 1 3/4 

1/2 X 1 1/2 

1/2 X 1 3/8 

1/2 X 1 1/4 

3/8X2 
3/8 X 1 3/4 
3/8 X 1 1/2 



7/8 
7/8 
7/8 
7/8 
11/16 
11/16 
11/16 



890 
980 
1070 
1160 
1590 
1710 
1830 



1.6 
1.4 
1.2 
1.2 
1.0 
1.0 
1.0 



Rails 8 to 121b. per Yard. 



■/8 XI 1/4 11/16 2010 1.0 





Length and Number of Cut Nails to the Pound 






Size. 





s 
s 




i 

6 


8 




1 


1 
PQ 


'i 








1 



I 

3d 
4d 
5d 
6d 
7d 
8d 
9d 
lOd 
12d 
16d 
20d 
30d 
40d 
50d 
60d 














800 
500 
376 
224 
180 











1 V4 
1 V2 

.3/. 

31/4 
31/2 
4 
41/2 




















m' 

480 

288 

200 

168 

124 

88 

70 

58 

44 

34 

23 

18 

14 

10 

8 






1100 

720 

523 

410 

268 

188 

146 

130 

102 

76 

62 

54 


1000 
760 
368 


























398 














130 
96 
82 
68 


'.;..; 


95 
74 

62 
53 
46 
42 
38 
33 
20 


84 
64 
48 
36 
30 
24 
20 
16 






224 


126 
98 
75 
65 
55 
40 
27 










128 
110 
91 
71 
54 
40 
33 
27 












.^^j 












U 
v\ 

6 

















































































RAILROAD MATERIAL. 



245 



Total 

Weight 

per 

Mile 

of 
Single 
Track, 
Gross 
Tons. 


Tj- CO ir> f<^ (N 


T}-m(Noouo 


(NOMAf^r* 

OoOOr^O^ 


O^OOTfcOvO 




CO 


Tj-vor^ooo 


— 0(Nr<Mr^ 
<N — O0^00 


r>^r>.o^o — 


cosOcoOvO 
CO «N<N CM- 


1 

'ft 


Willi 


00000 
oc 00 00 00 00 


00 00 00 00 00 


on- CO 0^O^ 

ooo^r^inm 


CO— r>.tN» CO 

tooot^r^-^ 


CO 


<N <N rsj CsJ <N 


<N(N<NfSfS 


^ 


— 








80000 


00000 
'<r -^ -n -^ Tf 















to «o 


CO 


to 

Oi ^ r-l ,-1 ,-H 

XXXXX 


xxxxx 

CO CO CO CO <N 


10 

X 


a> Oi oi 05 

XXXXX 


05 Oi 05 (35 CS 

xxxxx 


m 

pq 


|yif|i 


TfcosOiA^r 


— CO^OvO'«}• 




vO lAuO wor> 
















sO ^O vO vO ^ 
u-^ m uTi tn ur> 


CT^ f<^ (^ r<^ r*^ 


vO vOvOsOsO 
m iTMn ltma 


vOsD vOvOvO 
m uo uo mm 


ms 












05 rt< rt< 00 

XXXXX 

00 -*^ Tt< 

"" t^ CO CC M 


CO CO T-H ^ T-H 

f^ f^ f**\ c<^ f^ 

xxxxx 

CO CO CO CO CO 


XXXXX 

-^\!\ 00 <M 

CO CO 10 lo rt 


CO^CO CO T-l 

xxxxx 

^^ cq,^ 00 


X 
-5° 


:z;fto 


^0 '^D ^0 ^^5 ^0 


vO'^^^'^ 


'"^'"^TTrf^ 


'^'^'<f '^'^ 


rr 


1 


iiiiiji 


vOr^<Nr^<N 


-Ot"^ — — 
0^ — r^fsr^ 


•^rsr^Oc^ 
vO o~^ t^ C^ 


ON — vOvOfN 

t^t^mmrj- 


CO 
CO 


<NOO^O^oO 


^sinTj-TTco 


C<^(N 




turn 


\Q ^D ^D ^O ^0 
fN<NfN<N(N 

CO f<*) f<^ CO CO 


\^ \Q \Q \Q \^ 
C<^ f<^ f<^ (^ (^ 


^0 ^0 nO ^0 ^0 
c<^ r<^ r<^ f<^ CO 


vO ^ ^ ^ ^ 
CO cc, CO CO CO 


1 




S§!2!2S 


Tj-ir>000 
\0 u^ -^ c^ m 


mOOmo 


vOvOtJ-tJ-O 
OOco n- "^ sO 


8 


r>. Tj- 00 c<^ 00 
oot^^OvOm 




oovOfNOm 


"^•^fOCOCN 


5" . 


r^ c^ CO ro CO 


pr, (N (N (N <N 


00 00 00 

vO 'O vO 


00 jx) 00 00 00 
"nO ^0 nO ^O ^0 


00 

NO 


TO* 


•53 ft.-S ^ 2 »: 


— Tf cnr>iCO 


— (NTT u-\ 


t>^c0O — rsi 


POrJ-OvO — 

^ — Ooor>> 


m 




O(vj-^v0 00 

— O^OOt^ 


OfNmt^O^ 
t^^vOm-^co 


— mfsoom 
CO<N<N — — 




s 

CO eo CO T-i 


^ "= ^ ^ ^ 
00 -H '^^ « 

10 t^ ^ 1-. i-^ 

tj- -"t -.I- Tf cr>( 


<t^ 2 00 •* 

m ^ ^ CO 

CO CO CO CO <N 


00 00 2 ^ 
»o CO T-4 CO 


to 

05 


ia|d 


OO^OOCO^s 


OiTiOmo 


momOvA 
'T "^cocoes 


OvO^rjO 


00 



246 



NUMBER OF WIRE NAILS PER POUND. 





- 1 


^<^ <^ "^ in 




























These approximate numbers are an average only, 
and the figures given may be varied either way by 
changes in the dimensions of the heads or points. 
Brads and no-head nails will run more to the pound 
than the table shows, and large or thick-headed 
nails will run less. 


























M 


00 (T^ cs^ CM 








































00 


^ ■ 
ininr>»ooo-- ; 




















rN 


sor^ooos — r^moo 
















- 1 


r^ooo-c2u.co-jnos 














in 


OOOs — f^MTiOO — mom — O 
— — — — Csirvjt^pr^x^in 












^ 

-^ 


OsOf^'^t^O'^OOf^OsvOmO 










_,. O — "^ vO OS c^ vO — r^ r^ CM rsj OS «^ 








f 


(Nt^sOOstNsOOmmOsOs — Orxr^ 

— — — — <Nr^cop«^TrTrint^Os — m 






- 


'■rmOsfSLnom — or^Os<^mr>>oovO 






sO r^ t^ sO O sO (S O O OS <N OS m -^ TT TT o 

— — CNCsjrr^r'^'^mvOsOooOsr-lsC — oom • ■ • 












<N| 


O — 00 rsj 00 m f^ fsq m vo f^ -"^ r-N ■<*■ QO o CO — Os 
(N rsl cs) M^ f^ TT in so r>i 00 o fN ir, o so m rr^ {>, t^ . 
— — — (N esq ?^ -T in l>*i . 










C3 


«" 


OOMOsinsOsOOr^Orsi 
^^lnrs^^>»t<^ — o — moo — '^r^f^oooinosQO 
cs^(^lf<^c<^Trlr^sor^Qoas — — — cNr<-\Trmsooo — 










C 
O 
1-5 


C^ 


t>*osoo'*oo — rsjomoomos'^t^t^'^- ooosoo 

(N<Sf<^"^mvor>iOOO — rnsoor^mr>^QOsOr^r^r>. 

— — — — <S<Nf<^Trmr^Or^h> 










Zl 


r<^-^mrsio<Minosot^mQO — OsOsoo — roivommo 

fnp^"n-insor>.ooosrs|<^soosm(Nrqvoo — 'Tmr^o 

»— — — — rsjr<~>'^mr>.osrsiso — o 

— — csim 








- 






r^msOOsOr^Osrslt>.00'^ — vOOsOf^oOOst^O-^ 

— — — — rs)rsjr<^'^mr>oo — mosot^Tj- 






co~ 










»—•—•— — (SCS<Sfn"^mt>«Os — miOt>»moossO 
— — rsirsir^mmr>. 




-5S 














os^NOsm — t^r<joor>>vorsjoomor^o — (^ 

v00smt^r<^0s0mmrf>0rs40s — sOO — -^ 
— — Csirs)c<^p(^m\O0O — "^QO-^r^^fNO- — 

— — — rsjcT^Tror^os 




(M 














— r^osm'<rsooocs3Cs)orsiosooo"^oooQO 

— "^Os-^- 0^<N(Nt^(NmoO — P<-^^^-\OOO^s^ 

csj(NcQfn-rTroooo^r^(N ^fr^?;5o=^ 

— — — rsir<^Trmr»»QO — 




00 
























•soooo-^oorno — in — ooors) 
— — — «s fo -^ in t^ o — m 




^ 
































• O"^ — fAsoooorN.NO 
•"^Oh>ifnt^oorN.m» 
•oommrsjrsjsoor^oo 
•rgcA'^soooomr^tvj 






































o r^ vo 
oor>. 
or^'t 
O r^ O 
rs) rsj m 


£ 
'^ 


6o 

¥. 





0= 


1/ 


u 

? 


It^ 


\'« 


•It 


%x 


ar 


*x 





NO 


; 


-r 


Ar4 


^ ■^ in s© i>» 00 » 


^ 


5J; 


J^ 


! 



STEEL WIRE NAILS. 



247 



i 










^'trinvor^ooo^ofMscooooo 

— — — fsj cr, -^ in sO 


•saqouj 'q^Saa^ 


— — — — rg<NCN(N<^<^n^Tr'<ruMrivO 


•S85iids 9JIM 




















— ooornt^mooo 
■^ c<^ m cs — — — 


•SuiuiT 1 |§2 


































•oootjqox 1 












CN fN — — 
















•oiSuiqg 










1 


•^ in tt o^ m -^ r<^ 

r^ f^ O m <N — 00 
















•SugooH paqj^a | Sli 


— O sO — r<^ 
ir\ p«^ r^ lr^ o 
(SI CM — — — 






















•Supuig 1 




^ 


m 
^ 


r^ (N m 
oo -^ o 
























> 














inoorANOCT^'^OMinsO'^oointA 
«0 — Ol>.sOininrrroCN4CS — — — 


3 














-^c^^fvjfMNt^OfA — oo — t^in 




> 














^ 


s 


i? 


Trf<^c^^o 










+3 

bJD 














S3 


s 


s 


?^^2:£ 










•spBjg Sauooi^ 
















inmoo^sOin'^fn 










•xog paqj^a j 
puB q^^oouig 

pUB 'gUIStJQ 1 




o 
o 








•(ajj^a 


c*^ o t>. r->. ur. TT c<^ • 
























•am J S^§S 




3 : 
























Suiqsiui^ paqj^a 
"puB q;oomg 






i 


oooomoot^(N — ovvo 










•80U8J 








•rg-<r(N(N(NOOOm 

•^(NOvOOsOinTTmCN 










•qoayio | 




o 


1 


Tj-int^ovo^oc><NO^rx 
r>.minma^o^vOvO"^f<^ 










•spBjg pa's 

^II^N UOUIIIIOQ 




00 


in 


sO — — — vOOO^mO^ — TQC^ — 
— r^QOOOO^sOO'^cACg — — — 


— — — — — — «N rg (M fsi f^ pr^ r<^ -^f •^ in in o 










is 


: a 
. c 

l5 


c 
E 
S 

';5 


5 


i5 




':i 


'S 


;5 


'5 


i|^ 


1 


3T 


L 


!i 


IT 


i^ 


3 



248 



MATERIALS. 



WROUGHT SPIKES. 

Number of Nails in Keg of 150 Pounds. 



Length, 
Inches. 


1/4 in. 


5/16 in. 


3/8 in. 


Length, 
Inches. 


1/4 in. 


5/i6 in. 


3/8 in. 


7/i6in. 


1/2 in. 


3 


2250 
1890 
1650 
1464 
1380 
1292 






7 
8 
9 
10 
11 
12 


1161 


662 
635 
573 


482 
455 
424 
391 


445 
384 
300 
270 
249 
236 


306 


31/2 

4 

41/2 


1208 
1135 
1064 
930 

868 


"742' 
570 


256 
240 
222 






203 


6 








180 



For sizes and weights of wire spikes see Steel Wire Nails, page 235. 

BOAT SPIKES. 

Number in Keg of 200 Pounds. 



Length. 


1/4 


5/16 


3/8 


1/2 


4 inch 


2375 
2050 
1825 








5 " 


1230 
1175 
990 
880 


940 
800 
650 
600 

525 
475 




6 " 


450 


7 •• 


375 


8 •• 




335 


9 •• 




300 


10 •• 






275 



WIRES OF DIFFERENT METALS AND ALLOYS. 

(J. Bucknall Smith's Treatise on Wire.) 

Brass Wire is commonly composed of an alloy of 1 M to 2 parts of 
copper to one part of zinc. The tensile strength ranges from 20 to 40 
tons per square inch, increasing with the percentage of zinc in the alloy. 

German or Nickel Silver, an alloy of copper, zinc, and nickel, is 
practically brass whitened by the addition of nickel. It has been 
drawn into wire as fine as 0.002 inch diameter. 

Platinum wire may be drawn into the finest sizes. On account of its 
high price its use is practically confined to special scientific instruments 
and electrical appliances in which resistances to high temperature, 
oxygen, and acids are essential. It expands less than other metals 
when heated. Its coefficient of expansion being almost the same as 
that of glass permits its being sealed in glass without fear of cracking 
the latter. It is therefore used in incandescent electric lamps. 

Phosphor-bronze Wire contains from 2 to 6 per cent of tin and 
from 1/20 to 1/8 per cent of phosphorus. The presence of phosphorus 
is detrimental to electric conductivity. 

"Delta-metal" wire is made from an alloy of copper, iron, and zinc. 
Its strength ranges from 45 to 62 tons per square inch. It is used for 
some kinds of wire rope, also for wire gauze. It is not subject to 
deposits of verdigris. It has great toughness, even when its tensile 
strength is over 60 tons per square inch. 

Aluminum Wire.— Specific gravity 2.68. Tensile strength between 
10 and 15 tons per square inch. It has been drawn as fine as 11,400 
yards to the ounce, or 0.042 grain per yard. 

Aluminum Bronze, 90 copper, 10 aluminum, has high strength and 
ductility; is inoxidizable, sonorous. Its electric conductivity is 12.6 
per cent. See page 396. 

Silicon Bronze, patented in 1882 by L. Weiler of Paris, is made as 
follows: Fluosilicate of potash, pounded glass, chloride of sodium and 
calcium, carbonate of soda and lime, are heated in a plumbago crucible, 
and after the reaction takes place the contents are thrown into the 
molten bronze to be treated. Silicon-bronze wire has a conductivity 
of from 40 to 98 per cent of that of copper wire and four times more 
than that of iron, while its tensile strength is nearly that of steel, or 

{Continued on page 250.) 



PROPERTIES OF STEEL WIRE. 



249 



PROPERTIES OF STEEL WIRE. 

(John A. Roebling's.Sons Co., 1908.) 



No.. 


Diam., 


Area, 


Breaking 
strain, 100, 


Weight in pounds. 


Feet in 


Roebling 
Gauge. 








in. 


square 
inches. 


000 lb. per 
sq. inch. 


Per 
1000 ft. 


Per 

mile. 


2000 lb. 


000000 


0.460 


0.166191 


16,619 


558.4 


2,948 


3,582 


00000 


0.430 


0.145221 


14,522 


487.9 


2,576 


4,099 


0000 


0.393 


0.121304 


12,130 


407.6 


2,152 


4,907 


000 


0.362 


0.102922 


10,292 


345.8 


1,826 


5,783 


00 


0.331 


0.086049 


8,605 


289.1 


1,527 


6,917 





0.307 


0.074023 


7,402 


248.7 


1,313 


8,041 


1 


0.283 


0.062902 


6,290 


211.4 


1,116 


9,463 


2 


0.263 


0.054325 


5,433 


182.5 


964 


10,957 


3 


0.244 


0.046760 


4,676 


157.1 


830 


12,730 


4 


0.225 


0.039761 


3,976 


133.6 


705 


14,970 


5 


0.207 


0.033654 


3,365 


113.1 


597 


17,687 


6 


0.192 


0.028953 


2,895 


97.3 


514 


20,559 


7 


0.177 


0.024606 


2,461 


82.7 


437 


24,191 


8 


0.162 


0.020612 


2,061 


69.3 


366 


28,878 


9 


148 


0.017203 


1,720 


57.8 


305 


34,600 


10 


0.135 


0.014314 


1,431 


48.1 


254 


41,584 


11 


0.120 


0.011310 


1,131 


38.0 


201 


52,631 


12 


0.105 


0.008659 


866 


29.1 


154 


68,752 


13 


0.092 


0.006648 


665 


22.3 


118 


89,525 


14 


0.080 


0.005027 


503 


16.9 


89.2 


118,413 


15 


0.072 


0.004071 


407 


13.7 


72.2 


146,198 


16 


0.063 


0.003117 


312 


10.5 


55.3 


191,022 


17 


0.054 


0.002290 


229 


7.70 


40.6 


259,909 


18 


0.047 


0.001735 


174 


5.83 


30.8 


343,112 


19 


0.041 


0.001320 


132 


4.44 


23.4 


450,856 


20 


0.035 


0.000962 


96 


3.23 


17.1 


618,620 


21 


0.032 


0.000804 


80 


2.70 


14.3 


740,193 


22 


0.028 


0.000616 


62 


2.07 


10.9 


966,651 


23 


0.025 


0.000491 


49 


1.65 


8.71 




24 


0.023 


0.000415 


42 


1.40 


7.37 






25 


0.020 


0.000314 


31 


1.06 


5.58 






26 


0.018 


0.000254 


25 


0.855 


4.51 






27 


0.017 


0.000227 


23 


.763 


4.03 






28 


0.016 


0.000201 


20 


.676 


3.57 






29 


0.015 


0.000177 


18 


.594 


3.14 






30 


0.014 


0.000154 


15 


.517 


2.73 






31 


0.0135 


0.000143 


14 


.481 


2.54 






32 


0.013 


0.000133 


13 


.446 


2.36 






33 


0.011 


0.000095 


9.5 


.319 


1.69 






34 


0.010 


0,000079 


7.9 


.264 


1.39 






35 


0.0095 


0.000071 


7.1 


.238 


1.26 






36 


0.009 


0.000064 


6.4 


.214 


1.13 







The above table was calculated on a basis of 483.84 lb. per cu. ft. for steel 
wire. Iron wire is a trifle lighter. The breaking strains are calculated for 
100,000 lb. per sq. in. throughout, simply for convenience, so that the 
breaking strains of wires of any strength per sq. in. may be quickly deter- 
mined by multiplying the values given in the tables by the ratio between 
the strength per square inch and 100,000. Thus, a No. 15 wire, with a 

strength per sq. in. of 150,000 lb., has a breaking strain of 407 X ?^^'^^^ 



= 610.5 lb. 



100.000 



250 



MATERIALS. 



28 to 55 tons per square inch of section. The conductivity decreases 
as the tensile strength increases. Wire whose conductivity equals 95 
per cent of that of pure copper gives a tensile strength of 28 tons per 
square inch, but when its conductivity is 34 per cent of pure copper, 
its strength is 50 tons per square inch. It is being largely used for 
telegraph wires. It has great resistance to oxidation. 

Ordinary Drawn and Annealed Copper Wire has a strength of from 
15 to 20 tons per square inch. 

" PLOW "-STEEL WIRE. 

Experiments by Dr. Percy on the English plow-steel (so-called) 
gave the following results: Specific gravity, 7.814; carbon, 0.828 per 
cent; manganese, 0.587 per cent; silicon, 0.143 per cent; sulphur, 0.009 
per cent; phosphorus, nil; copper, 0.030 per cent. No traces of chro- 
mium, titanium, or tungsten were found. The breaking strains of the 
wire were as follows: 

Diameter, inch 0.093 0.132 0.159 0.191 

Pounds per sq. inch. 344,960 257,600 224,000 201,600 
The elongation was only from 0.75 to 1.1 per cent. 

STRENGTH OF PIANO-WIRE. 

The average strength of English piano-wire is given as follows by 
Webster, Horsfals & Lean: 



Size, 

Music-wire 

Gauge. 


Equivalent 

Diameters, 

Inch. 


Ultimate 
Tensile 

Strength, 
Pounds. 


Size, 

Music-wire 

Gauge. 


Equivalent 

Diameters, 

Inch. 


Ultimate 

Tensile 

Strength, 

Pounds. 


12 
13 
14 
15 
16 
17 


0.029 
.031 
.033 
.035 
.037 
.039 


225 

250 

285 

305. 

340 

360 


18 
19 
20 
21 
22 


0.041 
.043 
.045 
.047 
.052 


395 
425 
500 
540 
650 



These strength range from 300,000 to 340,000 lbs. per sq. in. The 
composition of this wire is as follows: Carbon, 0.570; silicon, 0.090; 
sulphur, 0.011; phosphorus, 0.018; manganese, 0.425. 

GALVANIZED IRON WIRE FOR TELEGRAPH AND 
TELEPHONE LINES. 

(Trenton Iron Co.) 
Weight per Mile-Ohm. — Tliis term is to be understood as dis- 
tinguishing the resistance of material only, and means the weight of such 
material required per mile to give the resistance of one ohm. To ascer- 
tain the mileage resistance of any wire, divide the " weight per mile- 
ohm" by the weight of the wire per mile. Thus in a grade of Extra 
Best Best, of whicli the weight per mile-ohm is 5000, the mileage resist- 
ance of No. 6 (vveight per mile 525 lbs.) would be about 91/2 ohms; and 
No. 14 steel wire, 6500 lbs. weight per mile-ohm (95 lbs. weight per mile), 
would show about 69 ohms. 

Sizes of Wire used in Telegraph and Telephone Lines, 

No. 4. Has not been much used until recently; is now used oa 
important lines where the multiplex systems are applied. 

No. 5. Little used in the United States. 

No. 6. Used for important circuits between cities. 

No. 8. Medium size for circuits of 400 miles or less. 

No. 9. For similar locations to No. 8, but on somewhat shorter cir- 
cuits; until lately was the size most largely used in this country. 

Nos. 10, 11. For shorter circuits, railway telegraphs, private lines, 
police and fire-alarm lines, etc. 

No. 12. For telephone lines police and fire-alarm lines, etc. 



TELEGRAPH AND TELEPHONE WIRE. 



251 



B^^St^TE'^r^y^^^^^^^^ B^--,to the trade as "Extra 

'Extra Best Best" is made of the very best iron as nearly nnre «, 
M"Jtv°°i'Jl™^''P'?;'/''°"' soft, tough, uniform, and of Vt?y higK c'S^du?? 
■T^J. " D^*;'^5t P?r mile-ohm being about 5000 lbs conauc- 

goodres.at?astheF'R°R'''hntfi''''V"^i" mechanical tests almost as 
fn£af^?%yt-p''er ^^lU^oh^ aC,! llo^S^"^ ^°--'>^' ^°-^ 
an|jL ^^I'ht ;rn;fle!otm^trS[ ll'o^t^ ^ ^"^-^ *«'^^-P>^ '--• 

No. 4, 5, 6, 7, 8. 9, 10, 11, 12, 13 14 

Lbs. 720. 610, 525, 450, 375, 310, 250, 200, 160, 125, 95.' 

Tests of Telegraph Wire. 

in J'JS ^fi!?^"/^'*i^ ^X^ t^^en from a table given by Mr Prescott relat 
Telegraph Co°' ^^ ^^ ^- ^^'^^"i^^d wire furmshed^trWestern Union 



Size 


Diam., 
Inch. 


Weight. 


Length. 

Feet 

per 
pound. 


Resistance. 
Temp. 75.8° Fahr. 


Ratio of 

Breaking 

Weight to 

Weight 

per mile. 


of 

Wire 


Grains 
per foot. 


Pounds 
per mile. 




Feet 
per ohm 


Ohms 
per mile. 


4 
5 
6 
7 
8 
9 

10 

II 

12 

14 


0.238 
.220 
.203 
.180 
.165 
.148 
.134 
.120 
.109 
.083 


1043.2 
891.3 
758.9 
596.7 
501.4 
403.4 
330.7 
265.2 
218.8 
126.9 


886.6 
673.0 
572.2 
449.9 
378.1 
304.2 
249.4 
200.0 
165.0 
95.7 


6.00 
7.85 
9.20 
11.70 
14.00 
17.4 
21.2 
26.4 
32.0 
55.2 


958 
727 
618 
578 
409 
328 
269 
216 
179 
104 


5.51 
7.26 
8.54 
10.86 
12.92 
16.10 
19.60 
24.42 
29 60 
51.00 


3.05 
3.40 
3.07 
3.38 
3.37 
2.97 
3.43 
3.05 



sizes. Weights and Strengths of Hard-Copper Telegraph and 
Telephone Wire. 

(J. A. Roebling's Sons Co., 1908.) 




kiSs'' bends ^scmJhet n'i^^f**''^* P^""^ ^1?°".^ be observed to avoid 
Mclr^^^^r^^^t^^J^^ c?nZ'c^ti^ity™btllf, ^SK^^ 



252 



MATERIALS. 



times that of E. B. B. iron wire, and its breaking strength over three 
times its weight per mile, copper may be used of which the section is 
smaller and the weight less than an equivalent iron wire, allowing a 
greater number of wires to be strung on the poles. Besides this advan- 
tage, the reduction of section materially decreases the electrostatic 
capacity, while its non-magnetic character lessens the self-induction of 
the line, both of which features tend to increase the possible speed of 
signaling in telegraphing, and to give greater clearness of enunciation 
over telephone lines, especially those of great length. 



Weight of Bare and Insulated Copper Wire, Pounds. 

(John A. Roebling's Sons Co., 1908.) 





Weight per 


1000 Feet, Solid. 




Weight 


per Mile, Solid 








Weather- 








Weather- 






2 
^ 


proof. 




bi) 


1 


proof. 




bil 






il 


O fH 




O 3 


0000 


641 


723 


767 


862 


925 


3384 


3817 


4050 


4550 


4890 


000 


509 


587 


629 


710 


760 


2687 


3098 


3320 


3750 


4020 


00 


403 


467 


502 


562 


600 


2127 


2467 


2650 


2970 


3170 





320 


377 


407 


462 


495 


1689 


1989 


2150 


2440 


2610 


1 


253 


294 


316 


340 


365 


1335 


1553 


1670 


1800 


1930 


2 


202 


239 


260 


280 


300 


1066 


1264 


1370 


1480 


1585 


3 


159 


185 


199 


230 


270 


840 


977 


1050 


1220 


1425 


4 


126 


151 


164 


190 


220 


665 


795 


865 


1000 


1160 


5 


100 


122 


135 


155 


190 


528 


646 


710 


820 


1000 


6 


79 


100 


112 


127 


160 


417 


529 


590 


670 


840 


8 


50 


66 


75 


85 


110 


264 


349 


395 


450 


580 


9 


39 


54 


62 






206 


283 


325 






10 


32 


46 


53 


60 


• 80 


169 


241 


280 


3i5 


420 


12 


20 


30 


35 


42 


55 


106 


158 


185 


220 


290 


14 


12.4 


20 


25 


30 


40 


66 


107 


130 


160 


210 


16 


7.9 


16 


20 


24 


30 


42 


83 


105 


130 


160 


18 


4.8 


12 


16 


19 


24 


25 


64 


85 


100 


130 


20 


3.1 


9 


12 






16 


48 


65 




... 



Specifications for Hard-Drawn Copper Wire. 

The British Post Office authorities require that hard-drawn copper 
wire supplied to them shall be of the lengths, sizes, weights, strengths, 
and conductivities as set forth in the annexed table. 



Weight 


per Statute 


Approximate Equiv- 




o O 


w^^^t/ 


^o 


W ile, lb. 


alent Diameter, mils. 


r^ 


-§ 


"m O d S 


.SP« 








^=2 


^3 




^2 












a 

3 

a 


i 

rt 

'C 


a 
a 


a 
a 


1^ 


en 

a-s 


mum 
ce per 
re (whe 
60° F., 


a u 


"1 


c 


X 




c 




c 


'5 ^ 


d c3^ 03 


.'i'B? 


c^ 


J^ 


S 


m 


s 


^ 


^ 


^ 


s 


100 


971/2 


1021/2 


79 


78 


80 


330 


30 


9.10 


50 


150 


1461/4 


1533/4 


97 


951/2 


98 


490 


25 


6.05 


50 


200 


195 


205 


112 


1101/2 


1131/4 


650 


20 


4.53 


50 


400 


390 


410 


158 


1551/2 


1601/4 


1300 


10 


2.27 


50 



WIRE ROPE. 



253 



stranded Copper Feed Wire, Weight in Pounds. 

(John A. Roebling's Sons Co., 1908.) 





Weight 


per 1000 Feet. 


Weight per Mile. 






Weather- 








Weather- 




^ 






proof 








proof 






l^ 








'^ bi 


fcj) 






'Q 5r! 




oj o m 


2 

c3 




ti 


(i> rt § 




c3 


II 


-S-^ 

•&'^ 






zn'6^ 


PQ 


Q« 


HPQ 


s|£ 


GOCQ 


pq 


QPQ 


H^ 


fe^£ 


5q 


2,000,000 


6100 


6690 


7008 




7540 


32208 


35323 


37000 




39800 


1,750,000 


5338 


5894 


6193 




6700 


28184 


31119 


32700 




35400 


1,500,000 


4375 


5098 


5380 




5830 


24156 


26915 


28400 




30800 


1,2^0,000 


3813 


4264 


4508 




4940 


20132 


22516 


23800 




20000 


1,000,000 


3050 


3456 


3674 


3860 


3980 


16104 


18246 


19400 


20400 


26100 


900,000 


2745 


3127 


3332 


3520 


3640 


14493 


16513 


17600 


18600 


11000 


800,000 


2440 


2799 


2992 


3180 


3280 


12883 


14779 


15800 


16800 


19200 


750,000 


2288 


2635 


2822 


3000 


3100 


12080 


13913 


14900 


15850 


17300 


700,000 


2135 


2471 


2650 


2820 


2920 


11272 


13045 


14000 


14900 


16300 


600,000 


1830 


2093 


2235 


2350 


2450 


9662 


11052 


11800 


12400 


15400 


500,000 


1525 


1765 


1894 


1990 


2080 


8052 


9318 


10000 


10500 


13100 


450,000 


1373 


1601 


1724 


1820 


1900 


7249 


8452 


9100 


9600 


10000 


400,000 


1220 


1436 


1553 


1650 


1700 


6441 


7584 


8200 


8700 


9000 


350,000 


1068 


1248 


1345 


1440 


1500 


5639 


6589 


7100 


7600 


7900 


300,000 


915 


1083 


1174 


1270 


1310 


4831 


3721 


6200 


6700 


6900 


250,000 


762 


907 


985 


1060 


1120 


4023 


4788 


5200 


5600 


5900 


B.&S. 






















645 


745 


800 


900 


960 


3405 


3935 


4220 


4750 


5070 


000 


513 


604 


653 


735 


785 


2708 


3190 


3450 


3880 


4150 


00 


406 


482 


522 


583 


625 


2143 


2544 


2760 


3080 


3300 





322 


388 


424 


480 


510 


1700 


2051 


2240 


2530 


2700 


1 


255 


303 


328 


355 


380 


1346 


1599 


1735 


1870 


2000 


2 


203 


246 


270 


290 


335 


1071 


1301 


1425 


1540 


1770 


3 


160 


190 


206 


240 


280 


844 


1004 


1090 


1270 


1480 


4 


127 


155 


170 


195 


230 


670 


820 


900 


1030 


1220 


5 


101 


126 


140 


160 


195 


533 


668 


740 


845 


1030 


6 


80 


103 


115 


132 


165 


422 


544 


610 


695 


870 


8 


50 


68 


78 


87 


105 


264 


359 


410 


460 


555 



WIRE ROPE. 

The following notes and tables are compiled from data furnished 
by the American Steel & Wire Co., Cleveland, 1915. 

Wire ropes, which have almost entirely superseded chains and 
manila rope for haulage and hoisting purposes, are made with a vary- 
ing number of wires to the strand, and a varying number of strands 
to the rope, according to the service in which they are to be used and 
the degree of flexibiUty required. Five grades of rope are usually 
manufactured, as regards the material used, viz.: Iron, crucible 
cast steel, extra strong crucible cast steel, ' 'plow-steel, ' ' and an improved 
grade of plow-steel called "Monitor." Haulage rope, for mines, 
docks, etc., usually consists of 6 strands of 7 wires each laid around a 
hemp core. Hoisting rope, for elevators, mines, coal and ore hoists, 
conveyors, derricks, steam shovels, dredges, logging, etc., consists of 
6 strands of 19 wires each, with a single hemp core. A more flexible 
rope, for crane service, etc., consists of 6 37-wire strands wound around 
a single hemp core. In general, the flexibility of the rope is increased 
by increasing the number of wires in the strands. The most flexible 



254 MATERIALS. 

standard rope made consists of 6 61-wire strands and one hemp core. 
Other varieties comprise flattened strand ropes for haulage, hoisting, 
and transmission, non-spinning rope for the suspension of loads at the 
end of a single line, steel clad rope for severe conditions of service, 
guy and rigging ropes, and hawsers for towing or mooring. 

Breaking Strength of Wire Rope. — The various manufacturers 
have adopted standard figures for the strength of all sizes and qualities 
of wire rope. Formerly, it was the custom to test the individual wires 
and to consider their combined strength as the strength of the rope 
as a whole. These strengths were greater than the actual strength 
obtained by breaking the finished rope. The figm^es given in the 
tables herewith represent actual breaks of the various ropes, and range 
from 95 to 80 per cent or less of the combined strength of the single 
wires, depending on the construction. The figures, wliich were 
adopted May 1, 1910, are considerably lower than those given in 
earlier tables. In general, a factor of safety of five is allowed in giving 
the working loads. 

Lay of Wire Rope. — Lang Lay. — The regular lay of wire rope com- 
prises wires in the strands laid to the left, the strands being laid to 
the right, known as right-hand rope; or wires laid to the right, and 
strands laid to the left, known as left-hand rope. In Lang lay rope 
the wires in the strands and the strands themselves are laid in the 
rope in the same direction, either right or left. Lang lay rope is some- 
what more flexible than ordinary rope, and as the wires are laid more 
axially in the rope, longer surfaces are exposed to wear, and the en- 
durance is thereby increased. 

Sheaves and Drums. — Drums and sheaves of the largest practicable 
diameter are recommended in all wire rope installations. If possible, 
drums should be lagged, and where feasible, a grooved drum on hoists 
is more desirable than a flat drum. The grooves should give ample 
clearance between successive windings ; thus a drum for ^i-inch rope 
should have the grooves at least T/g-inch apart on centers. The 
grooves should be made smooth in order not to cut the rope, and they 
should be of slightly larger radius than the rope in order to avoid wedg- 
ing or pinching it. Overwinding, that is, the winding, of the rope in 
more than one layer, is to be .avoided if possible, by making the drum 
large enough to take all the rope in a single layer. Overwinding will 
rapidly destroy the rope, and the extra cost of the larger drum will be 
more than compensated by the greater hfe of the rope. The best 
possible alignment of sheaves and drums should be made to avoid 
undue wear on the sides of the sheaves and the rope. In general, the 
lead sheaves over which the rope runs from the drum should be aligned 
with the center of the drum, or if the drum is not entirely filled, with 
the center of the portion on which the rope is wound. The distance 
between the drum and lead sheave should be such as to cause an angle 
not exceeding 1° 30' between the line from the center of the sheave to 
the center of the drum, and the line from the center of the sheave to the 
outer side of the drum. When the sheaves become worn, they should 
be replaced or the grooves turned before they are used with a new 
wire rope, otherwise the rope will not work properly. For many 
purposes, particularly mine service, the grooves can advantageously 
be lined with Avell-seasoned, hardwood blocks set on end, which can 
be renewed when worn. Large sheaves, running at lugh velocity, 
should be lined with leather set on end, or with india-rubber. This 
is the practice for power transmission between distant points, where 
the rope frequently runs at a velocity of 4,000 feet per minute. 

Reversed Bending. — Reverse bending, that is, bending the wire 
rope first in one direction over sheaves and then in the opposite direc- 
tion, is to be avoided wherever possible. This practice will wear out 
a rope more quickly than any other known method. A little care in 
design will usually eliminate all situations which call for reversed 
bending, and it is even desirable to change existing constructions if 
necessary to remove this condition. The expense of rope renewals 
will more than equal the cost of change as a rule. 

Handling Wire Rope. — Wire rope must not be coiled or uncoiled 
like hemp rope. When received in a coil it should be rolled on the 
ground like a hoop and straightened out before being put on the 
sheaves. If on a reel, it should be mounted on a spindle or a flat 



GALVANIZED WIRE ROPE. 



255 



Galvanized Iron and Steel Wire Rope. 

For Ship and Yacht Rigging, Guys, etc. 
6 Strands, 7 or 12 Wires per Strand, 1 Hemp Core; 6 Strands, 









19 Wires per Strand, 


L Hemp Core. 














7 or 12-Wire 


19- Wire 








7 or 12-Wire 


19- Wire 








Strand 


, Iron 


Stranc 


I, Steel 








Strand, Iron. 


Strand 


, Steel 




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42.0 


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3.75 


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19.0 


7.5 


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1.42 


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1.75 






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Galvanized Steel Wire Strand. 

7 or 19 Wires Twisted into a Single Strand. 





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11000 


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900 


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1610 


24000 


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8500 


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19-wire strand is made only from 1 to H in. diam., 7-wire strand is 
made only from % to 3/32 in. diam. 



Galvanized Steel Cables for Suspension Bridges. 

Composed of 6 Strands — with Wire Center. 



Diam., 
In. 


Wt. per 

Foot, 

Lb. 


Approx. 
Breaking 

Strain, 

Tons 

(2000 Lb.) . 


Diam., 
In. 


Wt. per 

Foot, 

Lb. 


Appro. 
Break- 
ing 
Strain, 
Tons. 


Diam., 
In. 


Wt. per 

Foot, 

Lb. 


Approx. 

Break- 
ing 
Strain, 
Tons. 


2 3/4 

2 5/8 
21/2 
2 3/8 


12.7 
11.6 
10.5 
9.50 


310 
283 
256 
232 


21/4 
2 1/8 
2 

17/8 


8.52 
7.60 
6.73 
5.90 


208 
185 
164 
144 


13/4 

1 5/8 
1 1/2 
13/8 


5.10 
4.34 
3.70 
3.10 


124 
106 
90 
75 



256 MATERIALS. 

turntable and properly unwound. Kinking or untwisting must be 
avoided. 

Protection of Wire Rope. — Wire rope should be protected by a 
suitable lubricant, both internally and externally, to prevent rust and 
to keep it pUable. If chis is omitted rust will set in and stiffen the 
rope, resulting in poor service. Raw linseed oil, applied with a piece 
of sheepskin, the wool inside, is a good preservative; the oil also may 
be mixed with Spanish brown or lamp-black. Wire rope running 
under water should be treated with mineral or vegetable tar, one 
bushel of fresh slacked hme being added to each barrel of tar to 
neutralize the acid. The tar is well boiled and the rope saturated 
with it. Wire rope manufacturers furnish special compounds for the 
treatment of wire ropes. 

Exposure to Heat. — Where wire rope is exposed to int-ense heat, as 
in foundry or steel mill service, a soft iron core is often substituted for 
the hemp core. Asbestos also is sometimes used, but it rapidly dis- 
integrates and is not recommended. The use of the iron core adds 
from 7 to 10 per cent to the strength of the rope, but the wear on the 
center is as great as on the outside strands, and the hemp center 
is to be preferred wherever possible. 



VARIETIES AND USES OF WIRE ROPE. 

Transmission, Haulage or Standing Rope. — Usually made of 6 
7-wire strands and one hemp core, in all five grades noted above. Iron 
rope is comparatively Uttle used except in the smaller sizes. It is 
composed of very soft wires of low tensile strength. Crucible cast 
steel rope is particularly adapted to mine haulage work, including tail 
rope and endless haulage systems, gravity hoists, and coal and ore dock 
haulage, roads operating small grip cars. The sizes, s/g to s/g inch 
inclusive, are used for sand lines in oil wells, and from s/g to 1 inch for 
oil-well drilhng. In general it can be used for severe service, and 
where the flexibility required is a minimum. Extra strong crucible 
cast steel rope has practically the same applications as the preceding 
rope, except that being stronger a smaller rope can be used for the 
same service. The plow-steel rope is advised for situations similar 
to those for which the cast steel ropes are used, but where it is neces- 
sary to secure increased strength, without altering the working con- 
ditions. The wires are harder and capable of standing greater wear 
than any of the foregoing ropes. ]Monitor plow-steel rope is the 
strongest and stiff est of all and is used for work demanding the greatest 
strength and lightest rope possible. Sheaves for this rope should, if 
possible, be somewhat larger than for other grades. For working loads, 
strength, etc., of these ropes, see table, page 257. 

Standard Hoisting Rope. — Composed of 6 19-wire strands and a 
hemp core; made in the following grades: Iron, mild steel, crucible 
cast steel, extra strong crucible cast steel, plow-steel, and IMonitor 
plow-steel. The wires are smaller than those in transmission ropes of 
the same size, and it is more flexible. It will not stand as much 
abrasion as transmission rope. The iron rope is used for elevator 
hoisting, where the strength is sufficient, and is almost universally 
employed for counterweights, except on traction elevators. Where 
the pulleys are comparatively small it is sometimes used for power 
transmission. The mild steel rope is made especially for traction 
elevators, where quick starting and stopping is required. The cru- 
cible cast steel rope is adapted to mine hoisting, logging, elevators, 
derricks, hay presses, dredges, cableways, inclined planes, coal hoists, 
conveyors, ballast unloaders, ship hoists, and similar applications. 
The extra strong crucible cast steel rope is adapted to the same pur- 
poses and may be used for heavier loads than the former rope. It is 
extensively used for oil-well drilling and tubing lines. Plow-steel rope 
is used for heavy mine work, inclined planes, dredges, cableways, for 
heavy logging, etc. It is especially desirable for deep mine shafts 
and long inclines on account of its great strength per unit of weight. 
It is the most economical rope where the weight of the rope is to be 
considered or the capacity of the machinery is to be increased without 
changing sheaves or drums. Monitor plow-steel rope is somewhat 



TRANSMISSION, HAULAGE AND HOISTING ROPE. 257 









Tran 


ismi 


ssion. 


Hai 


ilage 


, or 


Standing Rope 








6 Strands, 7 Wires per Strand, 1 Hemp Core. 






l-H 


1 


Approximate Breaking 

Strength, Tons 

(2000 lbs.) 


Allowable Working 
Load, Tons (2000 lbs.) 


Min. Dia. 

Drum or 

Sheave,In. 


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3.55 


32.0 


63.0 


73.0 


82.o'90.0 


6.4 


12.6 


14.6 


16.4 


18.0 


16.0 


11.0 


13/8 


41/4 


3.00 


28.0 


53.0 


63.0 


72.0 


79.0 


5.6 


10.6 


12.6 


14.4 


16 


15.0 


10.0 


11/4 


4 


2.45 


23.0 


46.0 


54.0 


60.0 


67.0 


4.6 


9.2 


10.8 


12.0 


13.0 


13.0 


9.0 


11/8 


31/;^ 


2.00 


19.0 


37.0 


43.0 


47.0 


52.0 


3.8 


7.4 


8.6 


9.4 


10.0 


1.20 


8.0 


I 


3 


1.58 


15.0 


31.0 


35.0 


38.0 


42.0 


3.0 


6.2 


7 


7 6 


8 4 


10.5 


7.0 


7/8 


2 3/4 


1.20 


12.0 


24.0 


28.0 


31.0 


33.0 


2.4 


4.8 


5.6 


6.2 


6.6 


9.0 


6.0 


3/4 


21/4 


0.89 


8.8 


18.6 


21.0 


23.0 


25.0 


1.7 


3.7 


4.2 


4.6 


5.0 


7.5 


5.0 


5/8 


21/8 


0.75 


7.3 


15.4 


16.7 


18.0 


20.0 


1.5 


3.1 


3.3 


3.6 


4.0 


7.25 


4.75 


9/1 R 


2 


0.62 


6.0 


13.0 


14.5 


16.0 


17.5 


1.2 


2.6 


2.9 


3.2 


3.5 


7.0 


4.50 


ll/lfi 


13/4 


0.50 


4.8 


10.0 


11.0 


12.0 


13.0 


0.96 


2.0 


2.2 


2.4 


2.6 


6.0 


4.00 


V^ 


11/;^ 


0.39 


3.7 


7.7 


8.85 


10. 


11.0 


0.74 


1.5 


1.8 


2.0 


2.2 


5.5 


3.50 


7/lfi 


11/4 


0.30 


2.6 


5.5 


6.25 


7.0 


7.75 


0.52 


1.1 


1.25 


1.4 


1.5 


4.5 


3.00 


3/8 


11/8 


0.22 


2.2 


4.6 


5.25 


5.9 


6.5 


0.44 


0.92 


1.05 


1.2 


1.3 


4.0 


2.75 


5/lfi 


1 


0.15 


1.7 


3.5 


3.95 


4.4 




0.34 


0.70 


0.79 


0.88 




3.5 


2.25 


9/32 


7/8 


0.125 


1.2 


2.5 


2.95 


3.4 




0.24 


0.50 


0.59 


0.68 




3.0 


1.75 













Standard Hoisting Rope. 














6 Strands, 19 Wires per Strand, 1 Hemp Core. 








Approximate Breaking 


Allowable Working Loads, 


Min. Dia. 
Sheave or 
Drum, Ft. 




i 




Strength, Tons (2000 Lbs). 


Tons (2000 Lbs). 






1 


n 


S 


o 






§1 


1 




i 
1— 1 


i 


1 

s 


1 

< 




2 
1— 1 


5^ 




^ 
ai 

^ 

o^ 

S 




o 


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23/4 


8 5/8 


11.95 


111.0 


211.0 


243.0 


275.0 


315.0 


22.2 


42.2 


48.6 


55.0 


63.0 


17.0 


11 


21/^ 


7 7/8 


9.85 


92.0 


170.0 


200.0 


229.0 


263.0 


18.4 


34.0 


40.0 


46.0 


53.0 


15.0 


10.0 


21/4 


71/8 


8.00 


72.0 


133.0 


160.0 


1R6.0 


210.0 


14.4 


26.6 


32.0 


37.0 


42.0 


14.0 


9.0 


2 


61/4 


6.30 


55.0 


106.0 


123.0 


140.0 


166.0 


11.0 


21.2 


24.6 


28.0 


33.0 


12.0 


8.0 


17/8 


5 3/4 


5.55 


50.0 


96.0 


112.0 


127.0 


150.0 


10.0 


19.0 


22.4 


25.0 


30.0 


12.0 


8.0 


13/4 


51/^ 


4.85 


44.0 


85.0 


99.0 


112.0 


133.0 


8.8 


17.0 


19.8 


22.0 


27.0 


11.0 


7.0 


15/8 


5 


4.15 


38.0 


72.0 


83.0 


94.0 


110,0 


7.6 


14.4 


16.6 


19.0 


22.0 


10.0 


6.5 


11/2 


4 3/4 


3.55 


33.0 


64.0 


73.0 


82.0 


98.0 


6.6 


12.8 


14.6 


16.0 


20.0 


9.0 


6.0 


13/8 


41/4 


3.00 


28.0 


56.0 


64.0 


72.0 


84.0 


5.6 


11.2 


12.8 


14.0 


17.0 


8.5 


5.5 


11/4 


4 


2.45 


22.8 


47.0 


53.0 


58.0 


69.0 


4.56 


9.4 


10.6 


12.0 


14.0 


7.5 


5.0 


11/8 


3i/:> 


2.00 


18.6 


38.0 


43.0 


47.0 


56.0 


3.72 


7.6 


8.6 


9.4 


Il.O 


7.0 


4.5 


1 


3 


1.58 


14.5 


30.0 


34.0 


38.0 


45,0 


2.90 


6.0 


6.80 


7.6 


9.0 


6.0 


4.0 


7/8 


2 3/4 


1.20 


11.8 


23.0 


26.0 


29.0 


35.0 


2.36 


4.6 


5.20 


5.8 


7.0 


5.5 


3.5 


3/4 


21/4 


0.89 


8.5 


17.5 


20.2 


23.0 


26.3 


1.70 


3.5 


4.04 


4.6 


5.3 


4.5 


3.0 


5/8 


2 


0.62 


6.0 


12.5 


14.0 


15.5 


19.0 


1.20 


2.5 


2.80 


3.1 


3.8 


4.0 


2,5 


9/16 


13/4 


0.50 


4.7 


10.0 


11.2 


12.3 


14.5 


0.94 


2.0 


2.24 


2.4 


2.9 


3.5 


2.25 


1/2 


11/2 


0.39 


3.9 


8.4 


9.2 


10.0 


12.1 


0.78 


1.68 


1.84 


2.0 


2.4 


3,0 


2.0 


7/16 


11/4 


0.30 


2.9 


6.5 


7.25 


8.0 


9.4 


0.58 


1.30 


1.45 


1.6 


1.9 


2.75 


1.75 


3/8 


11/8 


0.22 


2.4 


4.8 


5.30 


5.75 


6.75 


0.48 


0.96 


1.06 


1.15 


1.35 


2.25 


1.50 


5/16 


I 


0.15 


1.5 


3.1 


3.50 


3.80 


4.5C 


0.30 


0.62 


0.70 


0.76 


0.9 


2.0 1.25 


1/4 


3/4 


0.10 


1.1 


2.2 


2.43 


2.65 


3.15 


0.22 


0.44 


0.49 


0.53 


0.63 


1.5 1.00 



258 MATERIALS. 

stiffer than the same diameter of crucible and plow-steel ropes, but 
strength for strength, it is equally flexible. A smaller rope of this 
grade than any of the others can be used for a given service. It is 
particularly adapted to derricks, dredges, skidders, and stump pullers. 
The sheaves should be somewhat larger, if possible, than for the other 
grades. See tables, page 257. 

Extra Flexible Hoisting Rope. — Consists of 8 19-wire strands and 
one hemp core. The greater flexibility permits its use on smaller 
sheaves and drums, such as are usually found on derricks. It is not 
advisable to use it where there is much overwinding, as it will flatten 
much more quickly than the 6 X 19 standard rope. It is m.ade in 
the five grades of iron, crucible cast steel, extra strong crucible cast 
steel, plow-steel, and Monitor plow-steel. Its uses are the same as 
those of standard hoisting rope, noted above. See tables, page 259. 

Special Flexible Hoisting Rope. — Consists of 6 3 7- wire strands and 
one hemp core. It is extremely flexible, and is especially adapted 
to service on cranes where the sheaves are rather small. It is made 
in the grades crucible cast steel, extra strong crucible cast steel, plow- 
steel, and ^Monitor plow-steel. It will not stand as much abrasion 
as the 6 19-wire strand rope, but it is particularly efficient, as over 
50 per cent of the wires are in the inner layers and are protected from 
abrasion. The crucible steel ropes are used for general hoisting work 
where the sheaves are small, while the plow-steel varieties are recom- 
mended for crane service. The [Monitor plow-steel rope is largely 
used on dredges for both main and spud ropes. See table, page 259. 

Flattened Strand Rope. — Flattened strand ropes are used where an 
increased wearing surface is desired above that obtained with a round 
strand rope. They are made both for haulage and transmission, 
and for hoisting, and are always made Lang lay. 

The haulage rope is made in three types, each of which has one 
hemp core. The first has 5 9-wire strands, the center wire being 
of elliptical section; the second has 6 8- wire strands, the center wire 
being of triangular section; the third has 5 11-wire strands, the tlu'ee 
center wires being of smaller diameter than the others and laid along- 
side of each other in the same plane. These ropes are made in the 
iron, crucible cast steel, extra strong crucible cast steel, and Monitor 
plow-steel grades. They are made in diameters ranging from 1 Yi 
inch, down to 3 § inch. Thfe 1-inch 6 8-wire strand rope weighs 
1.80 lb. per ft. and has an approximate strength of 34 tons, in the 
crucible cast steel grade. ]Monitor plow-steel rope of the same diam- 
eter and weight lias an approximate breaking strength of 36 tons. 
The similar figures for 3 2-inch rope, weighing 0.45 lb. per ft., are: 
Crucible cast steel, 9.6 tons; Monitor plow -steel, 11.9 tons. 

Flattened strand hoisting rope is made in two types, each with 
one hemp core: (A) 5 28-wire strands, the center wire being of ellip- 
tical section; and (B) 6 25-wire strands, the center wire being of 
triangular section, and the 12 wires immediately surrounding it being 
of smaller diameter than the outer wires. These ropes compare in 
flexibility with the standard hoisting ropes, but have about 150 per 
cent greater wearing surface. Type A is made in the grades of iron, 
crucible cast steel, extra strong crucible cast steel, and jNlonitor plow 
steel. Type B is made in the grades of crucible cast steel, extra strong 
crucible cast steel, and Monitor plow steel. They are made in sizes 
ranging from 21/4 in. diam. down to s/s inch. Type B rope, 2 in. 
diam., weighing 7.25 lb. per ft., has the following breaking strength: 
Crucible cast steel, 117 tons; Monitor plow steel, 183 tons. The 
similar figures for U-inch rope of the same type, weighing 0.45 lb. 
per ft., are: Crucible cast steel, 9.3 tons; INIonitor plow steel, 13.3 
tons. 

Non-Spinning Hoisting Rope. — Comprises 18 7- wire strands and 
one hemp core. 6 strands, long lay, being laid around the core to the 
left, and 12 strands, regular lay being laid to the right around them. 
A free object suspended from the end of a rope of this character will 
not rotate and endanger the lives of persons below it. Furthermore, 
the attention required to handle and guide the load is decreased. 
Tliis rope is recommended for b^^ck haul or single-line derricks, and 
for shaft sinking and min(^ hoisting, where the bucket swings without 
guides. This rope; works best where it does not overwind on the 



FLEXIBLE HOISTING ROPE. 



259 



Extra Flexible Steel Hoisting Rope. 

8 Strands, 19 Wires per Strand, 1 Hemp Core. 





C 




Approximate Strength, 


Allowable Work 


ing 


6 
2 

On- 




i 


^ 


Tons (2000 Lbs.). 


Load 


Tons 


(2000 Lbs.). 






4J 








-t-> 






•«fci 


*-* 


>< 

o 




4J . 
Oo 


a Strong 
cible Cas 
1 Rope. 


72 a 




O o 


I Strong 
cible Cas 
3l Rope. 


1 . 


1 

o a; 


. oT 
0^ 


s 


a 
< 




U 

o 

58 


-£3 2 o 


Pm 




Sc/2 
O 


xo^ 




§« 
S 




11/2 


4 3/4 


3.19 


66.0 


74.0 


80.0 


11.6 


13.0 


14.8 


16.0 


3.75 


13/8 


41/4 


2.70 


51.0 


57.0 


64.0 


68.0 


10 2 


11.0 


12.8 


13.0 


3.50 


U/4 


4 


2.20 


42.0 


47.0 


52.0 


56.0 


8.4 


9.4 


10.4 


11.0 


3.20 


n/8 


31/? 


1.80 


34.0 


38.0 


43.0 


46.0 


6.8 


7.6 


8.6 


9.2 


2.83 


1 


3 


1.42 


26.0 


29.7 


33.0 


36.0 


5.2 


5.9 


6.6 


7.2 


2.50 


7/8 


2 3/4 


1.08 


20.0 


23.0 


26.0 


28.0 


4.0 


4.6 


5.2 


5.6 


2.16 


3/4 


21/4 


0.80 


15.3 


17.6 


20.0 


22.0 


3.06 


3.5 


4.0 


4.4 


1.83 


5/8 


2 


0.56 


10.9 


12.4 


14.0 


15.0 


2.18 


2.5 


2.8 


3.0 


1.75 


9/16 


13/4 


0.45 


8.7 


10.1 


11.6 


12.0 


1.74 


2.0 


2.32 


2.4 


1.50 


1/2 


1 1/2 


0.35 


7.3 


8.0 


8.7 


9.5 


1.46 


1.6 


1.74 


1.9 


1.33 


7/16 


1 1/4 


0.27 


5.7 


6.30 


6.90 




1.14 


1.26 


1.38 




1.16 


3/8 


1 1/8 


0.20 


4.2 


4.66 


5.12 




0.84 


0.93 


1.02 




1.00 


5/16 


1 


0.13 


2.75 


3.05 


3.35 




0.55 


0.61 


0.67 




0.83 


1/4 


3/4 


0.09 


1.80 


2.02 


2.25 




0.36 


0.40 


0.45 




0.75 



Special Flexible Steel Hoisting Rope. 

6 Strands, 37 Wires per Strand, 1 Hemp Core. 





d 


+J 


Breaking Strength, 


Allowable Working Load, 


B 




i 

;3 




Tons (2000 Lbs.). 


Tons (2000 Lbs.). 


¥ 


d 


S. 


4-> 


.n1 . 




g . 


7} • 






^ . 


M 




+i M 


OJ OJ 


§6^ 

fc; 0) o 




o a> 


C3 0) 


CO OJ 




_o o 






O 


^n 


OS- 


1. 


E& 


0& 


2 0) o 


S 


^& 


SS 


•§ 


x' 
o 


^ 


01 p^ 

3^ 


^a^ 


S« 




^gp5 


-2^ 


IS 




5 


< 


p< 
<3 


■^1 
5^ 






1^ 
1^ 


6^ 


^2| 




11 


P 


2 3/4 


8 5/8 


11.95 


200.0 


233.0 


265.0 


278.0 


40.0 


47.0 


53.0 


55.0 




21/2 


7 7/8 


9.85 


160.0 


187.0 


214.0 


225.0 


32.0 


37.0 


43.0 


45.0 




21/4 


7 1/8 


8.00 


125.0 


150.0 


175.0 


184.0 


25.0 


30.0 


35.0 


37.0 




2 


61/4 


6.30 


105.0 


117.0 


130.0 


137.0 


21.0 


23.0 


26.0 


27.0 




17/8 


5 3/4 


5.55 


94.0 


106.0 


119.0 


125.0 


18.8 


21.2 


23.8 


25,0 




13/4 


51/2 


4.85 


84.0 


95.0 


108.0 


113.0 


17.0 


19.0 


22.0 


23.0 




15/8 


5 


4.15 


71.0 


79.0 


90.0 


95.0 


14.0 


16.0 


18.0 


19.0 




11/2 


4 3/4 


3.55 


63.0 


71.0 


80.0 


84.0 


12.0 


14.0 


16.0 


17.0 


3 75 


13/8 


41/4 


3.00 


55.0 


61.0 


68.0 


71.0 


11.0 


12.0 


14.0 


14.0 


3 50 


11/4 


4 


2.45 


45.0 


50.0 


55.0 


58.0 


9 


10.0 


11.0 


11.0 


3 20 


11/8 


31/2 


2.00 


34.0 


39.0 


44.0 


46.0 


7.0 


8.0 


9.0 


9.2 


2 83 


1 


3 


1.58 


29.0 


32.0 


35.0 


37.0 


6.0 


6.4 


7.0 


7.4 


2 50 


7/8 


23/4 


1.20 


23.0 


25.0 


27.0 


29.0 


5.0 


5.0 


5.0 


5 8 


2 16 


3/4 


21/4 


0.89 


17.5 


19.0 


21.0 


23.0 


3.5 


3.8 


4.0 


4.6 


1.83 


5/8 


2 


0.62 


11.2 


12.6 


14.0 


16.0 


2.2 


2 5 


3 


3.2 


1 75 


9/16 


13/4 


0.50 


9.5 


10.5 


11.5 


12.5 


1.9 


2.1 


2.3 


2 5 


1 50 


1/2 


1 1/2 


0.39 


7.25 


8.25 


9.25 


9.75 


1.45 


1.65 


1.85 


1.9 


1 33 


7/16 


11/4 


0.30 


5.5 


6.35 


7.2 


7.50 


1.1 


1.27 


1.4 


1 5 


1 15 


3/8 


1 1/8 


0.22 


4.2 


4.65 


5.1 


5.30 


0.84 


0.93 


1.0 


1.06 


1.00 



260 



MATERIALS. 



drum. The best fastening is an open or closed socket, but the wire 
rope makers recommend that fastenings be attached at the factory. 
This rope should not be as heavily loaded as ordinary hoisting rope. 
It is made in the grades of iron, crucible cast steel, extra strong crucible 
cast steel, plow steel, and Monitor plow steel. See table, page 261. 

Extra Flexible Iron Hoisting Rope. 

8 Strands, 19 Wires per Strand, 1 Hemp Core. 

Diam. In 1 Vs 3/4 s/g Q/u 1/2 

Approx. Circum., in 3 2M 2}4 2 1% II/2 

Weight per ft., lb 1.42 1.08 0.80 0.56 0.45 0.35 

Approximate Strength, tons 

(2000 lbs.) 16.0 13.0 9.5 7.0 6.0 5.0 

WorkingLoad,tons (2000 lbs.) 3.1 2.6 1.9 1.4 1.2 1.0 
Min. Diam of Drum, ft 6.0 5.5 4.5 4.0 3.5 3.0 

Steel-Clad Hoisting Rope. — The regular grades of hoisting ropes, 
as well as the special flexible and extra flexible, are furnished, if de- 
sired, with a flat strip of steel wound spirally around each strand. 
These give additional wearing surface without sacrificing the flexibiUty. 
When the flat winding is worn through, a complete rope remains with 
unimpaired strength. These ropes are designed for severe conditions 
of service, and an additional service of 50 to 100 per cent over that of 
the unprotected rope is frequently obtained. The hoisting rope 
tables on pages 257 and 259 may be used for the strength of steel- 
clad rope, by referring to the diameter of the rope, as it would be were 
no wrapping applied. The steel wrapping is not considered as adding 
any strength to the rope, but merely serving to increase its hfe. 

Flat Rope. — Flat rope consists of a number of "flat-rope" strands, 
twisted alternately right and left, placed side by side and served with 
soft Swedish iron or steel wire, to form a flat rope of the desired width 
and thickness. The soft sewing wires wear much quicker than the 
rope wire, and have to be replaced from time to time, at which time 
worn strands can also be renewed. Flat rope is used principally for 
hoisting heavy loads out of deep shafts, it requiring a reel but Uttle 
larger than the width of the rope, whereas round rope necessitates 
the use of a large drum. Its. use is recommended where saving of 
machinery space is an object. It does not twist or spin in the shaft. 
It is also used for operating spouts on coal and ore docks, and for raising 
and lowering emergency gates on canals and similar machinery. For 
details of methods of fastening it to drums, the manufacturers should 
be consulted. Drums and sheaves should be as large as possible. A 
rule for the diameter of the drum is D = c t, where D is diameter of 
drum at bottom; ft., t = thickness of rope; in. and c = 100 for drums 
and 160 for sheaves. Sheaves should be crowned at the center and 
have deep flanges to guide the rope. See table, page 261. 

Track Cable for Aerial Tramways. — Composed of several successive 
layers of wires wrapped around a single wire core, the number of 
wires varying with the diameter of the cable. The cable is made in 
plow steel and crucible steel grades. 









Track 


Cable for Aerial Tramways. 
















Breaking 








Breaking 








Breaking 




s 




Stress Tons 




w 




Stress Tons 




oa 




St'ssTons 


d 


'^ 


i 


(2000 Lbs.). 


d 


i 


, 


(2000 Lbs.). 


d 


^ 

g 




(2000 Lbs.) 




wR 






tH-Q 






w^ 






'q 


6 


ft . 




^1 


5 


d 






|i 


.1 


d 




'0 S 
60.0 


|1 


21/2 


91 


1310 


285.0 


335.0 


13/4 


61 


659 


145.8 


171.0 


11/8 


37 


270 


70 


21/4 


91 


1036 


233.0 


266.0 


15/8 


61 


563 


124.0 


146.0 


1 


19 


220 


49 2 


58 7 


21/8 


91 


9351 204.0 


240.0 


u/? 


37 


488 


108.4 


127.5 


7/8 


19 


169 


37.6 


44.4 


2 


61 


840, 185.0 


218.0 


13/8 


37 


401 


88.8 


105.0 


3/4 


19 


124 


27.6 


32.5 


IV8 


61 


7281 161.0 


189.0 


11/4 


37 


323 


71.8 


84.6 


5/8 


19 


86 


19.2 


22.3 



STEEL FLAT ROPE, 



261 



Non-Spinning Hoisting Rope. 

18 Strands, 7 Wires per Strand, 1 Hemp Core. 





d 




Approximate Breaking 


Allowable Working Load, 


r^ 




i 


4 


Strength, Tons (2000 Lb.). 




Tons (2000 Lb.). 


o P 


4 


i 


4^ 


ii oj o 


-qJ 


r^ 


i 




S o 








1 






o 

S-i 

1— t 








15 
II 
1^ 


1 

o 
1— ) 


II 

5^ 


m 




15 
§1 
1^ 


.2 o 


13/4 


51/? 


5.50 


45.80 


85.90 


101.00 


111.10 


122.00 


9.1 


17.1 


20.2 


22.2 


24.04 


7.00 


15/8 


5 


4.90 


39.80 


74.40 


87.60 


96.30 




7.9 


14.8 


17.5 


19.2 




6.50 


11/?, 


43/4 


4.32 


34.00 


63.80 


75.00 


82.50 


90. 7C 


6.8 


12.7 


15.0 


16.5 


18.1 


6.00 


13/8 


41/4 


3.60 


28.2052.00 


62.40 


68.60 


75. 5C 


5.6 


10.4 


12.4 


13.7 


15.1 


5.50 


11/4 


4 


2.80 


23.40 43.80 


51.60 


56.80 


62. 5C 


4.6 


8.7 


10.3 


11.3 


12.5 


5.00 


11/8 


31/? 


2.34 


19.60!36.80 


43.20 


47.50 


52.20 


3.9 


7.3 


8.6 


9.5 


10.4 


4.50 




3 


1.73 


14.95 


28.00 


33.00 


36.30 


39.00 


2.9 


5.6 


6.6 


7.2 


7.8 


4.00 


V8 


23/4 


1.44 


11.95 


22.50 


26.50 


31.80 


35.00 


2.3 


4.5 


5.3 


6.3 


7.0 


3.50 


3/4 


21/4 


1.02 


8.85 


16.70 


19.60 


24.60 


27. OC 


1.7 


3.3 


3.9 


4.9 


5.4 


3.00 


' 5/8 


2 


0.70 


5.90 


11.10 


13.10 


15.75 


17.30 


1.1 


2.2 


2.6 


3.1 


3.4 


2.50 


9/16 


13/4 


0.57 


4.85 


9.10 


10.70 


12.80 




0.97 


1.8 


2.1 


2.5 




2.25 


1/^ 


11/? 


0.42 


3.65 


6.90 


8.10 


9.75 


10. 7C 


0.73 


1.3 


1.6 


1.9 


2.1 


2.00 


7/16 


11/4 


0.31 


2.63 


4.90 


5.80 


6.85 




0.52 


0.98 


1.1 


1.3 




1.75 


3/8 


U/S 


0.25 


2.10 


3.90 


4.60 


5.55 


6.i6 


0.42 


0.78 


0.92 


1.1 


i.2 


1.50 



Steel Flat Rope. 









Allow- 








Allow- 








Allow- 








able 








able 








able 








Working 








Working 








Working 








Load, 








Load, 








Load, 






^ 


Tons 






d 
(—1 


Tons 






^ 


Tons 


d 




J 


(2000 


d 




(2000 


d 




h:; 


(2000 


M 


, 


£ 


Lbs.). 


M 




-M 


Lbs.). 




§ 


£ 


Lbs.). 


1 


I— 1 


^^ 


. 


01 


l-H 


P^ 


<i^-; 


. 


o 


hH 


<!>-: 


. 


1 


11/? 


0.65 


IS 

O 
2.6 


1 
3.10 


1 

Eh 


^ 
'O 

g 




3 ^ 








a 

-M 
^ 


3 ^ 


1^ 


1/4 


3/8 


41/? 


2.85 


12.6 


6.6 


5/8 


41/2 


4.55 


18.2 


21.0 


1/4 


2 


0.82 


3.4 


4.00 


3/8 


5 


3.10 


13.6 


16.2 


5/8 


5 


5.10 


20.4 


23.8 


1/4 


21/? 


1.06 


4.4 


5.30 


3/8 


51/2 


3.50 


15.4 


18.4 


5/8 


51/2 


5.65 


22.8 


26.4 


1/4 


3 


1.23 


5.2 


6.20 


3/8 


6 


3.73 


16.2 


19.4 


5/8 
5/8 
5/8 


6 
7 
8 


6.15 
7.30 
8.40 


25.0 
29.6 
34.0 


29.0 
34.2 
39.4 


5/1 fi 


11/? 


0.79 


3.6 


4.4 


1/? 


21/? 


2.20 


9.0 


10.8 


5/16 
5/16 


2 

21/? 


1.10 
1.35 


4.6 
6.0 


5.6 
7.0 


1/2 

V? 


3 

31/? 


2.50 
2.80 


10.4! 12.6 
12.0 14.4 












3/4 


5 


6.85 


27.0 


31.4 


5/16 


3 


1.60 


7.2 


8.6 


1/? 


4 


3.15 


13.8 


16.4 


3/4 


6 


7.50 


30.2 


35.0 


5/16 


31/? 


1.88 


8.2 


10.0 


V? 


41/? 


3.85 


16.6 


19.8 


3/4 


7 


8.25 


33.6 


38.8 


5/16 


4 


2.15 


9.6 


11.4 


1/9 


5 


4.20 


18.0 


21.6 


3/4 


8 


9.75 


40.4 


46.8 












1/2 
1/? 


51/2 

6 


4.55 
4.90 


19.6 
21.0 


23.6 
25.2 












3/8 


2 


1.30 


5.4 


6.6 


7/8 


5 


7.50 


31.0 


34.4 


3/8 


21/? 


1.70 


7.2 


8.6 


1/? 


7 


5.90 


25.6 


30.6 


7/8 


6 


8.53 


36.0 41.8 


3/8 

3/8 


3 
31/? 


1.89 
2.30 


8.2 
10.0 


9.8 
12.0 












7/8 
7/8 


7 

8 


9.56 
10.60 


40 f\\ AA A 


5/8 


31/? 


3.50 


13.6 


15.8 


45^0 


51^6 


3/8 


4 


2.43 


10.8 


13.0 


5/8 


4 


4.00 


15.8 


18.4 













The allowable working load in the above table is 1/5 of the approxi- 
mate breaking stress of the rope. 



262 



MATEBiALS. 



Locked Wire Cable. — Locked wire cable and locked coil-track 
cable, of the general form shown in Fig. 77, are used as track cables 
for aerial tramways. They differ only in the number and size of 




Fig. 77. 



wires used, and both are made of crucible cast steel. The locked 
wire cable is the more flexible of the two. These cables are smoother 
than the track cable described on page 260. 

Locked Coil and Locked Wire Cable. 







Break- 






Break- 






Break- 






ing 






ing 






ing 




Wt. per 


Stress, 




Wt. per 


Stress, 




Wt. per 


Stress 




Ft., Lb. 


Tons 




Ft., Lb. Tons 




Ft., Lbs. 


Tons 






(2000 






(2000 






(2000 


a 




Lbs.). 


fl 




Lbs.). 


d 




Lbs.). 


., 


'TJ 


'^ -; 


Ti 


-^ : 


^ 


'^ ! '^ -r 


TJ 


'^ .; 


^ 


^3 


'^ .; 


Ti i T3 . 


g 


^t 


0) OJ 


<i>-^ 

^•■z 




g 




0) 0) 


g 


Sd^ 




s 


J^ 


2^ 


J- 


2^ 


(5 


J"|J^iJ" 


3^ 


5 


U6 


FJ" 


2^ 


21/?, 




15.60 




240 


1 1/2 5.30 5.70' 89 


89 


7/« 


1.80 


1.88 30 


30 


21/4 




12.50 




190 


13/8! 4.40 4.75 75 


75 


3/4 




1.30| .. 


22 


2 




10.00 




160 


1 1/4I 3.70 3.80 62 


62 


5/8 




0.90 .. 


15.5 


13/4 




7.65 




120 


U/si 3.00 3.15 50 


50 


9/lfi 




0.72 .. 


12.5 


15/8 


6.30 


6.60 


m 103 


1 I 2.35 2.50 40 


40 


1/2 




0.571 .. 


10 



Galvanized Steel Hawser. 

For Lake and Deep Sea Towing and Mooring Lines. 







Six 3 7- Wire 


Six 24-Wire 






Six 3 7- Wire 


Six 24-Wire 






Strands, 1 


Strands, 7 






Strands, 1 


Strands, 7 






Hemp Core 


Hemp Cores. 


d 


d 


Hemp Core. 


Hemp Cores 




i 


CO 


HA 


£ 


§ 

"53 


i 


05 

H- 




"53 


1 


1 










i 






15 s=^S 




1^1 


Q 


U 


^^ 


m^^- 


^^ 


m^^^ 


Q 





^^ 


&^'- 


^^ 


«^- 


23/8 


71/2 


8.82 


188 






11/2 


43/4 


3.55 


76 


3 10 


63 


25/16 


71/4 


8.36 


182 






17/16 


41/^ 


3.24 


72 


2 92 


55 


21/4 


71/8 


8.00 


171 






13/8 


41/4 


3.00 


66 


2 62 


50 


21/8 


6 3/4 


7.06 


155 






11/4 


4 


2.45 


54 


2 15 


42 


21/16 


6 1/2 


6.65 


140 


5.81 


113 


13/16 


33/4 


2.21 


47 


1 93 


38 


2 


6 1/4 


6.30 


132 


5.51 


106 


11/8 


31/? 


2.00 


42 


1 75 


34 


1 15/16 


6 


5.84 


123 


5,09 


98 


11/16 


31/4 


1.77 


38 


1 54 


27 


1 13/16 


53/4 


5. 13 


112 


4.48 


88 




3 


1 58 


31 5 


1 38 


25 


13/4 


5 1/2 


4.85 


104 


4.24 


82 


7/8 


2 3/4 


1.20 


26 


1 05 


20 


111/16 


51/4 


4.42 


97 


3.86 


76 


13/16 


21/2 


1.03 


22 


90 


17 


15/8 


5 


4.15 


87 


3.63 


74 


3/4 


21/4 


0.89 


20 


0.78 


14 



SPLICING WIRE ROPES. 



263 



To Splice a Wire Rope. — The tools required will be a small marline 
spike, nipping cutters, and either clamps or a small hemp-rope sUng witti 
which to wrap around and untwist the rope. If a bench- vise is acces- 
sible it will be found convenient. 

In sphcing rope, a certain length is used up in making the spUce. An 
allowance of not less than 16 feet for 1/2-inch rope, and proportionately 
longer for larger sizes, must be added to the length of an endless rope in 
ordering. 

Having measured, carefully, the length the rope should be after sphcing, 
and marked the points M and M', Fig. 78, unlay the strands from each 
end E and E' to M and M' and cut oh' the center at M and M\ and then: 

(1). Interlock the six unlaid strands of each end alternately and draw 
them together so that the points M and M' meet, as In Fig. 79. 

(2). Unlay a strand from one end, and following the unlay closely, lay 
into the seam or groove it opens, the strand opposite it belonging to the 
other end of the rope, until witliin a length equal to three or four times 
the length of one lay of the rope, and cut the other strand to about the 
same length from the point of meeting as at A, Fig. 80. 

(3). Unlay the adjacent strand in the opposite direction, and following 
the unlay closely, lay in its place the corresponding opposite strand, cut- 
ting the ends as described before at B, Fig. 80. 

There are now four strands laid in place terminating at A and B, with 
the eight remaining at MM\ as in Fig. 80. 

It will be well after laying each pair of strands to tie them temporarily 
at the points A and B, 




Fig. 80. 
A a' a'' M B b' B" 



Fig. 81. Splicing Wire Rope. Fig. 82. 

Pursue the same course with the remaining four pairs of opposite 
strands, stopping each pair about eight or ten turns of the rope short of 
the preceding pair, and cutting the ends as before. 

We now have all the strands laid in their proper places with their re- 
spective ends passing each other, as in Fig. 81. 

All methods of rope-splicing are identical to this point: their variety 
consists in the method of tucking the ends. The one given below is the 
one most generally practiced. 

Clamp the rope either in a vise at a point to the left of A, Fig. 81, and 
by a hand-clamp applied near A, open up the rope by untwisting suffi- 
ciently to cut the core at A, and seizing it with the nippers, let an assis- 
tant draw it out slowly, you following it closely, crowding the strand in 
its place until it is all laid in. Cut the core where the strand ends, and 
push the end back into its place. Remove the clamps and let the rope 
close together around it. Draw out the core in the opposite direction 
and lay the other strand in the center of the rope, in the same manner. 
Repeat the operation at the five remaining points, and hammer the rope 
lightly at the points where the ends pass each other at A, A, B, B, etc., 
with small wooden mallets, and the spUce is complete, as shown in Fig. 82- 

If a clamp and vise are not obtainable, two rope slings and short 
wooden levers may be used to untwist and open up the rope. 

A rope spliced as above will be nearly as strong as the original rope 
and smooth everyw^here. After running a few days, the splice, if well 
made, cannot be found except by close examination. 

The above instructions have been adopted by the leading rope manu- 
facturers of America. 



264 



MATERIALS. 



CHAINS. 

Weight per Foo^ Proof Test and Breaking Weight. 

(Pennsylvania Railroad SpecificatioTis, 1903.) 



Nominal 

Diameter 

of Wire. 

Inches. 



5/32 
3/16 
3/16 

1/4 
5/16 
3/8 
3/8 
7/16 
7/16 
1/2 
1/2 
5/8 
5/8 
3/4 
3/4 
7/8 
1 
1 

11/8 
11/4 
11/2 
13/4 
2 



Description. 



Twisted chain . 



Perfection twisted chain 
StraightMink chain. . 



Crane chain 

Straight-link chain . . . . 

Crane chain 

Straight-link chain . . . . 

Crane chain 

Straight-link chain . . . . 

Crane chain 

Straight-link chain . . . . 
Crane chain 



Straight-link chain. 
Crane chain 



Maximum 

Length of 

100 Links 

Inches. 



1031/8 
961/4 
1511/4 
102 
1143/4 
1143/4 
1135/8 
1271/2 
1261/4 
153 
1511/2 
1781/2 
1763/4 
204 
202 
2521/2 
277 ?/4 
2801/9 
303 " 
3531/2 
4165/8 
4793/4 
5551/2 



Weight 

per 

Foot. 

Lbs. 



0.20 

0.35 

0.27 

0.70 

1.10 

1.60 

1.60 

2.07 

2.07 

2.50 

2.60 

4.08 

4.18 

5.65 

5.75 

7.70 

9.80 

9.80 

12.65 

15.50 

22.50 

30.00 

39.00 



Proof 

Test. 
Lbs. 



1,600 

2,500 

3,600 

4,140 

4,900 

5,635 

6,400 

7,360 

10,000 

11,500 

14,400 

16,560 

22,540 

29,440 

25,600 

38,260 

46,000 

66,240 

90,160 

117,760 



Breaking 

Weight. 
Lbs. 



3,200 

5,000 

7,200 

8,280 

9,800 

11,270 

12,800 

14,720 

20,000 

23,000 

28,800 

33,120 

45,080 

58,880 

51,200 

76,520 

92,000 

132,480 

180,320 

235,520 



Elongation of all sizes, 10 per cent. All chain must stand the proof 
test without deformation. A piece 2 ft. long out of each 200 ft. is 
tested to destruction. 

British Admiralty Proving Tests of Chain Cables. — Stud-links. 
Minimum size in inches and lOths. Proving test in tons of 2240 lbs. 
Min. Size: H f H i il 1 1^ H U% H 1^ 1| 
Test, tons: 8i 10.1 11.9 13| lof 18 20.3 22f 25^"^ 28.1 31 34 
Min. Size: !/« li 1t% H 1H U Ui H lit 2 2^ 
Test, tons: 375I 40^ 43 9 47i oii 55.1 59.1 63i 67^^ 72 8H 

Wrought-iron Chain Cables. — The strength of a chain link is less 
than twice that of a straight bar of a sectional area equal to that of one 
side of the link. A weld exists at one end and a bend at the other, each 
requiring at least one heat, which produces a decrease in the strength. 
The report of the committee of the U. S. Testing Board (1879), on tests 
of wrought-iron and chain cables, contains the following conclusions. 
That beyond doubt, when made of American bar iron, with cast-iron 
studs, the studded link is inferior in strength to the unstudded one. 

" That when proper care is exercised in the selection of material, a varia- 
tion of 5 to 17 per cent of the strongest may be expected in the resistance 
of cables. Without this care, the variation may rise to 25 per cent. 

"That with proper material and construction the ultimate resistance of 
the chain may be expected to vary from 155 to 170 per cent of that of the 
bar used in making the links, and show an average of about 163 per cent. 

"That the proof test of a chain cable should be about 50 per cent of 
the ultimate resistance of the weakest link." 

The decrease of the resistance of the studded below the unstudded 
cable is probably due to the fact that in the former the sides of the link 
do not remain parallel to each other up to failure, as they do in the latter. 
The result is an increase of stress in the studded link over the.unstudded 
in the proportion of unity, to the secant of half the inclination of the 
sides of the former to each other. 

From a great number of tests of bars and unfinished cables, the commit- 
tee considered that the average ultimate resistance, and proof tests of 
chain cables made of the bars, whose diameters are given, should be 
such as are shown in the accompanying table. 



CHAINS. 



265 



ULTIMATE RESISTANCE AND PROOF TESTS OF CHAIN CABLES. 



Diam. 

of 

Bar. 


Average resist. 
= 163% of Bar. 


Proof Test. 


Diam. 

of 
Bar. 


Average resist. 
= 163% of Bar. 


Proof Test 


Inches. 


Pounds. 


Pounds. 


Inches. 


Pounds. 


Pounds. 


1 


71,172 


33,840 


19/16 


162,283 


77,159 


n/i6 


79,544 


37,820 


15/8 


174,475 


82,956 


U/8 


88,445 


42,053 


1 11/16 


187,075 


88,947 


13/16 


97,731 


46,468 


13/4 


200,074 


95,128 


11/4 


107,440 


51,084 


1 13/16 


213,475 


101,499 


15/16 


117,577 


55,903 


17/8 


227,271 


108,058 


13/8 


128,129 


60,920 


1 15/16 


241,463 


114,806 


17/16 


139^,103 


66,138 


2 


256,040 


121,737 


11/2 


150,485 


71,550 









Pitch, 


Breaking, Proof and Working Strains of Chains. 






(Bradlee & Co., Philadelphia.) 








* 


i 


* 

• 

(V 


D.B.G. Special Crane. 


Crane. 


a 
"S 


CO 




dinary Safe 
oad . Genera 
se, lb. 


C4-I 




dinary Safe 
oad. General 
se, lb. 


m 


s 


< 


3 

o 


£ 


> a 


5^^ 


^ 


> C 


6^^ 


1/4 


25/32 


3/4 


15/16 


1,932 


3,864 


1,288 


1,680 


3,360 


1,120 


5/16 


27/32 


1 


11/8 


2,898 


5,796 


1,932 


2,520 


5,040 


1,680 


3/8 


31/32 


11/2 


15/16 


4,186 


8,372 


2,790 


3,640 


7,280 


2,427 


7/16 


15/32 


2 


11/2 


5,796 


11,592 


3,864 


5,040 


10,080 


3,360 


1/2 


I 11/32 


21/2 


1 13/16 


7,728 


15,456 


5,152 


6,720 


13,440 


4,480 


9/16 


1 15/32 


33/10 


2 


9,660 


19,320 


6,440 


8,400 


16,800 


5,600 


5/8 


123/32 


41/10 


23/16 


11,914 


23,828 


7,942 


10,360 


20,720 


6,907 


11/16 


1 13/16 


• 5 


23/8 


14,490 


28,980 


9,660 


12,600 


25,200 


8,400 


3/4 


1 15/16 


62/10 


29/16 


17,388 


34,776 


11,592 


15,120 


30,240 


10,080 


13/16 


21/16 


67/10 


23/4 


20,286 


40,572 


13,524 


17,640 


35,280 


11,760 


7/8 


23/16 


83/8 


215/16 


22,484 


44,968 


14,989 


20,440 


40,880 


13,627 


15/16 


27/16 


9 


33/16 


25,872 


51,744 


17,248 


23,520 


47,040 


15,680 


1 


21/2 


101/2 


33/8 


29,568 


59,136 


19,712 


26,880 


53,760 


17,920 


11/16 


25/8 


12 


39/16 


33,264 


66,538 


22,176 


30,240 


60,480 


20,160 


11/8 


23/4 


135/8 


313/16 


37,576 


75,152 


25,050 


34,160 


68,320 


22,773 


13/ie 


31/16 


137/10 


4 


41,888 


83,776 


27,925 


38,080 


76,160 


25,387 


11/4 


31/8 


16 


43/16 


46,200 


92,400 


30,800 


42,000 


84,000 


28,000 


15/16 


33/8 


161/2 


43/8 


50,512 


101,024 


33,674 


45,920 


91,840 


30,613 


13/8 


39/16 


191/4 


49/16 


55,748 


111,496 


37,165 


50,680 


101,360 


33,787 


17/16 


311/16 


197/10 


43/4 


60,368 


120,736 


40,245 


54,880 


109,760 


36,587 


11/2 


37/8 


23 


51/8 


66,528 


133,056 


44,352 


60,480 


120,960 


40,320 


19/16 


4 


25 


55/16 


70,762 


141,524 


47,174 


65,520 


131,140 


43,180 


13/4 


43/4 


31 


57/8 


82,320 


164,640 


54,880 








2 


53/4 


40 


63/4 


107,520 


215,040 


71,680 








21/4 


63/4 


523/4 


75/8 


136,080 


272,160 


90,720 








21/2 


7 


641/2 


83/8 


168,000 


336,000 


112,000 








2 3/4 


71/4 


73 


91/8 


193,088 


386,176 


128,725 








3 


73/4 


86 


97/8 


217,728 


435.456 


145,152 









The distance from center of one link to center of next is equal to the 
inside length of link, but in practice 1/32 in. is allowed for weld. This is 
approximate, and where exactness is required, chain should be made so. 

For Chain Sheaves. — The diameter, if possible, should be not less 
than thirty times the diameter of chain used. 

Example. — For 1-inch chain use 30-inch sheaves. 



266 



MATERIALS. 




J'WEDGE AND 
^ BULLHEAD 



\r:— 6- 




FEATHER EDGE 





CIRCLE AND 
CUPOLA BLOCK 




J- 



SHAPES AND SIZES OF FIRE-BRICK. 

(Stowe-Fuller Co., Cleveland, 1914.) 



Name of 

Brick 

or 

Tile. 



Length, 
Inches. 


Width, 
Inches. 

c d 


Thick-' 

ness. 

Inches. 


1° 


top 
a 




e f 



Straight Brick. 



9-inch 

Large 9-inch . . 
Small 9- " .. 

Checker 

Soap 

No. 1 Split. .. . 
No. 2 " 

Checker Tile . | 

Mill 

Mill Block 
No. 1 Bridgewall 
No. 2 



9 

9 

9 

9 

9 

9 

9 
18,20, 

24 
18,20, 
24 
1 

13 
13 



j lo,2U, » 
I 24 f 
1A 1 



41/2 




21/2 


63/4 




21/2 


31/2 




21/2 


3 




3 


21/2 




21/4 


41/2 




11/4 


41/2 




2 


^ 




3 


9 




3 


9 




6 


61/2 




6 


61/2 




3 



Wedge Shape and Taper Bricks. 



Large 9-in. No 

1 Wedge . . 
Large 9-in. No 

2 Wedge . . 
No. 1 Wedge 
No. 2 

No. 1 Key=^. 
No. 2 " * 
No. 3 " * 
No. 4 " * 
No. 1 Archf 
No. 2 " t 
Side Skew . 
End Skew . 
Skew Back. 
No. 1 Neck 
No. 2 " 
No. 3 " 
Feather Edge 
Jamb .... 
Bullhead . 
Edge Arch 



I 



41/2 

2 





,63/4 

'63/4 
41/2 
41/2 
41/2 
41/2 
41/2 
41/2 
41/2 
41/2 
41/2 
41/2 
41/2 
41/9 
41/2 
41/2 
41/2 
41/2 
41/2 
41/2 



4 

31/2 

3 

21/4 



11/2 



Circle Brick, Curved Edges. 



No. 1 . 
No. 2. 
No. 3. 
No. 4. 
No. 5. 

Cupola Blocks. 
No. 1 
No. 2 
No. 3 
No. 4 



81 /2 

9 
9 
9 
9 



51/4 
69/ic 

73/16 
79/16 



41 '0 , 

41/2,. 

41/2L 
41/2. 
41/2I. 



21/2 
21/2 

21/2 

21/2 
21/2 
21/2 
21/2 
21/2 
21/2 
21/2 
21/2 
21/2 
21/2 

21/2 

21/2 
21/2 
21/2 
21/2 

3 

21/; 

21/2 

21/2 
21/2 
21/2 
21/2 



17/8 


102 


60 


11/? 


63 


30 


2 


102 


60 


11/2 


63 
112 
65 
41 
26 


30 
144 
72 
36 
18 


2 


72 


48 


11/2 


42 


24 






























fi/g 






1/8 










2 




36 



9 


63/8 


6 .... 


4 




15 


9 


63/4 


6 .... 


4 




17 


9 


71/8 


6 .... 


4 




21 


9 


71/2 


6 .... 


4 




52 



NO. 3 JAMB *Tapers lengthwise. tTapers breadthwise. 

Other special shapes of brick and tile manufactured are: Locomo- 
tive tile, 32. 34, and 40 in. X 10 in. X 3 in. ; 34 and 36 in. X 8 in. X 3 in. 
Blast Furnace Shapes, 13 H X 6 X 2 M in. straight; No. 1, 12 ft. Key 



NUMBER OF FIRE BRICK FOR CIRCLES. 



267 



13 1^X6X5X2^ in. thick, 91 brick to circle; No. 2, 6 ft. Key 
13 34 X 6 X 43/8 X 2 3^4 in. thick, 53 brick to circle; bottom blocks, 
18 X 9 X 4 1/^ in. straight. Standard Block Linings, 9X9, 12 x 9, 
15 X 9, 18 X 9, all 4 M in. thick, made straight, and as key-brick 
for use with straight brick to line any diameter of furnace ; the key- 
bricks are made for radii of 5, 7 >^, and 10 ft. Pottery Kiln Brick, 
flat back, 9X6 X 2 32 in.; flat back arch, 9 X 6 X 3 34 X 2 32 in.; 
56 brick to a 32-inch inside diam. circle, No. 2 flat back arch, 9X6 
X 3 34 X 2 in., 31 brick to a 22-inch inside diam. circle. 

A straight 9-inch fire-brick weighs 7 lbs., a silica brick, 6.2 lbs.; a 
magnesia brick, 9 lbs.; a chrome brick, 10 lbs. A siUca brick expands 
about 1 8 inch per foot when heated to 2,500° F. 

Clay brick expand or shrink, dependent upon the proportion of 
silica to alumina contained in the brick; but most fire clay brick 
contain alumina sufficient to show some shrinkage. 

One cubic foot of wall requires 17. 9-inch bricks; one cubic yard, 
requires 460. Whers keys, wedges, and other "shapes" are used, add 
10 per cent, in estimating the number required. 

To secure the best results, fire-brick should be laid in the same clay 
from which they are manufactured. One ton of ground clay should 
be sufficient to lay 3,009 ordinary bricks. It should be used as a 
thin paste and not as mortar. The thinner the joint the better the 
furnace wall. In ordering bricks, the service for which they are to be 
used should be stated. 

Silica brick should be laid in silica cement and with the smallest 
joint possible. 

Ground fire-brick or old cupola blocks mixed with fire-clay make 
the best cupola daub known. 



NUMBER OF FIRE-BRICK REQUIRED FOR VARIOUS 
CIRCLES. 



Diam. 




Key Bricks. 






Arch Bricks. 




V\'edge Bricks. 


of 
Circle. 


d 


d 


d 


d 

12; 





r4 

d 


d 







d 


^ 


.s 


i 


fr. in. 
] 6 


25 
17 
9 








23 
30 
34 
38 
42 
46 
51 
55 
59 
63 
67 
71 
76 
80 
84 
88 
92 
97 
101 
105 
109 
113 
117 


















2 


13 
25 
38 
32 
25 
19 
13 
6 






42 
31 
21 
10 

.... 






42 
49 
57 
64 
72 
80 
87 
95 
102 
110 
117 
125 
132 
140 
147 
155 
162 
170 
177 
185 
193 










2 6 






18 
36 
54 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 
72 


"8" 

15 

23 

30 

38 

45 

53 

60 

68 

75 

83 

90 

98 

105 ■ 
113 
121 


60 
43 
36 
24 
12 






60 


3 






20 
40 
59 
79 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 
98 


15 
23 
30 
38 
46 
53 
61 
68 
76 
83 
91 
98 
106 


68 


3 6 

4 

4 6 

5 

5 6 

6 


10 

21 
32 
42 
53 
63 
58 
52 
47 
42 
37 
31 
26 
21 
16 
11 
5 


•••9 • 

19 

29 

38 

47 

57 

66 

76 

85 

94 
104 
113 
113 


76 
83 
91 
98 
106 
113 


6 6 






121 


7 






128 


7 6 






136 


8 






144 


8 6 






151 


9 






159 


9 6 






166 


10 






174 


10 6 






181 


II 






189 


11 6 






196 


12 






204 


12 6 



































For larger circles than 12 feet use 113 No. 1 Key, and as many 9-inch 
brick as may be needed in addition. 



268 



MATERIALS. 



Refractoriness of Some American Fire-Brick.— (R. F. Weber, 
A. I. M. E., 1904.) Prof. Heinrich Ries notes that the fusibility of New 
Jersey brick is influenced largely by its percentage of silica, but also in 
part by the texture of the clay. It was found that the fustion-point of 
almost any of the New Jersey fire-bricks could be reduced four or five 
Seger cones by grinding the brick sufficiently fine to pass through a 
700-mesh sieve. 

Mr. Weber draws the conclusion from his tests of 44 bricks that it is 
evident that the refractoriness of a fire-brick depends on the total quan- 
tity of fluxes present, the silica percentage and the coarseness of grain; 
moreover, chemical analysis alone cannot be used as an index of the 
refractoriness except within rather wide limits. The following table 
shows the composition, fusion-point, and physical properties of six 
most refractory and of five least refractory of the 44 bricks. 



J5 


Locality. 


Si02. 


AI2O3. 


Fe203. 


Ti02. 


< 


si 




1.... 


Missouri 


Per 

cent. 

51.59 

54.90 

53.05 

93.57 

44.77 

68.70 

61.28 

74.83 

67.19 

60.76 

60.58 


Per 
cent. 
38.26 
38.19 
41.16 
2.53 
43.08 
20.75 
27.13 
16.40 
25.05 
31.66 
32.49 


Per 

cent. 
1.84 
2.18 
2.65 
0.62 
2.78 
1.20 
2.90 
3.25 
2.83 
5.67 
2.25 


Per 

cent. 

1.97 

1.55 

1.80 

0.27 

2.54 

5.54 

1.37 

0.77 

0.71 

1.58 

1.69 


Per 

cent. 

6.34 

3.18 

1.34 

3.01 

6.83 

3.81 

7.31 

4.74 

4.22 

0.33 

2.99 


Per 
cent. 
10.25 
6.91 
5.79 
3.90 
12.15 
10.55 
11.58 
8.77 
7.76 
7.58 
6.93 


No. 
32 to 33 


2 ... 


Kentucky 


32 to 33 


3.... 
4 ... 


Pennsylvania 

Colorado 


32 to 33 
32 to 33 


5.... 


Kentucky 


31 to 32 


6 


New York 


31 to 32 


40.... 
41.... 
42.... 


Pennsylvania 

Pennsylvania 

Alabama 


26 
26 
26 


43 


Indiana . . . 


26 


44.... 


Kentucky 


26 



1 Fairly uniform, angular flint-clay particles, constituting body of 
brick. Largest pieces 5 to 6 mm. in diameter. White. 

2 Coarse-grained ; angular pieces of flint-clay as large as 9 mm. Aver- 
age 4 to 5 mm. Light buff. 

3 Coarse, angular flint-clay particles, varying from 1 to 5 mm. in 
diameter. Average 4 to 5 mm. Buff. 

< Fine-grained quartz particles. Largest 2 to 3 mm. in diameter. 
White. 

6 Medium grain; flint-clay particles, fairly uniform in size, 3 to 4 mm. 
Light buff. 

^ Coarse grain; quartz particles, 4 to 5 mm. in diameter, forming 
about 50 per cent of brick. White. 

*o Fine grain; small, white flint-clay particles, not over 2 mm. in 
diameter and not abundant. Buff. 

^ Medium grain; pieces of quartz with pinkish color and angular flint- 
clay particles. About 3 mm. in diameter. Buff. 

*2 Fine grain; even texture. Few coarse particles. Brown. 

^3 Fine grain; some particles as large as 1 to 2 mm. in diameter. Buff. 

4^ Angular, dark-colored, flinty-clay particles. Maximum size 5 mm. 
Throughout a reddish-brown matrix. 



SliAG BRICKS AND SI.AG BLOCKS. 

Slag bricks are made by mixing granulated basic slag and slaked lime, 
molding the mixture in a brick press or by hand, and drving. The silica 
in the slag ranges from 22.5% to 35%; the alumina and iron oxide together, 
from 16.1% to 21%; the hme, from 40% to 51.5%. The granulated slag 
IS dried and pulverized. Powdered slaked lime is added in sufficient auan- 



ANALYSES OP PIBE CLAYS. 



269 



tity to bring the total calcium oxide in the mixture up to about 55%. 
Usually a small amount of water is added. The mixture is then molded 
into shape, and the bricks are then dried for six to ten days in the open 
air. Slag bricks weigh less than clay bricks of equal size, require less 
mortar in laying up, and are at least equal to them in crushing strength. 

Slag blocks are made by running molten slag direct from the furnaces 
into molds. If properly made, they are stronger than slag bricks. They 
are, however, impervious to air and moisture; and on that account 
dwellings constructed of them are apt to be damp. Their chief uses are 
for foundations or for paving blocks. The properties required in a slag 
paving block, viz: density, resistance to abrasion, toughness, and rough- 
ness of surface, vary with the chemical composition of the slag, the 
rapidity of cooling, and the character of the molds used. Blocks cast in 
sand molds, and heavily covered with loose sand, cool slowly, and give 
much better results than those cast in iron molds. — E. C. Eckel. Ena, 
News, April 30, 1903. 

ANALYSES OF FIRE CLAYS. 





< 


O 


-T 


flT 


^9 

o 


O 


cf 


9. 


9, 


Bi 




Brand. 


'SO 


1 


.So 

< 




O 


1 


So 

s to 


1 

o 

P4 






2 


Mt. Savagei . . . 




50.46 


35.90 


12.744 


1.50 


0.13 


0.02 


Trace 


1.65 




Mt. Savage2 . . . 


1.15 
1.53 


56.80 
44.40 


30.08 
33.56 


10.50 
14.575 


1.12 
1.08 






0.80 
0.247 


1.92 
1.47 




Mt. Savage^. . . 


Tr. 


0.11 




Mt. Savage^ . . . 


.... 


56.15 


33.30 


9.68 


0.59 


0.17 


0.12 






0.88 




Strasburg, O . . . 


0.45 


55.87 


41.39 




1.60 


0.40 


0.30 


0.29 


0.20 


2.79 




Cumberland, Md 


1.15 


56.80 


30.08 


7.69 


1.67 






2.30 




3.97 




Woodbridge,NJ 




67.84 


21.83 


5.98 


1.57 


0.28 


6.24 


2.24 




4.33 




Carter Co., Ky. 




68.01 


24.09 


3.03 


1.01 


3.01 








4.02 




Clearfield Co.,Pa 




48.35 


36.37 


10.56 


2.00 


0.07 


0.12 


2.54 


4.73 




Clearfield^ and 




44.80 


39.00 


14.70 


0.30 


0.20 


1.00 








Cambria Cos., 








Pa.6 




51.50 
63.18 


44.85 
23.70 


1.94 
6.87 


0.33 
1.20 


0.23 
0.17 


1.15 
0.47 








Clinton Co., Pa. 


1.46 


2.52 


4.55 


SO2O.19 


Clarion Co., Pa. 


1.02 


44.61 


38.01 


13.63 


1.25 


0.08 


0.41 


1.74 


3.47 




FarrandsvillePa 




45.26 


37.85 


13.30 


2.03 


0.08 


0.02 


1.26 


3.59 


0.20 


St.LouisCo.,Mo 




67.47 


19.33 


10.45 


2.56 


0.41 


0.07 


1.07 


5.14 




Gottwerth, Aus. 




65.60 


20.75 


11.00 


2.00 


1.65 


Tr. 


Tr. 




'3.65 


Stourbridge, En. 




73.82 


15.88 


6.45 


2.95 


Tr. 


Tr. 


0.90 


3.85 




Glenboig, Scot. 


1.33 


65.41 


30.55 




1.70 








3.58 




La Bouchade,Fr 




53.40 


26.40 


12.00 


4.20 


0.69 


0.64 


0.55 


4.20 




Coblentz, Ger. 




55.46 


31.74 


9.37 


0.59 


0.19 


0.14 


2.49 


0.68 


4.09 




Diesdorf, Rhine- 
























land 




73.71 
67.12 


18.33 


5.17 


0.89 
1.85 


Tr. 
0.32 


0.10 
0.84 


2.12 
2.02 


0.24 


3.85 
5.93 




Dowlair, Wales. 




21.18 


6.21 


0.90 



1 Mass. Inst, of Technology, 1871. 2 Report on Clays of New Jersey. 
Prof. G. H. Cook, 1877. 3 Second Geological Survey of Penna., 1878. 
4 Dr. Gtto Wuth (2 samples), 1885. ^ Flint clay from Clearfield and 
Cambria counties, Pa., average of himdreds of analyses by Harbison- 
Walker Refractories Co., Pittsburg, Pa. ^ Same material calcined. 
All other analyses from catalogue of Stowe-FuUer Co., 1914. 



MAGNESIA BRICKS. 

"Foreign Abstracts" of the Institution of Civil Engineers, 1893, gives a 
paper by C. Bischof on the production of magnesia bricks. The material 
most in favor at present is the magnesite of Styria, which, although less 
pure considered as a source of magnesia than the Greek, has the property 
of fritting at a high temperature without melting. 

At a red heat magnesium carbonate is decomposed into carbonic acid 
and caustic magnesia, which resembles lime in becoming hydrated and 



270 MATERIALS. 

recarbonated when exposed to the air, and possesses a certain plasticity, 

so that it can be moulaed when subjected to a heavy pressure. By long- 
continued or stronger heating the material becomes dead-burnt, giving a 
form of magnesia of high density, sp. gr. 3.8, as compared with 3.0 in the 
plastic form, which is unalterable in the air but devoid of plasticity. A 
mixture of two volumes of dead-burnt with one of plastic magnesia can 
be moulded into bricks which contract but little in firing. Other binding 
materials that have been used are: clay up to 10 or 15 per cent; gas-tar, 
perfectly freed from water, soda, silica, vinegar as a solution of magnesium 
acetate which is readily decomposed by heat, and carbolates of alkalies 
or lime. Among magnesium compounds a weak solution of magnesium 
cliloride may also be used. For setting the bricks lightly burnt, caustic 
magnesia, with a small proportion of siUca to render it less refractory, is 
recommended. The strength of the bricks may be increased by adding 
iron, either as oxide or silicate. If a porous product is required, sawdust 
or starch may be added to the mixture. When dead-burnt magnesia is 
used alone, soda is said to be the best binding material. See also papers 
by A. E. Hunt, Trans. A. I. M. E,, xvi, 720, and by T. Egleston, Trans, 
A.I. M. E., xiv, 458. 

The average composition of magnesite, crude and calcined, is given as 
follows by the Harbison-Walker Refractories Co., Pittsburg (1907). 

Grecian. Styrian. 

Crude. Calcined. Crude. Calcined. 

Carbonate of magnesia 97.00% 92.50% 

Magnesia 94.00% 85.50% 

Silica 1.25 2.75 1.50 3.00 

Alumina 0.40 0.70 0.50 1.00 

Iron Oxide 0.40 0.80 3.90 8.00 

Lime 0.75 1.50 1.25 2.50 

Loss 0.40 0.50 

100.05 100.15 99.65 100.50 

With the calcined Styrian magnesite of the above analysis it is not 
necessary to use a binder either for making brick or for forming the 
bottom of an open-hearth furnace. 

ZmCONLi. 

Zirconiaore (84.1 Zr02; 7.74 Si02; 3.10Fe2O3: 1.21 TiOa; O.66AI2O3: 
loss on ignition 2.72) vitrifies slightly at 1830° C. (3326° F). Mixed with 
different percentages of clay and molded into cones it vitrifies at some- 
what lower temperatures. A zirconia brick containing 5% clay be- 
came plastic on its face at 1800° C. (3272°F.). (H. Conrad Meyer, 
Met. c& Chem. Enp., Vol. xii. No. 12, 1914, Vol. xiii, No. 4, 1915; 
Circular of Foote Mineral Co., Philadelphia.) 

ASBESTOS. 
The following analyses of asbestos are given'by J. T. Donald, Eng, and 
M. Jour., June 27, 1891. 

Canadian. 
ItaHan. Broughton. Templeton. 

Silica 40.30% 40.57% 40.52% 

Magnesia 43.37 41.50 42.05 

Ferrous oxide .87 2.81 1.97 

Alumina 2.27 .90 2.10 

Water 13.72 13.55 13.46 

100.53 99.33 100.10 

Chemical analysis throws light upon an important point in connection 
with asbestos, i.e., the cause of the harshness of the fibre of some varieties. 
Asbestos is principally a hydrous silicate of magnesia, i.e., siUcate of mag- 
nesia combined with water. When harsh fibre is analyzed it is found to 
contain less water than the soft fibre. In fibre of very fine quaUty from 
Black Lake analysis showed 14.38% of water, while a harsh-fibred sample 
gave only 11.70%. If soft fibre be heated to a temperature that will drive 
off a portion of the combined water, there results a substance so brittle 
that it may be crumbled between thumb and finger. There is evidently 
some connection between the consistency of the fibre and the amount oj 
water in its composition, 



STANDARD CROSS SECTIONS. 

Recommended by a Committee of the Am. Soc. M, E., 1912. 



^71 




Cast Iron Wroug-ht Iron Cast Steel Wrought Steel 






'/w//'//\ 


/ //^/ /X-y 


////////// 


/ X ^ / ^X/ X X 


■"^'^///V' 




Babbitt or 
^yhite Metal 




Copper, Brass 
or Composition 



Aluminum Rubber, Vulcanite 
or Insulation 




Glass 



Wood 



Water 



Puddle 



Pr\ ^ .n. d 



^ 



tztt: 






Concrete 



Brick 



Coursed Uncoursed 

Rubble 



Ashlar 




Wrought Steel Nickel Steel 



Chrome Steel Vanadium Steel 



X6v 


x^ 


yxS\ 


:-:a>:. 


"•^V 


:C$X 


$X: 


■^^^ 




:^XSX 







^^^ 



tSife'X;^- 



':t^- 



-^lMS 



Concrete 






■; ::y--.v<?:/; 



WfS, 



Concrete Blocks 



Cyclopean 
Concrete 



Expanded Wire or 
Metal Rods 

Reinforced Concrete 



272 STRENGTH OF MATERIALS. 



STRENGTH OP MATERIALS. 

stress and Strain. — There is much confusion among writers on 
strength of materials as to the definition of these terms. An external 
force applied to a body, so as to pull it apart, is resisted by an internal 
force, or resistance, and the action of these forces causes a displacement 
of the molecules, or deformation. By some writers the external force is 
called a stress, and the internal force a strain; others call the external 
force a strain, and the internal force a stress; this confusion of terms is 
not of importance, as the words stress and strain are quite commonly 
used synonymously, but the use of the word strain to mean molecular 
displacement, deformation, or distortion, as is the custom of some, is a 
corruption of the language. See Engineering News, June 23, 1892. 
Some authors in order to avoid confusion never use the word strain in 
their writings. Definitions by leading authorities are given below. 

Stress. — A stress is a force which acts in the interior of a body, and 
resists the external forces which tend to change its shape. A deformation 
is the amount of change of shape of a body caused by the stress. The 
word strain is often used as synonymous with stress, and sometimes it is 
also used to designate the deformation. (Merriman.) 

The force by which the molecules of a body resist a strain at any point 
is called the stress at that point. 

The summation of the displacements of the molecules of a body for a 
given point is called the distortion or strain at the point considered. 
(Burr.) 

Stresses are the forces which are applied to bodies to bring into action 
their elastic and cohesive properties. These forces cause alterations of 
the forms of the bodies upon which they act. Strain is a name given to 
the kind of alteration produced by the stresses. The distinction between 
stress and strain is not always observed, one being used for the other. 
(Wood.) 

The use of the word stress as synonymous with " stress per square inch," 
or with "strength per square inch," should be condemned as lacking in 
precision. 

Stresses are of different kinds, viz.: tensile, compressive, transverse, tor- 
sional, and shearing stresses. 

A tensile stress, or pull, is a force tending to elongate a piece. A com- 
pressive stress, or push, is a force tending to shorten it. A transverse stress 
tends to bend it. A torsional stress tends to twist it. A shearing stress 
tends to force one part of it to slide over the adjacent part. 

Tensile, compressive, and shearing stresses are called simple stresses. 
Transverse stress is compounded of tensile and compressive stresses, and 
torsional of tensile and shearing stresses. 

To these five varieties of stresses might be added tearing stress, which is 
either tensile or shearing, but in which the resistance of different portions 
of the material are brought into play in detail, or one after the other, 
instead of simultaneously, as in the simple stresses. 

Effects of Stresses. — The following general laws for cases of simple 
tension or compression have been established by experiment (Merriman): 

1. When a small stress is applied to a body, a small deformation is pro- 
duced, and on the removal of the stress the body springs back to its original 
form. For small stresses, then, materials may be regarded as perfectly 
elastic. 

2. Under small stresses the deformations are approximately proportional 
to the forces or stresses which produce them, and also approximately pro- 
portional to the length of the bar or body. 

3. When the stress is great enough a deformation is produced which is 
partly permanent, that is, the body does not spring back entirely to its 
original form on removal of the stress. This permanent part is termed a 
set. In such cases the deformations are not proportional to the stress. 

4. When the stress is greater still the deformation rapidly increases and 
the body finally ruptures. 

5. A sudden stress, or shock, is more injurious than a steady stress or 
than a stress gradually applied. 



ELASTIC LIMIT AND YIELD POINT. 273 

Elastic Limit. — The elastic limit is defined as that load at which 
the deformations cease to be proportional to the stresses, or at which 
the rate of stretch (or other deformation) begins to increase. It is also 
defined as the load at which a permanent set first becomes visible. The 
last definition is not considered as good as the first, as it is found that with 
some materials a set occurs with any load, no matter how small, and that 
with others a set which might be caUed permanent vanishes with lapse of 
time, and as it is impossible to get the point of first set without removing 
the whole load after each increase of load, which is frequently inconven- 
ient. The elastic limit, defined, however, as that stress at which the 
extensions begin to increase at a higher rate than the applied stresses, 
usually corresponds very nearly with the point of first measurable per- 
manent set. 

Apparent Elastic Limit. — Prof. J. B. Johnson (Materials of Con- 
struction, p. 19) defines the " apparent elastic limit " as " the point on the 
stress diagram [a plotted diagram in which the ordinates represent loads 
and the abscissas the corresponding elongations] at which the rate of 
deformation is 50% greater than it is at the origin," [the minimum rate]. 
An equivalent definition, proposed by the author, is that point at which 
the modulus of extension (length X increment of load per unit of section 
-^ increment of elongation) is two thirds of the maximum. For steel, 
with a modulus of elasticity of 30,000,000, this is equivalent to that 

f)oint at which the increase of elongation in an 8-inch specimen for 1000 
bs. per sq. in. increase of load is 0.0004 in. 

Yield-point. — The term yield-point has recently been introduced into 
the literature of the strength of materials. It is defined as that point at 
which the rate of stretch suddenly increases rapidly with no increase of 
the load. The difference between the elastic limit, strictly defined as 
the point at which the rate of stretch begins to increase, and the yield- 
point, may in some cases be considerable. This difference, however, will 
not be discovered in short test-pieces unless the readings of elongations 
are made by an exceedingly fine instrument, as a micrometer reading to 
0.0001 inch. In using a coarser instrument, such as calipers reading to 
1/100 of an inch, the elastic limit and the yield-point will appear to be 
simultaneous. Unfortunately for precision of language, the term yield- 
point was not introduced until long after the term elastic limit had been 
almost universally adopted to signify the same physical fact which is now 
defined by the term yield-point, that is, not the point at w^hich the first 
change in rate, observable only by a microscope, occurs, but that later 
point (more or less indefinite as to its precise position) at which the 
increase is great enough to be seen by the naked eye. A most convenient 
method of determining the point at which a sudden increase of rate of 
stretch occurs in short specimens, when a testing-machine in which the 
pulling is done by screws is used, is to note the weight on the beam at 
the instant that the beam "drops." During the earlier portion of the 
test, as the extension is steadily increased by the uniform but slow rota- 
tion of the screw^s, the poise is moved steadily along the beam to keep it 
in equipoise; suddenly a point is reached at which the beam drops, and 
will not rise until the elongation has been considerably increased by the 
further rotation of the screws, the advancing of the poise meanwhile 
being suspended. This point corresponds practically to the point at which 
the rate of elongation suddenly increases, and to the point at which 
an appreciable permanent set is first found. It is also the point 
which has hitherto been called in practice and in text-books the elastic 
limit, and it will probably continue to be so called, although the use of 
the newer term " yield-point " for it, and the restriction of the term elastic 
limit t-o mean the earlier point at which the rate of stretch begins to 
increase, as determinable only by micrometric measurements, is more 
precise and scientific. In order to obtain the yield-point by the drop of 
the beam with approximate accuracy, the screws of the testing machine 
must be run very slowly as the yield-point is approached, so as to cause 
an elongation of not more than, say, 0.005 in. per minute. 

In tables of strength of materials hereafter given, the term elastic limit 
is used in its customary meaning, the point at which the rate of stress has 
begun to increase as observable by ordinary instruments or by the drop of 
the beam. With this definition it is practically synonymous with yield- 
point. 



f 
274 STRENGTH OF MATERIALS. 

Coefficient (or Modulus) of Elasticity. — This is a term express- 
ing the relation between the amount of extension or compression of a mate- 
rial and the load producing that extension or compression. 

It is defined as the load per unit of section divided by the extension per 
tinit of length. 

Let P be the applied load, k the sectional area of the piece, I the length 
of the part extended, A the amount of the extension, and E the coefficient 
of elasticity. Then P ~ k = the load on a unit of section; \ -i- I = the 
elongation of a unit of length. 

k ' I k\ 

The coefficient of elasticity is sometimes defined as the figure express- 
ing the load which would be necessary to elongate a piece of one square 
inch section to double its original length, provided the piece woula not 
break, and the ratio of extension to the force producing it remained con- 
stant. This definition follows from the formula above given, thus: 
If k = one square inch, I and A each = one inch, then E = P. 

Within the elastic limit, when the deformations are proportional to the 
stresses, the coefficient of elasticity is constant, but beyond the elastic 
limit it decreases rapidly. 

In cast iron there is generally no apparent limit of elasticity, the defor- 
mations increasing at a faster rate than the stresses, and a permanent 
set being produced by small loads. The coefficient of elasticity therefore 
is not constant during any portion of a test, but grows smaller as the load 
increases. The same is true in the case of timber. In wrought iron and 
steel, however, there is a well-defined elastic limit, and the coefficient of 
elasticity within that limit is nearly constant. 

Resilience, or Work of Resistance of a Material. — Within the 
elastic limit, the resistance increasing uniformly from zero stress to the 
stress at the elastic limit, the work done by a load applied gradually is 
equal to one half the product of the final stress by the extension or other 
deformation. Beyond the elastic limit, the extensions increasing more 
rapidly than the loads, and the strain diagram (a plotted diagram showing 
the relation of extensions to stresses) approximating a parabolic form, the 
work is approximately equal to two thirds the product of the maximum 
stress by the extension. 

The amount of work required to break a bar, measured usually in inch- 
pounds, is called its resilience; the work required to strain it to the elastic 
limit is called its elastic resilience. (See below.) 

Under a load applied suddenly the momentary elastic distortion is 
equal to twice that caused by the same load applied gradually. 

When a solid material is exposed to percussive stress, as when a weight 
falls upon a beam transversely, the work of resistance is measured by the 
product of the weight into the total fall. 

Elastic Resilience. — In a rectangular beam tested by transverse 
stress, supported at the ends and loaded in the middle, 

in which, if P is the load in pounds at the elastic limit, R = the modulus of 
transverse strength, or the stress on the extreme fibre, at the elastic limit, 
E = modulus of elasticity, A = deflection, /, 6, and d = length, breadth, 
and depth in inches. Substituting for P in (2) its value in (1), A= 1/6 RP 
-i-Ed. 

The elastic resilience = half the product of the load and deflection = 
V2P ^, and the elastic resilience per cubic inch = 1/2 PA -r- Ibd. 

Substituting the values of P and A, this reduces to elastic resilience per 
1 R^ 
cubic inch = t-o tt , which is independent of the dimensions; and therefore 

lo ti 

the elastic resilience per cubic inch for transverse strain may be used as a 
modulus expressing one valuable quality of a material. 



e'levation of the elastic limit. 275 

Similarly for tension: Let P = tensile stress in pounds per square inch 
at the elastic limit; e = elongation per unit of length at the elastic limit 
E = modulus of elasticity = P -r- e; whence e = P ^ E 

1 P^ 

Then elastic resilience per cubic inch = 1/2 -P^ = 2 ^ 

Elevation of Ultimate Resistance and Elastic Limit. — It was 

first observed by Prof. R. H. Thurston, and Commander L. A, Beardslee, 
U.S. N., independently, in 1873, that if wrought iron be subjected to a 
stress beyond its elastic limit, but not beyond its ultimate resistance, and 
then allowed to "rest" for a definite interval of time a considerable 
increase of elastic limit and ultimate resistance may be e-xperienced. In 
other words, the application of stress and subsequent "rest" increases 
the resistance of wrought iron. This "rest" may be an entire release 
from stress or a simple holding the test-piece at a given intensity of 
stress. 

Commander Beardslee prepared twelve specimens and subjected them 
to a stress equal to the ultimate resistance of the mateiiaj. without 
breaking the specimens. These were then allowed to rest, entirely free 
from stress, from 24 to 30 hours, after which they were again stressed 
until broken. The gain in ultimate resistance by the rest was lound to 
vary from 4.4 to 17 per cent. 

This elevation of elastic and ultimate resistance appears to be peculiar 
to iron and steel; it has not been found in other metals. 

Relation of the Elastic Limit to Endurance under Repeated 
Stresses (condensed from Engineering, August 7, 1891). — When engi- 
neers first began to test materials, it w^as soon recognized that if a speci- 
men was loaded beyond a certain point it did not recover its original 
dimensions on removing the load, but took a permanent set; this point 
was caUed the elastic limit. Since below this point a bar appeared to 
recover completely its original form and dimensions on removing the 
loa,d, it appeared obvious that it had not been injured by the load, and 
hence the working load might be deduced from the elastic limit by using 
a small factor of safety. 

Experience showed, however, that in many cases a bar would not carry 
safely a stress anywhere near the elastic limit of the material as deter- 
mined by these e;cperiments, and the whole theory of any connection 
between the elastic limit of a bar and its working load became almost 
discredited, and engineers employed the ultimate strength only in deduc- 
ing the safe working load to which their structures might be subjected. 
Still, as experience accumulated it was observed that a higher factor of 
safety was required for a live load than for a dead one. 

In 1871 Wohler published the results of a number of experiments on 
bars of iron and steel subjected to live loads. In these experiments the 
stresses were put on and removed from the specimens without impact, 
but it was, nevertheless, found that the breaking stress of the materials 
was in every case much below the statical breaking load. Thus, a bar 
of Krupp's axle steel having a tenacity of 49 tons per square inch broke 
with a stress of 28.6 tons per square inch, when the load was completely 
removed and replaced without impact 170,000 times. These experiments 
were made on a large number of different brands of iron and steel, and 
the results w^ere concordant in showing that a bar would break with an 
alternating stress of only, say, one third the statical breaking strength of 
the material, if the repetitions of stress were sufficiently numerous. At 
the same time, how-ever, it appeared from the general trend of the experi- 
ments that a bar would stand an indefinite number of alternations of 
stress, provided the stress was kept below the limit. 

Prof. Bauschinger defines the elastic limit as the point at which stress 
ceases to be sensibly proportional to extension, the latter being measured 
with a mirror apparatus reading to 1/5000 of a millimetre, or about 
1/100000 in. This limit is always below the yield-point, and may on 
occasion be zero. On loading a bar above the yield-point, this point 
rises with the stress, and the rise continues for weeks, months, and 
possibly for years if the bar is left at rest under its load. On the otner 
hand, when a bar is loaded beyond its true elastic limit, but below its 
yield-point, this limit rises, but reaches a maximum as the yield -point is 
approached, and then falls rapidly, reaching even to zero. On leaving 
the bar at rest under a stress exceeding that of its primitive breaking- 



276 



STRENGTH OF MATERIALS. 



down point the elastic limit begins to rise again, and may, if left a suffi- 
cient time, rise to a point much exceeding its previous value. 

A bar has two limits of elasticity, one for tension and one for com- 
pression. Bauschinger loaded a number of bars in tension until stress 
ceased to be sensibly proportional to deformation. The load was then 
removed and the bar tested in compression until the elastic limit in this 
direction had been exceeded. This process raises the elastic limit in 
compression, as would be found on testing the bar in compression a second 
time. In place of this, however, it v/as now again tested in tension, when 
it was found that the artificial raising of the limit in compression had 
lowered that in tension below its previous value. By repeating the 
process of alternately testing in tension and compression, the two limits 
took up points at equal distances from the line of no load, both in tension 
and compression. These limits Bauschinger calls natural elastic limits 
of the bar, which for wrought iron correspond to a stress of about 8I/2 tons 
per square inch, but this is practically the limiting load to which a bar 
of the same material can be strained alternately in tension and com- 
pression, without breaking when the loading is repeated sufficiently often, 
as determined by Wohler's method. 

As received from the rolls the elastic limit of the bar in tension is above 
the natural elastic limit of the bar as defined by Bauschinger, having been 
artificially raised bj^ the deformations to which it has been subjected in 
the process of manufacture. Hence, when subjected to alternating 
stresses, the limit in tension is immediately lowered, while that in com- 
pression is raised until they both correspond to equal loads. Hence, in 
Wohler's experiments, in which the bars broke at loads nominally below 
the elastic limits of the material, there is every reason for concluding that 
the loads were really greater than true elastic limits of the material. 
This is confirmed by tests on the connecting-rods of engines, which work 
under alternating stresses of equal intensity. Careful experiments on 
old rods show that the elastic limit in compression is the same as that in 
tension, and that both are far below the tension elastic limit of the 
material as received from the rolls. 

The common opinion that straining a metal beyond its elastic limit 
injures it appears to be untrue. It is not the mere straining of a metal 
beyond one elastic limit that injures it, but the straining, many times 
repeated, beyond its two elastic limits. Sir Benjamin Baker has shown 
that in bending a shell plate for a boiler the metal is of necessity strained 
beyond its elastic limit, so that stresses of as much as 7 tons to 15 tons 
per square inch may obtain in it as it comes from the rolls, and unless the 
plate is annealed, these stresses will still exist after it has been built into 
the boiler. In such a case, however, when exposed to the additional 
stress due to the pressure inside the boiler, the overstrained portions of 
the plate will relieve themselves by stretching and taking a permanent 
set, so that probably after a year's working very little difference could be 
detected in the stresses in a plate built into the boiler as it came from the 
bending rolls, and in one which had been annealed, before riveting into 
place, and the first, in spite of its having been strained beyond its elastic 
limits, and not subsequently annealed, would be as strong as the other. 



Resistance of Metals to Repeated Shocks. 

More than twelve 3^ears were spent by Wohler at the instance of the 
Prussian Government in experimenting upon the resistance of iron and 
steel to repeated stresses. The results of his experiments are expressed 
in what is known as Wohler's law, which is given in the following words 
in Dubois's translation of Weyrauch: 

'* Rupture may be caused not only by a steady load which exceeds the 
carrying strength, but also by repeated applications of stresses, none of 
which are equal to the carrying strength. The differences of these stresses 
are measures of the disturbance of continuity, in so far as by their increase 
the minimum stress which is still necessary for rupture diminishes." 

A practical illustration of the meaning of the first portion of this law 
may be given thus: If 50,000 pounds once applied will just break a bar 
of iron or steel, a stress very much less than 50,000 pounds will break it 
if repeated sufficiently often. 



EFFECT OF VIBRATION AND LOAD. 277 

This is fully confirmed by the experiments of Fairbairn and Spangenberg, 
as well as those of Wohler; and, as is remarked by Weyrauch, it may be 
considered as a long-known result of common experience. It partially 
accounts for what Mr. Holley has called the "intrinsically ridiculous 
factor of safety of six." 

Another "long-known result of experience" is the fact that rupture may 
be caused by a succession of shocks or impacts, none of which alone would 
be sufficient to cause it. Iron axles, the piston-rods of steam hammers, 
and other pieces of metal subject to continuously repeated shocks, 
invariably break after a certain length of service. They have a "hfe" 
which is limited. 

Several years ago Fairbairn wrote: " We know that in some cases 
wrought iron subjected to continuous vibration assumes a crystalline 
structure, and that the cohesive powers are much deteriorated, but we 
are ignorant of the causes of this change." We are still ignorant, not 
only of the causes of this change, but of the conditions under which it 
takes place. Who knows whether wrought iron subjected to very slight 
continuous vibration will endure forever? or whether to insure final 
rupture each of the continuous small shocks must amount at least to a 
certain percentage of single heavy shock (both measured in foot-pounds), 
which would cause rupture with one application? Wohler found in test- 
ing iron by repeated stresses (not impacts) that in one case 400,000 
applications of a stress of 500 centners to the square inch caused rupture, 
while a similar bar remained sound after 48,000,000 applications of a 
stress of 300 centners to the square inch (1 centner = 110.2 lbs.). 

Who knows whether or not a similar law holds true in regard to repeated 
shocks? Suppose that a bar of iron would break under a single impact of 
1000 foot-pounds, how many times would it be hkely to bear the repetition 
of 100 foot-pounds, or would it be safe to allow it to remain for fifty years 
subjected to a continual succession of blows of even 10 foot-pounds each? 

Mr. William Metcalf published in the Metallurgical Review, Dec, 1877, 
the results of some tests of the life of steel of different percentages of 
carbon under impact. Some sm.all steel pitmans were made, the specifi- 
cations for which required that the unloaded machine should run 41/2 
hours at the rate of 1200 revolutions per minute before breaking. 

The steel was all of uniform quality, except as to carbon. Here are the 
results. The 

0.30 C. ran 1 h. 21 m. Heated and bent before breaking. 

0.49 C. " 1 h. 28 m. 

0.53 C. " 4 h. 57 m. Broke without heating. 

0.65 C. " 3 h. 50 m. Broke at weld where imperfect. 

0.80 C. " 5 h. 40 m. 

0.84 C. " 18 h. 

0.87 C. Broke in weld near the end. 

0.96 C. Ran 4.55 m., and the machine broke down. 

Some other experiments by Mr. Metcalf confirmed his conclusion, viz, 
that high-carbon steel was better adapted to resist repeated shocks and 
vibrations than low-carbon steel. 

These results, however, would scarcely be sufficient to induce any 
engineer to use 0.84 carbon steel in a car-axle or a bridge-rod. Further 
experiments are needed to confirm or overthrow them. 

(See description of proposed apparatus for such an investigation in the 
author's paper in Trans. A. L M. E., vol. viii, p. 76, from which the above 
extract is taken.) 

Effect of Vibration and Load on Steel. (Prof. P. R. Alger, U. S. 
Navy, U. S. Naval Inst. Proc, Dec. 1910.)— In 1883, or thereabouts, 
a test of the theory that guns are weakened by the shock and vibration 
of repeated firing was made at the AVashington Navy Yard as follows: 
Heavy weights, sufficient to strain the wire nearly to its elastic limit, 
were suspended by pieces of wire, and small hammers were arranged 
so that, actuated by the machinery of the shop, they struck the taut 
wires at regular and frequent intervals. After months of constant 
vibration, all the time under severe strain, the wires, when tested 
showed unchanged physical qualities. IVIoreover, every gun, army 
and navy, that has suffered accident, since we first began to build 



278 STRENGTH OF MATERIALS. 

steel guns, has had the metal of the part that failed tested, and never 
has there been a case when any material difference was found between 
the physical quahties shown by the last tests and those shown by the 
original tests for acceptance. One of these guns, a 12-in., had been 
fired 481 rounds when its muzzle was blown off. (The fact stated in 
the last sentence tends to confirm the " theory" that guns are weakened 
by repeated firing, although the weakening may not be discovered by 
physical tests.) 

Stresses Produced by Suddenly Applied Forces and Shocks. 

(Mansfield Merriman, R. R. & Eng. Jour., Dec, 1889.) 

Let P be the wei,^ht which is dropped from a height h upon the end of a 
bar, and let y be the maximum elongation which is produced. The work 
performed by the faUing weight, then, is TF = P{h + y), and this must 
equal the internal work of the resisting molecular stresses. The stress in 
the bar, which is at first 0, increases up to a certain hmit Q, which is 
greater than P; and if the elastic hmit be not exceeded the elongation 
increases uniformly with the stress, so that the internal work is equal to 
the mean stress 1/2 Q multiplied by the total elongation y, or Tf =1/2 QV* 
Whence, neglecting the work that may be dissipated in heat, 

1/2 Qy = Ph -h Py. 
If e be the elongation due to the static l oad P, within the elastic limit 
2/ = ^e; whence Q = P (l + y 1 + 2 -V which gives the momentary 
maximu m stres s. Substituting this value of Q, there results y = e 
(l + y 1 + 2 -j , which is the value of the momentary maximum elon- 
gation. 

A shock results when the force P, before its action on the bar, is moving 
with velocity, as is the case when a weight P falls from a height h. The 
above formulas show that this height h may be small if e is a small quan- 
tity, and yet very great stresses and deformations be produced. For 
instance, let h = 4e, then Q = 4P and ?/ = 4e; also let h = 12^, then 
Q = 6P and y = Qe. Or take a wrought-iron bar 1 in. square and 5 ft. 
long: under a steady load of 5000 lbs. this will be compressed about 0.012 
in., supposing that no lateral flexure occurs; but if a weight of 5000 lbs. 
drops upon its end from the small height of 0.048 in. there will be produced 
the stress of 20,000 lbs. 

A suddenly applied force is one which acts with the uniform intensity P 
upon the end of the bar, but which has no velocity before acting upon it. 
This corresponds to the case of /i = in the above formulas, and gives 
Q = 2P and ?/ = 2e for the maximum stress and maximum deforma- 
tion. Probably the action of a rapidly moving train upon a bridge 
produces stresses of this character. For a further discussion of this 
subject, in which the inertia of the bar is considered, see Merriman's 
Mechanics of Materials, 10th ed., 1908. 



TENSILE STRENGTH. 

The following data are usually obtained in testing by tension in a testing- 
machine a sample of a material of construction: 

The load and the amount of extension at the elastic limit. 

The maximum load applied before rupture. 

The elongation of the piece, measured between gauge-marks placed a 
stated distance apart before the test; and the reduction of area at the 
point of fracture. 

The load at the elastic hmit and the maximum load are recorded in 
pounds per square inch of the original area. The elongation is recorded 
as a percentage of the stated length between the gauge-marks, and the 
reduction of area as a percentage of the original area. The coefficient of 
elasticity is calculated from the ratio the extension within tUe elastic 



PRECAUTIONS IN MAKING TENSILE TESTS. 



279 



limit per inch of length bears to the load per square inch producing that 
extension. 

On account of the difficulty of making: accurate measurements of the 
fractured area of a test-piece, and of the fact that elongation is more 
valuable than reduction of area as a measure of ductility and of resilience 
or work of resistance before rupture, modern experimenters are abandoning 
the custom of reporting reduction of area. The data now calculated 
from th? results of a tensile test for commercial purposes are: 1. Tensile 
strength in pounds per square inch of original area. 2. Elongation per 
cent of a stated length between gauge-marks, usually 8 inches. 3. Elastic 
limit in pounds per square inch of original area. 

The short or grooved test specimen gives with most metals, especially 
with wrought iron and steel, an apparent tensile strength much higher 
than the real strength. This form of test-piece is now almost entirely 
abandoned. Pieces 2 in. in length between marks are used for forgings. 

The following results of the tests of six specimens from the same V4-in. 
steel bar illustrate the apparent elevation of elastic limit and the changes 
in other properties due to change in length of stems which were turned 
down in each specimen to 0.798 in. diameter. (Jas. E. Howard, Eng. 
Congress 1893, Section G.) 



Description of Stem. 



1.00 in. long 

0.50 in. long 

0.25 in. long 

Semicircular groove, 0.4 

in. radius 

Semicircular groove, Vs 

in. radius 

V-shaped groove 



Elastic Limit, 
Lbs. per Sq. In. 



64,900 
65,320 
68,000 

75,000 

86,000, about 
90,000, about 



Tensile Strength, 
Lbs. per Sq. In. 



94,400 
97,800 
102,420 

116,380 

134,960 
117,000 



Contraction of 
Area, per cent. 



49.0 
43.4 
39.6 

31.6 

23.0 
Indeterminate. 



Test plates made by the author in 1879 of straight and grooved test- 
pieces of boiler-plate steel cut from the same gave the following results: 

5 straight pieces, 56,605 to 59,012 lbs. T. S. Aver. 57,566 lbs. 

4 grooved " 64,341 to 67,400 " " '' 65,452 " 

Excess of the short or grooved specimen, 21 per cent, or 12,114 lbs. 

Measurement of Elongation. — In order to be able to compare 
records of elongation, it is necessary not only to have a uniform length of 
section between gauge-marks (say 8 inches), but to adopt a uniform 
method of measuring the elongation to compensate for the difference 
between the apparent elongation when the piece breaks near one of the 
gauge-marks, and when it breaks midway between them. The following 
method is recommended {Trans. A. S. M. E., vol. xi, p. 622): 

MarK on the specimen divisions of 1/2 inch each. After fracture measure 
from the point of fracture the length of 8 of the marked spaces on each 
fractured portion (or 7 + on one side and 8 + on the other if the fracture 
is not at one of the marks). The sum of these measurements, less 8 
inches, is the elongation of 8 inches of the original length. If the fracture 
is so near one end of the specimen that 7 + spaces are not left on the 
shorter portion, then take the measurement of as many spaces (with the 
L'actional part next to the fracture) as are left, and for the spaces lacking 
add the measurement of as many corresponding spaces of the longer 
portion as are necessary to make the 7 -|- spaces. 

Precautions Required in making Tensile Tests. — The testing- 
machine itself should be tested, to determine whether its weighing 
apparatus is accurate, and whether it is so made and adjusted that 
m the test of a properly made specimen the line of strain of the testing- 
macliine is absolutely in line with the axis of the specimen. 



280 



STRENGTH OF MATERIALS. 



The specimen should be so shaped that it will not give an incorrect 
record of strength. . ^ ^ . ^, • u^ • u 

It should be of uniform minimum section for not less than eight inches 
of its length. Eight inches is the standard length for bars. For forgings 
and castings and in special cases shorter lengths are used; these show 
greater percentages of elongation, and the length between gauge marks 
should therefore always be stated in the record. 

Regard must be had to the time occupied in making tests of certain 
materials Wrought iron and soft steel can be made to show a higher 
than their actual apparent strength by keeping them under strain for & 
great length of time. , . ,.,,., ,_. r. n ^ 

In testing soft alloys, copper, tin, zmc, and the hke, which flow under 
constant strain, their highest apparent strength is obtained by testing 
them rapidly. In recording tests of such materials the length of time 
occupied in the test should be stated. , j. x • 

For very accurate measurements of elongation, corresponding to incre- 
ments of load during the tests, the electric contact micrometer, described 
in Trans A S. M. E., vol. vi. p. 479, will be found convenient. When 
readings of elongation are then taken during the test, a strain diagram 
may be plotted from the reading, which is useful in comparing the quali- 
ties of different specimens. Such strain diagrams are made automatically 
by the new Olsen testing-machine, described in Jour. Frank. Inst. 1891. 

The coefficient of elasticity should be deduced from measurement 
observed between fixed increments of load per unit section, say between 
2000 and 12,000 pounds per square inch or between 1000 and 11,000 
pounds instead of between and 10,000 pounds. 

Shapes of Specimens for Tensile Tests. — The shapes shown be- 
low were recommended by the author in 1882 when he was connected 
with the Pittsburgh Testing Laboratory. They are now in most general 
use; the earlier forms, with 5 inches or less in length between shoulders, 
being almost entirely abandoned. 




No. 1. Square or flat bar, as 
rolled. 



No. 2. Round bar, as rolled. 



No. 3. Standard shape for 
flats or squares. Fillets 
1/2 inch radius. 

No. 4. Standard shape for 
rounds. Fillets 1/2 inch 
radius. 

No. 5. Government shape 
formerly used for marine 
boiler-plates of iron. Not 
recommended, as results 
are generally in error. 



Increasing the Tensile Strength of Iron Bars by Twisting them. 

— Ernest L. Ransome of San Francisco obtained a patent, in 1888, for 
an "improvement in strengthening and testing wrought metal and steel 
rods or bars, consisting in twisting the same in a cold state. . . . Any 
defect in the lamination of the metal which would otherwise be concealed 
is revealed by twisting, and imperfections are shown at once. The 
treatment may be applied to bolts, suspension-rods or bars subjected to 
tensile strength of any description." ^ , . i 

Jesse J. Shuman (Am. See. Test. Mat., 1907) describes several series of 



COMPRESSIVE STRENGTH. 281 

experiments on the effect of twisting square steel bars. Following are 

some of the results: 

Soft Bessemer steel bars V2in. square. Tens. Strength, plain bar, 60,400, 

No. of turns per foot 3 43/4 5 53/4 57/8 

Yield point, lbs. per sq. in 65,600 72,400 84,800 84,000 80,800 

Ult. strength " " " " 83,200 89,600 92,000 90,000 88,800 

Elongation in 8 in., % 10 5.75 6.25 7.5 3.75 

Bessemer. 0.25 carbon, 1/2 in. sq. Tens, strength, plain bar, 75,000. 

No. of turns per foot 3 41/2 47/8 5 51/2 

Yield point, lbs. per sq. in 83,600 83,200 88,800 84,200 84,200 

Ult. strength " " " *' 99,600 99,200 104,000 102,000 100,800 

Elongation in 8 in., % 8 4.5 4 5.75 6 

Bars of each grade twisted off when given more turns than stated. 
Soft Bessemer, square bars, different sizes. 

Size, in. sq 1/4 ^/s V2 5/8 ^k 7/8 1 H/sHA 

No. of turns per ft 4 31/2 3 21/4 1 1/2 1 V4 1 7/8 8/4 

Yield point, increase %* 11182 64 83 85.5 77 82 64 59 

Ult. strength " %* 37 38.6 41 33.5 34.3 29.7 22.8 20.1 28.9 

* Average of two tests each. 

Mr. Schuman recommends that in twisting bars for reinforced concrete, 
in order not to be in danger of approaching the breaking point, the num- 
ber of turns should be about half the number at which the steel is at its 
maximum strength, which for Bessemer of about 60,000 lbs. tensile 
strength means one complete twist in 8 to 10 times the size of the bar. 

Steel bars strengthened by twisting are largely used in reinforced 
concrete. 

COMPRESSIVE STRENGTH. 

What is meant by the term "compressive strength" has not yet been 
settled by the authorities, and there exists more confusion in regard to 
this term than in regard to any other used by writers on strength of 
materials. The reason of this may be easily explained. The effect of a 
compressive stress upon a material varies with the nature of the material, 
and with the shape and size of the specimen tested. While the effect of a 
tensile stress is to produce rupture or separation of particles in the direc- 
tion of the line of strain, the effect of a compressive stress on a piece of 
material may be either to cause it to fly into splinters, to separate into 
two or more wedge-shaped pieces and fly apart, to bulge, buckle, or bend, 
or to flatten out and utterly resist rupture or separation of particles. A 
piece of speculum metal (copper 2, tin 1) under compressive stress will 
exhibit no change of appearance until rupture takes place, and then it 
will fly to pieces as suddenly as if blown apart by gunpowder. A piece 
of cast iron or of stone will generally split into wedge-shaped fragments. 
A piece of wrought iron will buckle or bend. A piece of wood or zinc 
may bulge, but its agtion will depend upon its shape and size. A piece 
of lead will flatten out and resist compression till the last degree; that is, 
the more it is compressed the greater becomes its resistance. 

Air and other gaseous bodies are compressible to any extent as long as 
they retain the gaseous condition. Water not confined in a vessel is com- 
pressed by its own weight to the thickness of a mere film, while when 
confined in a vessel it is almost incompressible. 

It is probable, although it has not been determined experimentally, 
that solid bodies when confined are at least as incompressible as water. 
When they are not confined, the effect of a compressive stress is not only 
to shorten them, but also to increase their lateral dimensions or bulge 
them. Lateral stresses are therefore induced by compressive stresses. 

The weight per square inch of original section required to produce any 
given amount or percentage of shortening of any material is not a constant 
quantity, but varies with both the length and the sectional area, with the 
shape of the sectional area, and with the relation of the area to the length. 
The "compressive strength" of a material, if this term be supposed to 
mean the weight in pounds per square inch necessary to cause ruoture, 
may vary with every size and shape of specimeD experimented upon. 



282 STRENGTH OF MATERIALS. 

Still more difficult would it be to state what is the "compressive strength" 
of a material which does not rupture at all, but flattens out. Suppose we 
are testing a cylinder of a soft metal like lead, two inches in length and 
one inch in diameter, a certain weight will shorten it one per cent, another 
weight ten per cent, another fifty per cent, but no weight that we can 
place upon it will rupture it, for it will flatten out to a thin sheet. What, 
then, is its compressive strength? Again, a similar cylinder of soft 
wrought iron would probably compress a few per cent, bulging evenly 
all around; it would then commence to bend, but at first the bend would 
be imperceptilbe to the eye and too small to be measured. Soon this 
bend would be great enough to be noticed, and finally the piece might be 
bent nearly double, or otherwise distorted. What is the "compressive 
strength" of this piece of iron? Is it the weight per square inch which 
compresses the piece one per cent or five per cent, that which causes the 
first bending (impossible to be discovered), or that which causes a per- 
ceptible bend? 

As showing the confusion concerning the definitions of compressive 
strength, the following statements from different authorities on the 
Btrength of wrought iron are of interest. 

Wood's Resistance of Materials states, "Comparatively few experiments 
have been made to determine how much wrought iron will sustain at the 
point of crushing. Hodgkinson gives 65,000, Rondulet 70,800, Weisbach 
72.000. Rankine 30,000 to 40,000. It is generally assumed that wrought 
iron will resist about two thirds as much crushing as to tension, but the 
experiments fail to give a very definite ratio." 

The following values, said to be deduced from the experiments of Major 
Wade, Hodgkinson, and Capt. Meigs, are given by Haswell: 



American wrought iron 127,720 lbs. 

'* (mean) 85,500 " 

English " •• I t^;2go:: 

Stoney states that the strength of short pillars of any given material, 
all having the same diameter, does not vary much, provided^the length of 
the piece is not less than one and does not exceed four or five diameters, 
and that the weight ^^ hich will just crush a short prism whose base equals 
one square inch, and whose height is not less than 1 to 1^^ and does not 
exceed 4 or 5 diameters, is called the crushing strength of the material. 
It would be well if experimenters would all agree upon some such defi- 
nition of the term "crushing strength," and insist that all experiments 
which are made for the purpose of testing the relative valuas of different 
materials in compression be made on specimens of exactly the same 
shape and size. An arbitrary size and shape should be assumed and 
agreed upon for this purpose. The size mentioned by Stoney is definite 
as regards area of section, viz., one square inch, but is indefinite as re- 
gards length, viz., from one to five diameters. In some metals a speci- 
men five diameters long would bend, and give a much lower apparent 
strength than a specimen having a length of one diameter. The words 
"will just crush" are also indefinite for ductile materials, in which the 
resistance increases without limit if the piece tested does not bend. In 
such cases the weight which causes a certain percentage of compression, 
as five, ten, or fifty per cent, should be assumed as the crushing strength. 

For future experiments on crushing strength three things are desir- 
able: First, an arbitrary standard shape and size of test specimen for 
comparison of all materials. Secondly, a standard limit of compression 
for ductile materials, which shall be considered equivalent to fracture 
in brittle materials. Thirdly, an accurate knowledge of the relation 
of the crushing strength of a specimen of standard shape and size to 
the crushing strength of specimens of all other shapes and sizes. The 
latter can only be secured by a very extensive and accurate series of 
experiments upon all kinds of materials, and on specimens of a great 
number of different shapes and sizes. 

The author proposes, as a standard shape and size, for a compressive 



COLUMNS, PILLARS, OR STRUTS. 283 

test specimen for all metals, a cylinder one inch in length, and one half 
square inch in sectional area, or 0.798 inch diameter; and for the limit 
of compression equivalent to fracture, ten per cent of the original length. 
The term " compressive strength," or " compressive strength of standard 
specimen," would then mean the weight per square inch required to 
fracture by compressive stress a cylinder one inch long and 0.798 inch 
diameter, or to reduce its length to 0.9 inch if fracture does not take 
place before that reduction in length is reached. If such a standard, or 
any standard size whatever, had been used by the earlier authorities on 
the strength of materials, we never would have had such discrepancies 
in their statements in regard to the compressive strength of wrought 
iron as those given above. 

The reasons why this particular size is recommended are: that the 
sectional area, one-half square inch, is as large as can be taken in the 
ordinary testing-machines of 100.000 pounds capacity, to include all 
the ordinary metals of construction, cast and wrought iron, and the 
softer steels; and that the length, one inch, is convenient for calcula- 
tion of percentage of compression. If the length were made two inches, 
many materials would bend in testing, and give incorrect results. Even 
in cast iron Hodgkinson found as the m.ean of several experiments on 
various grades, tested in specimens % inch in height, a compressive 
strength per square inch of 94,7:30 pounds, while the mean of the same 
number of specimens of the same irons tested in pieces li^ inches in 
height was only 88,800 pounds. The best size and shape of standard 
specimen should, however, be settled upon only after consultation and 
agreement among several authorities. 

The Committee on Standard Tests of the American Society of 'Me- 
chanical Engineers say (vol. xi, p. 624) : 

"Although compression tests have heretofore been made on diminu- 
tive sample pieces, it is highly desirable that tests be also made on long 
pieces from 10 to 20 diameters in length, corresponding more nearly with 
actual practice, in order that elastic strain and change of shape may be 
determined by using proper measuring apparatus. 

"The elastic limit, modulus or coefficient of elasticity, maximum and 
ultimate resistances, should be determined, as well as the increase of 
section at various points, viz., at bearing surfaces and at crippling point. 

"The use of long compression-test pieces is recommended, because the 
investigation of short cubes or cylinders has led to no direct application 
of the constants obtained by their use in computation of actual struc- 
tures, which have always been and are now designed according to em- 
pirical formulee obtained from a few tests of long columns." 

COLUMNS, PILLARS, OR STRUTS. 

Notation. — P = crushing weight in pounds; rf = exterior diameter 
in inches; a = area in square inches; L = length in feet: I = length in 
inches: S = compressive stress, lbs. per sq. in.; E = modulus of elasticity 
in tension or compression; r = least radius of gyration; <j>, an experimental 
coefficient. 

For a short column centrally loaded S = P/a, but for a long column 
which tends to bend under load, the stress on the concave side is greater^ 
and on the convex side less than P/a. 

Hodgkinson's Formula for Columns. 

Both ends rounded, the Both ends flat, the length 

T." ^ <? n 1 ^ length of the column of the column exceed- 

Kmdot Column. exceeding 15 times its ing 30 times its diam- 

diameter. eter. 



Solid cylindrical col-) p _ -i^ 3fiO ^^^^ 

umns of cast iron. . . ) ' L^'' 



Solid cylindrical col- 1 P_Q<5ft50^^^ 

umns of wrought iron ) ' L^ 

These formulae apply only in cases in which the length is so great that 



P - 98,920 jy^ 



//3'55 

P = 299,600 Vr 



284 



STRENGTH OF MATERIALS. 



the column breaks by bending and not by simple crushing. Hodgkinson's 
tests were made on small columns, and his results are not now con- 
sidered reliable. 

Euler's Formula for Long Columns. 

p/a = 7r2 E (r/0^ for columns with round or hinged ends. For columns 
with fixed ends, multiply by 4; with one end round and the other fixed, 
multiply by 21/4; for one end fixed and the other free, as a post set in the 
ground, divide by 4. P is the load which causes a slight deflection; a 
load greater than P will cause an increase of deflection until the column 
fails by bending. The formula is now little used. 

Christie's Tests (Trans. A. S. C. E. 1884: Merriman's Mechanics 
of Materials) . — About 300 tests of wrought-iron struts were made, the 
Quality of the iron being about as follows: tensile strength per sq. in., 
49,600 lbs., elastic Hmit 32,000 lbs., elongation 18% in 8 ins. 

The following table gives the average results. 



Ratio Ifr 
Length to 
Least Ra- 
dius of 
Gyration. 


Ultimate Load, P/a, in Pounds per Square Inch. 










Fixed Ends. 


Flat Ends. 


Hinged Ends. 


Round Ends. 


20 


46.000 


46.000 


46,000 


44,000 


40 


40.000 


40.000 


40.000 


36,500 


60 


36.000 


36.000 


36,000 


30,500 


80 


32.000 


32,000 


31,500 


25,000 


100 


30.000 


29,800 


28,000 


20,500 


120 


28.000 


26.300 


24,300 


16,500 


140 


25,500 


23.500 


21,000 


12,800 


160 


23.000 


20,000 


16,500 


9,500 


180 


20.000 


16.800 


12,800 


7,500 


200 


17,500 


14.500 


10,800 


6,000 


220 


15,000 


12.700 


8.800 


5,000 


240 


13,000 


11,200 


7,500 


4,300 


260 


11,000 


9.800 


6,500 


3,800 


280 


10.000 


• 8,500 


5,700 


3,200 


300 


9,000 


7,200 


5.000 


2,800 


320 


8,000 


6.000 


4.500 


2,500 


360 


6.500 


4,300 


3,500 


1,900 


400 


5,200 


3.000 


2.500 


1,500 



The results of Christie's tests agree with those computed by Euler's 
formula for round -end columns with llr between 150 and 400, but 
differ widely from them in shorter columns, and still more widely in 
columns with fixed ends. 

Rankine's Formula (sometimes called Gordon's), S = — (l +4> (- 

S 



Applying Rankine's formula to the results of 



P ^ 
^^ a 1+ ^ (l/r)^ 
experiments, wide variations are found in the values of the empirical 
coefficient <^. Merriman gives the following values, which are extensively 
employed in practice. 

Values of (f) for Rankine's Formula. 



Material. 


Both Ends 
Fixed. 


Fixed and 
Round. 


Both Ends 
Round. 


Timber 


1/3.000 
1 /5,000 
1/36.000 
1 /25,000 


1.78/3.000 
1.78/5,000 
1.78/36.000 
1.78/25.000 


4/3 000 


Cast Iron 


4/5 000 


Wrought Iron 


4/36 000 


Steel 


4/25,000 





The value to be taken for 5 is the ultimate compressive strength of the 



WORKING FORMULiE FOR STRUTS. 285 

material for cases of rupture, and the allowable compressive unit stress 
for cases of design. , o ^ , 

Burr gives the following values as commonly taken for S ana <f>. 

For solid wrought-iron columns, S = 36,000 to 40,000, ^ = 1/36,000 to 
1/40,000. 

For solid cast-iron columns. S = 80,000, <l> = 1/6,400. 

For hollow cast-iron columns, P/a = 80,000 -^ 1 +800 52^^"" outside 
diam. in inches). 

The coefficient of P/d"^ is given by different writers as 1/400, 1/500. 
1/600 and 1/800. (See Strength of Cast-iron Columns, below.) 

Sir Benjamin Baker gives for mild steel, *S = 67,000 lbs., = 1/22,400; 
for strong steel, S = 114,000 Ibs.,^ = 1/14,400. Prof. Burr considers 
these only loose approximations. (See Straight-line Formula, below). 

For dry timber, Rankine gives S = 7200 lbs., <^ = 1/3000. 

The Straight-line Formula. — The results of computations by Euler's 
or Rankine's formulas give a curved line when plotted on a diagram 
with values of l/r as abscissas and value of P/a as ordinates. The average 
results of experiments on columns within the limits of l/r commonly 
used in practice, say from 50 to 200, can be represented by a straight line 
about as accurately as by a curve. Formulas derived from such plotted 
lines, of the general form P/a = S — C l/r, in which C is an experimental 
coefficient, are in common use, but Merriman says it is advisable that the 
use of this formula should be limited to cases in which the specifications 
require it to be employed, and for rough approximate computations. 
Values of S and C given by T, H. Johnson are as follows: 

F H R F H R 

Wrought Iron: 

S =42,000 lbs., C = 128, 157, 203; limit of //r = 218, 178, 138 
Structural Steel: 

5=52,500" C = 179, 220, 284; " " " 195,159,123 
Cast Iron: *S =80,000 " C = 438, 537, 693; " " *' 122, 99, 77 
Oak, flat ends: 

S = 5,400 " C = 28: 128 

F, flat ends: H, hinged ends; R, round ends. 

Merriman says: "The straight-line formula is not suitable for investi- 
gating a column, that is for determining values of S due to given loads, 
because S enters the formula in such a manner as to lead to a cubic 
equation when it is the only unknown quantity. It may be used to find 
the safe load for a given column to withstand a given unit stress, or to 
design a column for a given load and unit stress. When so used, it is 
customary to divide the values of S and C given in the table by an 
assumed factor of safety. For example. Cooper's specifications require 
that the sectional area a for a medium-steel post of a through railroad 
bridge shall be found from P/a = 17,000 - 90 l/r lbs. per sq. in., in 
which P is the direct dead-load compression on the post plus twice the 
live-load compression; the values of S and C here used are a little less 
than one-third of those given in the table for round ends." 

Working Formulae for Wrought-iron and Steel Struts of Various 
Forms. — Burr gives the following practical formulae: 

p = Ultimate ^rveZTh"^^ 

Kind of Strut. Ibs^ ne^sn^'in ^/^ Ultimate, 

of Secti?)n ^bs- P^r sq. in. 

or bection. ^^ Section. 

Flat and fixed end iron angles and tees 44000 - 140 - (1) 8800-28- (2) 

Hinged-end iron angles and tees 46000 - 1 75 - (3) 9200 - 35 - (4) 

Flat-end iron channels and I-beams . . . 40000 - 1 10 - (5) 8000 - 22 - (6) 

r r 



286 



STRENGTH OF MATERIALS. 



Flat-end mild-steel angles 52000 - 180 - (7) 10400-36- (8) 

Flat-end high-steel angles 76000-290 ^ (9) 15200-58- (10) 



Pin-end solid wrought-iron columns . . . 32000 - 80 - 



6400 - 16 



32000 - 277 ^ J 6400 - 55^ J 

Equations (1) to (4) are to be used only between - =40 and - = 200 

r r 



(5) and (6) " •* 

'-) to (10) " " 

1) and (12) " " 



;; (7) to (loy 



" = 20 •• " = 200 
" = 40 " •' = 200 
" = 20 " " = 200 

or :5 = 6 and -^ = 65 

d d 



Comparison of Column Compression Formulae. — The Carnegie 
Steel Co. gives in its Pocket Companion (1913) a table comparing the 
allowable unit stresses in columns calculated from the formulae of the 
American Bridge Co., American Railway Engineering Association, 
Gordon, and the New York, Philadelpliia, and Boston Building Laws, 
for various values of l/r. The table below is condensed from this 
table and compares the values obtained by the American Bridge Co. 
formula with the average of all those, except that of the American 
Bridge Co. for values of l/r up to 120, and with the values obtained 
by Gordon's formula for values of l/r from 125 to 200. 





Allowable Unit Stresses — 


Pounds per Sq. In. 




l/r 


Am. Bridge 
Co. 


Average. 


l/r 


Am. Bridge 
Co. 


Average. 


l/r 


Am. Bridge 
Co. 


Gordon. 





14,000 


14,790 


65 


11,450 


11,803 


U5 


6,750 


8,715 


5 


1 4,000 


14,719 


70 


11,100 


11,466 


130 


6,500 


8,510 


10 


14,000 


14,620 


75 


10,750 


11,130 


135 


6,250 


8.300 


15 


14,000 


1 4,499 


80 


10,400 


10,794 


140 


6,000 


8,095 


20 


14,000 


14,355 


85 


10,050 


10,459 


145 


5,750 


7,890 


25 


14,000 


14,185 


90 


9,700 


10,127 


150 


5,500 


7,690 


30 


13,900 


13,977 


95 


9,350 


9,785 


155 


5,250 


7,495 


35 


13,550 


13,701 


100 


9,000 


9,473 


160 


5,000 


7,305 


40 


13,200 


13,410 


105 


8,650 


9,150 


165 


4,750 


7,120 


45 


12,850 


13,106 


110 


8,300 


8,837 


170 


4,500 


6,935 


50 


12,500 


12,790 


115 


7,950 


8,528 


180 


4,000 


6,580 


55 


12,150 


12,467 


120 


7,600 


8,221 


190 


3,500 


6,240 


60 


11,800 


12,137 








200 


3,000 


5,920 



Built Columns (Burr). — Steel columns, properly made, of steel 
ranging in specimens from 65,000 to 73,000 lbs. per square inch, should 
give a resistance 25 to 33 per cent in excess of that of wrought-iron 
columns with the same value ofl-i-r, provided that ratio does not exceed 
140. 

The unsupported width of a plate in a compression member should not 
exceed 30 times its thickness. 

In built columns the transverse distance between centre lines of rivets : 
securing plates to angles or channels, etc., should not exceed 35 times the 
plate thickness. If this width is exceeded, longitudinal buckling of the 
plate takes place, and the column ceases to fail as a whole, but yields in 
detail. 

The thickness of the leg of an angle to which latticing is riveted should 
not be less than 1/9 of the length of that leg or side if the column is purely 
a compression member. The above limit may be passed somewhat in stiff 
ties and compression members designed to carry transverse loads. 

The panel points of latticing should not be separated by a greater dis- 



working' strains allowed in bridge members. 287 

tance than 60 times the thickness of the angle-leg to which the latticing 
is riveted, if the column is wholly a compression member. 

The rivet pitch should never exceed 16 tim.es the thickness of the 
thinnest metal pierced by the rivet, and if the plates are very thick it 
should never nearly equal that value. 

Burr gives the following general principles which govern the resistance 
of built columns: 

The material should be disposed as far as possible from the neutral axis 
of the cross-section, thereby increasing r; 

There should be no initial internal stress; 

The individual portions of the column should be mutually supporting; 

The individual portions of the column should be so firmly secured to 
each other that no relative motion can take place, in order that the 
column may fail as a whole, thus maintaining the original value of r. 

Stoney says: "When the length of a rectangular wrought-iron tubular 
column does not exceed 30 times its least breadth, it fails by the bulging or 
buckling of a short portion of the plates, not by the flexure of the pillar 
as a whole." 

Tests of Five Large Built Steel Columns. {Proc. A. S. C. E., Feb.. 
1911; Eng. News, Mar. 16, 1911). — The lateral dimensions of the 
columns were about 20 X 30 in., and their sectional area 90 sq. in. 
They were made of two ribs 30 in. deep, spaced 207/8 in., laced by two 
lines of 2 1/2 X 3 g in. lacing. Each rib was made of an outside plate, 
30 Xii/ie in., and an inside plate, 17^2 X 5 g in., and two inner edging 
angles, 6 X 6 X ^ s in. Transverse plate diaphragms, 6 ft. apart, gave 
additional lateral rigidity. The test columns were fitted with 10-in. 
pins set parallel to the plane of the lacing. The columns were tested 
in the 1,200-ton hydraulic machine at Phoenixville, Pa.; tw^o of them 
(Nos. 1 and 2) did not reach failure. The results are as below: 

Section Length Max. Load Lb. per 

No. Area Sq. In. Ft. In. I r Lb. Sq. In. 

1 90.73 20 26.2 2.600,962 28,667 

2 90.33 36 5 47.2 2,600,962 28,794 

3 90.78 36 5 47.2 2,675,183 29,469 

4 90.32 36 5 47.2 2,726,815 30,191 

5 89.96 36 5 47.1 2,742,950 30,490 

Nos. 3 and 4 failed by bulging of plates in front of pins; No. 5 by 
web-plates bulging inward 12 1/2 in. from one end. The columns de- 
parted from strictly proportional compression at a load as low as 20,000 
lb. per sq. in. Plotted curves of the tests show that all the columns 
reached their elastic limit at about this figure, and an ultimate strength 
at about 30,000 lb. per sq. in. Eng. Neivs says that it does not appear 
that the lacing contributed to the failure. It shows that the com- 
pressive strength of these columns did not exceed 60 % of the tensile 
strength of the metal. 

WORKING STRAINS ALLOWED IN BRIDGE MEMBERS. 

Theodore Cooper gives the following in his Bridge Specifications: 
Compression members shall be so proportioned that the maximum load 
shall in no case cause a greater strain than that determined by the follow- 
ing formula: 



for square-end compression members; 



p 
p 


= 


1 


8000 


^ 40,000 r2 
8000 


1 


I ^' 


p 


' 30,000 r2 
8000 




1 


20,000 r^ 



for compression members with one pin and one square 

end; 

for compression members with pin-bearings; 



288 STRENGTH OF MATERIALS. 

(These values may be increased in bridges over 150 ft. span. See 
Cooper's Specifications.) 

P = the allowed compression per square inch of cross-section; 
I = the length of compression member, in inches; 
r = the least radius of gyration of the section in inches. 

No compression member, however, shall have a length exceeding 25 
times its least width. 

Tension Members. — All parts of the structure shall be so proportioned 
that the maximum loads shall in no case cause a greater tension than the 
following (except in spans exceeding 150 feet): 

Pounds per 
sq. in. 

On lateral bracing 15,000 

On solid rolled beams, used as cross floor-beams and stringers .... 9,000 

On bottom chords and main diagonals (forged eye-bars) 10,000 

On bottom chords and main diagonals (plates or shapes), net section 8,000 

On counter rods and long verticals (forged eye-bars) 8,000 

On counter and long verticals (plates or shapes), net section 6,500 

On bottom flange of riveted cross-girders, net section 8,000 

On bottom flange of riveted longitudinal plate girders over 20 ft. 

long, net section 8,000 

On bottom flange of riveted longitudinal plate girders under 20 ft. 

long, net section 7,000 

On floor-beam hangers, and other similar members liable to sudden 

loading (bar iron with forged ends) 6,000 

On floor-beam hangers, and other similar members liable to sudden 

loading (plates or shapes), net section 5,000 

Members subject to alternate strains of tension and compression shall be 
proportioned to resist each kind of strain. Both of the strains shall, how- 
ever, be considered as increased by an amount equal to 8/io of the least of 
the two strains, for determining the sectional area by the above allowed 
strains. 

The Phcenix Bridge Co. (Standard Specifications, 1895) gives the follow- 
ing: 

The greatest working stresses in pounds per square inch shall be as 
follows: 

Tension, 

Steel. Iron. 

P = 9,000 
P 



[ Min. stress "! For bars, p — j t^on f i -i- ^^"- stress "] 

Max. stressj forged ends. ~" ' L Max. stressj 

= 8.500 [l + Min^^ilSis] Plates or ^^^ r ^ Min. stress l 

L Max. stressj shapes net. L Max. stressj 



8,500 pounds. Floor-beam hangers, forged ends 7,000 pounds. 

7,500 " Floor-beam hangers, plates or shapes, net 

section 6,000 

10,000 '* Lower flanges of rolled beams 8,000 

20,000 " Outside fibres of pins 15,000 

30,000 " Pins for wind-bracing 22,500 

20,000 " Lateral bracing 15,000 

Shearing. 

9,000 pounds. Pins and rivets 7,500 pounds. 

Hand-driven rivets 20% less unit stresses. 
For bracing increase unit stresses 50%. 
6,000 pounds. Webs of plate girders 5,000 pounds. 

Bearing. 

16,000 pounds. Projection semi-intrados pins and rivets, 12,000 pounds. 
Hand -driven rivets 20% less unit stresses. For 
bracing increase unit stresses 50%. 



STRENGTH OF CAST-IRON COLUMNS. 289 

Comj/ression, 

Lengths less than forty times the least radius of gyration, P previously 
found. See Tension. 

Lengths more than forty times the least radius of gyration, P reduced 
by following formulae: 

p 

For both ends fixed, h = j^ 

^ "^ 36,000 r2 

P 

For one end hinged, h = y^ • 

1 + 

24,000 r2 

p 

For both ends hinged, h = t^ 

^ "^ 18,000 r2 

P = permissible stress previously found (see Tension); 6 = allowable 
working stress per square inch; I — length of member in inches; r = least 
radius of gyration of section in inches. No compression member, how- 
ever, shall have a length exceeding 45 times its least width. 

Pounds per 
sq. in. 

In counter w^eb members 10,500 

In long verticals 10,000 

In all main-web and lower-chord eye-bars 13,200 

In plate hangers (net section) 9,000 

In tension members of lateral and transverse bracing 19,000 

In steel-angle lateral ties (net section) 15,000 

For spans over 200 feet in length the greatest allowed working stresses 
per square inch, in lower-chord and end main-web eye-bars, shall be taken 
at 



10,000 (l + ^in- total stress x 
\ max. total stress/ 



whenever this quantity exceeds 13,200. 

The greatest allowable stress in the main-web eye-bars nearest the centre 
of such spans shall be taken at 13,200 pounds per square inch; and those 
for the intermediate eye-bars shall be found by direct interpolation 
between the preceding values. 

The greatest allowable working stresses in steel plate and lattice girders 
and rolled beams shall be taken as follows: 

Pounds per 
sq. in. 

Upper flange of plate girders (gross section) 10,000 

Lower flange of plate girders (net section) 10,000 

In counters and long verticals of lattice girders (net section) 9,000 
In lower chords and main diagonals of lattice girders (net 

section) 10,000 

In bottom flanges of rolled beams 10,000 

In top flanges of rolled beams 10,000 



THE STRENGTH OF CAST-IRON COLUMNS. 

Hodgkinson's experiments (first published in Phil. Trans. Royal Socy., 
1840, and condensed in Tredgold on Cast Iron, 4th ed., 1846), and Gordon's 
formula, based upon them, are still used (1898) in designing cast-iron col- 
umns. They are entirely inadequate as a basis of a practical formula 
suitable to the present methods of casting columns. 

Hodgkinson's experiments were made on nine "long" pillars, about 71/2 
ft. long, whose external diameters ranged from 1.74 to 2.23 in., and 
average thickness from 0.29 to 0.35 in., the thickness of each column also 
varying, and on 13 "short" pillars, 0.733 ft. to 2.251 ft. long, with exter- 



290 



STRENGTH OF MATERIALS. 



nal diameters from 1.08 to 1.26 in., all of them less than 1/4 in. thick. 
The iron used was Low Moor, Yorkshire, No. 3, said to be a good iron, not 
very hard, earlier experiments on which had given a tensile strength of 
14,535 and a crushing strength of 109.801 lbs. per sq. in. Modern cast- 
iron columns, such as are used in the construction of buildings, are very 
different in size, proportions, and quality of iron from the slender "long" 
pillars used in Hodgkinson's experiments. There is usually no check, by 
actual tests or by disinterested inspection, upon the quality of the material. 
The tensile, compressive, and transverse strength of cast iron varies 
through a great range (the tensile strength ranging from less than 10,000 
to over 40,000 lbs. per sq. in.), With variations in the chemical composition 
of the iron, according to laws which are as j^et very imperfectly under- 
stood, and With variations in the method of melting and of casting. 
There is also a wide variation in the strength of iron of the same melt 
when cast into bars of different thicknesses. 

Another difficulty in obtaining a practical formula for the strength of 
cast-iron columns is due to the uncertainty of the quality of the casting, 
and the danger of hidden defects, such as internal stresses due to unequal 
cooling, cinder or dirt, blow-holes, "cold-shuts," and cracks on the inner 
surface, which cannot be discovered by external inspection. Variation 
in thickness, due to rising of the core during casting, is also a common 
defect. 

In addition to these objections to the use of Gordon's formula, for cast- 
iron columns, we have the data of experiments on full-sized columns, 
made by the Building Department of New York City (Eng'g News, Jan. 13 
and 20, 1898). Ten columns in all were tested, six 15-inch, 1901/4 inches 
long, two 8-inch, 160 inches long, and two 6-inch, 120 inches long. The 
tests were made on the large hydraulic machine of the Phoenix Bridge Co., 
of 2,000,000 pounds capacity, which was calibrated for frictional error by 
the repeated testing within the elastic limit of a large Phoenix column, 
and the comparison of these tests with others made on the government 
machine at the Watertown Arsenal. The average frictional error was 
calculated to be 15.4 per cent, but Engineering News, revising the data, 
makes it 17.1 per cent, with a variation of 3 per cent either way from the 
average with different loads. The results of the tests of the columns are 
given below. 

TESTS OF CAST-IRON COLUMNS. 









Thickness. 


Breaking Load. 


Num- 
ber. 


Diam. 
Inches. 


























Max. 


Min. 


Average. 


Pounds. 


Pounds 
per Sq. In. 


1 


15 


1 




1 


1,356,000 


30,830 


2 


15 


15/16 




11/8 


1,330,000 


27,700 


3 


15 


11/4 




11/8 


1,198,000 


24,900 


4 


151/8 


17/32 




11/8 


1,246,000 


25,200 


5 


15 


1 11/16 




1 11/64 


1,632,000 


32,100 


6 


15 


11/4 


11/8 


13/16 


2,082. 000 -f 


40,400 + 


7 


7 3/4 to 8 1/4 


11/4 


5/8 


1 


651,000 


31,900 


8 


8 


13/32 




13/64 


612,800 


26,800 


9 


61/16 


15/32 


11/8 


19/64 


400.000 


22,700 


10 


63/32 


11/8 


11/16 


17/64 


455.200 


26.300 



Column No. 6 was not broken at the highest load of the testing 
machine. 

Columns Nos. 3 and 4 were taken from the Ireland Building, which 
collapsed on August 8, 1895; the other four 15-inch columns were made 
from drawings prepared by the Building Department, as nearly as possible 
duplicates of Nos. 3 and 4. Nos. 1 and 2 were made by a foundry in New 
York with no knowledge of their ultimate use. Nos. 5 and 6 were made 



SAFE LOADS FOft CAST-IRON COLUMNS. 



291 



by a foundry in Brooklyn with the knowledge that they were to be tested. 
Nos. 7 to 10 were made from drawings furnished by the Department. 
Applying Gordon's formula, as used by the Building Department, 

S — z — 72", to these columns gives for the breaking strength per square 

1 + -— — 
^ 400 d2 

inch of the 15-inch columns 57,143 pounds, for the 8-inch columns 40,000 

pounds, and for the 6-inch columns 40,000, The strength of columns Nos. 

3 and 4 as calculated is 128 per cent more than their actual strength; their 

actual strength is less than 44 per cent of their calculated strength; and 

the factor of safety, supposed to be 5 in the Building Law, is only 2.2 for 

central loading, no account being taken of the likelihood of eccentric 

loading. 

Prof. Lanza, Applied Mechanics, p. 372, quotes the records of 14 
tests of cast-iron mill columns, made on the Watertown testing-machine in 
1887-88, the breaking strength per square inch ranging from 25,100 to 
63,310 pounds, and showing no relation between the breaking strength 
per square inch and the dimensions of the columns. Only 3 of the 14 
columns had a strength exceeding 33,500 pounds per square inch. The 
average strength of the other 1 1 was 29,600 pounds per square inch. Prof. 
Lanza says that it is evident that in the case of such columns we cannot 
rely upon a crushing strength of greater than 25,000 or 30,000 pounds 
per square inch of area of section. 

He recommends a factor of safety of 5 or 6 with these figures for crush- 
ing strength, or 5000 pounds per square inch of area of section as the 
highest allowable safe load, and in addition makes the conditions that 
the length of the column shall not be greatly in excess of 20 times the 
diameter, that the thickness of the metal shall be such as to insure a good 
strong casting, and that the sectional area should be increased if necessary 
to insure that the extreme fibre stress due to probable eccentric loading 
shall not be greater than 5000 pounds per square inch. 

Prof. W. H. Burr (Eng'g News, June 30, 1898) gives a formula derived 
from plotting the results of the Watertown and Phoenixville tests, above 
described, which represents the average strength of the columns in pounds 
per square inch. It is p = 30,500 - 160 l/d. It is to be noted that this 
IS an average value, and that the actual strength of many of the columns 
was much lower. Prof. Burr says: "If cast-iron columns are designed 
with anything like a reasonable and real margin of safety, the amount of 
metal required dissipates any supposed economy over columns of mild 
steel." 

Square Columns. — Square cast-iron columns should be abandoned. 
They are liable to have serious internal strains from difference in con- 
traction on two adjacent sides. John F. Ward, Eng. News, Apr. 16, 1896. 

Safe Lioad, in Tons of 3000 Lbs., for Round Cast-iron Columns, 
with Turned Capitals and Bases. 

Loads being not eccentric, and length of column not exceeding 20 times 
the diameter. Based on ultimate crushing strength of 25,000 lbs. per 
sq. in. and a factor of safety of 5. 



Thick- 












Diameter, Inches. 










ness, 
Inches. 


6 


7 


8 


9 


10 

54.5 
62.7 
70.7 
78.4 
85.9 
93.1 


11 


13 


13 


14 


15 


16 


18 


5/8 

Vs 


26.4 
30.9 
35.2 
39.2 


31.3 
36.8 
42.1 
47.1 


42.7 
48.9 
55.0 
60.8 


48.6 
55.8 
62.8 
69.6 
76.1 


69.6 
78.5 
87.2 
95.7 
103.9 


76.5 
86.4 
96.1 
105.5 
114.7 
123.7 


94.2 
104.9 
115.3 
125.5 
135.5 


102.1 
113.8 
125.2 
136.3 
147.3 
168.4 


1 10.0 
122.6 
135.0 
147.1 
159.0 
182.1 
204.2 


131.4 
144.8 
157.9 
170.8 
195.8 
219.9 


164.4 


13/8 








179 5 


11/2 










194.4 


13/4 














223 3 


2 


















251.3 

























292 STRENGTH OF MATERIALS. 

For lengths greater than 20 diameters the allowable loads should be 
decreased. How much they should be decreased is uncertain, since suflB- 
cient data of experiments on full-sized very long columns, from which a 
formula for the strength of such columns might be derived, are as yet 
lacking. There is, however, rarely, if ever, any need of proportioning 
cast-iroa columns with a length exceeding 20 diameters. 



Safe Loads in Tons of 2000 Pounds for Cast-iron Columns. 

(By the Building Laws of New York City, Boston, and Chicago, 1897.) 



Square columns . 



New York. Boston. Chicago. 

8a 5a 5a 



1 + iTTTT^ 1 + TT^^o 1 + 



500 cP " " 1067^2 ^ ^ 800 (P 



( 8a 5a 5a 

Round columns .... J p 



1 + t;^?7^, 1 + ^7^, 1 + '' 



400 d2 " ' 800 d2 * ^ 600 cP 

a = sectional area in square inches; I = unsupported length of column 
in inches; d = side of square column or thickness of round column in 
inches. 

The safe load of a 15-inch round column 1^^ inches in thickness, 16 
feet long, according to the laws of these cities would be, in New York, 361 
tons; in Boston, 264 tons; in Chicago, 250 tons. 

The allowable stress per square inch of area of such a column would be, 
in New York, 11,350 pounds; in Boston, 8300 pounds; in Cliicago, 7850 
pounds. A safe stress of 5000 pounds per square inch would give for the 
safe load on the column 159 tons. 

Strength of Brackets on Cast-iron Columns. — The columns tested 
by the New York Building Department referred to above had brackets 
cast upon them, each bracket, consisting of a rectangular shelf sup- 
ported by one or two triangular ribs. These were tested after the 
columns had been broken in the principal tests. In 17 out of 22 cases the 
brackets broke by tearing a hole in the body of the column, instead of by 
shearing or transverse breaking of the bracket itself. The results were 
surprisingly low and very irregular.- Reducing them to strength per 
square inch of the total vertical section through the shelf and rib or rioa, 
they ranged from 2450 to 5600 lbs., averaging 4200 lbs., for a load con- 
centrated at the end of the shelf, and 4100 to 10,900 lbs., averaging 8000 
lbs., for a distributed load. (Eng'g News, Jan. 20, 1898.) 

Maximum Permissible Stresses in columns used in buildings. 
(Building Ordinances of City of Chicago, 1893.) 

For riveted or other forms of wrought-iron columns: 

g _ 12000 a ^ I = length of column in inches; 

P r = least radius of gyration in inches; 

36000 r2 ^= ^^^^ ^f column in square inches. 

For riveted or other steel columns, if more than 60 r in length: 

S = 17,000 - ^- 
r 

If less than 60 r in length: S = 13,500 a. 
For wooden posts: 

<? — ac a = area of post in square inches; 

'^ ~ /2 ' d = least side of rectangular post in inches; 

^ ^' ognw2 ^ = length of post in inches; 

^^^" ( 600 for white or Norway pine; 

c = <800 for oak; 

( 900 for long-leaf yellow pine. 



MOMENT OF INERTIA AND RADIUS OF GYRATION. 293 

MOMENT OF INERTIA AND RADIUS OF GYRATION. 

The moment of inertia of a section is the sum of the products of 
each elementary area of the section into the square of its distance from an 
assumed axis of rotation, as the neutral axis. 

Assume the section to be divided into a great many equal small areas, 
a, and that each such area has its own radius, r, or distance from the 
assumed axis of rotation, then the sum of all the products derived by 
multiplying each a by the square of its r is the moment of inertia, /, or 
7 = 2 ar^, in which 2 is the sign of summation. 

For moment of inertia of the weight or mass of a body see Mechanics. 

The radius of gyration of the section equals the square root of the 
quotient of the moment of inertia divided by the area of the section. If 
R = radius of gyration, / = moment of inertia and A = area 

R =\^T/A. I/A = R\ 

The center of gyration is the point where the entire area might be 
concentrated and have the same moment of inertia as the actual area. 
The distance of this center from the axis of rotation is the radius of 
gyration. 

The moments of inertia of various sections are as follows: 

d = diameter, or outside diameter; di = inside diameter; b = breadth; 
h = depth; 6i, ^i, inside breadth and depth; 

Solid rectangle I = i/i2bh^; Hollow rectangle 7 = Vnibh^ - bihi^); 
Solid square 7 = V12&*; Hollow square 7 = Vuib* — 6i<); 
Solid cylinder 7 = V647rd*: Hollow cylinder 7 = i/647r(d* — di*). 

Moment of Inertia about any Axis. — U b = breadth and h = 
depth of a rectangular section its moment of inertia about its central 
axis (parallel to the breadth) is 1/12 bh^-, and about one side is 1/3 bh^. If 
a parallel axis exterior to the section is taken, and d = distance of this 
axis from the farthest side and di = its distance from the nearest side, 
(d — di = h), the moment of inertia about this axis is 1/3 ^ (d^ — di^). 

The moment of inertia of a compound shape about any axis is equal to 
the sum of the moments of inertia, with reference to the same axis, of ali 
the rectangular portions composing it. 

Moment of Inertia of Compound Shapes. (Pencoyd Iron 
Works.) — The moment of inertia of any section about any axis is equal 
to the 7 about a parallel axis passing through its centre of gravity + (the 
area of the section X the square of the distance between the axes). 

By this rule, the moments of inertia or radii of gyration of any single 
sections being known, corresponding values may be obtained for any 
combination of these sections. 

E. A. Dixon {Am. Mach., Dec. 15, 1898) gives the following formula for 
the moment of inertia of any rectangular element of a built up beam: 
I = 1/3 {h^ — hi^)b, I = moment of inertia about any axis parallel to the 
neutral axis, h = distance from the assumed axis to the farthest fiber, 
hi = distance to nearest fiber, b = breadth of element. The sum of the 
moments of inertia of all the elements, taken about the center of gravity 
or neutral axis of the section, is the moment of inertia of the section. 

The polar moment of inertia of a surface is the sum of the products 
obtained by multiplying each elementary area by the square of its dis- 
tance from the center of gravity of the surface; it is equal to the sum of 
the moments of inertia taken with respect to two axes at right angles to 
each other passing through the center of gravity. It is represented by 
J. For a solid shaft J = 1/32 rd^; for a hollow shaft, J = V32 7t{d^ - di*), 
in which d is the outside anddi the Inside diameter. 

The polar radius of gyration, Rp = Vj/A, is defined as the radius of 
a circumference along which the entire area might be concentrated and 
have the same polar moment of inertia as the actual area. 

For a solid circular section iR^^ = 1/3 7)2. for a hollow circular sec- 
tion i2p2 = l/3((/2 + dl2). 

Moments of Inertia and Radius of Gyration for Various Sec- 
tions, and their Use in the Formulas for Strength of Girders and 
Columns. — The strength of sections to resist strains, either as 
girders or as columns, depends not only on the area but also on the 
form of the section, and the property of the section which forms the 



294 STRENGTH OF MATERIALS. 

basis of the constants used in the formulas for strength of girders and 
columns to express the effect of the form, is its moment of inertia about 
its neutral axis. The modulus of resistance of any section to transverse 
bending is its moment of inertia divided by the distance from the neutral 
axis to the fibres farthest removed from that axis; or 

C3 .' J , Moment of inertia ^ 7 

Section modulus = -rr^- : ;^t: — — • z = -• 

Distance of extreme fibre from axis c 

Moment of resistance = section modulus X unit stress on extreme fibre. 

Radius of Gyration of Compound Shapes. — In the case of a 
pair of any shape without a web the value of R can always be found with- 
out considering the moment of inertia. 

The radius of gyration for any section around an axis parallel to another 
axis passing through its centre of gravity is found as follows: 

Let r = radius of gyration around axis through centre of gravity; R = 
radius of gyration ar ound an other axis parallel to above; d = distance 
between axes: R = ^cP + r-. 

When r is small, R may be taken as equal to d without material error. 

Graphical 3Iethod for Finding Radius of Gyration. — Benj. F. 
La Rue, Eng. News, Feb. 2, 1893, gives a short graphical method for 
finding the radius of gyration of hollow, cylindrical, and rectangular 
columns, as follows: 

For cylindrical columns: 

Lay off to a scale of 4 (or 40) a right-angled triangle, in which the base 
equals the outer diameter, and the altitude equals the inner diameter 
of the column, or vice versa. The hypothenuse, measured to a scale of 
unity (or 10), will be the radius of gyration sought. 

This depends upon the formula 



G= Vjviom. of inertia -j- Area = 1/4 ^D- + d'^ 
in which A = area and D = diameter of outer circle, a = area an d d = 
diameter of inner circle, and G = radius of gyration. Vz)2 + rf2 jg the 
expression for the hypothenuse of a right-angled triangle, in which D and 
d are the base and altitude. 

The sectional area of a hollow round column is 0.7854(D2 — d"^). By 
constructing a right-angled triangle in which D e quals the hypothenuse 
and d equals the altitude, the base will equal ^D^ - d'\ Calling the 
value of this expression for the base B, the area will equal 0.785452. 

Value of G for square columns: 

Lay off as before, but using a scale of 10, a right-angled triangle of which 
the base equals D or the side of the outer square, and the altitude equals d, 
the side of the inner square. With a scale of 3 measure the hypothenuse, 
which will be, approximately, the radius of gyration. 

This process for square columns gives an excess of slightly more than 
4%. By deducting 4% from the result, a close approximation will be 
obtained. 

A very close result is also obtained by measuring the hypothenuse with 
the same scale by which the base and altitude were laid off, and multiplying 
by the decimal 0.29; more exactly, the decimal is 0.28867. 

The formula is 



=\^ 



Mom. of inertia 



Area " Vli ^^' + ^'' = ^'^^S^' ^^' + ^'* 



This may also be applied to any rectangular column by using the lesser 
diameters of an unsupported column, and the greater diameters if the 
column is supported in the direction of its least dimensions. 

ELEMENTS OF USUAL SECTIONS. 

Moments refer to horizontal axis through centre of gravity. This table 
is intended for convenient application where extreme accuracy is not 
Important. Some of the terms are only approximate; those marked * are 
correct. Values for radius of gyration in flanged beams apply to standard 
minimum sections only. A = area of section; b = breadth; h = depth* 
D = diameter. 



ELEMENTS OF USUAL SECTIONS. 



295 



Shape of Section. 


Moment 
of Inertia. 


Section 
Modulus. 


Square of 

Least 
Radius of 
Gyration. 


Least 
Radius of 
Gyration. 




4 


SoHd Rect- 
angle 


6^3* 

12 


bh^* 
6 


(Least side)2* 


Least side ♦ 




12 


3.46 


^ 


-6-. 








Hollow Rect- 
angle. 


12 


bh^-b^Jn^* 

6h 


A2+V* 
12 


h+h^ 
4.89 


U- 


^)--i 




i 


B 


Solid Circle. 


= 0.0491 D4 


1/32 ttDS * 
= 0.O982i)3 


2)2* 

16 


D* 
4 




Hollow Circle 
A, area of 
la^^;e section; 
a, area of 
small section. 


AD^-ad^* 
16 


Ai)2-ad'^* 


Z)2+d2* 

16 


D+d 


80 


5.64 


K-6— i 


Solid Triangle. 


36 


6/l2 

24 


The least of 
the two; 

/l2 62 

18^^24 


The least 

of the two: 

h b 

4.24^^4.9 






Even Angle. 


Ah^ 
10.2 


.4/1 
7.2 


fc2 

25 


b 
5 




1 




^ Y 




^- 


6-^ 








Uneven Angle. 


9.5 


6.5 


(;i6)2 
j3(;i2+62) 


/i6 




2.6(;i+6) 




W^ 


-^3 


Even Cross. 


A?i^ 
19 


.4/i 
9.5 


h'^ 
22.5 


h 

4.74 


fi 


t 


Even Tee. 


11.1 


Ah 
8 


62 
22.5 


4.74 


P-^-H 




1 




1 Beam. 


Ah-^ 
6.66 


.4;i 

3.2 


62 

21 


b 
4.58 




Channel. 


.4/i2 
7.34 


3.67 


62 
12.5 




^ 


Li J 


6 
3.54 


1 




Deck Beam. 


^;i2 

6.9 


Ah 
4 


62 

36.5 


6 
6 













Distance of base from centre of gravity, solid triangle, -; even angle, -r-^- 

uneven angle, tt^; even tee, ^-r ; deck beam, -^r-^; ail other shapes 
0.0 0.0 z.o 

given in the table, o ^^ "o* 



296 STRENGTH OF MATERIALS. 

ECCENTRIC LOADING OF COLUMNS. 

In a given rectangular cross-section, such as a masonry joint under 
pressure, the stress will be distributed uniformly over the section only 
when the resultant passes through the centre of the section; any deviation 
from such a central position will bring a maximum unit pressure to one 
edge and a minimum to the other; when the distance of the resultant 
from one edge is one third of the entire width of the joint, the pressure at 
the nearer edge is twice the mean pressure, while that at the farther edge 
is zero, and that when the resultant approaches still nearer to the edge 
the pressure at the farther edge becomes less than zero; in fact, becomes 
a tension, if the material (mortar, etc.) there is capable of resisting tension. 
Or, if, as usual in masonry joints, the material is practically incapable of 
resisting tension, the pressure at the nearer edge, when the resultant 
approaches it nearer than one third of the width, increases very rapidly 
and dangerously, becoming theoretically infinite when the resultant 
reaches the edge. 

With a given position of the resultant relatively to one edge of the joint 
or section, a similar redistribution of the pressures throughout the section 
may be brought about by simply adding to or diminishing the width of 
the section. 

Let P = the total pressure on any section of a bar of uniform thickness. 

w =- the width of that section = area of the section, when thickness = 1. 
p =- P/w = the mean unit pressure on the section. 

M = the maximum unit pressure on the section. 

m = the minimum unit pressure on the section. 
d = the eccentricity of the resultant = its distance from the centre of 
the section. 

Then M = p (l 4- ^) and m = p (l - ^ • 

When d = - w then M = 2p and m = O. 
o 

When d is greater than 1/6 v;, the resultant in that case being less than 
one third of the width from one edge, p becomes negative. (J. C. Traut- 
wine, Jr., Engineering News, Nov. 23, 1893.) 

Eccentric Loading of Cast-iron Columns. — Prof. Lanza writes 
the author as follows: The table on page 276 applies when the result- 
ant of the loads upon the column acts along its central axis, i.e., passes 
through the centre of gravity of every section. In buildings and other 
constructions, however, cases frequently occur when the resultant load 
does not pass through the centre of gravity of the section; and then the 
pressure is not evenly distributed over the section, but is greatest on the 
side where the resultant acts. (Examples occur when the loads on 
the floors are not uniformly distributed.) In these cases the outside 
fibre stresses of the column should be computed as follows, viz.: 
Let P = total pressure on the section; 

d = eccentricity of resultant = its distance from the centre of 

gravity of the section; 
A = area of the section, and / its moment of inertia about an axis in 
its plane, passing through its centre of gravity, and perpendic- 
ular to d\ 
ci = distance of most compressed and C2 = that of least compressed 

fibre from above stated axis; 
si = maximum and S2 = minimurh pressure ner unit of area. Then 

P , (Pd)ci , P (Pd)c2 

«i = "7 + — r— and 52 = -T - J ' 
A I A I 

Having assumed a certain trial section for the column to be designed, si 
should be computed, and, if it exceed the proper safe value, a difterent 
section should be used for which si does not exceed this value. 

The proper safe value, in the case of cast-iron columns whose ratio of 
length to diameter does not greatly exceed 20, is 5000 pounds per square 
inch when the eccentricity used in the computation of si is liable to occur 
frequently in the ordinary uses of the structure; but when it is one which 
can only occur in rare cases the value 8000 lbs. per sq. in. may be used. 

A long cap on a column is more conducive to the production of eccen- 
tricity of loading than a short one, hence a long cap is a source of weakness. 



TRANSVERSE STRENGTH. 297 



TRANSVERSE STRENGTH. 

In transverse tests the strength of bars of rectangular section is found to 
vary directly as the breadth of the specimen tested, as the square of its 
depth, and inversely as its length. The deflection under any load varies 
as the cube of the length, and inversely as the breadth and as the cube of 
the depth. Represented algebraically, if S = the strength and D the 
deflection, / the length, b the breadth, and d the depth, 

S vajies as — and D varies as r-^- 

For the purpose of reducing the strength of pieces of various sizes to 
a common standard, the term modulus of rupture (represented by R) is 
used. Its value is obtained by experiment on a bar of rectangular section 
supported at the ends and loaded in the middle and substituting numerical 
values in the following formula: 

^- 2bd^* 

in which P = the breaking load in pounds, I = the length in inches, h the 
breadth, and d the depth. 

The modulus of rupture is sometimes defined as the strain at the instant 
of rupture upon a unit of the section which is most remote from the neu- 
tral axis on the side which first ruptures. This definition, however, is 
based upon a theory which is yet in dispute among authorities, and it is 
better to define it as a numerical value, or experimental constant, found 
by the application of the formula above given. 

From the above formula, making I 12 inches, and h and d each 1 inch, it 
follows that the modulus of rupture is 18 times the load required to break 
a bar one inch square, supported at two points one foot apart, the load 
being appfied in the middle. 

Coefficient of transverse strength - SP^^ i^^ feet X load at middle in lbs. 

VAJclllClclll Ul liallbVclotJ fell cllg 111 — r -rr\ . . \ TTTj 7\ — : '• ^ T7^» 

breadth in inches X (depth in inches)^ * 
= —^th of the modulus of rupture. 

io 

Fundamental Formulse for Flexure of Beams (Merriman). 

Resisting shear = vertical shear; 

Resisting moment = bending moment; 

Sum of tensile stresses = sum of compressive stresses; 

Resisting shear = algebraic sum of all the vertical components of the 
internal stresses at any section of the beam. 

If A be the area of the section and Sg the shearing unit stress, then 
resisting shear = AS^', and if the vertical shear = y, then V= ASs. 

The vertical shear is the algebraic sum of all the external vertical forces 
on one side of the section considered. It is equal to the reaction of one 
support, considered as a force acting upward, minus the sum of all the 
vertical downward forces acting between the support and the section. 

The resisting moment = algebraic sum of all the moments of the inter- 
nal horizontal stresses at any section with reference to a point in that 

s/ 
section, = — .in which S = the horizontal unit stress, tensile or com?- 

c 
pressive as the case may be, upon the fibre most remote from the neutral 
axis, c = the shortest distance from that fibre to said axis, and / = the 
moment of inertia of the cross-section with reference to that axis. 

The bending moment M is the algebraic sum of the moment of the 
exteriml forces on one side of the section with reference to a point in that 
section = moment of the reaction of one support minus sum of moments 
of loads between the support and the section considered. 

M = — . 
c 

The bending moment is a compound quantity = product of a force by 
the distance of its point of application from the section considered, the 
distance being measured on a line drawn from the section perpendicular 
to the direction of the action of the force. 



298 



STRENGTH OF MATERIALS. 



Concerning the formula, M=^Slfc, p. 297, Prof. Merriman, Eng. News, 
July 21, 1894, says: The formula quoted is true when the unit-stress S on 
the part of the beam farthest from the neutral axis is within the elastic limit 
of the material. It is not true when this limit is exceeded, because then 
the neutral axis does not pass through the center of gravity of the cross- 
section, and because also the different longitudinal stresses are not pro- 
portional to their distances from that axis, these two requirements being 
involved in the deduction of the formula. But in all cases of design the 
permissible unit-stresses should not exceed the elastic limit, and hence 
the formula applies rationally, without regarding the ultimate strength 
of the material or any of the circumstances regarding rupture. Indeed, 
so great reliance is placed upon this formula that the practice of testing 
beams by rupture has been almost entirely abandoned, and the allowable 
unit-stresses are mainly derived from tensile and compressive tests. 



APPROXI3IATE GREATEST SAFE LOADS IX LBS. ON STEEL 
BEAMS. (Pencoyd Iron Works.) 

Based on fiber strains of 16,000 lbs. for steel. (For iron the loads should 
bo one-eighth less, corresponding to a fibre strain of 14,000 lbs. per square 
inch.) Beams supported at the ends and uniformly loaded. 

L = length in feet between supports; a -= interior area in square 
A == sectional area of beam in square inches; 

inches; d = interior depth in inches. 

D = depth of beam in inches. w = working load in net tons. 



Shape of 


Greatest Safe Load in Pounds. 


Deflection in Inches. 


Section. 


Load in 
Middle. 


Load 
Distributed. 


Load in 
Middle. 


Load 
Distributed. 


Solid Rect- 
angle. 


S90 AD 
L 


\780AD 


32AD^ 


wU 
52AD^ 


Hollow 


S90(AD-ad) 
L 


\im{AD-ad) 
L 


wU 


wU 


Rectangle. 


32{AD^-ad') 


52(AZ)2-ad2) 


Solid 


667AD 
L 


\333AD 
L 


24 A D^ 


wL^ 


Cylinder. 


38AZ)2 


Hollow 


667(AD-ad) 
L 


\333{ AD-ad) 
L 


wU 


wU 


Cylinder. 


24{ A D~aa') 


38{AD^ad'^) 


Even- 
legged 
Angle or 
Tee. 


8S5AD 
L 


\770 AD 
L 


wU 
32AZ)2 


wU 
52AZ)2 


Channel or 


\525AD 
L 


3050AD 
L 


wL3 


wL^ 


Z bar 


53AZ>2 


aSAD^ 


Deck 


\3Q0AD 
L 


2760AD 
L 


10 U 


wL^ 


Beam. 


50ylZ)^ 


80AZ>2 


I Beam. 


\695AD 
L 


3390AD 
L 


wU 
58 A Z)^ 


93AD' 


I 


II 


III 


IV 


V 



The above formulae for the strength and stiffness of rolled beams of 
various sections are intended for convenient application in cases where 
strict accuracy is not required. 



TRANSVERSE STRENGTH OP BEAMS. 



299 



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300 



STRENGTH OF MATERIALS. 



The rules for rectangular and circular sections are correct, while those 
for the flanged sections are approximate, and limited in their application 
to the standard shapes as given in the Pencoyd tables. When the section 
of any beam is increased above the standard minimum dimensions, the 
flanges remaining unaltered, and the web alone being thickened, the ten- 
dency will be for the load as found by the rules to be in excess of the 
actual; but within the limits that it is possible to vary any section in the 
rolling, the rules will apply without any serious inaccuracy. 

The calculated safe loads will be approximately one half of loads that 
would injure the elasticity of the materials. 

The rules for deflection apply to any load below the elastic limit, or 
less than double the greatest safe load by the rules. 

If the beams are long without lateral support, reduce the loads for the 
ratios of width to span as follows: 

Proportion of Calculated Load 
forming Greatest Safe Load. 
Length of Beam. 
20 times flange width. 
30 " 
40 •* 
50 ** 
60 •• 
70 •• 

These rules apply to beams supported at each end. For beams supported 
otherwise, alter the coefficients of the table as described below, referring 
to the respective columns indicated by number. 

Changes of Coefficients for Special Forms of Beams. 



Whole calculated load. 


9- 


-10 


. (i 


8- 


-10 


U M 


7- 


-10 


< tt 


6-10 


i «I 


5- 


-10 


1 4< 



Kind of Beam. 


Coefficient for Safe 
Loado 


Coefficient for Deflec- 
tion. 


Fixed at one end, loaded 
at the other. 


One fourth of the coeffi- 
cient, col. II. 


One sixteenth of the co- 
efficient of col. IV. 


Fixed at one end, load 
evenly distributed. 


One fourth of the coeffi- 
cient of col. III. 


Five forty-eighths of the 
coefficient of col. V. 


Both ends rigidly fixed, 
or a continuous beam, 
with a load in middle. 


Twice the coefficient of 
col. II. 


Four times the coeffi- 
cient of col. IV. 


Both ends rigidly fixed, 
or a continuous beam, 
with load evenly dis- 
tributed. 


One and one-half times 
the coefficient of col. 
III. 


Five times the coefficient 
of col. V. 



Formulae for Transverse Strength of Beams. — Referring to table 
on page 299, 

t* = load at middle; 
W = total load, distributed uniformly; 
I = length, b = breadth, d = depth, in inches; 
E = modulus of elasticity; 

^ = modulus of rupture, or stress per square inch of extreme fiber; 
/ = moment of inertia; 

c = distance between neutral axis and extreme fibre. 
For breaking load of circular section, replace fecP by 0.59#. 



BEAMS OF UNIFOKM STRENGTH. 



301 



The value of R at rupture, or the modulus of rupture (see page 282), 
is about 60,000 for structural steel, and about 110,000 for strong steel. 
(Merriman.) 

For cast iron the value of R varies greatly according to quality. Thurs- 
ton found 45,740 and 67,980 in No. 2 and No. 4 cast iron, respectively. 

For beams fixed at both ends and loaded in the middle. Barlow, by 
experiment, found the maximum moment of stress = 1/6 PI instead of 
1/8 PI, the result given by theory. Prof. Wood (Resist. Matls. p. 155) 
says of this case: The phenomena are of too complex a character to admit 
of a thorough and exact analysis, and it is probably safer to accept the 
results of Mr. Barlow in practice than to depend upon theoretical results. 



BEAMS OF UNIFORM STRENGTH THROUGHOUT THEIR 
LENGTH. 

The section is supposed in all cases to be rectangular throughout. The 
beams shown in plan are of uniform depth throughout. Those shown in 
elevation are of uniform breadth throughout. 

B = breadth of beam. D = depth of beam. 






ELEVATION. ^^ 




Fixed at one end, loaded at the other2 
curve parabola, vertex at loaded end ; BD 
proportional to distance from loaded end- 
The beam may be reversed, so that the 
upper edge is parabolic, or both edges may 
be parabolic. 

Fixed at one end, loaded at tne other; 
triangle, apex at loaded end ; BZ>2 propor- 
tional to the distance from the loaded end. 

Fixed at one end; load distributed; tri- 
angle, apex at unsupported end ; BD'^ pro- 
portional to square of distance from unsup- 
ported end. 

Fixed at one end; load distributed; 
curves two parabolas, vertices touching 
each other at unsupported end; BD"^ 
proportional to distance from unsupported 
end. 

Supported at both ends; load at any one 
point; two parabolas, vertices at the 
points of support, bases at point loaded; 
BD"^ proportional to distance from nearest 

Eoint of support. The upper edge or 
oth edges may also be parabolic. 

Supported at both ends; load at any one 
point; two triangles, apices at points of 
support, bases at point loaded; BD"^ pro- 
portional to distance from the nearest 

nnint nf siir»r»nrf. 



point of support. 



Supported at both ends; load distri- 
buted; curves two parabolas, vertices at 
the middle of the beam; bases centre Hue 
of beam; BD'^ proportional to product of 
distances from points of support. 

Supported at both ends; load distri- 
buted; curve semi-ellipse; BD^ propor- 
tional to the product of the distances 
from the points of support. 



STRENGTH OF MATERIALS. 



DIMENSIONS AND WEIGHTS OF STRUCTUEAL STEEL 
SECTIONS COMMONLY ROLLED. 

( Carnegie Steel Co., 1913.) 






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WEIGHTS AND DIMENSIONS OF ANGLES. 



303 












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304 



STRENGTH OF MATERIALS. 



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PROPERTIES OP ROLLED STRUCTURAL STEEL. 305 







Weights and Dimensions of I-Beams. 








Wt. 




Wt. 




Wt. 




Wt. 




Wt. 




Wt. 


Size, 


per 


Size, 


per 


Size, 


per 


Size, 


per 


Size, 


per 


Size, 


per 


In. 


Ft., 


In. 


Ft., 


In. 


Ft., 


In. 


Ft., 


In. 


Ft., 


In. 


Ft., 




Lb. 




Lb. 




Lb. 




Lb. 




Lb. 




Lb. 


27 


83.0 


20 


90.0 


18 


55.0 


12 


45.0 


9 


21.0 


5 


12.25 


24 


115.0 




85.0 




46.0 




40.0 


8 


25.5 


•' 


9.75 




110.0 




80.0 


15 


75.0 




35.0 




23.0 


4 


10.5 




105.0 




75.0 






70.0 




31.5 




20.5 


" 


9.5 




100.0 




70.0 






65.0 




27.5 


" 


18.0 


" 


8.5 




95.0 




65.0 






60.0 


10 


40.0 




17.5 


" 


7.5 




90.0 


18 


90.0 






55.0 




35.0 


7 


20.0 


3 


7.5 




85.0 




85.0 






50.0 




30.0 


" 


17.5 


«♦ 


6.5 




80.0 




80.0 






45.0 




25.0 




15.0 


" 


5.5 




69.5 
57.5 
100.0 
95.0 




75.0 
70.0 
65.0 
60.0 






42.0 
36.0 
55.0 
50.0 


9 


22.0 
35.0 
30.0 
25.0 


6 
5 


17.25 
14.75 
12.25 
14.75 






21 






20 


12 

















Weights and Dimensions of Channels. 



55.0 
50.0 
45.0 
40.0 
35.0 
33.0 
50.0 
45.0 
40.0 



13 



10 



37.0 
35.0 
32.0 
40.0 
35.0 
30.0 
25.0 
20.5 
35.0 



10 



8 



30.0 

25.0 

20.0 

15.0 

25.0 

20.0 

15.0 

13.25 

21.25 



18.75 
16.25 
13.75 
11.25 
19.75 
17.25 
14.75 
12.25 
9.75 



15.5 
13.0 
10.5 
8.0 
11 5 


4 
3 


5.25 
6.0 
5.0 
4.0 


9 






6 5 






7 ?5 






6.25 







PROPERTIES OF ROLLED STRUCTURAL STEEL. 

Explanation of Tables of the Properties of I-Beams, Channels, 
Angles, Z-Bars, Tees, etc. (Carnegie Steel Co.) 

The tables of properties of I-beams and channels, pp. 307 to 313, 
are calculated for all standard sizes and weights to which each pattern 
is rolled, excepting for five weights of the 13-in. channel which is omitted 
in the tables. The table of properties of angles are calculated for the 
maximum, intermediate, and minimum weights of each size, excepting 
that only maximum and minimum weights are given for a few of the 
smaller sizes as noted in the tables. The properties of Z-bars are given 
for thicknesses differing by Vie in. The table of properties of Tee shapes 
lists the lightest section of each size. In the case of angles there will 
be two section moduli for each position of the neutral axis, since the 
distance between the neutral axis and the extreme fiber is different on 
either side of the axis. With T-sections there are two section moduli 
where the neutral axis is parallel to the flange. In these cases only 
the smaller section moduli are given. 

The column headed x, in the table of the properties of standard 
channels, giving the distance of the center of gravity of channel from 
the outside of web, is used to obtain the radius of gyration for columns 
or struts consisting of two channels latticed, for the case of the neutral 
axis passing through the center of the cross-section parallel to the webs 
of the channels. This radius of gyration is equal to the distance be- 
tween the center of gravity of the channel and the center of the section, 
i.e., neglecting the moments of inertia of the channels around their own 
axes, thereby introducing a slight error on the side of safety. 

In the tables of safe loads of beams and channels, the safe loads for 
various lengths of span are given only for the lightest weight of each 
section rolled in the various sizes. The safe loads of the heavier weights 
of each section can be calculated from the data given in the tables of 
properties. The safe loads given in the tables are for a uniform load 
per running foot on the beam or channel. If the load, instead of being 
uniform, is concentrated at the center of the span, multiply it by 2 
and then consider it as a uniform load. The deflection will be 0.8 X 



306 



STRENGTH OF MATERIALS. 



the deflection for the uniform load. The safe loads in the tables are 
calculated solely with reference to the safe unit stresses due to flexure, 
and the values given will not produce average shearing stresses in the 
web greater than 10,000 lb. per sq. in., the maximum allowed in the 
American Bridge Co.'s specifications. When the beams carry con- 
centrated loads, the buckling or shearing strssses In the web, rather 
than the resistance of the flanges to bending stresses may limit the 
carrying capacity. 

The tables of safe loads for angles, tees, and Z-bars give the safe loads 
on a span of 1 ft., from which the safe load for any length of span may 
be obtained by direct division. They also give the values at which 
the allowed safe load will produce the maximum allowable deflection 
of 1/360 of the span length. 

The tables are based on an extreme fiber stress of 16,000 lb. per sq. in., 
which is the customary figure for quiescent loads, as in buildings. 
Where running loads are involved, as in bridges, crane runways, etc., an 
extreme fiber stress of 12,500 lb. per sq. in. should be used and the values 
reduced accordingly. For suddenly applied loads, the extreme fiber 
stresses should be reduced to 8,000 lb. per sq. in. 

It is assumed in the tables that the load is applied normal to the 
neutral axis perpendicular to the web at the center, and that the beam 
deflects only vertically in the plane of bending. For other conditions 
of loading, the safe load must be determined by the general theory of 
flexure (see page 297) in accordance with the mode of application -of the 
load and its character. Under these conditions the safe loads will be 
considerably lower than those given in the tables. It is also assumed 
in the tables that the compression flanges of the various sections are 
secured against lateral deflection by the use of the rods at proper inter- 
vals. The lateral unsupported length of beams and girders should not 
exceed forty times the width of the compression flange. When the 
unsupported length exceeds ten times this width, the tabular safe loads 
should be reduced as follows, W being the width of the compression 
flange: 
Length of unsupported 

flange 5W lOW 15W 20W 25W SOW 35W 40W 

Percentage of full safe 

load allowed 100. 100 90.6 81.2 71.9 62.5 53.1 43.8 

In addition to the lateral deflection induced by pure bending stresses 
in the beam, there may be deflection due to the thrust of arches or 
other loads acting on a line perpendicular to the line of the principal 
stresses. These should be neutralized by tie rods so that in no case 
wiU the unit stresses exceed 16,000 lb. per sq. in. 

(For much other important information concerning rolled structural 
shapes, see the "Pocket Companion" of the Carnegie Steel Co., Pitts- 
burgh, Pa., price $2.) 

Allowable Tension Values in Bars — Thousands of Pounds. 

(Carnegie Steel Co., 1913.) 





Round Bars. 


Square Bars. 


Size, 


Round Bars. 


Square Bars. 


Size, 


Unit 


Unit 


Unit 


Unit 


Unit 


Unit 


Unit 


Unit 


In. 


Stress 


Stress 


Stress 


Stress 


In. 


Stress 


Stress 


Stress 


Stress 




16,000 


20,000 


16,000 


20,000 




16,000 


20,000 


16,000 


20,000 




Lb. per 


Lb. per 


Lb. per 


Lb. per 




Lb. per 


Lb. per Lb. per 


Lb. per 




Sq. In. 


Sq. In. 


Sq. In. 


Sq. In. 




Sq. In. 


Sq. In. 


Sq. In. 


Sq. In. 


V4 


0.8 


1.0 


1.0 


1.3 


13/4 


38.5 


48.1 


49.0 


61.3 


1/2 


3.1 


3.9 


4.0 


5.0 


2 


50.3 


62.8 


64.0 


80.0 


3/4 


7.1 


8.8 


9.0 


11.3 


21/4 


63.6 


79.5 


81.0 


101.3 


1 


12.6 


15.7 


16.0 


20.0 


21/^ 


78.5 


98.2 


100.0 


125.0 


11/4 


19.6 


24.5 


25.0 


31.3 


23/4 


95.0 


118.8 


121.0 


151.3 


11/2 


28.3 


35.3 


36.0 


45.0 


3 


113.1 


141 .4 


144.0 


180.0 



PROPERTIES OF ROLLED STRUCTURAL STEEL. 307 



Properties of Carnegie Standard I-Beams — Steel.* 









. 


Neutral Axis 


Coin- 


Neutral Axis Per- 




^ 




^ 


■s 


cident with Center 


pendicular to Web 


i 


1 


1 


00 




Line 


of Web. 


at Center. 


m 


•*H 


a 


en 




c 


m 




•a 


(A 
< 




Eh 






B' Section 

Modulu 


11 


ll 

1^ 


in.! lb. 


sq. in. 


in. 


in. 


in.4 


in. 


in.4 


in. 


in.3 


27 


83.0 


24.41 


7.500 


0.424 


2888.6 


10.88 


214.0 


53.1 


1.47 


14.1 


24 


115.0 


33.98 


8.000 


0.750 


2955.5 


9.33 


246.3 


83.2 


1.57 


20.8 




110.0 


32.48 


7.938 


0.688 


2883.5 


9.42 


240.3 


81.0 


1.58 


20.4 


<* 


105.0 


30.98 


7.875 


0.625 


2811.5 


9.53 


234.3 


78.9 


1.60 


20.0 


« 


100.0 


29.41 


7.254 


0.754 


2379.6 


9.00 


198.3 


48.6 


1.28 


13.4 


<« 


95.0 


27.94 


7.193 


0.693 


2309.0 


9.09 


192.4 


47.1 


1.30 


13.1 


« 


90.0 


26.47 


7.131 


0.631 


2238.4 


9.20 


186.5 


45.7 


1.31 


12.8 


«< 


85.0 


25.00 


7.070 


0.570 


2167.8 


9.31 


180.7 


44.4 


1.33 


12.6 


«' 


80.0 


23.32 


7.000 


0.500 


2087.2 


9.46 


173.9 


42.9 


1.36 


12.3 


«* 


69.5 


20.44 


7.000 


0.390 


1928.0 


9.71 


160.7 


39.3 


1.39 


11.2 


21 


57.5 


16.85 


6.500 


0.357 


1227.5 


8.54 


116.9 


28.4 


1.30 


8.8 


20 


100.0 


29.41 


7.284 


0.884 


1655.6 


7.50 


165.6 


52.7 


1.34 


14.5 


«« 


95.0 


27..94 


7.210 


0.810 


1606.6 


7.58 


160.7 


50.8 


1.35 


14.1 


" 


90.0 


26.47 


7.137 


0.737 


1557.6 


7.67 


155.8 


49.0 


1.36 


13.7 


« 


85.0 


25.00 


7.063 


0.663 


1508.5 


7.77 


150.9 


47.3 


1.37 


13.4 


«« 


80.0 


23.73 


7.000 


0.600 


1466.3 


7.86 


146.6 


45.8 


1.39 


13.1 


** 


75.0 


22.06 


6.399 


0.649 


1268.8 


7.58 


126.9 


30.3 


1.17 


9.5 


" 


70.0 


20.59 


6.325 


0.575 


1219.8 


7.70 


122.0 


29.0 


1.19 


9.2 


*« 


65.0 


19.08 


6.250 


0.500 


1169.5 


7.83 


117.0 


27.9 


1.21 


8.9 


18 


90.0 


26.47 


7.245 


0.807 


1260.4 


6.90 


140.0 


52.0 


1.40 


14.4 


" 


85.0 


25.00 


7.163 


0.725 


1220.7 


6.99 


135.6 


50.0 


1.42 


14.0 


" 


80.0 


23.53 


7.082 


0.644 


1181.0 


7.09 


131.2 


48.1 


1.43 


13.6 


« 


75.0 


22.05 


7.000 


0.562 


1141.3 


7.19 


126.8 


46.2 


1.45 


13.2 


" 


70.0 


20.59 


6.259 


0.719 


921.2 


6.69 


102.4 


24.6 


1.09 


7.9 


<« 


65.0 


19.12 


6.177 


0.637 


881.5 


6.79 


97.9 


23.5 


1.11 


7.6 


« 


60.0 


17.65 


6.095 


0.555 


841.8 


6.91 


93.5 


22.4 


1.13 


7.3 


" 


55.0 


15.93 


6.000 


0.460 


795.6 


7.07 


88.4 


21.2 


1.15 


7.1 


** 


46.0 


13.53 


6.000 


0.322 


733.2 


7.36 


81.5 


19.9 


1.21 


6.6 


15 


75.0 


22.06 


6.292 


0.882 


691.2 


5.60 


92.2 


30.7 


1.18 


9.8 


«• 


70.0 


20.59 


6.194 


0.784 


663.7 


5.68 


88.5 


29.0 


1.19 


9.4 


** 


65.0 


19.12 


6.096 


0.686 


636.1 


5.77 


84.8 


27.4 


1.20 


9.0 


" 


60.0 


17.67 


6.000 


0.590 


609.0 


5.87 


81.2 


26.0 


1.21 


8.7 


** 


55.0 


16.18 


5.746 


0.656 


511.0 


5.62 


68.1 


17.1 


1.02 


5.9 


tt 


50.0 


14.71 


5.648 


0.558 


483.4 


5.73 


64.5 


16.0 


1.04 


5.7 


** 


45.0 


13.24 


5.550 


0.460 


455.9 


5.87 


60.8 


15.1 


1.07 


5.4 


" 


42.0 


12.48 


5.500 


0.410 


441.8 


5.95 


58.9 


14.6 


1.08 


5.3 


*i 


36.0 


10.63 


5.500 


0.289 


405.1 


6.17 


54.0 


13.5 


1.13 


4.9 


12 


55.0 


16.18 


5.611 


0.821 


321.0 


4.45 


53.5 


17.5 


1.04 


6.2 


" 


50.0 


14.71 


5.489 


0.699 


303.4 


4.54 


50.6 


16.1 


1.05 


5.9 


** 


45.0 


13.24 


5.366 


0.576 


285.7 


4.65 


47.6 


14.9 


1.06 


5.6 


«* 


40.0 


11.84 


5.250 


0.460 


269.0 


4.77 


44.8 


13.8 


1.08 


5.3 


«( 


35.0 


10.29 


5.086 


0.436 


228.3 


4.71 


38.0 


10.1 


0.99 


4.0 


" 


31.5 


9.26 


5.000 


0.350 


215.8 


4.83 


36.0 


9.5 


1.01 


3.8 


" 


27.5 


8.04 


5.000 


0.255 


199.6 


4.98 


33.3 


8.7 


1.04 


3.5 


10 


40.0 


11.76 


5.099 


0.749 


158.7 


3.67 


31.7 


9.5 


0.90 


3.7 


** 


35.0 


10.29 


4.952 


0.602 


146.4 


3.77 


29.3 


8.5 


0.91 


3.4 


" 


30.0 


8.82 


4.805 


0.455 


134.2 


3.90 


26.8 


7.7 


0.93 


3.2 


** 


25.0 


7.37 


4.660 


0.310 


122.1 


4.07 


24.4 


6.9 


0.97 


3.0 


« 


22.0 


6.52 


4.670 


0.232 


113.9 


4.18 


22.8 


6.4 


0.99 


2.7 



* See notes on next page. 



(Table continued on next page.) 



308 



STRENGTH OF MATERIALS. 







Properties of Carnegie Standard I-Beams — Steel. — Continued. 












Neutral Axis 


Coin- 


Neutral Axis Per- 




• 






j= 


cident with Center 


pendicular to Web 


s 


1 


§ 




! 


Line of Web. 


at Center. 
















PQ 
& 




1 
a 

< 






^ a 

eg 
1^ 


4 


1 


1^ 


d 

■It 


.il 
1^ 


in. 


lb. 


sq. in. 


in. 


in. 


in.4 


in. 


in.3 


in.4 


in. 


in.3 


9 


35.0 


10.29 


4.772 


0.732 


111.8 


3.29 


24.8 


7.3 


0.84 


3.1 




* 


30.0 


8.82 


4.609 


0.569 


101.9 


3.40 


22.6 


6.4 


0.85 


2.8 




' 


25.0 


7.35 


4.446 


0.406 


91.9 


3.54 


20.4 


5.7 


0.88 


2.5 




* 


21.0 


6.31 


4.330 


0.290 


84.9 


3.67 


18.9 


5.2 


0.90 


2.4 




8 


25.5 


7.50 


4.271 


0.541 


68.4 


3.02 


17.1 


4.8 


0.80 


2.2 




* 


23.0 


6.76 


4.179 


0.449 


64.5 


3.09 


16.1 


4.4 


0.81 


2.1 




* 


20.5 


6.03 


4.087 


0.357 


60.6 


3.17 


15.2 


4.1 


0.82 


2.0 




' 


18.0 


5.33 


4.000 


0.270 


56.9 


3.27 


14.2 


3.8 


0.84 


1.9 




* 


17.5 


5.15 


4.330 


0.210 


58.3 


3.37 


14.6 


4.5 


0.93 


2.1 




7 


20.0 


5.88 


3.868 


0.458 


42.2 


2.68 


12.1 


3.2 


0.74 


1.7 




« 


17.5 


5.15 


3.763 


0.353 


39.2 


2.76 


11.2 


2.9 


0.76 


1.6 




( 


15.0 


4.42 


3.660 


0.250 


36.2 


2.86 


10.4 


2.7 


0.78 


1.5 




6 


17.25 


5.07 


3.575 


0.475 


26.2 


2.27 


8.7 


2.4 


0.68 


1.3 




* 


14.75 


4.34 


3.452 


0.352 


24.0 


2.35 


8.0 


2.1 


0.69 


1.2 




* 


12.25 


3.61 


3.330 


0.230 


21.8 


2.46 


7.3 


1.9 


0.72 


1.1 




5 


14.75 


4.34 


3.294 


0.504 


15.2 


1.87 


6.1 


1.7 


0.63 


1.0 




* 


12.25 


3.60 


3.147 


0.357 


13.6 


1.94 


5.5 


1.5 


0.63 


0.92 




1 


9.75 


2.87 


3.000 


0.210 


12.1 


2.05 


4.8 


1.2 


0.65 


0.82 




4 


10.5 


3.09 


2.880 


0.410 


7.1 


1.52 


3.6 


1.0 


0.57 


0.70 




* 


9.5 


2.79 


2.807 


0.337 


6.8 


1.55 


3.4 


0.93 


0.58 


0.66 




( 


8.5 


2.50 


2.733 


0.263 


6.4 


1.59 


3.2 


0.85 


0.58 


0.62 




* 


7.5 


2.21 


2.660 


0.190 


6.0 


1.64 


3.0 


0.77 


0.59 


0.58 




3 


7.5 


2.21 


2.521 


0.361 


2.9 


1.15 


1.9 


0.60 


0.52 


0.48 




< 


6.5 


1.91 


2.423 


0.263 


2.7 


1.19 


1.8 


0.53 


0.52 


0.44 




'* 


5.5 


1.63 


2.330 


0.170 


2.5 


1.23 


1.7 


0.46 


0.53 


0.40 



L = safe loads in pounds, uniformly distributed ; I = span in feet 
M = moments of forces in foot-pounds; / = fiber stress. 
8f_S 
12 

for/ = 12,500 lb. per sq. in. (for bridges) L = 



ings) ; L 



L^lif.forf- 



31 



16,0001b. per sq. in. (for build- 

25,000 S 
SI 



Properties of Carnegie Trough Plates — Steel. 



Sec- 
tion 
Index. 



Size, in 
Inches. 



Weight 


Area 


Thick- 


per 


of Sec- 


ness in 


Foot. 


tion. 


Inches. 


lb. 


sq. in. 




16.3 


4.78 


1/2 


18.0 


5.28 


9/16 


19.7 


5.79 


5/8 


21.4 


6.30 


11/16 


23.2 


6.97 


3/4 



Moment of 

Inertia, 

Neutral 

Axis 

Parallel to 
Length. 



Section 

Modulus, 

Axis as 

before. 



Radius 
of Gy- 
ration, 
Axis as 
before. 



M 10 
M 11 
M 12 
M 13 
M 14 



9 1/2X3 3/4 

91/2x33/4 
91/2x33/4 
91/2x33/4 
91/2x33/4 



/ 

3.7 
4.1 
4.6 
5.0 
5.5 



S 

1.4 
1.6 
1.8 
2.0 
2.2 



r 
0.91 
0.91 
0.90 
0.90 
0.90 



i 



PKOPERTIES OF ROLLED STRUCTURAL STEEL. 



309 



Safe Loads, in Thousands of Pounds, Uniformly Distributed for 
Carnegie Steei I-Beams. 



,? 


[ 


24-inch 






20-inch. 


18-inch. 


1 5-inch. 




27 in 








21 in 












83 

lb. 


105 

lb. 


80 1b. 


69H 
lb. 


571^ 
lb. 


80 lb. 


65 lb. 


75 lb. 


46 lb. 


60 Ibt 


42 lb. 


36 

lb. 


4 


229.0 


300.0 


240.0 


187.2 


150.0 


240.0 


200.0 


202.3 


115.9 


177.0 


123.0 




5 


173.2 
144.4 
123.7 
108.3 
96.2 
86.6 




6 


104.8 
89.8 
78.5 
69.8 
62.8 


86.7 


7 


223.4 
195.5 
173.8 
156.4 


178.2 
155.9 
138.6 
124.7 


193.2 
169.1 
150.3 
135.3 


§I3 


8 


231.9 
206.1 
185.5 


108.6 
96.6 
86.9 


72.0 


9 


277.7 
249.9 


138.6 

124.7 


64.0 


10 


228.2 


171.4 


57.6 


11 


207.5 


227.2 


168.7 


155.8 


113.4 


142.2 


113.4 


123.0 


79.0 


78.7 


57.1 


52.4 


12 


190.2 


208.3 


154.6 


142.8 


103.9 


130.3 


104.0 


112.7 


72.4 


72.2 


52.4 


48.0 


13 


175.6 


192.2 


142.7 


131.8 


95.9 


120.3 


96.0 


104.1 


66.8 


66.6 


48.3 


44.3 


14 


163.0 


178.5 


132.5 


122.4 


89.1 


111.7 


89. 


96.6 


62.1 


61.9 


44.9 


41.2 


15 


152.2 


166.6 


123.7 


114.3 


83.1 


104.3 


83.2 


90.2 


57.9 


57.7 


41.9 


38.4 


16 


142.6 


156.2 


116.0 


107.1 


77.9 


97.7 


78.0 


84.5 


54.3 


54.1 


39.3 


36.0 


17 


134.3 


147.0 


109.1 


100.8 


73.4 


92.0 


73.4 


79.6 


51.1 


50.9 


37.0 


33.9 


18 


126.8 


138.8 


103.1 


95.2 


69.3 


86.9 


69.3 


75.1 


48.3 


48.1 


34.9 


32.0 


19 


120.1 


131.5 


97.6 


90.2 


65.6 


82.3 


65.7 


71.2 


45.7 


45.6 


33.1 


30.3 


20 


114.1 


125.0 


92.8 


85.7 


62.4 


78.2 


62.4 


67.6 


43.4 


43.3 


31.4 


28.8 


21 


108.7 


119.0 


88.3 


81.6 


59.4 


74.5 


59.4 


64.4 


41.4 


41.2 


29.9 


27.4 


22 


103.7 


113.6 


84.3 


77.9 


56.7 


71.1 


56.7 


61.5 


39.5 


39.4 


28.6 


26.2 


23 


99.2 


108.7 


80.7 


74.5 


54.2 


68.0 


54.2 


58.8 


37.8 


37.7 


27.3 


25.1 


24 


95.1 


104.1 


77.3 


71.4 


52.0 


65.2 


52.0 


56.4 


36.2 


36.1 


26.2 


24.0 


25 


91.3 


100.0 


74.2 


68.6 


49.9 


62.6 


49.9 


54.1 


34.8 


34.6 


25.1 


23.0 


26 


87.8 


96.1 


71.4 


65.9 


48.0 


60.2 


48.0 


52.0 


33.4 


33.3 


24.2 


22.2 


27 


84.5 


92.6 


68.7 


63.5 


46.2 


57.9 


46.2 


50.1 


32.2 


32.1 


23.3 


21.3 


28 


81.5 


89.3 


66.3 


61.2 


44.5 


55.9 


44.6 


48.3 


31.0 


30.9 


22.4 


20.6 


29 


78.7 


86.2 


64.0 


59.1 


43.0 


53.9 


43.0 


46.6 


30.0 


29.9 


21.7 


19.9 


30 


76.1 
73.6 


83.3 
80.6 


61.8 
59.8 


57.1 
55.3 


41.6 

40.2 


52.1 
50.5 


41.6 
40.2 


45.1 
43.6 


29.0 
28.0 


28.9 


20.9 


19.2 


31 


27.9 


20.3 


18.6 


32 


71.3 


78.1 


58.0 


53.6 


39.0 


48.9 


39.0 


42.3 


27.2 


27.1 


19.6 


18.0 


33 


69.2 


75.7 


56.2 


51.9 


37.8 


47.4 


37.8 


41.0 


26.3 








34 


67.1 


73.5 


54.6 


50.4 


36.7 


46.0 


36.7 


39.8 


25.6 








35 


65.2 


71.4 


53.0 


49.0 


35.6 


44.7 


35.6 


38.6 


24.8 








36 


63.4 
61.7 


69.4 
67.5 


51.5 
50.1 


47.6 
46.3 


34.6 
33.7 


43.4 
42.3 


34.7 
33.7 


37.6 


24.1 








37 


36.6 


23.5 




38 


60.1 


65.8 


48.8 


45.1 


32.8 


41.2 


32.8 


35.6 


22.9 








39 


58.5 


64.1 


47.6 


43.9 


32.0 


40.1 


32.0 












40 


57.1 
55.7 


62.5 
61.0 


46.4 
45.3 


42.8 
41.8 


31.2 
30.4 


39.1 


31.2 






.... 






41 


38.1 


30.4 




42 


54.3 
53.1 


59.5 
58.1 


44.2 
43.1 


40.8 
39.9 


29.7 


37.2 


29.7 












43 


29.0 




44 


51.9 


56.8 


42.2 


38.9 


28.3 
















45 


50.7 


55.5 


41.2 


38.1 


















46 


49.6 
48.6 


54.3 
53.2 


40.3 
39.5 


37.3 
36.5 


















47 














48 


47.5 


52.1 


38J 


35.7 












Table con- 


49 


46.6 


51.0 


37.9 


35.0 












tinued on 


50 


45.6 


50.0 


37.1 


34.3 












next page. 







Loads above upper horizontal lines will produce maximum allow- 
able shear in webs. Loads below lower horizontal lines will produce 
excessive deflections and must not be used with plastered ceilings. 
Maximum fiber stress, 16,000 lb. per sq. in. Safe loads given include 
the weight of beam, which should be deducted to give net load. 



310 



STRENGTH OF MATERIALS. 





Safe Loads, 


In Thousands of Pounds, Uniformly Distributed for 
Carnegie Steel I-Beams. — Continued. 




1 2-inch. 


10-inch. 


9-in. 


8-inch. 


7-in. 


6-in. 


5-in. 4-in. 


3-in. 


ei 
Ok 


401b. 


31H|27^ 
lb. lb. 


25 

lb. 


22 
lb. 


21 
lb. 


18 
lb. 


\l^ 


15 
lb. 


12^ 
lb. 


9H 
lb. 


7H 
lb. 


5^ 
lb. 


1 

2 


110.4 


84.0 
76.7 
63.9 
54.8 
48.0 
42.6 
38.4 
34.9 
32.0 


61.2 
59.1 
50.7 
44.4 
39.4 
35.5 
32.3 
29.6 
27.3 
25.3 
23.7 
22.2 
20.9 
19.7 
18.7 
17.7 
16.9 
16.1 
15.4 
14.8 
14.2 
13.6 


62.0 


46.4 
"4U3 
34.7 
30.4 
27.0 
24.3 
22.1 
20.2 
18.7 
17.4 
16.2 
15.2 
14.3 
13.5 
12.8 
12.1 


52.2 




35.0 


27.6 


21.0 


15.2 


10.2 
8.8 


3 


43.2 




25.8 
19.4 
15.5 
12.9 
11.1 
9.7 
8.6 
7.7 

7.0 
6.5 


17.2 

12.9 

10.3 

8.6 

7.4 

6.4 

5.7 
5.2 

4.7 
4.3 


10.6 
8.0 
6.4 
5.3 

4.5 
4.0 


5.9 


4 


50.3 
40.3 
33.6 
28.8 
25.2 
22.4 
20.1 
18.3 
16.8 
15.5 
14.4 
13.4 
12.6 
11.8 
11.2 


37.9 
30.3 
25.3 
21.7 
19.0 
16.9 
15.2 
13.8 
12.6 
11.7 
10.8 
10.1 
9.5 


33.6 


27.6 
22.1 
18.4 
15.8 
13.8 
12.3 
11.0 
10.0 
9.2 

8.5 
7.9 


4.4 


5 
6 
7 
8 


95.6 
79.7 
68.3 
59.8 
53.1 
47.8 
43.5 
39.8 


52.1 
43.4 
37.2 
32.6 
28.9 
26.0 
23.7 
21.7 
20.0 
18.6 
17.4 
16.3 
15.3 
14.5 
13.7 
13.0 


31.1 
25.9 
22.2 
19.4 

17.3 
15.6 

14.1 
13.0 
12.0 
11.1 
10.4 
9.7 


3.5 
2.9 
2.5 
2.2 


9 
10 
11 
12 


3.5 
3.2 




13 
14 


36.8 29.5 
34.2 27.4 

31.9 25.6 
29.9 24.0 

28.1 22.6 
26.6 21.3 

25.2 20.2 
23.91 19.2 


6.0 
5.5 


Loads above 
t, Vip nnner 


15 
16 


7.4 
6.9 


horizontal lines 
will produce maxi- 


17 
18 


8.9 
8.4 


9.2 
8.6 


mum allowable 
shear in webs. 


19 
20 


10.6 
10.1 


horizontal lin( 


Loads be ow lower 
3s will produce ex- 


21 
22 
23 

24 


22.8 
21.7 
20.8 
19.9 


18.3 
17.4 
•16.7 
16.0 
15.3 
14.8 


12.4 
11.8 


11.6 
11.0 


not be used with plastered ceilings. 
Maximum fiber stress, 16.000 lb. 
per sq. in. Safe loads given include 

•fitlg wAicrVit. rkf Vkf^am -cpViiph shmilH 


25 
26 


19.1 
18.4 


be ( 


ieduc 


ted t( 


3 give net load. 


1 





Properties of Carnegie Corrugated Plates - 


- Steel. 




Sec- 
tion 
Index. 


Size, in 
Inches. 


Weight 

per 

Foot. 


■ 

Area 
of Sec- 
tion. 


Thick- 
ness in 
Inches. 


Moment of 

Inertia, 

Neutral 

Axis 

Parallel to 
Length. 


Section 

Modulus, 

Axis as 

before. 


Radius 
of Gy- 
ration, 
Axis as 
before. 


M30 
M31 
M32 
M33 
M34 
M35 


83/4 X 1 1/2 
83/4 XI 9/16 
83/4 XI 5/8 
123/16X23/4 
123/16X213/16 
123/16X27/8 


lb. 

8.1 
10.1 
12.0 
17.8 
20.8 
23.7 


2.96 
3.53 
5.22 
6.10 
6.97 


1/4 

5/16 

3/8 

3/8 

7/16 

1/2 


/ 
0.64 
0.95 
1.3 
4.8 
5.8 
6.8 


S 

0.8 
1.1 
1.4 
3.3 
3.9 
4.5 


r 
0.52 
0.57 
0.62 
0.96 
0.98 
0.99 



SPACING OF I-BEAMS FOR UNIFORM LOAD. 311 



Spacing of Carnegie Steel I-Beams for Uniform Load of 100 Lbs. 
per Square Foot. 



(Figures in 


table 


give the proper distance 


, feet, 


center to center of beams.) 


?i^ 


27-in. 
83 lb 


24-inch. 


21 -in. 


20-inch. 


1 8-inch. 


1 5-inch. 


5II 


105 


80 


(>9M 


573^ 


80 


65 


75 


46 


60 


42 


36 




lb. 


lb. 


lb. 


lb. 


lb. 


lb. 


lb. 


lb. 


lb. 


lb. 


lb. 


Ft. 
10 


228.2 


249.9 


185.5 


171.4 


124.7 


156.4 


124.8 


135.3 


86.9 


86.6 


62.8 


57.6 


11 


188.6 


206.5 


153.3 


141.6 


103.1 


129.3 


103.1 111.8 


71.8 


71.6 


51.9 


47.6 


12 


158.5 


173.6 


128.8 


119.0 


86.6 


108.6 


86.6 


93.9 


60.4 


60.1 


43.6 


40.0 


13 


135.0 


147.9 


109.8 


101.4 


73.8 


92.6 


73.8 


80.0 


51.4 


51.3 


37.2 


34.1 


14 


116.4 


127.5 


94.7 


87.4 


63.6 


79.8 


63.7 


69.0 


44.3 


44.2 


32.1 


29.4 


15 


101.4 


111.1 


82.5 


76.2 


55.4 


69.5 


54.4 


60.1 


38.6 


38.5 


27.9 


25.6 


16 


89.2 


97.6 


72.5 


66.9 


48.7 


61.1 


48.7 


52.8 


33.9 


33.8 


24.5 


22.5 


17 


79.0 


86.5 


64.2 


53.3 


43.2 


54.1 


43.2 


46.8 


30.1 


30.0 


21.7 


19.9 


18 


70.4 


77.1 


57.3 


52.9 


38.5 


48.3 


38.5 


41.8 


26.8 


26.7 


19.4 


17.8 


19 


63.2 


69.2 


51.4 


47.5 


34.5 


43.3 


34.6 


37.5 


24.1 


24.0 


17.4 


16.0 


20 


57.1 


62.5 


46.4 


42.8 


31.2 


39.1 


31.2 


33.8 


21.7 


21.7 


15.7 


14.4 


21 


51.8 


56.7 


42.1 


38.9 


28.3 


35.5 


28.3 


30.7 


19.7 


19.6 


14.3 


13.1 


22 


47.2 


51.6 


38.3 


35.4 


25.8 


32.3 


25.8 


28.0 


18.0 


17.9 


13.0 


11.9 


23 


43.1 


47.2 


35.1 


32.4 


23.6 


29.6 


23.6 


25.6 


16.4 


16.4 


11.9 


10.9 


24 


39.6 


43.4 


32.2 


29.8 


21.7 


27.2 


21.7 


23.5 


15.1 


15.0 


10.9 


10.0 


25 


36.5 


40.0 


29.7 


27.4 


20.0 


25.0 


20.0 


21.6 


13.9 


13.9 


10.1 


9.2 


26 


33.8 


37.0 


27.5 


25.4 


18.5 


23.1 


18.5 


20.0 


12.9 


12.8 


9.3 


8.5 


27 


31.3 


34.3 


25.5 


23.5 


17.1 


21.5 


17.1 


18.6 


11.9 








28 


29.1 


31.9 


23.7 


21.9 


15.9 


20.0 


15.9i 17.3 


11.1 









PI 

G ii 


12-inch. 


10-inch. 


9-in 


8-inch. 


7-in. 


6-in. 


5-in. 


4-in 3-in 


15^ 


40 

lb. 


313^ 
lb. 


273^ 
lb. 


25 

lb. 


22 
lb. 


21 

lb. 


18 
lb. 


173^ 
lb. 


15 
lb. 


12M 
lb. 


9H 
lb. 


7^ 5^ 
lb. lb. 


Ft. 

5 

51/2 

6 


132'.8 


106:6 


98!6 


72:4 


67.5 


55.9 


60.7 
50.1 
42.1 


62.2 
51.4 
43.2 


44.2 
36.5 
30.7 


31.0 
25.6 
21.5 


20.6 
17.1 
14.3 


12.7i 7.1 
10.51 5.8 
8.8 4.9 


61/2 
8 


97.6 

74.7 
59.0 
47.8 


78'.3 
60.0 

47.4 
38.4 


7214 
55.4 
43.8 
35.5 


53:2 
40.7 
32.2 
26.1 


4916 
38.0 
30.0 
24.3 


4V.I 
31.5 
24.9 
20.1 


35.9 
31.0 
23.7 
18.7 
15.2 


36.8 
31.8 
24.3 
19.2 
15.6 


26.1 
22.5 
17.3 
13.6 
11.0 


18.3 12.2 
15.8 10.5 
12.1 8.1 


7.5 
6.5 
5.0 


4.2 
3.6 


9 
10 


9.6 6.4 
7.8| 5.2 


3.9 
3.2 




11 
12 


39.5 
33.2 


31.7 
26.6 


29.3 
24.6 


21.5 
18.1 


20.1 
16.9 


16.6 
14.0 


12.5 
10.5 


12.9 
10.8 


9.1 

7.7 


6.4! '"O 
5.4: 3.6 






13 
14 


28.3 
24.4 


22.7 
19.6 


21.0 
18.1 


15.4 
13.3 


14.4 
12.4 


11.9 
10.3 


9.0 

7.7 


9.2 
7.9 


6.5 
5.6 


■■■4.6 

4.0 








15 
16 


21.3 
18.7 
165 
14.8 


17.1 
15.0 
13.3 
11.8 


15.8 
13.9 
12.3 
11.0 


11.6 
10.2 
9.0 
8.0 


10.8 
9.5 
8.4 
7.5 


9.0 
7.9 
7.0 
6.2 


6.7 
5.9 


6.9 
6.1 


4.9 
4.3 










17 
18 


"5.3 
4.7 


4.8 




19 
20 


13.2 
12.0 
10.8 
9.9 
9.0 
8.3 


10.6 
9.6 
8.7 
7.9 
7.3 
6.7 


9.8 
8.9 
8.1 
7.3 
6.7 
6.2 


7.2 
6.5 


6.7 
6.1 


■5.6 
5.0 


... 














21 


: 5.9 

i 5.4 


5.5 
5.0 




22 


















23 

24 












... 1 . . 





For any other load than 100 lb. per sq. ft., divide the spacing given 
by the ratio the given load per sq. ft. bears to 100. Thus for a load 
of 150 lb. per sq. ft. divide by 1.5. Maximum fiber stress 16,000 lb. 
per sq. in. 

Spacings given below the dotted horizontal lines will produce exces- 
sive deflection, and should not be used with pla/Stered ceilings. 



312 



eTRENGTH OP MATERIALS. 





Properties of Carnegie Standard Cliannels 


-Steel. 














HB 


13 fi 


6^ 


i:g 


2- 


1^ 


>-ja 


1 
1 


4J 

1 


1 


1 
1 


§ 


is 

l| 

Ill 

4J a 


-.6 

2S| 


^1 

ih 

^<'2 


11! 


ii 

c4 


111 

o2o 


g| 

Ii 
Ii 


i 


4J 

-a 




T3 


Hi 


o< ^ 






1^^ 




Q 


^ 


_f_ 


% 


S 


p^ 


P5 


0) 


w 


Q 


in. 


lbs. 


sq. in. 


in. 


in. 


I 


r 


r 


r' 


S 


5' 


X 


15 


55. 


16.18 


0.82 


3.82 


430.2 


12.2 


5.16 


0.868 


57.4 


4.1 


0.82 




50. 


14.71 


0.72 


3.72 


402.7 


11.2 


5.23 


0.873 


53.7 


3.8 


0.80 




45. 


13.24 


0.62 


3.62 


375.1 


10.3 


5.32 


0.882 


50.0 


3.6 


0.79 




40. 


11.76 


0.52 


3.52 


347.5 


9.4 


5.43 


0.893 


46.3 


3.4 


0.78 




35. 


10.29 


0.43 


3.43 


319.9 


8.5 


5.58 


0.908 


42.7 


3.2 


0.79 




33. 


9.90 


0.40 


3.40 


312.6 


8.2 


5.62 


0.912 


41.7 


3.2 


0.79 


12 


40. 


11.76 


0.76 


3.42 


196.9 


6.6 


4.09 


0.751 


32.8 


2.5 


0.72 




35. 


10.29 


0.64 


3.30 


179.3 


5.9 


4.17 


0.757 


29.9 


2.3 


0.69 




30. 


8.82 


0.51 


3.17 


161.7 


5.2 


4.28 


0.768 


26.9 


2.1 


0.68 




25. 


7.35 


0.39 


3.05 


144.0 


4.5 


4.43 


0.785 


24.0 


1.9 


0.68 




201/2 


6.03 


0.28 


2.94 


128.1 


3.9 


4.61 


0.805 


21.4 


1.7 


0.70 


10 


35. 


10.29 


0.82 


3.18 


115.5 


4.7 


3.35 


0.672 


23.1 


1.9 


0.70 




30. 


8.82 


0.68 


3.04 


103.2 


4.0 


3.42 


0.672 


20.7 


1.7 


0.65 




25. 


7.35 


0.53 


2.89 


91.0 


3.4 


3.52 


0.680 


18.2 


1.5 


0.62 




20. 


5.88 


0.38 


2.74 


78.7 


2.9 


3.66 


0.696 


15.7 


1.3 


0.61 




15. 


4.46 


0.24 


2.60 


66.9 


2.3 


3.87 


0.718 


13.4 


1.2 


0.64 




25. 


7.35 


0.62 


2.82 


70.7 


3.0 


3.10 


0.637 


15.7 


1.4 


0.62 




20. 


5.88 


0.45 


2.65 


60.8 


2.5 


3.21 


0.646 


13.5 


1.2 


0.59 




15. 


4.41 


0.29 


2.49 


50.9 


2.0 


3.40 


0.665 


11.3 


1.0 


0.59 




131/4 


3.89 


0.23 


2.43 


47.3 


1.8 


3.49 


0.674 


10.5 


0.97 


0.61 




211/4 


6.25 


0.58 


2.62 


47.8 


2.3 


2.77 


0.600 


11.9 


1.1 


0.59 




18 3/4 


5.51 


0.49 


2.53 


43.8 


2.0 


2.82 


0.603 


11.0 


1.0 


0.57 




161/4 


4.78 


0.40 


2.44 


39.9 


1.8 


2.89 


0.610 


10.0 


0.95 


0.56 




13 3/4 


4.04 


0.31 


2.35 


36.0 


1.6 


2.98 


0.619 


9.0 


0.87 


0.56 




111/4 


3.35 


0.22 


2.26 


32.3 


1.3 


3.11 


0.630 


8.1 


0.79 


0.58 




19 3/4 


5.81 


0.63 


2.51 


33.2 


1.9 


2.39 


0.565 


9.5 


0.96 


0.58 




171/4 


5.07 


0.53 


2.41 


30.2 


1.6 


2.44 


0.564 


8.6 


0.87 


0.56 




14 3/4 


4.34 


0.42 


2.30 


27.2 


1.4 


2.50 


0.568 


7.8 


0.79 


0.54 




121/4 


3.60 


0.32 


2.20 


24.2 


1.2 


2.59 


0.575 


6.9 


0.71 


0.53 




9 3/4 


2.85 


0.21 


2.09 


21.1 


0.98 


2.72 


0.586 


6.0 


0.63 


0.55 




151/2 


4.56 


0.56 


2.28 


19.5 


1.3 


2.07 


0.529 


6.5 


0.74 


0.55 




13. 


3.82 


0.44 


2.16 


17.3 


1.1 


2.13 


0.529 


5.8 


0.65 


0.52 




101/2 


3.09 


0.32 


2.04 


15.1 


0.88 


2.21 


0.534 


5.0 


0.57 


0.50 




8. 


2.38 


0.20 


1.92 


13.0 


0.70 


2.34 


0.542 


4.3 


0.50 


0.52 




111/2 


3.38 


0.48 


2.04 


10.4 


0.82 


1.75 


0.493 


4.2 


0.54 


0.51 




9. 


2.65 


0.33 


1.89 


8.9 


0.64 


1.83 


0.493 


3.6 


0.45 


0.48 




61/2 


1.95 


0.19 


1.75 


7.4 


0.48 


1.95 


0.498 


3.0 


0.38 


0.49 




71/4 


2.13 


0.33 


1.73 


4.6 


0.44 


1.46 


0.455 


2.3 


0.35 


0.46 




61/4 


1.84 


0.25 


1.65 


4.2 


0.38 


1.51 


0.454 


2.1 


0.32 


0.46 




5 1/4 


1.55 


0.18 


1.58 


3.8 


0.32 


1.56 


0.453 


1.9 


0.29 


0.46 




6. 


1.76 


0.36 


1.60 


2.1 


0.31 


1.08 


0.421 


1.4 


0.27 


0.46 




5. 


1.47 


0.26 


1.50 


1.8 


0.25 


1.12 


0.415 


1.2 


0.24 


0.44 




4. 


1.19 


0.17 


1.41 


1.6 


0.20 


1.17 


0.409 


1.1 


0.21 


0.44 



L = safe load in pounds, uniformly distributed; I = span in feet; 
M = moment of forces in foot-pounds;/ = fiber stress. 

LI = S[M = ?^; L = ^-^; for/ = 16.000 lbs. per sq. in. (for build- 
ings); 1,^ 32,0005 ^^^ ^ ^2,500 lb. per sq. in. (for bridges) , L= ^^'^^^ ^ 



21 



31 



PROPERTIES OF ROLLED STRUCTURAL STEEL. 313 



Maximuin Safe Load for Carnegie Channels In Thousands of Pounds. 




Depth and Weight of Sections. 




Span. 


15 in. 

331b. 


Bin. 

321b. 


12 in. 

201^ 
lb. 


10 in. 
151b. 


9 in. 
I3M 
lb. 


8 in. 


7 in. 
9% 
lb. 


6 in. 
8 1b. 


5 in. 

63^ 
lb. 


4 in. 
5M 
lb. 


3 in. 

4 1b. 


1 


120.0 


97.5 


67.2 


48.0 


41.4 


35.2 


29.4 


24.0. 


19.0 


14.4 


10.2 


2 


23.1 
15.4 
11.6 
9.2 
7.7 
6.6 
5.8 
5.1 
4.6 
4.2 
3.9 


15.8 
10.5 
7.9 
6.3 
5.3 
4.5 
4.0 
3.5 
3.2 


10.1 
6.7 
5.1 
4.1 
3.4 
2.9 
2.5 


5.8 


3 


47.6 

35.7 

28.5 

23.8 

20.4 

17.8 

15.9 

14.3 

13.0 

11.9 

11.0 

10.2 

9.5 

8.9 

8.4 

7.9 

7.5 


37.4 

28.0 

22.4 

18.7 

16.0 

14.0 

12.5 

11.2 

10.2 

9.3 

8.6 

8.0 

7.5 

7.0 

6.6 

6.2 


28.7 

21.5 
17.2 
14.4 
12.3 
10.8 
9.6 
8.6 
7.8 
7.2 
6.6 
6.2 
5.7 
5.4 


21.4 

16.1 
12.9 
10.7 
9.2 
8.0 
7.1 
6.4 
5.8 
5.4 
4.9 
4.6 


3.9 


4 
5 
6 
7 
8 


111.1 
88.9 
74.1 
63.5 
55.6 
49.4 
44.5 
40.4 
37.0 
34.2 
31.8 
29.6 
27.8 
26.1 
24.7 
23.4 
22.3 
21.2 
20.2 
19.3 
18.5 
17.8 
17.1 
16.5 
15.9 
15.3 
14.8 


97.5 
78.0 
65.0 
55.7 
48.7 
43.3 
39.0 
35.4 
32.5 
30.0 
27.9 
26.0 
24.4 
22.9 
21.7 
20.5 
19.5 
18.6 
17.7 
17.0 
16.2 
15.6 
15.0 


56.9 
45.5 
38.0 
32.5 
28.5 
25.3 
22.8 
20.7 
19.0 
17.5 
16.3 
15.2 
14.2 
13.4 
12.7 
12.0 
11.4 
10.8 
10.4 
9.9 
9.5 


2.9 
2.3 
1.9 
1.7 
1.5 


9 
10 


2.2 
2.0 




12 


2.9 
2.6 




13 
14 


3.6 
3.3 




15 
16 


4.3 

4.0 

.... 




17 
18 


5.1 
4.8 




19 
20 


5.9 
5.6 




21 

22 
23 
24 


6.8 
6.5 




25 
26 


9.1 
8.8 




Loads above upper horizontal lines 
will produce maximum allowable shear 
in webs. Loads below lower horizontal 
lines will produce excessive deflections. 


27 
28 
29 
30 


14.4 
13.9 


31 
32 


14.3 
J 3.9 


per s 


q. in. 










1 







Properties of Carnegie T-Shapes — SI 


eel. 








Mini- 
mum 






Neutral Axis through C. 


Neutral Axis Cou 
incident with Cen-^ 


Size, 
Flange 


Thick- 
ness, In. 




i 


of G. Parallel to Flange. 


ter Line of Stem* 








II 




1— 1 




4,a 




1— 1 




by 
Stem. 

In. 


i 

a 


m 




< 


11 


§2 

5^ 


1 


Distance N 
tral Axis toT 
of Flange, I 


1" 


=1 


1^ 


5 X3 


1/2 


13/3? 


13.4 


3.93 


2.4 


0.78 


1.1 


0.73 


5.4 


1.17 


2.2"^ 


5 X 21/2 


3/8 


7/1 fi 


10.9 


3.18 


1.5 


0.68 


0.78 


0.63 


4.1 


1.14 


1.6 


41/2 X 31/2 


7/16 


11/16 


15.7 


4.60 


5.1 


1.05 


2.1 


1.11 


3.7 


0.90 


1.7 


41/2 X 3 


3/8 


3/8 


9.8 


2.88 


2.1 


0.84 


0.91 


0.74 


3.0 


1.02 


1.3 


41/2X3 


5/16 


5/16 


8.4 


2.46 


1.8 


0.85 


0.78 


0.71 


2.5 


1.01 


1.1 


41/2X21/2 


3/8 


3/8 


9.2 


2.68 


1.2 


0.67 
0.68 


0.63 


0.59 


3.0 


1.05 1 1.3 


41/2 X 21/2 


5/16 


5/16 


7.8 


2.29 


1.0 


0.54 


0.57 


2.5 


1.05 1 1.1 



{Table continued on next page.) 



314 



STRENGTH OF MATERIALS. 



Properties of Carnegie T-Shapes 


— Steel. — Continued. 






Mini- 
mum 
Thick- 






Neutral Axis through C. 
of G. Parallel to Flange. 


Neutral Axis Co- 
incident with Cen- 
ter Line of Stem. 




ness, In. 




.. w 














Size, 








o-S 








1 CL 








Flange 








.2 « 




c 




i stance Neu 
al AxistoTo] 
Flange, In. 




a 




by 
Stem. 


i 

c3 


0) 


^4 


•si 


°2 

11 


■It 


.il 




if 




In. 


fe 


4J 


^ 


< 


s 


« 


^ 


Oh'Z 


s 


p^ 


^. 


4 X 5 


1/2 


1/2 


15.3 


4.50 


10.8 


1.55 


3.1 


1.56 


2.8 


0.79 


1.4 


4 X5 


3/8 


3/8 


11.9 


3.49 


8.5 


1.56 


2.4 


1.51 


2.1 


0.78 


1.1 


4 X 41/2 


1/2 


1/2 


14.4 


4.23 


7.9 


1.37 


2.5 


1.37 


2.8 


0.81 


1.4 


4 X 41/2 


3/8 


3/8 


11.2 


3.29 


6.3 


1.39 


2.0 


1.31 


2.1 


0.80 


l.I 


4 X 4 


1/2 


1/2 


13.5 


3.97 


5.7 


1.20 


2.0 


1.18 


2.8 


0.84 


1.4 


4 X 4 


3/8 


3/8 


10.5 


3.09 


4.5 


1.21 


1.6 


1.13 


2.1 


0.83 


1.1 


4 X3 


3/8 


3/8 


9.2 


2.68 


2.0 


0.86 


0.90 


0.78 


2.1 


0.89 


1.1 


4 X 3 


5/16 


5/16 


7.8 


2.29 


1.7 


0.87 


0.77 


0.75 


1.8 


0.88 


0.88 


4 X 21/2 


3/8 


3/8 


8.5 


2.48 


1.2 


0.69 


0.62 


0.62 


2.1 


0.92 


1.0 


4 X 21/2 


5/16 


5/16 


7.2 


2.12 


1.0 


0.69 


0.53 


0.60 


1.8 


0.91 


0.88 


4 X 2 


3/8 


3/8 


7.8 


2.27 


0.60 


0.52 


0.40 


0.48 


2.1 


0.96 


1.1 


4 X2 


5/16 


5/16 


6.7 


1.95 


0.53 


0.52 


0.34 


0.46 


1.8 


0.95 


0.88 


31/2 X 4 


1/2 


1/2 


12.6 


3.70 


5.5 


1.21 


2.0 


1.24 


1.9 


0.72 


1.1 


31/2X4 


3/8 


3/8 


9.8 


2.88 


4.3 


1.23 


1.5 


1.19 


1.4 


0.70 


0.81 


31/2 X 31/2 


1/2 


1/2 


11.7 


3.44 


3.7 


1.04 


1.5 


1.05 


1.9 


0.74 


1.1 


31/2 X 31/2 


3/8 


3/8 


9.2 


2.68 


3.0 


1.05 


1.2 


1.01 


1.4 


0.73 


0.81 


31/2X3 


1/2 


1/2 


10.8 


3.17 


2.4 


0.87 


1.1 


0.88 


1.9 


0.77 


1.1 


31/2 X 3 


3/8 


3/8 


8.5 


2.48 


1.9 


0.88 


0.89 


0.83 


1.4 


0.75 


0.81 


31/2 X 3 


5/16 


3/8 


7.5 


2.20 


1.8 


0.91 


0.85 


0.85 


1.2 


0.74 


0.68 


3 X4 


1/2 


1/2 


11.7 


3.44 


5.2 


1.23 


1.9 


1.32 


1.2 


0.59 


0.81 


3 X4 


7/16 


7/16 


10.5 


3.06 


4.7 


1.23 


1.7 


1.29 


1.1 


0.59 


0.70 


3 X4 


3/8 


3/8 


9.2 


2.68 


,4.1 


1.24 


1.5 


1.27 


0.90 


0.58 


0.60 


3 X 31/2 


1/2 


1/2 


10.8 


3.17 


3.5 


1.06 


1.5 


1.12 


1.2 


0.62 


0.80 


3 X 31/2 


7/16 


7/16 


9.7 


2.83 


3.2 


1.06 


1.3 


1.10 


1.0 


0.60 


0.69 


3 X 31/2 


3/8 


3/8 


8.5 


2.48 


2.8 


1.07 


1.2 


1.07 


0.93 


0.61 


0.62 


3 X3 


1/2 


1/2 


9.9 


2.91 


2.3 


0.88 


1.1 


0.93 


1.2 


0.64 i 0.80 


3 X3 


7/16 


7/16 


8.9 


2.59 


2.1 


0.89 


0.98 


0.91 


1.0 


0.63 1 0.70 


3 X3 


3/8 


3/8 


7.8 


2.27 


1.8 


0.90 


0.86 


0.88 


0.90 


0.63 0.60 


3 X3 


5/16 


5/16 


6.7 


1.95 


1.6 


0.90 


0.74 


0.86 


0.75 


0.62 0.50 


3 X 21/2 


3/8 


3/8 


7.1 


2.07 


1.1 


0.72 


0.60 


0.71 


0.89 


0.66 1 0.59 


3 X 21/2 


5/16 


5/l6 


6.1 


1.77 


0.94 


0.73 


0.52 


0.68 


0.75 


0.65 1 0.50 


3 X 21/2 


1/4 


1/4 


5.0 


1.47 


0.78 


0.73 


0.43 


0.66 


0.61 


0.64 1 0.40 


21/2X3 


3/8 


3/8 


7.1 


2.07 


1.7 


0.91 


0.84 


0.95 


0.53 


0.51 ! 0.42 


21/2X3 


5/16 


5/16 


6.1 


1.77 


1.5 


0.92 


0.72 


0.92 


0.44 


0.50 i 0.35 


21/2 X 21/2 


3/8 


3/8 


6.4 


1.87 


1.0 


0.74 


0.59 


0.76 


0.52 


0.53 1 0.42 


21/2 X 11/4 


3/16 


3/16 


2.87 


0.84 


0.08 


0.31 


0.09 


0.32 


0.29 


0.58 0.23 


21/4 X 21/4 


5/16 


5/16 


4.9 


1.43 


0.65 


0.67 


0.41 


0.68 


0.33 


0.48 0.29 


2X2 


5/16 


5/l6 


4.3 


1.26 


0.44 


0.59 


0.31 


0.61 


0.23 


0.43 0.23 


2 X 11/2 


1/4 


1/4 


3.09 


0.91 


0.16 


0.42 


0.15 


0.42 


0.18 


0.45 ! 0.18 


13/4 X 13/4 


1/4 


1/4 


3.09 


0.91 


0.23 


0.51 


0.19 


0.54 


0.12 


0.37 


0.14 


11/2 X 11/2 


1/4 


1/4 


2.47 


0.73 


0.15 


0.45 


0.14 


0.47 


0.08 


0.32 


0.10 


11/4 X 11/4 


1/4 


1/4 


2.02 


0.59 


0.08 


0.37 


0.10 


0.40 


0.05 


0.28 


0.07 


r X 1 


3/16 


3/16 


1.25 


0.37 


0.03 


0.29 


0.05 


0.32 


0.02 


0.22 


0.04 



Ten light-weight Ts of sizes qnder 2 K X 2 K in. are omitted. 



PROPERTIES OF ROLLED STRUCTURAL STEEL. 315 



Maximum Safe Loads on Carnegie T-Sliapes. 

Allowable Uniform Load in Thousands of Pounds. Neutral Axis Parallel 
to Flange. Maximum Bending Stress, 16,000 Pounds Per Square Inch. 











Maximum 










Maximum 








I Ft. 


Span. 








1 Ft. 


Span. 


Size. 


Wgt. 


Span 


360 X De- 
flection. 


Size. 


Wgt. 
per 


Span 


360 X De- 
flection. 


flT 




Foot, 




j 


en 




Foot, 


1 




Stem, 
In. 


Lb. 


Safe 
Load. 


Safe Lgth., 
Load, j Feet. 


IS 


Stem, 
In. 


Lb. 


Safe , Safe 
Load.. Load. 


Lgth., 
Feet. 


5 


3 


13.4 


11.41 


1.25i 9.1 




3 1/2 


9.7 


14.191 1.46 


9.7 


2 1/2 


10.9 


8.96 


1.20 7.5 




3 1/2 J8.5 


12.371 1.26 


9.8 




3 1/2 


15.7 


22.72 


2.37 


9.6 




3 


9.9 


11 .73 1.41 


8.3 




3 


9.8 


9 71 


1 07 


9 1 




3 


8.9 


10.45 1.24 


8.4 


4 1/2 


3 


8.4 


8.32 


0.90 9.2 


3 


3 


7.8 


9.17 1.08 


8.5 




2 1/2 


9.2 


6.72 


0.87| 7.7 




3 


6.7 


7.89 0.92 


8.6 




2 1/2 


7.8 


5.76 


0.74| 7.8 




2 1/2 


7.1 


6.40 0.89 


1.1 








—.- — 






2 1/9 


6 1 


5.55 0.76 


7.3 




5 
5 


15.3 
11.9 


33.39 
25.92 


2.40 13.9 
1 .84 14.1 





2 1/2 1 5.0 


4.59 0.62 


7.4 




4 1/2 


14.4 


27.09 


2.15 12.6 




3 7.1 


8.96 1 .08 


8.3 




4 1/2 
4 


11 2 


21 12 


1 .65 12 8 




3 6.1 


7.68 0.91 


8.4 




13.5 


21 55 


1 89 1 1 4 


2 1/2 


2 1/2 6.4 


6.29 0.90 


7.0 


4 


4 


10.5 


16.85 


1 .45 116 




2 1/2 1 5.5 


5.33 0.75 


7.1 


3 
3 


9.2 
7.8 


9.60 
8.21 


1.08| 8.9 
0.90| 9.1 


2 1/4 


I 1/4 
"2 1/4 


2.87 
4.9 


0.93 0.25 


3.7 




4.37, 0.69 


6.3 




2 1/2 


8.5 


6.61 


0.87| 7.6 


2 1/4 


4.1 


3.41| 0.53 


.6.4 




2 1/2 


7.2 


5.65 


0.73| 7.7 




2 


4.3 


3 310 59 


5 6 




2 


7.8 


4.27 


0.70! 6.1 


2 


2 


3.56 


2.77 0.49 


5.7 




2 


6.7 


3.63. 


0.59 6.2 
1.90 11.1 


1 3/4 


1 V2 


3.09 


1.60 


0.36 

inn 


4.4 




4 


12.6 21 .12' 


1 3/4 


3.09 


"2703 


4.9 




4 


9 8 16 53 


1 46 1 1 3 




■- 








3 1/2 


11.7 16.32 


1.65 9.9 




2 !2.45 


2.03 0.37 


5.5 


3 1/2 


3 1/2 


9.2 12.69 


1 .27 10.0 


11/2 


1 1/2 2.47 


1 .49 0.36 


4.1 




3 


10 8 12 05 


1 42 8.5 


1 1/2 1 1 .94 1.1/ 0.27 


4.3 




3 8.5 9.49 


1.09 8.7 
1.04 8.7 
1 92 10 8 




1 1/4 ! 1.25 j 0.57; 0.15 


3.7 




3 


7.5 9.07 


11/4 


1 1/4 ' 2.02 i 1.01 0.30 


3.4 




4 


n 7 


20 69 


1 1/4 ' " ' " 


1 .59 i 0.78 0.22 


3.5 


3 


4 1 iO.5 


18.35! 


1.63 10.9 




5/8 


0.88 1 0.14 0.07 


1.9 


4 1 9.2 


16.11 


1.47 11. 


1 


~\ 


1 .25 i 0.49 0.18 


~TT 




3 1/2 1 10.8 


15.89! 


1.66 9.6 


1 


1 


0.89 0.35 0.12 


2.9 



316 



STRENGTH OF MATERIALS. 



Properties of Carnegie Z-Bars. 













'^1 


• '3 


.2 4, 


|| 




4J u 

1! 


II 














II 

ZU 




II 

2" 


Jo 


. 
.20^ 


.2 

1^ 


i 


6 


1 


1 


1 







Pi 


go 

1 . 


^"o 






1 






1 


< 


. O 

s|t: 
1"- 


05. 


^6^ 
fl. 


Sd| 
xn 






.. 


in. 


in. 


in. 


lb. 


sq. in. 


/ 


/ 


S 


S 


r 


r 


r 


6 


31/2 


3/8 


15.7 


4.59 


25.32 


9.11 


8.44 


2.75 


2.35 


1.41 


0.83 


61/16 


3 9/16 


7/16 


18.4 


5.39 


29.80 


10.95 


9.83 


3.27 


2.35 


1.43 


0.83 


61/8 


3 5/8 


1/2 


21.1 


6.19 


34.36 


12.87 


11.22 


3.81 


2.36 


1.44 


0.84 


6 


31/2 


9/16 


22.8 


6.68 


34.64 


12.59 


11.52 


3.91 


2.28 


1.37 


0.81 


61/16 


3 9/16 


6/8 


25.4 


7.46 


38.86 


14.42 


12.82 


4.43 


2.28 


1.39 


0.82 


61/8 


3 5/8 


11/16 


28.1 


8.25 


43.18 


16.34 


14.10 


4.98 


2.29 


1.41 


0.84 


6 


31/2 


3/4 


29.4 


8.63 


42.12 


15.44 


14.04 


4.94 


2.21 


1.34 


0.81 


61/16 


3 9/16 


13/16 


32.0 


9.40 


46.13 


17.27 


15.22 


5.47 


2.22 


1.36 


0.82 


6 1/8 


3 5/8 


7/8 


34.6 


10.17 


50.22 


19.18 


16.40 


6.02 


2.22 


1.37 


0.83 


5 


31/4 


5/16 


11.6 


3.40 


13.36 


6.18 


5.34 


2.00 


1.98 


1.35 


0.75 


51/16 


3 5/16 


3/8 


14.0 


4.10 


16.18 


7.65 


6.39 


2.45 


1.99 


1.37 


0.76 


51/8 


3 3/8 


7/16 


16.4 


4.81 


19.07 


9.20 


7.44 


2.92 


1.99 


1.38 


0.77 


5 


31/4 


1/2 


17.9 


5.25 


19.19 


9.05 


7.68 


3.02 


1.91 


1.31 


0.74 


51/16 


3 5/16 


9/16 


20.2 


5.94 


21.83 


10.51 


8.62 


3.47 


1.91 


1.33 


0.75 


51/8 


3 3/8 


5/8 


22.6 


6.64 


24.53 


12.06 


9.57 


3.94 


1.92 


1.35 


0.76 


5 


31/4 


11/16 


23.7 


6.96 


23.68 


11.37 


9.47 


3.91 


1.84 


1.28 


0.73 


51/16 


3 5/16 


3/4 


26.0 


7.64 


26.16 


12.83 


10.34 


4.37 


1.85 


1.30 


0.74 


51/8 


3 3/8 


13/16 


28.4 


8.33 


28.70 


14.36 


11.20 


4.84 


1.86 


1.31 


0.76 


4 


31/16 


1/4 


8.2 


2.41 


6.28 


4.23 


3.14 


1.44 


1.62 


1.33 


0.67 


41/16 


31/8 


5/16 


10.3 


3.03 


7.94 


5.46 


3.91 


1.84 


1.62 


1.34 


0.68 


41/8 


3 3/16 


3/8 


12.5 


3.66 


9.63 


6.77 


4.67 


2.26 


1.62 


1.36 


0.69 


4 


31/16 


7/16 


13.8 


4.05 


9.66 


6.73 


4.83 


2.37 


1.55 


1.29 


0.66 


41/16 


31/8 


1/2 


15.9 


4.66 


11.18 


7.96 


5.50 


2.77 


1.55 


1.31 


0.67 


41/8 


3 3/16 


9/16 


18.0 


5.27 


12.74 


9.26 


6.18 


3.19 


1.55 


1.33 


0.68 


4 


31/16 


5/8 


18.9 


5.55 


12.11 


8.73 


6.05 


3.18 


1.48 


1.25 


0.66 


41/16 


31/8 


11/16 


20.9 


6.14 


13.52 


9.95 


6.65 


3.58 


1.48 


1.27 


0.67 


41/8 


3 3/16 


3/4 


23.0 


6.75 


14.97 


11.24 


7.26 


4.00 


1.49 


1.29 


0.68 


3 


211/16 


1/4 


6.7 


1.97 


2.87 


2.81 


1.92 


1.10 


1.21 


1.19 


0.55 


31/16 


23/4 


Vl6 


8.5 


2.48 


3.64 


3.64 


2.38 


1.40 


1.21 


1.21 


0.56 


3 


211/16 


3/8 


9.8 


2.86 


3.85 


3.92 


2.57 


1.57 


1.16 


1.17 


0.54 


31/16 


2 3/4 


7/16 


11.5 


3.36 


4.57 


4.75 


2.98 


1.88 


1.17 


1.19 


0.55 


3 


211/16 


1/2 


12.6 


3.69 


4.59 


4.85 


3.06 


1.99 


1.12 


1.15 


0.53 


31/16 


23/4 


9/16 


14.3 


4.18 


5.26 


5.70 


3.43 


2.31 


1.12 


1.17 


0.54 



PROPERTIES OF ROLLED STRUCTURAL STEEL. 317 



Properties 


» of Carnegie 


Unequal Angles; 


Minimum, 


Intermediate, 




and 


Maximum Tiiicknesses and Weights. 






^> 






Moment of 


' Section 


Radius of Gyra- 




0) 



1 


4 


j Inertia. — /. 


1 Modulus.— S. 


tion. — r. 


Size, 
In. 


ral Axis 
allel to 
g Flange. 


ral Axis 
allel to 
rt Flange. 


ral Axis 
allel to 
Ig Flange. 


ral Axis 
allel to 
rt Flange. 


ral Axis 
allel to 
g Flange. 


ral Axis 
allel to 
"t Flange. 
; Radius, 
Diagonal.! 




be Q 




+j »-i c3 


-!-> t-. 


■^J u C 


4J lU, 


-M Ui c 


-fcj 1- :; +i .- 








d c« 5 


3 cax 


13 c« 


3 «J.S 


P c« 


Neu 

Pa 

She 

Leas 

Axis 




H 


< 


2 "^ 


7^ 


Z 


;z; 


:z; 


8 X6 


1 


44.2 


13.00 


38.8 


80.8 


8.9 


15.1 


1.73 


2.49 'l.28 




3/4 


33.8 


9.94 


30.7 


63.4 


6.9 


11.7 


1.76 


2.53 1.29 




7/16 


20.2 


5.93 


19.3 


39.2 


4.2 


7.1 


1.80 


2.57 1.30 


8 X31/2 




35.7 


10.50 


7.8 


66.2 


3.0 


13.7 


0.86 


2.51 


0.73 




3/i 


27.5 


8.06 


6.3 


52.3 


2.3 


10.6 


0.88 


2.55 


0.73 




7/16 


16.5 


4.84 


4.1 


32.5 


1.5 


6.4 


0.92 


2.59 


0.74 


7 X31/2 


1 


32.3 


9.50 


7.5 


45.4 


3.0 


10.6 


0.89 


2.19 


0.74 




11/16 


23.0 


6.75 


5.7 


33.5 


2.1 


7.6 


0.92 


2.23 


0.74 




3/8 


13.0 


3.80 


3.5 


19.6 


1.3 


4.3 


0.96 


2.27 


0.76 


6 X4 


1 


30.6 


9.00 


10.8 


30.8 


3.8 


8.0 


1.09 


1.85 


0.85 




11/16 


21.8 


6.40 


8.1 


22.8 


2.8 


5.8 


1.13 


1.89 


0.86 




3/8 


12.3 


3.61 


4.9 


13.5 


1.6 


3.3 


1.17 


1.93 


0.88 


6 X31/2 


1 


28.9 


8.50 


7.2 


29.2 


2.9 


7.8 


0.92 


1.85 


0.74 




II/I6 


20.6 


6.06 


5.5 


21.7 


2.1 


5.6 


0.95 


1.89 


0.75 




V16 


9.8 


2.87 


2.9 


10.9 


1.0 


2.7 


1.00 


1.95 


0.77 


5 X4 


7/8 


24.2 


7.11 


9.2 


16.4 


3.3 


5.0 


1.14 


1.52 10.84 




5/8 


17.8 


5.23 


7.1 


12.6 


2.5 


3.7 


1.17 


1.55 


0.84 




3/8 


11.0 


3.23 


4.7 


8.1 


1.6 


2.3 


1.20 


1.59 


0.86 


5 X31/2 


7/8 


22.7 


6.67 


6.2 


15.7 


2.5 


4.9 


0.96 


1.53 


0.75 




5/8 


16.8 


4.92 


4.8 


12.0 


1.9 


3.7 


0.99 


1.56 


0.75 




5/16 


8.7 


2.56 


2.7 


6.6 


1.0 


1.9 


1.03 


1.61 


0.76 


5 X3 


13/16 


19.9 


5.84 


3.7 


14.0 


1.7 


4.5 


0.80 


1.55 


0.64 




9/16 


14.3 


4.18 


2.8 


10.4 


1.3 


3.2 


0.82 


1.58 


0.65 




5/16 


8.2 


2.40 


1.8 


6.3 


0.75 


1.9 


0.85 


1.61 


0.66 


41/2X3 


13/16 


18.5 


5.43 


3.6 


10.3 


1.7 


3.6 


0.81 


1.38 


0.64 




9/16 


13.3 


3.90 


2.8 


7.8 


1.3 


2.6 


0.85 


1.41 |0.64 




5/1 6 


7.7 


2.25 


1.7 


4.7 


0.75 


1.5 


0.87 


1.44 


0.66 


4 X31/2 


13/16 


18.5 


5.43 


5.5 


7.8 


2.3 


2.9 


1.01 


1.19 


0.72 




9/16 


13.3 


3.90 


4.2 


5.9 


1.7 


2.1 


1.03 


1.23 


0.72 




^5/16 


7.7 


2.25 


2.6 


3.6 


1.0 


1.3 


1.07 


1.26 


0.73 


4 X3 


13/16 


17.1 


5.03 


3.5 


7.3 


1.7 


2.9 


0.83 


1.21 


0.64 




9/16 


12.4 


3.62 


2J 


5.6 


1.2 


2.1 


0.86 


1.24 


0.64 




1/4 


5.8 


1.69 


1.4 


2.8 


0.60 


1.0 


0.89 


1.28 


0.65 


31/2X3 


13/16 


15.8 


4.62 


3.3 


5.0 


1.7 


2.2 


0.85 


1.04 


0.62 




9/16 


11.4 


3.34 


2.5 


3.8 


1.2 


1.6 


0.87 


1.07 


0.62 




1/4 


5.4 


1.56 


1.3 


1.9 


0.58 


0.78 


0.91 


1.11 0.63 


31/2X21/2 


11/16 


12.5 


3.65 


1.7 


4.1 


0.99 


1.9 


0.69 


1.06 


0.53 




1/2 


9.4 


2.75 


1.4 


3.2 


0.76 


1.4 


0.70 


1.09 


0.53 




1/4 


4.9 


1.44 


0.78 


1.8 


0.41 


0.75 


0.74 


1.12 


0.54 


3 X21/2 


9/16 


9.5 


2.78 


1.4 


2.3 


0.82 


1.2 


0.72 


0.91 


0.52 




7/16 


7.6 


2.21 


1.2 


1.9 


0.66 


0.93 


0.73 


0.92 


0.52 




■1/4 


4.5 


1.31 


0.74 


1.2 


0.40 


0.56 


0.75 


0.95 


0.53 


3 X2 


1/2 


7.7 


2.25 


0.67 


1.9 


0.47 


l.O 


0.55 


0.92 


0.43 




3/8 


5.9 


1.73 


0.54 


1.5 


0.37 


0.78 


0.56 


0.94 


0.43 




1/4 


4.1 


1.19 


0.39 


1.1 


0.25 


0.54 


0.57 


0.95 


0.43 


21/2X2 


1/2 


6.8 


2.00 


0.64 


11 


0.46 


0.70 


0.56 


0.75 0.42 




5/16 


4.5 


1.31 


0.45 


0.79 


0.31 


0.47 


0.58 


0.78 0.42 




1/8 


1.86 


0.55 


0.20 


0.35 


0.13 


0.20 


0.61 


0.89 0.43 


21/2X 11/2 


5/16 


3.92 


1.15 


0.19 


0.71 


0.17 


0.44 


0.41 


0.79 0.32 




3/16 


2.44 


0.72 


0.13 


0.46 


0.11 


0.28 


0.42 


0.80 0.33 


21/4X11/2 


1/2 


5.6 


1.63 


0.26 


0.75 


0.26 


0.54 


0.40 


0.68 0.32 




3/16 


2.28 


0.67 


0.12 


0.34 


0.11 


0.23 


0.43 


0.72 0.33 



{Table continued on next page.) 



318 



STRENGTH OF MATERIALS. 



Properties of Carnegie 


Unequal Angles. 


— Continued. 






i 


^ 




Moment of 


Section 


Radius of Gyra- 




^ 





► M 


Inertia. — /. 


Modulus.-S. 


tion. — r. 


Size, 
In. 


c 


t3 


II 

m 


•Pi 

2^ 


Axis 
el to 
Flange. 






Axis 
lei to 
Flange. 


Axis 
el to 
Flange. 






s 


f.§ 


'o <A 






U^ 


^ u, 


22^ 


SI? 


v° 








S^ ^ 


3 c^ 


p PiX 


3 rt 


3 c«^ 


3 oj 


3 53x 






^ 


^^ 


^m 


Spmh-^ 


a»PHC/. 


ajOHH-l 


<^^m 


Splhh:; 


O/P^iW 


n^d 




Eh 


^ 


< 


z^ 


^ 


2; 


Z 


Z 


2; 


h:i< 


2 X 1 1/2 


3/8 


3.99 1.17 


0.21 


0.43 


0.20 


0.34 


0.42 


0.61 


0.32 




1/8 


1.44 , 0.42 


0.09 


0.17 


0.08 


0.13 0.45 


0.64 


0.33 


2 X 11/4 


1/4 


2.55 1 0.75 


0.09 


0.30 


0.10 


0.23 


0.34 


0.63 


0.27 




3/16 


1.96 0.57 


0.07 


0.23 


0.08 


0.18 


0.35 


0.64 


0.27 


1 V4X 11/4 


1/4 


2.34 0.69 


0.09 


0.20 


0.10 


0.18 


0.35 


0.54 


0.27 




1/8 


1.23 0.36 


0.05 


0.11 


0.05 


0.09 


0.37 


0.56 


0.27 


1 V2X 11/4 


5/16 


2.59 0.76 


0.10 


0.16 


0.11 


0.!6 


0.35 


0.45 


0.26 




3/16 


1 .64 1 0.48 


0.07 ! 0.10 


0.07 


0.10 


0.37 


0.46 


0.26 



]Maximiiiii and minimum sizes only are given for angles less than 
2y2 X 2 in. 

Safe Loads, in Thousands of Pounds, for Carnegie Unequal Angles 
Used as Beams. Minimum, Intermediate, and Maximum Thick- 
ness and Weights. 





Size of Angle, 
Inches. 


Neutral Axis Parallel 
to Shorter Leg. 


Neutral Axis Parallel 
to Longer Leg. 




Safe 
Load, 
1 Foot 
Span. 


Maximum Span, 
360 X Deflec- 
tion. 


Safe 
Load, 
1 Foot 
Span. 


Maximum Span, 
360 X Deflec- 
tion. 




Safe 
Load. 


Lgth., 
Feet. 


Safe 
Load. 


Lgth., 
Feet. 


8 
8 
8 


X6 X 1 
X6 X 3/4 
X 6 X '/16 


161.17 
124.48 
75.41 


7.49 
5.68 
3.37 


21.5 
21.9 
22.4 


95.15 
73.92 
45.12 


5.44 
4.13 
2.47 


17.5 
17.9 
18.3 


8 
8 
8 


X 3 1/2 XI 
X31/2X 3/4 
X31/2X V16 


146.03 
113.17 
68.80 


7.53 
5.72 
3.39 


19.4 
19.8 
20.3 


32.21 
25.07 
15.57 


3.10 
2.33 
1.38 


10.4 
10.8 
11.3 


7 
7 

7 


X 3 1/2 XI 
X31/2X 11/16 

X31/2X 3/8 


112.85 
81.07 
46.19 


6.52 

4.58 
2.54 


17.3 
17.7 
18.2 


31.57 
22.83 
13.44 


3.10 
2.14 
1.19 


10.2 
10.7 
11.2 


6 
6 
6 


X4 XI 

X4 X 11/16 
X4 X 3/8 


85.55 
61.65 
35.41 


5.56 
3.88 
2.16 


15.4 
15.9 
16.4 


40.43 
29.44 
17.07 


3.55 
2.47 
1.39 


11.4 
11.9 
12.3 


6 
6 
6 


X31/2X 1 
X31/2X 11/16 
X31/2X V16 


83.52 
60.27 
29.23 


5.57 

3.89 
1.83 


15.0 
15.5 
16.0 


30.93 
22.51 
11.09 


3.09 
2.14 
1.00 


10.0 
10.5 
11.1 


5 

5 
5 


X4 X 7/8 
X 4 X 5/8 
X4 X 3/8 


53.23 
39.79 
24.96 


4.00 
2.92 
1.78 


13.3 
13.6 
14.0 


35.31 
26.45 
16.75 


3.15 
2.28 
1.40 


11.2 
11.6 
12.0 


5 
5 
5 


X31/2X 7/8 
X31/2X 5/8 
X31/2X 5/16 


52 05 
38.93 
20.69 


4.04 
2.93 
1.51 


12.9 
13.3 
13.7 


26.88 
20.27 
10.88 


2.71 
1.97 
1.02 


9 9 

10.3 
10.7 



{Table continued on next page.) 
Maximum bending stress. 16,000 lb. per sq. in. Safe loads for other 
spans are inversely proportional to the span in feet. Safe loads include 
the weight of the angle, which should be deducted to give net load 
which can be carried. 



PROPERTIES OF ROLLED STRUCTURAL STEEL. 319 



Safe Loads, in Thousands of Pounds, for Carnegie Unequal Angles 
Used as Beams. — Continued. 




le. 


Neutral Axis Parallel 
to Shorter Leg. 


Neutral Axis Parallel 
to Longer Leg. 


Size of Ang 
Inches. 


Safe 
Load, 
1 Foot 
Span. 


Maximum Span, 
360 X Deflec- 
tion. 


Safe 
Load 
1 Foot 
Span. 


Maximum Span, 
360 X Deflec- 
tion. 




Safe 
Load. 


Lgth., 
Feet. 


Safe 
Load. 


Lgth., 
Feet. 


5 X3 X 
5 X3 X 
5 X3 X 


13/16 
9/16 
Vl6 


47.47 
34.45 
20.16 


3.77 
2.65 
1.51 


12.6 
13.0 
13.4 


18.56 
13.55 
8.00 


2.16 
1.51 
0.85 


8.6 
9.0 
9.4 


41/2X3 X 
4 1/2 X 3 X 
41/2X3 X 


13/lfi 

9/16 
5/16 


38.61 
28.16 
16.43 


3.36 
2.38 
1.35 


11.5 
11.8 
12.2 


18.24 
13.33 
8.00 


2.15 
1.51 
0.87 


8.5 

8.8 
9.2 


4 X 3 1/2 X 
4 X 3 1/2 X 
4 X 3 1/2 X 


13/16 
9/16 
Vl6 


31.15 
22.93 
13.44 


2.94 
2.08 
1.18 


10.6 
11.0 
11.4 


24.53 
17.92 
10.67 


2.56 
1.79 
1.03 


9.6 
10.0 
10.4 


4 X3 X 
4 X3 X 
4 X3 X 


13/16 

9/16 

1/4 


30.61 
22.40 
10.67 


2.97 
2.09 
0.96 


10.3 
10.7 
11.1 


17.92 
13.12 
6.40 


2.15 
1.51 
0.70 


8.3 
8.7 
9.1 


31/2X3 X 
31/2X3 X 
31/2X3 X 


13/16 
9/16 
1/4 


23.47 
17.17 
8.32 


2.57 
1.81 
0.84 


9.1 
9.5 
9.9 


17.60 
12.91 
6.19 


2.17 
1.52 
0.70 


8.1 
8.5 
8.9 


3 1/2 X 2 1/2 X 
31/2X2 1/2 X 
31/2 X 2 1/2 X 


11/16 

1/2 
1/4 


19.73 
15.04 
8.00 


2.19 9.0 
1.63 9.2 
0.83 1 9.6 


10.56 
8.11 
4.37 


1.51 
1.13 
0.58 


7.0 
7.2 
7.6 


3 X 2 1/2 X 
3 X 2 1/2 X 
3 X21/2X 


9/16 

7/16 
1/4 


12.27 
9.92 
5.97 


1.53 
1.22 
0.71 


8.0 
8.1 
8.4 


8.75 
7.04 
4.27 


1.25 
0.99 
0.58 


7.0 
7.1 
7.4 


3 X2 X 
3 X2 X 
3 X2 X 


1/2 
3/8 
1/4 


10.67 
8.32 
5.76 


1.39 
1.05 
0.71 


7.7 
7.9 
8.1 


5.01 
3.95 
2.77 


0.88 
0.67 
0.46 


5.7 
5.9 
6.1 


21/2X2 X 
21/2X2 X 
21/2X2 X 


1/2 
Vl6 
1/8 


7.47 
5.01 
2.13 


1.15 
0.74 
0.30 


6.5 
6.8 
7.1 


4.91 
3.31 
1.49 


0.89 
0.57 
0.23 


5 5 

5.8 
6.1 


*2 1/2 X 1 1/2 X 

*2 1/2 X n/2 X 


Vl8 
3/16 


4.69 
2.99 


0.73 
0.45 


6.4 
6.6 


1.81 
1.17 


0.41 
0.25 


4.4 
4.6 


*2 1/4 X 1 1/2 X 
*2 1/4 X 1 1/2 X 


1/2 
3/16 


5.76 
2.45 


1.02 
0.40 


5.6 
6.0 


2.77 
1.17 


0.67 
0.25 


4.T 

4.6 


*2 X 1 1/2 X 
*2 X 1 1/2 X 


3/8 

1/8 


3.63 
1.39 


0.70 
0.24 


5.2 
5.6 


2.13 
0.80 


0.51 
0.17 


4.2 
4.6 


*2 X 1 1/4 X 
*2 X 1 1/4 X 


1/4 
3/16 


2.45 
1.92 


0.47 ' 5.2 
0.36 5.3 


1.04 
0.80 


0.28 
0.21 


3.7 
3.8 


*1 3/4 X 1 1/4 X 
*1 3/4 X 1 1/4 X 


1/4 
1/8 


1.92 
1.00 


0.42 4.6 
0.21 4.8 


1.01 
0.56 


0.28 
0.15 


3.6 
3.8 


*|1/2X11/4X 
*1 1/2 X 1 1/4 X 


Vie 

3/16 


1.71 
1.07 


0.44 1 3.9 
0.26 4.1 


1.17 
0.78 


0.34 
0.22 


3.4 
3.6 



Maximum bending stress, 16,000 lb. per sq. in. Safe loads for other 
spans are inversely proportional to the span in feet. Safe loads include 
the weight of the angle, which should be deducted to give net load 
which can be carried. 

* Only maximum and minimum sizes are given for angles smaller 
than 2 H X 2 in. 



320 



STRENGTH OF MATERIALS- 



Properties of Carnegie Angles with Equal Legs. Minimum, Inter- 
mediate and Maximum Thielinesses and Weights. 













1 1 ^^ 




1 1 ^-< 















3 ^S 


3 flii 

0) 0)3 


0) oS 


tri 


m 




ji 




Jh-^ 


:z;o2 


zot 


^0 2 


1 


fi 


1 

i 


k 






ulus, 
rough 
ity Pa 


§1^ 


.f Gyra 
is thr 
Gravit 
to Fla 


1. 


7 

1 


1 


0^ 

II 




t of Ir 
xis th 
Grav] 
nge. 


Mod 
xis th: 

Gravi 
nge. 




idius 
al Ax 
r of < 
of 45° 


1 






c^ 


rt 03 5 


[omen 
tral A 
ter of 
to Fla 


3ction 
tral A 
ter of 
to Fla 


adius < 
tral A 
ter of 
to Fla 


iast Ri 
Neutr 
Cente 
Angle 


5 


H 


^ 


<1 


Q 


g 


m 


P5 


^ 


8 X8 


11/8 


56.9 


16.73 


2.41 


98.0 


17.5 


2.42 


1.55 


8 X8 


13/16 


42.0 


12.34 


2.30 


74.7 


13.1 


2.46 


1.57 


8 X8 


1/2 


26.4 


7.75 


2.19 


48.6 


8.4 


2.51 


1.58 


6 X6 


1 


37.4 


11.00 


1.86 


35.5 


8.6 


1.80 


1.16 


6 X6 


II/16 


26.5 


7.78 


1.75 


26.2 


6.2 


1.83 


1.17 


6 X6 


3/8 


14.9 


4.36 


1.64 


15.4 


3.5 


1.88 


1.19 


5 X5 


1 


30.6 


9.00 


1.61 


19.6 


5.8 


1.48 


0.96 


5 X5 


11/16 


21.8 


6.40 


1.50 


14.7 


4.2 


1.51 


0.97 


5 X5 


3/8 


12.3 


3.61 


1.39 


8.7 


2.4 


1.56 


0.99 


4 X4 


13/16 


19.9 


5.84 


1.29 


8.1 


3.0 


1.18 


0.77 


4 X4 


9/16 


14.3 


4.18 


1.21 


6.1 


2.2 


1.21 


0.78 


4 X4 


1/4 


6.6 


1.94 


1.09 


3.0 


1.0 


1.25 


0.79 


31/2X31/2 


13/16 


17.1 


5.03 


1.17 


5.3 


2.3 


1.02 


0.67 


31/2X31/2 


9/I6 


12.4 


3.62 


1.08 


4.0 


1.6 


1.05 


0.68 


31/2X31/2 


1/4 


5.8 


1.69 


0.97 


2.0 


0.79 


1.09 


0.69 


3 X3 


5/8 


11.5 


3.36 


0.98 


2.6 


1.3 


0.88 


0.57 


3 X3 


7/16 


8.3 


2.43 


0.91 


2.0 


0.95 


0.91 


0.58 


3 X3 


1/4 


4.9 


1.44 


0.84 


1.2 


0.58 


0.93 


0.59 


21/2X21/2 


1/2 


7.7 


2.25 


0.81 


1.2 


0.73 


0.74 


0.47 


21/2X21/2 


V16 


5.0 


1.47 


0.74 


0.85 


0.48 


0.76 


0.49 


21/2X21/2 


1/8 


2.08 


0.61 


0.67 


0.38 


0.20 


0.79 


0.50 


2 X2 


7/16 


5.3 


1.56 


0.66 


0.54 


0.40 


0.59 


0.39 


2 X2 


1/4 


3.19 


0.94 


0.59 


0.35 


0.25 


0.61 


0.39 


2 X2 


1/8 


1.65 


0.48 


0.55 


0.19 


0.13 


0.63 


0.40 


13/4X13/4 


7/16 


4.6 


1.34 


0.59 


0.35 


0.30 


0.51 


0.33 


13/4X13/4 


V16 


3.39 


1.00 


0.55 


0.27 


0.23 


0.52 


0.34 


13/4X13/4 


1/8 


1.44 


0.42 


0.48 


0.13 


0.10 


0.55 


0.35 


11/2X11/2 


3/8 


3.35 


0.98 


0.51 


0.19 


0.19 


0.44 


0.29 


11/2X11/2 


1/4 


2.34 


0.69 


0.47 


0.14 


0.13 


0.45 


0.29 


U/2XII/2 


1/8 


1.23 


0.36 


0.42 


0.08 


0.07 


0.46 


0.30 


11/4X11/4 


5/16 


2.33 


0.68 


0.42 


0.09 


0.11 


0.36 


0.24 


11/4X11/4 


3/16 


1.48 


0.43 


0.38 


0.06 


0.07 


0.38 


0.24 


11/4X11/4 


1/8 


1.01 


0.30 


0.35 


0.04 


0.05 


0.38 


0.25 


1 XI 


1/4 


1.49 


0.44 


0.34 


0.04 


0.06 


0.29 


0.19 


1 XI 


3/16 


1.16 


0.34 


0.32 


0.03 


0.04 


0.30 


0.19 


1 XI 


1/8 


0.80 


0.23 


0.30 


0.02 


0.03 


0.31 


0.19 



RIVET SPACING FOR STRUCTURAL WORK. 321 



Safe Loads, In Thousands of Pounds, Uniformly Distributed for 
Carnegie Equal Angles Used as Beams. 

(Maximum, Intermediate and Minimum Thicknesses and Weights.) 









Maximum 






Maximum 






Safe 


Span, 




Safe 


Span, 


Size of Angle, 
Inches. 


Load 
One- 
Foot 
Span. 


360 X De- 
flection. 


Size of Angle, 
Inches. 


Load 
One- 
Foot 
Span. 


360 XDe- 
flection. 






Safe 


LRth. 




Safe 


Lgth. 








Load 


Feet. 






Load 


Feet. 


8 X8 


X\W8 


186.99 


8.31 


22.5 


21/2X21/2X1/2 


7.79 


1.15 


6.8 




13/16 


139.84 


6.08 


23.0 


V16 


5.12 


0.72 


7.1 




1/2 


89.28 


3.82 


23.4 


1/8 


2.13 


0.29 


7.4 


6 X6 


XI 


91.41 


5.48 


16.7 


2 X2 X7/16 


■4.27 


0.79 


5.4 




11/16 


65.81 


3.85 


17.1 


1/4 


2.67 


0.46 


5.7 




3/8 


37.65 


2.14 


17.6 


1/8 


1.39 


0.24 


5.8 


5 X5 


XI 


61.87 


4.55 


13.6 


13/4X13/4X7/16 


3.20 


0.68 


4.7 




11/16 


44.80 


3.18 


14.1 


5/16 


2.45 


0.51 


4.8 




3/8 


25.81 


1.78 


14.5 


1/8 


1.07 


0.21 


5.1 


4 X4 


X 13/16 


32.11 


2.95 


10.9 


11/2X11/2X3/8 


2.03 


0.51 


4.0 




9/16 


23.36 


2.07 


11.3 


V4 


1.39 


0.33 


4.2 




1/4 


11.20 


0.96 


11.7 


1/8 


0.77 


0.17 


4.4 


31/2X31/2X13/16 


24,00 


2.55 


9.4 


11/4X1 1/4 XV16 


1.17 


0.36 


3.3 




9/16 


17.60 


1.81 


9.7 


3/16 


0.76 


0.22 


3.5 




1/4 


8.43 


0.83 


10.2 


1/8 


0.52 


0.14 


3.6 


3 X3 


X 5/8 


13.87 


1.69 


8.2 


1 XI X 1/4 


0.60 


0.22 


2.6 




7/16 


10.13 


1.21 


8.4 


3/16 


0.47 


0.17 


2.7 




1/4 


6.19 


0.71 


8.7 


1/8 


0.33 


0.12 


2.8 



Maximum bending stress, 16,000 lb. per sq. In. Safe loads for 
other spans are inversely proportional to the span in feet. Safe loads 
given include weight of angle which should be deducted to give net 
load that can be carried. 

Biyet Spacing for Structural Worli. — The following rules are con- 
densed from those of the Cambria Steel Co. The minimum pitch of 
rivets should be at least three times the diameter, and in bridge work 
should not exceed 6 in., or 16 times the thickness of the thinnest outside 
plate. The minimum distance between edge of any piece and the 
center of the rivet is II/4 in. for 3/4 and T/s in. rivets except in bars 
less than 21/2 in. wide. If possible this distance should be at least 
two rivet diameters for all sizes, and should not exceed eight times the 
thickness of the plate. The maximum pitch for flanges of girders and 
chords carrying floors is 4 in. Where plates are in compression, the 
maximum pitch in the Unes of stress is sixteen times the plate thickness, 
and in the line at right angles to the line of stress, thirty-two times the 
plate thickness, except in the case of cover plates, top chords, and 
end posts, where the maximum pitch may be forty times the plate 
thickness. The minimum space between the rivet center and the ad- 
jacent leg when rivets are adjacent to the corners of angles is 1/2 the 
diameter of the head, plus s/s in. clearance. When there is a row of 
rivets in the adjacent leg, the 3/8 in. clearance should be measured from 
the rivet heads. 

The table below, and those on page 322, give the standards adopted 
by the American Bridge Co. for rivet spacing in structural and bridge 
. work: 

Gages for Angles, Inches. 



1 rM 


Leg 
gi 

g2 

g3 

Max. 
Rivet 


8 

41/2 

3 
11/8 


7 

4 

21/2 
3 

1 


6 

31/2 
21/2 
21/4 

7/8 


5 

I 

13/4 

7/8 


4 

21/2 


31/2 
2 


3 

IV4 


21/2 

13/8 


2 

11/8 


13/4 


11/2 

7/8 


11/4 

3/4 


I 

5/8 


3/4 


ir 


- 


1/2 


't 






















k. 


7/8 


7/8 


7/8 


3/4 


5/8 


1/2 


3/8 


3/8 


1/4 


1/4 



322 



STRENGTH OF MATERIALS. 



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CN CN 




1 










" -^11 




00 


CO 2 CO CO 


CO 






1e 












a 




^ 


^ ^^^ < < 


■^ ^ ^ 


00 •<»• 










CO «o 


.^^ 




























;^ 










^e^t^f*^ 


3 






,— — ^- ^- pNl <N <N 


CN CN CN 


rs CN 


2o 




























•^1 




00 










CO CO 




- 




>>^^> > 


CO CO cc 


> 




■" 










(sq 


s 




- 




— .» — ~ ~ rs (N 


CN CN CN CN 


CN 


3i 








00 •^ 00 e^ 


•ui '(:y) 




CO CO 2 CO CO 


CO CO 




aauBJBBio 








i^i^^^ 






00 






^ ^ eo 


\ 


rt b£ 


mnuiiuij\ 














•^^ 




r^oskOcot^^-Hco 
— — — — — — CNfN 


CN CN CN 


CN 




•UI '(X) 


^^ ^00 00 












^ c5 


SuiOBdg 


^^ >-o~ ^ 




1 






11 


uinuiraii\ 


— — — <N«Nr>^f«^^<^ 




A 


oo-<i<ooe^oo'*oo oO'««<ooe^ 








5- 


H 


>>;^>:^;^;> >>>> 


"iS be 


•UI'-UIBIQ 


>5:>>;?s^ > 




a' 


» — — — — CMCN(S(N(N 


















-»— 


































•*5 



PLATE AND ANGLE COLUMNS. 



323 



Notes on Tables of Channel and Plate and Angle Columns. 

(Carnegie Steel Co.) 

The tables on pages 324 to 330 give the safe loads in thousands of 
pounds which can be imposed on channel and plate and angle columns 
of the form and dimensions shown in the illustrations, which experience 
has shown to be desirable for ordinary bridges and buildings. They 
also give the moments of inertia and radii of gyration about both axes 
of symmetry, areas of section and weights per foot without allowances 
for rivet heads, or other details. The tables have been computed for 
the least radius of gyration in accordance with the American Bridge Co. 
formula for ratios of l/r up to 120, 5 = 19,000 - 100 l/r, in which 5 is 
the axial compressive strength, lb. per sq. in.. I is the length, in., and 
r is the radius of gyration, in. The maximum value of 3 is not to 
exceed 13,000. For ratios of l/r up to 120 and for greater ratios up 
to 200 the maximum values of 5 allowed are as follows : 



l/r 


S 


l/r 


s 


l/r 


S 


l/r 


S 


60 
70 
80 
90 


13.000 
12.000 
11.000 
10,000 


100 

no 

120 
130 


9.000 
8,000 
7.000 
6.500 


140 
150 
160 
170 


6.000 
5.500 
5.000 
4.500 


180 
190 


4.000 
3.500 



The values given in the table may be compared with the values given 
by other formulae by means of the comparative table on page 286. 
It is assumed in the tables that the loads are direct and equally dis- 
tributed over the cross section of the column or balanced on opposite 
sides of it. In the case of unbalanced loads bending stresses are pro- 
duced, and the column must be so proportioned that the combined fiber 
stresses do not exceed the allowable axial compression. (See page 296.) 

The ratio l/r =120 should not be exceeded for main members under 
heavy stress. For secondary members such as wind bracing, under 
higher ratios, which, however, must not exceed 200, may be used. 

|«— 9'i_-^ U— Hi'-- 4 U— 11^/-^ k--i3y__^ 



A^ 



1/^ 



'^ T^ 



-8^2- 



1^ T^ 



^ 



l<^ — 12'-'— ">| k^— L4^'-"4 k 

^ig. 83 



i^ ^ "^ 



■-10- 



7^ 



—14-'—-^ 



k^— 16"— ^^ 
Fig. 86 






(^ 



k 16--—^ k 18'- 



-16- 
Fig. 87 




H^ 






; c 


\ c 




^i 






iJ 


r ^ 


k 



Fig. 88 



Fig. 89 



Dimensions of Channel Columns. 
(See tables, pages 324 — 327.) 



324 



STEENGTH OP MATERIALS. 



Safe Loads on Carnegie 10-Inch Channel Columns In Thousands 
of Pounds. (See Figs. 83 and 84, page 323.) 


n 

1 




Lat. 


Effective Length of Column, Feet. 


^1 


"3:72" 
3.60 
3.59 
3.58 
3.58 
3.55 




18 

T76 
213 

252 
271 
152 


20 

m 

203 

221 
239 

257 
144 
271 
289 
307 
325 


22 


24 


26 

"95 

170 

185 
200 
215 


28 


30 


32 


34 






106 100 
192 181 

209' 197 
226 213 
243,229 
136 128 
256 240 
272 256 
289272 
307 288 


89 
159 

173 
187 
201 


83 j 77 


72 
126 
137 
148 
159 


3.87 
4.50 
4.58 
4.65 
4.71 


37.8 


15 


12 


5/16 

3/8 
7/16 
1/2 
Lat. 


148 

161 

174 
187 


137 
149 
161 
173 


55.5 
60.6 
65.7 
70.8 




120 112 


104 


96j 88 


3.66 


47.8 


20 


12 


7/16 

1/2 
9/16 

5/8 


286 
305 
324 
343 


225 210 
240 223 
255237 
270j252 


195 
207 
220 
233 


179 
191 
203 
215 


164 
174 
185 
196 


4.46 
4.53 
4.60 
4.66 


3.51 
3.50 
3.50 
3.50 


75.7 
80.8 
85.9 
91.0 






Lat. 


186 


176 


165 


155 


1451134 


124j 114| 103 


3.52 


3.41 


57.8 


25 
30 
35 


12 
12 

12 




9/16 
5/8 
9/16 
5/8 
9/16 
5/8 
Lat. 


359 
378 
392 
411 
424 
444 
116 
252 
275 
298 


339 
357 
370 
388 
400 
418 

m 

^252 
275 
298 


319 
336 
348 
364 
375 
392 
109 
251 
273 
295 


300 
316 
326 
341 
350 
366 
103 
241 
261 
282 


280 260 
2952^ 
303 '281 
318,295 
325 301 
341 315 
98 92 


241 
253 
259 
271 
276 
289 
87 


2211 201 
233L212 

23 7| 216' 
248J 227 
251 "232 
263 i 243 
81 75 


4.45 
4.52 
4.33 
4.39 

4.22 
4.29 
3.87 


3.44 
3.44 
3.37 
3.37 
3.30 
3.31 
4.70 
4.36 
4.33 
4.31 


95.9 
101.0 
105.9 
111.0 
115.9 
121.0 

39.3 


15 


14 


3/8 
7/l6 

1/2 


230 219 
250 238 
270 257 


209 
226 

244 


198 187 
2141 203 
231 219 


4.63 
4.70 
4.76 


65.7 
71.7 
77.6 






Lat. 


153 


146 


139 


131 
295 
316 
337 
357 


123 115 
282 268 
301 287 
321 306 
341 324 
149 139 

353 336 
373 355 
393 373 
412392 


108, 100 92 
255 j 24 li 228 
272 258 243 
290 275 259 
308; 291 274 
1291 1191 109 


3.66 
4.52 
4.59 
4.66 
4.72 
3.52 
4.52 
4.58 
4.64 
4.70 
3.42 


4.53 
4.29 
4.27 
4.26 
4.24 
4.39 
4.22 
4.21 
4.20 
4.19 
4.28 


49.4 


20 


14 


7/16 
1/2 
9/16 

5/8 


312 
335 
358 
380 


'312 
335 
358 
380 


308 
330 
352 
374 


81.7 
87.6 
93.6 
99.5 






Lat. 


189 


179 


169 


159 


59.4 


25 


14 


9/16 
5/8 
11/16 
3/4 


396 
419 
441 
464 


396 
419 
441 
464 


388 371 
410 392 
432,412 
453,433 


319 
336 
354 
372 
149 


301 
318 
335 
351 
137 


284 
300 
315 
331 
125 


103.6 
109.5 
115.5 
121.4 






Lat. 


224 


211 


199 187 


174 162 


69.4 


30 


14 


11/16 

3/4 

13/16 
7/8 
15/16 
1 


480 
502 
525 
548 
571 
593 


480 
502 
525 
548 
571 
593 


467 '446 
488 466 
510487 
532 508 
554 529 
575 549 


424'403 
444 421 
464 440 
483 459 
503 478 
522 496 


382 
399 
417 
434 
452 
469 


360 
377 
394 
410 
427 
443 


339 
354 
370 
385 
401 
416 


4.53 
4.59 
4.65 
4.70 
4.76 
4.81 


4.16 
4.15 
4.15 
4.14 
4.14 
4.13 


125.5 
131.4 
137.4 
143.3 
149.3 
155.2 


35 


14 


15/16 

11/16 

11/8 
13/16 

11/4 


609:609 
632632 
654654 
677 677 
700 700 
723 723 


5881561 
610 582 
632 603 
654 624 
675 644 
697 665 


533506 
553 525 
5731544 
593 563 
612581 
632599 


479 
4% 
514 
532 
549 
567 


451 
468 
485 
502 
517 
534 


424 
440 
455 
471 
486 
502 


4.66 

4.72 
4.77 
4.82 
4.87 
4.92 


4.10 
4.10 
4.10 
4.10 
4.09 
4.09 


159.3 
165.2 
171.2 
177.1 
183.1 
189.0 



Safe loads enclosed between heavy lines are for ratios of l/r not over 
60; between the dotted lines are for ratios of l/r not over 200; all 
other safe loads are for ratios l/r up to 120. Allowable fiber stress 
13,000 lb. for lengths of 60 radii or over. Weights do not include rivet 
heads or other details. 



SAFE LOADS ON CHANNEL COLUMNS. 



325 



Safe Loads for Carnegie 12-Inch Channel Columns in Thousands 


of Pounds. (See Figs. 85 and 86, page 323.) 




i 




1 


Effective Length of Column, Feet. 


i° 




d 


S ' 


•s 










1 




lis 

ogPn 


J 




18 


20 


22 


24 


26 


28 


30 


32 


34 


i 
1 


i^ 




H 




















Pi 


Pi 


'^ 




Lat. 


Hi 


157 


157 


152 


146 


139 


133 


126 

227 


120 

214 


4.61 
5.40 


4.50 


50.4 




3/8 


293 


293 


290 277 


265 


252 


239 


4.29 


76.7 






7/lfi 


316 


316 


312 298 


284 


271 


257 


243 


230 


5.48 


4.27 


82.7 


20H 


14 


V?, 


339 


339 


334 319 


304 


290 


275 


260 


246 


5.55 


4.26 


88.6 






9/16 


362 


362 


355 


339 


324 


308 


292 


277 


261 


5.62 


4.24 


94.6 






5/8 


384 


384 


377 


360 


344 


327 


310 


293 


277 
142 
283 


5.68 
4.43 
5.47 


4.23 
4.36 
4.20 


100.5 






Lat. 


191 


191 


190 


182 


174 


166 


158 


150 
300 


59.4 






9/16 


396 


396 


387 


370 


352 


335 


318 


103.6 






5/8 


419 


419 


409 


390 


372 


354 


335 


317 


298 


5.53 


4.19 


109.5 


25 


14 


11/16 


441 


441 


431 


411 


392 


372 


353 


333 


314 


5.60 


4.18 


115.5 






3/4 


464 


464 


453 


432 


412 


391 


371 


350 


330 


5.66 


4.18 


121.4 






13/16 


487 


487 


474 


453 


431 


410 


388 


367 


345 


5.71 


4.17 


127.4 






Lat. 


229 


229 


225 


215 


205 


195 


185 


175 


165 
352 


4.28 


4.23 


69.4 






3/4 


502 


502 


487 


465 


442 


420 


397 


375 


5.52 


4.13 


131.4 






13/16 


525 


525 


509 


486 


462 


439 


415 


392 


368 


5.58 


4.13 


137.4 


30 


14 


7/8 


548 


548 


531 


506 


482 


457 


432 


408 


383 


5.64 


4.12 


143.3 






15/16 


571 


571 


553 


527 


502 


476 


450 


425 


399 


5.70 


4.12 


149.3 








593 


593 


575 


548 


522 


495 


468 


442 


415 


5.75 


4.12 


1S5.2 






Lat. 


268 


268 


259 


248 


236 


224 


212 


200 


188 


4.17 


4.13 


79.4 






15/16 


609 


609 


587 


559 


532 


504 


477 


449 


421 


5.58 


4.08 


159.3 






1 


632 


632 


609 


580 


552 


523 


494 


466 


437 


5.64 


4.08 


165.2 






1 1/16 


654 


654 


631 


601 


571 


542 


512 


483 


453 


5.69 


4.08 


171.2 






1 1/8 


677 


677 


653 


622 


591 


561 


530 


499 


469 


5.74 


4.08 


177.1 


35 


H 


1 3/16 


700 


700 


674 


642 


610 


578 


547 


515 


483 


5.80 


4.07 


183.1 




1 1/4 


723 


723 


695 


663 


630 


597 


564 


532 


499 


5.85 


4.07 


189.0 






1 6/16 


745 


745 


717 


684 


650 


616 


582 


548 


515 


5.89 


4.07 


195.0 






13/8 


768 


768 


739 


704 


670 


635 


600 


565 


530 


5.94 


4.07 


200.9 






I 7/16 


791 


791 


761 


725 


689 


654 


618 


582 


546 


5.99 


4.07 


206.9 






1 1/2 


814 


814 


783 


746 


709 


672 
575 


635 
552 


599 
528 


562 
504 


6.04 
5.76 


4.07 
4.85 


212.8 






15/16 


619 


619 


619 


619 


599 


162.0 






1 


645 


645 


645 


645 


623 


599 


574 


549 


525 


5.81 


4.84 


168.8 


30 


16 


1 1/16 


671 


671 


671 


671 


648 


622 


596 


571 


545 


5.87 


4.83 


175.6 




1 1/8 


697 


697 


697 


697 


673 


646 


619 


593 


566 


5.92 


4.83 


182.4 






1 3/16 


723 


723 


723 


723 


697 


669 


642 


614 


586 


5.97 


4.82 


189.2 




— 


1 1/4 
1 3/16 
1 1/* 


749 


749 


749 


749 


721 


693 


664 


635 


606 


6.01 


4.81 


196.0 




762 
788 


762 
788 


762 
788 


762 


732 
756 


703 
726 


674 
696 


644 
665 


615 
635 


5.87 
5.91 


4.80 
4.79 


199.2 




787 


206.0 






1 5/lfi 


814 


814 


814 


813 


781 


750 


719 


687 


656 


5.% 


4.79 


212.8 






1 3/8 


840 


840 


840 


838 


805 


773 


741 


708 


676 


6.01 


4.78 


219.6 






I 7/16 


866 


866 


866 


864 


830 


797 


764 


730 


697 


6.06 


4.78 


226.4 






1 1/2 


892 


892 


892 


889 


854 


820 


785 


751 


716 


6.10 


4.77 


233.2 


35 


16 


1 9/16 


918 


918 


918 


915 


879 


844 


808 


773 


737 


6.15 


4.77 


240.0 






1 5/8 


944 


944 


944 


940 


903 


867 


830 


794 


757 


6.19 


4.76 


246.8 






111/16 


970 


970 


970 


966 


928 


891 


853 


815 


778 


6.24 


4.76 


253.6 






1 3/4 


996 


996 


996 


992 


953 


914 


876 


837 


799 


6.28 


4.76 


260.4 






113/16 


1022 


1022 


1022 


1017 


977 


937 


897 


858 


818 


6.32 


4.75 


267.2 






1 7/8 


1048 


1048 


1048 


1042 


1002 


961 


920 


880 


839 


6.36 


4.75 


274.0 






115/16 


107^ 


1074 


1074 


1068 


1027 


985 


943 


901 


860 


6.41 


4.75 


280.8 






2 


1100 


1100 


1100 


1093 


1050 


1 007 1 965 


922 


879 


6.45 


4.74 


287.6 



Safe loads enclosed between heavy lines are for ratios of l/r not 
over 60; all others are for ratios t/r not over 120. Allowable fiber stress 
13,000 lb. for lengths of 60 radii or over. Weights do not include rivet 
head or other details. 



326 



STRENGTH OF MATERIALS. 



Safe Loads on 15-Iiich Carnegie Channel Columns in [Tliousands 
of Pounds.* (See Figs. 87 and 88, page 323.) 





d 




Effective Length of Column, Feet. 




CO 


-8 

11 




n, 


1 


0) 
73 




















^• 




















Xi 


r 


^ 


W 




















a3 




4J 




n 


. 

03 fl 


18 


20 


22 


24 


26 


28 


30 


32 


34 


OB 

*o'3 




o 

-a 


^ 

TS 
^ 


II 




















Is 


3-2 «J 


■p 

1 






Lat. 


257! 257 


257 


257 


252 


243 


233 224 


214 5.62 


4.98 


80.2 






3/8 


413; 413 


413 


413 


400 


384 


368 352 


3376.48 


4.85 


106.8 






7/16 


439 439 


439 


439 


424 


407 


390 3/3 


3576.57 


4.83 


113.6 


33 


16 


l/:> 


465; 465 


465 


465 


448 


431 


413 395 


3776.66 


4.82 


120.4 






9/lfi 


491 491 


491 


491 


473 


454 


435 416 


39816.74 


4.81 


127.2 






Vs 


517| 517 


517 


517 


498 


478 


458 


438 


418 


6.81 


4.80 


134.0 






Lat. 


268 268 


268 


268 


261 


251 


241 


231 


221 


5.58 


4.95 


84.2 






5/8 


528, 523 


528 


527 


507 


486 


4661 


446 


425 6.77 


4.79 


138.0 






11/16 


5541 554 


554 


552 


531 


510 


488 


467 


446; 6. 84 


4.78 


144.8 


33 


16 


3/4 


580 580 


580 


578 


555 


533 


511 


488 


4666.91 


4.77 


151.6 






1V16 


606| 606 


606 


604 


580 


557 


533 


510 


487 6.98 


4.77 


158.4 






7/8 


632| 632 


632 


629 


605 


580 


556 


531 


507|7.04 


4.76 


165.2 




— 


Lat. 

13/16 


306 
644 


306 


306 


306 


295 


284 


272 
564 


260 
539 


249 5.43 
5146.85 


4.84 


92.1 




644 


644 


639 


614 


589 


4.73 


168.4 






7/8 


670 670 


670 


665 


638 


612 


586 


560 


5346.91 


4.72 


175.2 


40 


16 


15/16 


696 696 


696 


690 


663 


636 


609 


581 


5546.97 


4.72 


182.0 


1 


722 722 


722 


715 


687 


659 


631 


602 


574 7.03 


4.71 


188.8 






11/16 


748! 748 


748 


741 


712 


683 


653 


624 


595 7.09 


4.71 


195.6 






11/8 


774, 774 


774 


767 


737 


706 


676 


646 


615 


7.15 


4.71 


202.4 






Lat. 


344 344 


344 


343 


329 


316 


302 


289 


276 
622 


5.32 
6.98 


4.75 
4.68 


102.2 






11/16 


786 786 


786 


777 


746 


715 


684 


653 


205.6 






11/8 


812, 812 


812 


802 


770 


738 


705 


673 


641 


7.04 


4.67 


212.4 






13/Ifi 


838 838 


838 


827 


794 


761 


728 


695 


66217.09 


4.67 


219.2 


45 


16 


11/4 


864 854 


864 


853 


819 


785 


751 


716 


682 7.15 


4.67 


226.0 


15/16 


890' 890 


890 


879 


844 


808 


773 


738 


703 7.20 


4.67 


232.8 






13/8 


916 916 


916 


904 


868 


832 


796 


760 


723 7.25 


4.67 


239.6 






17/16 


9421 942 


942 


930 


893 


856 


818 


781 


744 7.30 


4.67 


246.4 






11/2 


968' 968 


968 


956 


918 


879 


841 


803 


76417.35 


4.67 


'253.2 






3/8 


433; 433 


433 


433 


433 


433 


421 


407 


393 6.54 


5.67 


111.9 






7/16 


462! 462 


462 


462 


462 


462 


449 


433 


4186.63 


5.64 


|119.6 


33 


18 


1/2 
9/16 


491 1 491 
521 521 


491 
521 


491 
521 


491 
521 


491 


476 


459 


443,6.72 
469'6.80 


5.61 
5.59 


127.2 




520 


503 1 486 


134.9 




- 


5/8 


550 550 


550 


550 


550 


549 


530' 512 


4946.87 


5.57 


142.5 




5/8 


560' 560' 


560 


560 


560 


558 


540 


521 


502'6.84 


5.56 


146.5 






11/16 


589 589 


589 


589 


589 


586 


567 


547 


5276.91 


5.54 


154.2 


35 


18 


3/4 


619 619 


619 


619 


619 


615 


594 


574 


5536.98 


5.53 


161.8 






13/16 


648 648 


648 


648 


648 


643 


621 


599 


578 7.04 


5.51 


169.5 




— 


7/8 


677 677 


677 


677 


677 


671 


649 


626 


603 7.10 


5.50 


177.1 




13/16 


686 686 


686 


686 


686 


680 


657 


634 


6106.92 


5.49 


179.5 






7/8 


715 715 


715 


715 


715 


708 


684 


66C 


6366.98 


5.48 


187.1 


40 


1 A 


15/16 


745 745 


745 


745 


745 


736 


711 


685 


6607.04 


5.46 


il94.8 


18, 


774 774 


774 


774 


77A 


764 


738 


712 


i 6857.10 


5.45 


202.4 




1 1/16 


803 803 


803 


803 


803 


793 


766 


738 


7117. 16 


5.45 


210.1 




1 1/8 


832 832 


832 


832 


832 


821 


793 


764 


1 73617.21 


5.44 


217.7 



♦Table continued on next page. See note at foot of page. 



SAFE LOADS ON CHANNEL COLUMNS. 



327 



Safe Loads on 15-Inch Carnegie Channel Columns in Thousands 
of Pounds.* (See Figs. 87 and 88. page 323.) 





fl 




Effective Length of Column, Feet. 


2 

.2 CD 

2l 


o 




n, 




0) 




Is 

2? 


























a 


r^ 


*s 




















>>o 


>> a> a; 


P^ 


























n^ 


o &-§ 




U 


\J1 
O 


r^ 


18 


20 


22 


24 


26 


28 


30 


32 


34 


o2 


oOhPm 




A 


1^ 




















3 t 


3.2 <i> 
.2 S'« 


b0 




r^ 


'r.^ 




















^^ 


'§<W 


^ 


V 


tS 


Eh 




















P^ 


(^ 


'f^ 






1 1/16 


641" 


64 1 


S41 


84 1 


841 


829 


800 


771! 743 


7.05 


5.42 


220.1 






1 1/8 


871 


871 


871 


871 


871 


857 


828 


798 


768 


7.11 


5.42 


227.7 






1 3/16 


900 


900 


900 [ 900 


900 


885 


855 


824 


793 


7.17 


5.41 


235.4 






1 1/4 


929 


929 


929 929 


929 


913 


882 


850 


818 


7.22 


5.40 


243.0 






1 5/16 


958 


958 


958 958 


958 


942 


909 


877 


844 


7.27 


5.40 


250.0 






1 3/8 


988 


988 


988 


988 


988 


970 


936 


902 


868 


7.32 


5.39 


258.3 


45 


18 


1 7/16 


1017 


1017 


1017 


1017 


1017 


998 


963 


928 


893 


7.37 


5.38 


266.0 


1 1/2 


1046 


1046 


1046 


1046 


1046 


1026 


991 


955 


919 


7.42 


5.38 


273.6 






1 9/16 


1075 


1075 


1075 


1075 


1075 


1054 


1017 


980 


943 


7.47 


5.37 


281.3 






1 5/8 


1105 


1105 


1105 


1105 


1105 


1083 


1045 


1007 


969 


7.52 


5.37 


288,9 






111/16 


1134 


1134 


1134 


1134 


1134 


1112 


1073 


1034 


995 


7.57 


5.37 


296.6 






1 3/4 


1163 


116311163 


1163 


1163 


1139 


1099 


10591019 


7.61 


5.36 


304.2 






I 7/8 


1222 


1222 1222 


1222 


1222 


1195 


1153 


nil 1069 


7.70 


5.35 


319,5 


'2 • 1 


1280 


1280 1280' 1280 


1280l 


125311208 


1164 1120 


7.79 


5.35 


334.8 



Safe Loads on 15-Inch Carnegie Channel Columns with Flange Plates 
in Thousands of Pounds.* (See Fig. 89, page 323.) 



t 


c 


fa 


.S 


C<] 

i 

O 


Effective Length of Column, Feet. 


.2 

'x a; 


•2^ 




£ 


5 






1^1 




rO 


c 




















•« 




























OB 


II 




o 

■a 


o 
18 


IB 
2 


14 


Eh 


18 


20 


22 


24 


26 


28 


30 


32 


34 




i't 

.2§ 
SI 


1 


35 


3/8 


1340 


1340 


1340 


1340 


1340 


1307 


1261 


1214 


1168 


7.65 


5.32350.5 




"is 


2 


14 


9/16 


1408 


1408 


1408 


1408 


1408 


1369 


1320 


1270 


1221 


7.52 


5.28 368.4 




9/16 


1485 


1485 


1485 


1485 


1485 


1439 


1387 


1335 


1283 


7.39 


5.25 


388.4 






17/8 


14 


5/8 


1547 


1547 


1547 


1547 


154711547 


1543 


1495 


1447 


7.33 


5.97 


404.5 






2 




5/8 


1612 


1612 


1612 


1612 


1612,1612 


1607 


1557 


1507 


7.43 


5.96 


421.5 






21/8 




5/8 


1677 


1677 


1677 


1677 


1677 


1677 


1670 


1618 


1566 


7.52 


5.95 


438.5 






21/4 




5/8 


1742 


1742 


1742 


1742 


1742 


1742 


1735 


1681 


1627 


7.61 


5.95 


455.5 


45 


20 


23/8 




5/8 


1807 


1807 


1807 


1807 


1807 


1807 


1798 


1742 


1686 


7.70 


5.94 


472.5 






21/2 




5/8 


1872 


1872 


1872 


1872 


1872 


1872 


1863 


1805 


1747 


7.79 


5.94 


489.5 






25/8 




5/8 


1937 


1937 


1937 


1937 


1937 


1937 


1926 


1866 


1806 


7.88 


5.93 


506.5 






23/4 




5/8 


2002 


2002 


2002 


2002 2002 


2002 


1991 


1929 


1866 


7.97 


5.93'523.5 






27/8 




5/8 


2067 


2067 


2067 


2067 2067 


2067 


205411989 


1925 


8.05 


5.92540.5 






3 




5/8 


2132 


2132 


2132 


21322132 

1 


2132 


211812052 


1985 


8.13 


5.92,557.5 



*Safe load values enclosed within the heavy lines are for ratios of 
l/r not over 60; all others are for ratios of I r not over 120. Allowable 
fiber stress per sq. in., 13,000 lb. for lengths of 60 radii or over. Weights 
do not include rivet heads or other details. 



328 



STRENGTH OF MATERIALS. 



Safe Loads on Carnegie Plate and Angle Columns In 
Thousands of Pounds.* 



1! 

+ % 


J 


> 


Web 
Plate. 


Effective Length in Feet. 




•1- 

in 




tl 


6 


11 


6 


8 10 


12 14 


16 18 


20 


22 


24 




Angles. 


2 1/2X2 X 1/4 


1/4 


69 


56 43 


[35 28 22 
"45 40' 34 
l50 42, 35 


""" 








2.45 

2.50 
2.51 


1.04 
1.28 

1.24 


196 


3 X2 X 1/4 

3 X2 I/2X 1/4 


""fj 72 60 
88| 76 63 


29 
29 
28 
36 
43 
52 


23 
22 






21.5 
23.1 


3 X2 1/2X 1/4 
3 X2 1/2X5/16 
31/2X21/2X1/4 

31/2X21/2X5/16 


8 


1/4' 


94/ 79 65 
"1 lO'l 95 78 
101 1 96 83 
1191115 100 


HM 43 
62) 52 
70 57 
85 70 
89 73 
104 86 
113 97 
131 114 
136 118 
155 135 
174 152 


49 
60 


28 
36 
45 


30 

38 


23 
30 


3.35 
3.38 
3.41 
3.43 


1.19 
1.23 
1.44 
1.49 
1.47 
1.51 
1.67 
1.71 
1.70" 
1.73 
1.77 


24.8 
29.2 
26.4 
31.2 


31/2X21/2X 5/16 

31/2x21/2x3/8 

4 X3 X 5/16 
4 X3 X 3/8 


8 


Vie 


125 
142 
141- 
161 


120 104 
138 121 
14r!128 
161 149 
168 154 
188 175 
208 196 


62 
73 
8! 
97 
100 
114 
130 


54 
64 

71 
83 


47 

55 

-63 

74 


39 
47 
55 
66 


31 
38 
48 
57 


3.38 
3.40 
3.35 
3.36 


32.9 
37.3 
37.3 
42.5 


4 X3 X 3/8 
4 X3 X V16 
4 X3 X 1/2 


8 


1 168 

3/8 188 

208 


86! 77 
981 88 
no' 100 


68 
78 
89 


59 

68 
78 


3 33 
3.34 
3.33 


44.2 
49.4 
54.S 




10 
10 

10 




Effective Length in Feet. 










8 |l0| 12| 14|l6|l8|20| 22 


24 


[26 




3 X2 1/2X1/4 
31/2X31/2X 1/4 

31/2X21/2X5/16 


V4 
5/16 


82! 66[32 
100 86 71 
119 103 87 
125'l08 91 
149 I33'll6 
170 154 135 


44 
57 
71 
73 
99 
117 


36 
50 
61 
64 

98 


-sr 
g 


36 

45 


29 
37 


30 




4.16 
4.23 
4.28 


1.15 
1.39 
1.45 
1.42 
1.62 
1.67 


26.5 
28.1 
32.9 


3 1/2X2 I/2X 5/16 

4 X3 X 5/16 
4 X3 X 3/8 


55 

73 
85 
88 
101 


T7 
64 
76 


38 
56 
67 


47 
57 


39 

48 


4.20 

4.18 
4.22 


35.0 
39.4 
44.6 


4 X3 X 3/8 
4 X3 X V16 


i 1781160 140 
11981 181 160 


12ri01 
138,116 


78 
90 


68 
79 
107 
123 


58 
68 
98 
113 


48 
57 
89 
103 
126 
144 
164 


4.17 
4.19 
4.18 
4.20 
4.19 
4.20 
4.20 


1.65 
1.69 
2.10 
2.15 
2.56 
2.61 
2.65 


46.8 
52.0 


5 X3 I/2X 3/8 
5 X3 1/2X 7/16 


!207 2u7!l94'l75'l57 
3/8|232 232|220 200,180 


1391121 
160,140 
192 175 
220 201 
247 226 


54.4 
60.8 


6 X4 X 3/8 
6 X4 X 7/16 
6 X4 X 1/2 




i236 
1266 
1296 
1312 
341 
370 


236 236 226 209 
266 266|257 238 
296 296|288 267 


158 

182 
206 


141 
163 
185 
192 
214 
236 


62.0 
70.0 
77.6 


6 X4 X 1/2 
6 X4 X 9/16 
6 X4 X 5/8 


10 


"■ 


312 3121 302*280 
341 341 1 333 309 
370 37CI363 337 


258 236 
285 262 
i312287 
'3251298 


214 

238 
261 


170 
191 
210 


4.14 
4.15 
4.15 


2.62 
2.66 
2 69 


81.8 
89.4 
97.0 


6 X4 X 5/8 


10' 5/8 i386;386 386!378'351 


272 


245 


218 


4.10 


2.68 


101.3 


3 1/2X2 1/2X 1/4 
31/2X2 1/2X5/16 

4 X3 X 5/16 


12 
12 


V. 


104, 89 73 

123 106 89 

ri48il31 114 


L59| 521 44 
7^ 63' 54 
97j8^ 71 


"36 
45 
63 


""28 
37 
55 


46 


38 


5.04 
5.11 
5.09 


1.35 
1.41 
1.61 


29.8 
34.6 
39.0 


4 X3 X 5/16 
4 X3 X 3/8 


1 15711381 120 
^/I6j'l78fl59!l39 


101 Jjfj 75 
119^ 87 


65 
77 


56 
67 


47 
57 


38 
47^ 


5.01 
5.06 


1.58 
1.63 


41.6 
46.8 



*Safe loads enclosed within dotted lines are for ratios of I ^r of not 
over 60. Those enclosed within heavy lines are for ratios of l/r not 
over 200. All others are for ratios of l/r up to 120. Allowable fiber 
stress 13. (KK) lb. per sq. in. for lengths of 60 radii or less. Each column 
consi.sts of four angles and one web plate. Weights given do not 
include nvet heads or otlier detaiLs. 



SAFE LOADS ON PLATE AND ANGLE COLUMNS. 329 



Safe Loads on Carnegie Plate and Angle Columns in 
Thousands of Pounds. — Continued. 



x> o 



■^ ^ 1^ ii f \ 



Angles. 



X3 X 3/8 
X3 1/2X 3/8 
X31/2X 7/16 
X3 1/2X1/2 
X4 X 7/16 
X4 X 1/2 



6 X4 X 1/2 

6 X4 X 9/16 

6 X4 X 5/8 

6 X4 Xll/16 

6 X4 X 3/4 



6 X4 X 3/4 



X4 X 3/4 



Web 
Plate. 






Effective Length in Feet. 



187! 



10 



il'r^. 



145 



3/8 



217 2171201 
242 2421226 

I 266 2661252 

I 276:276' 

1^305 

1325 



124 



16 



J, 



102 



1/2 



354 
1383 

411 
1439 
5/8 1 458 



3/4 I 4781478 



181 162 
2051184 
_ 229 206 
276j264:244 
305|295 274 
3251312288 
354!342'317 
383 373 346 
4111403 375 
403 
458i45T 
4781469 



18 



20 



80 



370 



22 



24 26 






581 4^ 
100 
114 
129| 



218 

242 
266 
290 
31 



325 



187 



19^ 

217' 
239 
262 
284 



31173] 4 

7 |T9r 5 



4.99 

5.02 
5.05 
5.07 
5.06 
5.07 



213 

234 
254 



294 262 



338 



305) 272 



99 
01 
5.02 
5.01 
5.01 



4.96 



4.91 



PhOh 



1.61 
2.06 
2.10 
2.15 
2.56 
2.61 



2.57 
2.61 
2.65 
2.69 
2.72 



2.70 



2.69 



I 

p. O 



49.3 
56.9 
63.3 
69.7 
72.5 
80.1 



85.2 
92.8 
100.4 
107.6 
114.8 



119.9 



125.0 



Safe loads enclosed within dotted lines are for ratios of l/r of not over 
60. Those enclosed within heavy lines are for ratios of l/r not over 200. 
All others are for ratios of l/r up to 120. Allowable fiber 
stress 13,000 lb. per sq. in. for lengths of 60 radii or less. -- 
Each column consists of four angles and one web plate. ^' 
Weights given do not include rivet heads or other details. + 



Safe Loads on Carnegie Plate and Angle Columns 
with Side Plates in Thousands of Pounds. 



fe: 



^ 



w 
^ 





Web 


Side 


















RadiusofGyration, 
Axis Perpendic- 
ular to Web Plate. 






.>^ 




Plate. 


Plates. 


Effective Length in Feet. 


-3 


,^ 


i 
'O 

g 


1 

d 




.2 


16 


18 


20 


22 


24 


26 


28 


30 


li 


»-57 cr- 

Angles. 


r- 


6X4X 3/8 
6X4X 3/8 
6X4X 7/16 
6X4X 1/2 


12 


3/8 


14 


3/8 

1/2 
1/2 
1/2 


379 357 

T28i 407 

458 434 

487| 461 


334 
383 
407 
433 


312 
358 
381 
405 


289 
334 
355 
377 


267 
310 
329 
349 


244 
285 
303 
321 


222 
261 
277 
293 


5.58 

5.71 
5.68 
5.65 


3.14 
3.25 
3.23 
3.22 


100.2 

112.1 
120.1 
127.7 


6X4X 1/2 

6X4X 1/2 
6X4X 9/16 
6X4X 5/8 


12 


1/2 


14 


1/2 J 5061 476 
5/8 r553i 526 
Vs 1 5821 553 
Vs 1 6101 579 


447 
495 
520 
544 


417 
463 
487 
509 


388 
432 
454 
475 


358 
401 
421 
440 


329 
369 
388 
405 


299 
338 
354 
370 


5.58 
5.69 
5.67 
5.64 


3.18 
3.26 
3.25 

3.24 


132.8 
144.7 
152.3 
159.9 


6X4X 5/8 
6X4X 5/8 
6X4X 5/8 
6X4X 5/8 


12 


5/8 


14 


5/8 ! 630" 594 

3/4 675 644 

7/8 721 694 

1 1 766! 742 


558 
606 
654 
700 


522 
568 
614 
658 


486 
529 
574 
616 


450 
491 
534 
574 


413 
453 
494 
532 


377 
415 
454 
490 


5.59 
5.69 
5.79 

5.88 


3.21 
3.27 
3.33 
3.37 


165.0 
176.9 
188.8 
200.7 



Safe loads enclosed in dotted Unes are for ratios of l/r not over 60. 
Those enclosed in heavy Unes are for ratios of l/r not over 200. All 
others are for ratios of l/r up to 120. Allowable fiber stress, 13,000 lb. 
per sq. in. for length of 60 radii and under. Each column consists of 
four angles, two side plates, and one web plate except those marked *, 
which have two web plates. Weights given do not include rivet heads 
and other details. Table continued on next page. 



330 



STRENGTH OF MATERIALS. 



Safe Loads on Carnegie Plate and Angle Columns with 
Side Plates in Thousands of Pounds. *— Continued, 













Web 
Plate. 


Side 
Plates. 


















C3 a> 


c 






•^ 
■^ 


r" 
K 


Effective Length in Feet. 


III 


•If 

oil 


to 


,0 



^i ^ 


J3 

14 





18 


20 


22 


24 


26 


28 


30 


32 






Angles. 


1^ 





la 


6X4X 5/8 
6X4X 5/8 
6X4X 5/8 
6X4X 5/8 
6X4X 5/8 
6X4X 5/8 
6X4X 5/8 
6X4X 5/8 


12 


5/8 


11/8 
11/4 
13/8 
11/2 
15/8 
13/4 
17/8 

2 


719 747 
840 794 
888 840 
937 887 
986 934 
1034 980 
1082,1026 
1130J1072 


703 

748 
793 
837 
882 
926 
970 
1014 


659 

702 
745 
787 
830 
872 
914 
956 


615 
657 
697 
738 
779 
818 
858 
898 


571 
611 
649 
688 
727 
764 
802 
840 


527 
565 
601 
638 
675 
710 
746 
782 


483 
519 
553 
588 
623 
657 
690 
725 


5.97 
6.06 
6.14 
6.22 
6.30 
6.38 
6.46 
6.54 


3.14 212.6 
3.45 224.5 
3.48 236.4 
3.51 [248.3 
3.54 260.2 
3.56 272.1 
3.58 284.0 
3.60 295 9 


6X4X 3/8 
6X4X 7/16 
6X4X 1/2 
6X4X 1/2 
6X4X 1/2 


14 


3/8 


14 


3/8 
3/8 
3/8 
7/16 
1/2 


363 340 317 
390 365 340 
417 390 363 
442 415 387 
468 439! 410 


293 270 246 223 
314 289 264 239 
336 309 282 255 
359 331 303 275 
381 353 324, 295 


205 
220 
236 
251 
267 


6.46 
6.45 
6.43 
6.49 
6.55 


3.10 102.8 
3.09 110.8 
3.09 118.4 
3.14 124.3 
3.19 1130.3 


6X4X 1/2 
6X4X 1/2 


14 


3/8 


14 


9/16 
5/8 


493 463 433 403 374 3441 314 284 6.61 
517 487' 456 426 395 364 334 303 6.67 


3.23 ,136.2 
3.27 !l42.2 


6X4X 1/2 
6X4X 9/16 
6X4X 5/8 


14 


1/2 


14 


5/8 
5/8 
5/8 


535 502 470 437 405 373 340 308 6.58 
561 527 493 459 424 390 356 322, 6.56 
587 551 515 479 443 407 372 336! 6.54 


3.22 !148.1 
3.21 155.7 
3.20 163.3 


6X4X 5/8 
6X4X 5/8 
6X4X 5/8 
6X4X 5/8 
6X4X 5/8 
6X4X 5/8 
6X4X 5/s 


14 
14 


5/8 
5/8 


14 
14 

16 
16 


5/8 
3/4 
7/8 
1 

11/8 
11/4 
13/8 


606| 568 530j 493, 455, 417 38o| 345[ 6.47 
655 615 576' 536' 497' 457' 418 378 6.58 
705 664 622' 581 540 498 457 415 6.68 
754 711! 668, 625 581 538 495 452 6.78 
803 758! 7l3i 667 622 577 532 487 6.87 
852 805j 758| 711 664 617| 569 522 6.96 
901 851 1 802 753 704 655 605 556, 7.05 


3.17 169.3 
3.23 181.2 
3.29 193.1 
3.34 205.0 
3.38 216.9 
3.42 228.8 
3.45 240.7 


6X4X 5/8 
6X4X 5/8 
6X4X 5/8 
6X4X 5/8 
6X4X 5/8 


1 1/2 i 949 898 
1 5/8 1 998 945 
1 3/4 1046 991 

1 7/8 jl095 1038 

2 1 1144 1084 

1 7/8 [1 19811 198 

2 125011250 
2 1315!l30l 
21/8 |1367jl364 

21/4 11419 r4!9 
23/8 |147i;i471 
21/2 11523 1523 


847 796 744 693 642 591' 7.13 
892 839 786 732 679 626 7.22 
935; 880 825 770 715 659 7.30 
931 924 867 810 753 696 7.38 
1025 966 907: 848 789 730 7.46 


3.48 
3.51 
3.53 
3.56 
3.58 ! 


252 6 
264.5 
276.4 
288.3 
300.2 
313.8 
327.4 
344.2 
357.8 
371.4 
385.0 
398.6 




6X4X 5/8 
6X4X 5/8 
6X6X 5/8 
6X6X 5/8 
6X6X 5/8 
6X6X 5/8 
6X6X 5/8 


1146 1091 1036 981 926 871 
1201 1144 1087 1030 973 916 
1246 1185' 1123' 1062 1000' 939 
1301 1237 1174,1111 1047 984 

1356 1290'l225'l160 10941029 
1409 1342 1274 1207 1139 1072 
1463 1393 1324 1254 1185 1115 


7.45 
7.53 
7.36 
7.44 
7.53 
7.61 
7.69 


4.02 ' 

4.05 ; 

3.95' 

3.98 

4.01 ' 

4.03 

4.05 


6X6X 5/8 
8X6X 5/8 
8X6X 5/8 
8X6X 5/8 
8X6X 5/8 
8X6X 5/8 


*14 
*14 


1/2 
5/8 


21/2 j 1592! 1590 
21/2 |!657T657 


1516 1443|1369| 1295 1222,1148 
1616 1543 1470 1397^ 1324 1251 


7.57 1 3.99 416.4 
7.54 1 4.18 '433.6 


18 
20 


2 3/8 11728 1728 
21/2 11787 1787 
25/8 11845 1845 
2 3/4 11904 1904 


1728il695 1626 1557 1488 1419 7.54 
1787|1756 1685 1614 1543 1471 7.62 
1845|i818 1744 1671 1598 1525 7.70 
1904|1879 1804 1729 1653 1578; 7.78 


4.61 452.3 
4.63 ;467.6 
4.65 482.9 
4.67 1498.2 


8X6X 5/8 


2 3/4 J1949 1949 


194911918 1841 1763 1686 1608 7.71 


4.64 J510.1 


8X6> - 

8X6> 

8X6> 

8X6> 

8X6>< 


C5/8 
C5/8 

:5/8 
:5/8 


2 5/8 
2 3/4 

2 7/8 1 

3 1/8 


2027 
2092 
2157 
2222 
2287 


2027 
2092 
2157 
2222 
2287 


2027^ 
2092 
2157 
2222 
2287 


2027|2009 1935 1862 1789 7.70 
2092|2077 2002 1926 1851 7.78 
2157|2146 2068 1991 1913 7.86 
2222|2214 2135 2055 1976; 7.94 
2287J2283 2202 2120 2039 8.01 


5.10 530.5 
5.12 547.5 
5.14 564.5 
3.16 581.5 
5.18 1598.5 



*See note at foot of page 329. 



PROPERTIES OF BETHLEHEM GIRDER BEAMS. 331 

Bethlehem, Girder and I-Beams, and H-Columns. — The tables of 
special and girder beams give the sections and weights usually rolled. 
Intermediate and heavier weights may be obtained by special arrange- 
ment The table of H-columns gives only the minimum and maximum 
weights for each section number. Many intermediate weights are 
regularly made. 

The coefficients of strength given n the tables are based on a maxi- 
mum fiber stress of 16,000 lb. per sq. in., which is allowable for quies- 
cent loads, as in buildings. For moving loads the fiber stress of 12,500 
lb. per sq. in. should be used, and the coeflicients reduced proportion- 
ately. For suddenly applied loads, as in railroad bridges, they should 
be still further reduced. For a fiber stress of 8000 lb. per sq. in. the 
coefficients would be one-half those given in the tables. The quotient 
obtained by d viding the coefficient given for the beam by the span in 
feet will give the uniformly distributed safe ^oad in pounds, including 
the weight of the beam. If the load is concentrated at the middle of the 
span the safe load is one half the uniformly distributed load. 

For further information see handbook of Structural Steel Shapes, 
Bethlehem Steel Co., South Bethlehem, Pa., 1911. 



Properties of Bethlehem Girder Beams. 






ft 



o 

ft§ 
4J O 

!53 









30 200.0 
30 180.0 



28 



180.0 
165.0 



26 160.0 
26 150.0| 

24 140.01 
24 120.0^ 

20 140.0! 
20 112.0 



58.71 
53.00 

52.86 
48.47 

46.91 
43.94J 

41.16i 
35.38 

41.19 
32.81 



fe^ 



92.0 27.12 

140.0 41.27 

104.0 30.50 

73.0; 21.49 

70.0 20.58 

55.0 16.18 

44.0 12.95 

38.0 11.22 

32.5! 9.54 



0.75 

.69 I 

.69 
.66 

.63 
.63 

.60 
.53 

.64 
.55 

.48 

.80 
.60 

.43 

.46 
.37 

.31 
.30 
.29 



Neutral Axis 
Perpendicular to 
Web at Center. 



I r 






15. 009150. 6' 
13.00:8194.5] 

14.357264.7! 
12.50 6562. 7i 

13.60 5620.8' 
12.00|5153.9| 

13.0o'4201.4' 
12.00 3607.3 

12.50 2934.7 
12.00 2342.1 



12.48 
12.43 



5o . 

b£ . CO 
C „ Cr ^ 

h D (_ ^ 
|SOO 

c 



610.0 6,507,100 
546.3 5,827,200 



11.72 518.9 

11.64 468.8 

10.95 432.4 

10.83, 396.5 



5,535,000 
5,000,100 

4,611,900 
4,228,800 



11.50 

11.75 
11.25 
10.50 

10.00 
9.75 

9.00 
8.50 
8.00 



10.10' 350.1 3,734,600 
10.10 300.6 3,206,500 



1591.4 

1592.7 
1220.1 
883.4 

538.8 
432.0, 

244.2 
170.9: 
114.4! 



8.44 
8.45 

7.66 

6.21 
6.32 
6.41 

5.12 
5.17 



293.5 
234.2 

176.8 

212.4 
162.7 
117.8 

89.8 
72.0 



4.34 48.8 
3.90 38.0 
3.461 28.6 



3,130,300 
2,498,300 

1,886,100 

2,265,200 
1,735,300 
1,256,600 

957,800 
768,000 

521,000 
405,000 
305,100 



^H 



go 

.5 o 

X) CO 



Neutral 

Axis Coin* 

cident with 

Center Line 

of Web. 






94.65 
82.60, 



80.75! 
75.15! 



67.95 
67.951 



60.85! 
49.25: 



62.10 
49.25 



630.2 
433.3 



533.3 
371.9 



435.7 
314.6 



346.9 
249.4 



348.9 
239.3 



38.05 182.6 



67.10 
47.15 
29.60 

28.60 
21.15 



331.0 
213.0 
123.2 

114.7 
81.1 



14.90 57.3 
13.35 44.1 
11.80 32.9 



3 >»fl 






3.28 
2.86. 

3.18 
2.77 

3.05 
2.68 

2.90 
2.66 

2.91 
2.70 

2.59 

2.83 
2.64 
2.39 

2.36 
2.24 

2.10 
1.98 
1.86 



W^=Safe load in pounds uniformly distributed, including weight of beam. 
L =Span in feet. M= Moment of forces in foot-pounds. /= fiber stress. 
W^C/L; M = C/8; C = T^L = 8 M = 2//,S. 



332 



STRENGTH OF MATERIALS. 









Properties of Bethlehem I-Beams. 








k 

o c 

43 "^ 


'53 




4 

H 


k 

o c 


Neutral Axis 
Perpendicular to 
Web at Center! 


P4 
^ C 


c3o 


Neutral 
Axis Coin- 
cident with 
Center Line 

of Web. 


1 OJ 

li 


r 


•11 » 


li 


CO I>> £2 


30 
28 
26 
24 


120 

105.0 
90.0 
84.0 


35.30 

30.88 
26 49 
24.80 


0.540 
.500 
.460 
.460 


10.500 
10.000 
9.500 
9.250 


5239.6 
4014.1 
2977.2 
2381.9 


12.18 
11.40 
10.60 
9.80 


349.3 
286.7 
229.0 
198.5 


3,726,000 
3,058,400 
2,442,800 
2,117,300 


51.90 
44.50 
37.65 
37.55 


165.0 
131.5 
101.2 
91.1 


2.16 
2.06 
1.95 
1.92 


24 
24 


83.0 
73.0 


24.59 
21.47 


.520 
.390 


9.130 
9.000 


2240.9 
2091.0 


9.55 

9.87 


186.7 
174.3 


1,991,900 
1,858,700 


46.55 
27.00 


78.0 
74.4 


1.78 
1.86 


20 
20 


82.0 
72.0 


24.17 
21.37 


.570 
.430 


8.890 
8.750 


1559.8 
1466.5 


8.03 
8.28 


156.0 
146.7 


1,663,800 
1,564,300 


51.20 
32.45 


79.9 
75.9 


1.82 
1.88 


20 
20 
20 


69.0 
64.0 
59.0 


20.26 
18.86 
17.36 


.520 
.450 
.375 


8.145 
8.075 
8.000 


1268.9 
1222.1 
1172.2 


7.91 
8.05 
8.22 


126.9 
122.2 
117.2 


1,353,500 
1,303,600 
1,250,300 


44.10 
34.70 
25.00 


51.2 
49.8 
48.3 


1.59 
1.62 
1.66 


18 
18 
18 
18 


59.0 
54.0 
52.0 

48.5 


17.40 
15.87 
15.24 
14.25 


.495 
.410 
.375 
.320 


7.675 
7.590 
7.555 
7.500 


883.3 
842.0 
825.0 
798.3 


7.12 

7.28 

. 7.36 

7.48 


98.1 
93.6 
91.7 
88.7 


1,046,900 
997,900 
977,700 
946,100 


39.00 
28.75 
24.60 
•18.35 


39.1 
37.7 
37.1 
36.2 


1.50 
1.54 
1.56 
1.59 


15 


71.0 


20.95 


.520 


7.500 


796.2 


6.16 


106.2 


1,132,400 


38.95 


61.3 


1.71 


15 
15 


64.0 
54.0 


18.81 
15.88 


.605 
.410 


7.195 
7.000 


664.9 
610.0 


5.95 
6.20 


88.6 
81.3 


945,600 
867,600 


46.95 
27.40 


41.9 
38.3 


1.49 
1.55 


15 
15 
15 


46.0 
41.0 
38.0 


13.52 
12.02 
11.27 


.440 
.340 
.290 


6.810 
6.710 
6.660 


484.8 
456.7 
442.6 


5.99 
6.16 
6.27 


64.6 
60.9 
59.0 


689.500 
649,400 
629,500 


30.00 
19.95 
15.05 


25.2 
24.0 
23.4 


1.36 
1.41 
1.44 


12 


36.0 


10.61 


.310 


6.300 


269.2 


5.04 


44.9 


478,600 


16.10 


21.3 


1.42 


12 
12 


32.0 
28.5 


9.44 
8.42 


.335 
.250 


6.205 
6.120 


228.5 
216.2 


4.92 
5.07 


38.1 
36.0 


406,200 
384,400 


17.90 
11.10 


16.0 
15.3 


1.30 
1.35 


10 
10 


28.5 
23 5 


8.34 
6.94 


.390 
.250 


5.990 
5.850 


134.6 
122.9 


4.02 
4.21 


26.9 
24.6 


287,100 
262,200 


19.90 
10.50 


12.1 
11.2 


1.21 
1.27 


9 
9 


24 
20.0 


7.04 
6.01 


.365 
.250 


5.555 
5.440 


92.1 
85.1 


3.62 
3.76 


20.5 
18.9 


218,300 
201,800 


16.95 
10.05 


8.8 
8.2 


1.12 
1.17 


8 
8 


19.5 
17.5 


5.78 
5.18 


.325 
.250 


5.325 
5.250 


60.6 
57.4 


3.24 
3.33 


15.1 
14.3 


161,600 
153,000 


13.45 
9.45 


6.7 
6.4 


1.08 
1.11 



W = Safe load in pounds uniformly distributed, including weight of beam. 
U " ^"^^^IL^". *^^^ ^^- .^^^=^^oment of forces in foot-pounds. / = fiber stress. 
C = Coefficients ^nven m the table. 
W=C/L, M = C/8- C=WL = 8M = 2/^fs. 



PROPERTIES OP BETHLEHEM H-COLUMNS. 



333 



Dimensions and Properties of Bethlehem Rolled Steel H- Columns.* 



i 


Dimensions, in Inches. 


eg 
< 


Neutral Axis 
Perpen. to Web. 


Neutral Axis on 
Center Line of Web. 


|3 


1 


.11 
SI 






Q 


1" 


1^ 


0.2 




3 

ll 
•rt o 


^1 

-SO 


14-Inch H-Columns 


83.5 
91.0 


13 3/4 

13 7/8 


11/16 
8/4 


13.92 
13.% 


0.43 
.47 


11.06 
11.06 


24.46 
26.76 


884.9 
976.8 


128.7 
140.8 


6.01 
6.04 


294.5 
325.4 


42.3 
46.6 


3.47 
3.49 


99.0 
162.0 


14 
15 


13/16 
15/16 


14.00 
14.31 


.51 
.82 


11.06 
11.06 


29.06 
47.71 


1070.6 
1894.0 


153.0 
252.5 


6.07 
6.30 


356.9 
626.1 


51.0 
87.5 


3.50 
3.62 


170.5 
227.5 


151/8 
16 


13/8 
1 13/16 


14.35 
14.62 


.86 
1.13 


11.06 
11.06 


50.11 
66.98 


2007.0 
2859.6 


265.4 
357.5 


6.33 
6.53 


662.3 
929.4 


92.3 
127.1 


3.64 
3.72 


236.0 
287.5 


161/8 
16 7/8 


17/8 
21/4 


14.66 
14.90 


1.17 
1.41 


11.06 
11.06 


69.45 
84.50 


2991.5 
3836.1 


371.0 
454.7 


6.56 
6.74 


970.0 
1226.7 


132.3 
164.7 


3.74 
3.81 


i:S-Inch H-Columns 


64.5 
71.5 


113/4 
117/8 


5/8 
11/16 


11.92 
11.96 


0.39 
.43 


9.21 
9.21 


19.00 
20.96 


499.0 
556.6 


84.9 
93.7 


5.13 
5.15 


168.6 
188.2 


28.3 
31.5 


2.98 
3.00 


78.0 
132.5 


12 
13 


3/4 
11/4 


12.00 
12.31 


.47 
.78 


9.21 
9.21 


22.94 
38.97 


615.6 
1141.3 


102.6 
175.6 


5.18 
5.41 


208.1 
380.7 


34.7 
61.9 


3.01 
3.13 


139.5 
161.0 


131/8 

131/2 


15/16 

n/2 


12.35 
12.47 


.82 
.94 


9.21 
9.21 


41.03 
47.28 


1214.5 
1444.3 


185.0 
214.0 


5.44 
5.53 


404.1 
477.0 


65.4 
76.5 


3.14 
3.18 


10-Inch H-Columns 


49.0 


9 7/8 


Vl6 


9.97 


0.36 


7.67 


14.37 


263.5 


53.4 


4.28 


89.1 


17.9 


2.49 


54.0 
99.5 


10 

n 


5/8 
11/8 


10.00 
10.31 


.39 
.70 


7.67 
7.67 


15.91 
29.32 


296.8 
607.0 


59.4 
110.4 


4.32 
4.55 


100.4 
201.7 


20.1 
39.1 


2.51 
2.62 


105.5 
123.5 


ni/8 
ni/2 


13/16 
13/8 


10.35 
10.47 


.74 
.86 


7.67 
7.67 


31.06 
36.32 


651.0 
790.4 


117.0 
137.5 


4.58 
4.67 


215.6 
259.3 


41.7 
49.5 


2.64 
2.67 


8-Inch H-Columns 


32.0 


7 7/8 


7/16 


8.00 


0.31 


6.14 


9.17 


i05.7 


26.9 


3.40 


35.8 


8.9 


1.98 


34.5 
71.5 


8 
9 


1/2 

1 


8.00 
8.32 


.31 
.63 


6.14 
6.14 


10.17 
21.05 


121.5 
285.6 


30.4 
63.5 


3.46 
3.68 


41.1 
94.4 


10.3 
22.7 


2.01 
2.12 


76.5 
90.5 


91/8 
91/2 


11/16 
11/4 


8.36 
8.47 


.67 
.78 


6.14 
6.14 


22.46 
26.64 


309.5 
385.3 


67.8 
81.1 


3.71 
3.80 


101.9 
125.1 


24.4 
29.6 


2.13 
2.17 



* The tables are greatly condensed from the original. The depth 
of section regularly rolled in each size advances by H inch from the 
smallest to the largest section shown in each table. The increased 
depth of each section in a given size is obtained by adding metal to 
the flanges, the depth of web remaining constant in each size. 



334 STRENGTH OF MATERIALS. 



TORSIONAL STRENGTH. 

Let a horizontal shaft of diameter = d be fixed at one end, and at the 
other or free end, at a distance = I from the fixed end, let there be fixed 
a horizontal lever arm with a weight = P acting at a distance = a from 
the axis of the shaft so as to twist it; then Pa = moment of the applied 
force. 

Resisting moment = twisting moment = SJ /c, in which S = unit 
shearing resistance, J = polar moment of inertia of the section with 
respect to the axis, and c = distance of the most remote fiber from the 
axis, in a cross-section. For a circle with diameter d 

J = 1/32 Tzd*', c = 1/2 d; 



For hollow shafts of external diameter d and internal diameter d%. 



Pa = 0.1963 ^^A's; rf= '/ 5.1 Pa 



8/ 5.1 Pc 



(-f)' 



In solving the last equation the ratio di/d is first assumed. 

For a rectangular bar in which b and d are the long and short sides of 
the rectangle. Pa = 0.2222 bd'^S; and for a square bar with side d, Pa = 
0.2222^3^. (Merriman, "Mechanics of Materials," 10th ed.) 

The above formulae are based on the supposition that the shearing 
resistance at any point of the cross-section is proportional to its distance 
from the axis; but this is true only within the elastic limit. In mate- 
rials capable of flow, while the particles near the axis are strained within 
the elastic limit those at some distance within the circumference may be 
strained neariy to the ultimate resistance, so that the total resistance is 
something greater than that calculated by the formulae. For working 
strength, however, the formulae may be used, with S taken at the safe 
working unit resistance. 

The ultimate torsional shearing resistance S is about the same as the 
direct shearing resistance, and may be taken at 20,000 to 25,000 lbs. per 
square inch for cast iron, 45,000 lbs. for WTOught iron, and 50,000 to 
150,000 lbs. for steel, according to its carbon and temper. Large factors 
of safety should be taken, especially when the direction of stress is re- 
versed, as in reversing engines, and when the torsional stress is com- 
bined with other stresses, as is usual in shafting. (See "Shafting.") 

Elastic Ee istance to Torsion. — Let i = length of bar being 
twisted, d = diameter, P = force applied at the extremity of a lever arm 
of length = a. Pa =^ twisting moment, G = torsional modulus of elas- 
ticity, S = angle through which the free end of the shaft, is twisted, 
measured in arc of radius = 1. 

For a cylindrical shaft, 

TT^Gd*. 32 Pal _ ^ 32 Pal . 32 .^.^^ 

^'^""32r' ^-l^d^' ^ = "^^^' - = 10.186. 

If a =«= angle of torsion in degrees, 

« = -^- = IMi 180 X 32 Pal ^ 583.6 Pal 

180' "* n ^ TzH^G ~ d*G 

The value of G is given by different authorities as from 1/3 to 2/5 of E, 
the modulus of elasticity for tension. For steel it is generally taken as 
12,000,000 lbs. per sq. in. 



COMBINED STRESSES. 335 



COMBINED STRESSES. 

Combined Tension and Flexure. — Let A = the area of a bar 
Bubjected to both tension and flexure, P = tensile stress applied at the 
ends, P -^ A = unit tensile stress, S = unit stress at the fiber on the 
tensile side most remote from the neutral axis, due to flexure alone, then 
maximum tensile unit stress = (P -i- A) -\- S. A beam to resist com- 
bined tension and flexure should be designed so that (P -i- A) -{- S shall 
not exceed the proper allowable working unit stress. 

Combined Compression and Flexure. — If P -h A = unit stress 
due to compression alone, and S = unit compressive stress at fiber most 
remote from neutral axis, due to flexure alone, then maximum compres- 
sive unit stress = (P -i- A) 4- «S. 

Combined Tension (or Compression) and Shear. — If applied 
tension (or compression) unit stress = p, applied shearing unit stress =» v, 
then from the combined action of the two forces 



Max. S = ±^v'^+ V4P^ Maximum shearing unit stress; 
Max. t = V2V-\-^v- + V4J'^ Maximum tensile (or compressive) unit stress. 
Combined Flexure and Torsion. — If «S = greatest unit stress due 
to flexure alone, and S^ = greatest torsional shearing unit stress due to 
torsion alone, then for the combined stresses 

Max. tension or compression unit stress t = l/2*S + ^ Sg^-{- ViS^; 
Max. shear s = ±^sJ+^TuS\ 

Equivalent bending moment = 1/2 M + 1/2 ^M^ + T^, where Af = bending 
moment and r = torsional moment. 

Formula for diameter of a round shaft subjected to transverse load 
while transmitting a given horse-power (see also Shafts of Engines): 



- = ^-¥v^ 



402,500,000 //2 



where M = maximum bending moment of the transverse forces in 
pound-inches, H = horse-power transmitted, n = No. of revs, per minute, 
and t = the safe allowable tensile or compressive working strength of 
the material. 

Gu est's Form ula for maximum tension or compression unit stress is 
t^V^S^^'^+S'^iPhiL Mag,, July, 1900). It is claimed by many writers to 
be more accurate th an Ran kine^s formula, given above. Equivalent 
bending moment = Vivp + T^. {Eng'g., Sept. 13 and 27, 1907; July 10, 
1908; April 23, 1909.) 

Combined Compression and Torsion. — For a vertical round shaft 
carrying a load and also transmitting a given horse-power, the result- 
ant maximum compressive unit stress 



t-^ + 1/321 0002 HL + l^fl 
^- nd? ^ V'^21.000 ^^2^2 + ^2^4 • 



in which P is the load. From this the diameter d may be found when t 
and the other data are given. 

Stress due to Temperature. — Let I = length of a bar, A = its sec- 
tional area, c = coefficient of linear expansion for one degree, t — rise or 
fall in temperature m degrees, E = modulus of elasticity, A the change 
of length due to the rise or fall t; if the bar is free to expand or contract, 
A = dl. 

If the bar is held so as to prevent its expansion or contraction the 
stress produced by the change of temperature = S = ActE. The fol- 
lowing are average values of the coefficients of linear expansion for a 
change in temperature of one degree Fahrenheit: 

For brick and stone a = 0.0000050, 

For cast iron = 0.0000056, 

Por wrought iron and steel.... a= 0.0000065. 



336 STRENGTH OF MATERIALS. 

The stress due to temperature should be added to or subtracted from 
the stress caused by other external forces according as it acts to increase 
or to relieve the existing stress. 

What stress will be caused in a steel bar 1 inch square in area by a 
change of temperature of 100° F.? S = AdE = 1 X 0.0000065 X 100 X 
30,000,000 = 19,500 lbs. Suppose the bar is under tension of 19,500 
lbs. between rigid abutments before the change in temperature takes 
place, a cooling of 100° F. will double the tension, and a heating of 100** 
will reduce the tension to zero. 



STRENGTH OF FLAT PLATES. 

For a circular plate supported at the edge, uniformly loaded, according 
to Grashof, 

^ 5r2 , a/Et^ 6/^2 

For a circular plate fixed at the edge, uniformly loaded, 
, 2r2 , . /2 r^p Sft^ 

in which / denotes the working stress; r, the radius in inches; t, the thick- 
ness in inches; and p, the pressure in pounds per square inch. 
For mathematical discussion, see Lanza, " Applied Mechanics.'* 
Lanza gives the following table, using a factor of safety of 8, with ten- 
sile strength of cast iron 20,000, of wrought iron 40,000, and of steel 80,000: 

Supported. Fixed. 

Cast iron ^ = 0.0182570 r v^ t = 0.0163300 r V£ 

Wrought iron t = 0.0U7850 r Vp_ t = 0.0105410 r Vp 

Steel t ^ 0.0091287 r "^p t ^ 0.0081649 r v^ 

For a circular plate supported at the edge, and loaded with a concen- 
trated load P applied at a circumference the radius of which is tq: 



tor 



^ =- 10 20 30 40 


50; 


c = 4.07 5.00 5.53 5.92 


6.22; 


<=i/^; P = ^-^. 





The above formulae are deduced from theoretical considerations, and 
give thicknesses much greater than are generally used in steam-engine 
cylinder-heads. (See empirical formulae under Dimensions of Parts of 
Engines.) The theoretical formulae seem to be based on incorrect or 
incomplete hypotheses, but they err in the direction of safety. 

Thickness of Flat Cast-iron Plates to resist Bursting Pressures. 
— - Capt^ John Ericsson (Church's Life of Ericsson) gave the following 
rules: The proper thickness of a square cast-iron plate will be obtained 
by the foUowmg: Multiply the side in feet (or decimals of a foot) by 
1/4 or the pressure in pounds and divide by 850 times the side in inches; 
the quotient is the square of the thickness in inches. 

For a circular plate, multiply 11-14 of the diameter in feet by 1/4 of 
the prassure on the plate In pounds. Divide by 850 times 11-14 of the 
diameter m inches. [Extract the square root.l 



STRENGTH OF FLAT SURFACES. 837 

Prof. Wm. Harkness, Eng'g News, Sept. 5, 1895, shows that these rules 
can be put in a more convenient form, thus: For square plates T =• 
0.00495 S Vp, and for circular plates T = 0.00439 D^p, where T =- 
thickness of plate, S = side of the square, D = diameter of the circle, 
and p = pressure in lbs. per sq. in. Professor Harkness, however, 
doubts the value of the rules, and says that uo satisfactory theoretical 
solution has yet been obtained. 

The Strength of Unstayed Flat Surfaces. — Robert Wilson 
{Eng'g, Sept. 24, 1877) draws attention to the apparent discrepancy 
between the results of theoretical investigations and of actual experi- 
ments on the strength of unstayed flat surfaces of boiler-plate, such as 
the unstayed flat crowns of domes and of vertical boilers. 

On trying to make the rules given by the authorities agree with the 
results of his experience of the strength of unstayed flat ends of cylin- 
drical boilers and domes that had given way after loner use, Mr. Wilson 
was led to believe that the rules give the breaking strength much lower 
than it actually is. He describes a number of experiments made by- 
Mr. Nichols of Kirkstall, which gave results varying widely from each 
Other, as the method of supporting the edges of the plate was varied, 
and also varying widely from the calculated bursting pressures, the 
actual results being in all cases very much the higher. Some conclusions 
drawn from these results are: 

1. Although the bursting pressure has been found to be so high, boiler- 
makers must be warned against attaching any importance to this, since 
the plates deflected almost as soon as any pressure was put upon them 
and sprang back again on the pressure being taken off. This springing 
of the plate in the course of time inevitably results in grooving or chan- 
neling, which, especially when aided by the action of the corrosive acids 
in the water or steam, will in time reduce the thickness of the plate, and 
bring about the destruction of an unstayed surface at a very low pressure. 

2. Since flat plates commence to deflect at very low pressures, they 
should never be used without stays; but it is better to dish the plates 
when they are not stayed by flues, tubes, etc. 

3. Against the commonly accepted opinion that the limit of elasticity 
should never be reached in testing a boiler or other structure, these ex- 
periments show that an exception should be made in the case of an un- 
stayed flat end-plate of a boiler, which will be safer when it has assumed 
a permanent set that will prevent its becoming grooved by the continual 
variation of pressure in working. The hydraulic pressure in this case 
simply does what should have been done before the plate was fixed, 
that is, dishes it. 

4. These experiments appear to show that the mode of attaching by 
flange or by an inside or outside angle-iron exerts an important influence 
on the manner in which the plate is strained by the pressure. 

When the plate is secured to an angle-iron, the stretching under pres- 
sure is, to a certain extent, concentrated at the line of rivet-holes, and 
the plate partakes rather of a beam supported than fixed round the edge. 
Instead of the strength increasing as the square of the thickness, when 
the plate is attached by an angle-iron, it is probable that the strength 
does not increase even directly as the thickness, since the plate gives 
way simpler by stretching at the rivet-holes, and the thicker the plate, 
the less uniformly is the strain borne by the different layers of which the 
plate may be considered to be made up. When the plate is flanged, the 
flange becomes compressed by the pressure against the body of the plate, 
and near the rim, as shown by the contrary flexure, the inside of the plate 
is stretched more than the outside, and it may be by a kind of shearing 
action that the plate gives way along the line where the crushing and 
stretching meet. 

5. These tests appear to show that the rules deduced from the theo- 
retical investigations of Lam6, Rankine, and Grashof are not confirmed 
by experiment, and are therefore not trustworthy. 

The rules of Lam6, etc., apply only within the elastic limit. (Eng'g, 
Dec. 13, 1895.) 

Unbraced Wrought-iron Heads of Boilers, etc. (The Locomo- 
Hve, Feb., 1890). — Few experiments have been made on the strength 
of flat heads, and our knowledge of them comas largely from theory. 
Experiments have been made on small plates Vie of an inch thick. 



338 STRENGTH OF MATERIALS. 

yet the data so obtained cannot be considered satisfactory when we 
consider the far thicker heads that are used in practice, although the 
results agreed well with Rankine's formula. Mr. Nichols has made ex- 
periments on larger heads, and from them he has deduced the following 
rule: "To find the proper thickness for a flat unstayed head, multiply 
the area of the head by the pressure per square inch that it is to bear 
safely, and multiply tliis by the desired factor of safety (say 8): then 
divide the product by ten times the tensile strength of the material 
used for the head." His rule for finding the bursting pressure when the 
dimensions of the head are given is: "Multiply the thickness of the end- 
plate in inches by ten times the tensile strength of the material used, 
and divide the product by the area of the head in inches." 

In Mr. Nichols's experiments the average tensile strength of the iron 
used for the heads was 44,800 pounds. The results he obtained are 
given below, with the calculated pressure, by his rule, for comparison. 

1. An unstayed flat boiler-head is 341/2 inches in diameter and 9/ie 
inch thick. What is its bursting pressure? The area of a circle 34 V2 
inches in diameter is 935 square inches; then 9/i6 X 44,800 X 10 = 
252,000, and 252,000 -^ 935 = 270 pounds, the calculated bursting 
pressure. The head actually burst at 280 pounds. 

2. Head 34 1/2 inches in diameter and 3/8 inch thick. The area = 935 
square inches: then, s/g X 44,800 X 10 = 168,000, and 168.000 -J- 935 
= 180 pounds, calculated bursting pressure. This head actually burst 
at 200 pounds. 

3. Head 26 1/4 inches in diameter, and S/g inch thick. The area 541 
square inches; then, 3/3 x 44,800 X 10 = 168,000, and 168,000 -f- 541 
= 311 pounds. This head burst at 370 pounds. 

4. Head 28V2 inches in diameter and 3/8 inch thick. The area = 638 
square inches; then, 3/8 x 44,800 X 10 = 168,000, and 168,000 -i- 638 
= 263 pounds. The actual bursting pressure was 300 pounds. 

In the third experiment, the amount the plate bulged under different 
pressures was as follows: 

At pounds per sq. in 10 20 40 80 120 140 170 200 

Plate bulged 1/32 Vie Vs Vi ^/a V2 ^/s ^/i 

The pressure was now reduced to zero, and the end sprang back 3/i« 
inch, leaving it with a permanent set of ^/iq inch. The pressure of 
200 lbs. was again applied on 36 separate occasions during an interval of 
five days, the bulging and permanent set being noted on each occasion, 
but without any appreciable difference from that noted above. 

The experiments described were confined to plates not widely different 
in their dimensions, so that Mr. Nichols's rule cannot be relied upon for 
heads that depart much from the proportions given in the examples. 

Strength of Stayed Surfaces. — A flat plate of thickness t is sup- 
ported uniformlv by stays whose distance from center to center is a, 
uniform load p lbs. per square inch. Each stay supports pa^ lbs. The 
greatest stress on the plate is 

. 2a2 .__ . . 

/=-g^P. (Unwm.) 

For additional matter on this subject see strength of Steam Boilers. 

Stresses in Steel Plating due to Water-pressure, as in plating of 
vessels and bulkheads {Engineering, May 22, 1891, page 629). 

Mr. J. A. Yates has made calculations of the stresses to which steel 
plates are subjected by external water-pressure, and arrives at the 
folio wmg conclusions: 

Assume 2a inches to be the distance between the frames or other 
ngid supports, and let d represent the depth in feet, below the surface 
of the water, of the plate under consideration, t = thickness of plate in 
inches, D the deflection from a straight line under pressure in inches, 
and P = stress per square inch of section. 

For outer bottom and ballast-tank plating, a = 420 t/d, D should not 
be greater than 0.05 X 2 a/12, and P/2 not greater than 2 to 3 tons; 
while for bulkheads, etc., a = 2352 t/d, D should not be greater tbaa 



THICK HOLLOW CYLINDERS UNDER TENSION. 339 

0.1 X 20/12, and P/2 not greater than 7 tons. To illustrate the appli- 
cation of these formulaB the following cases have been taken: 



For Outer Bottom, etc. 


For Bulkheads, etc. 


Thick- 


Depth 


Spacing of 


Thick- 


Depth of 
Water. 


Maximum Spac- 


ness of 


below 


Frames should 


ness of 


ing of Rigid 


Plating. 


Water. 


not exceed 


Plating. 


Stiff eners. 


in. 


ft. 


in. 


in. 


ft. 


ft. in. 


1/2 


20 


About 2 1 


1/2 


20 


9 10 


1/2 


10 


•' 42 


3/8 


20 


7 4 


3/8 


18 


" 18 


3/8 


10 


14 8 


8/8 


9 


" 36 


1/4 


20 


4 10 


1/4 


10 


" 20 


1/4 


10 


9 8 


1/4 


5 


" 40 


1/8 


10 


4 10 



It would appear that the course which should be followed in stiffening 
bulkheads is to fit substantially rigid stiffening frames at comparatively 
wide intervals, and only work such light angles between as are necessary 
for making a fair job of the bulkhead. 



SPHERICAL SHELLS AND DOMED BOILER-HEADS. 

To find the Thickness of a Spherical Shell to resist a given 
Pressure. — Let d = diameter in inches, and p the internal pressure 
per square inch. The total pressure which tends to produce rupture 
around the great circle will be '^Un(Pj>. Let *S = safe tensile stress per 
square inch, and t the thickness of metal in inches; then the resistance 
to the pressure will be ndt S. Since the resistance must be equal to the 
pressure, 



1/4 7:d^p = i:dtS. 



Whence ^ = -^^ • 



The same rule is used for finding the thickness of a hemispherical head 
to a cylinder, as of a cylindrical boiler. 

Thickness of a Domed Head of a Boiler. — If «S = safe tensile 
stress per square inch, d = diameter of the shell in inches, and t = thick- 
ness or the shell, i = pd -^ 2S; but the thickness of a hemispherical 
head of the same diameter is t = pd ^ 4S. Hence if we make the 
radius of curvature of a domed head equal to the diameter of the boiler, 



we shall have t = 



2pd 
45 



pd 
= -~^ , or the thickness 



of such a domed head 



wiil be equal to the thickness of the shell. 



THICK HOLLOW CYLINDERS UNDER TENSION. 

Lamp's formula, which is generally used, gives 



' = -{n)*-^} 



t = thickness; ri= inside and r2 = outside radius; 
h = maximum allowable hoop tension at the 

interior of the cylinder; 
p = intensity of interior pressure; 
5 = tension at the exterior of the cylinder. 






= P 



2ri2 



Vi 



-^^dHY 



340 STRENGTH OF MATERIALS. 

Example: Let maximum unit stress at the inner edge of the annulus 
= 8000 lbs. per square inch, radius of cylinder = 4 inches, interior 
pressure = 4000 lbs. per square inch. Required the thickness and the 
tension at the exterior surface. 

s = p / 2 = 4000 X ^t " = 4000 lbs. per sq. in. 
Tr- — r\ 4o — lb 

For short cast-iron cylinders, such as are used in hydraulic presses, it is 
doubtful if the above formulae hold true, since the strength of the cylindri- 
cal portion is reinforced by the end. In that case the strength would be 
higher than that calculated by the formula. A rule used in practice 
for such presses is to make the thickness = Vio of the inner circum- 
ference, for pressures of 3000 to 4000 lbs. per square inch. 

Hooped Cylinders. — For very high pressures, as in large guns, hoops 
or outer tubes of forged steel are shrunk on inner tubes, thus bringing a 
compressive stress on the latter which assists in resisting the tension due 
to the internal pressure. For discussion of Lam6's, and other formulse 
for built-up guns, see Merriman's "Mechanics of Materials," 

THIN CYLINDERS UNDER TENSION. 

Let p = safe working pressure in lbs. per sq. in.; 
d = diameter in inches; 

T = tensile strength of the material, lbs. per sq. in.; 
t — thickness in inches; 
/ = factor of safety; 
c = ratio of strength of riveted joint to strength of solid plate. 

If r = 50,000, / = 5, and c =F 0.7; then 

14,000^ , dp 
V = ;5 — ; i 



14,000 



The above represents the strength resisting rupture along a longitudinal 
seam. For resistance to rupture in a circumferential seam, due ia 

pressure on the ends of the cylinder, we have —— = ^. - ; 

4, Tie 
whence p => ^, •. 
df 

Or the strength to resist rupture around a circumference is twice as great 
as that to resist rupture longitudinally; hence boilers are commonly 
single-riveted in the circumferential seams and double-riveted in the 
longitudinal seams. 

CARRYING CAPACITY OF STEEL ROLLERS AND BALLS. 

Carrying Capacity of a Steel Roller between Flat Plates. — (Merri- 

man, Mech. of Mails.) Let S = maximum safe unit stress of the mate- 
rial, / = length of the roller in inches, d = diameter, E = modulus of 
elasticity, W = load, then W =2/^idS (2S/E)^. Taking w = W/l, 
and S = 15,000 and E = 30,000,000 lbs. per sq. in. for steel the formula 
reduces to w; = 316 d. Cooper's specifications for bridges, 1901, gives 
w = 300 d. (The rule given in some earlier specifications, w = 1200 >/d, 
is erroneous.) The formula assumes that only the roller is deformed by 
the load, but experiments show that the plates also are defonned, and 
that the formula errs on the side of safety. Experiments by Crandall 



RESISTANCE OF HOLLOW CYLINDERS. 341 

and Marston on steel rollers of diameters from 1 to 16 in. show that 
their crushing loads are closely given by the formula W = 880 Id. (See 
Roller Bearings.) 

Spherical Boilers. — With the same notation as above, d being the 
diameter of the sphere, 5= \/WE^i/\TTd2; IT = 1/4 7rrf252 -h .E. The 
diameter of a sphe re to carr y a given load with an allowable unit- 
stress S is d = 2 ^yWE^^nS'^. This rule assumes that there is no de- 
formation of the plates between which the sphere acts, hence it errs on 
the side of safety. (See Ball Bearings.) 

RESISTANCE OF HOLLOW CYLINDERS TO COLLAPSE. 

Fairbairn's empirical formula {Phil. Trans., 1858) is 

/2.19 

p = 9,675,600 i^. (1) 

where p = pressure in lb. per square inch, t = thickness of cylinder, 
d = diameter, and / = length, all in inches. 
He recommends the simpler formula 

p = 9,675.600^ (2) 

as sufficiently accurate for practical purposes, for tubes of considerable 
diameter and length. 

The diameters of Fairbairn's experimental tubes were 4, 6, 8, 10, and 
12 inches, and their lengths ranged between 19 and 60 inches. 

His formula (2) was until about 1908 generally accepted as the basis of 
rules for strength of boiler-flues. In some cases, however, limits were 
fixed to its application by a supplementary formula. 

Lloyd's Register contains the following formula for the strength of 
circular boiler-flues, viz., 

- = ^^^fF <3) 

The English Board of Trade prescribes the following formula for cir- 
cular flues, when the longitudinal joints are welded, or made with riveted 
butt-straps, viz., 

• ^ 90.000/2 

^ {L + l)d ^^^ 

For lap-joints and for inferior workmanship the numerical factor may 
be reduced as low as 60,000. 

The rules of Lloyd's Register, and those of the Board of Trade, pre- 
scribe further, that in no case the value of P must exceed 800 t/d. (5) 

In formulae (3), (4), (5) P is the highest working pressure in poimds 
per square inch, t and d are the thickness and diameter in inches, L is 
the length of the flue in feet measured between the strengthening rings, 
in case it is fitted with such. Formula (3) is the same as formula (2), 
with a factor of safety of 9. 

Ny Strom has deduced from Fairbairn's experiments the following 
formula for the collapsing strength of flues : 

t2 
p= 692.800 ;=-• (6) 

d\^ I 

where p, t, I, and d have the same meaning as in formula (1), Nystrom 
considers a factor of safety of 4 sufficient in applying his formula. (See 
"A New Treatise on Steam Engineering," by J. W. Nystrom, p. 106.) 

Formulae (1), (3), and (6) have the common defect that they make 
the collapsing pressure decrease indefinitely with increase of length, and 
vice versa. 

D. K. Clark, in his "Manual of Rules," etc., p. 696, gives the dimen- 
sions of six flues, selected from the reports of the Manchester Steam- 
users' Association, 1862-69, which collapsed while in actual use in boil- 
ers. These flues varied from 24 to 60 inches in diameter, and from 
3/16 to 3/g inch in thickness. They consisted of rings of plates riveted 
together, with one or two longitudinal seams, but all of them unfortified 
\>y intermediate flanges or strengthening rings. From the data Clark 



342 STRENGTH OF MATERIALS. 

deduced the following formula "for the average resisting force of 
common boiler-flues," viz., 

, /50,000 ^^^\ 
P = ^=1— ^ 500l (7) 

where p is the collapsing pressure in pounds per square inch, and d and t 
are the diameter and thicloiess expressed in inches. 

Instances of collapsed flues of Cornish and Lancashire boilers collated 
by Clark (S. E., vol. i, p. 643), showed that the resistance to collapse 
of flues of 3/8-in. plates, 18 to 43 ft. long, and 30 to 50 in. diameter, varied 
as the 1.75 power of the diameter. Thus, 

For diameters of 30 35 40 45 50 in. 

The collapsing pressures were. . . 76 58 45 37 30 lb. per sq. in. 
For 7/i6-in. plates the collapsing 

pressures were 60 49 42 lb. per sq. in. 

C. R. Roelker, in Van Nostrand's Magazine, March, 1881, says that 
Nystrom's formula, (6), gives a closer agreement of the calculated with 
the actual collapsing pressures in experiments on flues of every descrip- 
tion than any of the other formulae. 

Formula for Corrugated Furnaces (Eng'g, July 24, 1891, p. 102). — 
As the result of a series of experiments on the resistance to collapse 
of Fox's corrugated furnaces, the Board of Trade and Lloyd's Register 
altered their formulae for these furnaces in 1891 as follows: 

Board of Trade formula is altered from 

T = thickness in inches ; D = meandiameter of furnace; W P ^ work- 
ing pressure, lb. per sq. in. 

Lloyd's formula is altered from 

T = thickness in sixteenths of an inch; 
D = greatest diameter of furnace; 
WP = working pressure in pounds per square inch. 

Stewart's Experiments. — Prof . Reid T. Stewart {Trans. A.S.M.E., 
xxvii, 730) made two series of tests on Bessemer steel lap-welded tubes 
3 to 10 ins. diain. One series was made on tubes 85/8 in. outside diam. 
with the different commercial thicknesses of wall, and in lengths of 21/2, 
5, 10, 15 and 20 ft. between transverse joints tending to hold the tube in 
a circular form. A second series was made on single lengths of 20 ft. 
Seven sizes, from 3 to 10 in. outside diam., in all the commercial thick- 
nesses obtainable, were tested. The tests showed that all the old for- 
mulae were inapplicable to the wide range of conditions found in modern 
practice. The principal conclusions drawn from the research are as 
follows: 

1. The length of tube, between transverse joints tending to hold it 
in circular form, has no practical influence upon the collapsing pressure 
of a commercial lap-welded tube so long as this length is not less than 
about six diameters of tube. 

2. The formulae, based upon this research, for the collapsing pres- 
sures of modern lap-welded Bessemer steel tubes, for all lengths greater 
than six diameters, are as follows: 

P= 1,000(1 - y 1 - 1600^) (A) 

P = 86,670^ - 1386 (B) 

Where P = collapsing pressure, pounds per sq. inch, d = outside 
diameter of tube in mches, t = thickness of wall in inches. 

Formula A is for values of P less than 581 pounds, or for values of ^ 



RESISTANCE OF HOLLOW CYLINDERS. 343 

less than 0.023, while formula B is for values greater than these. When 
appl\ing these formulae, to practice, a suitable factor of safety must be 
applied. 

3. The apparent fibre stress under which the different tubes failed 
varied from about 7000 lbs. for the relatively thinnest to 35,000 lbs. 
per sq. ?n. for the relatively thickest walls. Since the average yield 
point of the material was 37,000 and the tensile strength 58,000 lbs. 
per sq. in., it would appear that the strength of a tube subjected to a 
fluid collapsing pressure is not dependent alone upon either the elastic 
limit or ultimate strength of the material constituting it. The element 
of greatest weakness in a tube is its departure from roundness, evea 
when this departure is relatively small. 

The table on the following page is a condensed statement of the principal 
results of the tests. 

Rational Formulae for Collapse of Tubes. (S. E. Slocum, Eng'g, 
Jan. 8, 1909.) 

Heretofore designers have been forced to rely either upon the anti- 
quated experiments of Fairbairn, which were known to be in error by 
as much as 100% in many cases, or else to apply the theoretical formu- 
Ise of Love and others, without knowing how far the assumptions on 
which these formulse are based are actually realized. 

A rational formula for thin tubes under external pressure, due to A. E. H. 
Love, is 

P = [2E/{1 -m'^)]{t/D)\ (1) 

in which P = collapsing pressure in lbs. per sq. in. 

E = modulus of elasticity in lbs. per sq. in. 
m = Poisson's ratio of lateral to transverse deformation. 
t = thickness of tube wall in ins. 
D = external tube diameter in ins. 

For thick tubes a special case of Lamp's general formula is 

P = 2u{{t/D) - {t/Dn (2) 

in which u = ultimate compressive strength in lbs. per sq. in. 

The average values of the elastic constants are for steel, E = 30,000,000, 
m = 0.295, u = 40,000; and for brass, E = 14,000,000, m = 0.357, 
u = 11,000. 

Hence, for thin steel tubes, P = 65,720,000 (t/Dy (3) 

For thick steel tubes, P = 80,000 [(t/D) - (t/D)^] .... (4) 

For thin brass tubes, P = 32,090,000 (t/D) 3 (5) 

For thick brass tubes, P = 22,000 [{t/D) - (t/Dy-] .... (6) 

It is desirable to introduce a correction factor C in (1) which shall 
allow for the average ellipticity and variation in thickness. The cor- 
rection for ellipticity = Ci = (i)min/-Dmax)^ and that for variation in 
thickness = C2 = (fmin/Wr.)^. From Stewart's twenty-five experiments 
Ci = 0.967 and C2 = 0.712. The correction factor C = Ci C2 = 0.69; 
and (1) becomes 

P = C[2£'/(l -m2)]a/D)3 (7) 

in which C = 0.69 for Stewart's lap-welded steel flues, t = average 
thickness in ins., and D = maximum diameter in ins. 

The. empirical formulas obtained by Carman (Univ. of Illinois, Bull. 
No. 17, 1906), are for thin cold-drawn seamless steel tubes, 

P = 50,200,000 (t/D)\ 
and for thin seamless brass tubes, 

P = 25,150,000 a/D)3. 

Carman assigns 0.025 as the upper limit of t/D for thin tubes and 0.03 
as the lower limit of t/D for thick tubes. Stewart assigns 0.023 as the 
limit of t/D between thin and thick tubes. 

Comparing these with (3) and (5), it is evident that they correspond 
to a correction factor of 0.76 for the steel tubes and 0.78 for the brass 
tubes. Since Carman's experiments were performed on seamless drawn 
tubes, while Stewart used lap-welded tubes, it might have been antici- 



344 



STRENGTH OF MATERIALS. 



Collapsing Pressure of Lap- Welded Steel Tubes. 
Outside Diameter, SS/g In.; Length of Pipe, 20 Ft. 



Thick- 


Length, 


Bursting 
Pressure, 


Aver- 


Outside 

Diam. 

In. 


Thick- 


Bursting 


Aver- 


ness, 
In. 


Ft. 


Lbs. per 
Sq. In. 


age. 


ness. 


Pressure. 


age. 


0.176 


2.21 


815-1085 


977 


3 


0.112 


1550-2175 


I860 


0.180 


4.70 


525-705 


792 


3 


0.143 


2575-3350 


2962 


0.181 


10.08 


455-650 


565 


3 


0.188 


3700-4200 


4095 


0.184 


14.71 


425-610 


548 


4 


0.119 


860-1030 


964 


0.185 


19.72 


450-625 


536 


4 


0.175 


2050-2540 


2280 


0.212 


2.21 


1240-1353 


1314 


4 


0.212 


3075-3375 


3170 


0.212 


4.70 


805-975 


907 


4 


0.327 


5425-5625 


5560 


0.217 


10.30 


700-960 


841 


6 


0.130 


450-640 


524 


0.219 


12.79 


750-1115 


905 


6 


0.167 


715-1110 


928 


0.266 


2.14 


1475-2200 


1872 


6 


0.222 


1200-2075 


1797 


0.274 


4.64 


1345-2030 


1684 


6 


0.266 


1750-2890 


2441 


0.272 


9.64 


1150-1908 


1583 


7 


0.160 


515-^75 


592 


0.273 


14.64 


1250-1725 


1483 


7 


0.242 


1525-1850 


1680 


0.268 


19.64 


1250-1520 


1419 


7 


0.279 


1835-2445 


2147 


0.311 


2.16 


2290-2490 


2397 


8.64 


0.185 


450-625 


536 


0.306 


4.64 


1795-2325 


2073 


8.66 


0.268 


1250-1520 


1419 


0.306 


9.64 


1585-2055 


1807 


8.67 


0.354 


1830-2180 


2028 


0.309 


14.64 


1520-2025 


1781 


10 


0.165 


210-240 


225 


0.302 


19.75 


1575-1960 


1762 


10 


0.194 


305-423 


383 










10 


0.316 


1275-1385 


1319 













Collapsing Pressure of Lap- Welded Steel Tubes 
Calculated by Stewart's Formulae. 


^Lbs. 1 


per Sq. In.) 




Outside Diameters, Inches. 


CO 

z 
S 


2 In. 


2V2 
In. 


3 In. 


4 In. 


5 In. 


6 In. 


7 In. 


8 In. 


9 In. 


10 In. 


II In, 


0.10 


2947 
3814 
4671 
5548 
6414 
7281 
8148 
9014 
9881 


2081 
2774 
3468 
4161 
4854 
5548 
6241 
6934 
7628 
8321 
9014 
9708 


1503 
2081 
2659 
3236 
3814 
4392 
4970 
5548 
6125 
6703 
7281 
7859 
8437 
9014 
9592 


781 
1214 
1647 
2081 
3514 
2947 
3381 
3814 
4248 
4681 
5114 
5548 
5981 
6414 
6848 
7281 
7714 
8148 
8581 
9014 
9448 
















0.12 


694 
1041 
1387 
1734 
2081 
2427 
2774 
3121 
3468 
3814 
4161 
4508 
4854 
5201 
5548 
5894 
6241 
6588 
6934 
7281 


400 
636 
925 
1214 
1503 
1792 
2081 
2370 
2669 
2947 
3236 
3525 
3814 
4103 
4392 
4681 
4970 
5259 
5548 
5887 












0.14 


400 
593 

843 
1090 
1338 
1586 
1833 
2081 
2328 
2576 
2824 
3071 
3319 
3567 
3814 
4062 
4309 
4557 
4805 


286 

400 

564 

781 

997 

1214 

1431 

1647 

1864 

2081 

2297 

2514 

2731 

2947 

3164 

3381 

3598 

3814 

4031 


217 

297 

400 

542 

733 

935 

1118 

1310 

1503 

1696 

1888 

2081 

2273 

2466 

2659 

2851 

3044 

3236 

3429 






0.16 
0.18 
0.20 
0.22 
0.24 
0.26 
0.28 
0.30 
0.32 
0.34 


232 
306 
400 
525 
694 
867 
1041 
1214 
1387 
1561 
1734 
1907 
2081 
2254 
2427 
2601 
2774 
2947 


187 
244 
314 
400 
512 
633 
820 
978 
1135 
1293 


0,36 






1450 


38 






1608 
1766 
1923 
2081 
2238 
2396 
2554 


40 







0.42 








0.44 








0.46 








048 


. ... 






0.50 

















HOLLOW COPPER BALLS. 345 

pated that the latter would develop a smaller percentage of the theo- 
retical strength for perfect tubes than the former. 

Formula (2) for thick tubes when corrected for eUipticity and varia- 
tion in thickness reads 

P = 2UcC(,t/D)[l - C(t/D)] (8) 

in which t = average thickness, and C = Ci, C2, Cx being equal to 

■^min/^maxi C2 = 'average /fmin- 

From Stewart's experiments, average ellipticity d == 0.9874, and 
average variation in thickness d = 0.9022; .*. C = 0.9874 X 0.9022 
= 0.89. 

We have then, for thick lap-welded steel flues, 

P = 2^^0.89 {t/D) [1 - 0.89 (f/D)] 
^nd for thin lai)-welded steel flues, 

P = 0.69 [2 E/{1 - w2)] a/Z))3 
in which E = 30,000,000, m = 0.295, and u^ = 38,500 lbs. per gq. in. 

The experimental data of Stewart and Carman have made it possible 
to correct the rational formulas of Love and Lame to conform to actual 
conditions; and the result is a pair of supplementary formulas (7) and 
(8), which cover the entire range of materials, diameters, and thicknesses 
for long tubes of circular section. All that now remains to be done is 
the experimental determination of the correction constants for other 
types of commercial tubes than those already tested. 

HOLLOW COPPER BALLS. 

Hollow copper balls are used as floats in boilers or tanks, to control 
feed and discharge valves, and regulate the water-level. 

They are spun up in halves from sheet copper, and a rib is formed on 
one half. Into this rib the other half fits, and the two are then soldered 
or brazed together. In order to facilitate the brazing, a hole is left on 
one side of the ball, to allow air to pass freely in or out ; and this hole is 
made use of afterwards to secure the float to its stem. The original 
thickness of the metal may be anything up to about Vie of an inch, if 
the spinning is done on a hand lathe, though thicker metal may be used 
when special machinery is provided for forming it. In the process of 
spinning, the metal is thinned down in places by stretching; but the 
thinnest place is neither at the equator of the ball (i.e., along the rib) 
nor at the poles. The thinnest points lie along two circles, passing 
around the ball parallel to the rib, one on each side of it, from a third 
to a half of the way to the poles. Along these lines the thickness may 
be 10, 15, or 20 per cent less than elsewhere, the reduction depending 
somewhat on the skill of the workman. 

The Locomotive for October, 1891, gives two empirical rules for deter- 
mining the thickness of a copper ball which is to work under an external 
pressure, as follows: 

t rrv,- ir — diameter in inches X pressure in pounds per sq. in. 

1. inicKness i6.00"Q " 

„ mu- 1 diameter X "^pressure 

2. Thickness = j^io 

These rules give the same result for a pressure of 166 lbs. only. Ex- 
ample: Required the thickness of a 5-inch copper ball to sustain 

Pressures of 50 100 150 166 200 250 Ibs.persq.ln. 

Answer by first rule 0156 .0312 .0469 .0519 .0625 .0781 inch. 

Answer by second rule .0285 .0403 .0494 .0518 .0570 .0637 *' 



346 STRENGTH OF MATERIALS. 

HOLDING-POWER OF NAILS, SPIKES, AND SCREWS. 

(A. W. Wright, Western Society of Engineers, 1881.) 
Spikes. — Spikes driven into dry cedar (cut 18 months): 

Size of spikes 5 X i/4in. sq. 6 X 1/4 6 X V2 5 X3/8 

Length driven in 4 1/4 in. 5 in. 5 in. 41/4 in. 

Pounds resistance to drawing. Av'ge. lbs. 857 821 1691 1202 

T^.^r>. A f^ Q +oe+o oanh i Max. " 1159 923 2129 1556 

From 6 to 9 tests each [^^^^ .. 7gg ^gg ^^20 687 

A. M. Wellington found the force required to draw spikes Q/ie X 9/i6 in., 
driven 41/4 inches into seasoned oak, to be 4281 lbs.; same spikes, etc., 
in unseasoned oak, 6523 lbs. 

"Professor W. R. Johnson found that a plain spike s/g inch square 
driven 33/8 inches into seasoned Jersey yellow pine or unseasoned chest- 
nut required about 2000 lbs. force to extract it; from seasoned white 
oak about 4000 and from well-seasoned locust 6000 lbs." 

Experiments in Germany, by Funk, give from 2465 to 3940 lbs. (mean 
of many experiments about 3000 lbs.) as the force necessary to extract a 
plain 1/2-inch square iron spike 6 inches long, wedge-pointed for one inch 
and driven 41/2 inches into white or yellow pine. When driven 5 inches 
the force required was about Vio part greater. Similar spikes ^/le inches 
square, 7 inches long, driven 6 inches deep, required from 3700 to 6745 
lbs. to extract them from pine; the mean of the results being 4873 lbs. 
In ail cases about twice as much force was required to extract them 
from oak. The spikes were all driven across the grain of the wood. 
When driven with the grain, spikes or nails do not hold with more than 
half as much force. 

Boards of oak or pine nailed together by from 4 to 16 tenpenny com- 
mon cut nails and then pulled apart in a direction lengthwise of the 
boards, and across the nails, tending to break the latter in two by a 
shearing action, averaged about 300 to 400 lbs. per nail to separate 
them, as the result of many trials. 

Resistance of Drift-bolts in Timber. — Tests made by Rust and 
Coolidge, in 1878. 

White Norway 
Pine. Pine. 

1 in. square iron drove 30 in. in is/ie-in. hole, lbs 26,400 19,200 

1 in. round " " 34 " " is/ie-in. " " 16,800 18,720 

1 in. square ** ** 18 " " i5/i6-in. " " 14,600 15,600 

1 in. round *' " 22 " " i3/i6„in. *' " 13,200 14,400 

Holding-power of Bolts in White Pine. (Eng'g News, Sept. 26, 1891.) 

Round. Square. 
Lbs. Lbs. 

Average of all plain 1-in. bolts 8224 8200 

Average of all plain bolts, 5/8 to 1 i/s in 7805 8110 

Average of all bolts 8383 8598 

Round drift-bolts should be driven in holes is/ie of their diameter, and 
square drift-bolts in holes whose diameter is u/iq of the side of the square. 

Force required to draw Screws out of Norway Pine. 

V?" ^^^P' drive screw 4 in. in wood. Power required, average 2424 lbs. 

[ " 4 threads per in. 5 in. in wood. " *' " 2743 ** 

D'blethr'd, 3 perin., 4in. in " ** " " 2730 " 

*' Lag-screw, 7 per in., 11/2 "" " ** ** 1465 " 

6 " " 21/2 " " ** '* *' 2026 " 

1/2 inch R.R. spike 5 "" " •• •* ,2191 " 

Force required to draw Wood Screws out of Dry Wood. — Tests 
made by Mr. Bevan. The screws were about two inches in length, 0.22 
diameter at the exterior of the threads, 0.15 diameter at the bottom, the 
depth of the worm or thread being 0.035 and the number of threads in one 
incli equal 12. They were passed through pieces of wood half an inch 
in thickne.ss and drawn out by the weights stated: Beech, 460 lbs • ash 



STRENGTH OF BOLTS. 347 

790 lbs.; oak, 760 lbs.; mahogany, 770 lbs.; elm, 665 lbs.; sycamore, 
830 lbs. 

Tests of Lag-screws In Various Woods were made by A. J. Cox, 
University of Iowa, 1891: 

Kind of Wood. gSf,^|„. J^ \^"^l^_ Regt. ^^ts. 

Seasoned white oak s/s in. V2 in. 41/2 in. 8037 3 

'• 9/16" 7/16 " 3 " 6480 1 

" 1/2 " 3/8 " 41/2 " 8780 2 

Yellow-pine stick s/g " 1/2 " 4 " 3800 2 

White cedar, unseasoned s/g " 1/2 " 4 " 3405 2 

Cut versus Wire Nails. — Experiments were made at the Watertown 
Arsenal in 1893 on the comparative direct tensile adhesion, in pine and 
spruce, of cut and wire nails. The results are stated by Prof. W. H. Burr 
as follows: 

There were 58 series of tests, ten pairs of nails (a cut and a wire nail 
in each) being used. The tests were made in spruce wood in most in- 
stances. The nails were of all sizes, from IVs to 6 in. in length. In 
every case the cut nails showed the superior holding strength by a large 
percentage. In spruce, in nine different sizes of nails, both standard 
and light weight, the ratio of tenacity of cut to wire nail was about 
3 to 2. With the" finishing" nails the ratio was roughly 3.5 to 2. With 
box nails (li to 4 inches long) the ratio was roughly 3 to 2. The mean 
superiority in spruce wood was 61%. In white pine, cut nails, driven 
with taper along the grain, showed a superiority of 100%, and with 
taper across the grain of 135%. Also when the nails were driven in the 
end of the stick, i.e., along the grain, the superiority of cut nails was 
100%, or the ratio of cut to wire was 2 to 1. The total of the results 
showed the ratio of tenacity to be about 3.2 to 2 for the harder wood, 
and about 2 to 1 for the softer, and for the whole taken together the 
ratio was 3.5 to 2. 

Xail-holding Power of Various Woods. — Tests at the Watertown 
Arsenal on different sizes of nails from 8d. to 60d., reduced to holding 
power per sq. in. of surface in wood, gave average results, in pounds, 
as follows: white pine, wire, 167; cut, 405. Yellow pine, wire, 318; cut 
662. White oak, wire, 940; cut, 1216. Chestnut, cut, 683. Laurel, 
wire, 651; cut, 1200. 

Experiments by F. W. Clay. {Eng'g News, Jan. 11, 1894.) 

rvr^^/, / Tenacity of 6d nails \ 

^^^^- Plain. Barbed. Blued. Mean. 

White pine 106 94 135 111 

Yellow pine 190 130 270 196 

Basswood 78 132 219 143 

White oak 226 300 555 360 

Hemlock 141 201 319 220 

STRENGTH OF BOLTS. 

Effect of Initial Strain in Bolts. — Suppose that bolts are used to 
connect two parts of a machine and that they are screwed up tightly 
before the effective load comes on the connected parts. Let Pi = the 
initial tension on a bolt due to screwing up, and P2 = the load after- 
wards added. The greatest load may vary but little from Pi or P2, 
according as the former or the latter is greater, or it may approach the 
value Pi + P2, depending upon the relative rigidity of the bolts and of 
the parts connected. Where rigid flanges are bolted together, metal to 
metal, it is probable that the extension of the bolts with any additional 
tension relieves the initial tension, and that the total tension is Pi or P2, 
but in cases where elastic packing, as india rubber, is interposed, the 
extension of the bolts may very little affect the initial tension, and the 
total strain may be nearly Pi + P2. Since the latter assumption is 
more unfavorable to the resistance of the bolt, this contingency should 
usually be provided for. (See Unwin, "Elements of Machine Design," 
for demonstration.) 



348 



STRENGTH OF MATERIALS. 



Forrest E. Cardullo (Machinery's Reference Series No. 22, 1908) states 
the effect of initial stress in bolts due to screwing them tight as follows: 

1. When the bolt is more elastic than the material it compresses, the 
stress in the bolt is either the initial stress or the force applied, whichever 
is greater. 

2. When the material compressed is more elastic than the bolt, the 
stress in the bolt is the sum of the initial stress and the force applied. 

Experiments on screwing up 1/2, 3/4, 1 and 1 1/4 in. bolts showed that the 
stress produced is often sufficient to break a X/2-in. bolt, and that the stress 
varies about as the square of the diameter. From these experiments 
Prof. Cardullo calculates what he calls the "working section" of a bolt as 
equal to its area at the root of the thread, less the area of a V2-in. bolt 
at the root of the thread times twice the diameter of the bolt, and gives 
the following table based on this rule. 





Working Strength of Bolts. 


U. S. Standard Threads. 


_J' 


'S2 


a 


^^ 


-M 


4^ 


_j- 


^•' 


*»* 


"o 


03 


•r^ 00 


"o 


"o 


"o 


3 


"O (c 


"3 m 


m 


a* 


1^ 


Wo, 


«<„ 


W<« 


«« 


W-c 


w-S 


*o 


;§■! 




'Si 


^1 


3 


H 


^§ 


Is 
5 


< 


6 






■Si.« 




m 




1/2 


0.126 























5/8 


0.202 


0.044 


220 


264 


308 


352 


440 


528 


3/4 


0.302 


0.113 


565 


678 


791 


904 


1,130 


1,356 


7/8 


0.420 


0.200 


1,000 


1,200 


1,400 


1,600 


2,000 


2,400 


1 


0.550 


0.298 


1,490 


1,788 


2,086 


2,384 


2,980 


3,476 


11/8 


0.694 


0.411 


2,055 


2,466 


2,877 


3,288 


4,110 


4.932 


11/4 


0.893 


0.578 


2,890 


3,468 


4,046 


4,624 


5,780 


6,936 


13/8 


1.057 


0.710 


3,550 


4,260 


4,970 


5,680 


7,100 


8,520 


11/2 


1.293 


0.917 


4,585 


5,502 


6,419 


7,336 


9,170 


10,504 


!o/8 


1.515 


1.105 


5,525 


6,630 


7,735 


8,840 


11,050 


13,2i>0 


3/4 


1.746 


1.305 


6,525 


7.830 


9,135 


10,440 


13,050 


15,660 


17/8 


2.051 


1.578 


7,890 


9,468 


11,046 


12,624 


15,780 


18,936 


2 


2.302 


1.798 


8,990 


10,788 


12,586 


14,384 


17,980 


21,576 


?y^ 


3.023 


2.456 


12.280 


14,736 


17,192 


19,648 


24,560 


29,472 


21/2 


3.719 


3.059 


15,445 


18,534 


21,623 


24,712 


30,890 


37,068 


23/4 


4.620 


3.927 


19,635 


23,562 


27,489 


31,416 


39,270 


A7,\2A 


3 


5.428 


4.672 


23,360 


28,032 


32,704 


37,376 


46,720 


56,064 


31/4 


6.510 


5.690 


28,450 


34,140 


39,830 


45,520 


56,900 


68,280 


31/2 


7.548 


6.666 


33,330 


39,996 


46,664 


53,328 


66,660 


79,992 



The stresses on bolts caused by tightening the nuts by a wrench may 
be calculated as follows: Let L = the effecrive length of the wrench in 
inches, P = the force in pounds apphed at the distance L, n = no. of 
threads per inch of the bolt, T = total tension on the bolt if there were 
no friction, then T == 2 nuLP. Wilfred Lewis, Trans. A. S. M. E„ gives 
for the efficiency of a bolt E = 1 -j- (1 4- wd), where d = external diameter 
of the screw. T XE = 2nnLP -^ (1 + nd) is the tension corrected 
for fnction. It also expresses the load that can be lifted by screwing a 
nut on a bolt op a bolt into a nut. 

STRENGTH OF CHAINS. 

Formulas for Safe Load on Chains.—Writing the formula for the safe 
loa<l on chains P = Kd'^, P in pounds, d in inches, the following figures for 
A are given by the authorities named. 

^^ ^ Open link Stud link 

Unwin 13,440; 11,200* 20,160 

Weisbach 13,350 17.800 

Bach 13,750; 11,000* 16,500; 13,200* 

* The lower figures are for much used chain, subject frequently to the 
maximum load. G. A Goodenough and L. E. Moore, Univ. of Illinois 



STAND-PIPES AND THEIR DESIGN, 



STAND-PIPES AND THEIR DESIGN. 



349 



(Freeman C. Coffin, New England Water Works Assoc, Eng. News, 
March 16, 1893.) See also papers by A. H. Rowland, Eng. Club of Phil., 
1887; B. F. Stephens, Amer. Water Works Assoc, Eng. News, Oct. 6 
and 13, 1888; W. Kiersted, Rensselaer Soc of Civil Eng., Eng'g Record, 
April 25 and May 2, 1891, and W. D. Pence, Eng. News, April and May, 
1894; also, J. N. Hazlehurst's " Towers and Tanks for Water Works." 

The question of diameter is almost entirely independent of that of 
height. The efficient capacity must be measured by the length from the 
high- water line to a point below which it is undesirable to draw the 
water on account of loss of pressure for fire-supply, whether that point 
is the actual bottom of the stand-pipe or above it. This allowable 
fluctuation ought not to exceed 50 ft., in most cases. This makes the 
diameter dependent upon two conditions, the first of which is the amount 
of the consumption during the ordinary interval between the stopping and 
starting of the pumps. This should never draw the water below a point that 
will give a good fire stream and leave a margin for still further draught 
for fires. The second condition is the maximum number of fire streams 
and their size which it is considered necessary to provide for, and the 
maximum length of time which they are liable to have to run before the 
pumps can be relied upon to reinforce them. 

Another reason for making the diameter large is to provide for stability 
against wind-pressure when empty. 

The following table gives the height of stand-pipes beyond which they 
are not safe against wind-pressures of 40 and 50 lbs. per square foot. 
The area of surface taken is the height multiplied by one half the 
diameter. 

Diameter, feet 20 25 30 35 

Max. height, wind 40 lbs 45 70 150 

50 " 35 55 80 160 

Any form of anchorage that depends upon connections with the side 
plates near the bottom is unsafe. By suitable guys the wind-pressure is 
resisted by tension in the guys, and the stand-pipe is relieved from 
wind strains that tend to overthrow it. The guys should be attached to 
a band of angle or other shaped iron that completely encircles the tank, 
and rests upon some sort of bracket or projection, and not be riveted to 
the tank. They should be anchored at a distance from the base equal 
to the height of the point at which they are attached, if possible. 

The best plan is to build the stand-pipe of such diameter that it will 
resist the wind by its own stability. 

Thickness of the Side Plates. 

The pressure on the sides tending to rupture the plates by tension, due 
to the weight of the water, increases in direct ratio to the height, and 
also to the diameter. The strain upon a section 1 inch in height at any 
point is the total strain at that point divided by two — for each side is 
supposed to bear the strain equally. The total pressure at any point is 
equal to the diameter in inches, multiplied by the pressure per square 
Inch, due to the height at that point. It may be expressed as follows: 

H = height in feet, and / = factor of safety; 
d = diameter in inches; 
p = pressure in lbs. per square inch; 
0.434 = p for 1 ft. in height; 

s = tensile strength of material per square inch; 
T = thickness of plate. 

Bulletin, No. 18, 1907. after an extensive theoretical and experimental 
investigation, find that these values give maximum stresses in the external 
fibers of from 26,400 to 40,320 lbs. per sq. in., which they consider much 
too high for safety. Taking 20,000 as a permissible maximum stress, 
they give the formulae for safe load P = 8000 cP for open links and 
P == 10,000 cP for stud links. They say that the stud Unk will within 
the elastic limit bear from 20 to 25% more load than the open link, but 
that the ultimate strength of the stud link is probably less than that of the 
open link. See also tables of Size and Strength of Chains, page 264. 



350 STRENGTH OF MATERIALS. 



Then the total strain on each side per vertical inch 

^ 0.434 Hd _ prf . rp ^ 0A34:Hdf _ pdf 
~ 2 2 • 2s 28 ' 

Mr. Ckjffin takes / = 5, not counting reduction of strength of joint, 
equivalent to an actual factor of safety of 3 if the strength of the riveted 
joint is taken as 60 per cent of that of the plate. 

The amount of the wind strain per square inch of metal at any joint 
can be found by the following formula, in which 



H . = height of stand-pipe in feet above joint ; 
T = tliickness of plate in inches; 
p = wind-pressure per square foot; 
W = wind -pressure per foot in height above joint; 
W = Dp where D is the diameter in feet; 
m = average leverage or movement about neutral axis 

or central points in the circumference; or, 
m = sine of 45°, or 0.707 times the radius in feet. 



Then the strain per square inch of plate 

(Hio) # 



circ. in ft. X mT 



Mr. Coffin gives a number of diagrams useful in the design of stand- 
pipes, together with a number of instances of failures, with discussion 
of their probable causes. 

Mr. Kiersted's paper contains the following: Among the most promi- 
nent strains a stand-pipe has to bear are: that due to the static pressure 
of the water, that due to the overturning effect of the wind on an empty 
stand-pipe, and that due to the collapsing effect, on the upper rings, of 
violent wind storms. 

For the thickness of metal to withstand safely the static pressure of 
water, let t = thickness of the plate iron in inches; H = height of stand- 
pipe in feet; D = diameter of stand-pipe in feet. 

Then, assuming a tensile strength of 48,000 lbs. per square inch, a 
factor of safety of 4, and efficiency of double-riveted lap-joint equaling 
0.6 of the strength of the soUd plate, t = 0.00036 H X D; H = 10,000 t 
-i-3.6D; which will give safe heights for thicknesses up to s/s to 3/4 of an 
inch. The same formula may also apply for greater heights and thick- 
nesses within practical limits, if the joint efficiency be increased by triple 
riveting. 

The conditions for the severest overturning wind strains exist when 
the stand-pipe is empty. 

Formula for wind-pressure of 50 pounds per square foot, whend = 
diameter of stand- pipe in incJhes; x = any unknown height of stand- 
pipe; X = ^807:dt = 15.85 ^dt. 

Failures of Stand-pipes. — A list showing 23 important failures 
inside of nine years is given in a paper bv Prof. W. D. Pence, Eng'g 
News, April 5, 12, 19 and 26, May 3, 10 and 24, and June 7, 1894. His 
discussion of the probable causes of the failures is most valuable. 

Water Tower at Yonkers, N.Y. — This tower, with a pipe 122 feet 
high and 20 feet diameter, is described in Engineering News, May 18, 1892. 

The thickness of the lower rings is n/ie of an inch, based on a tensile 
strength of 60,000 lbs. per square inch of metal, allowing 65% for the 
strength of riveted joints, using a factor of safety of 31/2 and adding a 
constant of i/g inch. The plates diminish in thickness by Vie inch to 
the last four plates at the top. which are 1/4 inch thick. 

The contract for steel requires an elastic limit of at least 33,000 lbs. 
per square inch; an ultimate tensile strength of from 56,000 to 66.000 lbs. 
per square inch: an eloneration in 8 inches of at least 20%, and a reduc- 
tion of area of at least 45%. The inspection of the work was made bv the 
Pittsburgh Testing Laboratory. According to their report the actual 
conditions developed were as follows: Elastic limit from 34,020 to 39,420; 



WROUGHT-IRON AND STEEL WATER PIPES. 



351 



the tensile strength from 58,330 to 65,390; the elongation in 8 inches 
from 221/2 to 32%; reduction in area from 52.72 to 71.32%; 17 plates 
out of 141 were rejected in the inspection. 

The following table is calculated by Mr. Kiersted's formulae. The 
stand-pipe is intended to be self-sustaining; that is, without guys or 
stiff eners. 

Heights of Stand-pipes for Various Diameters and Thicknesses of 

Plates. 



Thickness 
of Plate 
in Frac- 
tions of 
an Inch. 










Diameters 


in Feet. 












5 

50 
55 
60 
70 
75 
80 
85 


6 
55 


7 
60 


8 
65 


9 

55 
65 

75 
90 
100 
110 
115 
125 
130 


10 

50 
60 

70 
85 
100 
115 
120 
130 
135 
145 
150 


12 

35 
50 
55 
70 

85 
100 
115 
130 
145 
155 
165 


14 


15 


16 


18 


20 


25 


3/16 




7/32 


40 
50 
60 
75 
85 
100 

no 

120 
135 
145 
160 


40 
45 
55 
70 
80 
90 
100 
115 
125 
135 
150 
160 










1/4 

5/16 

3/8 

7/16. . . : . . 

1/2 

9/16 


65 
75 
80 
90 
95 


70 
80 
90 
95 
100 


75 
85 
95 
100 

no 

115 


40 
50 
65 
75 
85 
95 
105 
120 
130 
140 
150 
160 


35 
45 
55 
65 
75 
85 
95 
105 
115 
125 
135 
145 
155 


35 

40 

50 

60 

70 

80 

85 

95 

105 

110 

120 

130 

140 


25 
35 
40 
45 
55 
60 


5/8 








65 


11/16 










75 


3/4 












80 


13/16 












90 


17/8 
















95 


5/1 








. . . 










105 


1 




















110 



























Heights to nearest 5 feet. Rings are to build 5 feet vertically. 



WROUGHT-LRON AND STEEL WATER-PDPES. 

Riveted Steel Water-pipes {Engineering News, Oct. 11, 1890, and 
Aug. 1, 1891). — The use of riveted wrought-iron pipe has been common 
in the Pacific States for many years, the largest being a 44-inch conduit 
in connection with the works of the Spring Valley Water Co., which 
supplies San Francisco. The use of wrought iron and steel pipe has been 
necessary in the West, owing to the extremely high pressures to be with- 
stood and the difficulties of transportation. As an example: In connec- 
tion with the water supply of Virginia City and Gold Hill, Nev., there 
was laid in 1872 an 11 1/2-inch riveted wrought-iron pipe, a part of which 
is under a head of 1720 feet. 

In the East, an important example of the use of riveted steel water 
pipe is that of the East Jersey Water Co., which supplies the city of 
Newark. The contract provided for a maximum high service supply of 
25,000,000 gallons daily. In this case 21 miles of 48-inch pipe was laid, 
some of it under 340 feet head. The plates from which the pipe is made 
are about 13 feet long by 7 feet wide, open-hearth steel. Four plates 
are used to make one section of pipe about 27 feet long. The pipe is 
riveted longitudinally with a double row, and at the end joints with a 
single row of rivets. Before being rolled into the trench, two of the 
27-feet lengths are riveted together, thus diminishing the number of 
joints to be made in the trench and the extra excavation to give room 
for joining. 

The thickness of the plates varies with the pressure, but only three 
thicknesses are used, 1/4 , 5/i6, and 3/8 inches, the pipe made of these 
thicknesses having a weight of 160, 185, and 225 lbs. per foot, respec- 
tively. At the works all the pipe was tested to pressure II/2 times that 
to which it is to be subjected when in place. 

An important discussion of the design of large riveted steel pipes tp 



352 STRENGTH OF MATERIALS. 

resist not only the internal pressure but also the external pressure from 
moist earth in which they are laid, together with notes on the design of a 

§ipe 18 ft. diam. 6000 ft. long for the Ontario Water Power Co., Niagara 
'alls, by Joseph Mayer, will be found in Eng, News, April 26, 1906. 

STRENGTH OF VARIOUS 3IATERIALS. EXTRACTS FROM 
KIRKALDY'S TESTS. 

The publication, in a book by W. G. Kirkaldy, of the results of many 
thousand tests made during a quarter of a century by his father, David 
Kirkaldy, has made an important contribution to our knowledge con- 
cerning the range of variation in strength of numerous materials. A 
condensed abstract of these results was published in the American Ma- 
chinist, May 11 and 18, 1893, from which the following still further con- 
densed extracts are taken: 

The figures for tensile and compressive strength, or, as Kirkaldy calls 
them, pulling and thrusting stress, are given in pounds per square inch of 
original section, and for bending strength in pounds of actual stress or 

gounds per BD- (breadth X square of depth) for length of 36 inches 
etween supports. The contraction of area is given as a percentage of 
the original area, and the extension as a percentage in a length of 10 
inches, except when otherwise stated. The abbreviations T. S., E. L., 
Contr., and Ext. are used for the sake of brevity, to represent tensile 
strength, elastic limit, and percentages of contraction of area, and elon- 
gation, respectively. 

Cast Iron. —44 tests: T. S. 15,468 to 28,740 pounds; 17 of these 
were unsound, the strength ranging from 15,468 to 24,357 pounds. 
Average of all, 23,805 pounds. 

Thrusting stress, specimens 2 inches long, 1.34 to 1.5 in. diameter; 
43 tests, all sound, 94,352 to 131,912; one, unsound, 93,759; average of 
all, 113,825. 

Bending stress, bars about 1 in. wide by 2 in. deep, cast on edge. 
Ultimate stress 2876 to 3854; stress per BD^ = 725 to 892; average, 
820. Average modulus of rupture, R, = 3/2 stress per BD^ X length, 
= 44,280. Ultimate deflection, 0.29 to 0.40 in.; average, 0.34 inch. 

Other tests of cast iron, 460 tests, 16 lots from various sources, gave 
results with total range as follows: PuUing stress, 12,688 to 33,616 
pounds; thrusting stress, 66,363 to 175,950 pounds; bending stress, per 
BD^, 505 to 1128 pounds; modulus of rupture, R, 27,270 to 61,912. 
Ultimate deflection, 0.21 to 0.45 inch. 

The specimen which was the highest in thrusting stress was also the 
highest in bending, and showed the greatest deflection, but its tensile 
strength was only 26,502. 

The specimen with the highest tensile strength had a thrusting stress of 
143,939 and a bending strength, per BD\ of 979 pounds with 0.41 de- 
flection. The specimen lowest in T. S. was also lowest in thrusting and 
bending, but gave 0.38 deflection. The specimen which gave 0.21 deflec- 
tion had T. S., 19,188: thrusting, 104,281; and bending, 561. 

Iron Castings. — 69 tests; tensile strength, 10,416 to 31,652; thrust- 
ing stress, ultimate per square inch, 53,502 to 132,031. 

Channel Irons. — Tests of 18 pieces cut from channel irons. T. S. 
40,693 to 53,141 pounds per square inch; contr. of area from 3.9 to 
32.5%. Ext. in 10 in. from 2.1 to 22.5%. The fractures ranged all the 
way from 100% fibrous to 100% crystalUne. The highest T. S., 53,141, 
with 8.1% contr. and 5.3% ext., was 100% crystalline;' the lowest T. S., 
40,693, with 3.9 contr. and 2.1% ext., was 75% crystalline. All the 
fibrous irons showed from 12.2 to 22.5% ext., 17.3 to 32.5 contr., and 
T. S. from 43,426 to 49,615. The fibrous irons are therefore of medium 
ten.sile strength and high ductility. The crystalline irons are of variable 
T. S., highest to lowest, and low ductihty. 

LowTnoor Iron Bars. — Three rolled bars 21/2 inches diameter; ten- 
sile tests: elastic, 23,200 to 24,200; ultimate, 50,875 to 51,905; contrac- 
tion, 44.4 to 42.5; extension, 29.2 to 24.3. Three hammered bars, 41/2 
Inches diameter, elastic 25,100 to 24,200; ultimate, 46,810 to 49,223; 
contraction, 20.7 to 46.5; extension, 10.8 to 31.6. Fractures of all, 100 
per cent fibrous. In the hammered bars the lowest T. S. was accom« 
panied by lowest ductihty. 



kibkaldy's tests. 



353 



Iron Bars, Various. — Of a lot of 80 bars of various sizes, some 
rolled and some hammered (the above Lowmoor bars included), the 
lowest T. S. (except one) 40,808 pounds per square inch, was shown by 
the Swedish "hoop L" bar 3V4 inches diameter, rolled. Its elastic limit 
was 19,150 pounds; contraction 68.7% and extension 37.7% in 10 
inches. It was also the most ductile of all the bars tested, and was 100% 
fibrous. The highest T. S., 60,780 pounds, with elastic hmit, 29,400; 
contr., 36.6; and ext., 24.3%, was shown by a " Farnley " 2-inch bar, 
rolled. It was also 100% fibrous. The lowest ductiUty 2.6% contr., 
and 4.1% ext., was shown by a 33/4-inch hammered bar, without brand. 
It also had the lowest T. S., 40,278 pounds, but rather high elastic Hmit, 
25,700 pounds. Its fracture was 95% crystaUine. Thus of the two bars 
showing the lowest T. S., one was the most ductile and the other the 
least ductile in the whole series of 80 bars. 

Generally, high ductility is accompanied by low tensile strength, as in 
the Swedish bars, but the Farnley bars showed a combination of high 
ductility and high tensile strength. 

Locomotive Forcings, Iron. — 17 tests average, E. L., 30,420; 
T. S., 50,521; contr., 36.5: ext. in 10 inches, 23.8. 

Broken Anchor Forgings, Iron. — 4 tests: average, E. L., 23,825; 
T. S., 40,083; contr., 3.0; ext. in 10 inches, 3.8. 

Kirkaldy places these two irons in contrast to show the difference 
between good and bad work. The broken anchor material, he says, is 
of a most treacherous character, and a disgrace to any manufacturer. 

Iron Plate Girder. — Tensile tests of pieces cut from a riveted iron 
girder after twenty years' service in a railway bridge. Top plate, aver- 
age of 3 tests, E. L., 26,600; T. S., 40,806; contr., 16.1; ext. in 10 inches, 
7.8. Bottom plate, average of 3 tests, E. L., 31,200; T. S., 44,288; 
contr., 13.3; ext. in 10 inches, 6.3. Web-plate, average of 3 tests, E. L., 
28,000; T. S., 45,902; contr., 15.9; ext. in 10 inches, 8.9. Fractures 
all fibrous. The results of 30 tests from different parts of the girder 
prove that the iron has undergone no change during twenty years of use. 

Steel Plates. — Six plates 100 inches long, 2 inches wide, thickness 
various, 0.36 to 0.97 inch. T. S., 55,485 to 60,805; E. L., 29,600 to 33,200; 
contr., 52.9 to 59.5; ext., 17.05 to 18.57. 

Steel Bridge Links. — 40 Unks from Hammersmith Bridge, 1886. 





Fracture. 




T. S. 


E. L. 


Contr. 


Ext. in 
100 in. 


Silky. 


Gran- 
ular. 


Average of all 


67,294 
60,753 
75,936 
64,044 
63,745 
65,980 
63,980 


38,294 
36,030 
44,166 
32,441 
38,118 
36,792 
39,017 


34.5% 
30.1 
31.2 
34.7 
52.8 
40.8 
6.0 


14.11% 
15.51 
12.42 
13.43 
15.46 
17.78 
6.62 


30% 
15 
30 
100 
35 





Lowest T. S 


70% 


Highest T.S. and E.L.. . . 

Lowest E. L 

Greatest Contraction 

Greatest Extension 

Least Contr. and Ext 


85 

70 



65 

100 



The ratio of elastic to ultimate strength ranged from 50.6 to 65.2 per 
cent; average, 56.9 per cent. 

Extension in lengths of 100 inches. At 10,000 lbs. per sq. in., 0.018 to 
0.024; mean, 0.020 inch; at 20,000 lbs. per sq. in., 0.049 to 0.063; mean, 
0.055 inch; at 30,000 lbs. per sq. in., 0.083 to 0.100; mean, 0.090; set at 
30,000 pounds per sq. in., to 0.002; mean, 0. 

The mean extension between 10,000 to 30,000 lbs. per sq. in. increased 
regularly at the rate of 0.007 inch for each 2000 lbs. per sq. in. increment 
of strain. This corresponds to a modulus of elasticity of 28,571,429. 
The least increase of extension for an increase of load of 20,000 lbs. per 
sq. in., 0.065 inch, corresponds to a modulus of elasticity of 30,769,231, 
and the greatest, 0.076 inch, to a modulus of 26,315,789. 

Steel Rails. — Bending tests, 5 feet between supports, 11 tests of flange 
rails 72 pounds per yard, 4.63 inches high. 



354 



STRENGTH OF MATERIALS. 



Elastic stress. Ultimate stress. Deflection at 50,000 
Pounds. Pounds. Pounds. 
Hardest... 34,200 60,960 3.24 ins. 

Softest 32,000 56,740 3.76 " 

Mean 32,763 59,209 3.53 " 

All uncracked at 8 inches deflection. 

Pulling tests of pieces cut from same rails. Mean results. 


Ultimate 

Deflection. 

8 ins. 

8 " 
8 •• 


Top of rails 

Bottom of rails. . . . 


Elastic Ultimate 
Stress. Pounds, 
per sq. in. per sq. in 
. . 44,200 83,110 
. . 40.900 77,820 


Contraction of 
area of frac- 
ture. 
19.9% 
30.9% 


Extension 
in 10 ins. 

13.5% 
22.8% 


Steel Tires. — Tensile tests of specimens cut from steel tires. 


Highest . 
Mean. . . 
Lowest . 




Krupp Steel. — 262 Tests. 

E. L. T. S. Contr. 
69,250 119,079 31 9 
52,869 104,112 29.5 
41,700 90,523 45.5 


Ext. in 

5 inches. 

18.1 

19.7 

23.7 


Highest 
Mean. . . 
Lowest . 




ViCKERS, Sons & Co. 

"FT T T S 

58'606 120,789 
51,066 101,264 
43.700 87,697 


— 70 Tests. 

Contr. 
11.8 
17.6 
24.7 


Ext. in 
5 inches. 
8.4 

12.4 

16.0 



Note the correspondence between Krupp's and Vickers' steels as to 
tensile strength and elastic limit, and their great difference in contrac- 
tion and elongation. The fractures of the Krupp steel averaged 22 per 
cent silky, 78 per cent granular; of the Vicker steel, 7 per cent silky, 
93 per cent granular. 



Steel Axles. — Tensile tests of specimens cut from steel axles. 
Patent Shaft and Axle Tree Co. 



Highest . 
Mean 
Lowest. . 



E. L. 
49,800 
36,267 
31,800 



T. S. 
99,009 
72,099 
61,382 



Vickers, Sons & Co. — 125 Tests. 



Highest . 
Mean . . 
Lowest. . 



E. L. 
42,600 
37,618 
30,250 



T. S. 
83,701 
70,572 
56,388 



157 Tests. 






Ext. in 


Contr. 


5 inches. 


21.1 


16.0 


33.0 


23.6 


34.8 


25.3 


ts. 


Ext. in 


Contr. 


5 inches. 


18.9 


13.2 


41.6 


27.5 


49.0 


37.2 



The average fracture of Patent Shaft and Axle Tree Co. steel was 33 
per cent silky, 67 per cent granular. 

The average fracture of Vickers' steel was 88 per cent silky, 12 per 
cent granular. 

Steel Propeller Shafts. — Tensile tests of pieces cut from two shafts, 
mean of four tests each. Hollow shaft, Whitworth, T. S., 61,290; E. L., 
30.575; contr., 52.8: ext. in 10 inches, 28.6. Solid shaft, Vickers', T. S., 
46.870: E. L., 20,425; contr., 44.4; «xt. in 10 inches, 30.7. 

Thrusting tests, Whitworth, ultimate, 56,201; elastic, 29,300; set at 
30,000 lbs., 0.18 per cent; set at 40,000 lbs., 2.04 per cent; set at 50,000 
lbs.. 3.82 per cent. 

Thrusting tests, Vickers', ultimate, 44,602; elastic, 22,250; set at 
30,000 lbs., 2.29 per cent; set at 40,000 lbs., 4.69 per cent. 



kirkaldy's tests. 



365 



Shearing strength of the Whit worth shaft, mean of four tests. 40,654 
lbs. per square inch, or 66.3 per cent of the pulling stress. Specific 
gravity of the Whitworth steel, 7.867; of the Vickers', 7.856. 

Spring Steel. — Untempered, 6 tests, average, E. L., 67,916; T. S.. 
115,668; contr., 37.8: ext. in 10 inches. 16.6. Spiing steel untem- 
pered, 15 tests, average, E. L., 38,785; T. S., 69,496; contr.. 19.1; ext. 
in 10 inches, 29.8. These two lots w^ere shipped for the same purpose, 
viz., railwav carriage leaf springs. 

Steel Castings. —44 tests, E. L., 31,816 to 35,567; T. S.. 54,928 to 
63,840; contr., 1.67 to 15.8; ext., 1.45 to 15.1. Note the great varia- 
tion in ductility. The steel of the highest strength was also the most 
ductile. 

Riveted Joints, Pulling Tests of Riveted Steel Plates, Triple Riv- 
eted Lap Joints, Machine fiSveted, Holes Drilled, 

Plates, width and thickness, inches: 

13.50X0.25 13.00X0.51 11.75X0.78 12.25X1.01 14.00X0.77 
Plates, gross sectional area square inches: 

3.375 6.63 9.165 12.372 10.780 

Stress, total, pounds: 

199,320 332,640 423,180 528,000 455,210 

Stress per square inch of gross area, joint: 

59,058 50,172 46,173 42,696 42,227 

Stress per square inch of plates, solid: 

70,765 65,300 64,050 62,280 68,045 

Ratio of strength of joint to solid plate: 

83.46 76.83 72.09 68.55 62.06 

Ratio net area of plate to gross: 

73.4 65.5 62.7 64.7 72.9 

Where fractured: 

plate at plate at plate at plate at rivets 

holes. holes. holes. holes. sheared 

Rivets, diameter, area and number: 

0.45,0.159, 24 0.64,0.321, 21 0.95,0.708,12 1.08,0.916, 12 0.95,0.708,12 
Rivets, total area: 

3.816 6.741 8.496 10.992 8.496 

Strength of Welds. — Tensile tests to determine ratio of strength of 
weld to solid bar. 

Iron Tie Bars. — 28 Tests. 

Strength of solid bars varied from 43,201 to 57,065 lbs. 

Strength of welded bars varied from 17,816 to 44,586 lbs. 

Ratio of weld to solid varied from 37.0 to 79.1% 

Iron Plates. — 7 Tests. 

Strength of solid plate from 44,851 to 47,481 lbs. 

Strength of welded plate from 26,442 to 38,931 lbs. 

Ratio of weld to solid • 57.7 to 83.9% 

Chain Links. — 216 Tests. 

Strength of solid bar from 49,122 to 57,875 lbs. 

Strength of welded bar from 39,575 to 48,824 lbs. 

Ratio of weld to solid 72.1 to 95.4% 

Iron Bars. — Hand and Electric Machine Welded. 

32 tests, solid iron, average 52,444 

17 " electric welded, average 46,836 ratio 89.1% 

19 " hand " " 46,899 " 89.3% 

Steel Bars and Plates. — 14 Tests. 

Strength of solid 54.226 to 64,580 

Strength of weld 28,553 to 46,019 

Ratio weld to sohd 52.6 to 82.1% 

The ratio of weld to solid in all the tests ranging from 37.0 to 95.4 is 
proof of the great variation of workmanship in welding. 



356 



STRENGTH OF MATERIALS. 



Cast Copper. —4 tests, average, E. L. 5900; T. S., 24,781; contr., 
24.5; ext., 21.8. 

Cooper Plates. —As rolled. 22 tests, 0.26 to 0.75 in. thick; E. L., 9766 
to 18T650; T. S., 30,993 to 34,281; contr., 31.1 to 57.6; ext., 39.9 to 
52 2 ' The variation in elastic limit is due to difference in the heat at 
which the plates were finished. Annealing reduces the T. S. only about 
1000 pounds, but the E. L. from 3000 to 7000 pounds. 

Another series, 0.38 to 0.52 in. thick; 148 tests, T. S., 29,099 to 31,924; 
contr., 28.7 to 56.7; ext. in 10 inches, 28.1 to 41.8. Note the uniformity 
in tensile strength. 

Drawn Copper. — 74 tests (0.88 to 1.08 inch diameter); T. S., 31,634 
to 40,557; contr., 37.5 to 64.1; ext. in 10 inches, 5.8 to 48.2. 

Bronze from a Propeller Blade. — Means of two tests each from 
center and edge. Central portion (sp. gr. 8.320), E. L., 7550; T. S., 
26.312; contr., 25.4; ext. in *0 inches, 32.8. Edge portion (sp. gr. 
8.550). E. L., 8950; T. S., 35,960; contr., 37.8: ext. in 10 inches, 47.9. 

Cast German Silver. — 10 tests: E. L., 13,400 to 29,100; T. S., 
23,714 to 46,540; contr., 3.2 to 21.5; ext. in 10 inches, 0.6 to 10.2. 

Thin Sheet 3Ietal. — Tensile Strength. 

German silver, 2 lots 75,816 to 87,129 

Bronze, 4 lots 73,380 to 92,086 

Brass, 2 lots 44,398 to 58,188 

Copper, 9 lots 30,470 to 48,450 

Iron, 13 lots, lengthway 44,331 to 59,484 

Iron, 13 lots, crossway 39.838 to 57,350 

Steel, 6 lots.- 49,253 to 78,251 

Steel, 6 lots, crossway 55,948 to 80,799 



Wire Ropes. 

Selected Tests Showing Range of Variation. 





c 

11 
o 




Strands. 




Hemp Core. 




Description. 


6 

I 

6 
7 
7 
6 
6 
6 
6 
7 
6 
6 
6 
6 
6 
6 
6 
6 
6 
6 


^;^ 

19 
19 
19 
30 
19 
19 
30 
12 
7 

19 

7 

7 

12 

12 

7 

6 

12 

12 

7 

12 

12 


IP 


Galvanized 

Ungalvanized 

Ungalvanized 

Galvanized 

Ungalvanized 

Ungalvanized 

Galvanized 

Galvanized 

Galvanized 

Ungalvanized 

Ungalvanized 

Ungalvanized 

Galvanized 

Galvanized 

Ungalvanized ..... 

Ungalvanized 

Galvanized 

Galvanized 

Ungalvanized 

Galvanized 

Galvanized 


7.70 
7.00 
6.38 
7.10 
6.18 
6.19 
4.92 
5.36 
4.82 
3.65 
3.50 
3.82 
4.11 
3.31 
3.02 
2.68 
2.87 
2.46 
1.75 
2.04 
1.76 


53.00 

53.10 

42.50 

37.57 

40.46 

40.33 

20.86 

18.94 

21.50 

12.21 

12.65 

14.12 

11.35 

7.27 

8.62 

6.26 

5.43 

3.85 

2.80 

2.72 

1.85 


0.1563 

0.1495 

0.1347 

0.1004 

0.1302 

0.1316 

0.0728 

0. 1 1 04 

0.1693 

0.0755 

0.122 

0.135 

0.080 

0.068 

0.105 

0.0963 

0.0560 

0.0472 

0.0619 

0.0378 

0.0305 


Main 
Main and Strands 

Wire Core 

Main and Strands 

Wire Core 

Wire Core 

Main and Strands 

Main and Strands 

Main 

Main 
Wire Core 

Main 
Main and Strands 
Main and Strands 

Main 
Main and Strands 
Main and Strands 
Main and Strands 

Main 
Main and Strands 

Main 


339,780 

314,860 

295,920 

272,750 

268,470 

221,820 

190,890 

136,550 

129,710 

110,180 

101,440 

98,670 

75,110 

55,095 

49,555 

41,205 

38,555 

28,075 

24,552 

20,415 

14,634 



kirkaldy's tests. 357 



Wire. — Tensile Strength. 

German silver, 5 lots 81,735 to 92,224 

Bronze, 1 lot 78,049 

Brass, as drawn, 4 lots 81,114 to 98,578 

Copper, as drawn, 3 lots 37,607 to 46,494 

Copper annealed, 3 lots 34,936 to 45,210 

Copper (another lot), 4 lots 35,052 to 62,190 

Copper (extension 36.4 to 0.6%). 

Iron, 8 lots 59,246 to 97,908 

Iron (extension 15.1 to 0,7%). 

Steel, 8 lots 103,272 to 318,823 

The steel of 318,823 T. S. was 0.047 inch diam., and had an extension of 
only 0.3 per cent; that of 103,272 T. S. was 0.107 inch diam., and had an 
extension of 2.2 per cent. One lot of.0.044 inch diam. had 267,114 T. S., 
and 5.2 per cent extension. 

Hemp Ropes, Un tarred. — 15 tests of ropes from 1.53 to 6.90 inches 
circumference, weighing 0.42 to 7.77 pounds per fathom, showed an 
ultimate strength of from 1670 to 33,808 pounds, the strength per fathom 
weight varying from 2872 to 5534 pounds. 

Hemp Ropes, Tarred. — 15 tests of ropes from 1.44 to 7.12 inches 

circumference, weighing from 0.38 to 10.39 pounds per fathom, showed 
an ultimate strength of from 1046 to 31,549 pounds, the strength per 
fathom weight varying from 1767 to 5149 pounds. 

Cotton Ropes. — 5 ropes, 2.48 to 6.51 inches circumference, 1.08 to 
8.17 pounds per fathom. Strength 3089 to 23,258 pounds, or 2474 to 
3346 pounds per fathom weight. 

Manila Ropes. — 35 tests: 1.19 to 8.90 inches circumference, 0.20 to 
11.40 pounds per fathom. Strength 1280 to 65,550 pounds, or 3003 to 
7394 pounds per fathom weight. 

Belting. 

No. of Tensile strength 

lots. per square inch. 

11 Leather, single, ordinary tanned 3248 to 4824 

4 Leather, single, Helvetia 5631 to 5944 

7 Leather, double, ordinary tanned 2160 to 3572 

8 Leather, double Helvetia 4078 to 5412 

6 Cotton, solid woven 5648 to 8869 

14 Cotton, folded, stitched 4570 to 7750 

1 Flax, sohd, woven 9946 

1 Flax, folded, stitched 6389 

6 Hair, sohd, woven 3852 to 5169 

2 Rubber, sohd, woven 4271 to 4343 

Canvas. — 35 lots: Strength, lengthwise, 113 to 408 pounds per inch; 
crossways, 191 to 468 pounds per inch. 

The grades are numbered 1 to 6, but the weights are not given. The 
strengths vary considerably, even in the same number. 

3Iarbles. — Crushing strength of various marbles. 38 tests, 8 kinds. 
Specimens were 6-inch cubes, or columns 4 to 6 inches diameter, and 6 
and 12 inches high. Range 7542 to 13,720 pounds per square inch. 

Granite. — Crushing strength, 17 tests; square columns 4X4 and 
6 X 4, 4 to 24 inches high, 3 kinds. Crushing strength ranges 10,026 to 
13,271 pounds per square inch. (Very uniform.) 

Stones. — (Probably sandstone, local names only given.) 11 kinds, 42 
tests, 6X6, columns 12, 18 and 24 inches high. Crushing strength 
ranges from 2105 to 12,122. The strength of the column 24 inches long 
is generally from 10 to 20 per cent less than that of the 6-inch cube. 

Stones. — (Probably sandstone) tested for London & Northwestern 
Railway. 16 lots, 3 to 6 tests in a lot. Mean results of each lot ranged 
from 3785 to 11,956 pounds. The variation is chiefly due to the stones 
being from different lots. The different specimens in each lot gave 
results which generally agreed within 30 per cent. 



358 



STRENGTH OF MATERIALS. 



Bricks. — Crushing strength, 8 lots; 6 tests in each lot; mean results 
ranged from 1835 to 9209 pounds per square inch. The maximum 
variation in the specimens of one lot was over 100 per cent of the 
lowest. In the most uniform lot the variation was less than 20 per 
cent. 

Wood. — Transverse and Thrusting Tests. 



Pitch pine 

Dantzic fir 

English oak 

American white oak . . 









S= 


Sizes abt. In 


Span, 


Ultimate 


LW 


square. 


inches. 


Stress. 


4BD2 






45,856 


1096 


111/2 to 121/2 


144 


to 


to 






80,520 


1403 






37,948 


657 


12 to 13 


144 


to 


to 






54,152 


790 






32,856 


1505 


41/2 X 12 


120 


to 


to 






39,084 


1779 






23,624 


1190 


41/2 X 12 


120 


to 


to 






26,952 


1372 



Thrust- 
ing 
Stress 
per sq. 
in. 



3586 

to 
5438 
2478 

to 
3423 
2473 

to 
4437 
2656 

to 
3899 



Demerara greenheart, 9 tests (thrusting) 8169 to 10,785 

Oregon pine, 2 tests 5888 and 7284 

Honduras mahogan3^ 1 test 6769 

Tobasco mahogany, 1 test 5978 

Norway spruce, 2 tests 5259 and 5494 

American yellow pine, 2 tests. 3875 and 3993 

EngUsh ash, 1 test 3025 

Portland Cement. — (Austrian.) Cross-sections of specimens 2 X 21/2 
inches for pulling tests only; cubes, 3X3 inches for thrusting tests; 
weight, 98.8 pounds per imperial bushel; residue, 0.7 per cent with 
sieve 2500 meshes per square inch; 38.8 per cent by volume of water 
required for mixing; time of setting, 7 days; 10 tests to each lot. The 
mean results in lbs. per sq. in. were as follows: 

Cement Cement 1 Cement, 1 Cement, 1 Cement, 

alone, alone, 2 Sand, 3 Sand, 4 Sand, 

Age. PuUing. Thrusting. Thrusting. Thrusting. Thrusting. 

10 days 376 2910 893 407 228 

20 days 420 3342 1023 494 275 

30 days 451 3724 1172 594 338 

Portland Cement. — Various samples pulling tests, 2 X 21/2 inches 

cross-section, all aged 10 days, 180 tests; ranges 87 to 643 pounds per 
square inch. 

TENSILE STRENGTH OF WIRE. 

(From J. Bucknall Smith's Treatise on Wire.) 

Tons per sq. Pounds per 

in. sectional sq. in. sec- 

_, area. tional area. 

Black or annealed iron wire 25 56,000 

Bright hard drawn 35 78,400 

Bessemer, steel wire 40 89,600 

Mild Siemens-Martin steel wire 60 134,000 

High carbon ditto (or "improved") 80 179,200 

Crucible cast-steel "improved " wire 100 224,000 

" Improved " cast-steel " plough " 120 268,800 

Special qualities of tempered and improved 

cast steel wire may attain 150 to 170 336,000 to 380,800 



MISCELLANEOUS TESTS OF MATERIALS. 



359 



MISCELLANEOUS TESTS OF MATERIAXS. 

Reports of Work of the Watertown Testing-machine in 1883. 
TESTS OF RIVETED JOINTS, IRON AND STEEL PLATES. 





03 


i 
^ 


'S 


si 




i 


Mh 








5 

i 


5 


111 


ii 


2 

i 




Tensile Stre 

Joint in Net 

tion of Plate 

square inc 

pounds. 


Tensile Strei 

Plate per sq 

inch, poun 




* 


3/8 


11/16 


3/4 


101/2 


6 


13/4 


39,300 


47,180 


47.0 t 


* 


3/8 


11/16 


3/4 


101/2 


6 


13/4 


41,000 


47,180 


49.0 t 


* 


V? 


3/4 


13/16 


10 


5 


2 


35,650 


44,615 


45.6 t 


* 


V?, 


3/4 


13/16 


10 


5 


2 


35,150 


44,615 


44.9 t 


* 


3/8 


11/16 


3/4 


10 


5 


2 


46,360 


47,180 


59.9 § 


* 


3/8 


11/16 


3/4 


10 


5 


2 


46,875 


47,180 


60.5 I 


* 


y? 


3/4 


13/16 


10 


5 


2 


46,400 


44,615 


59.4 1 


* 


V?, 


3/4 


13/16 


10 


5 


2 


46,140 


44,615 


59.2 § 


* 


5/8 


1 


11/16 


101/2 


4 


25/8 


44,260 


44,635 


57.2 1 


* 


5/8 


1 


I1/I6 


101/2 


4 


25/8 


42,350 


44,635 


54.9 § 


* 


3/4 


u/s 


13/16 


11 .9 


4 


2.9 


42,310 


46,590 


52.1 § 


* 


3/4 


11/8 


13/16 


11 .9 


4 


2.9 


41,920 


46,590 


51.7 § 


* 


3/fi 


3/4 


13/16 


101/2 


6 


13/4 


61,270 


53,330 


59.5 t 


t 


3/8 


3/4 


13/16 


101/2 


6 


13/4 


60,830 


53,330 


59.1 t 




V?, 


15/16 


1 


10 


5 


2 


47,530 


57,215 


40.2 :: 


• 


V? 


15/16 


1 


10 


5 


2 


49,840 


57,215 


42.3 :: 


• 


3/8 


11/16 


3/4 


10 


5 


2 


62,770 


53,330 


71.7 § 


• 


3/8 


11/16 


3/4 


10 


5 


2 


61,210 


53,330 


69.8 § 


• 


V?, 


15/16 


1 


10 


5 


2 


68,920 


57,215 


57.1 § 


• 


1/-^ 


15/16 


1 


10 


5 


2 


66,710 


57,215 


55.0 § 


• 


5/8 


1 


11/16 


91/2 


4 


23/8 


62,180 


52,445 


63.4 § 


■ 


5/8 


1 


11/16 


91/2 


4 


23/8 


62,590 


52,445 


63.8 1 


■ 


3/4 


11/8 


13/16 


10 


4 


21/2 


54,650 


51,545 


54.0 § 


• 


3/4 


U/S 


13/16 


10 


4 


21/2 


54,200 


51,545 


53.4 § 



Iron. 



t Steel. 



t Lap-joint. 



§ Butt-joint. 



The efficiency of the joints is found by dividing the maximum tensile 
stress on the gross sectional area of plate by the tensile strength of the 
material. 



COMPRESSK 


)N TESTS OF 3 X 3 INCH WROUGHT-IRON BARS. 


Length, inches. 


Tested with Two 
Pin Ends, Pins II/2 
in. Diam. Com- 
pressive Strength, 
lbs. per sq. in. 


Tested with Two 
Flat Ends. Com- 
pressive Strength, 
lbs. per sq. in. 


Tested with One 
Flat and One Pin 
End. Compressive 
Strength, lbs. per 
sq. in. 


an 




[ 28,260 
131,990 

26,310 
[ 26,640 
[ 24,030 

25,380 
i 20,660 
[ 20,200 

16,520 

17,840 
(13,010 

15,700 












Mi 












90 


j 26,780 
1 25,580 
(23,010 
{ 22,450 


(25.120 
125,190 
j 22,450 
121,870 


120 


150 


180 




,, 









360 



STRENGTH OF MATERIALS. 



Tested with Two Pin 
Ends. Length of Bars 
120 inches. 



' Diameter Comp. Str., 

of Pins. per sq. in., lbs. 

7/8 inch 16,250 

1 1/8 inches 17,740 

17/8 *' 21,400 

21/4 ** 22,210 



COMPRESSION OF WROUGHT-IRON COLUMNS, LATTICED 
BOX AND SOLID WEB. 



ALL TESTED WITH PIN ENDS. 



Columns made of 



6-inch channel, solid web 

6 

6 " " •• •• 

8 •• " " " 

8 •• •• " •• 

8-inch channels, with 5/i(j-in. continuous 

plates 

5/i6-inch continuous plates and angles.. 

Widthof plates, 12 in., 1 in. and 7.35 in 
7/i6-inch continuous plates and angles.. 

Plates 12 in. wide 

8-inch channels, latticed 

8 " " " 

8 •• " •• , 

8-inch channels, latticed, swelled sides . . 
8 *' " " " " .. 

8 " •• '\ " •; .. 

1 0-inch channels, latticed, swelled sides. 
10 '• " *' 

10 ;; ;; ;; ....^ 

* 1 0-inch channels, latticed one side; con 
tinuous plate one side 

t lO-inch channels, latticed one side; con 
tinuous plate one side 



I 



10.0 
15.0 
20.0 
20.0 
26.8 

26.8 

26.8 

26.8 
13.3 
20.0 
26.8 
13.4 
20.0 
26.8 
16.8 
25.0 
16.7 
25.0 

25.0 

25.0 






9.831 
9.977 
9.762 
16.281 
16.141 

19.417 

16.168 

20.954 
7.628 
7.621 
7.673 
7.624 
7.517 
7.702 
1 1 .944 
12.175 
12.366 
1 1 .932 

17.622 

17.721 






432 

592 

755 

1,290 

1,645 

1,940 

1,765 

2,242 

679 

924 

1,255 

684 

921 

1,280 

1,470 

1,926 

1,549 

1,962 

1,848 

1,827 






30,220 
21,050 
16,220 
22,540 
17,570 

25,290 

28,020 

25,770 
33,910 
34,120 
29,870 
33,530 
33,390 
30,770 
33,740 
32,440 
31,130 
32,740 

26,190 

17.270 



* Pins in center of gravity of channel bars and continuous plate, 1.63 
inches from center line of channel bars. 

t Pins placed in center of gravity of channel bars. 



TENSILE TEST OF SIX STEEL EYE-BARS. 

COMPARED WITH SMALL TEST INGOTS. 

The steel was made by the Cambria Iron Company, and the eye-bar 
heads made by Keystone Bridge Company by upsetting and hammering. 
All the bars were made from one ingot. Two test pieces, 3/4-inch round, 
rolled from a test-ingot, gave elastic limit 48,040 and 42,210 pounds; 
ten.sile strength, 73,150 and 69,470 pounds, and elongation in 8 inches, 
22.4 and 25.6 per cent respectively. The ingot from which the eye-bars 
were made was 14 inches square, rolled to billet, 7X6 inches. The 
eye-bars were rolled to 6 1/2 X 1 inch. Chemical tests gave carbon 0.27 
to 0.30; manganese, 0.64 to 0.73; phosphorus, 0.074 to 0.098. 



MISCELLANEOUS TESTS OF IRON AND STEEL. 



361 



Gauged 


Elastic 


Tensile 


Elongation 


Length, 


limit, lbs. 


strength per 


per cent, in 


inches. 


per sq. in. 


sq. in., lbs. 


Gauged Length. 


160 


37,480 


67,800 


15.8 


160 


36,650 


64,000 


6.96 


160 


• • • . • 


71,560 


8.6 


200 


37,600 


68,720 


12.3 


200 


35,810 


65,850 


12.0 


200 


33,230 


64,410 


16.4 


200 


37,640 


68,290 


13.9 



The average tensile strength of the 3/4-inch test pieces was 71,310 lbs., 
that of the eye-bars 67,230 lbs., a decrease of 5.7%. The average elastic 
limit of the test pieces was 45,150 lbs., that of the eye-bars 36,402 lbs., a 
decrease of 19.4%. The elastic limit of the test pieces was 63.3% of 
the ultimate strength, that of the eve-bars 54.2% of the ultimate strength. 

Tests of 11 full-sized eye bars, 15 X 1 1/4 to 2Vi6in., 20.5 to 21.4 ft. long 
between centers of pins, made by the Phoenix Iron Co., are reported in 
Eng. News, Feb. 2, 1905. The average T.S. of the bars was 58,300 lbs. 
per sq. in., E.L., 32,800. The average T.S. of small specimens was 
63.900, E.L., 37,000. The T.S. of the full-sized bars averaged 8.8% 
and the E.L. 12.1% lower than the small specimens. 

EFFECT OF COLD-DRAWING ON STEEL. 

Three pieces cut from the same bar of hot-rolled steel: 

1. Original bar, 2.03 in. diam., gauged length 30 in., tensile strength 

55,400 lbs. per square in.; elongation 23.9%. 

2. Diameter reduced in compression dies (one pass) .094in.; T. S. 70,420; 

el. 2.7% in 20 in. 

3. " " " " " " " 0.222in.;T.S. 81,890; 

el. 0.075%, in 20 in. 
Compression test of cold-drawn bar (same as No. 3), length 4 in., diam. 
1.808 in.: (Compressive strength per sq. in., 75,000 lbs.; amount of com- 
pression 0.057 in.; set 0.04 in. Diameter increased by compression to 
1.821 in. in the middle; to 1.813 in. at the ends. 



3IISCELLAIVEOUS TESTS OF IRON AKD STEEL. 

Tests of Cold-rolled and Cold-drawn Steel, made by the Cambria 
Iron Co. in 1897, gave the following results (averages of 12 tests of each): 

E. L. T. S. El. in 8 in. Red. 

Before cold-rolling 35,390 59,980 28.3% 58.5% 

After cold-rolling 72,530 79,830 9.6% 34.9% 

After cold-drawing 76,350 83,860 8.9%, 34.2% 

The original bars were 2 in. and 7/3 in. diameter. The test pieces cut 
from the bars were 3/4 in. diam., 18 in. long. The reduction in diameter 
from the hot-rolled to the cold-rolled or cold-drawn bar was Vie in. in 
each case. 

Cold Rolled Steel Shafting (Jones & LaughHns) m/iein. diam. — 
Torsion tests of 12 samples gave apparent outside fiber stress, calculated 
from maximum twisting moment, 70,700 to 82,900 lbs. per sq.in.; fiber 
stress at elastic limit, 32,500 to 38,800 lbs. per sq. in.; shearing modulus 
of elasticity, 11,800,000 to 12,100,000; number of turns per foot before 
fracture, 1.60 to 2.06. — Tech. Quar., vol. xii, Sept., 1899. 

Torsion Tests on Cold Rolled Shafting. — {Tech. Quar. XIII, No. 3, 
1900, p. 229.) 14 tests. Diameter about 1.69 in. Gauged length, 40 to 
50 in. Outside fiber stress at elastic limit, 28,610 to 33,590 lbs. per sq. 
in.; apparent outside fiber stress at maximum load, 67,980 to 77,290. 
Shearing modulus of elasticity, 11,400,000 to 12,030,000 lbs. per sq. in. 
Turns per foot between jaws at fracture, 0.413 to 2.49. 

Torsion Tests on Refined Iron. — 1 3/4 in. diam. 14 tests. Gauged 
length, 40 ins. Outside fiber stress at elastic limit, 12,790 to 19,140 lbs. 
per sq. in.; apparent outside fiber stress at maximum load, 45,350 to 
58,340. Shearing modulus of elasticity, 10,220,000 to 11,700,000. Turnj 
per foot between jaws at fracture, 1.08 to 1.42. 



362 



STRENGTH OF MATERIALS. 



Tests of Steel Angles with Riveted End Connections. (F. P. 

Mclvibbin, Proc. A.S.T.M., 1907.) — The angles broke through the rivet 
holes in all cases. The strength developed ranged from 62.5 to 79.1% 
of the ultimate strength of the gross area, or from 73.9 to 92% of the 
calculated strength of the net section at the rivet holes. 

SHEARING STRENGTH. 

H. V. Loss in American Engineer and Railroad Journal, March and 
April, 1893, describes an extensive series of experiments on the shearing 
of iron and steel bars in shearing machines. Some of his results are: 

Depth of penetration at point of maximum resistance for soft steel 
bars is independent of the width, but varies with the thickness. If 
d = depth of penetration and t = thickness, d_= O.St for a flat knife, 
d = 0.25t for a 4° bevel knife, and d = 0.16 ^t^ for an 8° bevel knife. 
The ultimate pressure per inch of width in flat steel bars is approxi- 
mately 50,000 lbs. X t. The energy consumed in foot-pounds per inch 
width of steel bars is, approximately: 1'' thick, 1300 ft. -lbs.; II/2", 
2500; 13/4'', 3700; 17/8'', 4500; the energy increasing at a slower rate than 
the square of the thickness. Iron angles require more energy than steel 
angles of the same size; steel breaks while iron has to be cut off. For 
hot-roUed steel the resistance per square inch for rectangular sections 
varies from 4400 lbs. to 20,500 lbs., depending partly upon its hardness 
and partly upon the size of its cross-area, which latter element indirectly 
but greatly indicates the temperature, as the smaller dimensions require 
a considerably longer time to reduce them down to size, which time 
again means loss of heat. 

It is not probable that the resistance in practice can be brought very 
much below the lowest figures here given — viz., 4400 lbs. per sc[uare 
inch — as a decrease of 1000 lbs. will henceforth mean a considerable 
increase in cross-section and temperature. 

Relation of Shearing to Tensile Strength of Different 3Ietals. 
E. G. Izod, in a paper presented to the British Institution of Mechanical 
Engrs. (Jan., 1906), describes a series of tests on bars and plates of 
different metals. The specimens were firmly clamped on two steel 
plates with opposed shearing edges 4 ins. apart, and a shearing block, 
which was a sliding fit betweeu these edges, was brought down upon 
the specimen, so as to cut it in double shear, by a testing machine. 



Cast iron. A 

Cast iron. B 

Cast iron. C 

Cast aluminum- 
bronze 

Cast phosphor- 
bronze 

Cast phosphor- 
bronze 

Gun metal 

Yellow brass 

Yellow brass 



a 


b 


c 


9.7 




152 


13.4 




111 


11.3 




122 


33.1 


12.5 


60 


13.4 


2.2 


128 


19.7 


8.0 


93 


12.1 


7.8 


103 


7.5 


6.5 


126 


16.0 


35.0 


74 



Rolled phosphor- 
bronze 

Aluminum 

Aluminum alloy 

Wrought-iron bar.. 

Mild-steel, 0.14 car- 
bon 

Crucible steel, 0.12 c 

0.48 C 

0.71 C 

0.77C 



a 


b 


39.5 


n.7 


6.4 


25.5 


12.7 


9.6 


26.0 


22.5 


26.9 


34.7 


24.9 


43.0 


42.1 


26.0 


56.3 


15.0 


61.3 


11.0 



, a. Tensile strength of the metal, gross tons per sq. in.; b. elongation 
in 2 in.%: c. ratio shearing -^ tensile strength. The results seem to 
point to the fact that there is no common law connecting the ultimate 
shearing stress with the ultimate tensile stress, the ratio varving greatly 
with different materials. The test figures from crystalUne materials, 
such as cast iron or those with very little or no elongation, seem to indicate 
that the ultimate shear stress exceeds the ultimate tensile stress by as 
much as 20 or 25%, while from those with a fairly liigh measure of 
ductility, the ultimate shear stress may be anything "from to 50% less 
than the ultimate tensile stress. 

For shearing strength of rivets, see pages 240, 430 and 435. 



STRENGTH OF IRON AND STEEL PIPE. 



363 



STRENGTH OF IRON AND STEEL PIPE. 

Tests of Strength and Threading of Wrought-Iron and Steel 
Pipe. T. N. Thomson, in Proc. Am. Soc. Heat and Vent. Engineers, 
vol. xii., p. 80, describes some experiments on welded wrought iron and 
steel pipes. Short rings of 6-in. pipe were pulled in the direction of a 
diameter so as to elongate the ring. Four wrought iron rings broke at 
2400, 3000, 3100 and 4100 lbs. and four steel rings at 5300 (defective 
weld) 18,000, 29,000 and 35,000 lbs. Another series of 9 tests each 
were tested so as to show the tensile strength of the metal and of the 
weld. The average strength of the metal was, iron, 34,520, steel, 61,850 
lbs. The strength of the weld in iron ranged from 49 to 84, averaging 
71 per cent of the strength of the metal, and in steel from 50 to 93, 
averaging 72%. 

A large number of iron and steel pipes of different wsizes were tested by 
twisting, the force being applied at the end of a three-foot lever. The 
average pull on the steel pipes was: 1/2 in. pipe, 109 lbs.; 1 in., 172 lbs.; 
IV2 in., 300 lbs.; number of turns in 6 ft. length, respectively, 15, 8 and 
51/2. Per cent failed in weld, 0, 13 and 13 respectively. For different 
lots of iron pipe the average pull was: 1/2 in., 68, 81 and 65 lbs.; 1 in., 
154, 136, 107 lbs.; 1 1/2 in. 256, 250, 258 lbs. The number of turns in 



6 ieet for the nine lots were respectively, 41/2, 53/4, 21/2; 6 1/4, 31/2, 21/2; 
'1/2, 31/2, 21/4. The failures in the weld r ' " "" -~-^ . •- 

different lots. 



41/2, 31/2, 21/4. The failures in the weld ranged from 33 to 100% in the 



The force required to thread li/4-in. pipe with two forms of die was 
tested by pulUng on a lever 21 ins. long. The results were as follows: 

Old form of die, iron pipe. . 83 to 87 lbs. pull, steel pipe 100 to 111 lbs. 
Improved die, iron pipe 58 to 62 lbs. pull, steel pipe, 60 to 65 lbs. 

Mr. Thomson gives the following table showing approximately the 
steady pull in pounds required at the end of a 1 6-in. lever to thread 
twist and split iron and steel pipe of small sizes: 





To Thread with Oiled 
Dies. 


To 

Twist 
Lbs. 


To 

Split 
Lbs. 


Safety 

Margin 

Lbs. 




New 
Rake 
Dies. 


New 
Com- 
mon 
Dies. 


Old 
Com- 
mon 
Dies. 


1/2 in. steel 


34 
27 
44 
44 
69 
62 


56 
33 
60 
51 
\\] 
106 


60 
49 
91 
73 
124 
116 


122 
102 
150 
140 
286 
273 


152 
110 
240 
176 
420 
327 


74 


1/2 iti. iron 


46 


3/4 in. steel 


112 


3/4 in. iron 


81 


1 in. steel 


259 


1 in. iron . . 


173 







The margin of safety is computed by adding 30% to the pull required 
to thread with the old dies and subtracting the sum from the pull re- 
quired to spUt the pipe. If the mechanic pulls on the dies beyond the 
limit, due to imperfect dies, or to a hard spot in the pipe, he will split 
the pipe. 

Old Boiler Tubes used as Columns. (Tech. Quar. XIII, No. 3, 
1900, p. 225.) Thirteen tests were made of old 4-in. tubes taken from 
worn-out boilers. The lengths were from 6 to 8 ft., ratio l/r 53 to 71, 
and thickness of metal 0.13 to 0.18 in. It is not stated whether the tubes 
were iron or steel. The maximum load ranged from 34,600 to 50,000 
lbs., and the maximum load per sq. in. from 17,100 to 27,500 lbs. Six 
new tubes also were tested, with maximum loads 55,600 to 64,800 lbs., 
and maximum loads per sq. in. 31,600 to 38,100 lbs. The relation of 
the strength per sq. in. of the old tubes to the ratio l/r was very variable, 
being expressed approximately by the formula S = 41,000 — 300 Z/r 
± 5000. That of the new tubes is approximately S = 52,000 - 300 l/r 
i 2000. 



364 STRENGTH OF MATERIALS. 



HOLDING-POWER OF BOILER-TUBES EXPANDED INTO 
TUBE-SHEETS. 

Experiments by Chief Engineer W. H. Shock, U. S. N., on brass tubes, 
21/2 inches diameter, expanded into plates 3/4 inch thick, gave results 
ranging from 5850 to 46,000 lbs. Out of 48 tests 5 gave figures under 
10 000 lbs 12 between 10,000 and 20,000 lbs., 18 between 20,000 and 
30i000 lbs., 10 between 30,000 and 40,000 lbs., and 3 over 40,000 lbs. 

fexperiments by Yarrow & Co., on steel tubes, 2 to 21/4 inches diameter, 
gave results similarly varying, ranging from 7900 to 41,715 lbs., the 
majority ranging from 20,000 to 30,000 lbs. In 15 experiments on 
4 and 5 inch tubes the strain ranged from 20,720 to 68,040 lbs. Beading 
the tube does not necessarily give increased resistance, as some of the 
lower figures were obtained with beaded tubes. (See paper on Rules 
Governing the Construction of Steam Boilers, Trans. Engineering Con- 
gress, Section G, Chicago, 1893.) 

The Slipping Point of Rolled Boiler-Tube Joints. 

(0. P. Hood and G. L. Christensen, Trans. A. S. M. E., 1908). 

When a tube has started from its original seat, the fit may be no longer 
continuous at all points and a leak may result, although the ultimate 
holding power of tne tube may not be impaired. A small movement of 
the tube under stress is then the preliminary to a possible leak, and it 
is of interest to know at what stress this slipping begins. 

As results of a series of experiments with tube sheets of from 1/2 in. 
to 1 in. in thickness and with straight and tapered tube seats, the authors 
found that the sUpping point of a 3-in. 12-gage Shelby cold-drawn tube 
rolled into a straight, smooth machined hole in a 1-in. sheet occurs with 
a pull of about 7,000 lbs. The frictional resistance of such tubes is about 
750 lbs. per sq. in. of tube-bearing area in sheets 5/3 in. and 1 in. thick. 

Various degrees of rolling do not greatly affect the point of initial slip, 
and for higher resistances to initial slip other resistance than friction must 
be depended upon. Cutting a 10-pitch square thread in the seat, about 
0.01 in. deep will raise the slipping point to three or four times that in a 
smooth hole. In one test this thread was made 0.015 in. deep in a sheet 
1 in. thick, giving an abutting area of about 1.4 sq. in., and a resistance 
to initial slip of 45,000 lbs. The elastic limit of the tube was reached at 
about 34,000 lbs. 

Where tubes give trouble from slipping and are required to carry an 
unusual load, the slipping point can be easily raised by serrating the tube 
seat by rolling with an ordinary flue expander, the rolls of which are 
grooved about 0.007 in. deep and 10 grooves to the inch. One tube 
thus serrated had its slipping point raised between three and four times 
its usual value. 

METHODS OF TESTING THE HARDNESS OF METALS. 

Brinell's Method. J. A. Brinell, a Swedish engineer, in 1900 pub- 
lished a method for determining the relative hardness of steel which has 
come into somewhat extensive use. A hardened steel ball, 10 mm. 
(0.3937 in.), is forced with a pressure of 3000 kg. (6614 lbs.) into a flat 
surface on the sample to be tested, so as to make a slight spherical in- 
dentation, the diameter of which may be measured by a microscope or 
the depth by a micrometer. The hardness is deflned as the quotient 
of the pressure by the area of the indentation^ From the measurement 
the "hardness number" is calculated by one of the following formulsB: 



H = K (r + Vr2 ~ R2) ^ 2 t: rR\ oi H =^ K -i- 2 n rd. 

K = load, = .3000 kg., r = radius of ball, = 5 mm., R = radius and 
a = depth of indentation. 

^.J^^ following table gives the hardness number corresponding to 
different values of R and tZ. 



STRENGTH OF GLASS, 



365 



R 


H 


R 


H 


R 


H 


d 


H 


d 


H 


d 


H 


1 00 


945 


2.40 


156 


3.80 


54.6 


1.00 


95 5 


2.20 


43.4 


3.60 


26.5 


1 .20 


654 


2.60 


131 


4.00 


47.8 


1.10 


86 8 


2.40 


39.8 


3.80 


25.1 


1 40 


477 


2.80 


111 


4.20 


41.7 


1.20 


79.6 


2.60 


36.7 


4.00 


23.9 


1 60 


363 


3.00 


95.5 


4.40 


36.4 


1.40 


68.2 


2.80 


34.1 


4.50 


21.2 


1 .80 


285 


3.20 


82.5 


4.60 


31.4 


1.60 


59.7 


3.00 


31.8 


5.00 


19.1 


? 00 


229 


3.40 


71.6 


4.80 


26.5 


1.80 


53.0 


3.20 


29.8 


5.50 


17.4 


3.20 


187 


3.60 


62.4 


4.95 


22.2 


2.00 


48.0 


3.40 


28.1 


6.00 


15.9 



The hardness of steel, as determined by the Brinell method, has a 
direct relation to the tensile strength, and is equal to the product of a 
coefficient, C, into the hardness number. Experiments made in Sweden 
with annealed steel showed that when the impression was made trans- 
versely to the rolUng direction, with H below 175, C = 0.362; with H 
above 175, C = 0.344. When the impression was made in the roUing 
direction, with H below 175, C = 0.354; with H above 175, C = 0.324. 
The product, C X H, or the tensile strength, is expressed in kilograms 
per square millimeter. 

Electro-magnetic 3Iethod. — Several instruments have been de- 
vised for testing the hardness of steel by electrical methods. According 
to Prof. D. E. Hughes (Cass. Mag., Sept., 1908), the magnetic capacity 
of iron and steel is directly proportional to the softness, and the resist- 
ance to a feeble external magnetic force is directly as the hardness. The 
electric conductivity of steel decreases with the increase of hardness. 
(See Electric Conductivity of Steel, p. 477.) 

The Scleroscope. — This is the name of an instrument invented by 
A. F. Shore for determining the hardness of metals. It consists chiefly 
of a vertical glass tube in which slides freely a small cylinder of very 
hard steel, pointed on the lower end, called the hammer. This hammer 
is allowed to fall about 10 inches on to the sample to be tested, and the 
distance it rebounds is taken as a measure of the hardness of the sample. 
A scale on the tube is divided into 140 equal parts, and the hardness is 
expressed as the number on the scale to wliich the hammer rebounds. 
Measured in this way the hardness of different substances is as follows: 
Glass, 130; porcelain, 120; hardest steel, 110; tool steel, 1% C, may be 
as low as 31; mild steel, 0.5 C, 26 to 30; gray castings, 39; wrought 
iron, 18; babbitt metal, 4 to 10; soft brass, 12; zinc, 8; copper, 6; 
lead, 2. (Cass. Mag., Sept., 1908.) 



STRENGTH OF GLASS. 

(Falrbairn's "Useful Information for Engineers," Second Series.) 

Best Common Extra 
Flint Green White Crown 
Glass. 

Mean specific gravity 3.078 

Mean tensile strength, lbs. per sq. in., bars 2,413 

do. thin plates 4,200 

Mean crush'g strength, lbs. p. sq. in., cyl'drs 27,582 

do. cubes 13,130 

The bars in tensile tests were about 1/2 inch diameter. The crushing 
tests were made on cylinders about 3/4 inch diameter and from 1 to 2 
inches high, and on cubes approximately 1 inch on a side. The mean 
transverse strength of glass, as calculated by Fairbairn from a mean 
tensile strength of 2560 lbs. and a mean compressive strength of 30,150 
lbs. per sq. in., is, for a bar supported at the ends and loaded in the 
middle, w = 3140 bdVl, in which w = breaking weight in lbs., b *« 
breadth, d = depth, and I = length, in inches. Actual tests will prob- 
ably show wide variations in both directions from the mean calculated 
ttreoj^th. 



Glass. 


Glass. 


2.528 


2.450 


2,896 


2,546 


4,800 


6.000 


39,876 


31,003 


20,206 


21,867 



366 



STKENGTH OF MATERIALS. 



STRENGTH OF ICE. 

Experiments at the University of Illinois in 1895 {The Technograph, 
vol \x) gave 620 lbs. per sq. in. as the average crushing strength of cubes 
of manufactured ice tested at 23° F., and 906 lbs. for cubes tested at 
14° F Natural ice, at 12° F., tested with the direction of pressure parallel 
to the original water surface, gave a mean of 1070 lbs., and tested with 
the pressure perpendicular to this surface 1845 lbs. The range of varia- 
tion in strength of individual pieces is about 50% above and below the 
mean figures, the lowest and highest figures being respectively 318 and 
2818 lbs. per sq. in. The tensile strength of 34 samples tested at 19 to 
23° F. was from 102 to 256 lbs. per sq. in. 

STRENGTH OF TIMBER. 

Strength of Long-leaf Pine (Yellow Pine, Pinus Palustris) from 
Alabama (Bulletin No. 8, Forestry Div., Dept. of Agriculture, 1893. 
Tests by Prof. J. B. Johnson). 

The following is a condensed table of the range of results of mecnani- 
cal tests of over 2000 specimens, from 26 trees from four different sites 
in Alabama; reduced to 15 per cent moisture: 





Butt Logs. 


Middle Logs. 


Top Logs. 


Av'g 
of all 
Butt 
Logs. 


Specific gravity 

Transverse strength, -jr-r^ 

do. do. at elast. limit 

Mod. of elast., thous. lbs. 

Relative elast. resilience, 

inch-pounds per cub. in. 

Crushing endwise, str. 

per sq. in.-lbs 

Crushing across grain, 

strength persq. in., lbs. 
Tensile strength per sq. 

in 


0.449 to 1 .039 

4,762 to 16,200 

4,930 to 13,110 
i,119to 3,117 

0.23 to 4.69 
4,781 to 9,850 

675 to 2,094 
8,600 to 3 1,890 

464 to 1,299 


0.575 to 0.859 

7,640 to 17,128 

5,540 to 11,790 
1,136 to 2,982 

1.34 to 4.21 

5,030 to 9,300 

656 to 1,445 
6,330 to 29,500 

539 to 1,230 


0.484 to 0.907 

4,268 to 15,554 

2,553 to 11,950 
842 to 2,697 

0.09 to 4.65 

4,587 to 9,100 

584 to 1,766 
4, 170 to 23,280 

484 to 1,156 


0.767 

12,614 

9,460 
1,926 

2.98 

7.452 

1,598 

17,359 


Shearing strength (with 
grain), mean per sq. in. 


866 



Some of the deductions from the tests were as follows: 

1. With the exception of tensile strength a reduction of moisture is 
accompanied by an increase in strength, stiffness, and toughness. 

2. Variation in strength goes generally hand-in-hand with specific 
gravity. 

3. In the first 20 or 30 feet in height the values remain constant: then 
occurs a decrease of strength which amounts at 70 feet to 20 to 40 per 
cent of that of the butt-log. 

4. In shearing parallel with the grain and crushing across and par- 
allel with the grain, practically no difference was found. 

5. Large beams appear 10 to 20 per cent weaker than small pieces. 

6. Compression tests endwise seem to furnish the best average state- 
ment of the value of wood, and if one test only can be made, this is the 
safest, as was also recognized by Bauschinger. 

7. Bled timber is in no respect inferior to unbled timber. 

The figures for crushing across the grain represent the load required to 
cause a compression of 15 per cent. The relative elastic resilience, in 
inch-pounds per cubic inch of the material, is obtained by measuring 
the area of the plotted strain-diagram of the transverse test from the 
origin to the point in the curve at which the rate of deflection is 50 per 
cent greater than the rate in the earlier part of the test where the dia- 
gram is a straight line. This point is arbitrarily chosen since there is 
no definite "elastic hmit" in timber as there is in iron. The "strength 
at the elastic limit" is the strength taken at this same point. Timber 
is not perfectly elastiq for any load if left, on any great length of time, 

The long-leaf pine is found in all the Southern coast states from North 



STRENGTH OF TIMBER. 



367 



Carolina to Texas. Prof. Johnson says it is probably the strongest timber 
in large sizes to be had in the United States. In small selected speci- 
mens, other species, as oak and hickory, may exceed it in strength and 
toughness. The other Southern yellow pines, viz., the Cuban, short- 
leaf and the loblolly pines are inferior to the long-leaf about in the ratios 
of their specific gravities; the long-leaf being the heaviest of all the 
pines. It averages (kiln-dried) 48 pounds per cubic foot, the Cuban 47, 
the short-leaf 40, and the loblolly 34 pounds. 

Strength of Spruce Timber. — The modulus of rupture of spruce 
is given as follows by different authors: Hatfield, 9900 lbs. per square 
inch; Rankine, 11,100; Laslett, 9045; Trautwine, 8100; Rodman, 6168. 
Trautwine advises for use to deduct one-third in the case of knotty and 
poor timber. 

Prof. Lanza, in 25 tests of large spruce beams, found a modulus of 
rupture from 2995 to 5666 lbs.; the average being 4613 lbs. These 
were average beams, ordered from dealers of good repute. Two beams 
of selected stock, seasoned four years, gave 7562 and 8748 lbs. The 
modulus of elasticity ranged from 897,000 to 1,588,000, averaging 
1,294,000. 

Time tests show much smaller values for both modulus of rupture and 
modulus of elasticity. A beam tested to 5800 lbs. in a screw machine 
was left over night, and the resistance was found next morning to have 
dropped to about 3000, and it broke at 3500. 

Prof. Lanza remarks that while it was necessary to use larger factors 
of safety, when the moduli of rupture were determined from tests with 
smaller pieces, it will be sufficient for most timber constructions, except 
in factories, to use a factor of four. For breaking strains of beams, he 
states that it is better engineering to determine as the safe load of a 
timber beam the load that will not deflect it more than a certain fraction 
of its span, say about 1/300 to 1/400 of its length. 

Expansion of Timber Due to tlie Absorption of Water. 

(De Volson Wood, A. S. M. E., vol. x.) 

Pieces 36 X 5 in., of pine, oak, and chestnut, were dried thoroughly, 
and then immersed in water for 37 days. 

The mean per cent of elongation and lateral expansion were; 

Pine. Oak. Chestnut. 

Elongation, per cent 0.065 0.085 0.165 

Lateral expansion, per cent .... 2.6 3.5 3.65 

Expansion of Wood by Heat. — Trautwine gives for the expansion, 
of white pine for 1 degree Fahr. 1 part in 440,530, or for 180 degrees 
1 part in 2447, or about one-third of the expansion of iron. 

Shearing Strength of American Woods, adapted for Pins or 
Tree-nails. 



J. C. Trautwine {Jour. 


Franklin Inst.). (Shearing across the grain.) 




per sq. in. 


per. 


sq. in. 


Ash 


6280 


Hickory 


. 6045 


Beech 


.... 5223 


Hickory 


. 7285 


Birch 


5595 


Maple 


. 6355 


Cedar (white) 


.... 1372 


Oak 


. 4425 


Cedar (white) 


.... 1519 


Oak (live) 


. 8480 


Cedar (Central American^ 


.... 3410 


Pine (white) 


. 2480 


Cherry 


.... 2945 


Pine (Northern yellow) 


. 4340 


Chestnut 


.... 1536 


Pine (Southern yellow) 


. 5735 


Dogwood 


.... 6510 


Pine (very resinous yellow) . . 


. 5053 


Ebony 


.... 7750 


Poplar 


. 4418 


Gum 


.... 5890 


Spruce 


. 3255 


Hemlock 


.... 2750 


Walnut (black) 


. 4728 


Locust 


.... 7176 


Walnut (common) 


. 2830 



Transverse Tests of Pine and Spruce Beams. {Tech. Quar. XIII. 
No. 3, 1900, p. 226.)— Tests of 37 hard pine beams, 4 to 10 ins. wide, 6 to 
12 ins. deep, and 8 to 16 ft. length between supports showed great varia- 



368 STRENGTH OF MATERIALS. 

tions in strength. The modulus of rupture oT different beams was as 
follows: 1, 2970; 4, 4000 to 5000; 1, 5510; 1, 6220; 9, 7000 to 8000; 8, 
8000 to 9000; 4, 9000 to 10,000; 5, 10,000 to 11,000; 3, 11,000 to 12,000; 
1, 13,600. 

Six tests of white pine beams gave moduli of rupture ranging from 
1840 to 7810; and eighteen tests of spruce beams from 2750 to 7970 lbs. 
per sq. in. 

Drying of Wood. — Circular 111, U. S. Forest Service, 1907. Sticks 
of Southern loblolly pine 11 to 13 inches diameter, 9 to 10 ft. long, were 
weighed every two weeks until seasoned, to find the weight of water 
evaporated. The loss, per cent of weight, was as follows: 

Weeks 2 4 6 8 10 12 14 16 

Loss per cent of green wood 16 21 26 31 32 34 35 35 

Preservation of Timber. — U. S. Forest Service, Circular 111, 1907, 
discusses preservative treatment of timber by different methods, namely, 
brush treatment with creosote and with carbolinium; open tank treat- 
ment with salt solution, zinc chloride solution; and cyUnder treatment 
with zinc chloride solution and creosote. 

The increased life necessary to pay the cost of these several preserva- 
tive treatments is respectively: 6, 16, 7, 13, 41, 27, and 55%. The 
results of the experiments i)rove that it will pay mining companies to 
peel their timber, to season it for several months and to treat it with a 
good preservative. Loblolly and pitch pine have been most success- 
fully preserved by treatment with creosote in an open tank. 

Circular No. 151 of the Forest Service describes experiments on the 
best method of treating loblolly pine cross-arms of telegraph poles. The 
arms after being seasoned in air are placed in a closed air-tight cylinder, 
a vacuum is applied sufficient to draw the oil (creospte, dead oil of coal 
tar) from the storage tank into the treating cylinder. Sufficient pres- 
sure is then applied to force the oil into the heartwood portion of the 
timber, and continued until the desired amount of oil is absorbed, then a 
vacuum is maintained until the surplus oil is drawn from the sap wood. 
It is recommended that heartwood should finally contain about 6 lbs. 
of oil per cubic foot, and sapwood about 10 lbs. The preliminary bath 
of live steam, formerly used, has been found unnecessary. Much valu- 
able information concerning timber treatment and its benefits is con- 
tained in the several circulars on the subject issued by the Forest 
Service. 

STRENGTH OF COPPER AT HIGH TEMPERATURES. 

The British Admiralty conducted some experiments at Portsmouth 
Dockyard in 1877, on the effect of increase of temperature on the tensile 
strength of copper and various bronzes. The copper experimented upon 
was in rods 0.72 in. diameter. 

The following table shows some of the results: 



Temperature, 
Fahr. 


Tensile Strength 
in lbs. per sq. in. 


Temperature, 
Fahr. 


Tensile Strength 
in lbs. per sq. in. 


Atmospheric 
100° 
200° 


23,115 
23,366 
22,110 


300° 
400° 
500° 


21,607 
21,105 
19,597 



Up to a temperature of 400° F. the loss of strength was only about 
10 per cent, and at 500° F. the loss was 16 per cent. The temperature of 
steam at 200 lbs. pressure is 382° F., so that according to these experi- 
ments the loss of strength at this point would not be a serious matter. 
Above a temperature of 500° the strength is seriously affected. 

COFFEE CASTINGS OF HIGH CONDUCTIVITY. 

A method of making copper castings of high electric conductivity is 
described m The Foundry, Sept., 1910. The copper is melted under 
a coyer of charcoal and common salt. When thoroughly liquid, 2 oz. 
of stick magnesium is added per 100 lb. of copper, being plunged below 
the surface of the copper and held there until reaction ceases. The 
metal should be stirred for five minutes with a plumbago stirrer, and 
reheated before pouring. The castings have a conductivity of about 
o5% If nigh grade ingot copper is used. 



TESTS OF AMERICAN WOODS. 



369 



TESTS OF AMERICAN WOODS. (Watertown Arsenal Tests, 1883.) 

In all cases a large number of tests were made of each wood. Mini- 
mum and maximum results only are given. All of the test specimens 
had a sectional area of 1.575 X 1.575 inches. The transverse test speci- 
mens were 39.37 inches between supports, and the compressive test 
specimens were 12.60 inches long. Modulus of rupture calculated from 

3 PI 
formula R = ,^ ; P = load in pounds at the middle, I = length, in 

inches, b = breadth, d = depth: 



Name of Wood. 



Cucumber tree (Magnolia acuminata) . 
Yellow poplar white wood (Lirioden- 

dron tulipifera) 

White wood, Basswood {Tilia Ameri- 
cana) 

Sugar-maple, Rock-maple {Acer sac- 

charinum) 

Red maple (Acer rubrum) 

Locust (Robinia pseudacacia) 

Wild cherry (Prunus serotina) 

Sweet gum (Liquidambar styracifiua) . 

Dogwood (Cornus florida) 

Sour gum, Pepperidgel (yV2/ssa sylvatica) 
Persimmon (Diospyros Virginiana) . . 
White ash (Fraxiinis Americana) . . . . 

Sassafras (Sassafras officinale) 

Slippery elm (Ulmus fulva) 

White elm (Ulmus Americana) 

Sycamore; Buttonwood (Platanus 

oGcidentalis) 

Butternut; white walnut (Juglans 

cinerea) 

Black walnut (Juglans nigra) 

Shellbark hickory (Carya alba) 

Pignut (Carya porcina) 

White oak (Quercus alba) 

Red oak (Quercus rubra) 

Black oak (Quercus tinctoria) 

Chestnut (Castanea vulgaris) 

Beech (Fagus ferruginea) 

Canoe-birch, paper-birch (Betula pa- 

pyracea) 

Cottonwood (Populus monilifera) . . . . 

White cedar (Thuja occidentalis) 

Red cedar (Juniperus Virginiana) . . . 

Cypress (Saxodium Distichum) 

White pine (Pinus strobus) 

Spruce pine (Pinus glabra) 

Long-leaved pine, Southern pine 

(Pinus palustris) 

White spruce (Picea alba) 

Hemlock (Tsuga Canadensis) 

Red fir, yellow fir (Pseudotsuga Doug- 

lasii) 

Tamarack (Larix Americana) 



Transverse Tests. | 


ModL 


ilus of 


Rupture. 1 


Min. 


Max. 


7,440 


12,050 


6,560 


11,756 


6,720 


11,530 


9,680 


20,130 


8,610 


13,450 


12,200 


21,730 


8,310 


16,800 


7,470 


11,130 


10,190 


14,560 


9,830 


14,300 


10,290 


18,500 


5,950 


15,800 


5,180 


10,150 


10,220 


13,952 


8,250 


15,070 


6,720 


11,360 


4,700 


11,740 


8,400 


16,320 


14,870 


20,710 


11,560 


19,430 


7,010 


18,360 


9,760 


18,370 


7,900 


18,420 


5,950 


12,870 


13,850 


18,840 


11,710 


17,610 


8,390 


13,430 


6,310 


9,530 


5,640 


15,100 


9,530 


10,030 


5,610 


11,530 


3,780 


10,980 


9,220 


21,060 


9,900 


11,650 


7,590 


14,680 


8,220 


17,920 


10,080 


16,770 



Compression 

Parallel to 

Grain, pounds 

per square inch. 



Min. 



4,560 

4,150 

3,810 

7,460 
6,010 
8,330 
5,830 
5,630 
6,250 
6,240 
6,650 
4,520 
4,050 
6,980 
4,960 

4,960 

5,480 
6,940 
7,650 
7,460 
5,810 
4,960 
4.540 
3,680 
5,770 

5,770 
3,790 
2,660 
4,400 
5,060 
3,750 
2,580 

4,010 
4,150 
4,500 

4,880 
6,810 



Max. 



7,410 

5,790 

6,480 

9,940 
7,500 
11,940 
9,120 
7,620 
9,400 
7,480 
8,080 
8,830 
5,970 
8,790 
8,040 

7,340 

6,810 
8,850 
10,280 
8,470 
9,070 
8,970 
8,550 
6,650 
7,840 

-8,590 
6,510 
5,810 
7,040 
7,140 
5,600 
4,680 

10,600 
5,300 
7.420 

9,800 
10.700 



370 STRENGTH OF MATERIALS. 

TENSILE STRENGTH OF ROLLED ZINC PLATES. 

Herbert F. IMoore, in Univ. of III. Bulletin, No. 9, 1911, gives a 
table from which the following averages are taken: 



Thickness, 


Tensile 


Strength, 


Elongation 


In. 


Lb. per Sq 


In. 


in 8 In. 


%. 




with 




across 


with 


across 




grain. 




grain. 


grain. 


grain. 


1. 


21340 




23050 


4.85 


0.31 


0.6 


21490 




23550 


16.63 


3.33 


0.25 


23770 




22260 


11.90 


0.27 


0.10 


23580 




33620 


20.4 


14.3 


0.018 


24660 




32380 







THE STRENGTH OF BRICK, STONE, ETC. 

A great advance has recently (1895) been made in the manufacture 
of brick, in the direction of increasing their strength. Chas. P. Chase, in 
Engineering News, says: "Taking the tests as given in standard engi- 
neering books eight or ten years ago, we find in Trautwine the strength of 
brick given as 500 to 4200 lbs. per sq. in. :Now, taking recent tests in 
exDeriments made at Watertown Arsenal, the strength ran from 5000 to 
22J000 lbs. per sq. in. In the tests on Illinois paving-brick, by Prof. 
I. O. Baker, we find an average strength in hard paving brick of over 
5000 lbs. per square inch. The average crushing strength of ten varie- 
ties of paving-brick much used in the West, I find to be 7150 lbs. to the 
square inch." 

A test of brick made by the dry-clay process at Watertown Arsenal, 
according to Paving, showed an average compressive strength of 3972 lbs. 
per sq. in. In one instance it reached 4973 lbs. per sq. in. A test was 
made at the same place on a "fancy pressed brick." The first crack 
developed at a pressure of 305,000 lbs., and the brick crushed at 364,300 
lbs., or 11,130 lbs. per sq. in. This indicates almost as great compressive 
strength as granite paving-blocks, which is from 12,000 to 20,000 lbs. 
per sq. in. 

The three following notes on bricks are from Trautwine's Engineer's 
Pocket-hook: 

Strength of Brick. — 40 to 300 tons per sq. ft., 622 to 4668 lbs. per 
sq. in. A soft brick will crush under 450 to 600 lbs. per sq. in., or 30 to 
40 tons per square foot, but a first-rate machine-pressed brick will stand 
200 to 400 tons per sq. ft. (3112 to 6224 lbs. per sq. in.). 

Weight of Bricks. — Per cubic foot, best pressed brick, 150 lbs.; 
good pressed brick, 131 lbs.; common hard brick, 125 lbs.; good common 
brick, 118 lbs.; soft inferior brick, 100 lbs. 

Absorption of Water. — A brick will in a few minutes absorb 1/2 to 
3/4 lb. of water, the last being 1/7 of the weight of a hand-molded one. 
or 1/3 of its bulk. 

Strength of Common Red Brick. — Tests of 67 samples of Hudson 
River macliine-molded brick were made by I. H. Woolson, Eng. I\ews. 
April 13, 1905. The crushing strength, in lbs. per sq. in., of 15 pale brick 
ranged from 1607 to 4546, average 3010; 44 medium, 2080 to 8944, av. 
4080; 8 hard brick, 2396 to 6420, av. 4960. Five Philadelphia pressed 
brick gave from 3524 to 9425, av. 6361. The absorption ranged from 
8.7 to 21.4% by weight. The relation of absorption to strength varied 
greatly, but on the average there was an increase of absorption up to 
8000 lbs. per sq. in. crushing strength, and beyond that a decrease. 

The Strongest Brick ever tested at the Watertown Arsenal was a 
paving brick from St. Louis, Mo., which showed a compressive strength 
of 38,446 lbs. per sq. in. The absorption was 0.21% by weight and 
0.5% by volume. The sample was set on end, and measured 2.45 X 3.06 
ins. in cross section. — Eng. News, Mar. 14, 1907. 

Tests of Bricks, full size, on flat side. (Tests made at Watertown, 
Arsenal in 1883.) — The bricks were tested between flat steel buttresses. 
Compressed surfaces (the largest surface) ground approximately flat. 
The bricks were all about 2 to 2.1 inches thick, 7.5 to 8.1 inches long, 
and 3.5 to 3.76 inches wide. Crushing strength" per square inch: One 
lot ranged from 11.056 to 16,734 IJds.; a second, 12,995 to 22,351; a 



STRENGTH OF BRICK, STONE, ETC. 371 

third, 10,390 to 12,709. Other tests gave results from 5960 to 10,250 
lbs. per sq. in. 

Tests of Brick. (Tech. Quar., 1900.) — Different brands of brick tested 
on the broad surlaces, and on edge, gave results as follows, lbs. per sq. in. 

(Tech. Quar. XII, No. 3, 1899.) 38 tests. 





No. 
Test. 


Aver- 
age. 


Maxi- 
mum. 


Mini- 
mum. 


Per cent Wat 
Absorbed. 


er 


On broad surface 
Bay State, light hard 

Same, tested on edge . . 

On broad surface 
Dover River, soft 
burned 


71 

67 

38 
36 
36 
36 

36 

16 

16 


7039 
6241 

5350 

8070 

2190 

3600 

5360 

7940 
6430 


11,240 
10,840 

8630 

10,940 

3060 

4950 

8810 

9770 
10,230 


3587 
3325 

3930 

5850 

1370 

2080 

3310 

6570 
3830 


15.15 to 19.3av. 
13.67 to 18.2 " 

14.0 to 18.6 " 

4.7 to 10.1 '• 

17.8 to 22.0 •• 

16.6 to 23.4 " 

8.3 to 16.7 " 

7.6 to 12.9 " 
6.2 to 18.7 '• 


7.5 
7.4 

11 6 


Dover River, hard 
burned 


7 


Central N. Y., soft 
burned 


19 9 


Central N. Y., me- 
dium burned 

Central N. Y., hard 
burned 


18.6 
12 5 


Another lot,* hard 
burned . . . 


10 6 


Same,* tested on edge 


11.4 



* Brand not named. 

The per cent water absorbed in general seemed to have a relation to 
the strength, the greatest absorption corresponding to the lowest strength, 
and vice versa, but there were many exceptions to the rule. 

Crushing Strength of Masonry Materials. (From Howe's * 'Re- 
taining- V/alls.") — 

tons per sq. ft. tons per sq. ft. 

Brick, best pressed . 40 to 300 Limestones and m.arbles 250 to 1000 

Chal c 20 to 30 Sandstone 150 to 550 

Graii te 300 to 1200 Soapstone 400 to 800 

Strength of Granite. — The crushing strength of granite is commonly- 
rated at 12,000 to 15,000 lbs. per sq. in. when tested in two-inch cubes, 
and only the hardest and toughest of the commonly used varieties reach 
a strength above 20,000 lbs. Samples of granite from a quarry on the 
Connecticut River, tested at the Watertown Arsenal, have shown a 
strength of 35,965 lbs. per sq. in. (Engineering News, Jan. 12, 1893). 

Ordinary granite ranges fromi 20,000 to 30,000 lbs. compressive strength 
per sq. in. A granite from Asheville, N.C., tested at the Watertown 
Arsenal, gave 51,900 lbs. — Eng. News, Mar. 14, 1907. 

Strength of Avondale, Pa., Limestone. (Engineering News, 
Feb. 9, 1893.) — Crushing strength of 2-in. cubes: light stone 12,112, 
gray stone 18,040, lbs. per sq. in. 

Transverse test of lintels, tool-dressed, 42 in. between knife-edge bear- 
ings, load with knife-edge brought upon the middle between bearings: 

Gray stone, section 6 in. wide X 10 in. high, broke under a load of 20,950 lbs. 

Modulus of rupture 2,200 " 

Light stone, section 8I/4 in. wide XIO in. high, broke under. . . 14,720 " 

Modulus of rupture 1,170 *' 

Absorption. — Gray stone 0.051 of 1 % 

Light stone 0.052 of 1% 

Tests of Sand-lime Brick. (I. H. Woolson, Eng. News, June 14, 
1906). — Eight varieties of brick in lots of 300 to 800 were received from 
different manufacturers. They were tested for transverse strength, on 
supports 7 in. apart, loaded in the middle: and half bricks were tested by 



372 



STRENGTH OF MATERIALS. 



compression, sheets of heavy fibrous paper being inserted between the 
specimen and the plates of the testing machine to insure an even bearing. 
Tests were made on the brick as received, and on other samples after 
drying at about 150° F. to constant weight, requiring from four to six 
days. The moisture in two bricks of each series was determined, and 
found to range from 1 to 10 7o, average 5.9%. The figures of results 
given below are the averages of 10 tests in each case. Other bricks of 
each lot were tested for absorption by being immersed I/2 in. in water for 
48 hours, for resistance to 20 repeated freezings and thawings, and for 
resistance to fire by heating them in a fire testing room, the bricks being 
built in as 8-in. walls, to 1700° F. and maintaining that temperature 
three hours, then cooling them with a IVs-in! stream of cold water from 
a hydrant. Transverse and compressive tests were made after these 
treatments. The results given below are averages of five tests, except in 
the case of the bricks tested after firing, in which two samples are averaged. 

Effect of the Fire Test. — Several large cracks developed in both 
the sand-lime and the clay brick walls during the test. These were no 
worse in one wall than in the other. With the exception of surface 
deterioration the walls were solid and in good condition. After they 
were cooled the inside course of each wall was cut through and specimens 
of each series secured for examination and test. It was diflficult to 
secure whole bricks, owing to the extreme brittleness. 

In general the bricks were affected by fire about half way through. 
They were all brittle and many of them tender when removed from the 
wall. With the sand-lime brick, if a brick broke the remainder had to be 
chiseled out like concrete, whereas a clay brick under like conditions 
would chip out easily. The clay brick were so brittle and full of cracks 
that the wall could be broken down without trouble. The sand-lime 
bricks adhered to the mortar better^ were cracked less, and were not so 
brittle. 



Designation of Brick. 


A 


B 


C 


D 


E 


F 


G 


Modulus of ) 
Rupture j 


As received 

Dried 

Increase, % 
Wet 
After fire 


272 

•320 
15.0 

248 
17 


424 

505 
16.0 

349 
57 


377 

406 

7.1 
345 
20 


262 

334 

21.5 
241 

32 


190 

197 

3.5 
243 

24 


301 

570 

47.2 
250 
27 


365 

494 

26.2 
485 

37 



Compressive ) 


As received 


1875 


2300 


2871 


1923 


1610 


2460 


2669 


Strength, [ 


Dried 


2604 


2772 


3240 


2476 


1870 


3273 


3190 


lbs. per sq. in. ) 


Increase, % 


30.2 


17.1 


20.7 


22.3 


13.5 


24.8 


16.3 


'• 


Wet 


161] 


2174 


2097 


1923 


1108 


2063 


2183 


*' 


After freez- 


















ing 


1596 


1619 


2265 


1174 


1167 


1851 


1739 


" 


After fire 


1807 


2814 


2573 


2069 


1089 


2051 


4885 



% of lime in brick 

Pressure for hardening, lbs.. . 
Hours in hardening, lbs 



6 


10 


5 


<V2 


^'1/2 


5 


120 


135 


150 


125 


120 


150 


,0 


8 


7 


10 


10 


7 



8 

125 

10 



STRENGTH OF LIME AND CE3IENT MORTAR. 

(Engineering. October 2, 1891.) 

Tests made at the University of Illinois on the effects of adding cement 
to lime mortar. In all the tests a good quality of ordinary fat lime was 
used, slaked for two days in an earthenware jar, adding two parts by 
weight of water to one of lime, the loss by evaporation being made up 
by fresh additions of water. The cements used were a German Port- 
land, Black Diamond (Louisville), and Rosendale. As regards fineness 
of grinding, 85 per cent of the Portland passed through a No. 100 sieve, 
as did 72 per cent of the Rosendale. A fairly sharp sand, thoroughly 
washed and dried, passing through a No. 18 sieve and caught on a No. 30, 



CEMENT AND FLAGGING. 



373 



was used. The mortar in all cases consisted of two volumes of sand to 
one of lime paste. The following results were obtained on adding 
various percentages of cement to the mortar: 



Tensile Strength, pounds per square inch. 



Age. 



Lime mortar .... 
20 per cent Rosendale 



20 
30 
30 
40 
40 
60 
60 
80 
80 
100 
100 



Portland 

Rosendale 

Portland 

Rosendale 

Portland 

Rosendale 

Portland . 

Rosendale 

Portland 

Rosendale 

Portland 



4 


7 


14 


21 


28 


50 


Days. 


Days. 


Days. 


Days. 


Days. 


Days. 


4 


8 


10 


13 


18 


21 


5 


81/2 


91/2 


12 


17 


17 


5 


81/2 


14 


20 


25 


24 


7 


11 


13 


181/2 


21 


221/2 


8 


16 


18 


22 


25 


28 


10 


12 


161/2 


211/2 


221/2 


24 


27 


39 


38 


43 


47 


59 


9 


13 


20 


16 


22 


221/2 


45 


58 


55 


68 


67 


102 


12 


181/2 


221/2 


27 


29 


311/2 


87 


91 


103 


124 


94 


210 


18 


23 


26 


31 


34 


46 


90 


120 


146 


152 


181 


205 



84 
Days. 

26 

18 

26 

23 

27 

36 

57 

23 

78 

33 
145 

48 
202 



Tests of Portland Cement. 

{Tech. Quar. XIII. No. 3, 1900, p. 236.) 





IDay. 


2 Days. 


14 Days 


1 Mo. 


2Mos. 


6Mos. 


1 Year. 


Neat cement: . 
Tension, lbs. 
per sq. in... 

Compression, 
lbs. per sq. in 


268-312 
( 8650 

1 *^ 
( 10,250 

56-75 
( 1200 
{ to 
( 1585 


454-532 
13,080 

to 
14,860 

79-92 
1750 
to 
1885 


780-820 
23,640 

to 
34,820 

185-211 
3780 
to 
4420 


915-920 
211-230 


950-1100 
34,000 

to 
38,500 

217-240 
7850 
to 
8250 


1036-1190 


996-1248 
36,150 




to 
50 000 


3 sand, 1 cem. 
Tens 


300-382 


280-383 


3 sand, 1 cem. 
Comp 


8000 




to 




10,000 









TRANSVERSE STRENGTH OF FLAGGING. 

(N. J. Steel & Iron Co.'s Book.) 
Experiments made by R. G. Hatfield and Others. 

b = width of the stone in inches; d = its thickness in inches; I = dis- 
tance between bearings in inches. 

The breaking loads in tons of 2000 lbs., for a weight placed at the center 
of the space, will be as follows: 



I 

Bluestone flagging 0.744 

Qiiincy granite 0.624 

Little Falls freestone 0.576 

Belleville. N. J., freestone. . 0.480 
Granite (another quarry). . . 0.432 
Connecticut freestone 0.312 



^^ X 
I 

Dorchester freestone 0.264 

Aubigny freestone 0.216 

Caen freestone 0.144 

Glass 1.000 

Slate 1.2 to 2.7 



Thus a block of Quincy granite 80 inches wide and 6 inches thick, 
resting on beams 36 inches in the clear, would be broken by a load resting 

80 y 36 
midway between the beams = — -^ — X 0.624 = 49.92 tons. 



374 STRENGTH OF MATERIALS. 

MODULI OF ELASTICITY OF VARIOUS MATERIALS. 

The modulus of elasticity determined from a tensile test of a bar of any- 
material is the quotient obtained by dividing the tensile stress in pounds 
{)er square inch at any point of the test by the elongation per inch of 
ength produced by that stress; or if P = pounds of stress applied, 
K = the sectional area, I = length of the portion of the bar in which the 
measurement is made, and A = the elongation in that length, the modu- 
P A Pi 

lus of elasticity J^ = — -^ 7 = TTT. The modulus is generally measured 

within the elastic limit only, in materials that have a well-defined elastic 
limit, such as iron and steel, and when not otherwise stated the modulus 
is understood to be the modulus within the elastic limit. Within this 
limit, for such materials the modulus is practically constant for any 
given bar, the elongation being directly proportional to the stress. In 
other materials, such as cast iron, which have no well-defined elastic 
limit, the elongations from the beginning of a test increase in a greater 
ratio than the stresses, and the modulus is therefore at its maximum neaf 
the beginning of the test, and continually decreases. The moduli of 
elasticity of various materials have already been given above in treating 
of these materials, but the following table gives some additional values 
selected from different sources: 

Brass, cast 9,170,000 

Brass wire 14,230,000 

Copper 15,000,000 to 18,000,000 

Lead 1,000,000 

Tin, cast 4,600,000 

Iron, cast 12.000,000 to 27,000,000 (?) 

Iron, wrought 22,000,000 to 29,000,000 (?) 

Steel 28,000,000 to 32,000,000 (see below) 

Marble 25,000,000 

Slate 14,500,000 

Glass 8,000,000 

Ash 1,600,000 

Beech 1,300,000 

Birch 1,250,000 to 1,500,000 

Fir 869,000 to 2,191,000 

Oak 974,000 to 2,283,000 

Teak 2,414,000 

Walnut 306,000 

Pine, long-leaf (butt-logs) . 1,119,000 to 3,117,000 Avge. 1,926,000 

The maximum figures given by some early writers for iron and steel, 
viz., 40,000,000 and 42,000,000, are undoubtedly erroneous. The modulus 
of elasticity of steel (within the elastic limit) is remarkably constant, 
notwithstanding great variations in chemical analysis, temper, etc. It 
rarely is found below 29,000,000 or above 31,000,000. It is generally 
taken at 30,000,000 in engineering calculations. Prof. J. B. Johnson, 
in his report on Long-leaf Pine, 1893, says: "The modulus of elasticity 
is the most constant and reliable property of all engineering materials. 
The wide range of value of the modulus of elasticity of the various metals 
found in public records must be explained by erroneous methods of 
testing." 

In a tensile test of cast iron by the author (Van Nostrand's Science 
Series, No. 41, page 45), in which the ultimate strength was 23,285 lbs. 
per sq. in., the measurements of elongation were made to 0.0001 inch, 
and the modulus of elasticity was found to decrease from the beginning 
of the test, as follows: At 1000 lbs. per sq. in., 25,000,000; at 2000 lbs., 
16,666.000; at 4000 lbs., 15,384,000; at 6000 lbs., 13,636,000; at 8000 
lbs., 12,500,000; at 12,000 lbs., 11,250,000; at 15,000 lbs., 10,000,000; 
at 20,000 lbs., 8,000 000; at 23,000 lbs., 6,140,000. 

FACTORS OF SAFETY. 

A factor of safety is the ratio in which the load that is just sufficient to 
overcome instantly the strength of a piece of material is greater than the 
greatest safe ordinary working load. (Rankine.) 

Rankine gives the following "examples of the values of those factors 
which occur in machines"; 



FACTOR OF SAFETY 375 

Dead Load. Live Load, Live Load, 

Greatest. Mean, 

Iron and steel 3 6 from 6 to 40 

Timber 4 to 5 8 to 10 

Masonry 4 8 

The great factor of safety, 40, is for shafts in millwork which transmit 
very variable efforts. 

Unwin gives the following ** factors of safety which have been adopted 
In certain cases for different materials." They "include an^allowance 
for ordinary contingencies." 

. A Varying Load Producing ^ 

Stress of Equal Alternate In Structures 

Actual One Kind Stresses of subj. to vary- 

Material. Load only. different kinds, ing Loads and 

Shocks 

Cast iron 4 6 10 15 

Wrought iron and steel 3 5 8 12 

Timber 7 10 15 20 

Brickwork and Masonry 20 30 

In cast iron the factors are high to allow for unknown internal stresses. 

Prof. Wood in his "Resistance of Materials" says: "In regard to the 
margin that should be left for safety, much depends upon the character 
of the loading. If the load is simply a dead weight, the margin may be 
comparatively small; but if the structure is to be subjected to percus- 
sive forces or shocks, the margin should be comparatively large on account 
of the indeterminate effect produced by the force. In machines which 
are subjected to a constant jar while in use, it is very difficult to deter- 
mine the proper margin which is consistent with economy and safety. 
Indeed, in such cases, economy as well as safety generally consists in 
making them excessively strong, as a single breakage may cost much 
more than the extra material necessary to fully insure safety." 

For discussion of the resistance of materials to repeated stresses and 
shocks, see pages 275 to 285. 

Instead of using factors of safety, it is becoming customary in designing 
to fix a certain number of pounds per square inch as the maximum stress 
which will be allowed on a piece. Thus, in designing a boiler, instead of 
naming a factor of safety of 6 for the plates and 10 for the stay-bolts, the 
ultimate tensile strength of the steel being from 50,000 to 60,000 lbs. per 
sq. in., an allowable working stress of 10,000 lbs. per sq. in. on the plates 
and 6000 lbs. per sq. in. on the stay-bolts may be specified instead. So 
also in the use of formulse for columns (see page 285) the dimensions of a 
column are calculated after assuming a maximum allowable compressive 
stress per square inch on the concave side of the column. 

The factors for masonry under dead load as given by Rankine and by 
Unwin, viz., 4 and 20, show a remarkable difference, which may possibly 
be explained as follows: If the actual crushing strength of a pier of 
masonry is known from direct experiment, then a factor of safety of 4 is 
sufficient for a pier of the same size and quaUty under a steady load; 
but if the crushing strength is merely assumed from figures given by the 
authorities (such as the crushing strength of pressed brick, quoted above 
from Howe's Retaining Walls, 40 to 300 tons per square foot, average 
170 tons), then a factor of safety of 20 may be none too great. In this 
case the factor of safety is really a "factor of ignorance." 

The selection of the proper factor of safety or the proper maximum unit 
stress for any given case is a matter to be largely determined by the 
judgment of the engineer and by experience. No definite rules can be 
given. The customary or advisable factors in many particular cases will 
be found where these cases are considered throughout this book. In 
general the following circumstances are to be taken into account in the 
selection of a factor: 

1. When the ultimate strength of the material is known within narrow 
limits, as in the case of structural steel when tests of samples have been 
made, when the load is entirely a steady one of a known amount, and 
there is no reason to fear the deterioration of the metal by corrosion, the 
lowest factor that should be adopted is 3. 

2. When the circumstances of 1 are modified by a portion of the load 
being variable, as in floors of warehouses, the factor should be not less 
than 4. 



376 STRENGTH OF MATERIALS. 

3. When the whole load, or nearly the whole, is apt to be alternately 
put on and taken off, as in suspension rods of floors of bridges, the factor 
should be 5 or 6. 

4. When the stresses are reversed in direction from tension to com- 
pression, as in some bridge diagonals and parts of machines, the factor 
should be not less than 6. 

5. When the piece is subjected to repeated shocks, the factor should be 
not less than 10. 

6. When the piece is subject to deterioration from corrosion the section 
should be sufficiently increased to allow for a definite amount of corrosion 
before the piece be so far weakened by it as to require removal. 

7. When the strength of the material, or the amount of the load, or 
both are uncertain, the factor should be increased by an allowance suffi- 
cient to cover the amount of the uncertainty. 

8. When the strains are of a complex character and of uncertain 
amount, such as those in the crank-shaft of a reversing engine, a very 
high factor is necessary, possibly even as high as 40, the figure given by 
Rankine for shafts in milhvork. 

Formulas for Factor of Safety. — (F. E. Cardullo, Mach'y, Jan,. 
1906.) The apparent factor of safety is the product of four factors, or, 
F = aXbXcXd. 

a is the ratio of the ultimate strength of the material to its elastic limit, 
not the yield point, but the true elastic limit within which the material is, 
in so far as we can discover, perfectly elastic, and takes no permanent set. 
Two reasons for keeping the working stress within this limit are: (1) that 
the material will rupture if strained repeatedly beyond this limit; and 
(2) that the form and dimensions of the piece would be destroyed under 
the same circumstances. 

The second factor, b, is one depending upon the character of the stress 
produced within the material. The experiments of Wohler proved that 
the repeated application of a stress less than the ultimate strength of a 
material would rupture it. Prof. J. B. Johnson's formula for the relation 
between the ultimate strength and the "carrying strength" under con- 
ditions of variable loads is as follows: 

/ = ?7 -^ (2 - p,/p), 
where / is the "carrying strength" when the load varies repeatedly 
between a maximum value, p, and a minimum value, pi, and U is the 
ultimate strength of the material. The quantities p and pi have plus 
signs when they represent loads producing tension, and minus signs when 
they represent loads producing compression. 

If the load is variable the factor b must then have a value, 

6 = C7// = 2 - Pi/p. 
Taking a load varying between zero and a maximum, 
Pi/p = 0, and 6 = 2 — pi/p = 2. 

Taking a load that produces alternately a tension and a compression 
equal in amount, 

p' = — p and pi/p = - 1, and 6 = 2- pi/p = 2 - (- 1) = 3. 

The third factor, c, depends upon the manner in which the load is applied 
to the piece. When the load is suddenly applied c = 2. When not all 
of the load is applied suddenly, the factor 2 is reduced accordingly. If 
a certain fraction of the load, n/m, is suddenly applied, the factor is 
1 + n/m. 

The last factor, d, we may call the "factor of ignorance." All the 
other factors have provided against known contingencies; this provides 
against the unknown. It commonly varies in value between 1 1/2 and 3, 
although occasionally it becomes as great as 10. It provides against 
excessive or accidental overload, unexpectedly severe service, unreliable 
or imperfect materials, and all unforeseen contingencies of manufacture 
or operation. When we know that the load will not be likely to be 
increased, that the material is reliable, that failure will not result dis- 
astrously, or even that the piece for some reason must be small or fight, 
this factor will be reduced to its lowest limit, 1 1/2. When life or property 
wouldbe endangered by the failure of the piece, this factor must be made 



' THE MECHANICAL PROPERTIES OF CORK. 377 

larger. Thus, while it is 1 V2 to 2 in most ordinary steel constructions. 
It is rarely less than 2 1/2 for steel in a boiler. 

The reliability of the material in a great measure determines the value 
of this factor. For instance, in all cases where it would be 1 1/2 for mild 
steel, it is made 2 for cast iron. It will be larger for those materials 
subject to internal strains, for instance for complicated castings, heavy 
forgings, hardened steel, and the like, also lor materials subject to hidden 
defects, such as internal flaws in lorgings, spongy places in castings, etc. 
It will be smaller for ductile and larger for brittle materials. It will be 
smaller as we are sure that the piece has received uniform treatment, and 
as the tests we have give more uniform results and more accurate indi- 
cations of the real strength and quality of the piece itself. In fixing the 
factor d, the designer must depend on his judgment, guided by the general 
rules laid down. 

Table of Factors of Safety. 

The following table may assist in a proper choice of the factor of safety 
It shows the value of the four factors for various materials and conditions 
of service. 



Class of Service or Materials. 



-Factor- 



a bed F 

Boilers 2 I I 21/4-3 41/3- 6 

Piston and connecting rods for double- 
acting engines 1 1/2-2 3 2 1 1/2 13 1/2-I8 

Piston and connecting rod for single-acting 

engines 1 1/2-2 2 2 1 1/2 9 -12 

Shaft carrying bandwheel, fly-wheel, or 

armature 1 1/2-2 3 I 1 1/2 68/4- 9 

Lathe spindles 2 2 2 1 1/2 12 

Millshafting 2 3 2 2 24 

Steel work in buildings 2 I I 2 4 

Steel work in bridges 2 1 1 21/2 5 

Steel work for small work 2 1 2 1 1/2 6 

Cast iron wheel rims 2 1 I 10 20 

Steel wheel rims 2 1 1 4 8 

Materials. Minimum Values. 

Cast iron and other castings 2 1 12 4 

Wrought iron or mild steel 2 1 I 1 1/2 3 

Oil tempered or nickel steel IV2 I 1 1 1/2 21/4 

Hardened steel 1 V2 1 ^ 2 3 

Bronze and brass, rolled or forged 2 1 I IV2 3 

THE MECHANICAL PROPERTIES OF CORK. 

Cork possesses qualities which distinguish it from all other solid or 
liquid bodies, namely, its power of altering its volume in a very marked 
degree in consequence of change of pressure. It consists, practically, 
of an aggregation of minute air-vessels, having thin, water-tight, and 
very strong walls, and hence, if compressed, the resistance to compression 
rises in a manner more Uke the resistance of gases than the resistance of 
an elastic solid such as a spring. In a spring the pressure increases in 
proportion to the distance to which the spring is compressed, but with 
gases the pressure increases in a much more rapid manner: that is, in- 
versely as the volume which the gas is made to occupy. But from the 
permeability of cork to air, it is evident that, if subjected to pressure in 
one direction only, it will gradually part with its occluded air by effusion, 
that is, by its passage through the porous walls of the cells in which it is 
contained. The gaseous part of cork constitutes 53% of its bulk. Its 
elasticity has not only a very considerable range, but it is very persistent. 
Thus in the better kind of corks used in bottling the corks expand the 
instant they escape from the bottles. This expansion may amount to 
an increase of volume of 75%, even after the corks have been kept in a 
state of compression in the bottles for ten years. If the cork be steeped 
in hot water, the volume continues to increase till it attains nearly three 
times that which it occupied in the neck of the bottle. 

Wiien cork is subjected to pressure a certaan amount of permanent 



378 STRENGTH OF MATERIALS. 

deformation or "permanent set" takes place very quickly. This prop- 
erty is common to all solid elastic substances when strained beyond theii 
elastic limits, but with cork the hmits are comparatively low. Besides 
the permanent set, there is a certain amount of sluggish elasticity — that 
is, cork on being released from pressure springs back a certain amount 
at once, but the complete recovery takes an appreciable time. 

Cork which had been compressed and released in water many thousand 
times had not changed its molecular structure in the least, and had con- 
tinued perfectly serviceable. Cork which has been kept under a pressure 
of three atmospheres for many weeks appears to have shrunk to from 
80% to 85% of its original volume. — Van Nostrand's Eng'g Mag., 1886, 
XXXV. 307. 

VUI.CANIZED INDIA-RUBBER. 

The specific gravit^^ of a rubber compound, or the number of cubic 
inches to the pound, is generally taken by buyers as a correct index of 
the value, though in reaUty such is often very far from being the case. 
In the rubber works the qualities of the rubber made vary from floating, 
the best quaUty, to densities corresponding to 11 or 12 cu. in. to the 
pound, the latter densities being in demand by consumers with whom 
price appears to be the main consideration. Such densities as these can 
only be obtained by utilizing to the utmost the quality that rubber 
exhibits of taking up a large bulk of added matters. — Eng'g, 1897. 

Lieutenant L. Vladomiroff, a Russian naval officer, has recently carried 
out a series of tests at the St. Petersburg Technical Institute with view 
to establishing rules for estimating the quality of vulcanized india- 
rubber. The folio wng, in brief, are the conclusions arrived at, recourse 
being had to physical properties, since chemical analysis did not give 
any reliable result: 1. India-rubber should not give the least sign of 
superficial cracking when bent to an angle of 180 degrees after five hours 
of exposure in a closed air-bath to a temperature of 125° C. The 
test-pieces should be 2.4 inches thick. 2. Rubber that does not contain 
more than half its weight of metaUic oxides should stretch to five times 
its length without breaking. 3. Rubber free from all foreign matter, 
except the sulphur used in vulcanizing it, should stretch to at least seven 
times its length without rupture. 4. The extension measured immedi- 
ately after rupture should not exceed 12% of the original length, with 
given dimensions. 5. Suppleness may be determined by measuring the 
percentage of ash formed in incineration. This may form the basis for 
deciding between different grades of rubber for certain purposes. 6. Vul- 
canized rubber should not harden under cold. These rules have been 
adopted for the Russian navy. — Iron Age, June 15, 1893. 

Singular Action of India Rubber under Tension. — R. H. Thurston, 
Am. Mach., Mar. 17, 1898, gives a diagram showing the stretch at dif- 
ferent loads of a piece of partially vulcanized rubber. The results trans- 
lated into figures are: 

Load, lbs 30 50 80 120 150 200 320 430 

Stretch per in. of 

length, in 0.5 1. 2.2 4 5 6 7 7.5 

Stretchper 10 lbs. in- 
crease of load 0.17 0.25 0.4 0.45 0.33 0.20 0.08 0.04 

Up to about 30% of the breaking load the rubber behaves like a soft 
metal in showing an increasing rate of stretch with increase of load, 
then the rate of stretch becomes constant for a while and later decreases 
steadily until before rupture it is less than one-tenth of the maximum. 
Even when stretched almost to rupture it restores itself very nearly to 
its original dimensions on removing the load, and gradually recovers a 
part of the loss of form at that instant observable. So far as known, 
no other substance shows this curious relation of stretch to load. 

Rubber Goods Analysis. Randolph Boiling. (Iron Age, Jan. 28, 1909.) 

The loading of rubber goods used in manufacturing estabUshments 
with zmc oxide, lead sulphate, calcium sulphate, etc., and the employ- 
ment of theso-caUed "rubber substitutes" mixed with good rubber call for 
close mspection of the works chemist in order to determine the value of 
the samples and materials received. The following method of analysis is 
recommended: 

Thin strips of the rubber must be cut into small bits about the size of 



PROPERTIES OF NICKEL. 379 

No. 7 shot. A half gram is heated in a 200 c.c. flask with red fuming 
nitric acid on the hot plate until all organic matter has been decomposed, 
and the total sulphur is determined by precipitation as barium sulphate. 
The difference between the total and combined sulphur gives the per 
cent that has been used for vulcanization. Free sulphur indicates either 
that improper methods were used in vulcanizing or that an excessive 
per cent of substitutes was employed. Following is a scheme for the 
analysis of india-rubber articles: 

1. Extraction with acetone: A. Solution: Resinous constituents of 
india-rubber, fatty oils, mineral oils, resin oils, solid hydrocarbons, 
resins, free sulphur. B. Residue. 

2. Extraction with pyridine: C. Extract: Tar, pitch, bituminous 
bodies, sulphur in above. D. Residue. 

3. Extraction with alcoholic potash: E. Extract: Chlorosulphide 
substitutes, sulphide substitutes, oxidized (blown) oils, sulphur in 
substitutes, chlorine in substitutes. F. Residue. 

4. Extraction with nitro-naphthalane: G. Extract: India-rubber, sul- 
phur in india-rubber, chlorine in in<lia-rubber, the total of the above 
three estimated by loss. H. Residue. 

5. Extraction with boiling water: I. Extract: Starch (farina), 
dextrine. K. Residue: Mineral matter, free carbon, fibrous materials, 
sulphur in inorganic compoiuids. 

6. Separate estimations: Total sulphur, chlorine in rubber. 

SPECIFICATIONS FOR AIR HOSE. 

The Bureau of Construction and Repair of the U. S. Navy, in 1910, 
adopted the following specifications for air hose: 

1. The hose to be made up of an inner rubber tube, three or more 
canvas or braided layers, and an outer iTibber cover; to be of the in- 
ternal diameter required. 2. The tube and cover shall be free from 
pitting or other irregularities; the tube shall not be less than i/ie in., 
and the cover not less than 1/32 in. in thickness. The hose to be of 
the best quality rubber, duck and friction, and to be capable of stand- 
ing a hydrostatic pressure of 600 lb. 3. Samples will be submitted to 
the mechanical kinking test. The samples should stand the test for 
the following length of time without leakage at 90 lb. air pressure 
3/8 in 45 hours. 

7/16 in 40 hours. 

5/8 in 30 hours. 

3/4 in 25 hours. 

1 1/4 in 3 hours. 

The kinking test is conducted as follows: The test piece, 20 in. in 
length, is fastened to couplings made up on 45° elbows, the stationary 
end turned up and the moving end turned down. The ends of the 
couplings when level are 7 in. apart. The moving end travels vertically 
through a distance of 14 in., and the speed is such that the hose is 
kinked about 80 times a minute, the kinking occurring in two places 
about 4 in. from each end. During this test an air pressure of about 
90 lb. per sq. in. is maintained in the hose. The kinking is done on a 
special machine designed to kink the hose at the speed specified. 

NICKEL. 

Properties of Nickel.— (F. L. Sperry, Tran. A.I.M.E., 1895). Nickel 
has similar physical properties to those of iron and copper. It is less 
malleable and ductile than iron, and less malleable and more ductile 
than copper. It alloys with these metals in all proportions. It has 
nearly the same specific gravity as copper, and is slightly heavier than 
iron. It melts at a temperature of about 2900° to 3200° F. A small 
percentage of carbon in metallic nickel lowers its melting-point per- 
ceptibly. Nickel is harder than either iron or copper; is magnetic, but 
will not take a temper. It has a grayish-white color, takes a fine polish, 
and may be rolled easily into thin plates or drawn into wire. It is 
imappreciably affected by atmospheric action, or by salt water. Com- 
mercial nickel is from 98 to 99 per cent pure. The impurities are iron, 
copper, silicon, sulphur, arsenic, carbon, and (in some nickel) a kernel 
of unreduced oxide. It is not diflacult to cast, and acts Like some irons 



380 STRENGTH OF MATERIALS. 

in being cold-short. Cast bars are likely to be porous or spongy, 
but, after hammering or rolling, are compact and tough. 

The average results of several tests are as follows: Castings, tensile 
strength, 85,000 lbs. per sq. in., elongation, 12% ; wrought nickel, T. S., 
96,000, EL, 14%; wrought nickel, annealed, T. S., 95,000, El., 23%; 
hard rolled, T. S., 78,000, EL, 10%. (See also page 473.) 

Nickel readily takes up carbon, and the porous nature of the meta) 
is undoubtedly due to occluded gases. According to Dr. Wedding, 
nickel may take up as much as 9% of carbon, which may exist either 
as amorphous or as graphitic carbon. 

Dr. Fleitmann, of Germany, discovered that a small quantity of pure 
magnesium would free nickel from occluded gases and give a metal 
capable of being drawn or rolled perfectly free from blow-holes, to such 
an extent that the metal may be rolled into thin sheets 3 feet in width. 
Aluminum or manganese may be used equally as well as a purifying 
agent; but either, if used in excess, serves to make the nickel very 
much harder. Nickel will alloy with most of the useful metals, and 
generally adds the quaUties of hardness, toughness, and ductiUty. 

ALUMINUM— ITS PROPERTIES AND USES. 

(Compiled from notes by Alfred E. Hunt, and from publications 
of the Aluminum Co. of America, 1914.) 

The specific gravity of aluminimi varies according to its treatment, 
as foUows: Pure cast, 2.56; sheets, wire, etc., rolled and imannealed, 
2.68; ditto, annealed, 2.66. The casting alloys range in specific 
gravity from 2.82 to 2.91. Based on these values, an ingot of cast 
aluminum 12 in. square, 1 in. thick, weighs 13.3024 lb.; a rolled sheet 
12 in. square, 1 in. thick, weighs 13.9259 lb.; a 1-in. cast round bar, 
12 in. long, weighs 0.8706 lb.; a 1-in. rolled bar, 12 in. long, weighs 
0.9114 lb.; a cubic foot of cast aluminum, 159.6288 lb.; and a cubic 
foot of rolled aluminum, 167.1114 lb. Taking the weight of rolled 
aluminum as 1, the weight of rolled wrought iron is 2.8742; of roUed 
steel, 2.9322; of rolled copper, 3.3321; of rolled brass, 3.19. Wood 
for structures can be taken as about one-third the weight of aluminum. 

Chemically, aluminum is readily soluble in hydrochloric acid, and 
in strong solutions of caustic alkaUes. Hot dilute sulphuric acid 
slowly dissolves it, but concentrated sulphuric acid acts very slowly. 
Nitric acid, cold, either dilute or concentrated, has but Uttle effect; 
hot, it acts very slowly. Sulphur has no action at less than a red 
heat. Chlorine, fluorine, bromine, iodine, and fiuohydric acid rapidly 
corrode it. Salt water has Uttle effect on it, and it resists sea water 
better than does iron, steel, or copper. Aluminum strips on the sides 
of a wooden vessel in sea water corroded less than 0.005 inch in six 
months, about half the corrosion of copper strips. Ammonium solu- 
tions gradually attack the surface of alimiinimi, forming a coating 
which is more resistant than the metal, and which while rapidly attacked 
by concentrated acid or alkali solutions, resists dilute mineral and 
organic acids, and dry or moist air. It is not attacked by CO2, CO, or 
H2S, but wiU absorb these gases when heated. 

The presence of a considerable quantity of aluminum decreases its 
resistance to corrosion. Commercial aluminum, such as is used for 
rolling or casting alloys, contains, however, only a negligible quantity 
of impurities. Occluded gases in molten aluminum cause blow-holes 
in the ingots, which form laminated plates when the metal is rolled 
or hammered, which are more liable to corrode than sound metal. 
Sihcon and iron are the impurities usually found, the former ranging 
in commercial aluminum from 0.30 to 2.0 per cent, and the latter 
from 0.15 to 2.0 per cent. Other metals are frequently alloyed with 
aluminum to increase the hardness, rigidity, and strength. See 
Alloys of Aluminum, page 396. 

Aluminum is electro positive as regards the common metals, and forms 
a galvanic couple when in contact with them. In service it should be 
insulated from them by rubber gaskets, or washers, or by a liberal coat 
of heavy paint. 

In malleability pure aluminum is exceeded only by gold and silver. 
It is exceeded in ductility oiily_by gold, silver, platinum, iron, and 



ALUMINUM — ITS PROPERTIES AND USES. 381 

copper. Sheets of aluminum have been rolled down to 0.0005 in. 
thick and beaten into leaf nearly as tliin as gold leaf. The metal is 
most malleable at a temperature of between 400° and 600° F,, and at 
this temperature it can be drawn down between rolls with nearly as 
much draught upon it as with heated steel. It has also been drawn 
into the finest wire. By the Mannesmann process aluminum tubes 
have been made in Germany. 

The electrical conductivity of aluminum is 61.67, silver being taken 
as 100. On the same scale, the conductivity of copper is 97.62; of 
gold, 76.61; of zinc, 29.57; of iron, 14.57; of platinum, 14.42. Aliuni- 
num wire, weight for weight, has a conductivity of 206, taking copper 
as 100 and aluminum as 62, the aluminum wire having an area 3.33 
that of the copper wire. Pure aluminum is practically non-magnetic. 

Almninum melts at 1215° F. It does not volatilize at any tem- 
perature produced by the combustion of carbon, but it is inadvisable 
to heat it much beyond the melting point or to allow it to remain 
molten for a great length of time, on account of its capacity to absorb 
gases. It may be cast in dry or green sand molds or in metal chills, 
and should be melted in plumbago crucible. Cores should be as soft 
as wiU permit safe manipulation. A good core mixture is 15 parts 
core sand, 1 part rosin. The core should be sprayed with molasses 
water, baked and washed in plimibago water. 

The mean specific heat of aluminum is 0.2185 (water = 1), being 
higher than any other metal except magnesium and the alkah metals. 
Its latent heat of fusion is 51.4 B.T.U. per lb. The coefficient of 
linear expansion of aluminum is 0.0000130 per degree F. The thermal 
conductivity, according to Roberts- Austen, is 31.33 (silver = 100), 
copper being the only baser metal which exceeds it. Wiederman 
and Franz give the thermal conductivity for the metal unannealed as 
38.87, and annealed as 37.96. Its shrinkage in cooUng is 0.2031 in. 
per foot, slightly more than ordinary brass. The shrinkage varies 
somewhat with the thickness — thicker castings shrinking more than 
thinner ones. The hardness of aluminum varies with the purity, the 
purest metal being the softest. In the Bottone scale the hardness of 
the diamond is 3010, while that of aluminum is 821. 

Aluminum under tension, and section for section, is about as strong 
as cast iron. Its tensile strength is increased by cold rolUng or cold 
forging, and there are alloys which add considerably to the tensile 
strength without increasing the specific gravity to over 3 or 3.25. 

The strength of commercial aluminum is given in the following 
table as the result of many tests: 

Elastic Limit Ultimate Strength Percentage 

per sq. in. in per sq. in. in of Reduction 

Form. Tension, Tension, of Area in 

lbs. lbs. Tension. 

Castings 8,500 12,000-14.000 15 

Sheet 12,500-25,000 24,000-40,000 20-30 

Wire 16,000-33,000 25,000-65,000 40-60 

Bars 14,000-33,000 28,000-40,000 30-40 

The elastic limit per square inch under compression in cast cylin- 
dric columns of length twice the diameter is 3500 lb. The ultimate 
strength per square inch under compression in cylinders of the same 
form is 12,000. The modulus of elasticity of cast aluminum is about 
9,000,000. It is rather an open metal in its texture, and for cylinders 
to stand pressure an increase in thickness must be given to allow for 
tMs porosity. Its maximum shearing stress in castings is about 
12,000, and in forgings about 16,000, or about that of pure copper. 
Its texture and strength are improved by forging or pressing at a 
temperature of about 600° F. 

Pure aluminum is too soft and lacking in tensile strength and rigidity 
for many purposes. Valuable alloys are now being made which seem 
to give great promise for the future. They are alloys containing from 
2% to 7% or 8% of copper, manganese, iron, and nickel. See alloys 
of aluminum, page 396. 

Aluminum can be worked by any of the common mechanical proc- 
esses, as rolhng, stamping, drawing, tapping, spinning, forging, ex- 



382 STRENGTH OF MATERIALS. 

truding or machining. Owing to tJie ductility of the metal, sheet 
aluminmn can be given a deeper stamp or heavier draw than most 
9ietals. A draw of over one-quarter to one-third more in depth than 
can be taken with copper, brass or steel can be made on aluminum 
sheet of 20 B. & S. gauge or heavier. The same sort of tools and proc- 
esses are used for stamping as are used for other metal. The tools 
should be lubricated with vaseUne or any greasy oil which is free from 
grit. It is practically unnecessary to anneal the work between re- 
draws. 

In spinning it is also unnecessary to anneal the shells after they come 
from the press, when the first operation is done in the drawing press. 
The speed of the lathe should range from 2,000 to 3,000 r. p. m., and the 
best results in spinning will be obtained by the use of hard wood 
spinning stocks and metal chucks. For finisliing and burnishing, steel 
tools should be used. The best lubricant is soap, tallow, or paraflQn 
candles. In drop forging aluminum, the castings to be forged should 
be made a Uttle smaller in their horizontal diameter and a Uttle greater 
in the vertical diameter than is desired for the finished forging. They 
should be heated to the annealing temperature, about 700° F., before 
being placed in the die. 

Almninum can be extruded into shapes which can be obtained in no 
other way. In these shapes, the metal has a continuity of structure 
which renders it easier in machining than fabricated shapes made by 
other methods. It is difficult at the present time (1914), to extrude a 
shape of greater diameter than 6 inches or one having a thickness of 
wall of less than i/g inch. 

In machining, the tools should have a highly whetted edge, such as 
would be used in wood working, and they should also have a large 
clearance. That is, the thickness of the blades should iacrease very 
slowly from its edge. The tools should operate somewhat faster than 
for brass, and the feed should be slightly slower in proportion. A good 
lubricant should be freely used: No. 1 grade lard oil, or lard oil or 
carbon oil mixed with 25 per cent of some animal oil, give satisfactory 
results. Another satisfactory lubricant is a mixture of lard oil 25 per 
cent by volume mth benzine 75 per cent. 

In sawing, an ordinary circular saw on a table may be used. The 
teeth should have no " set," the saw should be thinner at the center than 
at the periphery, and should run at a peripheral speed of 3,500 to 4,000 
feet per minute. 

For drilhng, an ordinary twist driU may be used, but it should be 
exceedingly sharp. The drill should rotate about 50 per cent faster, 
with a feed about 25 per cent slower, than would be used for brass. In 
tapping, a sharp tap only should be used and a hole drilled with a drill 
from one to three sizes larger than for brass. The best tap is one having 
a single spiral flute with a lead of about one turn in every three inches. 
The best tapping lubricant is the lard oil — benzine mixture noted 
above. 

Aluminum may be finished by caustic dipping and scratch brushing. 
In caustic dipping, the article is first dipped into the benzine and then 
into a strong solution of caustic alkaU, which is kept at the boiling 
point, after which it should be placed in a strong hot solution of nitric 
acid. After draining the acid, the almninimi should be dipped in 
boiUng hot water, which should be constantly drained off and renewed 
by an addition of fresh water. On removal from the water, it should 
be rapidly dried over a steam coil. In scratch brusliing, the metal is 
carefully cleaned and then apphed to the scratch brush wheel, which 
rotates at from 1500 to 2000 r. p. m. 

Soldering and Welding Aluminum. — Aluminum can be readily 
electrically welded, but soldering is not altogether satisfactory. The 
high heat conductivity of the aluminum withdraws the heat of the 
molten solder so rapidly that it "freezes" before it can fiow sufficiently. 
A German solder said to give good results is made of 80% tin to 20^ r 
zinc, using a flux composed of 80 parts stearic acid, 10 parts chloride of 
zinc, and 10 parts of chloride of tin. Pure -tin, fusing at 250° C, 
has also been used as a solder. The use of chloride of silver as a flux has 
been patented, and used with ordinary soft solder has given some suc- 
cess. A pure nickel soldering-bit should be used, as it does not dis- 
color aluminum as copper bits do. 



ALUMINUM— ITS PROPERTIES AND USES. 



383 



The following table of aluminum solders which have been successfully- 
used appeared in Machinery, Dec, 1914. See also page 410. 



Tin. 


Alum- 
inum. 


Zinc. 


Cop- 
per. 


Bis- 

muth. 


Lead. 


Phos- 
phor- 
Tin* . 


Silver 


Anti- 
mony 


Cad- 
mium. 


Mag- 
nes- 
ium. 


95.00 








5.00 














78.50 


2.06 
66.70 


19 .60 








6.50 


33.30 








26.66 


70.00 












10.00 








97.00 








3.60 
















'6.00 


89.50 


4.50 


















7i'.25 


2.25 


26.00 








0.50 












60.00 


4.00 


8.00 


4.06 




iz.oo 




12 


00 








37.50 


's.oo 


25.00 
92.00 


37.50 


















36.66 




20.00 
















50.66 




80.00 


■2.'25 


17.00 




.... 




0.75 












66.00 


15.50 






9.00 










7.60 




'2. '25 


15.50 


2.50 
20.00 


7'8.'25 
65.00 


i'5.6o 




'2.50 


V.'2'5 












49.65 




20.31 


1.15 




26.06 








3 .43 






30.00 


76.00 
4.00 


94. OO 


'2. 00 


















85. 16 


10.80 


















i;35 


■2.'75 


60.00 




15.00 




*5.00 


10.00 








5.00 




..t. 


86.00 








14.00 
















98 00 


Y.OO 






1.00 
















20.00 


70.00 




loVoo 


















48.00 


2.00 


27 .00 






23.00 














90.00 


5.00 






■5. 00 
















84.95 








15.05 

















* 10% phosphorus. fThis solder also 

t This solder also contains 5 % 



contains 0.25 % vanadiimi. 
chromiimi. 



Aluminum Wire. — Tension tests. Diam. 0.128 in. 14 tests. E.L. 
12,500 to 19,100; T. S. 25,800 to 26.900 lbs. per sq. in.; el. 0.30 to 1.02% 
in 48 ins.; Red. of area, 75.0 to 83.4%. Mod. of el. 8,800,000 to 
10,700.000.— Trc/i. Quar., xii, 1899. 

Aluminum Rod.— Torsion tests. 10 samples, 0.257 in. diam. Appar- 
ent outside fiber stress, lbs. per sq. in. 15,900 to 18,300 lbs. per sq. in. 
11 samples. 0.367 in. diam. Apparent outside fiber stress, 18,400 to 
19,200. 10 samples, 0.459 in. diam. Apparent outside fiber stress, 
20,700 to 21,500 lbs. per sq. in. The average number of tiu*ns per inch 
for the three series were respectively, 1.58 to 3.65; 1.20 to 2.64; 0.87 to 
l.OQ.—Ibid. 



384 



ALLOYS. 



ALLOYS. 

AIXOYS OF COPPER AND TIN. 

(Extract from Report of U. So Test Board.*) 





Mean Com- 
position by 
Analysis. 


is 

a . 






+3" 






Torsion 
Tests. 


& 






^ 






^ vx 

'ti 


II 

S 


gal 

3 


1 3 2 

III 




c a a 





ii 


;z; 


Cop- 
per. 


Tin. 


< 


1 


100. 




ii,m^ 


14,000 


6.47 


29,848 


bent. 


42,000 


143 


153 


la 


100. 




12,760 


11,000 


0.47 


21,251 


2.31 


39,000 


65 


40 


2 


97.89 


i.90 


24,580 


10,000 


13.33 






34,000 


150 


317 


3 


96.06 


3.76 


32,000 


16,000 


14.29 


33,232 


bent. 


42,048 


157 


247 


4 


94.11 


5.43 








38,659 


** 






• • • 


5 


92.11 


7.80 


28,540 


19,000 


*5.'53 


43,731 


" 


42,660 


160 


126 


6 


90.27 


9.58 


26,860 


15,750 


3.66 


49,400 


" 


38,000 


175 


114 


7 


88.41 


11.59 








60,403 


" 








8 


87 15 


12.73 


29,430 


20, 000 


3.33 


34,531 


4.00 


53,000 


i82 


idd* 


9 


8^.70 


17.34 








67,930 


0.63 








10 


80.95 


18.84 


32.980 




' 0.04 


56,715 


0.49 


78,000 


190 


16 


11 


77.56 


22.25 






0. 


29,926 


0.16 








12 


76.63 


23.24 


22"6io 


22,6 io 


0. 


32,210 


0.19 


114,000 


i22 


*3;4 


13 


72.89 


26.85 






0. 


9,512 


0.05 




, 




14 


69.84 


29.88 


5"585 


5,585 


0. 


12,076 


0.06 


147,dOO 


'18 


i".5 


15 


68.58 


31.26 






0. 


9,152 


0.04 








16 


67.87 


32.10 






0. 


9,477 


0.05 








17 


65.34 


34.47 


2,201 


2,201 


0. 


4,776 


0.02 


84,700 


'i6 


1 


18 


56.70 


43.17 


1,455 


1,455 


0. 


2,126 


0.02 








19 


44.52 


55.28 


3,010 


3,010 


0. 


4,776 


0.03 


35,800 


*23 


T 


20 


34.22 


65.80 


3,371 


3,371 


0. 


5,384 


0.04 


19,600 


17 


2 


21 


23.35 


76.29 


6.775 


6,775 


0. 


12,408 


0.27 








22 


15.08 


84.62 








9,063 


0.86 


6,500 


*23 


25* 


23 


11.49 


88.47 


6,380 


3', 500 


4.io 


10,706 


5.85 


10,100 


23 


62 


24 


8.57 


91.39 


6,450 


3,500 


6.87 


5,305 


bent. 


9,800 


23 


132 


25 


3.72 


96.31 


4,780 


2,750 


12.32 


6,925 




9,800 


23 


220 


26 


0. 


100. 3,505 




35.51 


3,740 


•• 


6,400 


12 


557 



* The tests of the alloys of copper and tin and of copper and zinc, the 
results of which are published in the Report of the U. S. Board appointed 
to test Iron, Steel, and other Metals, Vols. I and II, 1879 and 1881, were 
made by the author under direction of Prof. R. H. Thurston, chairman of 
the Committee on Alloys. See preface to the report of the Committee, 
in Vol. I. 

Nos. la and 2 were full of blow-holes. 
» Tests Nos. 1 and la show the variation in cast copper due to varying 
conditions of casting. In the crushing tests Nos. 12 to 20, inclusive, 
crushed and broke under the strain, but all the others bulged and flattened 
out. In these cases the crushing strength is taken to be that which 
caused a decrease of 10% in the length. The test-pieces were 2 in. long 
and 5'8 in. diameter. The torsional tests were made m Thurston's torsion- 
machine, on pieces -Vs in. diameter and 1 in. long between heads. 

Specific Gravity of the Copper-tin Alloys. — The specific gravity 
of copper, as found in these tests, is 8.874 (tested in turnings from the 
Ingot, and reduced to 39.1° F.). The alloy of maximum sp. gr. 8.956 
contained 62.42 copper. 37.48 tin, and all the alloys containing less than 



ALLOYS OF COPPER AND TIN. 385 

37% tin varied irregularly in sp. gr. between 8.65 and 8.93, the density 
depending not on the composition, but on the porosity of the casting. It 
is probable that the actual sp. gr. of all these alloys containing less than 
37% tin is about 8.95, and any smaller figure indicates porosity in the 
specimen. 

From 37% to 100% tin, the sp. gr. decreases regularly from the maxi- 
mum of 8.956 to that of pure tin, 7.293. 



Note on the Strength of the Copper-tin Alloys. 

The bars containing from 2% to 24% tin, inclusive, have considerable 
strength, and all the rest are practically worthless for purposes in which 
strength is required. The dividing Une between the strong and brittle 
alloys is precisely that at which the color changes from golden yellow to 
silver-white, viz., at a composition containing between 24% and 30% of 
tin. 

It appears that the tensile and compressive strengths of these alloys are 
in no way related to each other, that the torsional strength is closely pro- 
portional to the tensile strength, and that the transverse strength may de- 
pend in some degree upon the compressive strength, but it is much more 
nearly related to the tensile strength. The modulus of rupture, as ob- 
tained by the transverse tests, is, in general, a figure between those of 
tensile and compressive strengths per square inch, but there are a few 
exceptions in which it is larger than either. 

The strengths of the alloys at the copper end of the series increase 
rapidly with the addition of tin till about 4% of tin is reached. The 
transverse strength continues regularly to increase to the maximum, till 
the alloy containing about 17^% of tin is reached, while the tensile and 
torsional strengths also increase, but irregularly, to the same point. This 
irregularity is probably due to porosity of the metal, and might possibly 
be removed by any means which would make the castings more compact. 
The maximum is reached at the alloy containing 82.70 copper, 17.34 tin, 
the transverse strength, however, being very much greater at this point 
than the tensile or torsional strength. From the point of maximum 
strength the figures drop rapidly to the alloys containing about 27.5% of 
tin, and then more slowly to 37.5%, at which point the minimum (or 
nearly the minimum) strength, by all three methods of test, is reached. 
The alloys of minimum strength are found from 37.5% tin to 52.5% tin. 
The absolute minimum is probably about 45% of tin. 

From 52.5% of tin to about 77.5% tin there is a rather slow and irregu- 
lar increase in strength. From 77.5% tin to the end of the series, or all 
tin, the strengths slowly and somewhat irregularly decrease. 

The results of these tests do not seem to corroborate the theory given 
by some writers, that peculiar properties are possessed by the alloys 
which are compounded of simple multiples of their atomic weights or 
chemical equivalents, and that these properties are lost as the com- 
positions vary more or less from this definite constitution. It does 
appear that a certain percentage composition gives a maximum strength 
and another certain percentage a minimum, but neither of these com- 
positions is represented by simple multiples of the atomic weights. 

There appears to be a regular law of decrease from the maximum to 
the minimum strength which does not seem to have any relation to the 
atomic proportions, but only to the percentage compositions. 

Hardness. — The pieces containing less than 24 % of tin were turned in 
the lathe without difficulty, a gradually increasing hardness being noticed, 
the last named giving a very short chip, and requiring frequent sharpening 
of the tool. 

^ With the most brittle alloys It was found impossible to turn the test- 
pieces in the lathe to a smooth surface. No. 13 to No. 17 (26.85 to 34.47 
tin) could not be cut with a tool at all. Chips would fly off in advance 
of the tool and beneath it, leaving a rough surface; or the tool would 
sometimes, apparently, crush off portions of the metal, grinding it to 
powder. Beyond 40 % tin the hardness decreased so that the bars could 
be easily turned. 



386 



ALLOYS. 



ALLOYS OF COPPER AND ZINC. (U. S. Test Board.) 











Elastic 


rp . 


^ 




Torsional 




Mean 


Com- 




Limit 


t i 


verse 


rj • 


Crush- 


Tests. 




position Dy 


Tensile 


7o of 


§ -c 


Test 


Crs C 


ing 
Str'gth 
per sq. 
in., lbs. 






No. 


Analysis. 


Str'gth. 

lbs. per 

sq. in. 


Break- 
ing 

Load, 
lbs. per 

sq. in. 


.2 c 

^ .s 

o c 


Modu- 
lus of 
Rup- 
ture. 


Deflectic 

sq. bar 

long, i 






Cop- 
per. 


Zinc. 


l2 


1 


97.83 


1.88 


27,240 












130 


357 


2 


82.93 


16.98 


32.600 


26.'l 


2*6.7 


23,i97 


Bent 




155 


329 


3 


81.91 


17.99 


32,670 


30.6 


31.4 


21,193 


" 




166 


345 


4 


77.39 


22.45 


35,630 


20.0 


35.5 


25,374 


" 




169 


311 


5 


76.65 


23.08 


30,520 


24.6 


35.8 


22,325 


*• 


42,000 


165 


267 


6 


73.20 


26.47 


31,580 


23.7 


38.5 


25,894 


•' 


. • . 


168 


293 


7 


71.20 


28.54 


30,510 


29.5 


29.2 


24,468 


*' 




164 


269 


8 


69.74 


30.06 


28,120 


28.7 


20.7 


26,930 


" 




143 


202 


9 


66.27 


33.50 


37,800 


25.1 


37.7 


28,459 


** 




176 


257 


10 


63.44 


36.36 


48,300 


32.8 


31.7 


43,216 


•* 




202 


230 


n 


60.94 


38.65 


41,065 


40.1 


20.7 


38,968 


** 


75,000 


194 


202 


12 


58.49 


41.10 


50,450 


54.4 


10.1 


63,304 


" 




in 


93 


13 


55.15 


44.44 


44,280 


44.0 


15.3 


42,463 


" 


78,000 


209 


109 


14 


54.86 


44.78 


46,400 


53.9 


8.0 


47,955 


•' 




223 


72 


15 


49.66 


50.14 


30,990 


54.5 


5.0 


33,467 


1.26 


li 7,400 


172 


38 


16 


48.99 


50.82 


26,050 


100 


0.8 


40,189 


0.61 




176 


16 


17 


47.56 


52.28 


24,150 


100 


0.8 


48,471 


1.17 


12i,'000 


155 


13 


18 


43 36 


56.22 


9,170 


100 




17,691 


0.10 




88 


2 


19 


41.30 


58.12 


3,727 


100 




7,761 


0.04 




18 


2 


20 


32.94 


66.23 


1,774 


100 




8,296 


0.04 




29 


1 


21 


29.20 


70.17 


6,414 


100 




16,579 


0.04 




40 


2 


22 


20.81 


77.63 


9,000 


100 


0.2 


22,972 


0.13 


52,*152 


65 


1 


23 


12.12 


86.67 


12,413 


100 


0.4 


35,026 


0.31 




82- 


3 


24 


4.35 


94.59 


18,065 


100 


0.5 


26,162 


0.46 




81 


22 


25 


Cast. 


Zinc. 


5.400 


75 


, 0.7 


7,539 


0.12 


22,000 


37 


142 



Variation in Strength of Gun-bronze, and Means of Improving 
the Strength. — The figures obtained for alloys of from 7.8% to 12.7% 
tin, viz., from 26,860 to 29,430 pounds, are much less than are usually 
given as the strength of gun-metal. Bronze guns are usually cast under 
the pressure of a head of metal, which tends to increase the strength and 
density. The strength of the upper part of a gun casting, or sinking 
head, is not greater than that of the smaU bars which have been tested 
in these experiments. The following is an extract from the report of 
Major Wade concerning the strength and density of gun-bronze (1850): 
— Extreme variation of six samples from different parts of the same 
gun (a 32-pound er howitzer): Specific gravity, 8.487 to 8.835: tenacity. 
26,428 to 52,192. Extreme variation of aU the samples tested: Specific 
gravity, 8.308 to 8.850: tenacity. 23,108 to 54.531. Extreme variation of 
all the samples from the gun heads: Specific gravity, 8.308 to 8^756; 
tenacity. 23.529 to 35,484. 

Major Wade says: The general results on the quality of bronze as it is 
found in guns are mostly of a negative character. They expose defects 
in density and strength, develop the heterogeneous texture of the metal 
in different parts of the same gun, and show the irregularity and un- 
certainty of quality which attend the casting of all guns, although made 
from similar materials, treated in like manner. 

Navy ordnance l)ronze containing 9 parts copper and 1 part tin, tested 
at Washington, D.C.. in 1S75-6. showed a variation in tensile strength 
from 29.S00 to 51,400 lbs. per square inch, in elongation from 3% to 
58%, and in specific gravity from 8.39 to 8.88. 

That a great improvement may be made in the density and tenacity 
of gun-bronze bv compression has been shown by the experiments of 
Mr. S. B. Dean" in Boston. Mass., in 1869, and 'by those of General 
Uchatius in Austria in 1873. The former increased the density of the 



ALLOYS OF COPPER, TIN AND ZINC. 



387 



metal next the bore of the gun fiom 8.321 to 8.875, and the tenacity 
from 27,238 to 41,471 pounds per square inch. The latter, by a similar 
process, obtained the following figures for tenacity: 

Pounds per sq. in. 

Bronze with 10% tin 72,053 

Bronze with 8% tin 73,958 

Bronze with 6% tin 77,656 

ALLOYS OF COPPER, TIN, AND ZINC. 

(Report of U. S. Test Board, Vol. II, 1881.) 



No. 
in 


Analysis, 
Original Mixture. 


Transverse 
Strength. 


Tensile 
Strength per 
square inch. 


Elongation 

per cent in 

5 inches. 


Re- 








Mcdulus 
of 
Rup- 
ture. 


Deflec- 










port. 


Cu. 
90 


Sn. 


Zn. 


tion, 
ins. 


A. 


5. 


A. 


B. 


72 


5 


5 


41,334 


2.63 


23,660 


30,740 


2.34 


9.68 


5 


88.14 


1.86 


10 


31,986 


3.67 


32,000 


33,000 


17.6 


19.5 


70 


85 


5 


10 


44,457 


2.85 


28,840 


28,560 


6.80 


5.28 


71 


85 


10 


5 


62,470 


2.56 


35,680 


36,000 


2.51 


2.25 


89 


85 


12.5 


2.5 


62,405 


2.83 


34,500 


32,800 


1.29 


2.79 


88 


82.5 


12.5 


5 


69,960 


1.61 


36,000 


34,000 


0.86 


0.92 


77 


82.5 


15 


2.5 


69,045 


1.09 


33,600 


33,800 




0.68 


67 


80 


5 


15 


42,618 


3.88 


37,560 


32,300 


11.6' 


3.59 


68 


80 


10 


10 


67,117 


2.45 


32,830 


31,950 


1.57 


1.67 


69 


80 


15 


5 


54,476 


0.44 


32,350 


30,760 


0.55 


0.44 


86 


77.5 


10 


12.5 


63,849 


1.19 


35,500 


36,000 


1.00 


1.00 


87 


77.5 


12.5 


10 


61,705 


0.71 


36,000 


32,500 


0.72 


0.59 


63 


75 


5 


20 


55,355 


2.91 


33,140 


34,960 


2.50 


3.19 


85 


75 


7.5 


17.5 


62,607 


1.39 


33,700 


39,300 


1.56 


1.33 


64 


75 


10 


15 


58,345 


0.73 


35,320 


34,000 


1.13 


1.25 


65 


75 


15 


10 


51,109 


0.31 


35,440 


28,000 


0.59 


0.54 


66 


75 


20 


5 


40,235 


0.21 


23,140 


27,660 


0.43 




83 


72.5 


7.5 


20 


51,839 


2.86 


32,700 


34,800 


3.73 


3.78 


84 


72.5 


10 


17.5 


53,230 


0.74 


30,000 


30,000 


0.48 


0.49 


59 


70 


5 


25 


57,349 


1.37 


38,000 


32,940 


2.06 


0.99 


82 


70 


7.5 


22.5 


48,836 


0.36 


38,000 


32,400 


0.84 


0.40 


60 


70 


10 


20 


36,520 


0.18 


33,140 


26,300 


0.31 




61 


70 


15 


15 


37,924 


0.20 


33,440 


27,800 


0.25 




62 


70 


20 


10 


15,126 


0.08 


17,000 


12,900 


0.03 




6' 


67.5 


2.5 


30 


58,343 


2.91 


34,720 


45,850 


7.27 


3.09 


^4 


67.5 


5 


27.5 


55,976 


0.49 


34,000 


34,460 


1.06 


0.43 


75 


67.5 


7.5 


25 


46,875 


0.32 


29,500 


30,000 


0.36 


0.26 


po 


65 


2.5 


32.5 


56,949 


2.36 


41,350 


38,300 


3.26 


3.02 


55 


65 


5 


30 


51,369 


0.56 


37,140 


36,000 


1.21 


0.61 


36 


65 


10 


25 


27,075 


0.14 


25,720 


22,500 


0.15 


0.19 


57 


65 


15 


20 


13,591 


0.07 


6,820 


7,231 






58 


65 


20 


15 


11,932 


0.05 


3,765 


2,665 






79 


62.5 


2.5 


35 


69,255 


2.34 


44,400 


45,000 


2.i5 


2.V9 


78 


60 


2.5 


37.5 


69,508 


1.46 


57,400 


52,900 


4.87 


3.02 


52 


60 


5 


35 


46,076 


0.28 


41,160 


38,330 


0.39 


0.40 


53 


60 


10 


30 


24,699 


0.13 


21,780 


21,240 


0.15 




54 


60 


15 


25 


18,248 


0.09 


18,020 


12,400 






12 


58.22 


2.30 


39.48 


95,623 


1.99 


66,500 


67,600 


3. 13 


3.' 15 


3 


58.75 


8.75 


32.5 


35,752 


0.18 


Broke 


before te 


st; very 


brittle 


4 


57.5 


21.25 


21.25 


2,752 


0.02 


725 


1,300 






73 


55 


0.5 


44.5 


72,308 


3.05 


68,900 


68,900 


9.43 


i.is's 


50 


55 


5 


40 


38,174 


0.22 


27,400 


30,500 


0.46 


0.43 


51 


55 


10 


35 


28,258 


0.14 


25,460 


18,500 


0.29 


0.10 


49 


50 


5 


45 


20,814 


0.11 


23,000 


31,300 


0.66 


0.45 



'6HH ALLOYS. 

The transverse tests were made in bars 1 in. square, 22 in. between 
supports. The tensile tests were made on bars 0.798 in. diam. turned 
from the two halves of the transverse-test bar, one half bein6 marked A 
and the other B. 

Ancient Bronzes. — The usuaJ composition of ancient bronze was 
the same as that of modern gun-metal — 90 copper, 10 tin; but the 

Eroportion of tin varies from 5% to 15%, and in some cases lead has 
een found. Some ancient Egyptian tools contained 88 copper, 12 tin. 

Strength of the Copper-zinc Alloys. — The alloys containing less 
than 15% of zinc by original mixture were generally defective. The 
bars were full of blow-holes, and the metal showed signs of oxidation. 
To insure good castings it appears that copper-zinc alloys should con- 
tain more than 15% of zinc. 

From No. 2 to No. 8 inclusive, 16.98 to 30.06% zinc the bars show a 
remarkable similarity in all their properties. They have all neariy the 
same strength and ductility, the latter decreasing slightly as zinc 
increases, and are neariv alike in color and appearance. Between Nos. 8 
and 10, 30.06 and 36.36% zinc, the strength by all methods of test 
rapidly increases. Between No. 10 and No. 15, 36.36 and 50.14% zinc, 
there is another group, distinguished by high strength and diminished 
ductility. The alloy of maximum tensile, transverse and torsional 
strength contains about 41 % of zinc. 

The alloys containing less than 55% of zinc are all yellow metals. 
Beyond 55% the color changes to white, and the alloy becomes weak and 
brittle. Between 70% and pure zinc the color is bluish gray, the brit- 
tleness decreases and the strength increases, but not to such a degree as 
to make them useful for constructive purposes. 

Difference between Composition by Mixture and by Analysis. — 
There is in every case a smaller percentage of zinc in the average analy- 
sis than in the original mixture, and a larger percentage of copper. The 
loss of zinc is variable, but in general averages from 1 to 2%. 

Liquation or Separation of the 3Ietals. — In several of the bars a 
considerable amount of liquation took place, analysis showing a differ- 
ence in composition of the two ends of the bar. In such cases the 
change in composition was gradual from one end of the bar to the other, 
the upper end in general containing the higher percentage of copper. 
A notable instance was bar No. 13, in the above table, turnings from the 
upper end containing 40.36% of zinc, and from the lower end 48.52%. 

Specific Gravity. — The specific gravity follows a definite law, vary- 
ing with the composition, and decreasing with the addition of zinc. 
From the plotted curve of specific gravities the following mean values 
are taken: 

Per cent zinc 10 20 30 40 50 60 70 80 90 109 

Specific gravity . . . 8.80 8.72 8.60 8.40 8.36 8.20 8.00 7.72 7.40 7.20 7.14 

Graphic Representation of the Law of Variation of Strength of 
Copper-Tin-Zinc Alloys. — In an equilateral triangle the sum of the 
perpendicular distances from any point within it to the three sides is 
equal to the altitude. Such a triangle can therefore be used to show 
graphically the percentage composition of any compound of three parts, 
such as a triple alloy. Let one side represent copper, a second tin, 
and the third zinc, the vertex opposite each of these sides representing 
100 of each element respectively. On points in a triangle of wood rep- 
resenting different alloys tested, wires were erected of lengths propor- 
tional to the tensile strengths, and the triangle then built up with plaster 
to the height of the wires. The surface thus formed has a characteristic 
topography representing the variations of strength with variations of 
composition. The cut shows the surface thus made. The vertical 
section to the left represents the law of tensile strength of the copper-tin 
alloys, the one to the right that of tin-zinc alloys, and the one at the 
rear that of the copper-zinc alloys. The high point represents the 
strongest possible allovs of the three metals. Its composition is copper 
55, zinc 43. tin 2, and its strength about 70,000 lbs. The high ridge from 
this point to the point of maximum height of the section on the left is 
the line of the strongest alloys, represented by the formula zinc 4- (3 X tin) 
= 55. 

All alloys lying to the rear of the ridge, containing more copper and 
less tin or zinc are alloys of greater ductility than those on the line of 



ALLOYS OP COPPER, TIN AND ZINC. 



389 



maximum strength, and are the valuable commercial alloys; those in 
front on the declivity toward the central valley are brittle, and those in 
the valley are both brittle and weak. Passing from thejvalley toward the 
section at the right the alloys lose their brittleness and become soft, the 
maximum softness being at tin =100, but they remain weak, as is shown 
by the low elevation of the surface. This model was planned and con- 
structed by Prof. Thurston in 1877. (See Trans. A. S. C. E., 1881. 
Report of the U. S. Board appointed to test Iron, Steel, etc., vol. ii, 
Washington, 1881, and Thurston's Materials of Engineering, vol. ill.) 




Fig. 90. 

The best alloy obtained in Thurston's research for the U. S, Testing 
Board has the composition, copper 5-5, tin 0.5, zinc 44.5. The tensile 
strength in a cast bar was 68,900 lbs. per sq. in., two specimens giving 
the same result; the elongation was 47 to 51 per cent in 5 inches. 
Thurston's formula for copper-tin-zinc alloys of maximum strength 
(Trans. A. S. C. E., 1881) is 2 4- 3 ^ = 55, in which z is the percentage of 
zinc and t that of tm. Alloys proportioned according to this formula 
should have a strength of about 40,000 lbs. per sq. in. + 500 2. The 
formula fails with alloys containing less than 1 per cent of tin. 

The following would be the percentage composition of a number of 
alloys made according to this formula, and their corresponding tensile 
strength in castings: 









Tensile 








Tensile 


Tin. 


Zinc. 


Copper. 


Strength, 
lbs. per 
sq. in. 


Tin. 


Zinc. 


Copper. 


Strength 
lbs. per 
sq. m. 


1 


52 


47 


66,000 


8 


31 


61 


55,500 


2 


49 


49 


64,500 


9 


28 


63 


54,000 


3 


46 


51 


63,000 


10 


25 


65 


52,500 


4 


43 


53 


61,500 


12 


19 


69 


49,500 


5 


40 


55 


60,000 


14 


13 


73 


46,500 


6 


37 


57 


58,500 


16 


7 


77 


43,500 


7 


34 


59 


57.000 


18 




81 


40,500 



390 



ALLOTS. 



These alloys, while possessing maximum tensile strength, would in 
general be too hard for easy working by machine tools. Another series 
made on the formula 2 -f 4« = 50 would have greater ductility, together 
with considerable strength, as follows, the strength being calculated as 
before, tensile strength in lbs. per sq. in. = 40,000 + 500 2. 









Tensile 








Tensile 


Tin. 


Zinc. 


Copper. 


Strength, 
lbs. per 
sq. in. 


Tin. 


Zinc. 


Copper. 


Strength, 
lbs. per 
sq. in. 


1 


46 


53 


63,000 


7 


22 


71 


51,000 


2 


42 


56 


61,000 


8 


18 


74 


49,000 


3 


38 


59 


59,000 


9 


14 


77 


47,000 


4 


34 


62 


57,000 


10 


10 


80 


45,000 


5 


30 


65 


55,000 


11 


6 


83 


43,000 


6 


26 


68 


53,000 


12 


2 


86 


41,000 



Composition of Alloys in E very-day Use in Brass Foundries. 

(American Machinist.) 



Admiralty metal . 

Bell metal 

Brass (yellow).. .. 

Bush metal 

Gun metal 

Steam metal 

Hard gun mietal . . 
Muntz metal 

Phosphor bronze . 



Brazing metal . 
solder.. 



Cop- 
per. 


Zinc. 


lbs. 
87 


lbs. 
5 


16 
16 


■"8" 


64 


8 


32 


1 


20 


1 


16 
60 


■ 40 ■ 


92 




90 




16 
50 


3 
50 



Tin. 



Lead 



lbs. 
8 


lbs. 


4 


■ '1/2 ■ 


4 


4 


3 




11/2 


1 


21/2 





8 phos. tin 
10 " " 



For parts of engines on 
board naval vessels. 

Bells for ships and factories. 

For plumbers, ship and house 
brass work. 

For bearing bushes for shaft- 
ing. 

For pumps and other hydrau- 
lic purposes. 

Castings subjected to steam 
pressure. 

For heavy bearings. 

Metal from which bolts and 
nuts are forged, valve spin- 
dles, etc. 

For valves, pumps and gen- 
eral work. 

For cog and worm wheels, 
bushes, axle bearings, slide 
valves, etc. 

Flanges for copper pipes. 

Solder for the above flanges. 



Admiralty Metal, for surface condenser tubes where sea water is used 
for cooling, Cu, 70: Zn, 29; Sn, 1. Power, June 1, 1909. 

Gurley's Bronze. — 16 parts copper, 1 tin, 1 zinc, I/2 lead, used by 
W & L. E. Gurley of Troy for the framework of their engineer's transits. 
Tensile strength 41,114 lbs. per sq. in., elongation 27% in 1 inch, sp. gr. 
8.696. (W. J. Keep, Trans, A. I. M, E., 1890.) 



ALLOYS OF COPPER, TIN, AND ZINC. 



391 



Composition of Various Grades of Rolled Brass, Etc, 








Trade Name. 


Copper. 


Zinc. 


Tin. 


Lead. 


Nickel. 


Commoii high brass 


61.5 

60 

662/3 

80 

60 

60 

662/3 

611/2 


38.5 
40 

40 
40 

331/3 
201/2 


*U/2 


*l"i/2 
ll/2to2 

... 




Yellow metal 








Cartridge brass 




Low brass .. 




Clock brass 




Drill rod 




Spring brass 




18 per cent German silver 


18 











The above table was furnished by the superintendent of a mill in Connec- 
ticut in 1894. He says: While each mill has its own proportions for various 
mixtures, depending upon the purposes for w^hich the product is intended, 
the figures given are about the average standard. Thus, between cartridge 
brass with 331/3 per cent zinc and common liigh brass with 381/2 per cent 
zinc, there are any number of different mixtures known generally as ** high 
brass," or specifically as "spinning brass," "drawing brass," etc., wherein 
the amount of zinc is dependent upon the amount of scrap used in the 
mixture, the degree of working to which the metal is to be subjected, etc. 



Useful Alloys of Copper, Tin, and Zinc. 

(Selected from numerous sources.) 



U.S. Navy Dept. journal boxes ) ^ 

and guide-gibs j 

Tobin bronze 

Naval brass 

Composition, U. S. Navy 

Brass bearings (J. Rose) 

Gun metal 

Tough brass for engines 

Bronze for rod-boxes (Lafond) 

" " pieces subject to shock. . 

Red brass parts 

" per cent 

Bronze for pump casings (Lafond). 
[| " eccentric straps. *' 

*' shrill whistles 

" low-toned whistles 

Art bronze, dull red fracture 

Gold bronze 

Bearing metal 

•• *• 

•• «t ' 

English brass of a.d. \5i)^ '.'...,. .... 



Copper. 


Tin. 


(82.8 


I 
13.8 


58.22 


2.30 


62 


1 


88 


10 


(64 

87.7 


8 


11.0 


92.5 


5 


91 


7 


87.75 


9.75 


85 


5 


83 


2 


P5 
176.5 


2 


11.8 


82 


16 


83 


15 


20 


I 


87 


4.4 


88 


10 


84 


14 


80 


18 


81 


17 


97 


2 


89.5 


2.1 


89 


8 


89 


21/2 


86 


14 


851/4 


123/4 


80 


18 


79 


18 


74 


91/2 


64 


3 



Zinc. 



1/4 parts. 

3.4 per cent. 
39.48 '* " 
37 •• " 

2 " •' 

1 parts. 

1 .3 per cent 

2.5 " " 

2 4« «• 

2.5 •• *• 

10 " •• 

15 " " 

2 parts. 
11.7 percent. 

2 slightly malleable. 

1.50 0.50 lead. 

I I 

4.3 4.3 •• 

2 

2 



> 2.0antiiixony. 
, 2.0 *• 



1 

5.6 2.8 lead. 

3 

81/2 



2 
2 

21/2 1/2 lead. 

91/2 7 lead. 

291/2 3 1/2 lead. 



392 



ALLOYS. 



" Steam Metal." Alloys of copper and zinc are unsuitable for steam 
valves and other like purposes, since their strength is greatly reduced at 
high temperatiu-es, and they appear to undergo a deterioration by con- 
tinued heating. Alloys of copper with from 10 to 12 9^ of tin, when cast 
without oxidation, are good steam metals, and a favorite alloy is what 
is known as "government mixture," 88 Cu, 10 Sn, 2 Zn. It has a 
tensile strength of about 33.000 lb. per sq. in., when cold, and about 
30,600 lb. when heated to 407° F., corresponding to steam of 250 lb. 
pressure. 

Analyses of Tobin bronze by Dr. Chas. B. Dudley gave the following: 

Pig metal Cu, 59.00; Zn, 38.40; Sn, 2.16; Fe, 0.11; Pb, 0.31 

Rolled bar Cu, 61.20; Zn, 37.14; Sn, 0.90; Fe, 0.18; Pb, 0.35 

The rolled bar gave 78,500 lb. tensile strength, 40% elongation in 
2 in. and 15% in 8 in. 

The original Tobin bronze in 1875, as described by Thurston, Trans. 
A. S. C. E., 1881, had copper 58.22, tin 2.30, zinc 39.48. As cast it 
had a tenacity of 66,000 lb. per sq. in., and as rolled 79,000 lb.; cold 
rolled it gave 104,000 lb. 

At a cherry-red heat Tobin bronze can be forged and stamped as 
readily as steel. Its great tensile strength and its resistance to the 
corrosive action of sea water make it a suitable metal for condenser 
plates and other marine purposes. 

Miscellaneous Alloys. (From a circular of the Titaniimi Alloy Mfg. 
Co., Niagara Falls, N. Y., 1915.) 

Analyses (Approximate). Physical Qualities (Averages). 

















c 


>i 


t 


ih 


^. 




No. 


Cu. 


Al. 


Sn. 


Zn. 


Pb. 


T.S. 






11 


5fe 

02 


4J fl 

|5 


m 


1 


90 

89 


10 








70,000 
37.500 


20 
8 


7.5 

8.5 


95 
75 


0.22 
.125 


0.27 
.31 


19,500 


3 


11 




.... 


21.600 


S 


90 
90 


10 








77.000 
37,500 


24.5 
17.5 


7.5 
8.6 


94 
67 


.22 
.125 


.27 
.31 


25,000 


9 


10 








10 


88 




10 


2 




35,000 


16 


8.7 


72 


.125 


.32 




11 


90 




6.5 


2 


1.5 


37.000 


29 


8.8 


55 


.14 


.32 




14 


88 




10 




2 


32,500 


6.5 


8.8 


67 


.125 


.32 


18.500 


15 


80 




10 




10 


30.000 


6 


9.0 


57 


.125 


.33 




16 


81 




7 


3 9 


32.500 


17 


8.9 


52 


.125 


.33 




18 


85 




5 


5 


5 


30.000 


18 


8.5 


55 


.14 


.31 




19 


83 




4 


7 


6 


30.500 


17.5 


8.5 


57 


.125 


.31 




24 


70 




1 


27 


2 


29.500 


25 


8.4 


52 


.186 


.30 




?8 


99.75 
56 










18.500 
70.000 


10 
28.5 


8.8 
8.4 


35 
111 


.25 
.25 


.32 
.30 




29 


0.5 




43.5 




30.000 


32 


8 


92 








18.000 


1.5 


2.8 


52 


.186 


.10 




33 


3 


82 




15 




23.000 


2 


3.1 


62 


.186 


.11 





Qualities and Uses: 

No. 1. Strength, toughness, resists corrosion. 

No. 3. Gear bronze; serviceable for worm wheels running against 
highly finished steel. 

No. 5. Similar to No. 1, but more easily machined. For large, heavy 
work. 

No. 9. Acid resisting; for mine-pump bodies, and for thrust collars 
or disks. 

No. 10. "Gun metal"; for heavy pressures and high speeds; for high- 
grade bearings. 

No. 11. Medium soft bronze; for small bearings lined with babbitt; for 
steam work. 

No. 14. Gear bronze, softer than No. 3; machines more easily. 

No. 15. Phosphor bronze; for high speed and heavy pressure; for bear- 
ings subject to shock. 

No. 16. Similar to No. 15, but somewhat softer and lower in price. 

No. 18. High grade red brass; a good steam metal. 



COPPER-ZINC-IRON ALLOYS. 



393 



No. 19. Commercial red brass. 

No. 24. A good yellow brass; casts well; takes a high polish. 

No. 28. Pure copper, deoxidized; high electrical conductivity. 

No. 29. "Manganese bronze"; for propeller blades, valve stems and 

other parts requiring high strength; not good for bearings. 
No. 32. Standard aliuninum alloy; for crank cases, automobile castings, 

etc. 
No. 33. Tougher than No. 32; takes an extra high poUsh, can be bent 

sUghtly without breaking. 

Special Alloys. (Engineering, March 24, 1893.) 
Japanese Alloys for art work: 





Copper. 


Silver. 


Gold. 


Lead. 


Zinc. 


Iron. 


Shaku-do 

Shibu-ichi.. .. . 


94.50 
67.31 


1.55 
32.07 


3.73 
traces. 


0.11 
0.52 


trace. 


trace. 



Gilbert's Alloy for cera-perduta process, for casting in plaster of 
par is. 

Copper 91.4 Tin 5.7 Lead 2.9 Very fusible. 



COPPER-ZINC-IRON ALLOYS. 

(F. L. Garrison, Jour. Frank. Inst., June and July, 1891.) 

Delta Metal. — This alloy, which was formerly known as sterro-metal, 
is composed of about 60 copper, from 34 to 44 zinc, 2 to 4 iron, and 1 to 2 
tin. 

The peculiarity of all these alloys is the content of iron, wliich appears 
to have the property of increasing their strength to an unusual degree. 
In making delta metal the iron is previously alloyed with zinc in known 
and definite proportions. When ordinary wrought-iron is introduced 
into molten zinc, the latter readily dissolves or absorbs the former, and 
will take it up to the extent of about 5% or more. By adding the zinc- 
iron alloy thus obtained to the requisite amount of copper, it is possi- 
ble to introduce any definite quantity of iron up to 5% into the copper 
alloy. Garrison gives the following as the range of composition ot 
copper-zinc-iron, and copper-zinc-tin-iroa alloys: 



I. 

Per cent. 

Iron 0.1 to 5 

Copper ■ 50 to 65 

Zinc •. 49.9 to 30 



II. 

Per cent. 

Iron 0.1 to 5 

Tin 0.1 to 10 

Zinc 1.8 to 45 

Copper 98 to 40 

The advantages claimed for delta metal are great strength and tough- 
ness. It produces sound castings of close grain. It can be rolled and 
forged hot, and can stand a certain amount of drawing and hammering 
when cold. It takes a high pohsh, and when exposed to the^atmosphere 
tarnishes less than brass. 

When cast in sand delta metal has a tensile strength of about 45,000 
pounds per square inch, and about 10% elongation; when rolled, ten- 
sile strength of 60,000 to 75,000 pjounds per square inch, elongation 
from 9% to 17% on bars 1.128 inch in diameter and 1 inch area. 

Wallace gives 'the ultimate tensile strength 33,600 to 51,520 pounds 
per square inch, with from 10% to 20% elongation. 

Delta metal can be forged, stamped and rolled hot. It must be forged 
at a dark cherry-red heat, and care taken to avoid striking when at a 
black heat. 

According to Lloyd's Proving House tests, made at Cardiff, December 
20, 1887, a half-inch delta metal-rolled bar gave a tensile strength of 
88,400 pounds per square inch, with an elongation of 30% in three 
inches. 



394 



ALLOYS. 



ALLOTS OP COPPER, TIN, AND LEAD, 

G. H. Clamer, In Castings, July, 1908, describes some experiments on 
the use of lead in copper alloys. A copper and lead alloy does not make 
what would be called p:ood castings; by the introduction of tin a more 
homogeneous product is secured. By the addition of nickel it was found 
that more than 15% of lead could be used, while maintaining tin at 8 to 
10%, and also that the tin could be dispensed with. A good alloy for 
bearings was then made without nickel, containing Cu 65, Sn 5, Pb 30. 
This alloy is largely sold under the name of "plastic bronze." If the 
matrix of tin and copper were so proportioneci that the tin remained 
below 9% then more than 20% of lead could be added with satisfactory 
results. As the tin is decreased more lead may be added. (See Bear- 
ing Metal Alloys, below.) 

The Influence of Lead on Brass. — E. S. Sperry, Trans. A.I.M.E., 
1897. As a rule, the lower the brass (that is, the lower in zinc) the 
more difficult it is to cut. If the alloy is made from pure copper and 
zinc, the chips are long and tenacious, and a slow speed must be era- 
ployed in cutting. For some classes of work, such as spinning or car- 
tridge brass, these qualities are essential, but for others, such as clock 
brass or screw rod, they are almost prohibitory. To make an alloy 
which will cut easily, giving short chips, the best method is the addition 
of a small percentage of lead. Experiments were made on alloys con- 
taining different percentages of lead. The following is a condensed 
statement of the chief results: 

Cu, 60; Zn, 30; Pb, 10. Difficult to obtain a homogeneous alloy. 
Cracked badly on roUing. 

Cu, 60; Zn, 35; Pb, 5. Good cutting qualities but cracked on rolling. 

Cu, 60; Zn, 37.5: Pb, 2.5. Cutting qualities excellent, but could 
only be hot-rolled or forged with difficulty. 

Cu, 60; Zn, 38.75; Pb, 1.25. Cutting qualities inferor to those of 
the alloy containing 2.5% of lead, but superior to those of pure brass. 

Cu, 60; Zn, 40. Perfectly homogeneous. Rolls easily at a cherry 
red heat, and cracks but slightly in cold rolling. Chips long and tena- 
cious, necessitating a slow speed in cutting. 

Tensile tests of these alloys gave the following results: 



Copper, % 

Zmc, % 

Lead, % 




60.0 
40.0 




60.0 

37.5 

? 5 






60.0 

35.0 

5 






60.0 
30.0 
in n 














T.S. per sq. in.* 

Elong. in 1 in., %.. . . 
Elong. in 8 in., %.. . . 
Red. of area, % 


C 

48 
27 
61 


A 

J 

33 

44 


H 

107 
1 


13 


C 

39 
28 
27 
30 


A 

51 
27 
23 
33 


H 

88 





C 

33 
28 
27 
26 


A 

42 
26 
22 
33 


H 

61 
1 





C 

36 
36 
30 
29 


A 

35 
20 
16 
25 


H 

63 
2 
3 

4 


P.R 


92 C7^ 


65% 


61 c%. 


38% 





























* Thousands of pounds. C, casting; A, annealed sheet; 
rolled sheet; P. R., possible reduction in rolling. 



H, hard 



_ The use of tin, even in small amounts, hardens and increases the ten- 
sile strength of brass, which is detrimental to free turning. Mr. Sperry 
givas analyses of several brasses which have given excellent results in 
turning, all included within the following range: Cu, 60 to 66%, Zn, 38 
to 32%, Pb, 1.5 to 2.5%. For cartridge-brass sheet, anything over 
0.10% of lead increases the liability of cracking in drawing. 

PHOSPHOR-BRONZE AND OTHER SPECIAL. BRONZES. 

Phosphor-bronze. — In the year 1868, Montefiore & Kunzel of Liege. 
Belgium, found by adding small proportions of phosphorus or "phos- 
phoret of tin or copper" to copper that the oxides of that metal, nearly 
always present as an impurity, more or less, were deoxidized and the 
copper much improved in strength and ductilitv, the grain of the frac- 
ture became finer, the color brighter, and a greater fluidity was attained. 



ALLOYS FOR CASTING UNDER PRESSURE. 



395 



Three samples of phosphor-bronze, tested by Kirkaldy, gave 

24,700 16,100 

46,100 44,448 

1.50 33.40 



23,800 

52,625 

8.40 



Elastic limit, lbs. per sq. In. . . . 
Tensile strength, lbs. per sq. in. 
Elongation, per cent 

The strength of phosphor-bronze varies like that of ordinary bronze 
according to the percentages of copper, tin, zinc, lead, etc., in the alloy. 

Phosphor-bronze Rod. — Torsion tests of 20 samples, 1/4 in. diam. 
Apparent outside fiber stress, 77,500 to 86,700 lbs. per sq. in.; average 
number of turns per inch of length, 0.76 to 1.50. — Tech. Quar., vol. xii, 
Sept., 1899. 

Penn. R. R. Co.'s Speciflcations for Phosphor-bronze (1902). — 
The metal desired is a homogeneous alloy of copper, 79.70; tin, 10.00; 
lead, 9.50; phosphorus, 0.80. Lots will not be accepted if samples do 
not show tin, betvreen 9 and 11%; lead, between 8 and 11%; phos- 
phorus, between 0.7 and 1%; nor if the metal contains a sum total 01 
other substances than copper, tin, lead, and phosphorus in greater quan- 
tity than 0.50 per cent. (See also p. 406.) 

Deoxidized Bronze. — This alloy resembles phosphor bronze some- 
what in composition and also delta metal, in containing zinc and iron. 
The following analysis gives its average composition: Cu, 82.67; Sn, 12.40; 
Zn, 3.23; Pb, 2.14; Fe, 0.10; Ag, 0.07; P, 0.005. 

Comparison of Copper, Silicon-bronze, and Phosphor-bronze 
Wires. (Engineering, Nov. 23, 1883.) 



Description of Wire. 



Pure copper 

Silicon bronze (telegraph). . . 

" (telephone). . . 

Phosphor bronze (telephone) 



Tensile Strength. Relative Conductivity. 



39,827 lbs. per sq. in 
41,696 " •• " " 
108,030 •• " •' " 
102,390 •' •' " •' 



100 per cent. 
96 " '* 
34 " " 
26 " " 



Silicon Bronze. (Aluminum World, May, 1897.) 

The most useful of the siUcon bronzes are the 3% (97% copper, 3% 
silicon) and the 5% (95% copper, 5% silicon), although the hardness 
and strength of the alloy can be increased or decreased at will by 
increasing or decreasing siUcon. A 3% siUcon bronze has a tensile 
strength, in a casting, of about 55,000 lbs. per sq. in., and from 50% to 
60% elongation. The 5% bronze has a tensile strength of about 75,000 
lbs. and about 8% elongation. More than 5% or 5 1/2% of silicon in cop- 
per makes a brittle alloy. In using silicon, either as a flux or for making 
silicon bronze, the rich alloy of siUcon and copper which is now on the 
market should be used. It should be free from iron and other metals if 
the best results are to be obtained. Ferro-siUcon is not suitable for use 
in copper or bronze mixtures. 

Copper and Vanadium Alloys. The Vanadium Sales Co. of America 
reports (1908) that the addition of vanadium to copper has given a tensile 
strength of 83,000 lbs. per sq. in.; with an elongation of over 60%. 

ALLOYS FOR CASTING UNDER PRESSURE IN IVIETAX 
MOLDS. E. L. Lake. Am. Mach., Feb. 13, 1908. 



No. 


Tin. 


Copper. 


Alumi- 
num. 


Zinc. 


Lead. 


Anti- 
mony. 


Iron 


I 


14.75 
19 
12 
30.8 


5.25 

5 

10.6 
20.4 


6.25 
1. 

3.4 
2.6 


73.75 
72.7 
73.8 
46.2 








2 

3 


2 


0.3 


0.2" 


4 

















Nos. 1 and 2 suitable for ordinary work, such as could be performed by 
average brass castings. No. 3 and 4 are harder. 



396 



ALLOYS. 



ALUMINUIVI ALLOYS. 

The useful alloys of aluminum so far found have been chiefly in two 
groups, the one of aluminum with not more than 35% of other metals, and 
the other of metals containing not over 15% of aluminum; in the one case 
the metals impart hardness and other useful qualities to the aluminum, 
and in the other the aluminum gives useful qualities to the metal with 
which it is alloyed. 

Aluminum-Copper Alloys. — The useful aluminum-copper alloys can 
be divided into two classes, — the one containing less than 11% of 
aluminum, and the other containing less than 15% of copper. The first 
class is best known as Aluminum Bronze. 

Aluminum Bronze. (Cowles Electric Smelting and Al. Co.*s circular.) 
The standard A No. 2 grade of aluminum bronze, containing 10% of 
aluminum and 90% of copper, has many remarkable characteristics 
which distinguish it from all other metals. 

The tenacity of castings of A No. 2 grade metal varies between 75,000 
and 90,000 lbs. to the square inch, with from 4 % to 14 % elongation. 

Increasing the proportion of aliuninum in bronze beyond 11% pro- 
duces a brittle alloy; therefore nothing higher than the A No. 1, which 
contains 11%, is made. 

The B, C, D, and E grades, containing 7 3^%, 5%, 2 M%, and 1H% 
of aluminum, respectively, decrease in tenacity in the order named, that 
of the former being about 65,000 pounds, while the latter is 25,000 
pounds. While there is also a proportionate decrease in transverse and 
torsional strengths, elastic limit, and resistance to compression as the 
percentage of aluminum is lowered and that of copper raised, the ductil- 
ity, on the other hand, increases in the same proportion. The specific 
gravity of the A No. 1 grade is 7.56. 

» Bell Bros., Newcastle, gave the specific gravity of the aluminum 
bronzes as follows: 

3%, 8.691; 4%, 8.621; 5%, 8.369; 10%, 7.689. 

In manufacturing aluminum bronze, only the purest metals should 
be used. The copper should be melted over a gas or oil fire in a plum- 
bago crucible, being covered with charcoal to prevent oxidation and 
the absorption of gases. If a coal fire is used, the copper will absorb 
gases from the coal and produce an unsatisfactory alloy. The aliuni- 
num is dropped through the charcoal into the molten copper. The alu- 
minum combines with the copper as soon as its melting point is reached, 
setting free latent heat and raising the temperature of the mass. The 
copper becomes brighter and more liquid when the union takes place, 
and the crucible then should be instantly removed from the fire, 
skimmed, and poured into ingot molds of convenient size. The liquid 
should be stirred until poured. The alloy may then be remelted for 
casting. Each remelting improves the quality of the aluminum bronze 
up to about four remeltings. (Aluminum Co. of x\merica, 1909.) 

Tests of Aluminum Bronzes. 

(John H. J. Dagger, British Association, 1889.) 



Per cent 


Tensile Strength. 


Elonga- 
tion, 
per cent. 


Specific 
Gravity. 


of 
Aluminum. 


Tons per 
square inch. 


Pounds per 
square inch. 


n 


40 to 45 
33 " 40 
25 " 30 
15 " 18 
13 " 15 
11 " 13 


89,600 to 100,800 
73,920 *♦ 89,600 
56,000 *• 67,200 
33,600 " 40,320 
29,120 " 33,600 
24,640 " 29,120 


8 
14 
40 
40 
50 
55 


7 23 


10 


7 69 


71/2 

5-51/2 


«.00 
8 37 


21/2 


8.69 


n/4 



Casting. — The melting point of aluminum bronze varies sUghtly with 
the amount of aluminum contained, the higher grades melting at a 
lower temperature than the lower grades. The A No. 1 grades melt 
at about 1700° F., a little higher than ordinary bronze or brass. 



ALUMINUM ALLOYS. 



397 



Aluminum bronze shrinks more than ordinary brass. As the metal 
sohdifies rapidly it is necessary to pour it quickly and to make the 
feeders amply large, so that there will be no "freezing" in them before 
the casting is properly fed. Baked-sand molds are preferable to green 
sand, except for small castings, and when fine skin colors are desired in 
the castings. (Thos. D. West. Trans. A. S. M. E., 1886, vol. viii.) 

All grades of aluminum bronze can be rolled, s wedged, spun, or drawn 
cold except A 1 and A 2. They can all be worked at a bright red heat. 

In roUing, s wedging, or spinning cold, it should be annealed very often 
and at a brighter red heat than is used for anneaUng brass. 

Seamless Tubes. — Leonard Waldo, Trans. A. S. M. E., vol. xviii, 
describes the manufacture of aluminum bronze seamless tubing. Many 
difficulties were met in all stages of the process. A cold drawn bar, 1.49 
in. outside diameter, 0.05 in. thick, showed a yield point of 68.700, and 
a tensile strength of 96,000 lb. per sq. in. with an elongation of 4.9% in 
10 in. ; heated to bright red and plunged in water, the yield point re- 
duced to 24,200 and the T. S. to 47,600 lb. per sq. in., and the elonga- 
tion in 10 in. increased to 64.9%. 

Brazing. — Aluminum bronze will braze as well as any other metal, 
using one-quarter brass solder (zinc 500, copper 500) and three-quarters 
borax, or, better, three-quarters cryoUte. 

Soldering. — Aliuninum bronze can be soldered by using a solder of 
pure block tin with a flux of zinc fiUngs and muriatic acid. It is advis- 
able to "tin" the two surfaces before putting them together. 

Aluminum Brass. — (E. H. Cowles, Trans. A. I. M. E., vol. xviii.) — 
Cowles aluminum brass is made by fusing together equal weights of A 1 
almninum bronze, copper, and zinc. The copper and bronze are first 
thoroughly melted and mixed, and the zinc is finally added. The 
material is left in the furnace imtil small test-bars are taken from it and 
broken. When these bars show a tensile strength of 80,000 pounds or 
over, with 2 or 3 per cent ductiUty, the metal is ready to be poured. 
Tests of this brass, on small bars, have at times shown as high as 
100,000 pounds tensile strength. 

The Alimiinum Co. of America says (1909) that aluminum brass has 
an elastic hmit of about 30,000 lb. per sq. in., an ultimate strength of 
40,000 to 50,000 lb. per sq. in., and an elongation of 3% to 10% in 8 in. 
Alunmium brass is used with aluminura ranging from 0.1% to 10%. 
The best results are obtained by introducing the aluminum in the form 
of aluminized zinc, a 5 % aluminized zinc being used where less than 1 % 
of aluminum is required and a 10 % almninized zinc for aluminum per- 
centages of over 1 %. The effect of aluminum in brass in quantities of 
less than 1 % is to make the brass flow freely and to insure a sounder 
casting, and it enables from one-half to one-third more castings to be 
made on a gate than is possible where aluminum is not used. In quan- 
tities over 1 % up to 10% the aluminum increases the strength of brass, 
enabling a cheaper grade of brass to be used than would otherwise be 
possible. Inasmuch as aluminum lowers the melting point of brass, 
great care must be taken not to overheat it in melting. 

Tests of Aluminum Brass. 

(Cowles E. S. & Al. Co.) 



Specimen (Castings) 



1 5%A grade Bronze 

17% Zinc 

68% Copper 

I part A Bronze. . 

1 part Zinc. -. 

1 part Copper 

1 part A Bronze. . 

\ part Zinc 

I part Copper 



Diameter 

of Piece, 

Inch. 



0.465 
0.465 
0.460 



Area 
sq. in. 



0.1698 
0.1698 
0.1661 



Tensile 

Strength, 

lbs. per 

sq. in. 



41,225 
78,327 
72,246 



Elasticl 
Limit, 
lbs. per 
sq. in. 



17,668 



Elonga- 
tion, 
per ct. 



4IV2 

2 1/2 

2V2 



Remarks. 



ft ^j-O 



The first brass on the above list is an extremely tough metal with low 



398 



ALLOYS. 



elastic limit, made pm*posely so as to "upset" easily. The other, which 
is called Aluminum brass No. 2, is very hard. 

Caution as to Reported Strength of Alloys. — The same variation in 
strength which has been found in tests of gun-metal (copper and 
tin) noted above, must be expected in tests of aluminum bronze and, in 
fact, of all aUoys. They are exceedingly subject to variation in density 
and in grain, caused by differences in method of molding and casting, 
temperature of pouring, size of and shape casting, depth of "sinking 
head," etc. ChiU-castiugs give higher results than sand-castings, and 
bars cast by themselves purposely for testing almost invariably run 
higher than test bars attached to castings. Bars cut out from castings 
are generally weaker than bars cast alone. 

Effect of Copper on Aluminum. — Tests of rolled sheets of aluminum, 
0.04 in. thick, with varying percentages of copper are reported in The 
Engineer, Jan. 2, 1891, as follows: 

Alimiinum, per cent 100 

Copper, per cent 

Specific gravity, calculated 

Specific gravity, determined. . 2.67 
Tensile strength, lb. per sq.in. 25,535 

Tests of Aluminum Alloys. 

(Engineer Harris, U. S. N., Trans. A. I. M. E., vol. xviii.) 



98 


96 


94 


92 


2 


4 


6 


8 


2.78 


2.90 


3.02 


3 14 


2.71 


2.77 


2.82 


2.85 


3,563 


44,130 


54,773 


50,374 



Composition. 


Tensile 

Strength 

per sq. 

in., lb. 


Elastic 
Limit, 
lb. per 
sq. in. 


Elonga- 
tion, 
per ct. 


Reduc- 
tion of 
Area, 
per ct. 


Copper. 


Alumi- 
num. 


Silicon. 


Zinc. 


Iron. 


91 .50% 

88.50 

91.50 

90.00 

63.00 

63.00 

91.50 

93.00 

88.50 

92.00 


6.50% 

9.33 

6.50 

9.00 

3.33 

3.33 

6.50 

6.50 

9.33 

6.50 


1.75% 

1.66 

1.75 

1.00 

0.33 

0.33 

1.75 

0.50 

1.66 

0.50 


33:33% 
33.33 


0.25% 

0.50 

0.25 

6:25' 
6:50 


60,700 
66,000 
67,600 
72,839 
82,200 
70,400 
59,100 
53,000 
69,930 
46,530 


18,000 
27,000 
24,000 
33,000 
60,000 
55,000 
19,000 
19,000 
33,000 
I 7,000 


23.2 
3.8 

13 

2.40 
2.33 
0.4 

15.1 
6.2 
1.33 
7.8 


30.7 
7.8 

21.62 
5.78 
9.88 
4.33 

23.59 

15.5 
3.30 

19.19 



For comparison with the above 6 tests of "Navy Yard Bronze," 
Cu 88, Sn 10, Zn 2, are given in which the T. S. ranges from 18,000 to 
24,590, E. L. from 10,000 to 13,000, El. 2.5 to 5.8%, Red. 4.7 to 10.89. 

Alloys of Aluminum, Silicon and Iron. 

M. and E. Bernard have succeeded in obtaining through electrolysis, 
by treating directly and without previous purification, the aluminum 
earths (red and white bauxites), the following: 

Alloys such as ferro-aluminum, ferro-sihcon-aluminum, and siUcon- 
almninum, where the proportion of silicon may exceed 10%, which are 
employed in the metallurgy of iron for refining steel and cast-iron. 

Also silicon-aluminum, where the proportion of silicon does not exceed 
10%, which may be employed in mechanical constructions in a roUed or 
hammered condition, in place of steel, on account of their great resist- 
ance, especially where the hghtness of the piece in construction consti- 
tutes one of the main conditions of success. 

The following analyses are given: 

1. Alloys apphed to the metallurgy of iron, the refining of steel and 
cast iron: No. 1, Al. 70%; Fe, 25%; Si, 5%. No. 2, Al, 70; Fe. 20; 
Si. 10. No. 3, Al, 70; Fe, 15; Si, 15. No. 4, Al. 70; Fe, 10; Si, 20. 
No. 5, Al, 70; Fe, 10; Si, 10; Mn, 10. No. 6, Al. 70; Fe, trace; Si, 20; 
Mn, 10. 

2 Mechanical alloys: No. 1, Al, 92; Si, 6.75; Fe, 1.25. No. 2, Al, 
90; Si, 9.25; Fe, 0.75. No. 3, Al, 90; Si, 10; Fe, trace. The best results 
were with alloys whene the proportion of iron was very low, and the 
proportion of silicon in the neighborhood of 10%. Above that pro- 
portion the alloy becomes crystaUine and can no longer be employed. 



ALtTMINUM ALLOYS. 399 

The density of the alloys of silicon is approximately the same as that of 
aluminum. — La Metallurgie, 1892. 

Aluminum-Tungsten Alloys have been somewhat used in Europe 
in the form of rolled sheets under the trade name of Wolfranium. An 
aluminum-tungsten alloy used in France (1898) for motor-car bodies 
has the following properties: Cast, sp. gr. 2.86; T.S., 17.000 to 24,000; 
elong., 12 to 6%. Rolled, sp. gr., 3.09; T.S., 45,500 to 53,600; elong.i 
8 to 6%. 

Aluminum -Antimony alloys have been produced, but have a scien- 
tific rather than a commercial interest. The alloy whose composition 
is Sb Al has a liigher meltmg pomt than either of its constituents. 

Aluminum and Manganese. — Manganese is one of the best harden- 
ers of alumimun. Professor Carpenter found that it increased the 
strength when added in quantities up to 10 %. 

Undesirable Aluminum Alloys. — While aluminum will combine 
with all the metalloids and gaseous elements, such as oxygen, mtrogen, 
sulphur, selenium, clilorine, iodine, boron, silicon, and carbon, no useful 
result has been recorded from the combination of metaUic aluminum 
with any of these elements. The prevention of the occlusion of gaseous 
metalloids m molten aluminum and the prevention of the union of car- 
bon and aluminum are among the chief precautions to be observed in 
the metallurgy of aluminum. The effect of sodimn and potassium on 
alumimun is as undesirable as the effect of phosphorus and sulphur on 
steel. (Aluminum Co. of America.) 

Aluminum -Magnesium. — Magnalium. — A patented aUoy of alumi- 
num. and magnesium, containing 90 to 98% Al has the trade name 
"magnaUum." It is Ughter than aluminum (sp. gr. 2.5), and is whiter, 
harder, and stronger. It can be forged, roUed, drawn, machined, and 
filed. It resists oxidation better than other light metals or alloys. 
Tensile strength: cast, 18,400 to 21,300 lb. per sq. m., with a reduction 
of area 3.75%; rolled, 52,200 lb. per sq. m., with a reduction of area 
of 3.7%; annealed, 42,200 lb. per sq. in., reduction, 17.8%. Al Mg 
aUoys are said by the Aluminum Co. of America to be as strong as Al 
Cu alloys. 

Aluminum and Iron. — Aluminum aUoys with cast-iron up to 15% 
Al, but the metal decreases in strength as the Al increases. Above 15 % 
Al the alloys are granular and have practically no coherence. (Trans. 
A. I. M. E., vol. xviii, A. S. M. E., vol. xix.) It is doubtful if aluminum 
has much effect on soft gray No. 1 foundry iron, except to keep the 
metal molten a longer time. With difficult castings, where loss is 
occasioned by defective castings or where the iron does not flow freely, 
the addition of aluminum wiU improve the quaUty of the casting, and 
give a closer gramed iron. The addition of 2 % or more of Al will de- 
crease the shrinkage of cast iron. In wrought iron, 1 % Al makes the 
metal more fluid at 2200° F. than it would be at 3500° F. without Al. 
An addition of 0.25 % Al to the bath causes the charge to stiffen more 
quickly. (Aluminum Co. of America, 1909.) 

Aluminum, Ck)pper, and Tin. — Prof. K. C. Carpenter, Trans, 
A. S. M. E., vol. xix., finds the following alloys of maximum strength in 
a series in which two of the three metals are in equal proportions : 

Al, 85; Cu, 7.5; Sn, 7.5; tensile strength, 30,000 lb. per sq. m. 
elongation in 6 in., 4%; sp. gr., 3.02. Al, 6.25; Cu, 87.5; Sn, 6.25 
T. S., 63,000; EL, 3.8; sp. gr., 7.35. Al, 5; Cu, 5; Sn, 90; T. S., 11,000 
El., 10.1; sp. gr., 6.82. 

From 85 to 95% Cu the bars have considerable strength, are close 
grained and of a golden color. Between 78 and 80 % the color changes 
to silver white and the bars become brittle. From 78 to 20% Cu the 
alloys are very hard and brittle, and worthless for practical purposes. 
Aluminum is strengthened by the addition of 3qual parts of copper and 
tm up to 7.5% of each, beyond which the strength decreases. All the 
alloys that contain between 20 and 60 % of either one of the three metals 
are very weak. 

Aluminum and Zinc. — (Alimiinum Co. of America, 1909.) Like the 
copper alloys, the zinc alloys can be divided into two classes, (1) those 
contaimng a relatively small amount of aluminum, and (2) those con- 
taining less than 35 % of zinc. The first class is known as *' aluminized 
zinc," and the second comprises the zinc casting alloys. Zinc produces 
the strongest alloy of aluminum, which strength can be increased by the 



400 ALLOYS. 

addition of other metals. The strongest zinc-aluminum alloy may be 
as High as 35,000 lb. per sq. in. The high zinc alloys are brittle and 
more liable to "draw in heavy parts or lugs than are copper alloys. 
This can often be overcome by suitable gating, chills, and risers. There 
is also danger of burning out the zinc and producing a weaker casting. 
For forging, a zinc-aluminum alloy of 10 to 15% zinc gives excellent 
results. It is tough, flows well in the dies, is easily machined and is 
remarkably strong per imit of area. , . . ^ . i • 

Aluminized zinc is used in the bath for galvamzmg and m alummmn 
brass. It is made by melting aluminum in the crucible and then grad- 
ually stirring in the zinc, after which it is cast into ingots. The 5% 
alloy is used in the galvanizing bath and for low grade aluminum 
brass, and the 10 % alloy for high-grade brass castings. It is introduced 
in the molten metal the same as pure zinc. In galvanizing it is added 
in such proportions that the total amount of aluminum in the bath 
will be about 1 lb. of aluminum per ton of bath, or about 20 lb. of 5% 
alloy per ton of bath. It should be added gradually, and as the bath is 
consumed fresh 5% alloy should be added about 1 lb. at a time for a 
5-ton bath. When aluminized zinc is used it is unnecessary to use 
sal ammoniac to clear the bath of oxide. In starting a new bath, how- 
ever, after adding the aluminized zinc, it is stirred well until the alunu- 
mun combines with the impurities, which rise to the surface as a scum. 
This is removed, some sal ammoniac is added to coimteract the effects 
of the aluminum, and the proportion of alloy added is reduced. ^ 

Aluminum and Tin. — (Aluminum Co. of America, 1909.) Tin, al- 
loyed with aluminum in proportions of from 1 to 15%, gives added 
strength and rigidity to heavy castings, increases the sharpness of 
outUne and decreases shrinkage. The aluminum-tin alloys are rather 
brittle, and although small proportions of tin in certain casting aUoys 
have been advantageously used to decrease shrinkage, they are com- 
paratively httle used on account of the relative cost and brittleness. 

Aluminum and Nickel. — (Aluminum Co. of America, 1909.) Al- 
uminum-nickel alloys with 2 to 5 % of the combined alloying metals are 
satisfactory for rolUng or hammering. A 7 to 9% aUoy produces good 
results in casting. _ „ ^^ t^^t ■• o • 

Other Aluminum Alloys. — Al 75.7, Cu. 3, Zn 20, Mn 1 3 is an 
excellent casting metal, having a tensile strength of oyer 35,000 lb. 
per SQ. in., and a sp. gr. sUghtly ^bove 3. It has very httle ductility ^ 

Al 96.5, Cu 2, and chromium 1.5 is a httle heavier than pure alumi- 
num and has a tensile strength of 26,300 lb. per sq. in. — A. S. M. is., 

vol. Xix. , . '. 'x.x^ n 

With the exception of lead and mercury, aluminum unites with all 
metals, though it unites with antimony with great diificulty. A smaU 
percentage of silver whitens and hardens the metal, and gives it addea 
strength; and this alloy is especiaUy appUcable to the manufacture of 
fine instruments and apparatus. The following aUoys have been found 
recently to be useful in the arts: Nickel- aluminum, composed of 20 parts 
nickel to 80 of aluminum; rosine, made of 40 parts nickel, 10 parts silver, 
30 parts aluminum, and 20 parts tin, for jewellers' work ; naettahne, made 
of 35 parts cobalt, 25 parts aluminum, 10 parts iron, and 30 parts copper. 
The aluminum-bourbouze metal, shown at the Paris Exposition of 1889, 
has a specific gravity of 2.9 to 2.96, and can be cast in very sohd shapes, 
as it has very httle shrinkage. From analysis the f9llo wing composi- 
tion is deduced: Aluminum, 85.74%; tin, 12.94%; silicon, 1.32%; u-on. 

Aluminum Alloys used in Automobile Construction (Am. Mach., 
Aug. 22, 1907.) 

(1) Al 2, Zn, 1, T.S. 35,000; Sp. gr. 3.1 

(2) Al 92, Cu, 8, T.S. 18,000; Sp. gr. 2.84 Ni, trace • 

(3) Al 83, Zn, 15, Cu, 2, T.S. 23,000; Sp. gr. 3.1 

(1) Unsatisfactory on account of failures under repeated vibration. 
(2) GeneraUy used. Resists vibrations well. (3) Used to some extent. 
Many motor-car makers dechne to use it because of uncertainty ot its 
behavior under vibration. , . . j 

The Thermit Process. — When finely divided aluminum is mixed 
with a mctalhc oxide and ignited the aluminum burns with great rapid- 
ity and intense heat, the chemical reaction being Al -h Fe203 ^ AI2U3 



ALLOYS OF MANGANESE AND COPPER. 



401 



+ Fe. The heat thus generated may be used to fuse or weld iron and 
other metals. See the Thermit Process, under Welding of Steel, page 
488. 

Resistance of Aluminum Alloys to Corrosion. — J. W. Richards, 
Jour. Frank, Inst., 1895, gives the following table showing the relative 
resistance to corrosion of aluminum (99 % pure) and alloys of aluminum 
with different metals, when immersed in the hquids named. The 
figures are losses per day in miUigrams per square centimeter of surface: 



3 per cent copper 

3 per cent German silver . 

3 per cent nickel 

2 per cent titanium 

99 per cent aluminimi .... 



Caustic 

Potash. 

Cold. 



265.0 
1534.4 

580.3 
73.4 
35.6 



3% 
Hydro- 
chloric 

Acid. 

Cold. 



53.3 

130.6 

180.0 

4.3 

5.8 



Strong 
Nitric 
Acid. 
Cold. 



36.1 
97.7 
83.0 
18.6 
9.6 



Strong 
Salt 

Solu- 
tion. 

150°F. 



0.1 

0.05 

0.13 

0.06 

0.04 



Strong 

Acetic 

Acid. 

140° F. 



0.4 

0.6 

0.75 

0.20 

0.15 



Car- 
bonic 
Acid. 
Water. 
77° F. 



0.0 

0.01 

0.04 

0.0 

0.01 



ALLOYS OF MANGANESE AND COPPER. 

Various Manganese Alloys. — E. H. Cowles, in Trans. A. I. M. E., 
vol. xviii, p. 495, states that as the result of numerous experiments on 
mixtures of the several metals, copper, zinc, tin, lead, aluminum, iron, 
and manganese, and the metalloid silicon, and experiments upon the 
same in ascertaining tensile strength, ductility, color, etc., the most 
important determinations appear to be about as follows: 

1. That pure metalUc manganese exerts a bleaching effect upon cop- 
per more radical in its action even than nickel. In other words, it was 
found that 18 }i % of manganese present in copper produces as white a 
color in the resulting alloy as 25 % of nickel would do, this being the 
amount of each required to remove the last trace of red. 

2. That upwards of 20 % or 25 % of manganese may be added to cop- 
per without reducing its ductility, although doubhng its tensile strength 
and changing its color. 

3. That manganese, copper, and zinc, when melted together and 
poured into molds behave very much like the most "yeasty" German 
silver, producing an ingot which is a mass of blow-holes, and which 
swells up above the mold before coohng. 

4. That the alloy of manganese and copper by itself is very easily 
oxidized. 

5. That the addition of 1.25% of aluminum to a manganese-copper 
alloy converts it from one of the most refractory of metals in the casting 

Erocess into a metal of superior casting qualities, and the non-corrodi- 
iUty of which is in many instances greater than that of either German 
or nickel silver. 

A "silver-bronze" alloy especially designed for rods, sheets, and wire 
has the following composition: Mn, 18; Al, 1.20; Si, 0.5; Zn, 13; and Cu, 
67.5%. It has a tensile strength of about 57,000 lbs. on small bars, and 
20% elongation. It has been rolled into thin plate and drawn into wire 
0.008 inch in diameter. A test of the electrical conductivity of this 
wire (of size No. 32) shows its resistance to be 41.44 times that of pure 
copper. This is far lower conductivity than that of German silver. 

Manganese Bronze. (F. L. Garrison, Jour. F. /., 1891.) — This 
alloy has been used extensively for casting propeller-blades. Tests of 
some made by B. H. Cramp & Co., of Philadelphia, gave an average 
elastic Umit of 30,000 lbs. per sq, in., tensile strength of about 60,000 lbs. 
per sq. in. with an elongation of 8% to 10% in sand castings. When 
rolled, the E. L. is about 80,000 lbs. per sq. in., tensile strength 95,000 to 
106,000 lbs. per sq. in., with an elongation of 12% to 15%. 

Compression tests made at United States Navy Department from the 
metal in the pouring-gate of propeller-hub of U. S. S. Maine gave in 
two tests a crushing stress of 126,450 and 135,750 lb. per sq. in. The 
specimens were 1 inch high by 0.7 x 0.7 inch in cross-section = 0.49 
square inch. Both specimens gave way by shearing, on a plane making 
an angle of nearly 45° with the direction of stress. 
A test on a specimen 1 X 1 X 1 inch was made from a piece of the 



402 



ALLOYS. 



same pouring*ga1ei "Under stress of ISO.OOT) pounds It was ^attertfed to 
0.72 inch high by about 1 1/4 x 1 V4 inches, but without rupture or any 
sign of distress. 

One of the great objections to the use of manganese bronze, or in fact 
any alloy except iron or steel, for the propellers of iron ships is on 
account of the galvanic action set up between the propeller and the 
stern-posts. This difficulty has in great measure been overcome by 
putting strips of rolled zinc around the propeller apertures in the stern- 
frames. 

The following analysis of Parsons' manganese bronze No. 2 was made 
from a chip from the propeller of Mr. W. K. Vanderbilt's vacht Alva. 
Cu, 88.64; Zn, 1.57; Sn, 8.70; Fe, 0.72; Pb, 0.30; P, trace. 

It will be observed there is no manganese present and the amount of 
zinc is very small. 

E. H. Cowles, Trans. A. I. M. E., vol. xviii, says: Manganese bronze, 
so called, is in reality a manganese brass, for zinc instead of tin is the 
chief element added to the copper. Mr. P. M. Parsons, the proprietor of 
this brand of metal, has claimed for it a tensile strength of from 24 to 
28 tons per sq. in. in small bars when cast in sand. 

E. S. Sperry, Am. Mach., Feb. 1, 1906, gives the following analyses of 
manganese bronze: 





Cu. 


Zn. 


Fe. 


Sn. 


Al. 


Mn. 


Pb. 


No. 1 


60.27 
56.11 
60.00 
56.00 


37.52 
41.34 
38.00 

42.38 


1.41 
1.30 
1.25 
1.25 


0.75 
0.75 
0.65 
0.75 


6:47" 


0.01 
0.01 
0.10 
0.12 


0.01 


" 2 


0.02 


" 3 




" 4 





No. 1 is Parsons' alloy for sheet. No. 2 for sand casting. No. 3 is Mr. 
Sperry 's formula for sheet, and No. 4 his formula for sand castings. 
The mixture for No. 3, allowing for volatilization of some zinc is: copper: 
60 lbs.; zinc, 39 lbs.; "steel alloy," 2 lbs. That for No. 4 is: copper, 
56 lbs.; zinc, 43 lbs.; "steel alloy," 2 lbs.; aluminum, 0.5 lb. The steel 
alloy is made by melting wrought iron, 18 lbs.; ferro-manganese 
(80 Fe, 20 Mn), 4 lbs.; tin, 10 lbs. The iron and ferro-manganese are 
first melted and then the tin is added. In making the bronzes about 
15 lbs. of the copper is first melted under charcoal, the steel alloy is 
added, melted and stirred, then the aluminum is added, melted and 
stirred, then the rest of the copper is added, and finally the zinc. The 
only function of the manganese is to act as a carrier to the iron, which 
is difficult to alloy with copper without such carrier. The iron is 
needed to give a high elastic limit. Green sand castings of No. 4 fre- 
quently give results as high as the following: T. S., 70,000; E L 
30,000 lbs. per sq. in.; elongation in 6 ins., 18%; reduction of areai 
26%. 

Magnetic Alloys of ]Von-3Iagnetic Metals. (El. World, April 15 
1905; Electrot.'Zeit. Mar. 2, 1905.) — Dr. Heusler has discovered that 
alloys of manganese, aluminum, and copper are strongly magnetic. The 
best results have been obtained when the Mn and Al are in the proportions 
of their respective atomic weights, 55 and 27.1. Two such allovs are 
described (1) Mn, 26.8; Al, 13.2; Cu, 60. (2) Mn, 20.1; Al, 9.9: Cu, 70, 
with 1% Pb added. The first was too brittle to be workable. The 
second was machined without difficulty. These alloys have as yet no 
commercial importance, as they are far inferior magnetically (at most 
1 to 4) to iron. 

GERMAN-SILVER AND OTHER NICKEL ALLOTS. 

German Silver. — The composition of German silver is a very un- 
certain tlung and depends largely on the honesty of the manufacturer 
ana the price the purchaser is willing to pay. It is composed of copper 
fl^^ i^Jl^ ."^^oH:^rl ^^c X^^y\^S proportions. The best varieties contain 
from 18% to 25% of nickel and from 20% to 30% of zinc, the remainder 
??S^ S^PP^-, ^J^? ™^^^ expensive nickel silver contains from 25% to 
33% of nickel and fr9m 75% to 66% of copper. The nickel is used as a 
whitenins: element; it also strengthens the alloy and renders it harder 
and more non-corrodible than the brass made without it, of copper and 



ALLOYS OF NICKEL. 



403 



7inc. Of all troublesome alloys to handle in the foundry or rolling-mill, 
German silver is the worst. It is unmanageable and refractory at every 
step in its transition from the crude elements into rods, sheets, or wire. 
CE. H. Cowles. Trans, A. I. M. 'E., xviii. p. 494.) 
The following list of copper-nickel alloys is from various sources: 





Copper. 


Nickel. 


Tin. 


Zinc. 


German silver 


51.6 
50.2 
51.1 
52 to 55 
75 to 66 
40.4 

8 

2 

8 

8 


25.8 

14.8 

13.8 

18 to 25 

25 to 33 

31.6 

3 

1 

2 
3 


22.6 
3.1 
3.2 






31.9 


it ii 


31.9 


<t «t 


20 to 30 


Nickel " 






Chinese packfong 




6.5 parts 
6.5 " 


" tutenag 




Germ.an silver 




1 


" *' (cheaper) 




3.5 •• 


** '* (resembles silver) . 




3 5** 









Nickel-copper Alloys. — (F. L. Sperry, A. I. M. E., 1895.) 





Copper. 


Nickel. 


Zinc. 


Iron. 


Cobalt. 


Berlin 


52 to 63 

50 

65.4 

50 
50 to 60 
45.7 to 60 

52.5 

50 

88 

75 


22 to 6 
18.7 to 20 

16.8 

50 
25 to 20 
31.6 to 15 

17.7 

25 

12 

25 


26 to 31 

31.3 to 30 

13.4 






French, tableware 






Maillechort 


3.4 




Christofle 




Austrian, tableware 


25 to 20 
25.4 to 17 

28.8 

25 






Engli.sh, Sheffield 

American, castings 


to 2.6 


to 3.4 


" bearings 






** one-cent coin 






Nickel coins 

















A refined copper-nickel alloy containing 50% copper and 49% nickel, 
with very small amounts of iron, silicon and carbon, is produced direct 
from Bessemer m-atte in the Sudbury (Canada) Nickel Works. German- 
silver manufacturers purchase a ready-made alloy, which melts at a 
low heat and requires only the addition of zinc, instead of buying the 
nickel and copper separately. This alloy, "50-50" as it is called, is 
almost indistinguishable from pure nickel. Its cost is less than nickel, 
its melting-point much lower, it can be cast solid in any form desired, 
and furnishes a casting which works easily in the lathe or planer, yield- 
ing a silvery- white surface unchanged by air or moisture. For bullet 
casings now used in various British and Continental rifles, a special alloy 
of 80% copper and 20% nickel is made. 

Monel Metal. — An alloy of about 72% Ni, 1.5 Fe. 26.5 Cu, made from 
the Canadian copper-nickel ores, is described in the Metal Worker, Oct. 10, 
1908. It has many valuable properties when rolled into sheets, making 
it especially suitable for roohng. It is ductile and flexible, is easily 
soldered, has a high resistance to corrosion, and a relatively small expan- 
sion and contraction under temperature changes. The tensile strength 
in castings is from 70,000 to 80,000 lbs. per sq. in., and in rolled sheets as 
high as 108,000 lbs. 

The Supplee-Biddle Hardware Co.'s Bulletin, Jan., 1915, gives the 
following results of tests of bars of monel metal. The test pieces were 
0.505 in. diam. 

Tensile El. Elong. Red. o 

Strength Limit. in 2 in. Area 

Bar from 1 in. sq. casting 79,600 31,800 49.2% 39.3% 

Hot rolled 1-in. rod. 88,150 58,000 36.0 67.9 

The strength of monel metal wire, used for window screen cloth, is 
given as 90,000 lb. per sq. in., and its analysis 68% Ni, 28% Cu., 2.5% 
Fe. 1.5% Mn. 

Constantan is an alloy containing about 60% copper and 40% nickel, 
which is much used for resistance wire in electrical instruments. Its 
electrical resistance is about twenty-eight to thirty times that of copper, 
and it possesses a very low temperature coefficient, -^^approximately 



404 



ALLOYS. 



.00003. This same material is also much used to form one element of 
base-metal thermo-couples. 

Manganin, Cu Mn Ni, high resistance alloy. See Electrical Resist- 
ance under Electrical Engineering. 

ALLOYS OF BISMUTH. 

By adding a small amount of bismuth to lead the latter may be 
hardened and toughened. An alloy consisting of three parts of lead 
and two of bismuth has ten times the hardness and twenty times the 
tenacity of lead. The alloys of bismuth with both tin and lead are 
extremely fusible, and take fine impressions of casts and molds. An 
alloy of one part Bi, two parts Sn, and one part Pb is used by pewter- 
workers as a soft solder, and by soap-makers for molds. An alloy of five 
parts Bi, two parts Sn, and three parts Pb imelts at 199° F., and is 
somewhat used for stereotyping, and for metallic writing-pencils. Thorpe 
gives the following proportions for the better-known fusible metals: 



Name of Alloy. 


Bis- 
muth. 


Lead. 


Tin. 


Cad- 
mium. 


Mer- 
cury. 


Melting- 
point. 


Newton's 


50 
50 
50 
50 
50 
50 
50 


31.25 
28.10 
25.00 
25.00 
25.00 
26.90 
20.55 


18.75 
24.10 
25.00 
25.00 
12.50 
12.78 
21.10 






202° F. 


Rose's 






203° '* 


D'Arcet's 






201° •• 


D' Arcet's with mercury 
Wood's 


'"i2!56' 
10.40 
14.03 


250.0 


113°'* 
149° " 


Lipowitz's 


149° " 


Guthrie's " Eutectic ". 


"Very low.** 



The action of heat upon some of these alloys is remarkable. Thus, 
Lipowitz's alloy, which soUdifies at 149° F., contracts very rapidly at 
first, as it cools from this point. As the coohng goes on the contrac- 
tion becomes slower and slower, until the temperature falls to 101.3" 
F From this point the alloy expands as it cools, until the temperature 
falls to about 77° F., after which it again contracts, so that at 32° F. 
a bar of the alloy has the same length as at 115° F. 

Alloys of bismuth have been used for making fusible plugs for boilers, 
but it is found that they are altered by the continued action of heat, 
so that one cannot rely upon them to melt at the proper temperature. 
Pure Banca tin is used by the U. S. Government for fusible plugs. 

FUSIBLE ALLOYS. 

(From various sources. Many of the figures are probably very 
inaccurate.) 

Sir Isaac Newton's, bismuth 5, lead 3, tin 2, melts at 212** F. 

Rose's, bismuth 2, lead 1, tin 1, melts at 200 " 

Wood's, cadmium 1, bismuth 4, lead 2, tin 1, melts at 165 ** 

Guthrie's, cadmium 13.29, bismuth 47.38, lead 19.36, tin 19.97, 

melts at 160 ** 

Lead 1, tin 1, bismuth 1, cadmium 1, melts at 155 ** 

Lead 3, tin 5, bismuth 8, melts at 208 ** 

Lead 1, tin 3, bismuth 5, melts at 212 *' 

Lead 1, tin 4, bismuth 5, melts at 240 '* 

Tin 1, bismuth 1, melts at 286 '* 

Lead 2, tin 3, melts at 334 to 367 ** 

Tin 2, bismuth 1, melts at « 336 " 

Lead 1 , tin 2, melts at 340 to 360 *' 

Tin 8, bismuth 1 , melts at 392 " 

Lead 2, tin 1 , melts at 440 to 475 ** 

Lead 1 , tin 1 , melts at 370 to 400 '* 

Lead 1 , tin 3, melts at 356 to 383 " 

Tin 3, bismuth 1 , melts at 392 " 

Lead 1 , bismuth 1 , melts at 257 '* 

Lead 1, tin 1 , bismuth 4, melts at 201 " 

Lead 6, tin 3, bismuth 8, melts at 202 ** 

Tin 3, bismuth 5, melts at 202 " 



BEARING METAL ALLOYS. 



405 



BEARING-METAL ALLOYS. 

(C. B. Dudley, Jour. F. I., Feb. and March, 1892.) 
Alloys are used as bearings in place of wrought iron, cast iron, or 
steel, partly because wear and friction are believed to be more rapid 
when two metals of the same kind work together, partly because the 
soft metals are more easily worked and got into proper shape, and partly 
because it is desirable to use a soft metal which will take the wear 
rather than a hard metal, which will wear the journal more rapidly. 

A good bearing-metal must have five characteristics: (1) It must be 
strong enough to carry the load without distortion. Pressures on car- 
journals are frequently as high as 350 to 400 lb. per square inch. 

(2) A good bearing-metal should not heat readily. The old copper- 
tin bearing, made of seven parts copper to one part tin, is more apt to 
heat than some other alloys. In general, research seems to show that 
the harder the bearing-metal, the more likely it is to heat. 

(3) Good bearing-metal should work well in the foundry. Oxidation 
while melting causes spongy castings. It can be prevented by a Uberal 
use of powdered charcoal while melting. The addition of 1% to 2% of 
zinc or a small amount of phosphorus greatly aids in the production of 
sound castings. This is a principal element of value in phosphor- 
bronze. 

(4) Good bearing-metals should show^ small friction. It is true that 
friction is almost w^holly a question of the lubricant used; but the metal 
of the bearing has certainly some influence. 

(5) Other things being equal, the best bearing-metal is that which 
wears slowest. 

The principal constituents of bearing-metal alloys are copper, tin, 
lead, zinc, antimony, iron, and aluminum. The following table gives 
the constituents of most of the prominent bearing-metals as analyzed at 
the Pennsylvania Railroad laboratory at Altoona. 

Analyses of Bearing- metal Alloys. . 



Metal. 


Copper. 


Tin. 


Lead. 


Zinc. 


Anti- 
mony. 


Iron. 


Camelia m.etal 


70.20 
1.60 


4.25 
98.13 


14.75 


10.20 




0.55 


Anti-friction metal 


trace 


White metal 


87.92 
84.87 

1.15 
67.73 
80.69 
14.57 
12.40 

5.10 
83.55 

78.44 
0.31 
15.06 
12.52 


"85:57 


12.08 
15.10 




Car-brass linin&r 




trace 
9.91 
14.38 




Salgee anti-friction 

Graphite bearing-metal. . . 
Antimonial lead 


4.01 




16.73 
18.83 


? (1) 




.... 
75.47 
77.83 
92.39 
trace 


9.72 
9.60 
2.37 


(2) 


Cornish bronze 


trace 




trace(3> 


Delta metal 


0.07 


* Magnolia metal 


trace 

0.98 
38.40 


16.45 
19.60 


trace(4) 


American anti-friction 
metal 


0.65 


Tobin bronze 


59.66 
75.80 
76.41 
90.52 
81.24 


2.i6 
9.20 

10.60 
9.58 

10.98 


O.ll 






Damascus bronze 














(5) 


Ajax metal 


7.27 
88.32 

■84!33' 

94.40 

9.61 

15.00 






(6) 


Anti-friction metal 


"42:67 
trace 


11.93 

"i4:38 
6.03 




Harrington bronze 

Car-box metal 


55.73 


0.97 


0.68 
0.61 


Hard lead 


. . 






Phosphor-bronze 


79.17 
76.80 


10.22 
8.00 


(7) 


Ex. B. metal 






(si 



Other constituents: 

(1) No graphite. 

(2) Possible trace of carbon. 

(3) Trace of phosphorus. 

(4) Possible trace of bismuth. 



(5) No manganese. 

(6) Phosphorus or arsenic, 0.37. 

(7) Phosphorus, 0.94. 

(8) Phosphorus, 0.20. 



* Dr. H. C. Torrey says this analysis is erroneous and that Magnolia 
metal always contains tin. 



406 ALLOYS. 

As an example of the influence of minute changes in an alloJ^ the Har- 
rington bronze, which consists of a minute proportion of iron in a cop- 
per-zinc alloy, showed after roUing a tensile strength of 75,000 lb. and 
20% elongation in 2 inches. , ^ , . ^ ., , 

In experimenting on this subject on the Pennsylvama Railroad, a 
certain number of the bearings were made of a standard bearing-metal, 
and the same number were made of the metal to be tested. These 
bearings were placed on opposite ends of the same axle, one side of the 
car having the standard bearings, the other the experimental. Before 
going into service the bearings were carefully weighed, and after a 
sufficient time they were again weighed. The standard bearing-metal 
used is the "S beariner-metal" of the Phosphor-Bronze Smelting Co. 
It contains about 79.70% copper, 9.50% lead, 10% tin, and 0.80% phos- 
phorus. A large number of experiments have shown that the loss of 
weight of a bearing of this metal is 1 lb. to each 18,000 to 25,000 miles 
traveled. Besides the measurement of wear, observations were made 
on the frequency of " hot boxes" with the different metals. 

The results of the tests for wear, so far as given, are condensed into 
the following table: ^ 

Composition. Rate 

Metal. f --* * of 

Copper. Tin. Lead. Phos. Arsenic. Wear. 

Standard 79.70 10.00 9.50 0.80 100 

Copper-tin 87.50 12.50 148 

Same, second experiment 153 

Same, third experiment 147 

Arsenic-bronze 89.20 10.00 0.80 142 

Arsenic-bronze 79.20 10.00 7.00 0.80 115 

Arsenic-bronze 79.70 10.00 9.50 0.80 101 

"K" bronze 77.00 10.50 12.50 92 

Same, second experiment 92.7 

Alloy "B" 77.00 8.00 15.00 86.5 

The old copper-tin alloy of 7 to 1 has repeatedly proved its inferiority 
to the phosphor-bronze metal. Many more of the copper-tin bearings 
heated than of the phosphor-bronze. The showing of these tests was so 
satisfactory that phosphor-bronze was adopted as the standard bearing- 
metal of the Pennsylvania R.R., and was used for a long time. 

The experiments, however, were continued. It was found that arsenic 
practically takes the place of phosphorus in a copper-tin alloy, and tkree 
tests were made with arsenic-bronzes as noted above. As the propor- 
tion to lead is increased to correspond with the standard, the durabihty 
increases as well. In view of these results the "K" bronze was tried, in 
which neither phosphorus nor arsenic were used, and in which the lead 
was increased above the proportion in the standard phosphor-bronze. 
The result was that the metal wore 7.30% slower than the phosphor- 
bronze. No trouble from heating was experienced with the **K" bronze 
more than with the standard. Dr. Dudley continues: 

At about this time we began to find evidences that wear of bearing- 
metal alloys variel in accordance with the following law: "That alloy 
which has the greatest power of distortion without rupture (resilience), 
will best resist wear." It was now attempted to design an alloy in 
accordance with this law, taking first the proportions of copper and tin. 
91/2 parts copper to 1 of in was settled on by experiment as the standard, 
although some evidence since that time tends to show that 12 or possi- 
bly 15 parts copper to 1 of tin might have been better. The influence of 
lead on this copper-tin alloy seems to be much the same as a still further 
diminution of tin. However, the tendency of the metal to yield under 
pressure increases as the amount of tin is diminished, and the amount 
of the lead increased, so a limit is set to the use of lead. A certain 
amount of tin is also necessary to keep the lead alloyed with the copper. 

Bearings were cast of the metal noted in the table as alloy *'B," and it 
wore 13.5% slower than the standard phosphor-bronze. This metal is 
now the standard bearing-metal of the Pennsylvania Railroad, being 
slightly changed in composition to allow tne use of phosphor-bronze 
scrap. The formula adopted is: Copper, 105 lbs.: phosphor-bronze, 
60 lbs.: tin. 93/4 lbs.: lead. 251/4 lbs. By using ordinary care in the 
foundry, keeping the metal well covered with charcoal during the melt- 



ALLOYS CONTAINING ANTIMONY. 



407 



lag, no trouble Is found in casting good bearings with this metal. The 
copper and the phosphor-bronze can be put In the pot before putting it 
in the melting-hole. The tin and lead should be added after the pot is 
taken from the fire. 

It is not known whether the use of a little zinc, or possibly some other 
combiaation, might not give still better results. For the present, how- 
ever, this alloy is considered to fulfill the various conditions required for 
good bearing-metal better than any other alloy. The phosphor-bronze 
had an ultimate tensile strength of 30,000 lb., with 6% elongation, 
whereas the alloy "B" had 24,000 lb. T. S. and 11% elongation. 

Bearing Metal Practice, 1907. (G. H. Clamer, Proc. A. S. T. M., vil, 
302, discusses the history of bearing metal practice since the date of 
Dr. Dudley's paper quoted above. It was found that tin could be dimin- 
ished and lead inceased far beyond the figures formerly used, and a satis- 
factory bearing metal was made with 65% copper, 5% tin and 30% lead. 
This allov is largely sold under the name of "plastic bronze." It has a 
compressive strenerth of about 15,000 lbs. per sq. in., and is found to 
operate without distortion in the bearings of the heaviest locomotives, 
not only for driving brasses, but also for rod brasses and bushings, and 
for beariners of cars of 100.000 lbs. capacity, the heaviest cars now in 
service. Specifications of different railroads cover bearing alloys with 
tin from 8 to 10% and lead from 10 to 15%, There is also used a vast 
quantity of bearings made from scrap. These contain copper, 65 to 75%, 
tin, 2 to 8%, lead, 10 to 18%, zinc, 5 to 20%, and they constitute from 
50 to 75 per cent of the car bearings now in use. 

White 3Ietal for Engine Bearings. (Report of a British Naval 
Committee, Eng'g, July 18, 1902.) — For lining bearings, crankpin 
bushes, and other parts exclusive of cross-head bushes: Tin 12, copper 1, 
antimony 1. Melt 6 tin 1 copper, and 6 tin 1 antimony separately and 
mix the two together. For cross-head bushes a harder alloy, viz., 85% 
tin, 5% copper, 10% antimony, has given good results. 

(For other bearing-metals, see " Alloys containing Antimony," below,) 

ALLOYS CONTAEVENG ANTIMONY. 

Various Analyses of Babbitt Metal and other Alloys Contain- 
ing Antimony. 



Tin. 




Copper. 


Antimony. 


Zinc. 


Lead. ] Bismuth. 


Babbitt metal 


1 50 

= 89.3 
. 96 

= 88.9 
85 7 


1 

1.8 

4 

3.7 

1.0 

"l" 
4 
10 
1.5 
1.8 
5 


5 parts 
8 9 per ct. 








for light duty 
Harder Babbitt 








8 parts 

7.4perct. 
10.1 
16. 2 
16 

25.5 
62 
13 

7.1 
10 








for bearings "^ 
Britannia . 








2.9 
1.9 
I 








...81.9 

...81.0 

70 5 






«i 






<« 






<« 


...22 

...45.5 

...89.3 


6 






" Babbitt " 


40.0 




Plate pewter 




1.8 


White metal 


...85 


Bearings 


onGer.loc 


omotives. 



* It is mixed as follows: Twelve parts of copper are first melted and 
then 36 parts of tin are added; 24 parts of antimony are put in, and 
then 36 parts of tin, the temperature being lowered as soon as the 
copper is melted in order not to oxidize the tin and antimony, the sur- 
face of the bath being protected from contact with the air. The alloy 
thus made is subsequently remelted in the proportion of 50 parts of 
alloy to 100 tin. (Joshua Rose.) 

White-metal Alloys. — The following alloys are used as lining metals 
by the Eastern Railroad of France (1890): 



Number. 


Lead. 


1 Antimony. 


Tin. 


Copper. 


1 


65 

70 
80 


25 
11.12 

20 
8 




83.33 
10 
12 


10 


2 


5.55 


3 





4 






No. 1 is used for lining cross-head slides, rod-brasses and axle-bear- 
ings; No. 2 for lining axle-bearings and connecting-rod brasses of heavy 



108 



ALLOYS. 



engines; No. 3 for lining eccentric straps and for bronze slide-vaiv^'; 
and No. 4 for metallic rod-packing. 

Some of the best-known white-metal alloys are the following (Circular 
of Hoveler & Dieckhaus, London, 1893): 





Tin. 


Anti- 
mony. 


Lead. 


Copper. 


Zinc.^ 


1 . Parsons* 


86 
70 
55 
16 

71/2 
85 


1 
15 

18 



71/2 


2 
101/2 

231/2 

7 



2 

41/2 

31/2 

5 
7 
71/2 


27 


2. Richards* 





3. Babbitt's 





4. Fenton*s 


79 


5. French Navy 


871/3 


6. German Navy 






"There are engineers who object to w^hite metal containing lead or 
zinc. This is, however, a prejudice quite unfounded, inasmuch as lead 
and zinc often have properties of great use in white alloys. 

It is a further fact that an "easy liquid" alloy must not contain more 
than 18% of antimony, which is an invaluable ingredient of white metal 
for improving its hardness; but in no case must it exceed that margin, 
as this would reduce the plasticity of the compound and make it 
brittle. 

Hardest tin-lead alloy: 6 tin, 4 lead. Hardest of all tin alloys (?) : 74 
tin, 18 antimony, 8 copper. 

Alloy for thin open-work, ornamental castings: Lead 2, antimony 1. 
White metal for patterns: Lead 10, bismuth 6, antimony 2, common 
brass 8, tin 10. 

T5T)e-inetal is made of various proportions of lead and antimony, 
from 17% to 20% antimony according to the hardness desired. 

Babbitt Metals. (C. R. Tompkins, Mechanical News, Jan., 1891.) 

The practice of lining journal-boxes with a metal that is sufficiently 
fusible to be melted in a common ladle is not always so much for the 
purpose of securing anti-friction properties as for the convenience and 
cheapness of forming a perfect bearing in line with the shaft without 
the necessity of boring them. Boxes that are bored, no matter how 
accurate, require great care in. fitting and attaching them to the frame 
or other parts of a machine. 

It is not good practice, however, to use the shaft for the purpose of 
casting the bearings, especially if the shaft be steel, for the reason that 
the hot metal is apt to spring it; the better plan is to use a mandrel 
of the same size or a trifle larger for this purpose. For slow-running 
journals, where the load is moderate, almost any metal that may be 
conveniently melted and will run free will answer the purpose. For 
wearing properties, with a moderate speed, there is probably nothing 
superior to pure zinc, but when not combined with some other metal it 
shrinks so much in cooUng that it cannot be held firmly in the recess, 
and soon works loose; and it lacks those anti-friction properties which 
are necessary in order to stand high speed. 

For line-shafting, and all work where the speed is not over 300 or 400 
r. p. m., an alloy of 8 parts zinc and 2 parts block-tin will not only wear 
longer than any composition of this class, but will successfully resist a 
heavy load. The tin counteracts the shrinkage, so that the metal, if not 
overheated, will firmly adhere to the box until it is worn out. But this 
mixture does not possess sufficient anti-friction properties to warrant its 
use in fast-running journals. 

Among all the soft metals in use there are none that i)ossess greater 
anti-friction properties than pure lead; but lead alone is impracticable, 
for it is so soft that it cannot be retained in the recess. But when by 
any process lead can be sufficiently hardened to be retained in the boxes 
without materially injuring its anti-friction properties, there is no metal 
that will wear longer in light fast-running journals. With most of the 
best and most popular anti-friction metals in use and sold under the 
name of the Babbitt metal, the basis is lead. 

Lead and antimony have the property of combining with each other 
In ail proportions witnout impainng the anti-friction properties of either. 
The antimony hardens the lead, and when mixed in the proportion of 80 



SOLDERS. iOd 

parts lead by weight with 20 parts antimony, no other known compo- 
sition of metals possesses greater anti-friction or wearing properties, or 
will stand a higher speed without heat or abrasion. It runs free in ita 
melted state, has no shrinkage, and is better adapted to light high- 
speed machinery than any other known metal. Care, however, should be 
manifested in using it, and it should never be heated beyond a temper- 
ature that will scorch a dry pine stick. 

Many different compositions are sold under the name of Babbitt 
metal. Some are good, but more are worthless: while but very little 
genuine Babbitt metal is sold that is made strictly according to the 
original formula. Most of the metals sold under that name are the 
refuse of type-foundries and other smelting- works, melted and cast into 
fancy ingots with special brands, and sold under the name of Babbitt 
metal. 

It is difficult at the present time to determine the exact formulas 
used by the original Babbitt, the inventor of the recessed box, as a num- 
ber of different formulas are given for that composition. Tin, copper, 
and antimony were the ingredients, and from the best sources of infor- 
mation the original proportions v/ere as follows: 

Another writer gives: 

50 parts tin = 89.3% 83.3% 

2 parts copper = 3.6% 8.3% 

4 parts antimony = 7.1% 8.3% 

The copper was first melted, and the antimony added first and then 
about ten or fifteen pounds of tin, the whole kept at a dull-red heat and 
constantly stirred until the metals were thoroughly incorporated, after 
which the balance of the tin was added, and after being thoroughly 
stirred again it was then cast into ingots. When the copper is thoroughly 
melted, and before the antimony is added, a handful of powdered char- 
coal should be thrown into the crucible to form a flux, in order to exclude 
the air and prevent the antimony from vaporizing; otherwise much of it 
will escape in the form of a vapor and consequently be wasted. This 
metal, when carefully prepared, is probably one of the best metals in use 
for lining boxes that are subjected to a heavy weight and wear; but for 
light fast-running journals the copper renders it more susceptible to 
friction, and it is more liable to heat than the metal composed of lead and 
antimony in the proportions just given. 

SOLDERS. 

Ck)mmon solders, equal parts tin and lead; fine solder, 2 tin to 1 lead; 
cheap solder, 2 lead, 1 tin. 

Fusing-point of tin-lead alloys (many figures probably inaccurate). 



Tin 



1 to lead 25 . . . 


...558°F. 


Tin 11/2 to lead 1 . . . 


. . . 334^ 


1 " " 10... 


...541 


" 2 " " 1... 


... 340 


1 •* •* 5... 


...511 


*' 3 " " 1... 


...356 


1 '* ** 3... 


...482 


•• 4 " " 1... 


... 365 


1 " *• 2... 


...441 


•• 5 " " 1... 


...378 


1 *• •• 1... 


...370 


*• 6 •' •• 1... 


...381 



The melting point of the tin-lead alloys decreases almost proportionately 
to the increase of tin, from 619°F, the melting point of pure lead, to 356°F 
when the alloy contains 68% of tin, and then increases to 448°F., the melt- 
ing point of pu e tin. Alloys on either side of the 68% mixture begin to 
soften materially at 356°F, because at that temperature the eutectic alloy 
melts and permits the whole alloy to soften. (Dr. J. A. Mathews.) 

Common pewter contains 4 lead to 1 tin. 

The relative hardness of the various tin and lead solders has been 
determined by Brinell's method. The results are as follows: 

% Tin 10 20 30 40 50 60 

Hardness 3.90 10.10 12.16 14.46 15.76 14.90 14.58 

% Tin 66 67 68 70 80 90 100 

Hardness 16.66 15.40 14.58 15.84 15.20 13.25 4.14 



410 



ROPES AND CABLES. 



The hardest solder is the one composed of 2 parts of tin and 1 part of 

lead. It IS the eutectic alloy, or the one with the lowest melting point ot 
all the mixtures. — Mechanical World. 

Gold solder: 14 parts gold, 6 silver, 4 copper. Gold solder for 14-carat 
gold; 25 parts gold, 25 silver, I21/2 brass, 1 zinc. 

Silver solder: Yellow brass 70 parts, zinc 7, tin 11 1/2. Another: Silver 
145 parts, brass (3 copper, 1 zinc) 73, zinc 4. 

German-silver solder: Copper 38, zinc 54, nickel 8. 

Novel's solders for aluminum: 



Tin 



100 parts, 


lead 5; 


100 " 


zinc 5; 


1000 *• 


copper 10 to 15; 


1000 " 


nickel 10 to 15; 



melts at 536° to 572« F, 

536 to 612 

662 to 842 

662 to 842 



See also p. 383. 

Novel's solder for aliuninum bronze: Tin, 900 parts, copper 100. bis- 
muth 2 to 3. It is claimed that this solder is also suitable for joining 
aluminum to copper, brass, zinc, iron or nickel. 



ROPES AND CABLES. 



(A. S. Newell & Co. 



STRENGTH OF ROPES. 

Birkenhead. Klein's Translation of Weisbach, 
vol. iii, part 1, sec. 2.) 



Hemp. 


Iron. 


Steel. 
















Tensile 
Strength, 




Weight 




Weight 




Weight 


Girth. 


per 


Girth. 


per 


Girth. 


per 


Gross tons. 


Inches. 


Fathom. 


Inches. 


Fathom. 


Inches. 


Fathom. 






Pounds. 




Pounds. 




Pounds. 




23/4 


2 


1 

n/2 


1 
•1/2 


J 


1 


2 

3 


33/4 


4 


1-V8 


2 






4 






13/4 


21/2 


11/2 


11/2 


5 


41/2 


5 


17/8 


3 






6 






2 


31/2 


1V8 


2 


7 


51/2 


7 


21/8 
21/4 


4 

41/2 


13/4 


21/2 


8 
9 


6 


9 


23/8 
21/2 


5 
51/2 


17/8 


3 


10 
11 


6 1/2 


10 


25/8 


6 


2 


31/2 


12 






23/4 


6 1/2 


21/8 


4 


13 


7 


12 


27/8 


7 
71/2 


21/4 


41/2 


14 
15 


71/2 


14 


31/8 

31/4 


8 

ei/2 


23/8 


5 


16 
17 


8 


16 


33/8 


9 


21/2 


51/2 


18 






31/2 


10 


2>/8 


6 


20 


81/2 


18 


3^8 
33/4 


11 

12 


23/4 


61/2 


22 
24 


?y2 


22 


37/8 


13 


31/4 


8 


26 


10 


26 


4 


14 






28 


11 


30 


41/4 
43/8 


15 
16 


33/8 


9 


30 
32 






41/2 


18 


31/2 


10 


36 


12 


34 


45/8 


zo 


33/4 


12 


40 














. 



STHENGTH OF ROPES. 411 

Length Sufficient to Cause the Maximum Working Stress. 

(Weisbach.) 

Hempen rope, dry and untarred 2855 feet. 

Hempen rope, wet or tarred 1975 ** 

Wire rope 4590 " 

Open-link chain 1360 " 

Stud chain 1660 ** 

Sometimes, when the depths are very great, ropes are given approxi- 
mately tne lonu oi a uoay ui uiuioriii sueugch, Dy maKmg inem oi separ- 
ate pieces, whose diameters diminish towards the lower end. It is evident 
that by tliis means the tensions in the fibres caused by the rope's own 
weight can be considerably diminished. 

Kupe lor Hoisting or Transmission. 31anila Rope. (U. W. Hunt 
Company, New York.) — Rope used for hoisting or for transmission of 
power is subjected to a very severe test. Ordinary rope chafes and grinds 
to powder in the center, while the exterior may look as though it was little 
worn. 

In bending a rope over a sheave, the strands and the yarns of these 
strands shde a small distance upon each other, causing friction, and wear 
the roDe internall.y. 

The ** Stevedore" rope used by the C. W. Hunt Company is made by lubri« 
eating the fibres with plumbago, mixed with sufficient tallow to hold it in 
position. This lubricates the yarns of the rope, and prevents internal 
chafing and wear. After running a short time the exterior of the rope 
gets compressed and coated with the lubricant. 

In manufacturing rope, the fibres are first spun into a yarn, this varn 
being twisted in a direction called "right hand." From 20 to 80 of these 
yarns, depending on the size of the rope, are then put together and 
twisted in the opposite direction, or "left hand," into a strand. Three of 
these strands, for a 3-strand, or four for a 4-strand rope, are then twisted 
together, the twist being again in the "right hand" direction. When the 
strand is twisted, it untwists each of the threads, and when the three 
strands are twisted together into rope, it untwists the strands, but again 
twists up the threads. It is tliis opposite twist that keeps the rope in its 
proper form. When a w^eight is hung on the end of a rope, the tendency 
is for the rope to untwist, and become longer. In untwisting the rope, it 
would twist the threads up, and the weight will revolve until the strain of 
the untwisting strands just equals the strain of the threads being twisted 
tighter. In making a rope it is impossible to make these strains exactly 
balance each other. It is this fact that makes it necessary to take out the 
"turns" in a new rope, that is, untwist it when it is put at work. The 
proper twist that should be put in the threads has been ascertained approx- 
imately by experience. 

The amount of work that the rope will do varies greatly. It depends 
not only on the quality of the fibre and the method of laying up the rope, 
but also on the kind of weather when the rope is used, the blocks or 
sheaves over which it is run, and the strain in proportion to the strain put 
upon the rope. The principal wear comes in practice from defective or 
badly set sheaves, from excess of load rnd exposure to storms. 

The loads put upon the rope should not exceed those given in the 
tables, for the most economical wear. The indications of excessive load 
will be the twist coming out of the rope, or one of the strands slipping out 
of its proper position. A certain amount of twist comes out in using It 
the first day or two, but after that the rope should remain substantially 
the same. If it does not, the load is too great for the durability of the 
rope. If the rope wears on the outside, and is good on the inside, it 
show^s that it has been chafed in running over the pulleys or sheaves. If 
the blocks are very small, it will increase the shding of the strands and 
threads, and result in a more rapid internal wear. Rope made for hoist- 
ing and for rope transmission is usually made with four strands, as expe- 
rience has shown this to be the most serviceable. 

The strength and weight of "Stevedore" rope is estimated as follows: 
Breaking strength in pounds == 720 (circumference in inches) *; 
Weight in pounds per foot = 0.032 (circumference in inches) *. 

The Technical Words relating to Cordage most frequently heard 
are: 

Yarn. — Fibres twisted together. 



412 ROPES AND CABLES. 

Thread. —Two or more amall yarns twisted together. 

String. — The same as a thread but a Uttle larger yarns. 

Strand. — Two or more large yarns twisted together. 

Cord. — Several threads twisted together. 

Rope. — Several strands twisted together. 

Hawser. — A rope of three strands. 

Shroud-Laid. — A rope of four strands. 

Cable. — Three hawsers twisted together. 

Yarns are laid up left-handed into strands. 

Strands are laid up right-handed into rope. 

Hawsers are laid up left-handed into a cable. 

A rope is: 

Laid by twisting strands together in making the rope. 

Spliced by joining to another rope by interweaving the strands. 

Whipped. — By winding a string around the end to prevent untwisting. 

Served. — When covered by winding a yarn continuously and tightly 
around it. 

Parceled. — By wrapping with canvas. 

Seized. — When two parts are bound together by a yarn, thread or 
string. 

Payed. — When painted, tarred or greased to resist wet. 

Haul. — To pull on a rope. 

Taut. — Drawn tight or strained. 

Splicing of Rope. — The splice in a transmission rope is not only the 

weakest part of the rope but is the first part to fail when the rope is worn 
out. If the rope is larger at the sphce, the projecting part will wear on 
the pulleys and the rope fail from the cutting off of the strands. The fol- 
lowing directions are given for splicing a 4-strand rope. 

The engravings show each successive operation in splicing a 13/4-lnch 
manila rope. Each engraving w^as made from a full-size specimen. 

Tie a piece of twine, 9 and 10, around the rope to be spliced, about 
6 feet from each end. Then unlay the strands of each end back to the 
twine. 

Butt the ropes together and twist each corresponding pair of strands 
loosely, to keep them from being tangled, as shown in Fig. 91. 

The twine 10 is now cut, and the strand 8 unlaid and strand 7 carefully 
laid in its place for a distance of four and a half feet from the junction. 

The strand 6 is next unlaid about one and a half.feet and strand 5 laid 
in its place. 

The ends of the cores are now cut off so they just meet. 

Unlay strand 1 four and a half feet, laying strand 2 in its place. 

Unlay strand 3 one and a half feet, laying in strand 4. 

Cut all the strands off to a length of about twenty inches for convenience 
in manipulation. 

The rope now assumes the form shown in Fig. 92 with the meeting 
points of the strands three feet apart. 

Each pair of strands is successively subjected to the following operation: 

From the point of meeting of the strands 8 and 7, unlay each one three 
turns; split both the strand 8 and the strand 7 in halves as far back as 
they are now unlaid and "whip" the end of each h?if strand with a small 
piece of twine. 

The half of the strand 7 is now laid in three turns and the half of 8 also 
laid in three turns. The half strands now meet and are tied in a simple 
knot, 11, Fig. 93, making the rope at this point its original size. 

The rope is now opened with a marUn spike and the half strand of 7 
worked around the half strand of 8 by passing the end of the half strand 7 
through the rope, as shown in the engraving, drawn taut, and again 
worked around this lialf strand until it reaches the half strand 13 that was 
not laid in. This half strand 13 is now split, and the half strand 7 drawn 
through the opening thus made, and then tucked under the two adjacent 
strands, as shown in Fig. 94. The other half of the strand 8 is now 
wound around the other half strand 7 in the same manner. After each 
pair of strands has been treated in this manner, the ends are cut off at 12, 
leaving them about four inches long. After a few days wear they will 
draw into the body of the rope or wear off, so that the locality of the 
splice can scarcely be detected. 



SPLICING OF ROPES. 



413 




Fig. 94. 
Splicing of Hopes. 



414 



ROPES AND CABLES, 



Cargo Hoisting. (C. W. Hunt Company.) •— The amount of coal that 
can be hoisted witli a rope varies grreatlv. Under the ordinary conditions 
of use a rope hoists from 5000 to 8000 tons. Where the circumstances are 
more favorable, the amounts run up frequentlv to 12,000 or 15,000 tons 
occasionally to 20,000 and in one case 32,400 tons to a single fall. 

When a hoisting rope Is first put in use, it is likely from the strain put 
upon it to twist up when the block is loosened from the load. This occurs 
in the first day or two only. The rope should then be taken down and 
the "turns" taken out of the rope. When put up again the rope should 
give no further trouble until worn out. 

It is necessary that the rope should be much larger than is needed to 
bear the strain from the load. 

Practical experience for many years has substantially settled the most 
economical size of rope to be used which is given in the table below. 

Hoisting ropes are not spliced, as it is difticult to make a splice that will 
not pull out while running over the sheaves, and the increased wear to be 
obtained in this way is very small. 

Coal is usually hoisted with what is commonly called a "double whip- " 
that is, with a running block that is attached to the tub which reduces the 
strain on the rope to approximately one-half the weight of the load 
hoisted. 

Hoisting rope is ordered by circumference, transmission rope by 
diameter. 

Working Loads for Manila Rope (C. 

xxiii, 125.) 



W. Hunt. Trans. A. S. M. E., 



Diameter 
of Rope, 
Inches. 


Ultimate 
Strength, 
Pounds. 


Working Load in Pounds. 


Minimum Diameter of 
Sheaves in Inches. 


Rapid. 


Medium. 


Slow. 


Rapid. 


Medium. 


Slow. 


1 

1V8 
11/4 
13/8 
tV2 
15/8 
13/i 


7,100 
9,000 
11,000 
13,400 
15,800 
18,800 
21.800 


200 
250 
300 
380 
450 
530 
620 


400 
500 
600 
750 
900 
1100 
1250 


1000 
1250 
1500 
1900 
2200 
2600 
3000 


40 
45 
50 
55 
60 
65 
70 


12 
13 
14 
15 
16 
17 
18 


8 
9 
10 
11 
12 
13 
14 



In this table the work required of the rope is, for convenience, divided 
into three classes — "rapid," "medium," and "slow," these terms being 
used in the following sense: "Slow" — Derrick, crane and quarry work; 
speed from 50 to 100 feet per minute. "Medium" — Wharf and cargo, 
hoisting 150 to 300 feet per minute. "Rapid" — 400 to 800 feet per 
minute. 

The ultimate strength given in the table is materially affected by the 
age and condition of a rope in active service, and also it is said to be 
weaker when it is wet. Trautwine states that a few months of exposed 
work weakens rope 20 to 50 per cent. The ultimate strength of a new 
rope given in the table is the result of tests of full sized specimens of 
manila rope, purchased in the open market, and made by three inde- 
pendent rope walks. 

The proper diameter of pulley-block sheaves for different classes of 
work given in the table is a compromise of the various factors affecting 
the case. An increase in the diameter of sheave will materiallj^ increase 
the life of a rope. The advantage, however, is gained by increased 
difficulty of installation, a clumsiness in handling, and an increase in 
first cost. The best size is one that considers the advantages and the | 
drawbacks as they are found in practical use, and makes a fair balance 
between the conflicting elements of the problem. 

Records covering many years have been kept by various coal dealers, 
of the diameter and cost of their rope per ton of coal hoisted from ves- 
sels, using sheaves of from 12 to 16 inches in diameter. These records 
show conclusively that, in hoisting a bucket that produces 900 pounds f 
etress upon the rope, a 11/4-inch diameter rope is too sm.all and a 13/4- 
inch rope is too large for economy. The Pennsylvania Railroad Company 
uses iy2 inch rope, running over 14-inch diameter sheaves for hoisting 



STRENGTH OF ROPES. 415 

freight on lighters in New Yorli harbor, and handles on a single part of 
the rope loads up to 3,000 poimds as a maximum. Greater weights are 
handled on a 6-part tackle. 

Life of Hoisting and Transmission Rope. A rope 1 1/2-in. diam. usu- 
ally hoists from a vessel from 7000 to 10,000 tons of coal, running with a 
working stress of 850 to 950 lbs. over three sheaves, one 12 in., and two 
16-in. diam. In hoisting 10,000 tons it makes 20,000 trips, bending in 
that time from a straight Hne to the curve of the sheave 120.000 times, 
when it is worn out. A 1000 ft. transmission in a tin-plate mill, with II/2 
in. rope, sheaves 5 ft., 17 ft., and 36 ft. apart, center to center, runs 5000 
ft. per minute making 13,900 bends per hour, or more bends in 9 hours 
than the hoisting rope made in its entire hfe, yet the hfe of a transmission 
rope is measured in years, not hours. This enormous difference in the 
Hfe of ropes of the same size and quality is wholly gained by reducing the 
stresses on the rooe and increasing the diameter of the shftavfts. 

Efficiency of Knots as a percentage of the full strength of the rope» 
and the factor of safety when used with the stresses given in the 5th col- 
umn of the table of working loads. 

Kind of Knot. Effy. Fact. S 

Eye splice over an iron thimble 90 6.3 

Short spUce in the rope 80 5.6 

Timber hitch, round turn, half-hitch 65 4.5 

Bowhne sUp knot, clove hitch 60 4.2 

Square knot, weaver's knot sheet bend 50 3.5 

Flemish loop, overhand knot 45 3.1 

Full strength of dry rope, average of four tests 100 7.0 

Efficiency of Rope Tackles. Robert Grimshaw in 1 893 tested a 3 3/4-in. , 
3-strand ordinary dry manila rope on a "cat and fish" tackle with a 
6-fold purchase. The sheaves were 8-in. diam., the three upper ones hav- 
ing roller bearings and the three lower ones sohd bushings. The results 
were as below: 

Net load on tackle, weight raised, lbs 600 800 1000 1200 

Theoretical force required to raise the weight 100 1333.3 166.7 200 

Actual force required 158 198 243 288 

Percentage above the theoretical 58 48 45. 8 44 

Weight and Strength of 31anila Rope. Spencer Miller (Eng'g News, 
Dec. 6, 1890) gives a table of breaking strength of manila rope, which he 
considers more reUable than the strength computed by Mr. Hunt's formula: 
Breaking strength = 720 X (circumference in inches) .2 Mr. Miller's formula 
is: Breaking weight lbs. = circumference 2 x a coefficient which varies 
from 900 for 1/2" to 700 for 2" diameter rope, as below: 

Circumference .. IV2 2 21/223/4 3 31/233/441/441/2 5 51/2 6 
Coefficient 900 845 820 790 780 765 760 745 735 725 712 700 

Knots. The principle of a knot is that no two parts, which would 
move in the same direction if the rope were to sUp, should lay along side 
of and touching each other. (See illustrations on the next page.) 

The bowline is one of the most useful knots, it will not slip, and after 
being strained is easily untied. Commence by making a bight in the 
roi>e, then put the end through the bight and under the standing part as 
shown in G, then pass the end again through the bight, and haul tight. 

The square or reef knot must not be mistaken for the "granny" knot 
that slips under a strain. Knots H, K and M are easily untied after 
being under strain. The knot M is useful when the rope passes through 
an eye and is held by the knot, as it will not slip and is easily untied 
after being strained. 

The timber hitch S looks as though it would give way, but it will not; 
the greater the strain the tighter it will hold. The wall knot looks com- 
pUcated, but is easily made by proceeding as follows: Form a bight with 
strand 1 and pass the strand 2 around the end of it, and the strand 3 
round the end of 2 and then through the bight of 1 as shown in the cut Z. 
Haul the ends taut when the appearance is as shown in AA. The end of 
the strand 1 is now laid over the center of the knot, strand 2 laid over 1 
and 3 over 2, when the end of 3 is passed through the bight of 1 as showc. 
in BB. Haul all the strands taut as shown in CC. 



416 



ROPES AND CABLES. 



Varieties of Knots. — A great number of knots have been devised of 
which a few only are illustrated, but those selected are the most frequently- 
used. In the cut, Fig. 95, they are shown open, or before being drawn 
taut, in order to show the position of the parts. The names usually 
given to them are: 



A. Bight of a rope. 

B. Simple or Overhand knot. 

C. Figure 8 knot. 

D. Double knot. 

E. Boat knot. 

F. BowUne, first step. 

G. Bowhne. second step. 
H. Bowline completed. 
I. Square or reef knot. 

J. Sheet bend or weaver's knot. 

K. Sheet bend \\1th a toggle. 

L. Carrick bend. 

M. Stevedore knot completed. 

N. Stevedore knot commenced. 

O. Slip knot. 



P. Flemish loop. 

Q. Chain knot with toggle. 

R. Half-hitch. 

S. Timber-hitch. 

T. Clove-hitch. 

U. Rolling-hitch. 

V. Timber-hitch and half-hitch. 

W. Blackwall-hitch. 

X. Fisherman's bend. 

Y. Round turn and half-hitch 

Z. Wall knot commenced. 

A A. Wall knot completed. 

BB. Wall knot crown commenced. 

CC. Wall knot crow^n completed. 




FiQ. 95. — Knots. 



SPRINGS. 417 



SPEINQS. 

Definitions. — A spiral spring is one which is wound around a fixed 
point or center, and continually receding from it, like a watch spring. A 
helical spring is one which is wound around an arbor, and at the same time 
advancing like the thread of a screw. An elliptical or laminated spring is 
made of flat bars, plaies, or "leaves," of regulariy varying lengths, super- 
posed one upon the other. 

Laminated Steel Springs. — Clark (Rules, Tables and Data) gives 
the following from his work on Railway Machinery, 1855: 

- 1-66 L3 . bf^n . ^ 1.66 L^ , 

^~ Wn • *^11.3L' ^ AWs ' 

A = elasticity, or defiection, in sixteenths of an inch per ton of load; 
s = working strength, or load, in tons (2240 lbs.); 
L = span, when loaded in inches; 
b = breadth of plates, in inches, taken as uniform; 
t = thickness of plates, in sixteenths of an inch; 
n = number of plates. 

Note. — 1. The span and the elasticity are those due to the spring 
when weighted. 

2. When extra thick back and short plates are used, they must be 
replaced by an equivalent number of plates of the ruling thickness, prior 
to the employment of the first two formulae. This is found by multiply- 
ing the number of extra thick plates by the cube of their thickness, and 
dividing by the cube of the ruling thickness. Conversely, the number 
of plates of the ruling thickness given by the third formula, required to 
be deducted and replaced by a given number of extra thick plates, are 
found by the same calculation. 

3. It is assumed that the plates are similarly and regularly formed, 
and that they are of uniform breadth, and but slightly taper at the ends. 

Reuleaux's Constructor gives for semi-eUiptic springs: 

r, Snbh'i , ^ 6PP , 

Ql ' Enbh^ 

S = max. direct fiber-strain in plate; b = width of plates; 

n = number of plates in spring; h = thickness of plates: 

I = one-half length of spring; / = deflection of end of spring; 

P = load on one end of spring; E = modulus of direct elasticity 

The above formula for defiection can be relied upon where all the plates 
of the spring are regularly shortened; but in semi-elliptic springs, as 
used, there are generally several plates extending the full length of the 
spring, and the proportion of these long plates to the whole number is 

5 5 Pl^ 
usually about one-fourth. In such cases/ = -ir-rr^' (G. R. Henderson, 

Trans. A. S. M. E., vol. xvi.) 

In order to compare the formulae of Reuleaux and Clark we may make 
the following substitutions in the latter: s in tons = P in lbs. -i- 1120; 
AS = 16/; L = 2l\ t = IQh; then 

Ao lAr 1.66X8Z3XP , ^ P/» 

A5 = 16 / = ^^oAs^iions.^>... » Whence ' - 



4096 X 1120 Xn&/i3* ^^ j 5,527, 133n6/i3 

which corresponds with Reuleaux's formula for deflection if in the latter 
we take E = 33,162,800. 

Aic^ „ P 256 715/12 12,687 n&/i2 

^^'^ ""ii2o"ii:3^^r ^^"^"^ ^ = — I 

which corresponds with Reuleaux's formula for working load when S ia 
the latter is taken at 76,120. 



418 



SPRINGS. 



The value of E Is usually taken at 30,000,000 and S at 80,000, in which 
case Reuieaux's formulae become 

^p^lS^SSSjtbh^ and /= ^^' 



I 



5,000,000nbh^ 



G. R. Henderson, in Trans. A. S. M. E., vol. xvii, gives a series of 
tables for use in designing both elliptical and helical springs. 

Helical Steel Springs. 

Notation. Let d = diam. of wire or rod of which the spring is made. 
D = outside diameter of coil, inches. 
R = mean radius of coil, = 1/2 (D-d), 
n = number of coils. 
P = load applied to the spring, lbs. 
G = modulus of torsional elasticity. 
S = stress on extreme fiber caused by load P. 
F = extension or compression of one coil, in., for load P. 
Fn= total extension or compression, for load P, 
W = safe carrying capacity of spring, lbs. 



F=» 



64 Pig3. 



Fn = 



64 PR^n . 



W = 



0.1963 >S6?3 
R 



16 R' 



Values of G according to different authorities range from 10,000,000 to 
14,000,000. 
The safe working value commonly taken for S = 60,000 lbs. per sq. in. 
Taking G at 12,000,000 and S at 60,000 the above formulae become 



PR^ 
187,500^4* 



W = 11.781^- 



If P = TF, then F = 0.06285 



R^ 



For square steel the values found for F and W are to be multiplied by 
0.59 ana 1.2 respectively, d being the side of the square. 

The stress in a heUcal spring is almost wholly one of torsion. For 
method of deriving the formulae for springs from torsional formulae see 
paper by J. W. Cloud, Trans. A. S. M. E., vol. 173. Mr. Cloud takes 
S = 80,000 and G = 12,600,000. 

Taking from the Pennsylvania Railroad Specifications (1891) the 
capacity when closed, Wi, of the following springs, and the total com- 
pression when closed H — h, in which H = height when free and h 
when closed, and assuming n = /i -4- d, we have the following compari- 
son of the specified values of capacity and compression with those ob- 
tained from the formulae. 



No. 


d, in. 


D 


D-d 


Wt 


W 


H 


h 


H-h 


Fn 


n 


T. 


Vi 


11/2 


11/4 


400 


295 


9 


6 


3 


3.20 


24 


S. 


V? 


3 


2y?, 


1900 


1178 


8 


5 


3 


3.16 


10 


K. 


3/4 


53/4 


5 


2100 


1988 


7 


41/4 


23/4 


3.15 


52/3 


D. 


I 


5 


4 


8100 


5890 


101/2 


8 


21/9 


2.76 


8 


I. 


11/4 


8 


63/4 


10000 


6788 


9 


53/4 


31/4 


3.86 


43/5 


C. 


11/8 


47/8 


3 3/4 


16000 


8946 


43/8 


33/8 


1 


1.05 


3 



The value of Fn in the table is calculated from the formula with P=Wi 
Wilson Hartnell (Proc. Inst. M. E., 1882, p. 426), says: The size of a 
spiral spring may be calculated from the formula on page 304 of " Rank- 
ine's Useful Rules and Tables;'* but the experience with Salter's springs 
has shown that the safe limit of stress is more than twice as great as there 
given, namely 60,000 to 70,000 lbs. per square inch of section with s/g-inch 
wire, and about 50,000 with 1/2-inch wire. Hence the work that can be 
done by springs of wire is four or five times ^9 grejit as R^nlane allows. 



SPRINGS. 419 

For 3/8-inch w-ire and under, 

^ 12.000 X 
' ~ Mean ra 

180,000 X (diam.)< 



^, . , ^ . ,u 12,000 X (diam. of wire)> 

Maximum load in lbs. = — rr ^p i ■■ 

Mean radius of springs 



Weight in lbs. to deflect spring 1 in.'= ,^ . . •, w / ^ x? 
^ ^ ^ ■ Number of coils X (rad.)' 

The work in foot-pounds that can be stored up in a spiral spring would 
lift it above 50 ft. 

In a few rough experiments made with Salter's springs the coefficient ol 
rigidity was noticed to be 12,600,000 to 13,700,000 with 1/4-inch wire; 
11,000,000 for 11/32 inch; and 10,600,000 to 10,900,000 for S/g-inch wire. 

Helical Springs. — J. Begtrup, in the American Machinist of Aug. 
18, 1892, gives formulas for the deflection and carrying capacity of helical 
springs of round and square steel, as follow: 

S(P PCD — d)^ 

W = 0.3927 yr^ , F = 8 ^^^, ^ , for round steel. 
D — d Ed^ 

Pr = 0.471 rT^^* F = 4.712 ^^^ ~ ^^\ for square steel. 
D — d Ed* ^ 

W = carrying capacity in pounds, 
S = greatest shearing stress per square inch of material, 
d = diameter of steel, 
D = outside diameter of coil, 
F = deflection of one coil, 
E = torsional modulus of elasticity, 
P = load in pounds. 

From these formulas the following table has been calculated by Mr. 
Begtrup. A spring being made of an elastic material, and of such shape 
as to allow a great amount of deflection, will not be affected by sudden 
shocks or blows to the same extent as a rigid body, and a factor of safety 
very much less than for rigid constructions may be used. 

HOW TO USE THE TABLE. 

When designing a spring for continuous w^ork, as a car spring, use a 
greater factor of safety than in the table; for intermittent working, as in 
a steam-engine governor or safety valve, use figures given in table; for 
square steel multiply fine W by 1.2 and fine F by 0.59. 

Example 1. — How much will a spring of 3/g" round steel and 3'' outside 
diameter carry with safety? In the fine headed D we find 3, and right 
underneath 473, which is the weight it will carry with safety. How many 
coils must this spring have so as to deflect 3" with a load of 400 pounds? 
Assuming a modulus of elasticity of 12 millions we find in the fine headed 
F the figure 0.0610; this is deflection of one coil for a load of 100 pounds; 
therefore 0.061 X 4 = 0.244'' is deflection of one coil for 400 pounds load, 
and 3 ^- 0.244 = 12 1/2 is the number of coils wanted. This spring will 
therefore be 43// long when closed, counting working coils only, and 
stretch to 73//. 

Example 2. — A spring 31// outside diameter of 7/i6^ steel is w^ound close; 
how much can it be extended without exceeding the Hmit of safety? We 
find maximum safe load for this spring to be 702 pounds, and deflection of 
one coil for 100 pounds load 0.0405 inches ; therefore 7.02 X 0.0405 = 0.284' 
is the greatest admissible opening between coils. We may thus, without 
knowing the load, ascertain whether a spring is overloaded or not. 

Carrying Capacity and Deflection of Helical Springs of 
Round Steel. 

d = diameter of steel. Z)=outside diameter of coil. W= safe work- 
ing load in pounds — tensile stress not exceeding 60,000 pounds per 
square inch. F = deflection by a load of 100 pounds of one coil, witn a 
modulus of elasticity of 12 millions. The ultimate carrying capacity 
will be about twice the safe load. (The original table gives three values 



420 



SPRINGS. 



of F, corresponding respectively to a modulus of elasticity of 10, 12 and 
14 millions. To find values of F for 10 million modulus increase the fig- 
ures here given by one-fifth; for 14 million subtract one-seventh.) 



d 

in. 
.065 


D 
W 

F 


0.25 
35 
0.0236 


0.50 
15 
0.3075 


0.75 
9 

1.228 


1. 00 

7 

3.053 


1.25 
5 

6.214 


1.50 
4.5 
11.04 


1.75 

3.8 
17.87 


2.00 

3.3 

27.06 








.120 


D 
W 
F 


0.50 
107 
0.0176 


0.75 
65 
0.0804 


1. 00 

46 

0.2191 


1.25 

36 

0.4639 


1.50 
29 

0.8448 


1.75 

25 

1.392 


2.00 
22 
2.136 


2.25 
19 
3.107 


2.50 
17 
4.334 






.180 


D 
W 

F 


0.75 
241 
0.0118 


1.00 
167 
0.0350 


1.25 

128 
0.0778 


1.50 
104 
0.1460 


1.75 

88 
0.2457 


2.00 
75 

0.3828 


2.25 
66 
0.5632 


2.50 
59 
0.7928 


2.75 
53 
1.077 


3.00 
49 
1.423 




1/4 


D 
W 
F 


1.25 

368 
0.0171 


1.50 
294 
0.0333 


1.75 

245 
0.0576 


2.00 
210 
0.0914 


2.25 

184 
0.1365 


2.50 
164 
0.1944 


2.75 

147 
0.2665 


3.00 
134 

0.3548 


3.25 
123 
0.4607 


3.50 
113 

0.5859 




5/16 


D 
W 
F 


1.50 
605 
0.0117 


1.75 

500 
0.0207 


2.00 
426 
0.0336 


2.25 
371 
0.0508 


2.50 
329 
0.0732 


2.75 
295 
0.1012 


3.00 
267 
0.1357 


3.25 
245 
0.1771 


3.50 
226 
0.2263 


3.75 
209 
0.2839 


4.00 
195 
0.3505 


S/8 


D 
W 
F 


2.00 
765 
0.0145 


2.25 
663 
0.0222 


2.50 
589 
0.0323 


2.75 
523 
0.0452 


3.00 
473 
0.0610 


3.25 

433 
0.0801 


3.50 
398 
0.1029 


3.75 

368 
0.1297 


4.00 
343 
0. 1606 


4.25 
321 
0.1963 


4.50 
301 
0.2367 


7/16 


D 
W 
F 


2.00 
1263 
0.0069 


2.25 
1089 
0.0108 


2.50 
957 
0.0160 


2.75 
853 
0.0225 


3.00 
770 
0.0306 


3.25 

702 
0.0405 


3.50 

644 
0.0529 


3.75 

596 
0.0661 


4.00 

544 
0.0823 


4.50 

486 
0.1220 


5.00 
432 
0.1728 


1/2 


D 
W 
F 


2.00 
1963 
0.0036 


2.25 
1683 
0.0057 


2.50 

1472 
0.0085 


2.75 

1309 
0.0121 


3.00 
1178 
0.0167 


3.25 
1071 
0.0222 


3.50 

982 
0.0288 


3.75 
906 
0.0366 


4.00 
841 
0.0457 


4.50 
736 
0.0683 


5.00 
654 
0.0972 


8/16 


D 
W 
F 


2.50 
2163 
0.0048 


2.75 

1916 
0.0070 


3.00 
1720 
0.0096 


3.25 

1560 
0.0129 


3.50 
1427 
0.0169 


3.75 
1315 
0.0216 


4.00 
1220 
0.0271 


4.25 

1137 
0.0334 


4.50 
1065 
0.0406 


5.00 
945 
0.0582 


5.50 
849 
0.0801 


6/8 


D 
W 
F 


2.50 
3068 
0.0029 


2.75 
2707 
0.0042 


3.00 

2422 
0.0058 


3.25 
2191 
0.0079 


3.50 
2001 
0.0104 


3.75 
1841 
0.0133 


4.00 
1704 
0.0168 


4.25 

1587 
0.0208 


4.50 

1484 
0.0254 


5.00 
1315 
0.0366 


5.50 
1180 
0.0506 


11/16 


D 
AV 
F 


3.00 
3311 
0.0037 


3.25 
2988 
0.0050 


3.50 
2723 
0.0066 


3.75 
2500 
0.0086 


4.00 
2311 
0.0108 


4.25 
2151 
0.0135 


4.50 
2009 
0.0165 


4.75 
1885 
0.0200 


5.00 
1776 
0.0239 


5.50 
1591 
0.0333 


6.00 
1441 
0.0447 


3/4 


D 
W 
F 


3.00 
4418 
0.0024 


3.25 
3976 
0.0033 


3.50 
3615 
0.0044 


3.75 
3313 
0.0057 


4.00 
3058 
0.0072 


4.25 
2840 
0.0090 


4.50 

2651 

0.0111 


4.75 
2485 
0.0135 


5.00 
2339 
0.0162 


5.50 
2093 
0.0226 


6.003 

1893 

0.005 


7/8 


D 
W 
F 


3.50 
6013 
0.0018 


3.75 
5490 
0.0024 


4.00 
5051 
0.0030 


4.25 
4676 
0.0038 


4.50 
4354 
0.0047 


4.75 
4073 
0.0058 


5.00 
3826 
0.0070 


5.25 
3607 
0.0083 


5.50 
3413 
0.0098 


6.00 
3080 
0.0134 


6.50 
2806 
0.0177 


1 


D 
W 
F 


3.50 

9425 
0.0010 


3.75 
8568 
0.0014 


4.00 

7854 
0.0018 


4.25 

7250 
0.0023 


4.50 
6732 
0.0028 


4.75 
6283 
0.0035 


5.00 
5890 
0.0043 


5.25 
5544 
0.0051 


5.50 
5236 
0.0061 


6.00 
4712 
0.0083 


6.50 
4284 
0.0111 



F. D. Howe, Am. Mach, Dec. 20, 1906, using Begtrup's formulae, com- 
putes a table for springs made from wire of Roebling's or Washburn and 
Moen gauges, Nos. 28 to 000. It is here given somewhat abridged, 
Talues of F corresponding to a torsional modulus of elasticity of 12,000,000 
only being used. 



SPRINGS. 



421 



No. 28 

0.0 1 e'' 


D 

W 
F 


0.20 
0.524 
6.32 


0.25 
0.41 
13.02 


0.3125 

0.31 

30.2 


0.375 

0.27 
47.0 


0.4375 
0.23 
76.0 


0.500 
0.20 
115 


0.5625 
0.175 
166 


0.625 
0.16 
230 


0.75 
0.13 
402 


0.875 
0.11 
695 


No. 24 
0.0225'' 


D 

W 

F 


0.25 

1.18 
2.78 


0.3125 
0.92 
6.31 


0.375 
0.76 
11.35 


0.4375 
0.45 
18.57 


0.500 
0.56 
28.2 


0.5625 
0.50 
40.8 


625 
0.45 
56.9 


0.75 
0.37 
97.5 


0.875 
0.31 
166 


0.100 
0.28 
242 


No. 22 
0.028' 


D 
W 

F 


0.25 
2.35 
1.19 


0.3125 
1.84 
2.50 


0.375 

1.49 

4.53 


0.4375 
1.26 
7.42 


0.50 
1.095 
11.40 


0.5625 
0.96 
16.5 


0.625 
0.865 
23.1 


0.75 

0.715 

40.8 


0.875 
0.61 
66.0 


1.00 
0.53 
99.5 


No. 20 
0.035' 


D 

W 
F 


0.25 

4.7 

0.451 


0.3125 

3.64 

0.952 


0.375 

2.97 

1.75 


0.4375 
2.5 
2.90 


0.50 
2.18 
4.47 


0.5625 
1.92 
6.51 


0.625 
1.72 
9.14 


0.75 
1.42 
16.3 


0.875 
1.20 
26.4 


1.00 
1.05 
40.0 


No. 18 
0.047' 


D 

W 
F 


0.25 
12.05 
0.1158 


0.3125 

9.2 
0.294 


0.375 

7.45 

0.488 


0.4375 

6.57 

0.824 


0.50 
5.40 
1.320 


0.625 
4.23 
1.870 


0.75 
3.48 
3.96 


0.875 
2.95 
7.85 


1.00 
2.85 
12.60 


1.125 
2.27 
17.5 


No. 14 
0.08' 


D 
W 
F 


0.375 

41 
0.0418 


0.5 
28.8 
0.121 


0.625 
22.2 
0.342 


0.75 
18.1 
0.572 


0.875 
15.2 
0.82 


1.00 

13.15 

1.27 


1.125 
11.6 
1.86 


1.25 
10.35 
2.60 


1.50 
8.52 
5.48 


1.75 
7.25 
7.57 


No. 12 
0.105' 


D 
W 
F 


0.625 

52.5 

0.069 


0.75 
42.25 
0.1480 


0.875 
35.4 
0.262 


1.00 
30.4 
0.395 


1.25 
23.8 
0.830 


1.50 
19.5 
1.49 


1.75 
16.6 
2.45 


2.00 
14.4 
3.74 


2.25 
12.7 
5.45 


2.50 
11.4 
7.34 


No. 10 
0.135' 


D 
W 
F 


0.875 

77 

0.081 


1.00 

67 

0.135 


1.25 

52 

0.276 


1.50 

42.5 
0.512 


1.75 

36 

0.846 


2.00 

31 

1.295 


2.25 
27 
1.910 


2.50 
24 
2.660 


2.75 

22 

3.58 


3.00 

20 

4.75 


No. 8 
0.162' 


D 
W 
F 


1.00 
120 
0.0570 


1.25 

98.5 

0.124 


1.50 

76 

0.199 


1.75 

64 

0.554 


2.00 
55.5 
0.597 


2.25 
48.8 
0.880 


2.50 
43.5 
1.26 


2.75 

39 

1.68 


3.00 

36 

2.20 


3.25 r 

33 

2.85 


No. 7 
0.177' 


D 
W 
F 


1.00 
159 
0.0382 


1.25 
122 
0.0828 


1.50 

99 

0.156 


1.75 
83.5 
0.265 


2.00 
72 
0.416 


2.25 
63 
0.603 


2.50 
56.4 
0.830 


2.75 

51 

1.15 


3.00 
46.5 
1.54 


3.25 
42.5 
1.96 


No. 6 
0.192' 


D 
W 

F 


1.25 
158 
0.0572 


1.50 
128 
0.108 


1.75 
107 
0.185 


2.00 
92.5 
0.284 


2.25 

81 

0.420 


2.50 
72 
0.590 


2.75 
65 
0.802 


3.00 
59.5 
1.07 


3.25 
55.5 
1.38 


3.50 

50 

1.74 


No. 5 
0.205' 


D 
W 

F 


1.50 
155 
0.0820 


1.75 

13! 

0.139 


2.00 
113 
0.218 


2.25 

99 

0.321 


2.50 
88.5 
0.412 


2.75 
80 
0.6175 


3.00 
70 

0.82 


3.25 

67 

1.60 


3.50 
61.5 
1.34 


4.00 
53.5 
2.22 


No. 4 
0.225' 


D 
W 

F 


1.50 

210 

0.0536 


1.75 
175 
0.093 


2.00 
150 
0.147 


2.25 

132 

0.220 


2.50 

118 

0.303 


2.75 
106 
0.412 


3.00 
97 
0.652 


3.25 

89 

0.715 


3.50 

82 

0.91 


4.00 

71 

1.30 


No. 2 
0.263' 


D 
W 
F 


1.50 

345 

0.0264 


1.75 

290 

0.0458 


2.00 

250 

0.0730 


2.25 

215 

0.109 


2.50 
192 
0.154 


2.75 
175 
0.214 


3.00 
156 
0.274 


3.25 

146 

0.371 


3.50 
134 
0.469 


4.00 

115 

0.720 


No. I 
0.283' 


D 
W 
F 


1.75 

360 

0.0328 


2.00 
310 
0.0550 


2.25 

270 

0.0778 


2.50 

240 

0.112 


2.75 
215 
0.155 


3.00 
195 
0.208 


3.25 

180 
0.270 


3.50 
165 
0.344 


4.00 
145 
0.530 


4.50 

127 

0.775 


No.O 
0J07' 


D 
W 
F 


1.75 

470 

0.0308 


2.00 
400 
0.0380 


2.25 

350 

0.0548 


2:50 
310 
0.0788 


2.75 
280 
0.109 


3.00 
250 
0.149 


3.25 

230 
0.199 


3.50 
212 
0.244 


4.00 
185 
0.327 


4.50 

162 

0.550 


No. 00 
0.331' 


D 
W 
F 


2.00 
510 
0.0289 


2.25 
445 
0.0388 


2.50 
390 
0.0564 


2.7.5 
350 
0.0780 


3.00 
320 
0.105 


3.25 
290 
0.137 


3.50 
270 
0.176 


4.00 
230 
0.273 


4.50 
205 
0.414 


5.00 

183 

0.562 



To find deflection of one coil by one pound, divide the values of F by 100. 



422 



SPRINGS. 



ELLIPTICAL SPRINGS, SIZES, AND PROOF TESTS. 

Pennsylvania Railroad Specifications, 1896. 



Class. 



E I, Triple 

E 2, Quadruple . 

E3, Triple 

E 4, Singlet 

E5, •• t 

E6, •• t-.^ 

E 7, Triple 

E 8, Double 

F 9 ' 

E 10, Quadruple. 

E 11, 

"P 12 " 

E 13', Double. .. .' 

E 14, " 

E 15, Quadruple. 
E 16, 

E 17, Double 

E 18, Singlet.... 
E 19, Double. 
E 20, 



E21, 
E 22, 
E 23, 
E 24, 



a 




o 




<D 




^ r^, 





ti^ c 






D 




> 




11 


40 


113/4 


40 


151/2 


36 


113/4 


40 




40 




42 




36 


113/4 


32 


71/?, 


36 


91/2 


40 


151/2 


40 


151/2 


34 


151/2 


30 


91/2 


40 


91/? 


36 


151/2 


30 


151/2 


36 


91/2 


42 




22 


101/2 


22 


101/2 


24 


101/2 


24 


101/2 


36 


10 


36 


10 



Plates, 
No. Size, In 



3x11/32 
3x3/8 
3x11/32 
3x11/32 

3x3/8 
31/2X3/8 

3 X 11/32 
3x3/8 
4x11/32 
3x3/8 
3x3/8 
3x3/8 
4x3/8 
4x11/32 
3x11/32 
3x11/32 
4x3/8 
31/2X3/8 
41/2X11/32 
41/2X11/32 
41/2X3/8 
41/2X3/8 

4 X.3/8 
4x3/8 



Tests. 



Ins. high. lbs. 
(a) -(6) 



33/4 

33/4 

4 

5* 

15/16* 

11/8* 

21/2 

3 

31/2 

4 

33/4 

33/4 

33/4 

33/8 

37/16 

41/2 

23/4 

1* 
13/16 
13/16 

1 

1 

21/4 

21/4 



93/8 
93/4 
95/8 



91/2 

9 

87/16 
10 

93/4 

93/4 

9 

9 

93/4 
101/8 

8 

67/16 
71/8 

71/4 
81/2 
8 



4,800 
6,650 
6,000 
free 
3,000 
4,375 
11,800 
8,000 
5,400 
8,000 
10,600 
13,100 
5,600 
6,840 
11,820 
8,000 
8,070 
5,250 
13,800 
15,600 
15,750 
18,000 
8,750 
7.500 



Ins. 

(a) 



lbs. 



5,500 
8,000 
8,000 
2,350 
4,970 
6,350 



6,000 
10,000 
12,200 
15,780 
10,600 
8,600 
21/2 14,370 
23/415,500 
2 9,540 
7,300 



28,800 
32,930 
1 1/4 10,750 
11/4 9,500 



(a) Between bands; (b) overall; a.p.t., auxiliary plates touching. 
* Between bottom of eye and top of leaf, t Semi-elliptical. 
Tracings are furnished for each class of spring. 



SPRINGS TO RESIST TORSIONAL FORCE. 



(Reuleaux's Constructor.) 



Flat spiral or helical spring P 



6 R ' 



Round helical spring p ^ ^^; 

32 R 

Round bar, in torsion P = vl » > 

16 R 



R& 



Rd 



12 



PIR^ 



Flat bar, in torsion. 



.F = 



SR vW+H^' 



f = R& = 



f = R&== 



^^ Ebh^' 


64 PI R^ 
" 7: E d*' 


32 P RH 
7t G d*' 


SPRH 62+ n» 



63/i8 



P = force applied at end of radius or lever-arm /?; i> = angular motion 
at end of radius R; S = permissible maximum stress, = Vsof permissible 
stress in flexure; E = modulus of elasticity in tension; G = torsional 
modulus, = VnE; I = developed length of spiral, or length of bar; d — 
diameter of wire; h = breadth of flat bar; h = thickness. 
(Compare Elastic Resistance to Torsion, p. 334.) 



HELICAL SPRINGS. 



423 



HELICAL. SPRINGS — SIZES AND CAPACITIES. 

(Selected from Specifications of Penna. R. R. Co., 1899.) 











1 - 


Test. Height and 


V 
M 


n 




1 




1 







Loads. 


a 










«4-l 


3 


i 

^ 


J3 





S 

^ 


'O - 




to 


m 


02 







c3 


C G 


s, 

d 





i6 






-^3 



13 


(U 


5 


^ 


H 


^ 





[^ 


02 


l-H 


1^ 










lbs. oz. 












H 26 


9/64 


571/2 


59 


4 


1 


53/4 


3 


31/4 


IIG 


130 


H 18 


11/64 


75 


761/4 


8 


1 


8 


5 


6 


170 


270 


H 55 


3/ie 


451/8 


465/16 


55/8 


1 


41/2 


35/16 


4 


103 


245 


H 73 


3/16 


426 


4273/4 


3 51/2 


15/16 


39 


221/2 


35 


45 


185 


H 29 


7/32 


201/2 


227/16 


31/2 


115/32 


111/16 


19/64 


13/8 


110 


200 


H 1 


1/4 


451/2 


47 


10 


11/4 


51/8 


35/8 


43/8 


250 


500 


H 5 


1/4 


251/4 


281/4 


6 


21/4 


21/4 


11/8 


11/2 


164 


240 


H 58 


5/16 


2531/2 


2561/2 


5 7 


21/4 


23 


13 


18 


248 


495 


H 74 


5/16 


180 


1821/8 


3 141/2 


111/16 


191/8 


13 


141/8 


587 


700 


H68i* 


3/8 


991/2 


1031/4 


3 11/2 


23/4 


9 


5 


7 


350 


700 


H 79 


3/8 


88 


903/4 


2 12 


21/8 


85/8 


6 


63/4 


676 


946 


H 8O2 


13/32 


1923/8 


1953/4 


7 11/2 


29/16 


18 


119/16 


151/2 


380 


975 


H 43 


7/16 


96 


1025/16 


4 1 


47/16 


815/16 


33/8 


51/8 


450 


660 


H 64 


7/16 


755/8 


781/2 


3 3 


29/32 


75/8 


55/8 


53/4 


1350 


1440 


H 532 


15/32 


1695/16 


1729/16 


8 4 


217/32 


16 1/2 


121/4 


151/2 


330 


1410 


H 272 


1/2 


903/4 


951/8 


5 


31/4 


8 1/2 


51/4 


63/4 


810 


1500 


H 61 


1/2 


151/2 


213/8 


133/4 


41/4 


13/8 


05/8 


1 


532 


1050 


H 19 


17/32 


81 1/2 


851/2 


5 2 


31/32 


8 


59/16 


67/16 


1200 


1900 


H 863 


17/32 


1535/8 


159 


9 10 


4 


133/4 


71/2 


87/16 


1156 


1360 


H 63 


9/16 


98 


103 


6 15 


33/4 


91/8 


51/2 


7 


1050 


1800 


H 333 


9/16 


80 1/4 


847/8 


5 101/2 


31/4 


8 


53/8 


613/16 


1000 


2200 


H 592 


5/8 


741/4 


773/4 


6 7 


27/8 


81/4 


69/16 


71/4 


2100 


3500 


H 8O1 


5/8 


1921/2 


1973/4 


16 11 


315/16 


18 


119/16 


151/2 


900 


2315 


H 722 


21/32 


601/8 


631/2 


5 117/8 


23/4 


75/16 


6 


63/8 


3260 


4240 


H 152 


11/16 


557/8 


593/4 


5 14 


31/2 


53/4 


45/16 


53/16 


1400 


3500 


H 41 


11/16 


1171/2 


1231/2 


12 10 


41/2 


107/8 


63/4 


85/8 


1500 


2720 


H 40 


3/4 


1771/2 


1865/8 


22 21/2 


6 1/2 


16 


73/8 


87/8 


1900 


2300 


H 70 


3/4 


62 


66 


7 12 


33/8 


7 


55/8 


6 1/4 


2750 


5050 


H 172 


13/16 


100 


1063/4 


14 12 


51/8 


91/8 


6 


75/8 


1700 


3700 


H 662 


13/16 


1051/4 


1103/8 


15 7 


45/32 


107/8 


81/8 


87/8 


3670 


5040 


H37 


27/32 


77 


817/8 


12 21/2 


315/16 


8 1/2 


611/16 


71/2 


3300 


6250 


H 872 


27/32 


13013/16 


13715/16 


20 9 


53/8 


121/4 


73/4 


87/16 


3540 


4165 


H 122 


7/8 


85 


911/2 


14 7 


5 


8 1/2 


53/4 


73/8 


2000 


5200 


H 332 


7/8 


82 


88U/16 


13 15 


51/8 


8 


53/8 


613/16 


2250 


5000 


H 2 


15/16 


46 


523/8 


8 151/4 


5 


45/8 


33/8 


4 


3250 


7000 


H 16 


15/16 


85 


927/8 


16 10 


6 


8 


5 


6 


3600 


5100 


H 10 


1 


85 


92 


18 14 


51/2 


8 1/2 


6 


7 


4500 


7000 


H 42i 


I 


36 


427/8 


8 


53/8 


35/8 


25/8 


33/8 


1795 


7180 


H4 


11/16 


987/8 


105 


24 12 


5 


107/8 


8 1/9 


93/8 


6000 


9570 


g?*' 


11/16 


1535/8 


1641/2 


38 9 


8 


133/4 


71/2 


87/16 


4624 


5440 


11/8 


353/8 


411/4 


9 15 


47/8 


41/8 


33/8 


33/4 


6000 


12000 


H I4i 


11/8 


51 


587/8 


14 4 


61/8 


51/8 


311/16 


43/16 


5000 


8950 


H6i 


13/16 


991/8 


1093/4 


31 1 


8 


91/8 


51/2 


7 


4550 


7750 


H 47 


13/16 


731/2 


791/2 


23 


5 7/16 


8 1/4 


69/16 


71/4 


7400 


12500 


H 9 


11/4 


971/2 


108 


33 12 


8 


9 


53/4 


71/2 


4000 


9100 


H 72i 


11/4 


621/8 


683/4 


21 8I/2 


53/8 


75/16 


6 


63/8 


10700 


14875 


H 8 


15/16 


96 


106 1/2 


36 12 


8 


91/8 


6 


71/4 


6350 


10600 


H 62 


15/16 


70 


771/16 


26 12 


513/16 


8 


6I/2 


71/4 


7900 


15800 


H 12i 


13/8 


87 


973/8 


36 7 


8 


8 1/2 


53/4 


73/8 


5000 


12200 


H 39i 


13/8 


755/8 


831/2 


31 11 


63/8 


83/8 


65/8 


71/2 


8150 


16300 


H 28i 


113/32 


8411/16 


95 


37 3 


8 


8 1/4 


53/4 


67/8 


7325 


13250 



* The subscript 1 means the outside coil of ^ concentric group pr 
ttluster; 2 and 3 are inner coils. 



424 RIVETED JOINTS. 

Phosphor-Bronze Springs. Wilfred Lewis (Engs'. aub, Phila., 1887) 

made some tests of a helical spring of phosphor-bronze wire, 0.12 in. 
diameter, II/4 in. diameter from center to center, making 52 coils. 

Such a spring of steel, according to the practice of the P. R. R., might 
be used for 40 lbs. A load of 30 lbs. gradually appUed gave a permanent 
set. With a load of 21 lbs. in 30 hours the spring lengthened from 205/8 
inches to 21 Vs inches, and in 200 hours to 21 1/4 inches. It was concluded 
that 21 lbs. was too great for durabiUty. For a given load the extension 
of the bronze spring was just double the extension of a similar steel 
spring, that is, for the same extension the steel spring is twice as strong. 
Chromium- Vanadium Spring Steel. (Proc. Inst. M. E.^ 1904, pp 
1263, 1305.) —A spring steel containing C, 0.44; Si, 0.173; Mn, 0.837; Cr, 
1.044; Va, 0.188 was made into a spring with dimensions as follows: length 
unstretched 9.6 in., mean diam. of coils (D) 5.22; No. of coils in) 4; diam. 
of wire, id) 0.561. It was tempered m the usual way. When stretched 
it showed signs of permanent set at about 1900 lbs. Compared with two 
springs of ordinary steels the following formulae are obtained: 

Load at which Permanent Set begins. Extension for a load W, 

Chrome-Vanadium Spring. . .56,300 d^lD lbs. TFnD' -h 1,468,000 d* 

West Bromwich Spring 28,400 d3/i> " WnD^ -^ 1,575,000 d« 

Turton & Piatt Spring 44,200 d^JD " WnD^ -*- 1,331,600 d< 

Test of a Vanadium-steel Spring. (Circular of the American Vana- 
dium Co., 1908). — Comparative tests of an ordinary carbon-steel loco- 
motive flat spring and of a vanadium-steel spring, made by the American 
Locomotive Co., showed the following: The vanadium spring, on 36-in. 
centers tested to 94,000 lbs., reached its elastic limit at 85,000 lbs., or 
234,000 lbs. per sq. in. fiber stress, and a permanent set of 0.48 in. The 
test was repeated three times without change in the deflection. The 
carbon spring was tested to 89,280 lbs. and reached an elastic limit at 
65,000 lbs., or 180,000 lbs. fiber stress, with a permanent set of 1.12 in. 
On repeating the test it took an additional set of 0.25 in.» and on the next 
test several of the plates failed. 

RIVETED JOINTS. 

Fairbairn's Experiments. — The eariiest published experiments on 
riveted joints are contained in the memoir by Sir W. Fairbairn in the 
Transactions of the Royal Society. Making certain empirical allow- 
ances, he adopted the following ratios as expressing the relative strength 

of riveted joints: Solid plate 100 

Double-riveted joint 70 

Single-riveted joint 56 

These celebrated ratios appear to rest on a very unsatisfactory analysis 
of the experiments on which they were based. 

Loss of Strength in Punched Plates. {Proc. Inst. M. E., 1881.) — 
A report by Mr. W. Parker and Mr. John, made in 1878 to Lloyd's Com- 
mittee, on the effect of punching and drilling, showed that thin steel 
plates lost comparatively little from punching, but that in thick plates 
the loss was very considerable. The following table gives the results for 
plates punched and not annealed or reamed: 

Thickness of plates 1/4 8/8 V2 S/4 

Loss of tenacity, per cent 8 18 26 33 

When "/8-in. punched holes were reamed out to IVsin. diameter, the loss 
of tenacity disappeared, and the plates carried as high a stress as drilled 
plates. Annealing also restores to punched plates their original tenacity. 

The Report of the Research Committee of the Institution of Mechanical 
Engineers, on Riveted Joints (1881), and records of investigations bj^ Prof. 
A. B. W. Kennedy (1881, 1882, and 1885), summarize the existwig in- 
formation regarding the comparative effects of punching and drilhng 
upon iron and steel plates. An examination of the voluminous tables 
given in Professor Unwin's Report, of the experiments made on iron and 
steel plates, leads to the general conclusion that, while thin plates, even 
of steel, do not suffer very much from punching, yet in those of 1/2 inch 
thickness and upwards the loss of tenacitv due to punching ranges from 
10% to 23% in iron plates, and from 11% to 33% in the case of mild 
steel. In drilled plates there is no appreciable loss ot strengtL. It is 



RIVETED JOINTS. 



425 



possible to remove the bad effects of punching by subsequent reaming or 
annealing. The introduction of a practicable method of drilling the 
plating of ships and other structures, after it has been bent and shaped, 
IS a matter of great importance. In the modern Enghsh practice (1887) 
of the construction of steam-boilers with steel plates punching is almost 
entirely abolished, and all rivet-holes are drilled after the plates have 
been bent to the desired form. 

Strength of Perforated Plates. (P. D. Bennett, Eng*g, Feb. 12, 
1886. p. 155.) — Tests were made to determine the relative effect pro- 
duced upon tensile strength of a flat bar of iron or steel: 1, By a 3/4.inch 
hole drilled to the required size; 2. By a hole punched Vs inch smaller 
and then drilled to the size of the first hole; and, 3. By a hole punched in 
the bar to the size of the drilled hole. The relative results in strength 
per square inch of original area were as follows: 



Unperforated bar 

Perforated by drilling 

Perforated by punching and drilling 
Perforated by punching only 



I. 



Iron. 
1.000 
1.029 
1.030 
0.795 



Iron. 
1.000 
1.012 
1.008 
0.894 



3. 



Steel. 
1.000 
1.068 
1.059 
0.935 



Steel. 
1. 000 
1.103 
1.110 
0.927 



In tests 2 and 4 the holes were filled with rivets driven by hjrdrauUc 
pressure. The increase of strength per square inch caused by drilling is 
a phenomenon of similar nature to that of the increased strength of a 
grooved bar over that of a straight bar of sectional area equal to the 
smallest section of the grooved bar. Mr. Bennett's tests on an iron bar 
0.84 in. diameter, 10 in. long, and a similar bar turned to 0.84 in. diam- 
eter at one point only, showed that the relative strength of the latter to 
the former was 1.323 to 1.000. 

Comparative Eflaciency of Riveting done by Different Methods, 

The Reports of Professors Unwin and Kennedy to the Institution of 
Mechanical Engineers (Proc, 1881, 1882, and 1885) tend to establish the 
four following points: 

1. That the shearing resistance of rivets is not highest in joints riveted 
by means of the greatest pressure; 

2. That the ultimate strength of joints is not affected to an appre- 
ciable extent by the mode of riveting; and, therefore, 

3. That very great pressure upon the rivets in riveting is not the in- 
dispensable requirement that it has been sometimes supposed to be; 

4. That the most serious defect of hand-riveted as compared with 
machine-riveted work consists in the fact that in hand-riveted joints 
visible slip commences at a comparatively small load, thus giving such 
joints a low value as regards tightness, and possibly also rendering them, 
liable to failure under sudden strains after slip has once commenced. 

The following figures of mean results give a comparative view of hand 
and hydraulic riveting, as regards their ultimate strengths in joints, and 
the periods at which in both cases visible slip commenced. 



Total breaking load. Tons . . . . | 
Load at which visible slip began j 



Hand 

Hydraulic 

Hand 

Hydraulic 



86.01 
85.75 
21.7 
47.5 



82.16 
82.70 
25.0 
53.7 



149.2 
145.5 
31.7 
49.7 



193.6 
183.1 
25.0 
56.0 



Some of the Conclusions of the Committee of Research on Riveted 

Joints. 

(Proc, Inst. M. E., April, 1885.) 
The conclusions refer to joints made in soft steel plate with steel rivets, 
the holes drilled, and the plates in their natural state (unannealed). 
The rivet or shearing area has been assumed to be that of the holes, not 
the area of the rivets themselves. The strength of the metal in the joint 
has been compared with that of strips cut from the same plates. 



426 



RIVETED JOINTS. 



The metal between the rivet-holes has a considerably greater tensile 
resistance per square inch than the unperforated metal. This excess 
tenacity amounted to more than 20%, both in s/g-inch and 3/4-inch plates, 
when the pitch of the rivet was about 1.9 diameters. In other cases 3/8-inch 
plate gave an excess of 15% at fracture with a pitch of 2 diameters, of 
10% with a pitch of 3.6 diameters, and of 6.6%, with a pitch of 3.9 
diameters; and 3/4-inch plate gave 7.8% excess with a pitch of 2.8 
diameters. 

In single-riveted joints it may be taken that about 22 tons per square 
inch is the shearing resistance of rivet steel, when the pressure on the 
rivets does not exceed about 40 tons per square inch. In double-riveted 
joints, with rivets of about 3/4-inch diameter, most of the experiments 
gave about 24 tons per square inch as the shearing resistance, but the 
joints in one series went at 22 tons. [Tons of 2240 lbs.] 

The ratio of shearing resistance to tenacity is not constant, but dimin- 
ishes very markedly and not very irregularly as the tenacity increases. 

The size of the rivet heads and ends plays a most important part in the 
strength of the joints — at any rate in the case of single-riveted joints. 
An increase of about one-third in the weight of the rivets (all this increase, 
of course, going to the heads and ends) was found to add about 8 1/2% to 
the resistance of the joint, the plates remaining unbroken at the full 
shearing resistance of 22 tons per square inch, instead of tearing at a 
shearing stress of only a little over 20 tons. The additional strength is 
probably due to the prevention of the distortion of the plates by the 
great tensile stress in the rivets. 

The intensity of bearing pressure on the rivet exercises, with joints 
proportioned in the ordinary way, a very important influence on their 
strength. So long as it does not exceed 40 tons per square inch (meas- 
ured on the projected area of the rivets), it does not seem to affect their 
strength; but pressures of 50 to 55 tons per square inch seem to cause 
the rivets to shear in most cases at stresses varying from 16 to 18 tons 
per square inch. For ordinary joints, which are to be made equally 
strong in plate and in rivets, the bearing pressure should therefore prob- 
ably not exceed 42 or 43 tons per square inch. For double-riveted butt- 
joints perhaps, as will be noted later, a higher pressure may be allowed, 
as the shearing stress may probably not be more than 16 or 18 tons per 
square inch when the plate tears. , 

A margin (or net distance from outside of hcdes to edge of i)late) equal 
to the diameter of the drilled hole has been found sufficient in all cases 
hitherto tried. 

To attain the maximum strength of a joint, the breadth of lap must be 
such as to prevent it from breaking zigzag. It has been found that the 
net metal measured zigzag should be from 30% to 35% in excess of that 
measured stra^ht across, in order to insure a straight fracture. This 
corresponds to a diagonal pitch of 2/3 p + rf/3, if p be the straight pitch 
and d the diameter of the rivet-hole. 

Visible slip or "give" occurs always in a riveted joint at a point very 
much below its breaking load, and by no means proportional to that load. 
A collation of the results obtained in measuring the slip indicates that it 
depends upon the number and size of the rivets in the joint, rather than 
upon anything else; and that it is tolerably constant for a given size of 
rivet in a given type of joint. The loads per rivet at which a joint will 
commence to shp visibly are approximately as follows: 



Diameter of Rivet. 


Type of Joint. 


Riveting. 


Slipping Load per 
Rivet. 


8/4 inch 
3/4 " 
3/4 •• 
linch 
1 " 
1 •• 


Single-riveted 
Double-riveted 
Double-riveted 
Single-riveted 
Double- riveted 
Double- riveted 


Hand 

Hand 

Machine 

Hand 

Hand 

Machine 


2.5 tons 
3.0 to 3.5 tons 
7 tons 

3.2 tons 

4.3 tons 

8 to 10 toni 



RIVETED JOINTS. 



427 



To find the probable load at which a joint of any breadth will commence 
to slip, multiply the number of rivets in the given breadth by the proper 
figure taken from the last column of the table above. The above figures 
are not given as exact; but they represent the results of the experiments. 

The experiments point to simple rules for the proportioning of joints of 
maximum strength. Assuming that a bearing pressure of 43 tons per 
square inch may be allowed on the rivet, and that the excess tenacity of 
the plate is 10% of its original strength, the following table gives the 
values of the ratios of diameter d of hole to thickness t of plate (d -^ t), 
and of pitch p to diameter of hole (p -r- d) in joints of maximum strength 
in 3/y-inch plate. 

For Single-riveted Plates. 



Original Tenacity of 
Plate. 


Shearing Resistance 
of Rivets. 


Ratio. 


Ratio. 

v^d 


Ratio. 
Plate Area 




Lbs. per 
Sq. In. 


Tons per 
Sq. In. 


Lbs. per 
Sq. In. 

49,200 
49,200 
53,760 
53,760 


Tons per 
Sq. In. 


Rivet Area 


30 

28 
30 
28 


67,200 
62,720 
67,200 
62,720 


22 
22 
24 
24 


2.48 
2.48 
2.28 
2.28 


2.30 
2.40 
2.27 
2.36 


0.667 
0.785 
0.713 
0.690 



This table shows that the diameter of the hole should be 2i/3 times the 
thickness of the plate, and the pitch of the rivets 23/8 times the diameter 
of the hole. Also, it makes the mean plate area 71% of the rivet area. 
If a smaller rivet be used than that here specified, the joint will not be of 
uniform, and therefore not of maximum, strength; but with any other 
size of rivet the best result will be got by use of the pitch obtained from the 
simple formula p = ad- ft + d, where, as before, rf is the diameter of the 
hole. 

The value of the constant a in this equation is as follows: 

For 30-ton plate and 22-ton rivets, a = 0.524 

" 28 " " " 22 " " " 0.558 

.. 3Q .. .. M 24 " " " 0.570 

.. 28 ♦* ♦♦ " 24 " *' *• 0.606 



Or, in the mean, the pitch p ■■ 



d2 
= 0.56 J + d. 



With too small rivets this 



gives pitches often considerably smaller in proportion than 23/8 times the 
diameter. 

For double-riveted lap-joints a similar calculation to that given 
above, but \sith a somewhat smaller allowance for excess tenacity, on 
account of the large distance between the rivet-holes, shows that for joints 
of maximum strength the ratio of diameter to thickness should remain 
precisely as in single-riveted joints; while the ratio of pitch to diameter 
of hole should be 3.64 for 30-ton plates and 22 or 24 ton rivets, and 3.82 
for 28-ton plates with the same rivets. 

Here, still more than in the former case, it is hkely that the prescribed 
size of rivet may often be inconveniently large. In this case the diameter 
of rivet should be taken as large as possible; and the strongest joint for 
a given thickness of plate and diameter of hole can then be obtained by 
using the pitch given by the equation p = adVt + d, where the values of 
the constant a for different strengths of plates and rivets may be taken 
as follows, for any thickness of plate from 3/8 to 3/4-inch: 



For 30-ton plate and 24-ton rivets ) ^ 



28 
30 " 

28 •• 



22 
" 22 

" 24 



1.16^+ d; 

p = 1.06 ^ + d; 

d^ 
p - 1.24 j+d. 



428 



RIVETED JOINTS. 



In double-riveted butt-joints it is impossible to develop the full 
shearing resistance of the joint without getting excessive bearing pressure, 
because the shearing area is doubled without increasing the area on which 
the pressure acts. Considering only the plate resistance and the bearing 
pressure, and taking this latter as 45 tons per square inch, the best pitch 
would be about 4 times the diameter of the hole. We may probably say 
with some certainty that a pressure of from 45 to 50 tons per square inch on 
the rivets will cause shearing to take place at from 16 to 18 tons per square 
inch. Working out the equations as before, but allowing excess strength 
of only 5% on account of the large pitch, we find that the proportions of 
double-riveted butt-joints of maximum strength, under given conditions, 
are those of the following table: 

Double-riveted Butt-joints. 



Original Ten- 
acity of Plate, 
Tons per Sq. 


Shearing Re- 
sistance of 

Rivets, Tons 
per Sq. In. 


Bearing Pres- 
sure, Tons per 
Sq. In. 


Ratio 
d 
1 


Ratio 

E 
d 


30 


16 


45 


1.80 


3.85 


28 


16 


45 


1.80 


4.06 


30 


18 


48 


1.70 


4.03 


28 


18 


48 


1.70 


4.27 


30 


16 


50 


2.00 


4.20 


28 


16 


50 


2.00 


4.42 



Practically, therefore, it may be said that we get a double-riveted butt- 
joint of maximum strength by making the diameter of hole about 1.8 
times the thickness of the plate, and making the pitch 4.1 times the 
diameter of the hole. 

The proportions just given belong to joints ot maximum strength. 
But in a boiler the one part of the joint, the plate, is much more affected 
by time than the other part, the rivets. It is therefore not unreasonable 
to estimate the percentage by which the fplates might be weakened by 
corrosion, etc., before the boiler would be unfit for use at its proper 
steam-pressure, and to add correspondingly to the plate area. Probably 
the best thing to do in this case is to proportion the joint, not for the 
actual thickness of plate, but for a nominal thickness less than the actual 
by the assumed percentage. In this case the joint \\\\\ be approximately 
one of uniform strength by the time it has reached its final workable 
condition; up to which time the joint as a whole will not really have been 
weakened, the corrosion only gradually bringing the strength of the plates 
down to that of rivets. 

Efficiencies of Joints. 

The average results of experiments by the committee gave: For double- 
riveted lap-joints in 3 g-inch plates, efficiencies ranging from 67.1% to 
81.2%. For double-riveted butt-joints (in double shear) 61.4% to 71.3%. 
These low results were probably due to the use of very soft steel in the 
rivets. For single-riveted lap-joints of various dimensions the efficiencies 
varied from 54.8% to 60.8%. The shearing resistance of steel did not in- 
crease nearly so fast as its tensile resista^nce. With very soft steel, for 
instance, of only 26 tons tenacity, the shearing resistance was about 80% 
of the tensile resistance, whereas with very hard steel of 52 tons tenacity 
the shearing resistance was only somewhere about 65% of the tensile 
resistance. 

Proportions of Pitch and Overlap of Plates to Diameter of Rivet- 
Hole and Thickness of Plate. 

(Prof. A. B. W. Kennedy, Proc. Inst. M. B., April, 1885.) 
t = thickness of plate: 

d = diameter of rivet (actual) in parallel hole; 
p == pitch of rivets, center to center- 
s «=« space between lines of rivets; 
I -= overlap of plate. 



EIVETED JOINTS. 



429 



The pitch is as wide as is allowable without impairing the tightness ol 
the joint under steam. 

For single-riveted lap-joints in the circular seams of boilers which hav6 
double-riveted longitudinal lap-joints, 

d = t X 2.25: p = d X 2.25 = ^X 5 (meariy);Z = ^ X 6. 

For double-riveted lap-joints: 

d = 2.25t; p = St; s = 4.5^, I = 10.5^. 



Single-riveted Joints. 


Double-riveted Joints. 


t 


d 


P 


I 


t 


d 


P 


s 


I 


3/16 


7/16 


15/16 


11/8 


3/16 


Vie 


11/2 


7/8 


2 


1/4 


9/16 


11/4 


11/2 


1/4 


9/16 


2 


13/16 


23/4 


5/lG 


11/16 


1 9/16 


17/8 


5/16 


11/16 


21/2 


11/2 


33/8 


3/8 


13/16 


1 7/8 


21/4 


3/8 


13/16 


3 


13/4 


4 


7/16 


1 


2 3/16 


25/8 


7/16 


1 


31/2 


2 


45/8 


V2 


11/8 


2 1/2 


3 


1/2 


11/8 


4 


21/4 


51/4 


9/16 


11/4 


213/16 


3 3/8 


9/16 


11/4 


41/2 


21/2 


57/8 



With these proportions and good workmanship there need be no fear of 
leakage of steam through the riveted joint. 

The net diagonal area, or area of plate, along a zigzag line of fracture 
should not be less than 30% in excess of the net area straight across the 
joint, and 35% is better. 

Mr. Theodore Cooper (R. R. Gazette, Aug. 22, 1890), referring to Prof. 
Kennedy's statement quoted above, gives as a sufficiently approximate 
rule for the proper pitch between the rows in staggered riveting, one-half 
of the pitch of the rivets in a row plus one-quarter the diameter of a 
rivet-hole. 

Test of Double-riveted Lap and Butt Joints. 

{Proc. Inst. M. E., October, 1888.) 
Steel plates of 25 to 26 tons per square inch T. S., steel rivets of 24.6 
tons shearing strength per square inch. 



Kind of Joint. 


Thickness of 
Plate. 


Diameter of 
Rivet-holes. 


Ratio of 

Pitch to 

Diameter. 


Comparative 

Efficiency of 

Joint. 


Lap 

Butt 


3/8" 

3/8 
3/4 
3/4 
3/4 

1 
1 


0.8'' 

0.7 

I.I 

1.6 

1.1 

1.6 

1.3 

1.75 

1.3 


3.62 
3.93 
2.82 
3.41 
4.00 
3.94 
2.42 
3.00 
3.92 


75.2 
76.5 


Lao 


68.0 


Lap 

Butt 


73.6 
72.4 


Butt 


76.1 


Lap 

Lap 

Butt 


63.0 
70.2 
76.1 







Diameter of Rivets for Different Thicknesses of Plates. 



Thickness 
of Plate. 


5/16 


3/8 


7/16 

5/8 
3/4 
3/4 
5/8 
15/16 
7/8 
9/16 


1/2 

3/4 

13/16 

3/4 

...... 

15/16 
11/16 


9/16 

3/4 
13/16 

7/8 
3/4 


5/8 

3/4 
7/8 

7/8 


11/16 

% 
7/8 
7/8 
13/16 


3/4 

7/8 
15/16 
1 

7/8 


13/16 

7/8 
1 


7/8 

1 

11/8 
11/8 
I 


15/16 

1 

13/16 

11/8 


1 


Diam. H).. 
Diam. (2).. 
Diam. (3).. 
Diam. (4) 


5/8 
5/8 
1/2 


5/8 
5/8 
5/8 
5/8 
7/8 
3/4 
1/2 


1 

11/4 
11/8 
11/16 


Diam. (5).. 
Diam (6) 


3/4 
11/16 
3/8 




1 

3/4 


1 
13/16 














Diam. (7).. 















430 



RIVETED JOINTS. 



(1) Lloyd's Rules. 
(4) French Veritas. 



(2) Liverpool Rules. (3) English Dock-yards. 
(5) Hartford Steam Boiler Inspection and Insur- 
ance Co., double riveted lap-joints. (6) Ditto, triple-riveted butt-joints. 
(7) F. E. Cardullo. (Vie less than diam. of hole.) 

Calculated Efficiencies — Steel Plates and Steel Rivets. — The 
following table has been calculated by the author on the assumptions that 
the excess strength of the perforated plate is 10%, and that the shearing 
strength of the rivets per square inch is four- fifths of the tensile strength 
of the plate (or, if no allowance is made for excess strength of the perfo- 
rated plate that the shearing strength is 72.7% qf the tensile strength). 
If t = thickness of plate, d = diameter of rivet-hole, p = pitch, and T = 
tensile strength per square inch, then for single-riveted plates 

(p - d)tX I.IOT = -d^xi T, whence p = 0.571? + d. 
4 o t . 

For double-riveted lap-joints, p = 1.142 -r- 4- d. 

The coefficients 0.571 and 1.142 agree closely with the averages of those 
given in the report of the committee of the Institution of Mechanical En- 
glneers, quoted on page 427, ante. 





> 

5 


Pitch. 


Efficiency. 


% 


> 

s 


Pitch. 


Efficiency. 


i 


be 


hC 


bio 


M 


bi; 


fcC 


bi) 


bb 


« 


*© 


^C 


C 


.£ 


C 


a» 


o 


c 


c 


.S 


c 


a 




-^'-^ 


cj-^ 




<Q'Z 


a 






<s'Z 




<a'Z ■ 


'i 


^ o 

5-= 


02 


II 


03 (U 




IS 


si 

e« 

5-^ 


bC> 


11 


.ss 


II 


in. 


in. 


in. 


in. 


% 


% 


in. 


in. 


in. 


in. 


% 


% 


3/16 


7/18 


1.020 


1.603 


57.1 


IIJ 


1/2 


3/4 


1.392 


2.035 


46.1 


63.1 


3/16 


1/2 


1.261 


2.023 


60.5 


75.3 


1/2 


7/8 


1.749 


2.624 


50.0 


66.6 


Vi 


1/2 


1.071 


1.642 


53.3 


69.6 


1/2 




2.142 


3.284 


53.3 


70.0 


V4 


9/16 


1.285 


2.008 


56.2 


72.0 


1/2 


11/8 


2.570 


4.016 


56.2 


72.0 


5/16 


9/16 


1.137 


1.712 


50.5 


67.1 


9/16 


3/4 


1.321 


1.892 


43.2 


60.3 


5/16 


5/8 


1.339 


2.053 


53.3 


69.5 


9/16 


7/8 


1.652 


2.429 


47.0 


64.0 


5/16 


11/16 


1.551 


2.415 


55.7 


71.5 


9/16 


1 


2.015 


3.030 


50.4 


67.0 


3/8 


5/8 


1.218 


1.810 


48.7 


65.5 


9/16 


11/8 


2.410 


3.694 


53.3 


69.5 


3/8 


3/4 


1.607 


2.463 


53.3 


69.5 


9/16 


11/4 


2.836 


4.422 


55.9 


71.5 


3/8 


7/8 


2.041 


3.206 


5" 1 


72.7 


5/8 


3/4 


1.264 


1.778 


40.7 


57.8 


7/16 


5/8 


1.136 


1.647 


45. 


62.0 


5/8 


7/8 


1.575 


2.274 


44.4 


61.5 


7/16 


3/4 


1.484 


2.218 


49. t. 


66.2 


5/8 


1 


1.914 


2.827 


47.7 


64.6 


7/16 


7/8 


1.869 


2.864 


53.2 


69.4 


5/8 


11/8 


2.281 


3.438 


50.7 


67.3 


7/16 


1 


2.305 


3.610 


56.6 


72.3 


5/8 


11/4 


2.678 


4.105 


53.3 


69.5 



Apparent Shearing Resistance of Rivet Iron and Steel. 

{Froc, Inst. M. E., 1879, Engineering, Feb. 20, 1880.) 

The true shearing resistance of the rivets cannot be ascertained from 
experiments on riveted joints (1) because the uniform distribution of the 
load to all the rivets cannot be insured; (2) because of the friction of the 
plates, which has the effect of increasing the apparent resistance to shear- 
ing in an element uncertain in amount. Probably in the case of single- 
riveted joints the shearing resistance is not much affected by the friction. 

Fairbairn's experiments show that a rivet is 6V2% weaker in a drilled 
than in a punched hole. By rounding the edge of the rivet-hole, the 
apparent shearing resistance is increased 12%. Messrs. Greig and Eyth's 
experiments indicate a greater resistance of the rivets in punched holes 
than in drilled holes. 

If the apparent shearing resistance is less for double than for single 
shear, it is probably due to unequal distribution of the stress on the twO' 
rivet sections. 



THE STRENGTH OF RIVETED JOINTS. 



431 



The shearing resistance of a bar, when sheared in circumstances which 
prevent friction, is usually less than the tenacity of the bar. The foi- 
lowing results show the decrease: 

Harkort, iron Tenacity, 26.4 Shearing, 16.5 Rario, 0.62 

Lavalley, iron " 25.4 " 20.2 ;• 0.79 

Greig and Eyth, iron. *' 22.2 ** 19.0 0.85 

Greig and Eyth, steel ** 28.8 " 22.1 " 0.77 

In Wohler's researches (in 1870) the shearing strength of iron was found 
to be four-fifths of the tenacity. Later researches of Bauschinger con- 
firm this result generally, but they snow that for iron the ratio of the 
shearing resistance and tenacity aepends on the direction of the stress 
relatively to the direction of rolling, Tne above ratio is valid only if the 
shear is in a plane perpendicular to the direction of rolling, and if the 
tension is applied parallel to the direction of rolling. If the plane of shear 
is parallel to the breadth of the bar, tne resistance is only half as great 
as in a plane perpendicular to the fibers. 

THE STRENGTH OF RIVETED JOINTS. 

Joint of Maximum Efficiency. — (F. E. Cardullo=) If a riveted joint 
is mjtde with sufficient lap, and a proper distance between the rows of 
rivets, it will break in one of the three following ways: 

1. By tearing the plate along a line, through the outer row of rivets, 

2. By shearing the rivets 

3. By crushing the plate or the rivets. 
Let t = the thickness of the main plates. 

d = the diameter of the rivet-holes. 

/ = the tensile strength of the plate in pounds per sq. in. 

s = the shearing strength of the rivets in pounds per sq. in. when 
in single shear. 

p = the distance between the centers of rivets of the outer row 
(see Figs. 96 and 97)= the pitch in single and double lap riveting = twice 



)"#"" Q"""§ 



_i© ©I© ©. 
[© © 0^© @ 



rSSM 



'W © 



Fig. 96. 
Triple Riveting, 




© 



© 






mUD Q o © 
M 5" © Q '^j 



ii. 



o 




Fig. 97. 
Quadruple Riveting. 



the pitch of the inner rows in triple butt strap riveting, in which alter- 
nate rivets in the outer row are omitted, = four times the pitch in quad- 
ruple butt strap riveting, in which the outer row has one-fourth of the 
number of rivets of the two inner rows. 

c = the crushing strength of the rivets or plates in pounds per 
sq. in, 

n = the number of rivets in each group in single shear. (A group 
is the number of rivets on one side of a joint corresponding to the dis- 
tance p; = 1 rivet in single riveting, 2 in double riveting, 5 in triple 
butt strap riveting, and 11 in quadruple butt strap riveting.) 

m = the number of rivets in each group in double shear. 

5" = the shearing strength of rivets in double shear, in pounds per 
sq. in., the rivet section being counted once. 

T = the strength of the plate at the weakest section. = ft (p - d), 

S = the strength of the rivets against shearing, = 0.7854 (? (ns + 
ms'). 

C = the strength of the rivets or the plates against crushing, =» 



432 RIVETED JOINTS. 

In order that the joint shall have the greatest strength possible, the 
tearing, snearing, and crushing strength must all be equal. In order to 
make it so, 

1. Substitute the known numerical values, equate the expressions for 
shearing and crushing strength, and find the value of d, taking it to the 
nearest Vie in. 

2. Next find the value of S in the second equation, and substitute it 
for T in the first equation. Substitute numerical values for the other 
factors in the first equation, and solve for p. 

The efficiency of a riveted joint in tearing, shearing and crushing, is 
equal to the tearing, shearing or crushing strength, divided by the quan- 
tity ftp, or the strength of the solid plate. 

The efficiency in tearing is also equal to (p — d) -j- v. 

The maximum possible efficiency for a well-designed joint is 



m -\- n -h (f -^ c) 

Empirical formula for the diameter of the rivet-hole when the crush- 
ing strength is unknown. Assuming that c = 1 .4 /, and s'' = 1 .75 s, we have 
by equating C and S, and substituting, 

d = 1.782 <^("+"> 



5(71+ 1.75 m) 



Margin. The distance from the center of any rivet-hole to the edge of 
the plate should be not less than 11/2^. The distance between two adja- 
cent rivet centers should be not less than 2d. It is better to increase 
each of these dimensions by Vsin. 

The distance between the rows of rivets should be such that the net 
section of plate material along any broken diagonal through the rivet- 
holes should be not less than 30 per cent greater than the plate section 
along the outer line of rivets. 

The thickness of the inner cover strap of a butt joint should be 3/4 of 
the thickness of the main plate or more. The thickness of the outer strap 
should be s/g of the thickness of the main plate or more. 

Steam Tightness. It is of great importance in boiler riveting that 
the joint be steam tight. It is therefore necessary that the pitch of the 
rivets nearest to the calked edge be limited to a certain function of the 
thickness of the plate. The Board of Trade rule for steam tightness is 

p='Ct + 15/8 in. 

where p = the maximum allowable pitch in inches. 
t = the thickness of main plate in inches. 
C = a constant from the following table. 

No. of Rivets p^r Group.. . 1 

Lap Joints C= 1 .31 

Double-strapped Joints.... C= 1.75 3.50 4.63 5.52 6.00 

The pitch should not exceed ten inches under any circumstances. 

When the joint has been designed for strength, it should be checked by 
the above formula. Should the pitch for strength exceed the pitch for 
steam tightness, take the latter, substitute it in the formula 

ft (p-d) =0.7854 d2 (ns + ms''), 

and solve for d. If the value of d so obtained is not the diameter of some 
standard size rivet, take the next larger Vie in. 

Calculation of Triple-riveted Butt and Strap Joints. — Formulae: 

T = ft (p~d), S = 0.7854d:2 (^s + ms''), C=-dtc (m + n) (notation on 
preceding page), n = 1, m = 4. 

Take / = 55,000; s = 0.8/, = 44,000; s" = 1.75s = 77,000, c = 1.4/ 
« 77,000. 

Then T = 55,000 « (p-d), S - 276,460 cf^, C = 385,000 d<. 



2 


3 


4 


2.62 


3.47 


4.14 


3.50 


4.63 


5.52 



THE STRENGTH OF RIVETED JOINTS. 



433 



For maximum strength, T — «5 = C; dividing by 55,000 <, (p- cO ■■ 
5.027rf = 7rf; whence d = 1.3925<; p = 8d. 
Thickness or plate, ^=5/16 3/g 7/i« 1/2 9/ie Va 

Diam, rivet hole, 

d = 1.3925^. ,,0. 0.4353 0.5222 0.6092 0.6962 0.7833 0.8703 

Pitch of outer row, 

p = 8d 3.4816 -^.1776 4.8736 5.5696 6.2664 6.9624 

T = 55,000 t(p-d) 52,360 75,390 102,610 134,020 169,630 209,420 
5= 276,460 d2 „. . 52,330 75,360 102,570 133,970 169,560 209,330 
C=385,000d<; ., 52,350 75,390 102,620 134,030 169,630 209,420 

Calculations by logarithms, to nearest 10 pounds. 

Efficiency of all joints (p — d)-^p = 87.5 per cent. 

Maximum efficiency by Cardullo's formula, — ; 7— = - . , .-, ^ 

n -h m + f/c 5 + 1/1.4 
= 87.5 per cent. 

Diameter of rivet-hole, next largest 16th, 7/i6 ^/le ^/s ^/i ^ViQ ^/g 
For the same thickness of plates the Hartford Steam Boiler Inspection 
and Insurance Co. gives the following proportions: 

Thickness, U ^/iQ ^/8 '^/i6 V2 9/i8 Vs 

Diam. rivet-hole, (?, 3/4 i3/ie is/^e 1 H/ie IV16 

Pitch of outer row, p, 6 1/4 6 1/2 63/4 71/2 73/4 73/4 

Using the same values for f, s, s^ and c, we obtain: 

r= 94,530 117,300 139,860 178,750 207,850 229,880 

S = 155,400 168,400 194,300 207,300 220,200 220,200 

C= 90.030 117,300 157,900 192,500 230,000 255,500 

Strength of solid 

plate, fpi = 107,360 134,060 162,420 206,250 239,770 266,400 

Efficiency T, S or 

C, lowest ^ fpt, 

per cent 83.9 87.5 86.1 86.7 86.7 82.6 

The 5/16 in. plate fails by crushing, the s/s by shearing, the others by 
tearing. 

Calculation of Quadruple Riveting. — In this case there are 11 rivets 
in the group. If the upper strap plate contains all the rivets except the 
outer row, then n = 1, m = 10. Using the same values for/, s, s" and 
c as above, we have ns + ms" = 814,000; T = 55,000^ (P - rf); 5 == 
639,315^2; c = Ml, 000 dt. 

For maximum strength, t (p — d) = 11.624c?2 = 15Adt; whence d -= 
1.32485^, p = 16.4 d. Efficiency (p - d)-^p = 93.9 per cent. Check by 

Cardullo's formula — ; — r— = — — -tkj— = 93.9 per cent. 

n-^ m + f/c 11+ 10/14 
British Board of Trade and Lloyd's Rules for Riveted Joints. — 

Board of Trade. — Tensile strength or rivet bars between 26 and 30 tons, 
el. in lO'^ not less than 25%, and contr. of area not less than 50%. 

The shearing resistance of the rivet steel to be taken at 23 tons per 
square inch, 5 to be used for the factor of safety independently of any 
addition to this factor for the plating. Rivets in double shear to have 
only 1.75 times the single section taken in the calculation instead of 2. 
The diameter must not be less than the thickness of the plate, and the 
pitch never greater than 8 1/2''. The thickness of double butt-straps 
(each) not to be less than 5/8 the thickness of the plate; single butt-straps 
not less than 9/8. 

Distance from center of rivet to edge of hole = diameter of rivet X IV2. 

Distance between rows of rivets 

= 2 X diam. of rivet or = [(diam. X 4) + 1] -1- 2, if chain, and 

^[(pitch X 11) 4- (diam. X 4)] X (pitch + diam. X 4) ,, . 
= —LAii i ^^ ^ ^±: i if zigzag. 

Diagonal pitch = (pitch X 6 + diam. X 4) -4- 10. 

Lloyd's. — T. S. of rivet bars. 26 to 30 tons; el. not less than 20% in 8". 
The material must stand bending to a curve, the inner radius of which ii 



434 



RIVETED JOINTS. 



not greater than II/2 times the thickness of the plate, after having been 
uniformly heated to a low cherry-red, and quenched in water at 82° F. 

Rivets in double shear to have only 1.75 times the single section taken 
in the calculation instead of 2. The shearing strength of rivet steel to 
be taken at 85% of the T. S. of the material of shell plates. In any case 
where the strength of the longitudinal joint is satisfactorily shown by 
experiment to be greater than given by the formula, the actual strength 
may be taken in the calculation. 



Proportions of Riveted Joints. (Hartford S. B. Insp. and Ins. Co.) 
Single-riveted Girth Seams of Boilers. 



ThicknesSo 


1/4 


5/16 


3/8 


7/16 


1/2 


Diam. rivet-hole. 
Pitch 


3/4 11/16 
21/16 21/16 
11/8 11/32 


13/16 3/4 
21/8 21/8 
17/32 11/8 


15/16 13/16 
23/8 21/8 
113/32 17/32 


1 15/16 
27/16 23/8 
11/2 113/32 


11/16 I 
21/2 21/2 


Center to edge . . 


19/32 11/2 



Double-riveted Lap Joints. 








Thickness of plate 


1/4 


5/16 


3/8 


7/16 


1/2 






Diam. rivet-hole 


3/4 
27/8 
1 15/16 
11/8 
0.74 


13/16 
27/8 
1 15/16 
17/32 
0.72 


15/16 
31/4 
23/16 
113/32 
0.70 


1 

31/4 
23/16 
11/2 
0.70 


II/16 


Pitch 


3.32 


Dist. bet. rows 


2 2 


Dist. inner row to edge 


IZ^ 


Efficiency 







Triple-riveted Lap Joints. 



Thickness 

Diam. rivet-hole. . 

Pitch 

Dist. bet. rows. . . 
Inner row to edge 
Efficiency 



1/4 


5/16 


3/8 


7/16 


11/16 


3/4 


13/16 


15/16 


3 


31/8 


31/4 


33/4 


2 


21/16 


23/18 


21/2 


11/32 


11/8 


17/32 


113/32 


0.7/ 


0.76 


0.75 


0.73 



1/2 



1 

315/16 
25/8 
11/2 
0.73 



Triple-riveted Buti-strap Joints. 



Thickness 

Diam. rivet-hole 

Pitch, inner rows. . . . 
Dist. bet. inner rows. 
Dist. outer to 2d row 
Edge to nearest row. 
Efficiency % 



5/16 


3/8 


7/16 


1/2 


9/16 


3/4 


13/16 


15/16 


1 


11/16 


31/8 


31/4 


33/8 


33/4 


37/8 


21/8 


2 3/16 


21/4 


23/8 


2 5/8 


23/8 


21/2 


23/4 


3 


33/16 


11/4 


17/32 


1 13/32 


11/2 


119/32 


88(?) 


87.5 


86 


86.6 


85.4 



11/16 

37/8 

25/8 

3 3/16 

119/32 

84(?) 



The distance to the edge of the plate is from the center of rivet-holes. 



THE STRENGTH OF RIVETED JOINTS. 



435 



Pressure Required to Drive Hot Rivets. 

Philadelphia, give the following table (1897): 



■R. D. Wood & Co. 



Power to Drive Rivets Hot. 



Size. 


Girder- 


Tank- 


Boiler- 


Size. 


Girder- 


Tank- 


Boiler- 


work. 


work. 


work. 


work. 


work. 


work. 


in. 


tons. 


tons. 


tons. 


in. 


tons. 


tons. 


tons. 


1/2 


9 


15 


20 


u/s 


38 


60 


75 


5/8 


12 


18 


25 


11/4 


45 


70 


100 


3/4 


15 


22 


33 


11/2 


60 


85 


125 


7/8 


22 
30 


30 
45 


45 
60 


13/4 


75 


100 


150 



The above Is based on the rivet passing through only two thicknesses of 
plate which together exceed the diameter of the rivet but little, if any. 

As the plate thickness increases the power required increases approxi- 
mately in proportion to the square root of the increase of thickness. Thus, 
if the total thickness of plate is four times the diameter of the rivet, we 
should require twice the power given above in order to thoroughly fill the 
rivet-holes and do good work. Double the thickness of plate would 
increase the necessary power about 40%. 

It takes about four or five times as much power to drive rivets cold as 
to drive them hot. Thus, a machine that will drive 3/4-in. rivets hot will 
usually drive 3/8 -in. rivets cold (steel). Baldwin Locomotive Works 
drive 1/2 -in. soft-iron rivets cold with 15 tons. 

Riveting Pressure Required for Bridge and Boiler Work. 

(Wilfred Lewis, Engineers' Club of Philadelphia, Nov., 1893.) 

A number of 3'g-inch rivets were subjected to pressures between 10,000 
and 60,000 lbs. At 10,000 lbs. the rivet sw^elled and filled the hole with- 
out forming a head. At 20,000 lbs. the head w-as forrhed and the plates 
were slightly pinched. At 30,000 lbs. the rivet w^as well set. At 40,000 
lbs. the metal in the plate surrounding the rivet began to stretch, and the 
stretching became more and more apparent as the pressure was increased 
to 50,000 and 60,000 lbs. From these experiments the conclusion might 
be drawn that the pressure required for cold riveting was about 300,000 
lbs. per square inch of rivet section. In hot riveting, until recently there 
was never any call for a pressure exceeding 60,000 lbs., but now pressures 
as high as 150,000 lbs. are not uncommon, and even 300,000 lbs. have been 
contemplated as desirable. 

Pressure Required for Heading Cold Rivets. — Experiments made 
by the author in 1906 on 1/2 and 5/8 in. soft steel rivets showed that the 
pressure required to head a rivet cold, with a hemispherical heading die, 
was a function of the final or maximum diameter of the head. The 
metal began to flow and fill the hole at about 50,000 lbs. per sq. in. press- 
ure, but it hardened and increased its resistance as it flowed until it reached 
a maximum of about 100,000 lbs. per sq. in. of the maximum area of the 
head. 

^ Chemical and Physical Tests of Soft Steel Rivets. — Ten rivet 
bars and ten rivets selected from stock of the Champion Rivet Co., Cleve- 
land, O., were analyzed by Oscar Textor, with results as follows: 

P. 0.008 to 0.027, av. 0.015; Mn, 0.31 to 0.69, av. 0.46: S, 0.023 to 
0.044, av. 0.033: Si, 0.001 to 0.008, av. 0.005: C, 0.06 to 0.19, av. 0.11. 
Only four of the 20 samples were over 0.14 C, and these were made for 
high strength. Ten bars and two rivets gave tensile strength, 46.735 to 
55.380,. av. 52,195 lbs. per sq. in.: elastic limit. 31,350 to 43,150. av. 
35,954: elongation, bars only, 28 to 35, av. 31.9% in 8 ins.: reduction of 
area. 65.6%. Eight bars in single shear gave shearing strength 35,660 
to 50.190, av. 44,478 lbs. per sq. in.: seven bars in double shear gave 
39,170 to 53,900, av. 45,720 lbs. The shearing strength averaged 86.3% 
of the tensile strength. 



436 



IRON AND STEEL. 



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,2 2 i54:33 



CAST IRON. 



437 



CAST IRON. 

The Manufacture of Cast Iron. — Pig iron is the name given to the 
crude form of iron as it is produced in the blast furnace. This furnace 
is a tall shaft, lined with fire brick, often as large as 100 ft. high and 20 ft. 
in diameter at its widest part, called the "bosh." The furnace is kept 
filled with alternate layers of fuel (coke, anthracite or charcoal), while a 
melting temperature is maintained at the bottom by a strong blast. 
The iron ore as it travels down the furnace is decarbonized by the carbon 
monoxide gas produced by the incomplete combustion of the fuel, and as 
it travels farther, into a zone of higher temperature, it absorbs carbon 
and silicon. The phosphorus originally in the ore remains in the iron. 
The sulphur present in the ore and in the fuel may go into combination 
with the lime in the slag, or into the iron, depending on the constitution 
of the slag and on the temperature. The silica and alumina in the ore 
unite with the lime to form a fusible slag, which rests on the melted iron 
in the hearth. The iron is tapped from the furnace several times a day, 
while in large furnaces the slag is usually run off continuously. 

Grading of Pig Iron. — Pig iron is apjDroximately graded according 
to Its fracture, the number of grades varying in different districts. In 
Eastern Pennsylvania the principal grades recognized are known as No. 
1 and 2 foundry, gray forge or No. 3, mottled or No. 4, and white or No. 
5. Intermediate grades are sometimes made, as No. 2 X, between No. 1 
and No. 2, and special names are given to irons more highly silicized than 
No, 1, as No. 1 X, silver-gray, and soft. Charcoal foundry pig iron is 
graded by numbers 1 to 5, but the quality is very different from the 
corresponding numbers in anthracite and coke pig. Southern coke pig 
iron is graded into ten or more grades. Grading by fracture is a fairly 
satisfactory method of grading irons made from uniform ore mixtures 
and fuel, but is unreliable as a means of determining quality of irons 
produced in different sections or from different ores. Grading by chemi- 
cal analysis, in the latter case, is the only satisfactory method. The 
following analyses of the five standard grades of northern foundry and 
mill pig irons are given by J. M. Hartman (Bull. I. & S. A., Feb., 1892): 





No. 1. 


No. 2. 


No. 3. 


No. 4. 


No.4B. 


No. 5. 


Iron 


92.37 
3.52 
0.13 
2.44 
1.25 
0.02 
0.28 


92.31 
2.99 
0.37 
2.52 
1.08 
0.02 
0.72 


94.66 
2.50 
1.52 
0.72 
0.26 

trace 
0.34 


94.48 
2.02 
1.98 
0.56 
0.19 
0.08 
0.67 


94.08 
2.02 
1.43 
0.92 
0.04 
0.04 
2.02 


94 68 


Graphitic carbon 

Combined carbon 

Silicon 


0.41 


Phosphorus 


04 


Sulphur 


02 


Manganese 


0.98 







Characteristics of These Irons. 

No. 1. Gray. — A large, dark, open-grain iron, softest of all the num- 
bers and used exclusively in the foundry. Tensile strength low. Elastic 
limit low. Fracture rough. Turns soft and tough. 

No. 2. Gray. — A mixed large and small dark grain, harder than No. 
1 iron, and used exclusively in the foundry. Tensile strv^ngth and elastic 
limit higher than No. 1. Fracture less rough than No. 1. Turns harder, 
less tough, and more brittle than No. 1. 

No. 3. Gray. — Small, gray, close grain, harder than No. 2 iron, used 
either in the rolling-mill or foundry. Tensile strength and elastic limit 
higher than No. 2. Turns hard, less tough, and more brittle than No. 2. 

No. 4. Mottled. — White background, dotted closely with small black 
spots of graphitic carbon: little or no grain. Used exclusively in the 
rolling-mill. Tensile strength and elastic limit lower than No. 3. Turns 
with difiaculty; less tough and more brittle than No. 3. The manganese 
in the B pig iron replaces part of the combined carbon, making the iron 
harder and closing the grain, notwithstanding the lower combined carbon. 



438 IRON AND STEEL, 

No. 5. White. — Smooth, white fracture, no grain, used exclusively ia 
the roIUng mill. Tensile strength and elastic limit much lower than No. 4. 
Too hard to turn and more brittle than No. 4. 

Southern pig irons are graded as follows, beginning with the highest in 
siUcon: Nos. 1 and 2 silvery, Nos. 1 and 2 soft, all containing over 3% 
of silicon; Nos. 1, 2, and 3 foundry, respectively about 2.75%, 2.5% and 
2% silicon; No. 1 mill, or "foundry forge;" No. 2 mill, or gray forge; 
mottled; white. 

Chemistry of Cast Iron. — Abbreviations, TO, total carbon; GC, 
graphitic carbon; CO, combined carbon. Numerous researches have been 
made and many papers written, especially between the years 1895 and 
1908, on the relation of the physical properties to the chemical constitu- 
tion of cast iron. Much remains to be learned on the subject, but the 
following is a brief summary of prevailing opinions. 

Carbon. — Carbon exists in three states in cast iron: 1, Combined 
carbon, w^hich has the property of making iron white and hard ; 2, Graphi- 
tic carbon or graphite, which is not alloyed with the iron, but exists in it 
as a separate body, since it may be removed from the fractured surface 
of pig iron by a brush; 3, a third form, called by Ledebur "tempering 
graphite carbon," into w-hich combined carbon may be changed by pro- 
longed heating. The relative percentages in which GC and CC may 
be found in cast iron differ with the rate of cooling from the liquid 
state, so that in a large casting, cooled slowly, nearly all the C may 
be GC, while in a small casting from the same ladle cooled quickly, 
it may be nearly all CC. The total C in cast iron usually is between 
3 and 4%. 

Combined Carbon. — CC increases hardness, brittleness and shrink- 
age. Up to about 1% it increases strength, then decreases it. The 
presence of S tends to increase the CC in a casting, while Si tends to 
change CC to GC. 

Graphite. — GC in a casting causes softness and weakness when 
above 3%; softness and strength when added to irons low in GC and over 
1% in CC. It increases with the size of the casting, with slow cooling, 
or rather with holding a long time in the mold at a high temperature. 

Silicon. — Si acts as a softener by counteracting the hardening effect 
of S, and by changing CC into GC, changes white iron to gray, increases 
fluidity and lessens shrinkage. When added to hard brittle iron, high in 
CC, it may increase strength by removing hard brittleness, but when it 
reduces the CC to 1% and less it weakens the iron. Above 3.5 or 4% it 
changes the fracture to silvery gray, and the iron becomes brittle and 
weak. The softening effect of Si is modified by S and Mn. 

Sulphur. — S causes the C to take the form of CC, increases hardness, 
brittleness, and shrinkage, and also has a weakening effect of its own. 
Above about 0.1% it makes iron very w^eak and brittle. When Si is 
below 1%, even 0.06 S makes the iron dangerously brittle. 

Manganese. — Mnin small amount, less than 0.5%, counteracts the 
hardening influence of S; in larger amounts it changes GC into CC, and 
acts as a hardener. Above 2% it makes the iron very hard. Mn com- 
bines with iron in almost all proportions. When it is from 10 to 30% 
the alloy is called spiegeleisen, from the German word for mirror, and has 
large, bright crystalline faces. Above 50% it is known as ferro-man- 
ganese. Mn has the property of increasing the solubility of iron for 
carbon; ordinary pig iron containing rarely over 4.2% C, while spiegel- 
eisen may have 5%, and ferro-manganese as high as 6%. Cast iron with 
1% Mn is used in making chilled rolls, in which a hard chill is desired. 
When softness is required in castings, Mn over 0.4% has to be avoided. 
Mn increases shrinkage. It also decreases the magnetism of iron. Iron 
with 25% Mn loses all its magnetism. It therefore has to be avoided in 
castings for dynamo fields and other pieces of electrical machinery. 

Phosphorus. — ; P increases fluidity, and is therefore valuable for thin 
and ornamental castings in which strength is not needed. It increases 
softness and decreases shrinkage. Below 0.7% it does not appear to 
decrease strength, but above 1% it is a weakener. 

Copper. — Cu is found in pig irons made from ores containing Cu. 
From 0.1 to 1% it closes the grain of caet iron, but does not appreciably 
cauBe brittleness. 



CAST IRON. 439 

Aluminum. — Al from 0.2 to 1.0% (added to the ladle in the form of 
a FeAl alloy) increases the softness and strength of white iron ; added to 
gray iron it softens and weakens it. Where loss is occasioned by 
defective castings, or where iron does not flow well, the addition of Al 
will give sounder, closer grained castings. In proportions of 2% and 
over Al will decrease the shrinkage of cast iron. 

Titanium. — An addition of 2 to 3% of a TiFe alloy containing 10% 
Ti caused an increase of 20 to 30% in strength of cast iron. A. J. Rossi, 
A.I.M.E., xxxiii, 194. Ti reacts with any O or N present in the metal 
and thus purifies it, and does not remain in the metal. After enough 
Ti for deoxidation has been added, further additions have no effect. 
R. Moldenke, A.I.M.E., xxxv, 153. 

Vanadium. — Va to the extent of 0.15% added to the ladle in the form 
of a ground FeVa alloy greatly increases the strength of cast iron. It 
acts as a deoxidizer and also by alloying. 

Oxide of Iron. — The cause of the difference in strength of charcoal 
and coke irons of identical composition is believed by Dr. Moldenke 
(A.I.M.E., xxxi, 988) to be the degree of oxidation to which they have 
been subjected in making or remelting. Since Mn, Ti, and Va all act as 
deoxidizers, it should be possible by additions to the ladle of alloys of 
FeMn, FeVa, or FeTi, to make the two irons of equal strength. 

Temper Carbon. The main part of the C in white cast iron is the carbide 
FeaC. This breaks down under annealing to what Ledebur calls " temper 
carbon," and in annealing in oxides, as in making maUeable iron, it is 
oxidized to CO. The C remaining in the casting at the end of the process 
is nearly all GC, since the latter is very slowly oxidized. 

Influence of Various Elements on Cast Iron. — W. S. Anderson, 
Castings, Sept., 1908, gives the following: 

Fluidity, increased by Si, P, G.C. Reduced by S, C.C. 
Shrinkage, increased by S, Mn, C.C. Reduced by Si, P, G.C. 
Strength, increased by Mn, C.C. Reduced by Si, S, P, G.C. 

Hardness, increased by S, Mn, C.C. Reduced by Si, G.C. 
Chill, increased by S, Mn, C.C. Reduced by Si, P, G.C. 

Microscopic Constituents. (See also Metallography, under Steel.) 

Ferrite, iron free from carbon. It is found in mild steel in small amounts 
in gray cast iron, and in malleable cast iron. 

Cementite, FeaC. Fe with 6.67% C. Harder than hardened steel. 
Hardness U on the mineralogical scale. Found in high C steel, and in 
white and mottled pig. 

Pearlite, a compound made up of alternate laminge of ferrite and cemen- 
tite, in the ratio of 7 ferrite to 1 cementite, and containing therefore 
0.83% C. Found in iron and steel cooled very slowly from a high temper- 
ature. In steel of 0.83 C it composes the entire mass. Steels lower or 
higher than 0.83 C contain pearlite mixed with ferrite or with cementite. 

Mariensite, the hardening component of steel. Found in iron and 
steel quenched above the recalescence point, and in tempered steel. It 
forms the entire structure of 0.83 C steel quenched. 

Analyses of Cast Iron. (Notes of the table on page 440.) 

1 to 7. R. Moldenke, Pittsbg. F'drymen's Assn., 1898; 1 to 5, pig irons; 
6, white iron cast in chills; 7, gray iron cast in sand from the same ladle. 
The temperatures were taken with a Le Chatelier pyrometer. Foi 
comparison, steel, 1.18 C, melted at 2450° F.; silico-spiegel, 12.30 Si, 
16.98 Mn, at 2190°; ferro-siUcon, 12.01 Si, 2.17 CC, at 2040°; ferro- 
tungsten, 39.02 W, at 2280°; ferro-manganese, 81.4 Mn, at 2255°; ferro- 
chrome, 62.7 Cr, at 2400°; ditto, 5.4 Cr., at 2180°. 

8. Gray foundry Swedish pig, very strong. 9. Pig to be used in mix- 
tures of gray pig and scrap, for castings requiring a hard close grain, 
machining to a fine surface, and resisting wear. 8 to 15, from paper by 
F. M. Thomas, Castings, July, 1908. 

16. Specification by J. E. Johnston, Jr., Am. Mach., Oct. 15, 1903. 
The results were excellent. Si might have been 0.75 to 1.25 if S had 
been kept below 0.035. 

17 to 22. G. R. Henderson, Trans. A.S.M.E., vol. xx. The chill is to 
be measured in a test bar 2 X 2 X 24 in., the chill piece being so placed 
as to form part of one side of the mold. The actual depth of white Iron 
will be measured. 



440 



IRON AND STEEL. 



Analyses of Cast Iron. 

(Abbreviations, TC, total carbon; GC, graphitic carbon; CC, combined 
carbon.) 



No. 


TC 

3.98 


GC 


CC 


Silicon. 


Man- 
ganese. 


Phos- 
phorus. 


Sul- 
phur. 




1 


0.39 


3.59 


0.38 


0.13 


0.20 


0.038 


Melts at 2048° F. 


2 


3.78 


1.76 


2.01 


0.69 


0.44 


0.53 


0.031 


Melts at 2156° F. 


3 


3.88 


2.60 


1.28 


1.52 


0.49 


0.46 


0.035 


Melts at 221 rp. 


4 


4.03 


3.47 


0.56 


2.01 


0.49 


0.39 


0.034 


Melts at 2248° F. 


5 


3.56 


3.43 


0.13 


2.40 


0.90 


0.08 


0.032 


Melts at 2280° F. 


6 


4.39 


0.13 


4.26 


0.65 


0.40 


0.25 


0.038 


Melts at 2000° F. 


7 


4.45 


2.99 


1.46 


0.67 


0.41 


0.26 


0.039 


Melts at 2237° F. 


8 


3.30 


2.80 


0.50 


2.00 


0.60 


0.08 


0.03 


Swedish char- 
coal pig. 


9 




2.25-2.5 


0.6-0.8 


0.8-1.2 


0.4-0.8 


0. 15-0.4 




For engine cylin- 
ders. 

English, high P. 
No. 1. 

English, high P. 
No. 3. 

For thin orna- 


10 


3.40 


3.40 


trace 


2.90 


0.50 


1.65 


0.04 


11 


3.40 


3.20 


0.20 


2.60 


0,50 


1.58 


0.04 


12 




3.2-3.6 


0.1-0.15 


2.5-2.8 


up to 


1.3-1.5 


.03-. 04 












1.0 






mental work. 


13 




3.0-3.2 


0.4-0.5 


2-2.3 


up to 
1.0 


1-1.3 


.06-. 08 


For medium size 
castings. 


14 




2.8-3.0 


0.4-0.6 


1.2-1.5 


0.6-0.9 


0.4-0.6 


.06-. 08 


Heavy rrachin- 
ery castings. 


15 




2.5-2.8 


0.6-0.8 


1.0-1.3 


0.5-0.7 


0.4-0.7 


.08-. 12 


Cylinders and 
hydraulic work. 


16 








1.2-1.8 


0.4-1.0 


0.4-0.7 


to .06 


For hydraulic 










cylinders. 


17 




2.7-3.0 


0.5-0.8 


0.5-0.7 


0.3-0.5 


0.3-0.5 


.05-. 07 


For car wheels. 


18 




2.6-3.1 


0.6-1.0 


0.6-0.7 


0.1-0.3 


0.3-0.5 


.05-. 08 


For car wheels. 


19 




2.5-3.0 


0.4-0.9 


1.3-1.7 


0.5-1.0 


0.3-0.4 


.03 max 


Charcoal pig. I/4 
in. chill. 


20 




2.3-2.7 


0.5-1.0 


1.0-1.5 


0.5-1.0 


0.3-0.4 


.03 •• 


Ditto 1/2 in. chill. 


21 




2.0-2.5 


0.8-1.2 


0.&-1.2 


0.5-1.0 


0.3-0.4 


.035 " 


Ditto 3/4 in. chill. 


22 




1.^2.2 


0.9-1.4 


0.5-1.0 


0.3-0.7 


0.3-0.4 


.035 " 


Ditto 1 in. chill. 


23 


3:87 


3.44 


0.43 


1.67 


0.29 


0.095 


0.032 


Series A. Am. 
F'dmen's Assn. 


24 


3.82 


3.23 


0.59 


1.95 


0.39 


0.405 


0.042 


Series B. ditto. 


25 


3.84 


3.52 


0.32 


2.04 


0.39 


0.578 


0.044 


Series C. ditto. 


26 




2.8-3.2 


0.5-0.7 


1.3-1.5 


0.3-0.6 


0.5-0.8 


.06-. 10 


For locomotive 
cylinders. 


27 




2.3-2.4 


0.8-1.0 


1.8-2.0 


0.8-1.0 


0.6-0.8 


.06-. 10 


'' Semi-steel.'* 


28 




2.4-2.6 


0.8-1.0 


0.9-1.0 


0.6-0.7 


0.1-0.3 


.04-. 06 


" Semi-steel." 


29 


4:33 


3.08 


1.25 


0.73 


0.44 


0.43 


0.08 


A strong car 
wheel, Cu, 0.03. 


30 


3.17 


2.72 


0.45 


1.99 


0.39 


0.65 


0.13 


Automobile cyl- 
inders. 


31 


3.34 


2.57 


0.77 


1.89 


0.39 


0.70 


0.09 


Ditto. 


32 


3.5 


2.9 


0.6 


0.7 


0.4 


0.5 


0.08 


Good car wheel. 


33 


3.55 


3.0 


0.55 


2.75 


2.39 


0.86 


0.014 


Scotch irons. 


34 








3.10 


1.80 


0.90 




" Am. Scotch ** 











Ohio irons. 


35 








0.75-1.5 


to 0.6 


to 0.22 


to 0.04 


Pig for malle- 


















able castings. 


36 








2-25 
1.2-1.5 


to 0.7 
0.3-0.8 


to 0.7 
0.35-0.6 


to 0.15 
to 0.09 


Brake-shoes. 


37 








Hard iron for 


















heavy work. 


38 








1.5-2 


0.5-0.8 


0.35-0.6 


to 0.08 


Medium iron for 


















general work. 


39 








2.2-2.8 


to 0.7 


to 0.7 


to 0.085 


Soft iron cast'gs 











CAST IRON. 441 

23 to 25. Series of bars tested by a committee of the assoclatloiL 
See results of tests on page 419. Series A, soft Bessemer mixture; B, 
dynamo-frame iron; C, light machinery iron. Samples for analysis were 
taken from the 1-in. square dry sand bars. 

26. Specifications by a committee of the Am. Ry. Mast. Mechs. Assn., 
1906. T.S., 25,000; transverse test, 3000 lb. on ll/4-in. round bar, 12 in. 
between supports; deflection, 0.1 in. minimum; shrinkage, l/s in. max. 
27, soft "serai-steel;" 28, harder do. They approach air-furnace iron 
in most respects, and excel it in strength; test bars 2 XI X 24 in. of the 
low Si semi-steel showing 2800 to 3000 lb. transverse strength, with 
7/16 in. deflection. M. B. Smith, Eng. Digest, Aug., 1908. 29. J. M. 
Hartman, Bull. I. & S. Assn., Feb., 1892. The chill was very hard, 1/4 in. 
deep at root of flange, 1/2 in. deep on tread. 30, 31. Strong and shock- 
resisting. T.S., 38,000. Castings, June, 1908. 32. Com. of A.S.T.M., 
1905, Proc, V. 65. Successful wheels varying quite considerably from 
these figures may be made. 33, 34. C. A. Meissner, Iron Age^ 1890. 
Average of several. 35. R. Moldenke, A.S.M.E., 1908. 36-39. J. W 
Keep, A.S.M.E., 1907. 

A Chilling Iron is one which when cooled slowly has a gray fracture, 
but when cast in a mold one side of which is a thick mass of cast-iron, 
called a chill, the fractured surface shows white iron for some depth on 
the side that was rapidly cooled by the chill. See Table Nos. 19-22. 

Specifications for Castings, recommended by a committee of the 
A.S.T.M., 1908. S in gray iron castings, Ught, not over 0.08; medium, 
not over 0.10; heavy, not over 0.12. Alight casting is one having no 
section over 1/2 in. thick, a heavy casting one having no section less than 
2 in. thick, and a medium casting one not included in the classification of 
light or heavy. The transverse strength of the arbitration bar shall not 
be under 2500 lb. for Ught, 2900 lb. for medium, and 3300 lb. for heavy 
castings; in no case shall the deflection be under 0.10 in. When a ten- 
sile test is specified this shall run not less than 18,000 lb. per sq. in. for 
light, 21,000 lb. for medium, and 24,000 lb. for heavy castings. 

The '• arbitration bar" is 1 1/4 in. diam., 15 in. long, cast in a thoroughly 
dried and cold sand mold. The transverse test is made with supports 
12 in. apart. The moduli of rupture corresponding to the figures for 
transverse strength are respectively 39115, 45373, and 51632, being the 
product of the figures given and the constant 15.646, the factor for RjP 
tor a 11/4-in. round bar 12 in. between supports.* The standard form of 
tensile test piece is 0.8 in. diam., 1 in. long between shoulders, with a 
fillet 7/32in. radius, and ends 1 in. long, II/4 in. diam., cut with standard 
thread, to fit the holders of the testing machine. 

Specifications by J. W. Keep, A.S.M.E., 1907. See Table of Analyses, 
Nos. 37-39, page 417. Transverse test, 1 xl xl2-in. bar, hard iron castmgs. 
No. 37, 2400 to 2600 lb.; tensile test of same bar, 22,000 to 25,000 lb. 
No. 38, medium, transverse, 2200 to 2400; tensile, 20,000 to 23,000. 
No. 39, soft, transverse, 2000 to 2200; tensile, 18.000 to 20,000. 

Specifications for Metal for Cast-iron Pipe. — Proc. A.S.T.M., 1905, 
A.I.M.E., XXXV, 166. Specimen bars 2 in. wide x 1 in. thick x 24 in. 
between supports, loaded in the center, for pipes 12 in, or less in diam. 
shall support 1900 lb. and show a deflection of not less than 0.30 in, 
before breaking. For pipes larger than 12 in., 2000 lb. and 0.32 in. 
The corresponding moduli of rupture are respectively 34,200 and 36,000 
lb. Four grades of pig are specified: No. 1, Si, 2.75; S, 0.035. No 2. 
6i, 2.25; S, 0.045. No. 3, Si, 1.75; S, 0.055. No. 4, Si, 1.25; S, 0.065. A 
variation of 10% of the Si either way, and of 0.01 in the S above the 
standard, is allowed. 

Chemical Standards for Iron Castings. — The following analyses are 
tentative standards, or probable best analyses, suggested by the 
CoEjmittee on Standards for Iron Castings, American Foundrymen's 
Association, June, 1910. "Heavy" castings are those in whach no 
section is less than 2 in. thick; "light" castings are those having any 
section less than 1/2-in. thick; "medium" castings are those not in- 
cluded in the definition of light and heavy castings. The desirable 

•Formula. MP' = RI/c; see page 283. J= VQ^ird*; c» Hd; d^lM 
In.; /= 12 in. 7=0.11983; R/P = HX 12X^^0.11983= 15.646. 



442 



IRON AND STEEL. 



percentage of silicon depends largely on the thickness of the casting 
and the practice followed in shaking out. These factors, being in 
many cases undetermined, are allowed for by giving fairly wide limits 
to this element. The effect of purifying alloys and the use of steel 
scrap have not been taken into account. In many cases a wide range 
of composition is compatible with the best results, and in such cases 
the question of cost will be the first element to be considered. 



Acid - resisting castings 

(stills, eggs, etc.) 

Agricultural machinery, 

ordinary 

Agricultural machinery, 

very thin 

Annealing boxes, etc 

Automobile castings 

Balls for ball mills 

Boiler castings 

Car castings, gray iron. . . 

Chilled castings 

Chills 

Crusher jaws 

Cutting-tools, chilled .... 
Cylinders: 

Air and ammonia 

Automobile 

Gas engine 

Hydraulic, heavy 

Hydraulic, medium 

Locomotive 

Steam engine, heavy. . . 

Steam engine, medium. 

Dies, drop-hammer 

Diamond polishing 

wheelsf 

Electrical machinery 

(frames, bases, spiders), 

large 

Electrical machinery, 

small 

Engine castings: 

Bedplates 

Flywheels 

Do., automobile. . . . 

Frames 

Pillow blocks 

Piston rings 

Fire pots and furnace 

castings 

Grate bars 

Grinding machinery, 

chilled castings f or . . . 

Gun carriages 

Gun iron 

Hardware (light) and 

hollow ware 

Heat resistant iron (re- 
torts) 

Ingot molds and stools. , 
Locomotive castings, 

heavy 



Si. 



S. 



.00-2.00 0.05-* 



2.00-2.50 

2.25-2.75 
1.40-1.60 
1.75-2.25 
1.00-1.25 
2.00-2.50 
1.50-2.25 
0.75-1.25 
1.75-2.25 
0.80-1.00 
1.00-1.25 



1.00-1, 
1.75-2, 
1.00-1, 
0.80-1, 
1.20-1. 
1.00-1 
1. 00-1 
1.25-1 
1.25-1 

2.70 



2.00-2.50 

2.50-3.00 

1.25-1.75 
.50-2.25 
2.25-2.50 
1.25-2.00 
1.50-1.75 
.50-2.00 

2.00-2.50 
2.00-2.50 

0.50-0.75 
1.00-1.25 
1.00-1.25 

2.25-2.75 

1.25-2.50 
1.25-1.50 

1.25-1.50 



0.06-0.08 

0.06-0.08 
0.06- 
0.08- 
0.08- 
0.06- 
0.08- 

0.08-0.10 
0.07- 

0.08-0.10 
0.08- 

0.09- 
0.08- 
0.08- 
0.10- 
0.09- 
0.08-0.10 
0.10- 
0.09- 
0.07- 

0.063 



0.08- 

0.08- 

0.10- 
0.08- 
0.07- 
0.09- 
0.08- 
0.08- 

0.06- 
0.06- 

0.15-0.20 
0.06- 
0.06- 

0.08- 

0.06- 
0.06- 

0.08- 



Mn. 



0.4O-* 

0.60-0.80 

0.70-0.90 

0.20- 
0.40-0.50 
0.20- 
0.20- 
0.40-0.60 
0.20-0.40 
0.20-0.40 
0.20-0.40 
0.20-0.40 

0.30-0.50 
0.40-0.50 
0.20-0.40 
0.20-0.40 
0.30-0.50 
0.30-0.50 
0.20-0.40 
0.30-0.50 
0.20- 

0.30 



1.00-1.50 

0.60-0.80 

0.50-0.70 
0.60-1.00 
0.60-0.80 
0.60-1.00 
0.60-1.00 
0.60-1.00 
0.80-1.20 
0.60-1.00 
0.80-1.20 
0.60-0.80 

0.70-0.90 
10.60-0.80 
0.70-0.90 
0.80-1.00 
0.70-0.90 
0.80-1.00 
0.80-1.00 
0.70-0.90 
0.60-0.80 

0.44 



0.50-0.80 
0.50-0.80 



0.30-0.50 
0.40-0.601 0.50-0.70 



0.30-0.40 
0.30-0.40 
0.60-0.80 



0.40-0.50 
0.30-0.50 
0.40-0.50 
0.30-0.50 

0.20- 
0.20- 

0.20-0.40 
0.20-0.30 
0.20-0.30 

0.50-0.80 

0.20- 
0.20- 

0.30-0.50 



0.50-0.70 
0.60-1.00 
0.60-0.80 
0.40-0.60 

0.60-1.00 
0.60-1.00 

1.50-2.00 
0.80-1.00 



0.50-0.70 



0.60-1.00 
0.60-1.00 



0.70-0.90 



C. 

(Comb.) 



C. 

(Total) 



3.00-3.50 



3.00-3.30 
0.55-0.65 3.00-3.25 

3.00-3.30 
low 
low 



low 
low 
2.97 

low 
low 



1.60 



0.20-0.30 
0.20-0.30 



0.30- 



0.80-1.00 



0.30- 



low 

low 
low 



low 
low 



low 



* AflQxed hyphens indicate that the percentages present- should bQ 
vnder those given, ' 



CAST IRON. 



443 



Loco. Castings, light. . . . 
Machinery castings, 

heavy 

Do., medium 

Do., light 

Friction clutches 

Gears, heavy 

Do., medium 

Do., small 

Pulleys, heavy 

Do., light 



Shaft collars and 

couplings 

Shaft hangers 

Ornamental work 

Permanent molds 

Permanent mold castings. 

Piano plates 

Pipe 

Pipe fittings 

Do., for superheated 

steam lines 

Plow points, chilled 

Propeller wheels 

Pumps, hand 

Radiators 

Railroad castings 

Rolling mill machinery: 

Housings 

Rolls, chilled 

Rolls, unchilled (sand- 

cast)t , 

Scales 

Slag car castings 

Soil pipe and fittings .... 

Stove plate 

Valves, large 

Do., small 

Water heaters 

Wheels, large 

Do., small 

White iron castingsf 



Si. 



1.50-2.00 

1.00-1.50 
1.50-2.00 
2.00-2.50 
1.75-2.00 
1.00-1.50 
1.50-2.00 
2.00-2.50 
1.75-2.25 
2.25-2.75 

1.75-2.00 
1.50-2.00 
2.25-2.75 
2.00-2.25 
1.50-3.00 
2.00-2.25 
1.50-2.00 
1.75-2.50 

1.50-1.75 
0.75-1.25 
1.00-1.75 
2.00-2.25 
2.00-2.25 
1.50-2.25 

1.00-1.25 
0.60-0.80 

0.75 
2.00-2.30 
1.75-2.00 
1.75-2.25 
2.25-2.75 
1.25-1.75 
1.75-2.25 
2.00-2.25 
1.50-2.00 
1.75-2.00 
0.50-0.90 



S. 



0.08-* 

0.10- 
0.09- 
0.08- 
1.08-0.10 
1.08-0.10 
0.09- 
0.08- 
0.09- 
0.08- 

0.08- 
0.08- 
0.08- 
0.07- 
0.06- 
0.07- 
0.10- 
0.08- 

0.08- 
0.08- 
0.10- 
0.08- 
O.OS- 
0.08- 

0.08- 
0.06-0.08 

0.03 
0.08- 
0.07- 
0.09- 
0.08- 
0.09- 
0.08- 
0.08- 
0.09- 
0.08- 
0.15-0.25 



P. 



0.40-0.60 

0.30-0.50 
0.40-0.60 
0.50-0.70 

0.30- 
0.30-0.50 
0.40-0.60 
0.50-0.70 
0.50-0.70 
0.60-0.80 



0.40-0. 
0.40-0. 
0.60-1. 
0.20-0. 

0.'4b-6. 
0.50-0. 
0.50-0. 



0.20-0.40 
0.20-0.30 
0.20-0.40 
0.60-0.80 
0.60-0.80 
0.40-0.60 

0.20-0.30 
0.20-0.40 

0.25 
0.60-1.00 

0.30- 
0.50-0.80 
0.60-0.90 
0.20-0.40 
0.30-0.50 
0.30-0.50 
0.30-0.40 
0.40-0.50 
0.20-0.70 



Mn. 



0.60-0.80 



80-1.00 
60-0.80 
50-0.70 
50-0.70 
80-1.00 
70-0.90 
60-0.80 
60-0.80 
50-0.70 



0.60-0.80 
0.60-0.80 
0.50-0.70 
0.60-1.00 

0.40- 
0.60-0.80 
0.60-0.80 
0.60-0.80 

0.70-0.90 
0.80-1.00 
0.60-1.00 
0.50-0.70 
0.50-0.70 
0.60-0.80 

0.80-1.00 
1.00-1.20 

0.66 
0.50-0.70 
0.70-0.90 
0.60-0.80 
0.60-0.80 
0.80-1.00 
0.60-0.80 
0.60-0.80 
0.60-0.80 
0.50-0.70 
0.17-0.50 



C. 

(Comb.) 



0.50-0.60 



1.20 



2.90 



C. 

(Total) 



low 



low 
low 



low 



low 
3.00-3.25 

4.10 



low 



2.50 



* Affixed hyphens indicate that the percentages present should be 
under those given. 

t But one or two analyses available — no suggestion made. 



Standard Specifications for Foundry Pig Iron. 

(American Foundrymen's Association, May, 1909.) 

Analysis. — It is recommended that foundry pig be bought by analysis. 

Sampling. — Each carload or its equivalent shall be considered as a 
unit. One pig of machine-cast, or one-half pig of sand-cast iron shall be 
taken to every four tons in the car, and shall be so chosen from different 
parts of the car as to represent as nearly as possible the average quality 
of the iron. Drillings shall be taken so as to fairly represent the composi- 
tien of the pig as cast. An equal quantity of the driUings from each pig 
shall be thoroughly mixed to make up the sample for analysis. 

Percentage or Elements. — When the elements are specified the fol- 
lowing percentages and variations shall be used. Opposite each percent- 
age of the different elements a syllable has been affixed so that buyers, 
by combining these syllables, can form a code word to be used in 
telegraphing. 



444 



IRON AND STEEL. 



Silicon 



StTLPHtm Total Carbott Manganese Phosphorus 





(max.) Code 


(miaj Code 


% Code ' 


% 


Code' 


% Code 


0.04 Sa 


3.00 Ca 


0.20 Ma 


0.20 


Pa 


1.00 La 


0.05 Se 


3.20 Ce 


0.40 Me 


0.40 


Pe 


1.50 Le 


0.06 Si 


3.40 a 


0.60 Mi 


0.60 


Pi 


2.00 li 


0.07 So 


3.60 Co 


0.80 Mo 


0.80 


Po 


2.50 Lo 


0.08 Su 


3.80 Cu 


1.00 Mu 


1.00 


Pu 


3.00 Lu 


0.09 Sy 
0.10 Sh 




1.25 My 
1.60 Mh 


1.25 


11 






1.50 



Percentages of any element specified one-half way between the above 
shall be designated by the addition of the letter x to the next lower symbol, 
thus Lex means 1.75 Si. 

Allowed variation: Si, 0.25; P, 0.20; Mn, 0.20. The percentages of P 
and Mn may be used as maximum or minimum figures when so specified. 

Example: — Le-sa-pi-me represents 1.50 Si, 0.04 S, 0.60 P, 0.40 Mn. 

Base or Quoting Price. — For market quotations an iron of 2.00 Si 
(with variation 0.25 either way) and S 0.05 (max.) shall be taken as the 
base. The following table may be fiUed out, and become a part of a 
contract; "B," or Base, represents the price agreed upon for a pig of 
2.00 Si and under 0.05 S. "C" is a constant differential to be deter- 
mined at the time the contract is made. 

Sul-/- Silicon -a 

phur 3.25 3.00 2.75 2.50 2.25 2.00 1.75 1.50 1.25 1.00 
0.04 B + 6C B + 5C B+4C B + 3C B + 2C B + C B B-IC B-2C B-3C 

0.05 B + 6C B+4C B+3C B + 2C B + IC B B-IC B-2C B-3C B-4C 

0.06 B + 4C B + 3C B + 2C B + IC B B-IC B-2C B-3C B-4C B-5C 

0.07 B + 3C B + 2C B + IC B B-lC B-2C B-3C B-4C B-5C B-6C 

0.08 B + 2C B + IC B B-IC B-2C B-3C B-4C B-5C B-6C B-7C 

0.09 B + IC B B-IC B-2C B-3C B-4C B-5C B-6C B-7C B-8C 

0.10 B B-IC B-2C B-3C B-4C B-5C B-6C B-7C B-SC B-9C 

Tensile Tests of Cast-iron Bars. 

(American Foundrymen's Association, 1899.) 



SiBe, in... 

(A)(7.c.. 

g. m, 

" d.s.. 

*' d.m. 
(B)(7. c. 

*' g. m. 

" d.c, 

•' d.m. 

iC)g.c.. 

* g. m. 

•• d. c. 

" d.m. 

av. g.,. . 

or. d., ,, 

av. c. . . . 

av. m. . . 



Square Bars. 



0.5x0.5 
15,900 



14,600 
V7j66 



16,300 

\7\m 
V6*,4d6 



13,600 
15,800 
14,700 



Ixl 
13,900 
15,400 
12,900 
13,800 
15,200 
17,600 
15,100 
18,400 
16,000 
18,500 
16,000 
17,100 
16,100 
15,500 
14,800 
16,800 



1.5x1.5 
12,100 
12,900 
12,300 
13.400 
12,900 
15,000 
13,300 
15,000 
12,500 
15,100 
12,200 
14,100 
13,400 
13,400 
12,500 
14,200 



2x2 

10,600 

10,900 

9,800 
12,100 
11,500 
11,800 
11,100 
12,100 
11,100 
11,700 
11,300 

9,800 
11,300 
11,000 
10,900 
11.400 



Round Bars. 



0.56 
16.000 



14,300 

\6\m 



16,700 
V7'866" 



16,400 



13,400 
15,800 
16.300 



1.13 
13,800 
13,800 
13,700 
13,600 
15,900 
19,000 
16,200 
16,900 
15,900 
17,400 
15,900 
17,700 
16,000 
15,700 
15,200 
16.400 



1.69 
12,000 
13,500 
11,700 
13,200 
13,100 
15,400 
13,200 
15,100 
14,200 
15,000 
14,000 
15,900 
13,900 
13,800 
13,000 
f4.600 



2.15 

11,000 

12,200 

10,500 

10,600 

11,400 

12,500 

11,000 

13,100 

12,000 

11,600 

11,600 

10,400 

11,600 

11,200 

11,200 

11.700 



Compression Tests of Cast-iron Bars. 



Size, 
(A) 



, m.. . 

0)... 



«• 

(C) 






0.5x0.5 
29,570 



(4). 



38,360 



38,360 



1x1 
20,010 
21.990 



23,000 
12.440 



24,890 
27,900 



1.5x1.5 
17,180 
17,920 
17,180 



20,980 
24,820 
20,980 



20,750 
22,060 
20,750 



2x2 
13,810 
13,750 
13.880 



18,130 
21,640 
18,740 
15,060 
18,010 
21,750 
19,340 
17,840 



2.5x2.5 
10,950 
12,040 
11,430 
10,950 
15,060 
18,270 
15,940 



17,840 
19,800 
18,050 



3x3 
9,830 
11,200 
10,270 
10,430 
13,790 
17,000 
14,410 
13,900 
15,950 
18,170 
16,850 
16,040 



3.5x3.5 
9,350 
10,770 
9,830 
9,540 
13,160 
15,970 
15,200 
13,560 
15,880 
17,100 
16,510 
16,080 



4x4 
9,100 
10,340 
9,950 
9,570 
12,430 
16,140 
13,950 
13,760 
14,220 
16,410 
15,250 
14,880 



CAST IRON. 



445 



Transverse Tests of Cast-iron Bars. Modulus of Rupture. 


Size * 


0.5x0.5 


Ixl 


1.5x1.5 


2x2 


2.5x2.5 


3x3 


3.5x3.5 


4x4 


Diam. t 

(A)rJ.c.... 


0.56 


1.13 


1.69 


2.15 


2.82 


3.38 


3.95 


4.51 


31,100 


33,400 


33,900 


31,700 


27,000 


26,600 


23,400 


22,600 


■ ** r. d,m, .. 




27,800 


38,000 


32,300 


28,000 


28,600 


22,400 


22,900 


(B) s,g,c 


* 44,466 


39,100 


39,500 


33,900 


31,900 


29,700 


27,200 


27,600 


** s, g.m, .. 




37,400 


40,300 


34,700 


35,800 


33,500 


30,100 


27,100 


" s,d,c,,.. 


'*3'5*,566' 


38,300 


34,000 


32,900 


31,900 


30,200 


29,300 


25,900 


•* s.d.m. .. 




30,200 


36,200 


33,300 


35,200 


30,900 


28,100 


25,800 


*• r.g.c. . .. 


"3(3*, 466' 


46,200 


41,200 


41,400 


41,300 


36,300 


34,800 


31,000 


" r. g.m. . . 




40,000 


44,800 


38,800 


37,100 


32,900 


32,700 


32,300 


" r d,c.... 


37.866 ■ 


49,000 


44,300 


39,200 


40,700 


31,800 


35,300 


31,100 


" r. d. m. . . 




39,100 


37,800 


37,700 


33,900 


32,800 


32,000 


31,200 


(C)s.g. c 


■5r,866' 


39,200 


33,600 


37,900 


32,200 


31,100 


31,300 


29,200 


" s.g. m, .. 






40,200 


37,000 


33,700 


33,300 


32,300 


27,900 


" s.d.c.,,. 


"A^^im' 


39,*106 


38,800 


35,100 


31,200 


29,300 


29,300 


27,800 


'* 5. d.m. . . 






38,900 


35,400 


33,500 


32,700 


29,100 


25,500 


•' r. ^. c 


'62,866 


48,'50d 


39,000 


44,500 


41,400 


41,200 


35,000 


32,300 


" r. ^. m. . . 





55,700 


49,200 


42,900 


41,500 


36,500 


34,100 


36,000 


•• r.rf.c... 


53,000 


50,400 


44,000 


40,200 


39,500 


37,800 


35,200 


32,100 


" r. rf. m. . . 




47,900 


51,300 


38,000 


38,900 


36,300 


32,200 


33,500 


Av. (B)s. ... 


' 39,966" 


36,200 


37,500 


33,700 


33,700 


31,100 


28,700 


26,600 


" " r. , . . 


37,100 


43,600 


42,000 


39,300 


38,200 


33,400 


33,700 


31,400 


•• (C)s 


49,900 


39,100 


37,900 


36,300 


32,600 


31,600 


30,500 


27,600 


*' " r. . . . . 


57,900 


50,600 


45,900 


41,400 


40,400 


37,900 


34,100 


33,200 


;'(B)&(C)f7. 


48,800 


43,100 


41,000 


38,800 


36,800 


33,900 


32,200 


30,400 


• d. 


43,300 


41,600 


40,700 


36,500 


35,600 


32,700 


31,300 


30,400 


Gen'lav 


46,100 


42,400 


40,800 


37,700 


36,200 


33,400 


31,700 


29,900 


Equiv. load. . 


320 


2356 


7650 


16,756 


31,424 


50,100 


75,516 


106,311 



* Size of sauare bars as cast^ in. t Diam. of round bars as cast. in. 

Notes on the Tables of Tests. — The machined bars were cut to 
the next size smaller than the size they were cast. The transverse bars 
were 12 in. long between supports. (A), (B), (C), three qualities of iron; 
for analyses see page 417; r, round bars; s, square bars; rf, cast in dry sand; 
f7, cast in green sand; r, bar tested as cast; m, bar machined to size. The 
general average (next to last line of the first table) is the average of the six 
lines preceding. The equivalent load (last line) is the calculated total 
load that would break a square bar whose modulus of rupture is that 
of the general average. 

Compression Tests. —The figures given are the crushing strengths, in 
pounds, of i in. cubes cut from the bars. Multiply by 4 to obtain lbs. 
per sq. in, (1) Cube cut from the middle of the bar; (2) first ^ in. from 
edge; (3) second i in. from e6.gQ\ (4) third 1 in from edge. 

Some Tests of Cast Iron. (G. Lanza, Trans, A.S.M.E., x, 187.) — 
The chemical analyses were as follows: Gun iron: TC, 3.51; GC, 2.80; 
S, 0.133; P, 0.155; Si, 1.140. Common iron: S, 0.173; P, 0.413; Si, 1.89. 

The test specimens were 26 in. long; those tested with the skin on being 
very nearly 1 in. square, and those tested with the skin removed being 
cast nearly IVi in. square, and afterwards planed down to 1 in. square. 

Tensile Elastic Modulus 
Strength. Limit. of 

Elasticity. 
Unplaned common.. 20,200 to 23,000 T.S. Av. = 22,066 6,500 13,194,233 

Planed common 20,300 to 20,800 ** " =20,520 5,833 11,943,953 

Unplaned gun 27,000 to 28,775 '* " =28,175 11,000 16,130,300 

Planed gun 29,500 to 31,000 ** ** =30,500 8,500 15,932,880 

The elastic limit is not clearly defined in cast iron, the elongations increas- 
ing faster than the increase of the loads from the beginning of the test. 
The modulus of elasticity is therefore variable, decreasing as the loads 
mcrease. 

The Strength of Cast Iron depends on many other things besides 
its chemical composition. Among them are the size and shape of the 
casting, the temperature at which the metal is poured, and the rapidity of 
cooling. Internal stresses are apt to be induced by rapid coohng, and 
Blow cooling tends to cause segregation of the chemical constituents and 



446 IRON AND STEEL. 

opening of the grain of the metal, making it weak. The author recom- 
mends that in making experiments on the strength of cast iron, bars of 

several different sizes, such as 1/2, 1, IV2, and 2 in. square (or round), 
should be taken, and the results compared. Tests of bars of one size 
only do not furnish a satisfactory criterion of the quality of the iron of 
which they are made. Trans. A.I.M.E., xxvi, 1017. 

Theory of the Relation of Strength to Chemical Constitution. — 
.T. E. Johnston, Jr. (Am. Mach., April 5 and 12, 1900), and H. M. Howe 
(Trans. A.I.M.E., 1901) have presented a theory to explain the variation 
in strength of cast iron with the variation in combined carbon. It is 
that cast iron is steel of CO ranging from to 4%, with particles of graph- 
ite, which have no strength, enmeshed with it. The strength of the cast 
iron therefore is that of the steel or graphiteless iron containing the same 
percentage of CC, weakened in some proportion to the percentage of GO. 
The tensile strength of steel ranges approximately from 40,000 lb. per 
sq. in. with C to 125,000 lb. with 1.20 C. With higher C it rapidly becomes 
weak and brittle. White cast iron with 3% CC is about 30,000 T.S.. 
and with 4% about 18,000. The amount of weakening due to GC is not 
known, but by making a few assumptions we may construct a table of 
hypothetical strengths of different compositions, with which results of 
actual tests may be compared. Suppose the strength of the steel-white 
cast-iron series is as given below for different percentages of CC, that 
6.25% GC entirely destroys the strength, and that the weakening effect 
of other percentages is proportional to the ratio of the square root of that 
percentage to the square root of 6.25, that the TC. in two irons is respec- 
tively 3% and 4%, then we have the following: 
Per cent CC. 0.2 0.4 0.6 0.8 1.0 1.2 1.5 2.0 2.5 3 3.5 4 

Steel, T.S 40 60 80 100 110 120 125 110 60 40 30 22 18 

Cast iron, 4% 

TC 8 13.2 19.2 26 31.2 37 41.5 40.5 26 20.7 18 15.8 18 

Cast iron, 3% 

TC 15.4 19.9 28.5 38 42.9 52.1 58 56.1 36 28.7 30 

The figures for strength are in thousands of pounds per sq. in. The 
table is calculated as follows: Take 0.6 CC; with 4% TC, this leaves 
3.4 GC, and with 3% TC, 2.4 G C. T he sq. root of 3.4 is 1.9, and of 2.4 is 
1.55. The ratio of these to ^^6.25 is respectively 74 and 62%, which 
subtracted from 100 leave 26 and 38% as the percentage of strength of 
the 0.6 C steel remaining after the effect of the GC is deducted. The 
table indicates that strength is increased as total C is diminished, and this 
agrees with general experience. 

Relation of Strength to Size of Bar as Cast. — If it is desired that a 
test bar shall fairly represent a casting made from the same iron, then 
the dimensions of the bar as cast should correspond to the dimensions of 
the casting, so as to have about the same ratio of cooling surface to 
volume that the casting has. If the test bar is to represent the strength 
of a plate, it should be cut from the plate itself if possible or else cut 
from a cyhndrical shell made of considerable diameter and of a thickness 
equal to that of the casting. If the test is for distinguishing the quality 
of the iron, then at least two test bars should be cast, one say I/2 or s/g in. 
and one say 2 or 2 1/2 in. diameter, in order to show the effect of rapid 
and slow cooling. 

In 1904 the author made some tests of four bars of " semi-steel " adver- 
tised to have a strength of over 30,000 lb. per sq. in. The bars were cast 
1/2, 1, 2, and 3 in. diam., and turned to 0.46, 0.69, 1.6, and 1.85 in. respec- 
tively. The results of transverse and tensile tests were: 

Mod. of rupture. .1/2 in., 100.000; 1 in., 61,613; 2 in., 67,619; 3 in., 58,543 
T.S. per sq. in... ** 38,510; " 37,005; " 25,685; *' 20,375 

The 1/2-in. piece was so hard that it could not be turned in a lathe and 
had to be ground. 

Influence of Length of Bar upon the Modulus of Rupture. — 

(R. Moldenke, Jour. Am. Foundrymen's Assn., Sept., 1899.) Seven 
sets, each of five 2-in. square bars, made of a heavy machinery mixture, 
and cast on end, were broken transversely, the distance between sup- 

eorts ranging from 6 to 16 ins. The average results were: 
>ist. bet. supports, ins 6 8 10 12 14 16 

Modulus of rupture 40.000 39,000 35,600 37,000 36,000 34.400 



CAST IRON. 



447 



The 10-in. bar in six out of seven cases gave a lower result than the 
12-in. It appears that the ordinary formulas used in calculating the 
cross breaking strength of beams are not only incorrect for cast iron, on 
account of the chemical differences in the iron itself when in different 
cross sections, but that with the cross sections identical the distance 
between the supports must be specially provided for by suitable con- 
stants in whatever formulae may be developed. As seen from the above 
results, the doubling of the distance between supports means a drop in 
the modulus of rupture in the same sized bar of nearly 10 per cent. 

Strength in Relation to Silicon and Cross-section. — In castings 
one half-inch square in section the strength increases as silicon increases 
from 1.00 to 3.50: in castings 1 in. square in section the strength is practi- 
cally-independent of silicon, while in larger castings the strength decreases 
as silicon increases. 

The following table shows values taken from Mr. Keep's curves of the 
approximate transverse strength of cast bars of different sizes reduced to 
the equivalent strength of a V2-in. x 12-in. bar. 



a 


Size of Square Cast Bars. 


1! 

'^1 


Size of Square Cast Bars. 


V2 in. 1 1 in. 1 2 in. 1 3 in. | 4 in. 


1/2 in.| 1 in. 1 2 in. | 3 in. | 4 in. 


H 


Strength of a 1/2-in. X 12-in. 
section, lb. 


Strength of a Vs-in. X 12-in. 
section, lb. 


1. 00 
1.50 
2.00 


290 
324 
358 


260 
272 
278 


232 
228 
220 


222 
212 
202 


220 
208 
196 


2.50 
3.00 
3.50 


392 
426 
446 


278 
276 
264 


212 
202 
192 


190 
180 
168 


184 
172 
160 



- »ou 

«X) 
. « 350 

•5 

*| 300 
A^ 250 



^.; 



1.00 81 
2.00 Si' 



'" >§ 1 2 3 4 

Inches Square 

Fig. 98. 

Fig. 98 shows the relation of the strength to the size of the cast-iron bar 
and to Si, according to the figures in the above table. Comparing the 
2-in. bars with the 1/2-in. bars, we find 

Si, per cent 1 1.5 2 2.5 3 3.5 

2-in.weaker than 1/2-in. .percent. . 20 30 35 46 53 57 

The fact that with the 1-in. bar the strength is nearly independent of 
Si, shows that it is the worst size of bar to use to distinguish the quality 
of the metal. If two bars were used, say 1/2-in. and 2-in., the drop in 
strength would be a better index to the quality than the test of any 
single bar could be. 

Shrinkage of Cast Iron. — W. J. Keep (A. S. M. E. xvi., 1082) gives a 
series of curves showing that shrinkage depends on silicon and on the 
cross-section of the casting, decreasing as the silicon and the section 
increase. The following figures are obtained by inspection of the curves: 



It 


Size of Square Bars. 




Size of Square Bars. 


72 in.| 1 in. 1 2 in. [ 3 in. | 4 in. 


1/2 in. I 1 in. 1 2 in. | 3 in. | 4 in. 


PL) 


Shrinkage, In. per Foot. 


Shrinkage, In. per Foot. 


1.00 
1.50 
2.00 


0.178 
.166 
.154 


0.158 
.145 
.133 


0.129 
.116 
.104 


0.112 
.099 
.086 


0.102 
.088 
.074 


2.50 
3.00 
3.50 


0.1421 0.121 
.1301 .109 
.1181 .097 


0.091 
.078 
.065 


0.072 
.058 
.045 


0.060 
.046 
.032 



Mr. Keep says : " The measure of shrinkage is practically equivalent to 
^ Cheinical analysis pf silicon. It tells whether n^ore or less silicon is 



448 IKON AND STEEL. 

needed to bring the quality of the casting to an accepted standard of 
excellence." 

A shrinkage of Vs in. per ft. is commonly allowed by pattern makers. 
According to the table, this shrinkage will be obtained by varying the Si 
in relation to the size of the bar as follows: 1/2 in., 3.25 Si; 1 in., 2.4 Si; 
2 in., 1.1 Si; 3 and 4, less than 1.0 Si. 

Shrinkage and Expansion of Cast Iron in Cooling. (T. Turner, 
Proc. I. & S. /., 1906.) — Some irons show the phenomenon of expanding 
immediately after pouring, and then contracting. Four irons were 
tested, analyzing as follows: (1) " Washed " white iron, CC 2.73; Si, 
0.01; P, 0.01; Mn and S, traces. (2) Gray hematite, GC, 2.53; CC, 0.86; 
Si, 3.47; Mn, 0.55; P, 0.04; S, 0.03. (3) Northampton, GC, 2.60; CC, 
0.15; Si, 3.98; Mn, 0.50; P, 1.25; S, 0.03. (4) Cast iron, GC, 2.73; CC, 
0.79; Si, 1.41; Mn, 0.43; P, 0.96; S, 0.07. No. 1 was stationary for 5 sec- 
onds after pouring, shrunk 125 sec, stationary 10 sec, then shrunk till 
cold. No. 2 expanded 15 sec, shrunk 20 sec. to original size, continued 
shrinking 90 sec. longer, stationary 10 sec, expanded 30 sec, then shrunk 
till cold. No. 3 expanded irregularly \\'ith three expansions and two 
shrinkages, until 125 sec. after pouring the total expansion was 0.019 in. 
in 12 in., then shrunk till cold. No. 4 expanded 0.08 in. in 50 sec, then 
shrunk till cold. 

Shrinkage Strains Relieved by Uniform Cooling. (F. Schumann, 
A.S.M.E.,^\\\, 433.) — Mr. Jackson in 1873 cast a flywheel with a very 
large rim and extremely small straight arms. Cast in the ordinary way, 
the arms broke either at the rim or at the hub. Then the same pattern 
was molded so that large chunks of iron were cast between the arms, a 
thickness of sand separating them. Cast in this way, all the arms re- 
mained unbroken. 

Deformation of Castings from Unequal Shrinkage. — (F. Schu- 
mann, A. S. M. E., vol. xvii.) A prism cast in a sand mold will main- 
tain its alignment, after cooling in the mold, provided all parts around 
its center of gravity of cross section cool at the same rate as to time and 
temperature. Deformation is due to unequal contraction, and this Is 
due chiefly to unequal cooling. 

Modifying causes that effect contraction are: Imperfect alloying of 
two or more different irons having different rates of contraction; varia- 
tions in the thickness of sand forming the mold; unequal dissipation of 
heat, the upper surface dissipating the greater amount of heat; position 
and form of cores, which tend to resist the action of contraction, also 
the difference in conducting power between moist sand and dry-baked 
cores; differences in the degree of moisture of the sand; unequal expos- 
ure by the removal of the sand while yet in the act of contracting: 
flanges, ribs, or gussets that project from the side of the prism, of sufla- 
cient area to cause the sand to act as a buttress, and thus prevent the 
natural longitudinal adjustment due to contraction; in light castings of 
sufficient length the unyielding sand between the flanges, etc., may 
cause rupture. 

Irregular Distribution of Silicon in Pig Iron. — J. W. Thomas 
{Iron Age, Nov. 12, 1891) finds in analyzing samples taken from every 
other bed of a cast of pig iron that the silicon varies considerably, the iron 
coming first from the furnace having generally the highest percentage. In 
one series of tests the silicon decreased from 2.040 to 1.713 from the first 
bed to the eleventh. In another case the third bed had 1.260 Si, the 
seventh 1.718, and the eleventh 1.101. He also finds that the siUcon 
varies in each pig, being higher at the point than at the butt. Some of 
his figures are: Point of pig, 2.328 Si; butt of pig, 2.157; point of pig, 
1.834; butt of pig, 1.787. 

White Iron Converted into Gray by Heating. (A. E. Outerbridge. 
Jr., Proc. Am. Socy. for Testing MaVls, 1902, p. 229.) — When white chilled 
iron containing a considerable amount of Si and low in GC is heated to 
about 1850° F. from 31/2 to 10 hours the CC is changed into C, which 
differs materially from graphite, and a metal is formed which has proj)- 
erties midway between those of steel and cast iron. The specific gravity 
is raised from 7.2 to about 7.8; the fracture is of finer grain than normal 
gray iron; and the metal is capable of being forged, hardened, and taking 
a sharp cutting edge, so that it may be used for axes, hatchets, etc. It 
differs from malleable cast iron, since the latter has its carbon removed 
by oxidation, while the converted cast iron retains its .original total 



CAST IRON. 449 

carbon, although in a changed form. The tensile strength of the new 
metal is high, 40,000 to 50,000 lb. per sq. in., with very small elongation. 
The pecuUar change from white to gray iron does not take place if Si 
is low The analysis of the original castings should be about TC, 3.4 to 
3.8; Si, 0.9 to 1.2; Mn, 0.35 to 0.20; S, 0.05 to 0.04; P, 0.04 to 0.03. The 
following shows the change effected by the heat treatment: 
Before anneaUng, GC, 0.72; CC, 2.60; Si, 0.71; Mn, 0.11; S, 0.045; P, 0.04 
After annealing, GC. 2.75; CC, 0.82; Si, 0.73; Mn, 0.11; S, 0.040; P. 0.04 
The GC after annealing is, however, not ordinary graphite, but an 
allotropic form, evidently identical with what Ledebur calls " tempering 
graphite carbon." 

Change of Combined to Graphitic Carbon by Heating. — (H. M. 

Howe, Trans. A. I. M. E., 1908, p. 483.) On heating white cast iron to dif- 
ferent temperatures for some hours, the carbon changes from the com- 
bined to the graphitic state to a degree which increases in general with 
the temperature and with the siUcon-content. With 0.05 Si, a little 
graphite formed at 1832° F.; with 0.13 Si, at 1652° F.; with 2.12 Si, graphite 
lormed at a moderate rate at 1112°, and with 3.15 Si, it formed rapidly 
at 1112° F. In iron free from Si, with 4.271 comb. C. and 0.255 graphitic, 
none of the C. was changed to graphite on long heating to from 1680° to 
2040° F., but in iron with 0.75 Si the graphite, originally 0.938%, rose 
to 1.69% on heating to 1787°, and to 2.795% on heating to 2057° F. On 
the other hand, when carbon enters iron, as in the cementation process 
in making blister-steel, it appears chiefly as cementite (combined carbon). 
Also on heating iron containmg graphite to high temperatures and cooling 
quickly, some of the graphite is changed to cementite. 

Mobility of Molecules of Cast Iron. (A. E. Outerbridge, Jr., 
A.I.M.E., xxvi, 176; xxxv, 223.) — Within limits, cast iron is materially 
strengthened by being subjected to repeated shocks or blows. Six bars 
1 in. sg., 15 in. long, subjected for about 4 hours to incessant blows in a 
tumbUng barrel, were 10 to 15% stronger than companion bars not 
thus treated. Six bars were struck 1000 blows on one end only with a 
hand hammer, and they showed a like gain in strength. The increase is 
greater in hard mixtures, or strong iron, than in soft mixtures, or weak 
iron; greater in 1-in. bars than in V2-in., and somewhat greater in 2-in. 
than in 1-in. bars. Bars were treated in a machine by dropping a 14-lb, 



weight on the middle of a 1-in. bar. supports 12 in. apart. Six bars 

were first broken by having the weight fail a sufficient distance to break 
them at the first blow, then six companion bars were subjected to from 



10 to 50 blows of the same weight falling one-half the former distance, 
and then the weight was allowed to fall from the height at which the first 
bars broke. Not one of the bars broke at the first blow; and from 2 to 
10, and in one case 15 blows from the extreme height were required to 
break them. Mr. Outerbridge believes that every casting when first 
made is under a condition of strain, due to the difference in the rate of 
cooling at the surface and near the center, and that it is practicable to 
reUeve these strains by repeatedly tapping the casting, allowing the parti- 
cles to rearrange themselves and assume a new condition of molecular 
equilibrium. The results, first reported in 1896, were corroborated by 
other experimenters. A report in Jour. Frank. Inst., 1898, gave tests of 
82 bars, in which the maximum gain in strength compared with untreated 
bars was 40%, and the maximum increase in deflection was 41%. 

In his second paper, 1904, Mr. Outerbridge describes another series of 
tests which showed that 1-in. sq. bars 15 in. long subjected to repeated 
heating and cooling grew longer and thicker with each successive oper- 
ation. One bar heated about an hour each day to about 1450° F. in a 
gas furnace for 27 times increased its length 1 n/ie in. and its cross-section 
1/8 in. Soft iron expands more rapidly than hard iron. White iron does 
not expand sufficiently to cover the original shrinkage. Wrought iron and 
steel bars similarly treated in a closed tube all contracted slightly, the 
average contraction after 60 heatings being i/s in. per foot. The strength 
and deflection of the cast-iron bars was greatly decreased by the treatment, 
1250 as compared with 2150 lb., and 0.1 in. deflection as compared with 
0.15 in. The specific gravity of the expanded bars was 5.49 to 6.01, as 
compared with 7.13 for the untreated bars. 

Grate bars of boiler furnaces grow larger in use, as do also cast-iron 
pipes in ovens for heating air. 



450 IRON AND STEEL. 

Castings from Blast Furnace Metal. Castings are frequently made 
from iron run directly from the blast furnace, or from a ladle filled with 
furnace metal. Such metal, if high in Si, is more apt to throw out " kish " 
or loose particles of graphite than cupola metal. With the same percen- 
tage of Si, it is softer than cupola metal, which is due to two causes: 1, 
lower S; 2, higher temperature. T. D. West, A.I.M.E., xxxv, 211, 
reports an example of furnace metal containing Si, 0.51; S, 0.045; Mn, 
0.75; P, 0.094; which was easily planed, whereas if it had been cupola 
metal it would have been quite hard. J. E. Johnson, Jr., ihid., p 213, 
says that furnace metal with S, 0.03, and Si, 0.7, makes good castings, not 
too hard to be machined. Should the metal contain over 0.9 Si, diffi- 
culty is experienced in preventing holes and soft places in the castings, 
caused by the deposition of kish or graphite during or after pouring. 
The best way to prevent this is to pour the iron very hot when making 
castings of smaU or moderate size. 

EflPect of Cupola 3Ielting. (G. R. Henderson, A.S.M.E., xx, 621.) — 

27 car-wheels were analyzed in the pig and also after remelting. The 
P remains constant, as does Si w^hen under 1%. Some of the Mn always 
disappears. The total C remains the same, but the GC and CC vary in 
an erratic m.anner. The metal charged into the cupola should contain 
more GC, Si and Mn than are desired in the castings. Fairbairn {Manu- 
facture of Iron, 1865) found that remelting up to 12 times increased the 
strength and the deflection, but after 18 remeltings the strength was only 
5/8 and the deflection 1/3 of the original. The increase of strength in the 
first remeltings was probably due to the change of GC into, CC, and tho 
subsequent weakening to the increase of S absorbed from the fuel. 

Hard Castings from Soft Pig. (B. F. Fackenthal, Jr., A.I.M.E., 
xxxv, 993.) — Samples from a car load of pig gave Si, 2.61 ; S, 0.023. Cast- 
mgs from the same iron gave 2.33 and 2.26 Si, and 0.26 and 0.25 S, or 
12 times the S in the original pig; probably due to fuel too high in S, but 
more probably to the use of too little fuel in remelting. 

The loss of Si in remelting, and the consequent hardening, is affected 
by the amount of Mn, as shown below: 

Mn. per cent 0.04 0.20 0.43 0.53 

Si lost in remelting, per cent 34 23 12 4 

Difficult Drilling due to LowMn.— H. Souther, A.JS.T.M., v, 219, 
reports a case where thin castings drilled easily while thick parts on the 
same castings rapidly dulled 1/2 and 3/4-in. drills. The chemical constitu- 
tion was normal except Mn; Si, 2.5; P, 0.7; S about 0.08; C, 3.5; Mn, 0.16. 
When the Mn was raised to 0.5 the trouble disappeared. 

Addition of Ferro-silicon in the Ladle. (A. E. Outerbridge, Proc. 
A.S.T.M., vi, 263.) — Half a pound of FeSi, containing 50% Si, added to a 
200-lb. ladle of soft cast iron used for making pulleys with rims 1/4 in. 
thick, prevented the chilling of the surface of the casting, and enabled 
the pulleys to be turned more rapidly. Analysis showed that the actual 
increase of the Si in the casting was less than the calculated increase. 
Tests of the metal treated with FeSi as compared with untreated metal 
showed a gain in strength of from 2 to 26%, and a gain in deflection of 2 
to 3%. The reason assigned for the increase of strength with increase of 
softness is that cuoola iron contains a small amount of iron oxide, which 
reacts with the Si added in the ladle, forming Si02, w^hich goes into the 
slag. 

Additions of Vanadium and Manganese. — R. Moldenke, Am. 
Fdrymen's Assn., 1908, Am. Mach., Feb. 20, '08. Experiments were 
made by adding to melted cast iron in the ladle a ground alloy of ferro- 
vanadium, containing 14.67 Va, 6.36 C, and 0.18 Si. In other experi- 
ments ferro-manganese (80% Mn) was added, together with the vana- 
dium. Four kinds of iron were used: burnt gray iron (gratebars, stove 
iron, etc.), burnt white iron, gray machinery iron (Si, 2.72, S, 0.065, 
P, 0.068, Mn, 0.54) and remelted car wheels (white, two samples anal- 
yzed: Si, 0.60 and 0.53, S, 0.122, 0.138; P. 0.399, 0.374: Mn, 0.38, 
0.44). The bars were IV4 in. diam.",' 12 in. between supports. The 
burnt gray iron was increased in breaking strength from 1310 to 2220 
lb. by the addition of 0.05% Va, and the burnt white iron from 1440 
to 1910 lb. by the addition of 0.05 Va and 0.50 Mn. The following are 
average results: 



CAST IRON. 



451 



Gray Machinery Iron. 


Remelted Car Wheels. 


Added Per cent. 


Breaking 

Strength, 

Lb. 


Deflec- 
tion, In. 


Added Per cent. 


Breaking 


Deflec- 


Va. 


Mn. 


Va. 


Mn. 


Lb. ' 


tion, In. 


0.0 


0.0 


1980 


0.105 


0.0 


0.0 


1470 


0.050 


0.0 


0.50 


1970 


0.100 




0.50 


2790 


0.070 


0.05 




1980 


0.100 


6.05 


. 


3020 


0.060 


0.05 


0.50 


2130 


0.100. 


0.05 


0.50 


2970 


0.090 


O.IO 




2372 


0.090 


0.10 




2800 


0.055 


0.10 


0.50 


2530 


0.120 


0.10 


0.50 


3030 


0.090 


0.15 




2360 


0.100 


0.15 




2950 


0.070 




bars 






0.15 


6.50 


3920 
3069 


0.095 


Average treated 


2224 






Mod. of rupture. . 


.35.800 




48,020 



Experiments with Titanium added to cast iron in the ladle are 
reported by R. Moldenke, Proc. Am. Fdrymen's Assn., 1908. Two 
irons were used: gray, with 2.58 Si, 0.042 S, 0.54 P, 0.74 Mn; and white, 
with 0.85 Si, 0.07 S, 0.42 P, 0.6 INIn. Two Fe Ti alloys with 10% Ti 
were used, one containing no C, and the other 5% C. The latter has 
the lower melting point. The results were as below : 



Original iron 

Plus 0.05 Ti 

Plus 0.10 Ti 

Plus 0.05 Ti and C 
Plus 0.10 Ti and C 
Plus 0.15 Ti and C 



9 tests 
4 tests 

3 tests 
6 tests 
6 tests 

4 tests 



Gray Iron. 



1720-2260 av. 2020 



2750-3140 
2880-3150 
2850-3230 
2850-3150 
3030-3270 



Average of treated iron. . 
Increase over original. . . 



3100 
3030 
3070 
2990 
3190 
3070 
52% 



8 tests 
1 1 tests 



9 tests 
10 tests 
10 tests 



White Iron. Lb. 



1920-21 10 av. 2050 
2210-2660 " 2400 



2230-2720 " 2420 

2320-2460 " 2400 

2280-2620 " 2520 

2430 

18% 



Modulus of rupture, treated iron 48.030 



38.020 



The test bars were I1/4 in. diam. 12 in. between supports. The im- 
provement is as marked whether 0.05, 0.10, or 0.15% Ti is used, which 
mdicates that if sufficient Ti is used for deoxidation of the iron, any 
additional Ti is practically wasted. 

Ti lessens the chiUing action, yet whatever chill remains shows much 
harder iron. Test pieces made with iron which chilled II/2 in. deep 
gave but 1 in. chill when the iron was treated in the ladle. The original 
iron crushed at 173,000 lbs. per sq. in. and stood 445 in Brinel's test 
for hardness, soft steel running about 105. The treated piece ran 
298,000 lbs. per sq. in. and showed a hardness of 557. Testing the soft 
metal below the chilled portion lor hardness gave 332 for the original 
and 322 for the treated piece. 

Strength of Cast-iron Beams. — C. H. Benjamin, MacKy, May, 
1906. Numerous tests were made of beams of different sections includ- 
ing hollow rectangles and cyhnders, I and T-shapes, etc. All the sec- 
tion's were made approximately the same area, about 4.4 sq. in., and all 
were tested by transverse loading, with supports 18 in. apart. The 
results, when reduced by the ordinary formula for stress on the extreme 
fiber, S = My /I, showed an extraordinary variation, some of the values 
being as follows: Square bar, 23,300; Round bar, 25,000. Hollow round, 
3.4 in. outside and 2.5 in. inside diam., 26,450, and 35,800. Hollow 
ellipse, 3 in. wide, 3.9 in. high, 0.9 in. thick, 36,000. 7-beam, 4 in. high, 
web 0.44 in. thick, 17,700. The hollow cyUndrical and elliptical sec- 
tioas are much stronger than the solid sections. This is due to the 
thinner metal, the greater surface of hard skin, and freedom from 
shrinkage strains. Professor Benjamin's conclusions from these tests are: 

(1) The commonly accepted formulas for the strength and stiffness 
of beams do not apply well to cored and ribbed sections of cast iron. 

(2) Neither the strength nor the stiffness of a section increases in pro- 
portion to the increase in the section modulus or the moment of inertia. 

(3) The best way to determine these, qualities for a cast-iron beam is 
by experiment with the particular section desired and not by reasoning 
from any other section. 



452 



IRON AND STEEL. 



Bursting Strength of Cast-iron Cylinders. — C. H. Benjamin, 
A.S. M. E., XIX, 697; Mach'7/, Nov., 1905. Four cylinders, 20 in. long. 
10 1/8 in. int. diam., 3/4 in. thick, with flanged ends and bolted covers, 
burst at 1350, 1400, 1350, and 1200 lbs. per sq. in. hydraulic pressure, 
the corresponding fiber stress, from the formula S = pd/2 t, being 9040, 
10,200, 9735 and 9080. Pieces cut from the shell had an average tensile 
strength of 14,000 lbs. per sq. in., and a modulus of rupture in trans- 
verse tests of 30.000. 

Transverse Strength of Cast-iron Water-pipe. (Technology Quar- 
terly, Sept., 1897.) — Tests of 31 cast-iron pipes by transverse stress gave 
a maximiun outside fibre stress, calculated from maximum load, as- 
suming each half of pipe as a beam fixed at the ends, ranging from 
12,800 lb. to 26,300 lb. per sq. in. 

Bars 2 in. wide cut from the pipes gave moduli of rupture ranging from 
28,400 to 51,400 lb. per sq. in. Four of the tests, bars and pipes: 

Moduli of rupture of bar 28,400 34,400 40,000 51,400 

Fibre stress of pipe .,,,,..•• 18.300 12,800 14,500 26.300 

These figures show a great variation in the strength of both bars and 
pipes, and also that the strength of the bar does not bear any definite 
relation to the strength of the pipe. 

Bursting Strength of Flanged Fittings. — Power, Feb. 4, 1908. 
The Crane Company, Chicago, published in the Valve World records of 
tests of tees and ells, standard and extra heavy, which show that the 
bursting strength of such fittings is far less than is given by the standard 
formulsB for thick cylinders. As a result of the tests they give the 
following empirical formula: B = TS/D, in which B = bursting pres- 
sures, lbs. per sq. in., T = thickness of metal, D = inside diam., and 
S = 65% of the tensile strength of the metal for pipes up to 12 in. diam., 
for larger sizes use 60%. The pipes were made of " ferro-steel " of 
33,000 lbs. T. S., and of cast iron of 22,000 lbs. as tested in bars. The 
following are the principal results of tests of extra heavy tees and ells 
compared with results of calculation by the Crane Company's formula: 

Bursting Strength of Pipe-Fittings. Pounds per Square inch. 



Inside Diam. 


6 


8 10 


12 


14 


16 


18 


20 


24 


Thickness. 


3/4 


13/16 


15/16 


1 


1 1/8 


13/16 


11/4 


15/16 


1 1/2 


B, Ferro-steel 


2733 


2250 


2160 


2033 


1825 


1700 


1450 


1275 


1300 


calculated 


2680 


2180 


2010 


1870 


1570 


1450 


1350 


1280 


1220 


B, Cast iron 


1687 


1350 


1306 


1380 


1100 


1025 


600 


750 


700 


calculated 


1790 


1450 


1340 


1190 


1060 


980 


920 


870 


620 


Ells, ferro steel . . . 


3266 
2275 


2725 
1625 


2350 
1541 


2133 
1275 












" cast-iron 


1075 


1250 









Specific Gravity and Strength, (Major Wade, 1856.) 

Third-class guns: Sp. Gr. 7.087. T. S. 20,148. Another lot: least Sp. 
Or. 7.163, T. S. 22,402. 

Second-class guns: Sp. Gr. 7.154. T. S. 24,767. Another lot: mean 
Sp. Gr. 7.302, T. S. 27,232. 

First-class guns: Sp. Gr. 7.204. T. S. 28,805. Another lot: greatest 
Sp. Gr. 7.402, T. S. 31,027. 

Strength of Charcoal Pig Iron. — Pig iron made from Salisbury 
ores, in furnaces at Wassaic and Millerton, N. Y., has shown over 40,000 
lbs. T. S. per square inch, one sample giving 42,281 lbs. Muirkirk, Md., 
iron tested at the Washington Navy Yard showed: average for No. 2 
iron, 21,601 lbs.; No. 3, 23,959 lbs.; No. 4, 41,329 lbs.; average den- 
sity of No. 4, 7.336 (J. C. I. W., v. p. 44). 

Nos. 3 and 4 charcoal pig iron from Chapinville, Conn., showed a 
tensile strength per square inch of from 34,761 lbs. to 41,882 lbs. Char- 
coal pig iron from Shelby, Ala. (tests made in August, 1891), showed a 
strength of 34,800 lbs. for No. 3; No. 4, 39,675 lbs.; No. 5, 46,450 lbs.; 
and a mixture of equal parts of Nos. 2, 3, 4, and 5, 41,470 lbs. (Bull. 
I. & S, A.) 

Variation of Density and Tenacity of Gun-Irons. — An increase of 
density invariably follows the rapid cooling of cast iron, and as a general 
rule the tenacity is increased by the same means. The tenacity gener- 
ally increases quite uniformly with the density, until the latter ascends 



CAST IRON. 453 

to some given point; after which an increased density is accompanied 
by a diminished tenacity. 

The turning-point ot density at which the best qualities of gun-iron 
attain their maximum tenacity appears to be about 7.30. At this point 
of density, or near it, whether in proof-bars or gun-heads, the tenacity is 
greatest. 

As the density of iron is increased its hquidity when melted is dimin- 
ished. This causes it to congeal quickly, and to form cavities in the 
interior of the casting. (Pamphlet of Builders' Iron Foundry, 1893.) 

" Semi-steel " is a trade name given by some founders to castings made 
from pig iron melted in the cupola with additions of from 20 to 30 per 
cent of steel scrap. Ferro-manganese is also added either in the cupola or 
in the ladle. The addition of the steel dilutes the Si of the pig iron, and 
changes some of the C from GC to CC, but the TC is unchanged, for any 
reduction made by the steel is balanced by absorption of C from the fuel. 
Semi-steel tnerefore is nothing more than a strong cast iron, low in Si 
and containing some Mn, and the name given it is a misnomer. 

Mixture of Cast Iron with Steel. — Car wheels are sometimes made 
from a mixture of charcoal iron, anthracite iron, and Bessemer steel. 
The following shows the tensile strength of a number of tests of wheel 
mixtures, the average tensile strength of the charcoal iron used being 
22,000 lbs. {Jour. C. I. W., iii, p. 184): 

lbs. per sq. in. 

Charcoal iron with 2V2% steel 22,467 

*• 33/4% steel 26,733 

" 61/4% steel and 6V4% anthracite 24,400 

" 71/3% steel and 71/2% anthracite 28,150 

•' 21/2% steel, 21/2% wro't iron, and 61/4% anth. 25,550 
" 5 % steel, 5% wro't iron, and 10% anth 26,500 

Cast Iron Partially Bessemerized. — Car wheels made of partially 
Bessemerized iron (blown in a Bessemer converter for 31/2 minutes), 
chilled in a chill test mold over an inch deep, just as a test of cold blast 
charcoal iron for car wheels would chill. Car wheels made of this blown 
iron have run 250,000 miles. {Jour. C. I. W., vi, p. 77.) 

Bad Cast Iron. — On October 15, 1891, the cast-iron fly-wheel of a 
large pair of Corhss engines belonging to the Amoskeag Mfg. Co., of Man- 
chester, N.H., exploded from centrifugal force. The fly-wheel was 30 
feet diameter and 110 inches face, with one set of 12 arms, and weighed 
116,000 lbs. After the accident, the rim castings, as well as the ends of 
the arms, were found to be full of flaws, caused chiefly by the drawing 
and shrinking of the metal. Specimens of the metal were tested for 
tensile strength, and varied from 15,000 lbs. per square inch in sound 
pieces to 1000 lbs. in spongy ones. None of these flaws showed on the 
surface, and a rigid examination of the parts before they were erected 
failed to give any cause to suspect their true nature. Experiments were 
carried on for some time after the accident in the Amoskeag Company's 
foundry in attempting to dupUcate the flaws, but with no success in 
approaching the badness of these castings. 

Permanent Expansion of Cast Iron by Heating. (Valve World, 
Sept., 1908.) — Cast iron subjected to continued temperatures of approx- 
imateljr 500° to 600° took a permanent expansion and did not return to 
its original volume when cooled. 

As steam is being superheated quite commonly to temperatures above 
675°, this fact is of great interest inasmuch as it modifies our ideas about 
the proper material to be used in the construction of valves and fittings 
for service under high temperatures. A permanent volumetric expan- 
sion is followed by a loss of strength, the loss in cast iron being fully 40 
per cent in four years. 

Crane Co. made an attempt to determine whether cast steel was affected 
in the same manner as cast iron. Three flanges were taken, one of cast 
iron, one of ferrosteel, and the third of cast steel. These flanges were 
exposed for a total period of 130 hours to temperatures ranging as follows: 

Less than 500°, 18 hours; 500° to 700°, 97 hours; 710° to 800°, 12 hours: 
over 800°, 3 hours. Average temp., 583°. 

The outside diameter in each case was 12 1/2 in. and the bore 6 29/54 in. 
, The results were: Cast-steel flange, no change. Cast-iron flange, out- 
side diam. increased 0.019 in. , inside diam. increased 0.007 in. Ferro-steel 
flange, outside diam. increased 0.033 in., inside diam. increased 0.017 in. 



454 IRON AND STEEL. 

If the permanent expansion of cast iron stopped at the figures given 
above, it would not be a serious matter; but all evidence points toward a 
steady increase as time goes on, as was shown by one of Crane Co.'s 
14-in. valves, which originally was 221/2 in. face to face, and increased 
5/ie in. in length in four years under an average temperature of about 
590°. 

MALLEABLE CAST IRON.* 

There are four great classes of w^ork for whose requirements malleable 
cast iron (commonly called "malleable iron" in America) is especially 
adapted. These are agricultural implements, railway supplies, carriage 
and harness castings and pipe fittings. Besides these main classes there 
are innumerable other unclassified uses. The malleable casting is sel- 
dom over 175 lb. in weight, or 3 ft. in length, or % in. thick. The 
great majority of even the heavier castings do not exceed 10 lb. 

When properly made, malleable cast iron should have a tensile 
strength of 42,000 to 48,000 lb. per sq. in., with an elongation of 5% in 
2 in. Bars 1 in. square and on supports 12 in. apart should show a 
transverse strength of 2500 to 3500 lb., with a deflection of at least K in- 

While the strength of malleable iron should be as stated, much of it 
will fall as low as 35,000 lb. per sq. in., and this will still be good for such 
work as pipe fittings, hardware castings and the like. On the other 
hand, even 63,000 lb. per sq. in. has been reached, with a load of 5000 
lb. and a deflection of 2 H in. in the transverse test. This high strength 
is not desirable, as the softness of the casting is sacrificed, and its resist- 
ance to continued shock is lessened. For the repeated stresses of severe 
service the malleable casting ranks ahead of steel, and only where a high 
tensile strength* is essential must it be replaced by that material. 

The process of making malleable iron may be summarized as follows: 
The proper cast irons are melted in either the crucible, the air furnace, 
the open-hearth furnace, or the cupola. The metal when cast into the 
sand molds must chill white or not more than just a little mottled. After 
removing the sand from the hard castings they are packed in iron scale, 
or other materials containing iron oxide, and subjected to a red heat 
(1250 to 1350° F.) tor over 60 hours. They are then cooled slowly, 
cleaned from scale, chipoed or ground, and straightened. Much of the 
malleable iron made to-day (1915) is annealed for a shorter time and at 
higher temperatures. The safe method, however, is the one given above. 

When hard, or just from the sand, the composition of the iron should 
be about as follows: Si, from 0.35 up to 1.00, depending upon the thick- 
ness and the purpose the casting is to be used for; P not over 0.225, Mn 
not over 0.20, S not over 0.08. The total carbon can be from 2.75 up- 
ward, 4.15 being about the highest that can be carried. The lower the 
carbon the stronger the casting subsequently. Below 2.75 there is apt to 
be trouble in the anneal, the black-heart structure may not appear, and 
the castings remain weak. A casting 1 in. thick would necessitate sihcon 
at 0.35, and the use of chills in the mold in addition, to get the iron white. 
For a casting 3^ in. thick, Si about 0.60 is the proper limit, except where 
great strength is desired, when it can be dropped to 0.45. Above 0.60 
there is danger of getting heavily-mottled if not gray iron from the sand 
molds, and this material, when annealed the long time required for the 
white castings, would be ruined. For very thin castings, Si can run up 
to 1.25 and still leave the metal white in fracture. 

Pig Iron for Malleable Castings. — The specifications run as follows: 
Si, 0.75, 1.00, 1.25, 1.50, 1.75, 2.00%, as required; Mn, not over 0.60; 
P, not over 0.225; S, not over 0.05. 

Works making heavy castings almost exclusively specify Si to include 
0.75 up to 1.50%. Makers of very light work take 1.25 to 2.00%. 

The Melting Furnace. — Malleable iron is melted in the reverbera- 
tory furnace, the open-hearth furnace, and the cupola, the reverberatory 
bemg the most extensively used. About 85 per cent of the entire output 
of the United States is melted by this process. Prior to about 1885. 
the standard furnace was one of 5 tons capacity. At present (1915) we 

* Refercnces.—R. Moldenke, Cass Mag., 1907, and Iron Trade 
Review, 1908; E. C. Wheeler, Iron Age, Nov. 9. 1899; C. H. Gale. Indnst. 
World, April 13, 1908; W. H. Hatfield, ibid. G. A. Akerlund, Iron Tr. 
Rev., Aug. 23, 1906; C. H. Day, Am. Mach., April 5, 1906. 



MALLEABLE CAST IRON. 



455 



have furnaces of 25 and 30 tons capacity, though furnaces of from 10 to 
15 tons are the most popular and give more uniform results than those 
of larger capacity. 

The adoption of the open-hearth furnace for malleable iron dates 
back to about 1893. It is used largely in the Pittsburg district. 

Cupola-melted iron does not possess the tensile strength nor ductility 
of iron melted in the reverberatory or open-hearth furnace, due partly to 
the higher carbon and sulphur caused by the metal being in contact 
with the fuel. This feature is rather an advantage than otherwise, as 
most of the product of cupola-melted iron consists of pipe fittings, cast- 
ings that are not subjected to any great stress or shock. The castings 
are threaded, and a strong, tough malleable iron does not cut a clean, 
smooth thread, but rather will rough up under the cutting tool. 

In the reverberatory and open-hearth furnaces the metal may be 
partly desiUconized at will, by an oxidizing flame or by additions of 
scrap or other low-silicon material, while the total carbon can be lowered 
by scrap steel additions. Manganese is also oxidized in the furnace. 

The composition of good castings in American practice is : Si. from 0.45 
to 1.00%; Mn up to 0.30%; P, up to 0.225%; S, up to 0.08%; total 
carbon in the hard casting, above 2.75%. 

In special cases, especially for very small castings, the silicon may go 
up as high as 1.25%, while for very heavy work it may drop down to 
0.35% with very good results. In the case of charcoal iron this figure 
gives the strongest castings. With coke irons, however, especially when 
steel scrap additions are the rule, 0.45 should be the lower limit, and 0.65 
is the best silicon for all-around medium and heavy work, such as rail- 
road castings. 

In American practice phosphorus is required not to exceed 0.225%, 
and is preferred lower. In European practice it is required as low as 
0.10%, but castings have been made successfully with P as high as 
0.40%. 

The heat treatment of metal during melting has an important bearing 
upon its tensile strength, elongation, etc. Excessive temperatures pro- 
mote the chances of burning. Iron is burnt mainly through the genera- 
tion in melting furnaces of higher temperatures than those prevailing 
during the initial casting at blast furnaces and an excess of air in the 
flame. The choicest irons may thus turn out poor material. 

Shrinkage of the Casting. — The shrinkage of the hard casting is 
about 1/4 in. to the foot, or double that of gray iron. In annealing about 
half of this is recovered, and hence the net result is the same as in ordi- 
nary foundry pattern practice. The effect of this great shrinkage is to 
cause shrinkage cracks or sponginess in, the interior of the casting. As 
soon as the liquid metal sets against the surface of the mold and the 
source of supply is cut off, the contraction of the metal in the interior 
as it cools causes the particles to be torn apart and to form minute 
cracks or cavities. " Every test bar, and for that matter every casting 
may be regarded as a shell of fairly continuous metal with an interior of 
slight planes of separation at right angles to the surface. This charac- 
teristic of malleable iron forms the basis of many a mysterious failure." 
(Moldenke.) 

Packing for Annealing. — After the castings have been chipped and 
sorted they are packed in iron annealing pots, holding about 800 pounds 
of iron, together with a packing composed of iron ore, hammer and 
rolhng mill scale, turnings, borings, etc. The turnings, etc., were form- 
erly treated with a solution of salammoniac or muriatic acid to form a 
heavy coating of oxide, but such treatment is now considered unnec- 
essary. Blast furnace slag, coke, sand, and fire clay have also been used 
for packing. The changes in chemical composition of J:he castings when 
annealed in slag and in coke are given as follows by C. H. Gale: 





Si. 


S. 


P. 


Mn. 


C. C. 


G. C. 


Hard iron 


0.63 
0.61 
0.61 


0.043 
0.049 
0.065 


0.147 
0.145 
0.150 


0.21 
0.21 
0.21 


2.54 
0.24 
0.25 


Trace 


Annealed in slag . 


1 65 


Annealed in coke 


2.00 



The Annealing Process. — The effect of the annealing is to oxidize 
and remove the carbon from the surface of the casting, to remove it 
to a greater or less degree below the surface, and to convert the remain- 



456 IRON AND STEEL. 

ing carbon from the combined form into the amorphous form called a 
•'temper carbon" by Professor Ledebur, the German metallurgist. It 
differs from the graphite found in pig iron, but is usually reported as 
graphitic carbon by the chemists. In the original malleable process, 
invented by Reaumur, in 1722, the castings were packed in iron ore and 
annealed thoroughly, so that most of the carbon was probably oxidized, 
but in American practice the annealing process is rather a heat treat- 
ment than an oxidizing process, and its effect is to precipitate the carbon 
rather than to eliminate it. According to the analysis quoted above, the 
metal annealed in slag lost 0.65% of its total C, while that annealed in 
coke lost only 0.29%. In the former, S increased 0.006% and in the 
latter 0.022%. The Si decreased 0.02% in both cases, while the P and 
Mn remained constant. 

As to the distribution of carbon in an annealed casting. Dr. Moldenke 
says: "Take a flat piece of malleable and plane off the skin, say Vie in. 
deep and gather the cliips for analysis. The carbon will be found, say, 
0.15% perhaps even less. Cut in another Vie in. and the total C will be 
nearer 0.60%. Now go down successively by sixteenths and the total 
C will rBrnge from, say, 1.70 to 3.65% and will then remain constant until 
the center is reached." "The malleable casting is for practical purposes 
a poor steel casting with a lot of graphite, not crystalUzed, between the 
crystals or groups of crystals of the steel." 

The heat in the annealing process must be maintained for from two to 
four days, depending upon the tliickness of sections of the castings and 
the compactness with which the castings or annealing boxes are placed 
in the furnace. An annealing temperature 1550° to 1600° Fahr. is often 
used, but it is not essential, as the annealing can be accomplished at 
1300°, but the time required will be longer than that at the higher tem- 
perature. Burnt iron in the anneal is no uncommon feature, and, gen- 
erally speaking, it is the result of carelessness. The most carefully pre- 
pared metal from melting furnaces can here be turned into worthless 
castings by some slight inattention of detail. The highest temperature 
for annealing should be registered in each foundry, and kept there by the 
daily and frequent use of a thermometer constructed for that sole pur- 
pose. Steady, continued heat insures soft castings, while unequal tem- 
peratures destroy all chances for successful work, although the initial 
metal was of the most excellent quaUty. 

After annealing, the castings are cleaned by tumblers or the sand 
blast; they are carefuUy examined for cracks or other defects, and if 
sprung out of shape are hammered or forced by hydraulic power to the 
correct shape. Such parts as are produced in great quantities are placed 
in a drop hammer and one or two blows will insure a correct form. They 
may be drop-forged or even welded when the iron has been made for that 

Eurpose. Castings are sometimes dipped into asphaltum diluted with 
enzine to give them a better finish. 

Malleable castings must never be straightened hot, especially when 
thick. In the case of very thin castings there is some latitude, as the 
material is so decarbonized that it is nearer a steel than genuine mal- 
leable cast iron. In heating portions of castings that were badly warped, 
it seems that the amorphous carbon in them was combined again, and 
while the balance of the casting remained black and sound, the heated 
parts became white and brittle, as in the original hard casting. Hence 
the advice to straighten the castings cold, preferably with a drop ham- 
mer and suitable dies, or still better in the hydraulic press. (R. Moldenke. 
Proc. A.S. T.M., vi, 244.) 

Physical Characteristics. — The characteristic that gives malleable 
iron its greatest value as compared with gray iron is its ability to resist 
shocks. Malleability in a light casting 1/4 in. thick and less means a 
soft, pliable condition and the ability to withstand considerable distor- 
tion without fracture, while in the heavy sections, 1/2 in. and over, it 
means the ability to resist shocks without bending or breaking. 

For general purposes it is not altogether desirable to have a metal 
very high in tensile strength, but rather one which has a high transverse 
strength, and especially a good deflection. It is not always that a strong 
and at the same time soft material can be produced in a foundry operat- 
ing on the lighter grades of castings. The purchaser, therefore, unless he 
requires very stiff material, should rather look upon the deflection of 



MALLEABLE CAST IKON. 457 

the metal coupled with the weight it took to do tliis bending before 
failure, than for a high tensile strength. 

The ductiUty of the malleable casting permits the driving of rivets, 
which cannot so readily be done with gray cast iron; and for certain 
parts of cars, like the journal boxes, malleable cast iron may be con- 
sideied supreme, leaving cast iron and "semi-steel " far behind. 

It was formerly the general belief that the strength of malleable iron 
was largely in the white skin ahvavs found on this material, but it has 
been demonstrated that the removal of the skin does not proportionately 
lessen the strength of the casting. 

Test Bars. — The rectangular shape is used for test bars m preference 
to the round section, because the latter is more apt to have serious cracks 
in the center, due to shrinkage, especially if the diameter is large. A 
round section, unless in very light hardware, is to be avoided, as the 
shrinkage crack in the center may have an outlet to the skin, and cause 
failure in service. 

It is customary to provide for two sizes of test bars, the heavy and 
the light. Thus the 1-in. square bar represents work 1/2 an inch thick 
and over, and a 1 X V2-in. section bar cares for the lighter castings. 
Both are 14 inches long. They should be cast at the beginning and at 
the end of each heat. 

Design of 31alleable Castings. — As white cast iron shrinks a great 
deal more than gray iron, and as the sections of malleable castings are 
lighter than those of similar castings of gray iron, fractures are very 
common. It is therefore the designer's aim to distribute the metal so 
as to meet these conditions. In long pieces the stiffening ribs should 
extend lengthways so as to produce as little resistance as possible to the 
contraction of the metal at the time of solidification. If this be not 
possible, the molder provides a "crush core" whose interior is filled with 
crushed coke. When the metal solidifies in the flask the core is crushed 
by the casting and thus prevents shrinkage cracks. At other times a 
certain corner or juncture of ribs in the casting will be found cracked. 
In order to prevent this a small piece of cast iron (chill) is embedded in 
the sand at this critical point, and the metal will cool here more quickly 
than elsewhere, and thus fortify this point, although it may happen that 
some other part of the casting will be found fractured instead, and in 
many cases the locations and the shape of strengthening ribs in the 
casting must be altered until a casting is procured free from shrinkage 
cracks. In designing of malleable cast-iron details the following rules 
should be observed: 

(1) Endeavor to keep the metal in different parts of the casting at a 
uniform thickness. In a small casting, of, say, 10 lbs. weight, V4-in. 
metal is about the practical thickness, s/^g in. for a casting of 15 to 20 
lbs., and 3/8 to 1/2 in. for castings of 40 lbs. and over. (2) Endeavor to 
avoid sharp junctions of ribs or parts, and if the casting is long, say 24 
inches or more, the ends should be made of such shape as to offer as 
little resistance as possible to the contraction of metal when cooling in 
the mold. 

Speciflcations for Malleable Iron. — The tensile strength of malle- 
able iron varies with the thickness of the metal, the lighter sections hav- 
ing a greater strength per square inch than the heavier sections. An 
Eastern railroad designates the tensile strength desired as follows: Sec- 
tions 3/8 in. thick or less should have a tensile strength of not less than 
40,000 lbs. per sq. in.; 3/3 to 3/4 in. thick, not less than 38,000; and over 
3/4 in., not less than 36,000 lbs. per sq. in. Test bars 5/8 and 7/8 in. diam. 
were made in the same mold and poured from the same ladle, and an- 
nealed together. The average tensile strength of five pairs of bars so 
treated, representing five heats, was, s/s-in. bars, 45,095; 7/8-in. bars, 
41,316 lbs. per sq. in. Average elongation in 6 in.: s/g-in. bars 5.3%; 
7/8-in. bars 4.2%. 

A very high tensile strength can be obtained approaching that of 
cast steel but at the expense of the malleability of the product. Malle- 
able test bars have been made with a tensile strength of between 60,000 
and 70,000 lbs. per sq. in., but the ductility and ability to resist shocks 
of these bars was not equal to that of bars breaking at 40,000 to 45,000 
pounds per sq. in. 

The British Admiralty specification is 18 tons (40,320 lbs.) per 
square inch, a minirmim elongation of 4^4% in three inches and a 



458 IRON AND STEEL. 

bending angle of at least 90° over a 1-in. radius, the bar being 1 X % 
in. in section. 

A committee of the American Society for Testing Materials re- 
ported, in 1915, a set of specifications for malleable castings which in- 
cludes the following: The specimen for tensile strength is a rouni 
bar 12 in. long, 3/4 in. diam. at the ends, tapering to a middle portion 
4 in. long, 5/8 in. diam. The transverse test specimen is 14 in. long, 

1 in. wide, and 1/2, 5/8, or 3/4 in. thick, according to the thickness of 
the casting it represents. Specimens are to be cast without chiUs, with 
the ends free in the mold. . The tensile strength shall be not less than 
38,000 lb. per sq. in. with an elongation not less than 5 % in 2 in. The 
transverse strength, the bar being tested with cope side up, on sup- 
ports 12 in. apart, pressure being applied at the center shall be respec- 
tively 900, 1400, and 2000 lb. with deflections 1.25, 1.00, and 0.75 in 
the 1/2, 5/8. and 3/4 in. test specimens. The specifications are intended 
to cover railroad malleable irons and the softer grades only. They in- 
clude directions as to the casting of the test specimens and as to 
inspection. 

Improvement in Quality of Castings. (Moldenke.) — The history 
of improvement in the malleable casting is admirably reflected in the 
test records of any works that has them. Going back to the early 90's, 
tae average tensile strength of malleable cast iron was about 35,000 lbs. 
per sq. in., with an elongation of about 2% in 2 in. The transverse 
Ltrength was perhaps 2800 lbs., with a deflection of 1/2 in. Toward the 
close of the 90's a fair average of the castings then made would run 
about 44,000 lbs. per sq. in., with an elongation of 5% in 2 in., and the 
transverse strength, about 3500 lbs., \Nith a deflection of 1/2 inch. These 
average figures were greatly exceeded in establishments where special 
attention was given to the niceties of the process. The tensile strength 
here would run 52,000 lbs. per sq. in. regularly, with 7% elongation in 

2 in., and the transverse strength, 5000 and over, with 1 1/2 in. deflection. 
Further Progress Desirable. (Moldenke.) — We do not know at 

the present time why cupola malleables require an annealing heat sev- 
eral hundred degrees higher than air or open-hearth furnace iron. The 
underlying principles of the oxidation of the bath, which is a frequent 
cause of defective iron, is practically unknown to the majority of those 
engaged in this industry. Heg.ts are frequently made that will not 
pour nor anneal properly, but the causes are still being sought. To 
produce castings from successive heats, so that with the same composi- 
tion they will have the same physical strength regardless of how they 
are tested, is a problem partially solved for steel, but not yet approached 
for malleable cast iron. 

Sufficient progress in the study of iron with the microscope has been 
made to warrant the belief that in the not distant future we may be 
able to distinguish the constituents of the material by means of etching 
with various chemicals. When the sulphides and phosphides of iron, 
or the manganese-sulphur compounds, can be seen directly under the 
microscope, it is probable that a method may be found by which the 
dangerous ingredients may be so scattered or arranged that they will 
do the least harm. 

The high sulphur in European malleable accounts to some extent for 
the comparatively low strength when contrasted with our product. 
Their castings being all very light, so long as they bend and twist prop- 
erly, the purpose is served, and hence until heavier castings become the 
rule instead of the exception, "white heart" and steely-looking frac- 
tures will remain the characteristic feature of European work. 

STRENGTH OF MALLEABLE CAST IRON. 

Tests of Square Bars, V2 in. and 1 in., by tension, compression and 
transverse stress, by M. H. Miner and F. E. Blake {Railway Age, Jan. 25, 
1901). 

Tension. Six 1/2-in. and six 1-in. round bars, also two 1-in. bars 
turned to remove the skin, from each of four makers. Average results: 

T. S., 1/2-in. bars, 37,470-42,950, av. 40,960; E. L., 16,500-21,100, av. 
19,176. 

T. S., 1-in. bars, 35,750-40,530, av. 38,300; E. L., 14,860-19,900, av. 
17,181. 

Tensile strenerth, turned bars. av. 35.090: Elastic limit, av. 15.660. 



WROUGHT IRON. 



459 



Elong. in 8 in., V^-in. bars, 4.75 % ; 1-in. bars, 4.32 % ; turned bars, 3.73 % . 

Modulus of elasticity, V2-in. bars, 22,289,000; 1-in. bars, 21,677,000. 

Compression. 16 short blocks, 2 in. long, 1 in. and 1/2 in. square 
respectively. 

8 long columns, 15 in. long, 1 in. sq., and 7.5 in. long, I/2 in. sq. respec- 
tively. 

Averages of blocks from each of four makers: 

Short blocks, 1/2-in. sq., 93,000 to 114,500 lbs. per sq. in. Mean, 
101,900 lbs. per sq. in. 

Short blocks, 1 in. sq., 137,600 to 165,300 lbs. per sq. in. Mean, 
152,800 lbs. per sq. in. 

Ratio of final to original length, 1/2 in., 61.7%; 1 in., 52.6%. A small 
part of the shortening was due to sliding on the 45° plane of fracture. 

Long columns: 1/2 in. X 7.5 In. Mean, 29,400 lbs. per sq. in.: 1 in. 
X 15 in., 27,500 lbs. per sq. in. Ratio of final to original length, 1/2 in., 
98.5%; 1 in., 98.8%. The long columns did not rupture, but reached 
the maximum stress after bending into a permanent curve. 

Transverse Tests. Maximum fiber stress, mean of 8 tests, 1/2-in. 
bars, 34,163 lbs. per sq. in. 1-in. bars, 36,125 lbs. per sq. in. Length 
between supports, 20 in. The bars did not break, but failed by bending. 
The 1/2-in. bars could be bent nearlv double. ^ . ,,. , ^ ^ . 

MaUeable Bars cast by Buhl JVlalleable Co., Detroit, Mich., tested as 
folloAvs. The tests were reported by Chas. H. Day, Am. Mach., April 5, 
1906. The castings were all made at the same time. The rectangular 
sections were approximately 1/4 X 3/4 in. The star sections were square 
crosses, 1 in. wide, with arms about 1/4 In. thick. The figures here given 
are the maximum and minimum results from three bars of each section. 
Tensile Tests. Compression Tests. 



Section. 


Area, 
sq. in. 


Tensile 
St'gth, 
lbs. per 
sq. in. 


Elong. 
in 8 in., 

%. 


Red. of 
Area, 

%. 


Area, 
sq. in. 


L'gth, 
in. 


Comp. 

Str., 

lbs. per 

sq. in. 


Final 
Area, 
sq. in. 


Round 


0.817 


43,000 


5.87 


4.76 


0.847 


15 


31,700 


0.901 




0.801 


43,400 


6.21 


3.98 


0.801 


15 


33,240 


0.886 


" 


0.219 


41,130 


7.70 


3.40 


0.209 


7.5 


32,600 


0.221 




0.202 


44,700 


13.00 


3.63 


0.204 


7.5 


34,600 


0.215 


Square 


0.277 


36,700 


4.70 


2.20 


0.263 


7.5 


33,200 


0.272 




0.277 


38,100 


3.72 


3.00 


0.254 


7.5 


31,870 


0.278 


*• 


1.040 


38,460 


4.10 


3.30 


1.051 


15 


29,650 


1.070 


'♦ 


1.050 


37,860 


2.38 


2.94 


1.040 


15 


30,450 


1.066 


Rect. 


0.239 


31,200* 


5.19 


1.50 


0.436 


15 


32,200 


0.448 




0.244 


37,600 


3.87 


3.80 


0.457 


15 


30,400 


0.467 


Star 


0.584 
0.575 


34,600 
37.200 


4.20 

4.80 


3.10 
3.50 











* Broke in flaw. 

Tests of Rectangular Cast Bars, made by a committee of the Mas- 
ter Car-builders' Assn. in 1891 and 1892, gave the following results 
(selected to show range of variation) : 



Size of 

Section, 

in. 



0.25x1.52 
0.5 XI. 53 
0.78x2 
0.88x1.54 
1.52x1.54 



Tensile 
St'gth, 
lbs. per 
sq. in. 



34,700 
32,800 
25,100 
33,600 
28,200 



Elastic 
Limit, 
lbs. per 
sq. i] 



21,100 
17,000 
15,400 
19,300 



Elonga- 
tion, % 
in 4 in. 



2 

2 

1.5 

1.5 

1.5 



Size of 

Section, 

in. 



0.29x2.78 
0.39x2.82 
0.53x2.76 
0.8 X2.76 
1.03x2.82 



Tensile 
St'gth, 
lbs. per 
sq. in. 



28,160 
32,060 

27,875 
25,120 
28,720 



Elastic 
Limit, 
lbs. per 
sq. in. 

22,650 
20,595 
19,520 
18,390 
18,220 



Elong. 
in 8 in., 

%. 

1.5 
1.1 
1.1 
1.3 



WROUGHT IRON. 

The Manufacture of Wrought Iron. — When iron ore, which is an 
oxide of iron, Fe203 or FesO*, containing silica, phosphorus, sulphur, 
etc., as impurities, is heated to a yellow heat in contact with charcoal or 
other fuel, the oxygen of the ore combines with the carbon of the fuel, 
part of the iron combines with silica to form a fusible cinder or slag, and 
the remainder of the iron agglutinates into a pasty mass which is inter- 
mingled with the cinder. Depending upon the time and the tempera- 



460 IRON AND STEEL* 

ture of the operation, and on the kind and quality of the impurities 
present in the ore and the fuel, more or less of the sulphur and phos- 
phorus may remain in the iron or may pass into the slag ; a small amount 
of carbon may also be absorbed by the iron. By squeezing, hammering, 
or rolling the lump of iron while it is highly heated, the cinder may be 
nearly all expelled from it, but generally enough remains to give a bar 
after being rolled, cooled and broken across, the appearance of a fibrous 
structure. The quality of the finished bar depends upon the extent to 
which the chemical impurities and the intermingled slag have been 
removed from the iron. 

The process above described is known as the direct process. It is 
now but Uttle used, having been replaced by the indirect process known 
as puddling or boihng. In this process pig iron which has been melted 
in a reverb eratory furnace is desilicomzed and decarbonized by the 
oxygen derived from iron ore or iron scale in the bottom of the furnace, 
and from the oxidizing flame of the furnace. The temperature being too 
low to maintain the iron, when low in carbon, in a melted condition, it 
gradually " comes to nature" by the formation of pastj^ particles in the 
bath, wmch adhere to each other, until at length all the iron is decarbon* 
ized and becomes of a pasty condition, and the lumps so formed wherl 
gathered together make the ** puddle-ball" which is consolidated into a 
bloom by the squeezer and then rolled into "muck-bar." By cutting 
the muck-bar into short lengths and making a "pile" of them, heating 
the pile to a welding heat and rerolling, a bar is made which is freer 
from cinder and more homogeneous than the original bar, and it may 
be further "refined" by another piling and rerollihg. The quaUty of 
the iron depends on the quality of the pig-iron, on the extent of the 
decarbonization, on the extent of dephosphorization which has been 
effected in the furnace, on the greater or less contamination of the iron 
by sulphur derived from the fuel, and on the amount of work done on 
the piles to free the iron from slag. Iron insufficiently decarbonized is 
irregular, and hard or " steely." Iron thoroughly freed from impurities 
is soft ani of low tensile strength. Iron high in sulphur is "hot-short," 
liable to break when being forged. Iron high in phosphorus is "cold- 
short," of low ductility when cold, and breaking with an apparently 
crystalline fracture. 

See papers on Manufacture and Characteristics of Wrought Iron, by 
J. P. Roe, Trans. A. I. M. E., xxxiii, p. 551; xxxvi, pp. 203, 807. 

iGlectrolytic Iron. (L. Guillet, Proc. Iron cfe Steel Inst.. 1914, Eng'g, 
Oct. 2, 1914.) — Using any pig iron in solution an iron can be obtained 
of the following average composition, after removal of the gases by 
annealing: C, 0.004; Si, 0.007; S, 0.006; P, 0.008. The metal de- 
posited from the solution is extremely brittle and hard, due to occluded 
hydrogen. The deposition of the iron takes place on a revolving metal 
mandrel, making tubes of from 4 to 8 in. diam., 12.8 ft. long, 0.004 to 
0.24 in. thick. After annealing, the metal becomes soft and ductile, with 
a tensile strength of from 44,000 to 47,000 lb. per sq. in. The in- 
dustrial uses of electrolytic iron include the direct manufacture of 
tubes, sheets, rods for autogenous welding, and the preparation of raw 
material for the manufacture of steel. In localities where cheap electric 
current can be obtained the cost is estimated to be as low as $30 to $38 
per gross ton. Patents on the process are owned by Compagnie Le Fer, 
Grenoble, Prance. 

Influence of Reduction in Rolling from Pile to Bar on the 
Strength of Wrought Iron. — The tensile strength of the irons used 
in Beardslee's tests ranged from 46,000 to 62,700 lbs. per sq. in., brand 
L, which was really a steel, not being considered. Some specimens of L 
gave figures as high as 70,000 lbs. The amount of reduction of sectional 
area in rolling the bars has a notable influence on the strength and elastic 
limit; the greater the reduction from pile to bar, the higher the strength. 

The following are a few figures from tests of one of the brands: 
Size of bar, in. diam.: 4 3 2 1 V2 ^U 
Area of pile, sq. in.: 80 80 72 25 9 3 
Bar per cent of pile: 15.7 8.83 4.36 3.14 2.17 1.6 
Tensile strength, lb.: 46,322 47,761 48,280 51,128 62,275 59,585 
Elastic hmit. lb.: 23.430 26,400 31,892 36,467 39,126 

Influence of Chemical Composition on the Properties of Wrought 
Iron, (Beardslee on Wrought Iron and Chain Cables. Abridgment by 



WROUGHT IRON. 



461 



W. Kent. Wiley & Sons, 1879.) — A series of 2000 tests of specimens 
from 14 brands of wrought iron, most of them of high repute, was made 
in 1877 by Capt. L. A. Beardslee, U.S.N., of the United States Testing 
Board. Forty-two chemical analyses were made of these irons, with a 
view to determine what influence the chemical composition had upon the 
strength, ductility, and welding power. From the report of these testa 
by A. L. HoUey the following figures are taken: 



Brand. 


Average 

Tensile 

Strength. 


Chemical Composition. 


S. 


P. 


Si. 


C. 


Mn. 


Slag. 


L 

P 
B 
J 


C 


66.598 

54.363 
52.764 
51.754 

51.134 
50,765 


trace 

(0.009 
\ 0.001 

0.008 
j 0.003 
1 0.005 
( 0.004 
\ 0.005 

0.007 


J 0.065 
] 0.084 
0.250 
0.095 
0.231 
0.140 
0.291 
0.067 
0.078 
0.169 


0.080 
0.105 
0.182 
0.028 
0.156 
0.182 
0.321 
0.065 
0.073 
0.154 


0.212 
0.512 
0.033 
0.066 
0.015 
0.027 
0.051 
0.045 
0.042 
0.042 


0.005 
0.029 
0.033 
0.009 
0.017 
trace 
0.053 
0.007 
0.005 
0.021 


0.192 
0.452 
0.848 
1.214 

■o'.678* 
1.724 
1.168 
0.974 



Where two analyses are given, they are the extremes of two or more 
analyses of the brand. Where one is given, it is the only analysis. 
Brand L should be classed as a puddled steel. 

Order of Qualities Graded from No. 1 to No. 19. 



Brand. 


Tensile 
Strength. 


Reduction of 
Area. 


Elongation. 


Welding Power. 


L 
P 
B 
J 

C 


1 

6 
12 
16 
18 
19 


'I 

16 

19 

1 

12 


19 
3 

15 

18 
4 

16 


most imperfect. 

badly. 

best. 

rather badly. 

very good. 



The reduction of area varied from 54.2 to 25.9 per cent, and the elonga- 
tion from 29.9 to 8.3 per cent. 

Brand O, the purest iron of the series, ranked No. 18 in tensile strength, 
but was one of the most ductile; brand B, quite impure, was below the 
average both in strength and ductiUty, but was the best in welding 
power; P, also quite impure, was one of the best in every respect except 
welding, while L, the highest in strength, was not the most pure, it had 
the least ductility, and its welding power w-as most imperfect. The 
evidence of the influence of chemical composition upon quaUty, there- 
fore, is quite contradictory and confusing. The irons differing remark- 
ably in their mechanical properties, it W'as found that a much more 
marked influence upon their qualities was caused bj: different treatment 
in rolling than by differences in composition. 

In regard to slag Mr. HoUey says: "It appears that the smallest and 
most worked iron often has the most slag. It is hence reasonable to 
conclude that an iron may be dirty and yet thoroughly condensed." 

In his summary of "What is learned from chemical analysis," he says: 
" So far, it may appear that little of use to the makers or users of wrought 
iron has been learned. . . . The character of steel can be surely pred- 
icated on the analyses of the materials ; that of wrought iron is altered 
by subtle and unobserved causes." 

Specifications for Wrought Iron. (F. H. Lewis, Engineers' Club of 
Philadelphia, 1891.) — 1. All wrought iron must be tough, ductile, 
fibrous, and of uniform quality. for each class, straight, smooth, free from 
cinder-pockets, flaws, buckles, bhsters, and injurious cracks along the 
edges, and must have a workmanlike finish. No specific process or 
provision of manufacture will be demanded, provided the material fulfills 
the requirements of these specifications. 

2. The tensile strength, limit of elasticity, and ductility shall be deter- 
mined from a standard test-piece not less than 1/4 inch thick, cut from 
the fuU-sized bar, and planed or turned parallel. The area of cross- 



462 IRON AND STEEL. 

section shall not be less than 1/2 sq. in. The elongation shall be 
measured after breaking on an original length of 8 in. 

3. The tests shall show not less than the following results: El. in 

8 in. 

For bar iron in tension T. S. = 50,000; E. L. = 26,000; 18% 

For shape iron in tension " =48,000; " = 26,000; 15% 

For plates under 36 in. wide " =48.000; •' = 26,000; 12% 

For plates over 36 in. wide " =46,000; " = 25,000; 10% 

4. When full-sized tension members are tested to prove the strength of 
their connections, a reduction in their ultimate strength of (500 X width 
of bar) pounds per square inch will be allowed. 

5. All iron shall bend, cold, 180 degrees around a curve whose diameter 
is twice the thickness of piece for bar iron, and three times the thickness 
for plates and shapes. 

6. Iron which is to be worked hot in the manufacture must be capable 
of bending sharply to a right angle at a working heat without sign of 
fracture. 

7. Specimens of tensile iron upon being nicked on one side and bent 
shall show a fracture nearly all fibrous. 

8. All rivet iron must be tough and soft, and be capable of bending 
cold until the sides are in close contact without sign of fracture on the 
convex side of the curve. 

Penna. R. R. Co.'s Specifications for 3Ierchant-bar Iron (1904). — 
One bar will be selected for test from each 100 bars in a pile. 

All the iron of one size in the sliipment will be rejected if the average 
tensile strength of the specimens tested full size as rolled falls below 
47,000 lbs. or exceeds 53,000 lbs. per sq. in., or if a single specimen falls 
below 45,000 lbs. per sq. in.; or when the test specimen has been reduced 
by machining if the average tensile strength exceeds 53,000 or falls below 
46,000, or if a single specimen falls below 44,000 lbs. per sq. in. 

All the iron of one size in the shipment will be rejected if the average 
elongation in 8 in. falls below the following limits: Flats and rounds, 
tested as rolled, 1/2 in. and over, 20%; less than 1/2 in., 16%. Flats and 
rounds reduced by machining 16%. 

Nicking and Bending Tests. — When necessary to make nicking and 
bending tests, the iron will be nicked lightly on one side and then broken 
by holding one end in a vise, or steam hammer, and breaking the iron by 
successive blows. It must when thus broken show a generally fibrous 
structure, not more than 25% crystalline, and must be free from admix- 
ture of steel. 

Stay-bolt Iron. (Penna. R. R. Co.'s specifications, 1902). — Sample 
bars must show a tensile strength of not less than 48,000 lbs. per sq. in. 
and an elongation of not less than 25% in 8 in. One piece from each lot 
will be threaded in dies with a sharp V thread, 12 to 1 in. and firmly 
screwed through two holders having a clear space between them of 5 in. 
One holder will be rigidly secured to the bed of a suitable machine, and the 
other vibrated ^t right angles to the axis over a space of 1/4 in. or 1/8 in. 
each side of the center hne. Acceptable iron should stand 2800 double 
vibrations before breakage. 

Mr. Vauclain, of fhe Baldwin Locomotive Works, at a meeting of the 
American Railway Master Mechanics' Association, in 1892, says: Many 
advocate the softest iron in the market as the best for stay-bolts. He 
beUeved in an iron as hard as was consistent with heading the bolt nicely. 
The higher the tensile strength of the iron, the more vibrations it will 
stand, for it is not so easily strained beyond the yield-point. The Baldwin 
specifications for stay-bolt iron caU for a tensile strength of 50,000 to 
52,000 lbs. per square inch, the upper figure being preferred, and the 
lower being insisted upon as the minimum. 

Speciflcations for Wrought Iron for the World's Fair Buildings. 
{Eng g News, March 26, 1892.) — All iron to be used in the tensile mem- 
bers of open trusses, laterals, pins and bolts, except plate iron over 
8 mches wide, and shaped iron, must show by the standard test-pieces 
a tensile strength in lbs. per square inch of: 

52 000 - 7000 X area of original bar in sq. in. 
circumference of original bar in inches ' 

with an elastic limit not less than half the strength given by this formula, 
and an elongation of 20% in 8 iu. 



METALS AT VARIOUS TEMPERATURES. 463 

Plate iron 8 to 24 inches ^Ide, T. S. 48,000, E. L. 26,000 lbs. per sq. in., 
elong. 12%. Plates over 24 inches wide, T. S. 46,000, E. L. 26,000 lbs. 
per sq. in. Plates 24 to 36 in. wide, elong. 10%; 36 to 48 in., 8%; over 
48 in., 5%. 

All shaped iron, flanges of beams and channels, and other iron not 
hereinbefore specified, must show a T. S. in lbs. per sq. in. of: 
7000 X area of original bar 
circumference of original bar* 
with an elastic limit of not less than half the strength given by this formula, 
and an elongation of 15% for bars s/g inch and less in thickness, and of 
12% for bars of greater thickness. For webs of beams and channels, 
specifications for plates will apply. 

All rivet iron must be tough and soft, and pieces of the full diameter of 
the rivet must be capable of bending cold, until the sides are in close con- 
tact, without sign of fracture on the convex side of the curve. 

TENACITY OF METALS AT VARIOUS TEMPERATURES. 

The British Admiralty made a series of experiments to ascertain what 
loss of strength and ductility takes place in gun-metal compositions when 
raised to high temperatures. It was found that all the varieties of gun 
metal suffer a gradual but not serious loss of strength and ductility up to 
a certain temperature, at which, within a few degrees, a great change 
takes place, the strength falls to about one-half the original, and the 
ductility is wholly gone. At temperatures above this point, up to 500° F., 
there is little, if any, further loss of strength; the temperature at which 
this great change and loss of strength takes place, although uniform in 
the specimens cast from the same pot, varies about 100° in the same 
composition cast at different temperatures, or with some varying condi- 
tions in the foundry process. The temperature at which the change took 
place in No, 1 series was ascertained to be about 370°, and in that of 
No. 2, at a little over 250°. Rolled Muntz metal and copper are satis- 
factory up to 500°, and may be used as securing-bolts with safety. 
Wrought iron increases in strength up to 500°, but loses slightly in duc- 
tility up to 300°, where an increase begins and continues up to 500°, 
where it is still less than at the ordinary temperature of the atmosphere. 
The strength of Landore steel is not affected by temperature up to 500**, 
but its ductility is reduced more than one-half. (Iron, Oct. 6, 1877.) 

Strength of Iron and Steel Boiler-plate at High Temperatures. 

(Chas. Huston, Jour. F. /., 1877.) 

Average of Three Tests of Each. 

Temperature F. 68° 575° 925° 

Charcoal iron plate, tensile strength, lbs 55,366 63,080 65,343 

contr. of area' % 26 23 21 

Soft open-hearth steel, tensile strength, lbs 54,600 66,083 64,350 

" contr. % 47 38 33 

" Crucible steel, tensile strength, lbs 64,000 69,266 68,600 

contr. % 36 30 21 

Tensile Strength of Iron and Steel at High Temperatures. — 

James E. Howard's tests (Iron Age, April 10, 1890) show that the tensile 
strength of steel diminishes as the temperature increases from 0° until a 
minimum is reached between 200° and 300° F., the total decrease being 
about 4000 lbs. per square inch in the softer steels, and from 6000 to 
8000 lbs. in steels of over 80,000 lbs. tensile strength. From this mini- 
mum point the strength increases up to a temperature of 400° to 650° F., 
the maximum being reached earlier in the harder steels, the increase 
amounting to from 10,000 to 20,000 lbs. per square inch above the mini- 
mum strength at from 200° to 300°. From this maximum, the strength 
of all the steel decreases steadily at a rate approximating 10,000 lbs. 
decrease per 100° increase of temperature. A strength of 20,000 lbs. 
per square inch is still shown by 0.10 C. steel at about 1000° F., and by 
0.60 to 1.00 C. steel at about 1600° F. 

The strength of wrought iron increases with temperature from 0° up 
to a maximum at from 400 to 600° F., the increase being from 8000 to 
10,000 lbs. per square inch, and then decreases steadily till a strength of 
only 6000 lbs. per square inch is shown at 1500° F. 



464 



IKON AND STEEL. 



Cast iron appears to maintain its strength, with a tendency to in- 
crease, until 900° is reached, beyond which temperature the strength 
gradually diminishes. Under the highest temperatures, 1500° to 1600° F., 
numerous cracks on the cylindrical surface of the specimen were devel- 
oped prior to rupture. It is remarkable that cast iron, so much inferior 
in strength to the steels at atmospheric temperature, under the highest 
temperatures has nearly the same strength the high-temper steels then 
have. 

Strength of Wrought Iron and Steel at High Temperatures. 
(Jour, F, I., cxii, 1881, p. 241.) — KoUmann's experiments at Oberhausen 
included tests of the tensile strength of iron and steel at temperatures 
ranging between 70° and 2000° F. Three kinds of metal were tested, 
viz., fibrous iron of 52,464 lbs. T. S., 38,280 lbs. E. L., and 17.5% 
elong.; fine-grained iron of 56,892 lbs. T. S., 39,113 lbs. E. L., and 20% 
elong.; and Bessemer steel of 84,826 lbs. T. S., 55,029 lbs. E. L., and 
14.5% elong. The mean ultimate tensile strength of each material 
expressed in per cent of that at ordinary atmospheric temperature is 
given in the following table, the fifth column of which exhibits, for pur- 
poses of comparison, the results of experiments by a committee of the 
FrankUn Institute in the years 1832-36. 



Temperature 


Fibrous 


Fine-grained 


Bessemer 


Franklin In- 


Degrees F. 


Iron, %. 


Iron, %. 


Steel, %. 


stitute. %. 





100.0 


100.0 


100.0 


96.0 


100 


100.0 


100.0 


100.0 


102.0 


200 


100.0 


100.0 


100.0 


105.0 


300 


97.0 


100.0 


100.0 


106.0 


400 


95.5 


100.0 


100.0 


106.0 


500 


92.5 


98.5 


98.5 


104.0 


600 


88.5 


95.5 


92.0 


99.5 


700 


81.5 


90.0 


68.0 


92.5 


800 


67.5 


77.5 


44.0 


75.5 


900 


44.5 


51.5 


36.5 


53.5 


1000 


26.0 


36.0 


31.0 


36.0 


1100 


20.0 
18.0 
13.5 
7.0 
4.3 
3.5 


30.5 
28.0 
19.0 
12.5 
8.5 
5.0 


26.5 
22.0 
15.0 
10.0 
7.5 
5.0 




1200 




1400 




1600 




1800 




2000 





Effect of Cold on the Strength of Iron and Steel. — The following 
conclusions were arrived at by Mr. Styffe in 1865: 

(1) The absolute strength of iron and steel is not diminished by cold, 
even at the lowest temperature which ever occurs in Sweden. 

(2) Neither in steel nor in iron is the extensibility less in severe cold 
than at the ordinary temperature. 

(3) The limit of elasticity in both steel and iron lies higher in severe 
cold. 

(4) The modulus of elasticity in both steel and iron is increased on 
reduction of temperature, and diminished on elevation of temperature; 
but that these variations never exceed 0.05% for a change of 1.8° F. 

W. H. Barlow (Proc. Inst. C. E.) made experiments on bars of wTought 
iron, cast iron, malleable cast iron, Bessemer steel, and tool steel. The 
bars were tested with tensile and transverse strains, and also by im- 
pact; one-half of them at a temperature of 50° F., and the other half at 
5°F. 

The results of the experiments were summarized as follows: 

1. When bars of wrought iron or steel were submitted to a tensile 
strain and broken, their strength w^as not affected by severe cold (5° F.), 
but their ductility was increased about 1% in iron and 3% in steel. 

2. When bars of cast iron were submitted to a transverse strain at a 
low temperature, their strength was diminished about 3% and their 
flexibility about 16%. 

3. When bars of wrought iron, malleable cast iron, steel, and ordinary 
cast iron were subjected to impact at 5° F., the force required to break 
them, and their flexibility, were reduced as follows: 



DURABILITY OP IRON, CORROSION, ETC. 



465 



Wrought iron, about 

Steel (best cast tool), about. 
Malleable cast iron, about . . 
Cast iron, about 



Reduction of 

Force of Im- 

pact, %. 



3 

3 1/2 

4 1/2 

21 



Reduction of 
Flexibility, 



18 

17 

15 

not taken 



The experience of railways in Russia, Canada, and other countries 
where the winter is severe, ie that the breakages of rails and tires are far 
more numerous in the cold weather than in the summer. On this 
account a softer class of steel is employed in Russia for rails than is usual 
in more temperate climates. 

The evidence extant in relation to this matter leaves no doubt that the 
capability of wrought iron or steel to resist impact is reduced by cold. On 
the other hand, its static strength is not impaired by low temperatures. 

Increased Strength of Steel at very Low Temperature. — Steel of 
72,300 lb. T. S. and 62,800 lb. elastic limit when tested at 76° F. gave 
97,600 T. S. and 80,000 E. L. when tested at the temperature of liquid 
air. — Watertown Arsenal Tests, Eng. Rec, July 21, 1906. 

Prof. R. C. Carpenter (Proc. A. A. A. S. 1897) found that the strength 
of wrought iron at — 70° F. was 20% greater than at 70° F. 

Effect of Low Temperatures on Strength of Railroad Axles. 
(Thos. Andrews, Proc. Inst. C. E., 1891.) — Axles 6 ft. 6 in. long be- 
tween centers of journals, total length 7 ft. 3V2 in., diameter at middle 
41/2 in., at wheel-sets 51/8 in., journals 33/4 x 7 in., were tested by impact 
at temperatures of 0° and 100° F. Between the blows each axle was 
half turned over, and was also replaced for 15 minutes in the water-bath. 

The mean force of concussion resulting from each impact was ascer- 
tained as follows: 

Let h = height of free fall in feet, w = weight of test ball, hw = W = 
" energy," or work in foot-tons, x = extent of deflections between bearings 

then F (mean force) = W /x = hw/x . 

The results of these experiments show that whereas at 0° F. a total 
average mean force of 179 tons was sufficient to cause the breaking of the 
axles, at 100° F. a total average mean force of 428 tons was required. 
In other words, the resistance to concussion of the axles at 0° F. was only 
about 42% of what it was at 100° F. 

The average total deflection at 0° F. was 6.48 in., as against 15.06 in. 
with the axles at 100° F. under the conditions stated: this represents an 
ultimate reduction of flexibility, under the test of impact, of about 57% 
for the cold axles at 0° F., compared with the warm axles at 100° F. 

EXPANSION OF lEON AND STEEL BY HEAT. 

James E. Howard, engineer in charge of the U. S. testing-machine at 
Watertown, INIass., gives the following results of tests made on bars 
35 in. long {Iron Age, April 10, 1890) : 





C. 


Mn. 


Si. 


Coeffi. of 

Expansion 

per degree 

F. 




C. 


Mn. 


Si. 


Coeffi. of 

Expansion 

per degree 

F. 


Wrought iron 
Steel 








0.0000067302 
.0000067561 
.0000066259 
.0000065149 
.0000066597 
.0000066202 


Steel 


0.57 
.71 
.81 
.89 
.97 


0.93 

.58 
.56 
.57 
.80 


.07 
.08 
.17 
.19 
.28 


0.0000063891 


0.09 
.20 
.31 
.37 
.51 


0.11 
.45 

.57 
.70 
.58 


M 




.0000064716 




«• 


.0000062167 


«• 


<« 


0000062335 


• • 


«« 


.0000061700 




Cast (gun) 
iron 


.0000059261 



DURABILITY OF IRON, CORROSION, ETC. 

Crystallization of Iron by Fatigue. — Wrought iron of the best 
quality is very tough, and breaks, on being pulled in a testing machine or 
bent after nicking, with a fibrous fracture. Cold-short iron, however, is 
nK)re brittle, and breaks square across the fibers with a fracture which is 



466 IRON AND STEEL. 

commonly called crystalline although no real crystals are present. Iron 
which has been repeatedly overstrained, and especially iron subjected 
to repeated vibrations and shocks, also becomes brittle, and breaks with 
an apparently crystalline fracture. See '* Resistance of Metals to Repeated 
Shocks." p. 276. 

Walter H. Finley (Am. Mach., April 27, 1905) relates a case of fail- 
ures of li/8-in. wrought-iron coupling pins on a train of 1-ton mine cars, 
apparently due to crystallization. After two pins were broken after a 
year's hard service, "several hitchings were laid on an anvil and the pin 
broken by a single blow from a sledge. Pieces of the broken pins were 
then heated to a bright red, and, after cooling slowly, were again put 
under the hammer, which failed entiiely to break them. After cutting 
witli a cleaver, the pins were broken, and the fracture showed a complete 
restoration of the fibrous structure. This annealing process was then 
appHed to the whole supply of hitchings. Piles of twenty-five or thirty 
were covered by a hot wood fire, which was allowed to die down and go 
out, leaving the hitchings in a bed of ashes to cool off slowly. By 
repeating this every six months the danger of brittle pins was avoided.** 
Durability of Cast Iron. — Frederick Graff, in an article on the 
Philadelphia water-supply, says that the first cast-iron pipe used there 
was laid in 1820. These pipes were made of charcoal iron, and were in 
constant use for 53 years. They were uncoated, and the inside was well 
filled with tubercles. In salt water good cast iron, even uncoated, will 
last for a century at least; but it often becomes soft enough to be cut by 
a knife, as is shown in iron cannon taken up from the bottom of harbors 
after long submersion. Close-grained, hard white metal lasts the longest 
in sea water. {Eng'g News, April 23, 1887, and March 26, 1892.) 

Tests of Iron after Forty Years' Service. — A square link 12 inches 
broad, 1 inch thick and about 12 feet long was taken from the Kieff 
bridge, then 40 years old, and tested in comparison with a similar link 
which had been preserved in the stock-house since the bridge was built. 
The following is the record of a mean of four longitudinal test-pieces, 
1 X IVsX 8 inches, taken from each link (Stahl und Eisen, 1890): 

Old Link T. S., 218 tons; E. L., 11.1 tons; Elong., 14.05% 

New Link " 22.2 " " 11.9 " " 13.42% 

Durability of Iron in Bridges. (G. Lindenthal, Eng*g, May 2, 1884, 
p. 139.) — The Old Monongahela suspension bridge in Pittsburg, built 
in 1845, was taken down in 1882. The wires of the cables were frequently 
strained to half of their ultimate strength, yet on testing them after 37 
years' use they showed a tensile strength of from 72,700 to 100,000 lbs. 
per sq. in. The elastic limit was from 67,100 to 78,600 lbs. per sq in. 
Reduction at point of fracture, 35% to 75%. Their diameter was 0.13 in. 

A new ordinary telegraph wire of same gauge tested for comparison 
showed: T. S., of 100.000 lbs.; E. L., 81,550 lbs.; reduction, 57%. Iron 
rods used as stays or suspenders showed: T.S., 43,770 to 49,720 lbs. E. 
L., 26,380 to 29,200. Mr. Lindenthal draws these conclusions: 

** The above tests indicate that iron highly strained for a long number 
of years, but still within the elastic limit, and exposed to slight vibration, 
will not deteriorate in quality. 

"That if subjected to only one kind of strain it will not change its 
texture, even if strained beyond its elastic limit, for many years. It will 
stretch and behave much as in a testing-machine during a long test. 

"That iron will change its texture only when exposed to alternate 
severe straining, as in bending in different directions. If the bending is 
slight but very rapid, as in violent vibrations, the effect is the same." 

Durability of Iron in Concrete. — In Paris a sewer of reinforced con- 
crete 40 years old was removed and the metal was found in a perfect state 
of preservation. In excavating for the foundations of the new General 
Post Office in London some old Roman brickwork had to be removed, 
and the hoop-iron bonds were still perfectly bright and good. (Eng'g, 
Aug. 16, 1907, p. 227.) 

Corrosion of Iron Bolts. — On bridges over the Thames in London, 
bolts exposed to the action of the atmosphere and rain-water were eaten 
away in 25 years from a diameter of 7/8 in. to 1/2 in., and from s/g in. diam- 
eter to 5/iQ inch. 

Wire ropes exposed to drip in colliery shafts are very liable to corrosion. 

Corrosive Agents in the Atmosphere. — The experiments of F. 
Grace Calvert (Chemical News, March 3. 1871) show that carbonic acid. 



DURABILITY OF IRON, CORROSION, ETC. 467 

in the presence of moisture, is the agent which determines the oxidation 
of iron in the atmosphere. He subjected perfectly cleaned blades of 
iron and steel to the action of different gases for a period of four months, 
with results as follows: 

Dry oxygen, dry carbonic acid, a mixture of both gases, dry and damp 
oxygen and ammonia: no oxidation. Damp oxygen: in three experi- 
ments one blade only was shghtly oxidized. 

Damp carbonic acid: sUght appearance of a white precipitate upon the 
iron, found to be carbonate of iron. Damp carbonic acid and oxygen: 
oxidation very rapid. Iron immersed in water containing carbonic acid 
oxidized rapidly. 

Iron immersed in distilled water deprived of its gases by boiling rusted 
the iron in spots that were found to contain impurities. 

Sulphurous acid (the product of the combustion of the sulphur in coal) 
is an exceedingly active corrosive agent, especially when the exposed iron 
is coated with soot. This accounts for the rapid corrosion of iron in 
railway bridges exposed to the smoke from locomotives. (See account of 
experiments by the author on action of sulphurous acid in Jour. Frank. 
Inst., June, 1875, p. 437.) An analysis of sooty iron rust from a railway 
bridge showed the presence of sulphurous, sulphuric, and carbonic acids, 
chlorine, and ammonia. Bloxam states that ammonia is formed from 
the nitrogen of the air during the process of rusting. 

Galvanic Action is a most active agent of corrosion. It takes place 
when two metals, one electro-negative to the other, are placed in contact 
and exposed to dampness. 

Corrosion in Steam-boilers. — Internal corrosion may be due either 
to the use of water containing free acid, or water containing sulphate 
or cnloride of magnesium, which decompose v/hen heated, liberating the 
acid, or to water containing air or carbonic acid in solution. External 
corrosion rarely takes place when a boiler is kept hot, but when cold it 
is apt to corrode rapidly in those portions where it adjoins the brick- 
work or where it may be covered by dust or ashes, or wherever damp- 
ness may lodge. (See Impurities of Water, p. 720, and Incrustation and 
Corrosion, p. 927.) 

Corrosion of Iron and Steel. — Experiments made at the Riverside 
Iron Works, Wheehng, W. Va., on the comparative liabihty to rust of 
iron and soft Bessemer steel: A piece of iron plate and a similar piece of 
steel, both clean and bright, were placed in a mixture of yellow loam and 
sand, with which had been thoroughly incorporated some carbonate of 
soda, nitrate of soda, ammonium chloride, and chloride of magnesium. 
The earth as prepared was kept moist. At the end of 33 days the pieces 
of metal were taken out, cleaned, and weighed, when the iron was found 
to have lost 0.84% of its weight and the steel 0.72%. The pieces were 
replaced and after 28 days weighed again, when the iron was found to 
have lost 2.06% of its original weight and the steel 1.79%. (Eng'g, June 
26, 1891.) 

Internal Corrosion of Iron and Steel Pipes by Warm Water. 
(T. N. Thomson, Proc. A.S.H. V. E., 1908.) —Three short pieces of iron 
and three of steel pipes, 2 in. diara., were connected together by nipples 
and made part of a pipe line conveving water at a temperature varying 
from 160° to 212° F. In one year 913/32 lbs. of wrought iron lost 203/4 oz., 
and 913/32 lbs. of steel 247/8 oz. The pipes were sawed in two lengthwise, 
and the deepest pittings were measured by a micrometer. Assuming that 
the pitting would have continued at a uniform rate the wrought-iron pipes 
would have been corroded through in from 686 to 780 days, and the steel 
pipes from 760 to 850 days, the average being 742 days for iron and 797 
days for steel. Two samples each of galvanized iron and steel pipe were 
also included in the pipe line, and their calculated life was: iron 770 and 
1163 days; steel 619 and 1163 days. Of numerous samples of corroded 
pipe received from heating engineers ten had given out within four years 
of service, and of these six were steel and four were iron. 

To ascertain whether Pipe is made of Wrought Iron or Steel, cut 
off a short piece of the pipe and suspend it in a solution of 9 parts of water, 
3 of sulphuric acid, and 1 of hydrochloric acid in a porcelain or glass dish 
in such a way that the end will not touch the bottom of the dish. After 
2 to 3 hours' immersion remove the pipe and wash off the acid. If the 
pipe is steel the end will present a bright, solid, unbroken surface, while 
if mad© of iron it will show faint ridges or rings, like the year rings in a 



468 IRON AND STEEL. 

tree, showing the different layers of iron and streaks of cinder. In order 
that the scratches made by the cutting-off tool may not be mistaken for 
the cinder marks, file the end of the pipe straight across or grind on an 
emery wheel until the marks of the cutting-off tool have disappeared 
before putting it in the acid. 

Relative Corrosion of Wrought Iron and Steel. (H. M. Howe, 
Proc. A. S. T. M., 1906.) — On one hand we have the very general 
opinion that steel corrodes very much faster than wrought iron, an opinion 
held so widely and so strongly that it cannot be ignored. On the other 
hand we have the results of direct experiments by a great many observers, 
in different countries and under widely differing conditions; and these 
results tend to show that there is no very great difference between the 
corrosion of steel and wrought iron. Under certain conditions steel seems 
to rust a little faster than wrought iron, and under oth:rs wrought iron 
seems to rust a little faster than steel. Taking the tests in unconfined 
sea water as a whole wTought iron does constantly a little better than 
steel, and its advantage seems to be still greater in the case of boiling sea 
water. In the few tests in alkaline water wrought iron seems to have the 
advantage over steel, whereas in acidulated water steel seems to rust more 
slowly than wrought iron. 

Steel which in the first few months may rust faster than wrought Iron 
may, on greatly prolonging the experiments, or pushing them to destruc- 
tion, actually rust more slowly, and vice versa. 

Carelessly made steel, containing blowholes, may rust faster than 
wrought iron, yet carefully made steel, free from blowholes, may rust 
more slowly. Any difference between the two may be due not to the 
inherent and intrinsic nature of the material, but to defects to which it 
is subject if carelessly made. Care in manufacture, and special steps to 
lessen the tendency to rust, might well make steel less corrodible than 
wrought iron, even if steel carelessly made should really prove more 
corrodible than wrought iron. 

For extensive discussions on this subject see Trans, A.I. M.E., 1905, 
Proc. A. S. T. M., 1906 and 1908, and Bulletins of National Tube Co. 

Corrosion of Fence Wire. (A. S. Cushman, Farmers' Bulletin, No. 
239, IT. S. Dept. of Agriculture, 1905.) — "A large number of letters w^ere 
received from all over the country in response to official inq^uiry, and 
all pointed in the same direction. As far as human testimony is capable 
of establishing a fact, there need be not the shghtest question that modern 
steel does not serve the purpose as well as the older metal manufactured 
twenty or more years ago." 

Electrolytic Theory, and Prevention of Corrosion. (A. S. Cush- 
man, Bulletin No. 30, U. S. Dept. of Agriculture, Office of Public Roads, 
1907. The Corrosion of Iron.) — The various kinds of merchantable iron 
and steel differ, within wide limits, in their resistance, not only to the 
ordinary processes of oxidation known as rusting, but also in other corro- 
sive infiuences. Different specimens of one and the same kind of iron or 
steel will show great variability in resistance to corrosion under the con- 
ditions of use and service. The causes of this variability are numerous 
and complex, and the subject is not nearly so well understood at the 
present time as it should be. All investigators are agreed that iron can- 
not rust in air or oxygen unless water, is present, and on the other hand 
it cannot rust in water unless oxygen is present. 

From the standpoint of the modern theory of solutions, all reactlong 
which take place in the wet way are attended with certain readjustments 
of the electrical states of the reacting ions. The electrolytic theory of 
rusting assumes that before iron can oxidize in the wet way it must first 
pass into solution as a ferrous ion. 

Dr. Cushman then gives an account of his experiments which he con- 
siders demonstrate that iron goes into solution up to a certain maximum 
concentration in pure water, without the aid of oxygen, carbonic acid or 
other reacting substances. It is apparent that the rusting of iron Is 
primarily due, not to attack by oxygen, but by hydrogen ions. 

Solutions of chromic acid and potassium bichromate inhibit the rusting 
of iron. If a rod or strip of bright iron or steel is immersed for a few 
hours in a 5 to 10 per cent solution of potassium bichromate, and is then 
removed and thoroughly washed, a certain change has been produced 
on the surface of the metal. The surface may be thoroughly washed 



I 



DURABILITY OF IRON, CORROSION, ETC. 469 

and wiped with a clean cloth without disturbing this new surface condi- 
tion. No visible change has been elffected, for the polished surfaces 
examined under the microscope appear to be untouched. If, however, 
the polished strips are immersed in water it wiU be found that rusting is 
inhibited. An ordinary untreated poUshed specimen of steel will show 
fasting in a few minutes when immersed in the ordinary distilled water of 
the laboratory* Chromated specimens will stand immersion for varying 
lengths of time before rust appears. In some cases it is a matter of 
hours, in others of days or weeks before the inhibiting effect is overcome. 

It would follow from the electrolytic theory that in order to have the 
highest resistance to corrosion a metal should either be as free as possible 
from certain impurities, such as manganese, or should be so homogene- 
ous as not to retain localized positive and negative nodes for a long time 
without change. Under the first condition iron would seem to have the 
advantage over steel, but under the second much would depend upon 
care exercised in manufacture, whatever process was used. 

There are two lines of advance by which we may hope to meet the 
difficulties attendant upon rapid corrosion* One is by the manufacture 
of better metal, and the other is by the use of inhibitors and protective 
coverings. Although it is true that laboratory tests are frequently 
unsuccessful in imitating the conditions in service, it nevertheless appears 
that chromic acid and its salts should under certain circumstances come 
into use to inhibit extremely rapid corrosion by electrolysis. 

Chrome Paints. — G. B. Heckel {Jour. F. /., Eng. Dig., Sept., 1908) 
quotes a letter from Mr. Cushman as foUows: "My observation that 
chromic acid and certain of its compounds act as inhibitives has led to 
many experiments by other workers along the same line. I have found 
that the chrome compounds on the market vary very much in their action. 
Some of them show up as strong inhibitors, while others go to the op- 
posite extreme and stimulate corrosion. Referring only to the labeled 
names of the pigments, I find among the good ones, in the order cited: 
Zinc chromate, American vermilion, chrome yellow orange, chrome 
yellow dd. Among the bad ones, also in the order given, I find: Chrome 
yellow medium, chrome green, chrome red. Much the worst of all is 
chrome yellow lemon. I presume that the difference is due to impurities 
that are present in the bad pigments." 

Mr. Heckel suggests the following formula for a protective paint: 40 
lbs. American vermilion^ 10 lbs. red lead, 5 lbs. Venetian red. Zinc 
oxide and lamp-black to produce the required tint or shade. Grind in 
1 Vagal, of raw linseed oil — increasing the quantity as required for added 
zinc oxide or lamp-black — and i/8 gal. crusher's drier. For use, thin 
with raw oil and very little turpentine or benzine. 

He states that the substitution of zinc chrome for the American ver- 
miUon; of any high-grade finely ground iron oxide for the Venetian red; 
and of American vermilion for the red lead, would probably improve the 
protective value of the formula; that the addition of a very little kauri 
gum varnish, if zinc oxide is used, might be found advantageous; and 
that the substitution of a certain proportion of China wood oil for some 
of the linseed oil might improve the wearing qualities of the paint. 

Dr. Cushman points out two dangers confronting us when we attempt 
to base an inhibitive formula on commercial products. The first is that 
all carbon pigments, excepting pure graphite, may contain sulphur com- 
pounds easily oxidizable to sulphuric acid when spread out as in a paint 
film. The second is the probability of variation in the composition of 
basic lead chromate or American vermilion. Because of these facts, it 
is necessary, before selecting any particular pigment for its inhibitive 
Guahty, to ascertain that it is free from acids or acid-forming impurities. 
As a result of his experiments he recommends the substitution of Prus- 
sian blue for the lamp-black in Mr. Meckel's formula, and lays down as a 
safe rule in the formulation of inhibitive paints, a careful avoidance oi 
all potential stimulators of the hydrogen ions and consequently of any 
substance which might develop acid ; preference being given to chromate 
pigments which are to some extent soluble in water, and to other pig- 
ments which in undergoing change tend to develop an alkaline rather 
than an acid reaction. Calcium sulphate, for example, in any form (as 
a constituent of Venetian red, for example), he deems dangerous to use 
because of. the possibility of its developing acid. Barium sulphate, on 
the other hand< he regards as safe, because of its chemical stability. 



470 IRON AND STEEL. 

Corrosion caused by Stray Electric Currents. (W. W. Churchill, 
Science, Sept. 28, 1906). — Surface condensers in electric lighting and 
other plants were abandoned on account of electrolytic corrosion. The 
voltage of the rails in the freight yard of the Long Island railroad at the 
peak of the load was 9 volts above the potential of the river, decreasing 
to 2 volts or less at light loads. This caused a destruction of water pipes 
and other things in the railroad yards. Experiments with various metal 
plates immersed in samples of East River water showed that it gave a 
more violent action than ordinary sea water. It was further observed 
that there was a local galvanic action going on, and that the amount of 
stray currents had something to do with the polarization of the surfaces, 
making the galvanic action exceedingly violent and destroying thin cop- 
per tubes at a very rapid rate. There was a violent local action between 
the zinc and the copper of the brass tubes which were in contact with the 
electrolyte, and this increased in the reaction as it progressed in stagnant 
conditions. By interposing a counter electromotive force against the 
galvanic couple v;hich should exceed in pressure the voltage of the couple, 
the actions of the electrolytic corrosion ceased. When unconnected, or 
electrically separated, plates were placed in the electrolyte, if they were 
of composite construction and had sharp projections into the fluid, raised 
by cutting and prying up with a knife, they would have these projections 
promptly destroyed, and if an electric battery having a pressure exceed- 
ing that of the couple in the East River water was caused to act to pro- 
duce a counter current, and having a pressure exceeding that of the 
galvanic couple (0.42 volt), the capacity of this electrolyte to drive off 
atoms of the mechanically combined metals in the alloys used was over- 
come and corrosion was arrested. 

It, therefore, became desirable not only to carefully provide the bal- 
ancing quantity of current to equal the stray traction currents arising 
from the ground returns of railway and other service, but to add to this 
the necessary voltage through a cathode placed in the circulating water 
in such a way as to bring to bear electrolytic action which would pre- 
vent the galvanic action due to this current coming into contact with 
alloys of mechanically combined metals such as the brass tubes (60% 
copper, 40% zinc). 

In order to accomplish these two things, it was first necessary to so 
install the condensers as to prevent undue amounts of stray currents 
flowing through them, thus tending to reduce the amount of power 
required to prevent injurious action of these currents and other\\ise to 
neutraUze them. This was done by insulating the joints in the piping 
and from ground connections, and even lining the large water connec- 
tions with glass melted on to the surface. 

To furnish electromotive force, a 3-K.W. motor generator was pro- 
vided. By m.eans of a system of wiring, with ammeters and voltmeters, 
and a connection to an outlying anode in the condensing supply intake 
at its harbor end, this generator was planned to provide current to neu- 
tralize the stray currents in the condenser structure to any extent that 
they had passed the insulated joints in the supports and connections, as 
well as through the columns of water in the pipe connections, and then 
to adjust the additional voltage needed to counteract and prevent the 
galvanic action. All connections were made in a manner to insure a 
uniform voltage of the various parts of the condenser to prevent local 
action, each connection being so made and provided with such measuring 
instruments as to insure ready adjustment to effect this. The apparatus 
was designed in accordance with the above statements. Its operation 
has extended over fourteen months (to date, 1906), and with the excep- 
tion of about ten tubes which have become pitted, the results have been 
satisfactory. The efficiency of the apparatus amply justifies the ex- 
pense of its installation, while its operation is not expensive, and the 
plant described will be followed by other protecting plants of the same 
character. 

Electrolytic Corrosion due to Overstrain. (C. F. Burgess, El. Rev., 
Sept. 19, 1908.) — Mild steel bars overstrained m their middle portion 
were subjected to corrosion by suspension in dilute hydrochloric acid 
solutions, and others by making them the anode in neutral solutions of 
ammonium chloride and causing current to flow under low current den- 
sity. In all cases a marked difference was noted in the rate at which th« 
strained portions corroded as compared with the unstrained. 



PRESERVATIVE COATINGS. 471 

Differences of potential of from five to nine millivolt? were noted 
between two electrodes, one of which constituted the strained portion 
and one the unstrained. 

The more rapid electrolytic corrosion of the strained portion appea/TS 
to be due to the fact that the strained metal is electropositive to the 
unstrained, the current finding the easier path through the surface of 
the electropositive metal. That the strained metal is the more electro- 
positive is also shown by a liberation of hydrogen bubbles on the un- 
strained portion. 

PRESERVATIVE COATINGS. 

The following notes have been furnished to the author by Prof. A. H. 
Sabin. (Revised, 1908.) 

Cement. — Iron- work is often bedded in concrete; if free from cracks 
and voids it is an efficient protection. The metal should be cleaned and 
then washed with neat cement before embedding. 

Asphaltum. — This is applied either by dipping (as water-pipe) or 
by pouring it on (as bridge floors). The asphalt should be slightly elastic 
when cold, with a high melting-point, not softening much at 100° F., 
appHed at 300° to 400°; the surface must be dry and should be hot; the 
coating should be of considerable thickness. 

Paint. — Composed of a vehicle or binder, usually linseed oil or some 
inferior substitute, or varnish (enamel paints); and a pigment, which is a 
more or less inert solid in the form of a powder, either mixed or ground 
together. Neariy all paint contains paint drier or japan, which is a lead 
or (and) manganese compound soluble in oil, and acts as a carrier of 
oxygen; as little should be used as possible. Boiled oil contains drier; 
no'^additional drier is needed. None should be used with varnish paints, 
nor with *' ready-mixed paints " in general. 

The principal pigments are white lead (carbonate or oxy-sulphate) and 
white zinc (oxide), red lead (peroxide), oxides of iron, hydrated and 
anhydrous, graphite, lampblack, bone black, chrome yellow, chrome 
green, ultramarine and Prussian blue, and various tinting colors. White 
lead has the greatest body or opacity of white pigments; three coats of It 
equal five of white zinc; zinc is more brilliant and permanent, but it is 
liable to peel, and it is customary to mix the two. These are the standard 
white paints for all uses, and the basis of all light-colored paints. Anhy- 
drous iron oxides are brown and purplish brown, hydrated oxides are 
yellowish red to reddish yellow, with more or less brown; most iron • 
oxides are mixtures of both sorts, and often contain a little manganese 
and much clay. They are cheap, and are serviceable paints on wood and 
are often used on iron, but for the latter use are falling into disrepute. 
Graphite used for painting iron contains from 10 to 90% foreign matter, 
usually silicates. It is very opaque, hence has great covering power and 
may be applied in a very thin coat, which is to be avoided. The best 
graphite paints give very good results. There are many grades of lamp- 
black; the cheaper sorts contain oily matter and are especially hard to 
dry; all lampblack is slow to dry in oil. In a less degree this is true of all 
paints containing carbon, including graphite. Lampblack is used with 
advantage with red lead; it is also an ingredient of many "carbon" 

f)aints, the base of which is either bone black or artificial graphite. Red 
ead dries by uniting chemically with the oil to form a cement; it is heavy, 
and makes an expensive paint, and is often highly adulterated. Pure red 
lead has long had a high reputation as a paint for iron and steel, and Is 
still used extensively, especially as a first coat; but of late years some of 
the new paints and varnish-like preparations have displaced it to aeon' 
siderable extent even, on the most important work. 

Varnishes. — These are made by melting fossil resin, to which is then 
added from half its weight to three times its weight of refined linseed oil, 
and the compound is thinned with turpentine; they usually contain a 
little drier. They are chiefly used on wood, being more durable and 
more brilliant than oil, and are often used over paint to preserve It. 
Asphaltum is sometimes substituted in part or in whole for the fossil 
resm, and in this way are made black varnishes which have been used on 
iron and steel with good results. Asphaltum and substances like it havB 



472 IRON AND STEEL. 

also been simply dissolved in solvents, as benzine or carbon disulphlde, 
and used for tne same purpose. 

All these preservative coatings are supposed to form impervious films, 
keeping out air and moisture; but in fact all are somewhat porous. On 
this account it is necessary to have a film of appreciable thickness, best 
formed by successive coats, so that the pores ot one will be closed by the 
next. The pigment is used to give an agreeable color, to help fill the 
pores of the oil film, to make the paint harder, so that it will resist abra- 
sion, and to make a tliicker film. In varnishes these results are sought to 
be attained by the resin wliich is dissolved in the oil. There is no sort of 
agreement among practical men as to which coating is best for any par- 
ticular case; tliis is probably because so much depends on the preparation 
of the surface and the care with which the coating is applied, and also 
because the conditions of exposure vary so greatly. 

Methods of Application. — From the surface of the metal mud and 
dirt must be first removed, then any rusty spots must be cleaned thor- 
oughly; loose scale may be removed with wire brushes, but thick and 
closely adherent rust must be removed with steel scrapers, or with hammer 
and chisel if necessary. The sand-blast is used largely and increasingly 
to clean before painting, and is the best method known. Pickling is 
usually done with 10% sulphuric acid; the solution is made more active 
by heating. All traces of acid must be removed by washing, and the 
. metal must be immediately dried and painted. Less than two coats of 
paint should never be used, and three or four are better. The first paint- 
ing of metal is the most important. Paint is always thin on angles and 
edges, also on bolt and rivet heads; after the first full coat apply a partial 
or striping coat, covering the angles and edges for at least an inch back 
from the edge, also all bolt and rivet heads. After this is dry apply the 
second full coat. At least a week should elapse between coats. 

Cast-iron water pipes are usually coated by dipping in a hot mixture of 
coal-tar and coal-tar pitch; riveted steel pipes by dipping in hot asphalt 
or by a japan enamel which is baked on at about 400° F. Ships' bottoms 
are coated with a varnish paint to prevent rusting, over which is a similar 
paint containing a poison, as mercury chloride, or a copper compound, 
or else for this second coat a greasy copper soap is applied hot; this 
prevents the accumulation of marine growths. Galvanized iron and tin 
surfaces should be thoroughly cleaned with benzine and scrubbed before 
painting. When new they are partly covered with grease and chemicals 
used in coating the plates, and these must be removed or the paint will 
not adhere. 

Quantity of Paint for a Given Surface. — One gallon of paint will 
cover 250 to 400 sq. ft. as a first coat, depending on the character of the 
surface, and from 350 to 500 sq. ft. as a second coat. 

Qualities of Paints. — The Railroad and Engineering Journal, vols, 
liv. and Iv., 1890 and 1891, has a series of articles on paint as applied to 
wooden structures, its chemical nature, application, adulteration, etc., by 
Dr. C. B. Dudley, chemist, and F. N. Pease, assistant chemist, of the 
Penna. R. R. They give the results of a long series of experiments on 
paints as applied to railway purposes. 

Inoxydation Processes. (Contributed by Alfred Sang, Pittsburg, 
Pa., 1908.) — The black oxide of iron (FeaO*) as a continuous coating 
affords excellent protection against corrosion. Lavoisier (1781) noted its 
artificial production and its stable qualities. Faraday (1858) observed 
the protective properties of the coating formed by the action of steam 
in superheating tubes. Berthier discovered its formation by the action 
of highly heated air. 

Bower-Barff Process. — Dr. Barff's method was to heat articles to be 
coated to about 1800° F. and inject steam heated to 1000° F. into the 
muffle. George and A. S. Bower used air instead of steam, then carbon 
monoxide (producer gas) to reduce the red oxide. In the combined 
process, the articles are heated to 1600° F. in a closed retort; super- 
heated steam is injected for 20 min., then producer gas for 15 to 25 min.; 
the treatment can be repeated to increase the depth of oxidation. Less 
heat is required for wrought than for cast iron or steel. By a later 
improvement, steam heated above the temperature of the articles was 
injected during the last 1 to 2 hours. By a further improvement known 
as the '* Wells Process." the work is finished in one operation, the steam 



PRESERVATIVE COATINGS. 473 

and producer-gas being injected together. Articles are slightly in- 
creased in size by the treatment. The surface is gray, changing to 
black when oiled ; it will chip off if too thin ; it will take paint or enamel 
and may be poUshed, but can not be either bent or machined; the 
coating itself is incorrodible and resists sea-water, mine-water and acid 
fumes; the strength of the metal is slightly reduced. The process is 
extensively used for small hardware. (See F. S. Barff, Jour. I. & S. 
Inst., 1877, p. 356; A. S. Bower, Trans. A. I. M. E., 1882, p. 329; B. H. 
Thwaite, Proc. Inst. C. E., 1883, p. 255; George W. Maynard. Trans. 
A. S. M. E., iv, 351.) 

Gesner Process. — Dr. George W. Gesner's process is in commercial 
operation since 1890. The coating retort is kept at 1200° F. for 20 
minutes after charging, then steam, partially decomposed by passing 
through a red-hot pipe, is allowed to act at intervals during 35 min.; 
finally, a small quantity of naphtha, or other hydrocarbon, is intro- 
duced and allowed to act for 15 min. The work is withdrawn when the 
heat has fallen to 800° F. The articles are neither increased in size nor 
distorted; the loss of strength and reduction of elongation are only 
slight. Large pieces can be treated. (See Jour. I. <&, S. Inst., 1890 (ii), 
p. 850; Iron Age, 1890, p. 544.) 

Hydraesfer Process."-An improvement of the Gesner process pat- 
ented by J. J. Bradley and in commercial operation. As its name im- 
plies, the coating is thought to be an alloy of hydrogen, copper, and iron. 
The sulphides and phosphides are claimed to be burned out of the sur- 
face of the metal by the action of hydrogen at a high temperature 
giving additional rust-proof qualities. The appearance of the finished 
work is that of genuine Bower-Barfflng. 

Russia and Planished Iron. — Russia iron is made by cementation 
and shght oxidation. W. Dewees Wood (U. S. Pat. No. 252,166 of 
1882) treated planished sheets with hydrocarbon vapors or gas and 
superheated steam within an air-tight and heated chamber. 

Niter Process. — An old process improved by Col. A. R. Bufflngton in 
1884. The articles are stirred about in a mixture of fused potassium 
nitrate (saltpeter) and manganese dioxide, then suspended in the vapors 
and finally dipped and washed in boiling water. Pure chemicals are 
essential. Used for small arms and pieces which cannot stand the high 
heat of other processes. (Trans. A. S. M. E., vol. vi, p. 628.) 

Electric Process. — A. de Meritens connected polished articles as 
anodes in a bath of warm distilled water and used a current as weak as 
could be conducted. A black film of oxide was formed; too strong a 
current produced rust. It being essential that hydrogen be occluded in 
the surface of the metal, it was found necessary, as a rule, to connect 
the articles as cathodes for a short time previous to inoxidation. {Bull. 
Soc. Intle. des Electr., 1886, p. 230.) 

Aluminum Coatings. — Aluminum can be deposited electrically, the 
main difficulties being the high voltage required and the readiness of the 
coating to redissolve. The metal-work of the tower of City Hall, Phila- 
delphia, was coated by the Tacony Iron & Metal Co., Tacony, Pa., with 
14 oz. per sq. ft. of copper, on which was deposited 2 H oz. of an alloy of 
tin and aluminum. The Reeves Mfg. Co., Canal Dover, Ohio, makes 
aluminum-coated conductor pipes, etc., said to be as durable as copper 
and as rust-proof as aluminum. 

Galvanizing is a method of coating articles, usually of iron or steel, 
with zinc. Galvanized iron resists ordinary corroding agencies, the 
zinc becoming covered with a film of zinc carbonate, which protects the 
metal from further chemical action. The coating is, however, quickly 
destroyed by mine-water, tunnel gases, sea- water and conditions that 
commonly exist in tropical countries. If the work is badly done and the 
coating does not adhere properly, and if any acid from the pickle or any 
chloride from the fiux remains on the iron, corrosion takes place under 
the zinc coating. (See M. P. Wood: Trans. A. S. M. E., xvi. 350. Al- 
fred Sang: Trans. Am. Foundry men's Assoc, 1907, Iron Age, May 23 
and 30, 1907, and Proc. Eng. Soc. of W. Penna., Nov., 1907.) 

The Penna. R. R. Specifications for galvanized sheets for car roofs 



474 IRON AND STEEL. 

(1907) prescribe that the black sheets before galvanizing should weigh 
16 oz. per sq. ft., the galvanized sheet 18 oz. Sheets will not be accepted 
if a chemical determination shows less than 1.5 oz. of zinc per sq. ft. 

Hot Galvanizing. — The articles to be galvanized are hrst cleaned by 
pickUng and then dipped in a solution of hydrochloric acid and immersed 
in a bath of molten zinc at a temperature of from 800 to 900° F.; when 
they have reached the temperature of the bath, they are withdrawn and 
the coating is set in water; sal-ammoniac is used on the pot as a flux, 
either alone or as an emulsion with glycerine or some other fatty medium. 
Wire, bands and similar articles are drawn continuously through the 
bath, and may be passed through asbestos wipers to remove the surplus 
metal; in this case it is advisable to use a very soft spelter free from iron. 
If wire is treated slowly and passed through charcoal dust instead of 
wipers the product is known as " double-galvanized. " Tin can be added 
to the bath to help bring out the spangles, but it gives a less durable 
coating. Aluminum is added as a Zn-Al alloy, with about 20% Al, to 
give fluidity. Sheets are galvanized continuously, and except in the 
case of so-called "flux sheets," are put through rolls as they emerge 
from the bath, to squeeze off the excess of zinc and improve the adherence. 

Test for Galvanized Wire. — Sir W. Preece devised the following 
standard test for the British Post Office: dip for one minute in a saturated 
neutral solution of sulphate of copper, wash and wipe; to pass, the 
material must stand 3 dips. 

The American standard test is as follows: prepare a neutral solution of 
sulphate of copper of sp. gr. 1.185, dip for one minute, wash and wipe dry; 
the wire must stand 4 dips without a permanent coating of copper show- 
ing on any part of the wire. 

Galvanizing by Cementation; Sherardizing. — The alloying of metals 
at temperatures below their melting points has been known since 1820 
or earlier. Berry (1838) invented a process of depositing zinc, in which 
the objects to be coated were placed in a closed retort and covered with 
a mixture of charcoal and powder of zinc ; the retort was heated to cherry- 
red for a longer or shorter period, according to the bulk of the article and 
to the desired thickness of the coating. Dumas gave iron articles a slight 
coating of copper by dipping them in a solution of sulphate of copper and 
then heated them in a closed retort with oxide of zinc and charcoal dust. 
Sheet steel cowbells are coated with brass by placing them in a mixture 
of finely divided brass and charcoal dust and heating them to redness in 
an air-tight crucible. 

S. Cowper-Coles's process, known as Sherardizing, patented in 1902, 
consists in packing the objects which are to be coated in zinc dust or 
pulverized zinc to which zinc oxide with a small percentage of charcoal 
dust is added, and heating in a closed retort to a temperature below the 
melting point of zinc. A large proportion of sand can be used to reduce 
the amount of zinc dust carried in the retort, to prevent caking and give 
a brighter finish; motion of the retort is in most cases necessary to obtain 
an even coating. The operation lasts from 30 minutes to several hours, 
depending on the size of the drum. Tempered steel is not affected by 
the process, but surfaces are hardened, there being a zinc-iron alloy 
formed to a depth varying with the time of treatment. This process is 
suitable for small work, giving a superior quality of zinc coating. (See 
Cowper-Coles, " Preservation and Ornamentation of Iron and Steel Sur- 
faces," Trans. Soc. Engrs. 1905, p. 183; "Sherardizing," Iron Age, 
1904. p. 12. Alfred Sang, "Theory and Practice of Sherardizing," 
EL Chem. and Metall. Ind., May, 19070 

T^ead Coatings. — Lead is a good protection for iron and steel pro- 
vided it is perfectly gas-tight. Electrically deposited lead does not 
bond well and the coating is porous. Sheets having a light coating of 
lead, produced by dipping in the molten metal, are known as terne 
plates; they have no lasting qualities. Lead-lined wrought pipe, fittings 
and valves are made for conveying acids and other corroding liquids. 



STEEL. 



475 



STEEL. 

The Manufacture of Steel. (See Classification of Iron and Steel, 
p. 436.) Cast steel is a malleable alloy of iron, cast from a fluid mass. 
It is distinguished from cast iron, wliich is not malleable, by being much 
lower in carbon, and from wrought iron, which is welded from a pasty 
mass, by being free from intermingled slag. Blister steel is a highly 
carbonized wrought iron, made by the "cementation" process, which 
consists in keeping wrought-iron bars at a red heat for some days in 
contact with charcoal. Not over 2% of C is usually absorbed. The 
surface of the iron is covered with small blisters, supposedly due to the 
action of carbon on slag. Other wTought steels were formerly made by 
direct processes from iron ore, and by the puddling process from wrought 
iron, but these steels are now replaced by cast steels. Blister steel is, 
however, still used as a raw material in the manufacture of crucible steel. 
Case-hardening is a process of surface cementation. 

Crucible Steel is commonly made in pots or crucibles holding about 
80 pounds of metal. The raw material may be steel scrap; blister steel 
bars; wrought iron with charcoal; cast iron with wrought iron or with 
iron ore; or any mixture that will produce a metal having the desired 
chemical constitution. Manganese in some form is usually added to 
prevent oxidation of the iron. Some silicon is usually absorbed from the 
crucible, and carbon also if the crucible is made of graphite and clay. 
The crucible being covered, the steel is not affected by the oxygen or 
sulphur in the flame. The quality of crucible steel depends on the free- 
dom from objectionable elements, such as phosphorus, in the mixture, 
on the complete removal of oxide, slag and blowholes by "dead-melting" 
or "killing" before pouring, and on the kind and quantity of different 
elements which are added in the mixture, or after melting, to give par- 
ticular quaUties to the steel, such as carbon, manganese, chromium, 
tungsten and vanadium. 

Bessemer Steel is made by blowing air through a bath of melted pig 
iron. The oxygen of the air first burns away the silicon, then the carbon, 
and before the carbon is entirely burned away, begins to burn the iron. 
Spiegeleisen or ferro-manganese is then added to deoxidize the metal 
and to give it the amount of carbon desired in the finished steel. In the 
ordinary or "acid" Bessemer process the lining of the converter is a 
silicious material, which has no effect on phosphorus, and all the phos- 
phorus in the pig iron remains in the steel. In the "basic" or Thomas 
and Gilchrist process the lining is of magnesian limestone, and limestone 
additions are made to the bath, so as to keep the slag basic, and the phos- 
phorus enters the slag. By this process ores that were formerly unsuited 
to the manufacture of steel have been made available. 

Open-hearth Steel. — Any mixture that may be used for making 
steel in a crucible may also be melted on the open hearth of a Siemens 
regenerative furnace, and may be desiliconized and decarbonized by the 
action of the flame and by additions of iron ore, deoxidized by the addi- 
tion of spiegeleisen or ferro-manganese, and recarbonized by the same 
additions or by pig iron. In the most common form of the process pig 
iron and scrap steel are melted together on the hearth, and after the 
manganese has been added to the bath it is tapped into the ladle. In the 
Talbot process a large bath of melted material is kept in the furnace, 
melted pig iron, taken from a blast furnace, is added to it, and iron ore 
is added which contributes its iron to the melted metal while its oxygen 
decarbonizes the pig iron. When the decarbonization has proceeded far 
enough, ferro-manganese is added to destroy iron oxide, and a portion 
of the metal is tapped out, leaving the remainder to receive another 
charge of pig iron, and thus the process is continued indefinitely. In 
the Duplex Process melted cast iron is desiliconized in a Bessemer con- 
verter, and then run into an open hearth, where the steel-making opera- 
tion is finished. 

The open-hearth process, like the Bessemer, may be either acid or 
basic, according to the character of the lining. The basic process is a 
dephosphorizing one, and is the one most generally available, as it can 
use pig irons that are either low or high in phosphorus. 



476 



STEEIi. 



Relation between the Chemical Composition and Physical 
Character of Steel. 

W. R. Webster (Trans. A. I. M. E., vols, xxi and xxii, 1893-4) gives re* 
suits of several hundred analyses and tensile tests of basic Bessemer steel 
plates, and from a study of them draws conclusions as to the relation of 
chemical composition to strength, the chief of which are condensed as 
follows: 

The indications are that a pure iron, without carbon, phosphorus, man- 
ganese, silicon, or sulphur, if it could be obtained, would have a tensile 
strength of 34,750 lbs. per sq. in., if tested in a 3/8-in. plate. With this as a, 
base, a table is constructed by adding the following hardening effects, as 
shown by increase of tensile strength, for the several elements named. 
Carbon, a constant effect of 800 lbs. for each 0.01%. 
Sulphur, '* " 500 ** " ** 0.01%. 
Phosphorus, the effect is higher in high-carbon than in low-carbon steela. 
With carbon hun- 
dredths % 9 10 11 12 13 14 15 16 17 

Each 0.01% Phas 
an effect of lbs.. 900 1000 1100 1200 1300 1400 1500 1500 1500 
Manganese, the effect decreases as the per cent of manganese increases. 



Mn being per 
cent 

Strength incr. 

for 0.01%... 
Total increase 

from Mn. . . 



.00 
to 
.15 



.15 
to 
.20 



.20 
to 
.25 



240 240 220 
3600 4800 5900 



.25 
to 
.30 

200 

6900 



.30 
to 
.35 



.35 
to 
.40 



.40 
to 
.45 



.45 
to 
.50 



.50 
to 
.55 



.55 
to 
.65 



180 160 140 120 100 100 lbs. 
7800 8600 9300 9900 10,400 11,400 



Silicon is so low in this steel that its hardening effect has not been con- 
sidered. 

With the above additions for carbon and phosphorus the following table 
has been constructed (abridged from the original by Mr. Webster). To 
the figures given the additions for sulphur and manganese should be made 
as above. 

Estimated Ultimate Streng^ths of Basic Bessemer-steel Plates. 

For Carbon, 0.06 to 0.24; Phosphorus, .00 to .10; Manganese and Sulphur, 
.00 in all cases. 



Carbon. 


0.06 


.08 


.10 


.12 


.14 


.16 


.18 


.20 


.22 


.24 


Phos. .005 


39,950 


41,550 


43,250 


44,950 


46,650 


48,300 


49,900 


51,500 


53,100 


54,700 


" .01 


40,350 


41,950 


43,750 


5,550 


47,350 


49,050 


50,650 


52,250 


53,850 


55,450 


•♦ .02 


41,150 


42,750 


44,750 


46,750 


48,750 


50,550 


52,150 


53,750 


55,350 


56,950 


•• .03 


41,950 


43,550 


45,750 


47,950 


50,150 


52,050 


53,650 


55,250 


56,850 


58,450 


•• .04 


42,750 


41,350 


46,750 


49,150 


51,550 


53,550 


55,150 


56,750 


58,350 


59,950 


•• .05 


43,550 


45,150 


47,750 


50,350 


52,950 


55,050 


56,650 


58,250 


59,850 


61,450 


•• .06 


44,350 


45,950 


48,750 


51,550 


54,350 


56,550 


58,150 


59,750 


61,350 


62,950 


•• .07 


45,150 


46,750 


49,750 


52,750 


55,750 


58,050 


59,650 


61,250 


62,850 


64,450 


•* .08 


45,950 


47,550 


50,750 


53,950 


57,150 


59,550 


61,150 


62,750 


64,350 


65,950 


•• .09 


46,750 


48,350 


51,750 


55,150 


58,550 


61,050 


62,650 


64,250 


65,850 


67,450 


•• .10 


47,550 


49,150 


52,750 


56,350 


59,950 


62,550 


64,150 


65,750 


67,350 


68,956 


0.001 P. = 


80 lbs. 


80 lbs. 


1001b. 


1201b. 


1401b. 


1501b. 


1501b. 


1501b. 


1501b. 


1501b. 



In all rolled steel the quality depends on the size of the bloom or ingot 
from which it is rolled, the work put on it, and the temperature at which 
it is finished, as well as the chemical composition. 

The above table is based on tests of plates 3/8 inch thick and under 70 
inches wide; for other plates Mr. Webster gives the following corrections 
for thickness and width. They are made necessary only by the effect of 
thickness and width on the finishing temperature in ordinary practice. 
Steel is frequently spoiled by being finished at too high a temperature. 



STEEL. 477 



Thickness, in. . 
Correction ( 1 ) . 
Correction (2) . 



3/4* 


11/16 


-2000 


-1750 


-1000 


- 750 



5/8 I 

-1500 
- 500 


9/16 
-1250 
-250 


1/2 

-1000 




7/16 I 3/8 I 5/16 
-5001 +3000 

±500+10001+5000 



* And over. (1) Plates up to 70 in. wide. (2) Over 70 in. wide. 

Comparing the actual result of tests of 408 plates with the calculated 
results, Mr. Webster found the variation to range as below. 

Within lbs. 1000 2000 3000 4000 5000 

Per cent... 28. 4 55.1 74.7 89.9 94.9 

The last figure would indicate that if specifications were drawn calling 
for steel plates not to vary more than 5000 lbs. T. S. from a specified 
figure (equal to a total range of 10,000 lbs.), there would be a probability 
of the rejection of 5% of the blooms rolled, even if the whole lot was made 
from steel of identical chemical analysis. 

Campbell's Formulae. (H. H. Campbell, The Manufacture and Prop' 
erties of Iron and Steel, p. 387.) — 

Acid steel, 40,000 + 1000 C + 1000 P + xMn = Ultimate strength. 
Basic steel, 41,500 + 770 C + 1000 P + yMn = Ultimate strength. 

The values of xMn and yMn are given by Mr. Campbell in a table, 
but they may be found from the formulae xMn = 8 CMn — 320 C and 
yMn = 90 Mn + 4 CMn - 2700 - 120 G, or, combining the formula 
we have: 

Ult. strength, acid steel, 40,000 + 680 C + 1000 P + 8 CMn. 

basic " 38,800 + 650 C + 1000 P + 90 Mn + 4 CMn^ 

In these formulae the unit of each chemical element is 0.01%. 

Examples. Required the tensile strength of two steels containing 
respectively C, 0.10, P, 0.10, Mn, 0.30, and C, 0.20, P, 0.10, Mn, 0.65. 

Answers, by Webster, 59,650 and 77,150; by Campbell, 57,700 and 72,850. 

Low Tensile Strength of Very Pure Steel. — Swedish nail-rod 
open-hearth steel, tested by the author in 1881, showed a tensile strength of 
only 42,591 lbs. per sq. in. A piece of American nail-rod steel showed 
45,021 lbs. per sq. in. Both steels contained about 0.10 C and 0.015 P, 
and were very low in S, Mn, and Si. The pieces tested were bars about 
2 X 3/8 in. section. 

R. A. Hadfield (Jour. Iron and Steel Inst., 1894) gives the strength of 
very pure Swedish iron, remelted and tested as cast, 45,024 lbs. per sq. 
in.; remelted and forged, 47,040 lbs. The analysis of the cast bar was: 
C, 0.08; Si, 0.04; S,0.02; P, 0.02; Mn, 0.01; Fe, 99.82. 

*' Armco Ingot Iron." — A very pure variety of open-hearth steel, 
made by the American Rolling Mill Co., Middletown, Ohio, has been 
given the trade name of Armco- American Ingot Iron. It is claimed 
for this product that it resists corrosion better than any other grade of 
wrought iron or steel. It is used chiefly in sheets. The tensile strength 
is given as 38,000 to 44,000 lb. per square inch; elastic limit one half 
the ultimate strength; elongation in 8 inches, 22%. The following 
analyses are given to show how Armco compares in composition with 
other iron products: 

S P C Mn Si Cu O H N Fe 

Armco 020 .003 .011 .019 .002 .025 .022 .001 .004 99.893 

Puddled Iron. . .024 .155 .040 .040 .050 .025 .150 .001 .005 99.510 

Mild Steel 050 .070 .115 .500 .005 .055 .023 .002 .009 99.171 

High Carb. Steel .030 .030 1.000 .450 .150 .055 .025 .001 .006 98.253 

Effect of Oxygen upon Strength of Steel. — A. Lantz, of the 
Peine works, Germany, in a letter to Mr. Webster, says that oxygen plays 
an important role — such that, given a like content of C, P, and Mn, a 
blow with greater oxygen content gives a greater hardness and less ductility 
than a blow with less oxygen content. The method used for determin- 
ing oxygen is that of Prof. Ledebur, given in Stahl und Eisen, May, 1892, 
p. 193. The variation in O may make a difference in strength of nearly 
V2 ton per sq. in. (Jour. I. and S. I., 1894.) 

Electric Conductivity of Steel. — Louis Campredon reports in Le 
Genie Civil [prior to 1895] the results of experiments on the electric resist- 
ance of steel wires of different composition, ranging from 0.09 to 0.14 C; 
0.21 to 0.54 Mn; Si, S, and P low. The figures show that the purer and 



478 



STEEL* 



softer the steel the better is its electric conductivity, and, furthermore, that 
manganese is the element which most influences the conductivity. The 
results may be expressed by the formula R = 5.2 -h 6.2S ± 0.3; in which 
R = relative resistance, copper being taken as 1, and S == the sum ot the 
percentages of C. P, S, Si, and Mn. The conclusions are confirmed by 
J. A. Capp, in 1903, Trans. A. I. M. E., vol. xxxiv, who made forty-five 
experiments on steel of a wide range of composition. His results may be 
expressed by the formula 7? = 5.5 + 4»S ± 1. High manganese increases 
the resistance at an increasing rate. Mr. Capp proposes the following 
specification for steel to make a satisfactory third rail, having a resistance 
eight times that of copper: C, 0.15; Mn, 0.30; P, 0.06; S, 0.06: Si, 0.05: 
none of these figures to be exceeded. 

Range of Variation in Strength of Bessemer and Open-Hearth 

Steels. 

The Carnegie Steel Co. in 1888 published a list of 1057 tests of Bes- 
semer and open-hearth steel from which the following figures are selected 



Kind of Steel. 


1^ 
1^ 


Elastic Limit. 


Ultimate ( ^^^01., 
Strength. j -^ g j^^ 




High't. 


Lowest. 


High't. 


Lowest.! High't. 


Lowest. 


(a) Bess, structural. 
(&) " " . 

(c) " angles .... 

(d) 0. H. firebox . . 


100 
170 
72 
25 
20 


46.570 
47.690 
41.890 


39.230 
39.970 
32,630 


71.300 
73.540 
63.450 
62.790 
69.940 


61.450 
65.200 
56,130 
50.350 
63.970 


33.00 
30.25 
34.30 
36.00 
30.00 


23.75 
23.15 
26.25 
25.62 


(e) 0. H. bridge... . 






22.75 



Requirements of Specifications. 
(a) E. L., 35,000; T. S., 62,000 to 70,000; elong., 22% in Sin. 
(6) E. L., 40,000; T. S., 67,000 to 75,000. 

(c) E. L., 30,000; T. S., 56,000 to 04,000; elong., 20% in 8 in. 

(d) T. S., 50,000 to 62,000; elong., 26% in 4 in. 

(e) T. S., 64,000 to 70,000; elong., 20% in 8 in. 

Bending Tests of Steel. (Pencoyd Iron Works.) ^ Steel below 0.10 C 
Bhould be capable of doubling flat without fracture, after being chilled 
from a red heat in cold water. Steel of 0.15 C will occasionally submit 
to the same treatment, but will usually bend around a curve whose radius 
is equal to the thickness of the specimen; about 90% of specimens stand 
the latter bending test without fracture. As the steel becomes harder its 
ability to endure this bending test becomes more exceptional, and when 
the carbon becom.es 0.20 little over 25% of specimens will stand the last- 
described bending test. Steel having about 0.40% C will usually harden 
sufficiently to cut soft iron and maintain an edge. 

EFFECT OF HEAT TREATMENT AND OF WORK ON STEEL. 

Low Strength Due to Insufficient Work. (A. E. Hunt, Trans, 
A. I. M. E., 1886.) — Soft steel ingots, made in the ordinary way for 
boiler plates, have only from 10,000 to 20,000 lbs. tensile strength per sq. 
in., an elongation of only about 10% in 8 in., and a reduction of area of 
less than 20%. Such ingots, properly heated and rolled down from 10 in. 
to 1/2 in. thickness, will give from 55,000 to 65,000 lbs. tensile strength, an 
elongation in 8 in. of from 23 7o to 33%, and a reduction of area of from 
55% to 70%. Any work stopping short of the above reduction in thick- 
ness ordinarily yields intermediate results in tensile tests. 

Effect of Finishing Temperature in Rolling. — The strength and 
ductility of steel depend to a high degree upon fineness of grain, and 
this may be obtained by having the temperature of the steel rather low, 
sav at a dull red heat, 1300° to 1400° F., during the finishing stage of 
rolling. In the manufacture of steel rails a great improvement in quality 
has been obtained by finishing at a low temperature. An indication of 
the finishing temperature is the amount of shrinkage by cooling after 
leaving the rolls. The Phila. & Reading Railway Co.'s specification for 
rails (1902) says, "The temperature of the ingot or bloom shall be such 
that with rapid rolling and without holding before or in the finishin«: 
passes or subsequently, and without artificial cooling after leaving the 



EFFECT OF HEAT TKEATMENT ON STEEL. 



479 



last pass, the distance between the hot saws shall not exceed 30 ft. 6 in. 
for a 30-ft. rail." 

Fining the Grain by Annealing. — Steel which is coarse-grained 
on account of leaving the rolls at too high a temperature may be made 
fine-grained and have its ductility greatly increased mthout lowering its 
tensile strength by reheating to a cherry-red and cooling at once in air. 
(See paper on "Steel Rails," by Robert Job, Trans. A. I. M. £?., 1902.) 

Effect of Cold Rolling. — Cold rolling of iron and steel increases the 
elastic limit and the ultimate strength, and decreases the ductility. 
Major Wade's experiments on bars rolled and polished cold by Lauth's 
process showed an average increase of load required to give a slight per- 
manent set as follows: Transverse, 162%; torsion, 130%; compression, 
161% on short columns 1 1/2 in. long, and 64% on columns 8 in. long; 
tension, 95%. The hardness, as measured by the weight required to 
produce equal indentations, was increased 50%; and it was found that 
the hardness was as great in the center of the bars as elsewhere. Sir 
W. Fairbairn's experiments showed an increase in ultimate tensile 
strength of 50%, and a reduct on in the elongation in 10 in. from 2 in. 
or 20% to 0.79 in. or 7.9%. 

Effect of Heat Treatment of a Motor-tFUck Axle. — (John Younger, 
Trans., A. S. M. E., 1915.) — Shafts 2 1/4 in. diam. whose analysis was 
approximately C, 0.20; Cr, 1.5; Mn, 6.30; Ni, 4.00; Si, 0.20; P and S 
below 0.04; elasticlimit, 90,000; tensile strength, 105,000; reduction in 
area, 66%; elongation in 2 in., 25%, were found to break in service. 
The maximum power transmittted was about 33 H.P. at 27 r.p.m. 
Experiments were made with heat treatment to raise the elastic limit. 
The material selected had C, 0.30; Mn, 0.50; Cr, 1.5; Ni, 3.5. After 
heat treatment the elastic limit was 175,000 lb. per sq. in.; tensile 
strength, 185,000; elongation in 2 in., 14% ; reduction of area, 53 %. The 
shafts are machined from hot-rolled bars already heat-treated to show 
an elastic limit of about 100,000. They are then heated to between 
1450° and 1500° F. and quenched in oil, then reheated to a little over 
700° F. and cooled slowly in air. They warped slightly, but were 
straightened when hot under a press. The BrineU hardness after 
treatment was 402 to 444. Not one of the shafts thus treated has 
broken in service. Other steels, such as 5% nickel steels, chrome- 
vanadium steels, and air-hardening steels have been tried, and all have 
been standing up to service. The success seems to be due entirely to 
the high elastic limit. The BrineU hardness test is an unfailing indication 
of the success or non-success of the heat treatment. 

Effect of Annealing on Boiled Bars. (Campbell, Mfr. of Iron and 
Steel p. 275.) 



Ultimate 


Elastic 


Elong. in 


Red. Area, 


Elas. 


Strength. 


Limit 


8in.,%. 


%. 


Ratio. 




An- 


Nat- 


An- 


Nat- 


An- 


Nat- 


An- 


Nat- 


An- 


Natural. ^ 


nealed. 


ural. 


nealed. 


ural. 


nealed. 


ural. 


nealed. 


ural. 


nealed* 


•^ r 58.568 
.S| J 62.187 
^ 1 1 70.530 


54.098 


40.300 


31,823 


29.7 


28.8 


60.8 


62.7 


68.8 


58.8 


58.364 


42,606 


35.120 


28.0 


28.6 


62.2 


63.5 


68.5 


60.2 


65.500 


49,000 


37.685 


26.9 


23.4 


61.1 


55.3 


69.5 


57.5 


'^ " 176.616 


69.402 


51.108 


40.505 


24.5 


23.0 


53.7 


56.5 


66.7 


58.4 


^^(58.130 
f -i 3 62.089 


51.418 


40.400 


30.393 


30.1 


31.1 


61.8 


60.5 


69.5 


59.1 


55.021 


42.441 


31.576 


30.1 


30.4 


60.9 


60.0 


68.4 


57.4 


X^ j 69.420 


60,850 


45.090 


34.000 


25.6 


26.5 


59.3 


52.1 


65.0 


55.9 


<N.S ( 75.865 


67.618 


49,691 


39.403 


24.7 


26.3 


54.4 


51.4 


65.5 1 58.3 



The bars were rolled from 4 X 4-in. billets of open-hearth steel. The 
figures are averages of from 2 to 12 tests of each heat. In annealing the 
bars were heated in a muflae and withdrawn when they had reached a 
dull yellow heat. 

.Hardening of Soft Steel. — A. E. Hunt (Trans. A.I.M.E., 1883, vol. 
xii) says that soft steel, no matter how low in carbon, will harden to a cer- 
tain extent upon being heated red-hot and plunged into water, and that it 
hardens more when plunged into brine and less when quenched in oil. 

A heat of open-hearth steel of 0.15% C and 0.29% Mn gave the follow^ 
ing results upon test-pieces from the same 14 in. thick plate, 



480 STEEL. j 

Unhardened T. S. 55,000 El. in 8 in. 27% Red. of Area 62% 

Hardened in water " 74,000 " 25% " 50% 

Hardened in brine " 84,000 " 22% " . 43% 

Hardened in oil " 67,000 " 26% ** 49% 

The greatly increased tenacity after hardening indicates that there must 
be a considerable molecular change in the steel thus hardened, and that 
if such a hardening should be created locally in a steel plate, there must 
be very dangerous internal strains caused thereby. 

Comparative Tests of Full-sized Eye-bars and Small Samples* 
(G. G. S. Morison, A.S.C. E., 1893.) — 17 full-sized eye-bars, of the steel 
used in the Memphis bridge, sections 10 in. wide X 1 to 23/iein. thick, and 
sample bars from the same melts. Average results: 

Eye-bars: E. L., 32,350; T. S., 63,330; El. in full length, 13.7%; Red. 
of area, 36.3%. 

Small bars: E. L., 40,650; T. S., 71,640; El. in 8 Ins., 26,2%; Red. 
of area, 46.7%. 

" Recalescence " of Steel. — If we heat a bar of copper by a flame 
of constant strength, and note carefully the interval of time occupied in 
passing from each degree to the next higher degree, we find that these in- 
tervals increase regularly, i.e., that the bar heats more and more slowly, 
as its temperature approaches that of the flame. If we substitute a bar of 
steel for one of copper, we find that these intervals increase regularly up 
to a certain point, when the rise of temperature is suddenly and in most 
cases greatly retarded or even completely arrested. After this the regular 
rise of temperature is resumed, though other like retardations may recur 
as the temperature rises farther. So if we cool a bar of steel slowly the 
fall of temperature is greatly retarded when it reaches a certain point in 
dull redness. If the steel contains much carbon, and if certain favoring 
conditions be maintained, the temperature, after descending regularly, 
suddenly rises spontaneously very abruptly, remains stationary a while 
and then redescends. This spontaneous reheating is known as " recales- 
cence." 

These retardations indicate that some change which absorbs or evolves 
heat occurs within the metal. A retardation while the temperature is 
rising points to a change which absorbs heat ; a retardation during cooling 
points to some change which evolves heat. (Henry M. Howe, on "Heat 
Treatment of Steel," Trans. A. I. M. E., vol. xxii.) 

Critical Point. (Campbell, p. 287.) — If a piece of steel containing over 
0.50 C be allowed to cool slowly from a high temperature the cooling at 
first proceeds at a uniformly retarded rate, but when about 700° C. is 
reached there is an interruption of this regularity. In some cases the 
rate of cooling may be very slow, in other cases the bar may not decrease 
in temperature at all, while in still other cases the bar may actually grow 
hotter for a moment. When this " critical point " is passed, the bar cools 
as before until it reaches the temperature of the atmosphere. 

In metallography such a critical point is denoted by the letter A, and 
the particular one just described is known as Ar. In heating a piece of 
Bteel an opposite phenomenon is observed, there being an absorption of 
heat by internal molecular action, with a consequent retardation in the 
rise of temperature, and this point, which is some 30° C. higher than Ar, 
is called Ac. 

In soft steels, below 0.30 C, three critical points are found in cooling a 
bar from a high temperature, called Ats, At2, Ari, Ari being the lowest, 
and in heating the bar there are also three points, Aci, Ac2, AC3, the first 
named being the lowest. At each of the points there is a change in the 
micro-structure of the steel. 

Metallography. — This is a name given to a study of the micro-structure 
of metals. The steel metallographist designates the different structures 
that are found in a polished and etched section by the names austenite, 
martensite, pearlite, cementite, ferrite, troostite, and sorbite. Austenite 
is produced by quenching steel of over 1.40 C in ice water from above 
1050° C. Martensite is produced by quenching this steel from tempera- 
tures between 1050° C. and Ar^ It is also found together with cementite 
or ferrite in carbon steels below 1.30 C quenched at any point above Afi. 
It is the constituent which confers hardness on steel. In steels cooled 
slowly to below Ari the structure is composed entirely of ferrite, or 
entirely of pearlite, or of pearlite mixed with ferrite or cementite. Ferrite 



EFFECT OF HEAT TREATMENT ON STEEL. 



481 



is Iron free from carbon and forms almost the whole of a low-carbon steel, 
while cementite is considered to be a compound of iron and carbon, FesC, 
the C of this form being known as cement carbon. Pearlite is an inti- 
mate mixture of definite proportions of ferrite and cementite, corre- 
sponding to a pure steel of about 0.80 C, wliich, unhardened, consists of 
pearlite alone. Steels lower in C contain pearlite with ferrite, and steels 
higher in C contain pearlite and cementite. Troostite is a structure found 
when steel is quenched while cooling through the critical range, and 
sorbite when it is quenched at the end of the critical range. Quenching 
in lead or reheating quenched steel to a purple tint may also produce 
sorbite. (Campbell, p. 296.) 

Effect of Work on the Structure of Soft and 3Iedium Steel. — Steel 
as usually cast, coohng slowly, forms in crystals or grains. Rolling tends 
to break up this grain, but immediately after the cessation of work the 
formation of grains begins and continues until the metal has cooled to 
the lower critical point. Hence the lower the temperature to which the 
steel is worked, the more broken up the structure will be, but on the 
other hand if the rolling be continued below the critical point, the effect 
of cold work will be shown and strains will be set up which will make the 
piece unfit for use without annealing. 

Effect of Heat Treatment. — In heating steel through the lowest 
critical point the crystalline structure is obliterated, the metal assuming the 
finest condition of which it is capable. Above this point the size of grain 
increases with the temperature. 

Effect of Heating on Crucible Steel. ( W. Campbell, Proc. A.S.T. M. , 
vi, 213.) — Six steels, containing carbon as follows: (1) 2.04, (2) 1.94, 
(3) 1.72, (4) 1.61, (5) 1.04, and (6) 0.70, were heated in a small gas 
furnace to the temperatures given in the table and allowed to cool 
slowly in the furnace, and were then tested, with results as below. 



As 


650° 


715° 


760° 


800° 


855° 


905° 


950° 


1070° 


Rolled 


C 


C 


C 


C 


C 


C 


C 


C 


144000 


1 134UU 


1 1 4JUU 


9«800 


95650 


93800 


95250 


95200 


99000 


104200 


84600 


83900 


57700 


57800 


55500 


55350 


49350 


49600 


4.0 


6.0 


7.0 


11.5 


12.5 


12.0 


11.5 


6.0 


4.5 


146400 


115200 


1 04100 


95000 


92000 


89000 


95350 


91800 


97000 


91000 


91500 


72600 


68650 


50500 


51000 


49450 


49800 


41750 


6.3 


8.0 


9.5 


15.0 


17.0 


12.5 


70 


9.5 


8.5 


153100 


126000 


114100 


100300 


98000 


94000 


94350 


95000 


92350 


98100 


78300 


75700 


50500 


48750 


47900 


48600 


45200 


43100 


7.2 


8.0 


11.5 


16.5 


10.0 


13.5 


11.0 


7.5 


6.0 


157700 


128100 


117000 


98650 


97700 


95000 


97350 


96350 


94400 


105200 


85300 


81300 


52300 


53350 


51350 


51350 


48500 


51400 


6.5 




14.5 




18.5 


15.0 


11.5 


7.5 


3.5 


141100 


105400 


97800 


86800 


96600 


111800 


115900 


111500 


106100 


75800 


57700 


55200 


44850 


46600 


47200 


50600 


46800 


56500 


12.8 


18.0 


22.0 


26.5 


19.0 


13.0 


13.0 


10.5 


11.0 


117000 


95200 


88700 


85600 


94300 


91350 


90300 


90500 


89500 


64700 


53250 


49700 


40200 


42150 


42100 


41400 


39700 


57350 


17.0 


23.0 


27.5 


27.0 


19.0 


18.5 


18.0 


16.5 


18 



(1) T.S... 

E.L 

El. in 2 in. 

(2) T.S... 

E.L 

El. in 2 in. 

(3) T.S... 

E.L 

El. in 2 in. 

(4) T. S. . . 

EL 

El. in 2 in. 

(5) T.S... 

E.L 

El. in 2 in. 

(6) T.S... 

E.L 

El. in 2 in. 



57400 
56000 

1.0 
61350 
47000 

2.0 
65300 
50600 

2.0 
69800 

'"i.o 

112600 
89600 

11.5 
90000 
58500 

16 



The critical points Ari and Aci were determined, and the six steels gave 
practically identical results; thus Ari ranged from 696 to 708, averaging 
704° C, and Aci ranged from 730 to 737, averaging 733° C. 

The temperatures at which the finest-grained and a very coarse-grained 
fracture were found are as follows: 

Steel No 12 3 4 5 6 

Finest fracture 800 760 715-760 760 715 715° C 

Very coarse fracture 1070 1070 1070 1070 855 800° O 

Mr. Campbell's paper gives a fist of fourteen papers by different authori- 
ties on the micro-structure and the heat treatment of steel. 

Burning, Overheating, and Restoring Steel. (G. B. Waterhouse. 
A.S. T. M., vi, 247.) — Burnt metal is defined as coarsely crystalline and 
exceedingly brittle iron or steel, in consequence of excessive heating. 
often with some layers of oxide of iron. It cannot be effectively restored 
by heat treatment or mechanical work. Overheated metal is coarsely 
crystalline from excessive heating, but with, no inter-crystalline spaces. 
It can be restored by lieat treatment or mechanical work. Seven lots of 



482 



STEEL. 



nickel steel bars, containing 3.8% Ni, and C as in the table, 
to various temperatures in a mufTle furnace, with results as 



were heated 
below. 



%c. 

0.41 


Heated to 


1000a 

90245 

26.0 

99109 

21.0 

115421 

16.5 

135194 

14.0 

156827 

7.5 

168697 

3.5 

145642 

10.5 


1000b 

71800 

26.0 

78600 

25.0 

89000 

20.5 

108960 

15.0 

130336 

■97510 
15.0 

63950 
23.6 


11 00b 
71700 

25.5 
78800 

24.0 
89400 

19.0 
111840 

14.0 
•138112 

3.5 
98183 

t.o 

66640 
25.0 


1200b 
74000 

11.0 

84900 

11.5 

99600 

7.0 
109600 

3.0 
83117 

0.5 
90729 

0.5 
97894 

8.0 


13C0b 
71320 

7.0 
79600 

5.0 
85200 

2.0 
66800 

0.5 
46648 

0.0 
60600 

0.0 
35480 

1.0 


1200c 

71487 

10.5 

81487 

15.5 

96040 

10.0 

102705 

6.0 

114107 

5.5 

95103 

1.5 

89045 

17.5 


1200d 


T. S 


74989 




El. % in 2 in 


25 


0.51 


T.S 


80793 




El. % in 2 in 


22 5 


0.63 


T.S 


89842 




El. % in 2 in.... 


21 


0.79 


T.S '. ■■ 


90214 




El. % in 2 in 


21 


0.97 


T.S 


103476 




El. % in 2 in 


18 


1.24 


T.S 


106304 




El. in 2 in 


3 5 


1.48 


T.S ..• 


7459'^ 




El. in 2 in 


24.0 



a. Heated to 1000 C, which took I hr. 25 min., held there 25 mm. and 
cooled in air. b. The time required to heat to the temperatures named 
was respectively 1 h. 10 m., 1 h. 45 m., 2 h. 35 m., and 2 h. 35 m. The 
bars were kept at the desired temperature for an hour and then cooled 
slowly in place, c. Reheated to 700 C. d. Reheated to 775 C. 

In the steels below 1 % C heating to 1200° is accompanied by an increase 
in ultimate strength and a drop in ductility. Heating above 1200° pro- 
duces a very coarse crystallization and a great loss in strength and 
ductility. Reheating the overheated bars to 700° does not materially 
affect their structure, but reheating to 775° restores the structure nearly 
to that found before overheating, and completely restores the ductility. 
Similar results are found with carbon steel. 

Working Steel at a Blue Heat. — Not only are wrought iron and 
Bteelmuch more brittle at a blue heat (i.e., the heat that would produce an 
oxide coating ranging from Ught straw to blue on bright steel, 430° to 
600° F.), but while they are probably not seriously affected by simple 
exposure to blueness, even if prolonged, yet if they be worked in this range 
of temperature they remain extremely brittle after cooling, and may 
Indeed be more brittle than when at blueness; this last point, however, 
is not certain. (Howe, Metallurgy of Steel, p. 534.) 

Tests by Prof. Krohn, for the German State Railways, show that work- 
ing at blue heat has a decided influence on all materials tested, the injury 
done being greater on wrought iron and harder steel than on the softer 
Bteel. The fact that wrought iron is injured by working at a blue heat 
was reported by Stromeyer. (Engineering News, Jan. 9, 1892.) 

A practice among boiler-makers for guarding against failures due to 
working at a blue heat consists in the cessation of work as soon as a plate 
which had been red-hot becomes so cool that the mark produced by 
rubbing a hammer-handle or other piece of wood will not glow. A plate 
which is not hot enough to produce this effect, yet too hot to be touched 
by the hand, is most probably blue hot, and should under no circumstances 
be hammered or bent. (C. E. Stromeyer, Proc. Inst. C. E., 1886.) 

Oil-tempering and Annealing of Steel Forgings. — H. F. J. Porter 
says (1897) that aU steel forgings above 0.1% carbon should be annealed, 
to relieve them of forging and annealing strains, and that the process 
of annealing reduces the elastic limit to 47% of the ultimate strength. 
Oil-tempering should only be practiced on thin sections, and large forgings 
should -be hollow for the purpose. This process raises the elastic limit 
above 50% of the ultimate tensile strength, and in some alloys of steel, 
notably nickel steel, will bring it up to 60% of the ultimate. 

Heat Treatment of Armor Plates. (Hadfield Process, Iron Tr, 
Rev., Dec. 7, 1905.) — A cast armor plate of nickel-chromium steel is 
heated to from 950° C. to 1100° C, then cooled, preferably in air, then 
reheated to about 700° and cooled slowly, preferably in the furnace in 
which the heating was previously effected, again heated to about 700° 
and allowed to cool slowly to 640° C, whereupon it is suddenly cooled by 
spraying with water or by an air blast, but preferably in water. It is 
then reheated to about 600° and again suddenly cooled, preferably by 
quenching in water. Steel treated as described is suitable for armor 
plates £^nd other articles including parts of safes. Satisfactory results 



TREATMENT OF STRUCTURAL STEEL. 483 

riave been obtained by thus treating cast 6-in. armor plates' containing 
about 0.3 to 0.4 C, 0.25 Mn, 1.8 Cr, and 3.3 Ni cast in a sand mold. 
Such a 6-in. plate attacked by armor-piercing projectiles of 4.7-in. and 
6-in. calibers, stood over 15,000 foot-tons of energy without showing a 
crack. Also a 4-in. plate treated as described and having a carbonized 
or cemented face has withstood the attack of a 5.7-in. armor-piercing shell. 

Brittleness Due to Long-continued Heating. If low-carbon steel, 
(say under 0.15%) is held for a very long time at temperatures between 
500 and 750° C. (930 and 1380° F.), the crystals become enormous and 
the steel loses a large part of its strength and ductility. It takes a long time, 
in fact days, to produce this effect to any alarming degree, so that it is 
not liable to^ occur during manufacture or mechanical treatment, but 
steel is sometimes placed in positions where it may suffer this injury, for 
example, in the case of the tie-rods of furnaces, supports of boilers, etc.. 
so that the danger should be borne in mind by all engineers and users of 
steel. A wrought-iron chain that supported one side of a 50-ton open- 
hearth ladle, which was heated many times to a temperature above 500° C, 
finally reached a condition of coarse crvstallization, so that it was unable 
to bear the strain upon it. This phenomenon ot coarse crystallization in 
low-carbon steel is known as "Stead's Brittleness," alter J. E. Stead, who 
bas explained its cause. The effect seems to begin at a temperature of 
about 500° C. and proceeds rnore rapidly with an increase in temperature 
until we reach 750° C. The damage may be repaired completely by heat- 
ing the steel to a temperature between 800 and 900° C. The remedy is 
the same as that for coarse crystallization, due to overheating, and all 
steel which is placed in positions where it is Uable to reach these tempera- 
tures frequently should be restored at intervals of a week or a month, or 
as often as may be necessary. (Stoughton.) 

Surface Decarburization of Steel Heated in Melted Salts. — A. M. 
Portevin {Proc. Iron <fe Steel Inst., 1914. Eng'g, Oct. 9, 1914) shows 
that the surface layer of steel, to a depth which varies with time and 
temperature, is greatly reduced in carbon when the steel is heated in 
a bath of molten alkaline salts. In a steel containing 0.78% C heated 
in melted potassium chloride at 900° C, the C at the surface was re- 
duced in 1/4 hour to 0.5, in 2 hours to 0.3, and in 5 hours to 0.15, the 
thickness of the decarburized layer being for 1/4, 2, and 5 hours heating, 
respectively, 0.1, 0.2, and 0.3 mm. When cyanide and cyanate of 
potassium were added to the chloride decarburization and recarburiza- 
tion took place simultaneously, the percentage of carbon at the surface 
being 0.25 at the end of both 1/4 hour and 5 hours, the thickness of the 
decarburized layer increasing from 0.06 mm. to 0.69 mm. 

Influence of Annealing upon Magnetic Capacity. 

Prof. D. E. Hughes (Eng'g, Feb. 8, 1884, p. 130) has invented a "Mag- 
netic Balance," for testing the condition of iron and steel, which consists 
chiefly of a delicate magnetic needle suspended over a graduated circular 
index, and a magnet coil for magnetizing the bar to be tested. He finds 
that the following laws hold with every variety of iron and steel: 

1. The magnetic capacity is directly proportional to the softness, or 
molecular freedom. 

2. The resistance to a feeble external magnetizing force is directly as 
the hardness, or molecular rigidity. 

The magnetic balance shows that annealing not only produces softness 
in iron, and consequent molecular freedom, but it entirely frees it from 
all strains previously introduced by drawing or hammering. Thus a bar 
of iron drawn or hammered has a peculiar structure, say a fibrous one, 
which gives a greater mechanical strength in one direction than another. 
This bar, if thoroughly annealed at high temperatures, becomes homo- 
geneous in all directions, and has no longer even traces of its previous 
strains, provided that there has been no actual separation into a distinct 
series of fibers. 

TREATMENT OF STRUCTURAL STEEL. 
(James Christie, Trans. A. S. C E., 1893.) 

Effect of Punching and Shearing. — The physical effects of punching 
and shearing as denoted by tensile test are for iron or steel: 

Reduction of ductility; elevation of tensile strength at elastic limit; 
reduction of ultimate tensile strength. 

In very thin material the disturbance described is less than in thick; 



484 STEEL. 

in fact, a degree of thinness is reached where this disturbance practi- 
cally ceases. On the contrary, as thickness is increased the injury becomes 
more evident. 

The effects described do not invariably ensue; for unknown reasons there 
are sometimes marked deviations from what seems to be a general result. 

By thoroughly annealing sheared or punched steels the ductility is to a 
large extent restored and the exaggerated elastic limit reduced, the change 
being modified by the temperature of reheating and the method of cooling. 

It is probable that the best results combined with least expenditure can 
be obtained by punching all holes where vital strains are not transferred by 
the rivets, and by reaming for important joints where strains on riveted 
joints are vital, or wherever perforation may reduce sections to a mini- 
mum. The reaming should be sufficient to thoroughly remove the mate- 
rial disturbed by punching; to accomplish this it is best to enlarge punched 
holes at least 1/8 in. diameter with the reamer. 

Riveting. — It is the current practice to perforate holes Vi6 in. larger 
than the rivet diameter. For work to be reamed it is also a usual require- 
ment to punch the holes from l/s to S/iq in. less than the finished diameter, 
the holes being reamed to the proper size after the various parts are 
assembled. 

It is also excellent practice to remove the sharp corner at both ends of 
the reamed holes, so that a fillet will be formed at the junction of the body 
and head of the finished rivets. 

The rivets of either iron or mild steel should be heated to a bright red or 
yellow heat and subjected to a pressure of not less than 50 tons per square 
inch of sectional area. 

For rivets of ordinary length this pressure has been found sufficient to 
completely fill the hole. If, however, the holes and the rivets are excep- 
tionally long, a greater pressure and a slower movement of the closing tool 
than is used for shorter rivets has been found advantageous. 

Welding. — No welding should be allowed on any steel that enters into 
structures. [See page 487.] 

Upsetting. — Enlarged ends on tension bars for screw-threads, eye- 
bars, etc., are formed by upsetting the material. With proper treatment 
and a sufficient increment of enlarged sectional area over the body of 
the bar the result is entirely satisfactory. The upsetting process should 
be performed so that the properly heated metal is compelled to flow 
without folding or lapping. 

Annealing. — The object of annealing structural steel is for the pur- 
pose of securing homogeneity of structure that is supposed to be impaired 
by unequal heating, or by the manipulation necessarily attendant on 
certain processes. The objects to be annealed should be heated through- 
out to a uniform temperature and uniformly cooled. 

The physical effects of annealing, as indicated by tensile tests, depend 
on the grade of steel, or the amount of hardening elements associated with 
it; also on the temperature to which the steel is raised, and the method 
or rate of cooling the heated material. 

The physical effects of annealing medium-grade steel, as indicated by 
tensile test, are reported very differently by different observers, some 
claiming directly opposite results from others. It is evident, when all the 
attendant conditions are considered, that the obtained results must vary 
both in kind and degree. 

The temperatures employed will vary from 1000° to 1500° F. In 
some cases the heated steel is withdrawn at full temperature from the 
furnace and allowed to cool in the atmosphere; in others the mass is 
removed from the furnace, but covered under a muffle, to lessen the free 
radiation; or, again, the charge is retained in the furnace, and the whole 
mass cooled with the furnace, and more slowly than by either of the other 
methods. 

The best general results from annealing will probably be obtained by 
Introducing the material into a uniformly heated oven in which the tem- 
perature is not so high as to cause a possibility of cracking by sudden and 
unequal changing of temperature, then gradually raising the temperature 
of the material until it is uniformly about 1200° F., then withdrawing the 
material after the temperature is somewhat reduced and cooling under 
shelter of a muffle sufficiently to prevent too free and unequal cooling on 
the one hand or excessively slow cooling on the other. 

G. G. Mehrtens, Trans. A, S. C, E„ 1893, says: "Annealing is of advan- 



MISCELLANEOUS NOTES ON STEEL. 485 

tage to all steel above 64,000 lbs. strength per square inch, but it is ques- 
tionable whether it is necessary in softer steels. The distortions due to 
heating cause trouble in subsequent straightening, especially of thin plates. 
*'In a general way all unannealed mild steel for a strength of 56,000 to 
64,000 lbs. may be worked in the same way as wrought iron. Rough 
treatment or working at a blue heat must, however, be prohibited. Shear- 
ing is to be avoided, except to prepare rough plates, which should after- 
wards be smoothed by machine tools or files before using. Drifting is also 
to be avoided, because the edges of the holes are thereby strained beyond 
the yield-point. Reaming drilled holes is not necessary, particularly 
when sharp drills are used and neat work is done. A slight counter- 
sinking of the edges of drilled holes is all that is necessary. Working the 
material while heated should be avoided as far as possible, and the 
engineer should bear this in mind when designing structures. Upsetting, 
cranking, and bending ought to be avoided, but when necessary the 
material should be annealed after completion. 

** The riveting of a mild-steel rivet should be finished as quickly as pos- 
sible, before it cools to the dangerous heat. For this reason machme work 
is the best. There is a special advantage in machine work from the fact 
that the pressure can be retained upon the rivet until it has cooled suffi- 
ciently to prevent elongation and the consequent loosening of the rivet." 

Punching and Drilling of Steel Plates. {Proc. Inst. M. E., Aug., 
1887, p. 326.} — In Prof. Unwin's report the results of the greater number 
of the expenments made on iron and steel p'ates lead to the general con- 
clusion that while thin plates, even of steel, do not suffer very much from 
Sunching, yet in those of 1/2 in. thickness and upwards the loss of tenacity 
ue to punching ranges from 10% to 23% in iron plates and from 11% to 
33% In the case of mild steel. 

MISCELLANEOUS NOTES ON STEEL. 

May Carbon be Burned Out of Steel ? — Experiments made at the 
Laboratory of the Penna. Railroad Co. (Specifications for Springs, 1888) 
with the steel of spiral springs, show that the place from which the borings 
are taken for analysis has a very important influence on the amount of 
carbon found. If^the sample is a piece of the round bar, and the borings 
are taken from the end of this piece, the carbon is always higher than if the 
borings are taken from the side of the piece. It is common to find a 
difference of 0.10% between the center and side of the bar, and in some 
cases tbe difference is as high as 0.23%. Apparently during the process 
of reducing the metal from the ingots to the round bar, with successive 
heatings, the carbon in the outside of the bar is burned out. 

Effect of Nicking a Steel Bar. — The statement is sometimes made 
that, owing to the homogeneity of steel, a bar with a surface crack or nick 
in one of its edges is liable to fail by the gradual spreading of the nick, and 
thus break under a very much smaller load than a sound bar. With iron 
it is contended this does not occur, as this metal has a fibrous structure. 
Sir Benjamin Baker has, however, shown that this theory, at least so far 
as statical stress is concerned, is opposed to the facts, as he purposely 
made nicks in specimens of the mild steel used at the Forth Bridge, but 
found that the tensile strength of the whole was thus reduced by only 
about one ton per square inch of section. In an experiment by the Union 
Bridge Company a full-sized steel counter-bar, with a screw-turned 
buckle connection, was tested under a heavy statical stress, and at the 
same time a weight weighing 1040 lbs. was allowed to drop on it from 
various heights. The bar was first broken by ordinary statical strain, 
and showed a breaking stress of 66,800 lbs. per square inch. The longer 
of the broken parts was then placed in the machine and put under the 
following loads, whilst a weight, as already mentioned, was dropped on it 
from various heights at a distance of five feet from the sleeve-nut of the 
turn-buckle, as shown below: 

Stress in pounds per sq. in 50,000 55,000 60,000 63,000 65,000 

ft. in. ft. in. ft. in. ft. in. ft. in. 
The weight was then shifted so as to fall directly on the sleeve-nut, and 
the test proceeded as follows: 

Stress on specimen in lbs. per square inch 65,350 65,350 68,800 

Height of fall, feet 3 6 6 



486 STEEL. 

It will be seen that under this trial the bar carried more than when 
originally tested statically, showing that the nicking of the bar by screw- 
ing had not appreciably weakened its power of resisting shocks. — Eng'g 
News. 

Specific Gravity of Soft Steel. (W. Kent, Trans. A. I. M. E., xiv, 
585.) — Five specimens of boiler-plate of C 0.14, P 0.03 gave an average 
sp. gr. of 7.932, maximum variation 0.008. The pieces w^ere first planed 
to remove all possible scale indentations, then filed smooth, then cleaned 
in dilute sulphuric acid, and then boiled in distilled water, to remove ail 
traces of air from the surface. 

The figures of specific gravity thus obtained by careful experiment on 
bright, smooth pieces of steel are, however, too high for use in determining 
the weights of rolled plates for commercial purposes. The actual average 
thickness of these plates is always a little less than is shown by the calipers, 
on account of the oxide of iron on the surface, and because the surface is 
not perfectly smooth and regular. A number of experiments on com- 
mercial plates, and comparison of other authorities^ led to the figure 
7.854 as the average specific gravity of open-hearth boiler-plate steel. 
This figure is easily^ remembered as being the same figure with change of 
position of the decimal point (.7854) which expresses the relation of the 
area of a circle to that of its circumscribed square. Taking the weight 
of a cubic foot of water at 62° F. as 62.36 lbs. (average of several authori- 
ties), this figure gives 489.775 lbs. as the weight of a cubic foot of steel, 
or the even figure, 490 lbs., may be taken as a convenient figure, and 
accurate within the limits of the error of observation. 

A common method of approximating the weight of iron plates is to con- 
eider them to weigh 40 lbs. per square foot one inch thicK. Taking this 
weight and adding 2% gives almost exactly the weight of steel boiler- 
plate given above (40 X 12 X 1.02 = 489.6 lbs. per cubic foot). 

Occasional Failures of Bessemer Steel. — G. H. Clapp and A. 
E. Hunt, in their paper on " The Inspection of Materials of Construction in 
the United States " {Trans. A. I. M. E., vol. xix), say: Numerous instances 
could be cited to show the unreliability of Bessemer steel for structural 
purposes. One of the most marked, however, was the following: A 
12-in. I-beam weighing 30 lbs. to the foot, 20 feet long, on being unloaded 
from a car broke in two about 6 feet from one end. 

The analyses and tensile tests qiade do not show any cause for the failure. 

The cold and cjuench bending tests of both the original 3/4-in. round test- 
pieces, and of pieces cut from the finished material, gave satisfactory re- 
sults; the cold-bending tests closing down on themselves without sign of 
fracture. 

Numerous other cases of angles and plates that were so hard in places as 
to break off short in punching, or, what was worse, to break the punches, 
have come under our observation, and although makers of Bessemer steel 
claim that this is just as likely to occur in open-hearth as in Bessemer steel, 
we have as yet never seen an instance of failure of this kind in open- 
hearth steel having a composition such as C 0.25%, Mn 0.70%, P 0.08%. 

J. W. Wailes, in a paper read before the Chemical Section of the British 
Association for the Advancement of Science, in speaking of mysterious 
failures of steel, states that investigation shows that *' these failures occur 
in steel of one class, viz., soft steel made by the Bessemer process." 

Dangerous Low Carbon Steel. — A remarkable failure of ship-plate 
steel is described in Jour. A. S. M. E., Jan., 1915 (from Trans. North 
East Coast Institution of Engineers and Shipbuilders). In punching 
the plates several of them cracked, and on riveting many of them 
cracked between the rivets; they also cracked on being struck with 
an ordinary hammer. The plates had passed all the usual chemical 
and physical tests of Lloyd's. A chemical analysis gave C. 0.05; Si. 
0.08; Mn. 0.86; S. 0.08; P. 0.06. A micrographic examination showed 
numerous dove-gray areas of sulphide of manganese. Alternating 
stress tests on bars 3/8 in. diameter, bent 3 /§ in. each way at 3 in. 
from the plane of maximum stress, gave only 100 alternations of stress 
before fracture, as compared with 300 for good steel. Prof. J. O. 
Arnold, of Sheffield, says the material appears to have been overheated 
m manufacturing the plates from the slab ingots, and that slow cooling 
from a high temperature after rolling, the plates being stacked in piles 
to cool, would make crystallization more perfect and hence more 
dangerous. 



MISCELLANEOUS NOTES ON STEEL. d87 

Segregation in Steel Ingots. (A. Pourcel, Trans. A.J. M. E., 1893.) 
— H. M. Howe, in his " Metallurgy of Steel," gives a resume of observations, 
with the results of numerous analyses, bearing upon the phenomena or 
segregation. . . , , 

A test-piece taken 24 inches from the head of an mgot 7.5 feet in length 
gave by analysis very different results from those of a test-piece taken 
30 inches from the bottom. ^ ^ ^. ^ ^ 

C. Mn. Si. S. P. 

Top 0.92 0.535 0.043 0.161 0.261 

Bottom 0.37 0.498 0.006 0.025 0.096 

Segregation is less marked in ingots of extra-soft metal cast in cast-iron 
molds of considerable thickness. It is, however, still important, and ex- 
plains the difference often shown by the results of tests on pieces taken 
from different portions of a plate. Two samples, taken from the sound 
part of a flat ingot, one on the outside and the other in the center, 7.9 
inches from the upper edge, gave: 

Center 0.14 0.053 0.072 0.576 

Exterior 0.11 0.036 0.027 0.610 

Manganese is the element most uniformly disseminated in hard or soft 
steel. 

For cannon of large caliber, if we reject, in addition to the part cast in 
sand and called the masselotte (sinking-head), one-third of the upper part 
of the ingot, we can obtain a tube practically homogeneous in composition, 
because the central part is naturally removed by the boring of the tube. 
With extra-soft steels, destined for ship- or boiler-plates, the solution for 
practically perfect homogeneity lies in the obtaining of a metal more 
closely deserving its name of extra-soft metal. 

The injurious consequences of segregation must be suppressed by redu- 
cing, as far as possible, the elements subject to liquation. 

Segregation in Steel Plates. (C. L. Huston, Proc. A. S. T. M., vi, 182.) 

A plate 370 X 76 X s/ie in. was rolled from a 16 X 18-in. ingot, weighing 
2800 lbs., the ladle test of which showed 0.18 C. Test pieces from the 
plate gave the Allowing: 
Top of Ingot: 

Tensile Strength 56,730 67,420 67,050 66,980 56,440 

Carbon 0.13 0.25 0.27 0.25 0.13 

Bottom of Ingot: 

Tensile Strength 56,120 

Carbon 0.13 

1 

Columns 1 and 5, edge of plate; 3, middle; 2 and 4, half way between 
middle and edge. 

Other tests of low-carbon steel showed a lower degree of segregation. 
A plate from an ingot of 0.23 C gave minimum 0.18 C T. S., 64,580: 
maximum 0.38 C, T. S., 70,340. One from an ingot of 0.26 C gave 
maximum 0.20 C, T. S., 59,600; maximum 0.50 C, T. S., 78,600. (See 
also paper on this subject by H. M. Howe in vol. vii, p. 75.) 

Endurance of Steel under Repeated Alternate Stresses. (J. E. 
Howard, A. S. T .M., 1907, p. 252.) — Small bars were rapidly rotated in a 
machine while being subjected to a transverse strain. Two steels gave 
results as follows: (1) 0.55 C, T. S., 111,200; E. L., 59,000; Elong., 12%; 
Red. of area, 33.57o. (2) 0.82 C, T. S., 142,000; E. L., 64,000; Elong., 
7%; Red. of area, 11.8%. 



57,720 


58,400 


58,140 


56,900 


0.13 


0.16 


0.16 


0.14 


2 


3 


4 


5 



Fiber stress 

No. of rotations be- 
fore rupture. 



60.0001 50.000 

(1) 12.490 33.160 

(2) 37.2501 213.150 



45.000 
166,240 
605.640 



40.000 

455.000 

202.000.000 



35.000 I 30.000 
900.000 176.326.240 
Not broken. 



Welding of Steel. — H. H. Campbell (Manuf. of Iron and Steel, 
p. 402) had numerous bars of steel welded by different skilled blacksmiths. 
The record of results, he says, "is extremely unsatisfactory." The 
worst weld by each of four workmen showed respectively 70, 54, 58, and 
44% of the strength of the original bar. Forging steel showed one weld 
with only 48%, common soft steel 44%, and pure basic steel 59%. In 
a series of tests by the Royal Prussian Testing Institute, the average 
strength of welded bars of medium steel was 58% of the natural, the 
poorest bar showing only 23%. In softer steel the average was 71%, 



488 STEEL. 

and the poorest 33 %, while in puddled iron the average was 81 % and the 
poorest 62 'r. Mr. Campbell concludes: " A weld as performed by 
ordinary blacksmiths, whether on iron or steel, is not nearly as good as 
the rest of the bar; and it is stiU more certain that welds of large rods of 
common forging steel are unreliable and should not be employed In 
structural work. Electric methods do not offer a solution of the problem, 
for the metal is heated beyond the critical temperature of crystallization, 
and only by heavy reductions under the hammer or press can much b© 
done towards restoring the ductility of the piece." 

Welding of Steel.— A. E. Hunt (A. I. M. E., 1892) says: "I have never 
seen so-called ' welded * pieces of steel pulled apart in a testing-machine 
or otherwise broken at the joint which have not shown a smooth cleavage 
plane, as it were, such as in iron would be condemned as an imperfect 
weld. My experience in this matter leads me to agree with the position 
taken by Mr. William Metcalf in his paper upon Steel (Trans. A.S.C.B.. 
vol. xvi, p. 301). Mr. Metcalf says, 'I do not believe steel can be welded 

The Thermit Welding Process. (Goldschmidt Thermit Co., New 
York.)— When powdered or finely divided aluminum is mixed with a 
metalUc oxide and ignited, the aluminum burns with great rapidity and 
intense heat, reducing the oxide to a metal and fusing it. It is said that 
iron oxide and aluminum will make a temperature of 5400° F., producing 
fused iron which will melt any iron or steel with which it comes in con- 
tact. The process is largely used for repairing breaks of large castings 
or forgings, such as the stern post of a steamship, a locomotive frame, 
etc. In the operation of welding a large fractured piece, the fracture 
is drilled out with a series of 3/4-in. holes close together, making a clear 
opening. A mold of fire-clay and sand is then made to fit all around 
the fracture, leaving a collar or ring surrounding it, baked in a furnace 
and then placed in position. The fractured section is then heated by a 
blow-torch inserted in the riser of the mold. A conical sheet iron cru- 
cible, lined with magnesia tar, is then inserted in the riser, and thermit 
(the mixture of aluminum and oxide of iron) poured into it. An ignition 
powder is placed on top of the thermit, and lighted with a storm match. 
The mixture begins to burn with great agitation; when this ceases the 
crucible is tapped, and white-hot fused iron or steel runs into the mold 
and thoroughly fuses with the pieces to be joined. 

Oxy-acetylene Welding and Cutting of 31etals. — Autogenous 
Welding. — By means of acetylene gas and oxygen, stored in tanks 
under pressure, and a properly constructed nozzle or torch in which the 
two gases are united and fired, an intense temperature said to be 6000° F., 
is generated, and it may be used to weld or fuse together iron, steel, alumi- 
num, brass, copper, or other metals. The process of uniting metals by heat 
without using either flux or compression is caUed autogenous welding. 
The oxy-acetylene torch may also be used for cutting metals, such as 
steel plates, beams and large forgings, and for repairing flaws or defects, 
or fiUing cavities by melting a strip of metal and flowing it into place. 
The apparatus, with instruction in its use, is furnished by the Davia- 
BournonviUe Co., Jersey City, N. J. 

Electric Welding. — For description see Electrical Engineering. 

Hydraulic Forging. — In the production of heavy forgings from 
cast ingots of mild steel it is essential that the mass of metal should be 
operated on as equally as possible throughout its entire thickness. When 
employing a steam-hammer for this purpose it has been found that the ex- 
ternal surface of the ingot absorbs a large proportion of the sudden impact 
of the blow, and that a comparatively small effect only is produced on the 
central portions of the ingot, owing to the resistance offered by the inertia 
of the mass to the rapid motion of the falling hammer — a disadvantage 
that is entirely overcome by the slow, though powerful, compression of the 
hydraulic forging-press, which appears destined to supersede the steam- 
hammer for the production of massive steel forgings. 

Fluid-compressed Steel by the ** Whitworth Process." (Proc. 
Inst. M. E., May, 1887, p. 167.) — In this system a graduaUy increasing 
pressure up to 6 or 8 tons per square inch is applied to the fluid ingot, and 
within half an hour or less after the application of the pressure the column 
of fluid steel is shortened 1 1/2 inches per foot or one-eighth of its length; the 
pressure is then kept on for several hours, the result being that the metal 
is compressed into a perfectly solid and homogeneous material free from 
blow holes. 



STEEL CASTINGS. 48& 

In large gun-ring ingots during cooling the carbon is driven to the center, 
the center containing 0.8 carbon and the outer ring 0.3. The center ig 
bored out until a test shows that the inside of the ring contains the same 
percentage of carbon as the outside. 

Fluid-compressed steel is made by the Bethlehem Steel Co. for gun and 
other heavy forgings. 

Putting suflScient pressure upon the outside of the ingot when the walls 
are solid but the interior is still liquid will prevent the formation of a 
pipe. In Whitworth's system the ingot is raised and compressed length- 
wise against a solid ram situated above it, during and shortly after sohdifi- 
cation. In Harmet's method the ingot is forced upward during solidifi- 
cation into its tapered mold. This causes a large radial pressure on its 
sides. In Lilienberg's method the ingots are stripped and then run on 
their cars between a solid and movable wall. The movable wall is then 
pressed against one side of the ingots. (Stoughton's Metallurgy of Iron 
and Steel.) 

For other methods of compressing ingots see paper by A. J. Capron ia 
Jour. I, & S. /.. 1906, Iron Tr, Rev., May 24, 1906. 

STEEL CASTINGS. 

(E. S. Cramp, Proc. Eng'g Congress, Dept. of Marine Eng'g, Chicago, 1893.) 

In 1891 American steel-founders had successfully produced a consider- 
able variety of heavy and difficult castings, of which the following are the 
most noteworthy specimens: 

Bed-plates up to 24,000 lbs.; stern-posts up to 54,000 lbs.; stems up to 
21,000 lbs.; hydraulic cylinders up to 11,000 lbs.; shaft-struts up to 32,000 
lbs.; hawse-pipes up to 7500 lbs.; stern-pipes up to 8000 lbs. 

The percentage of success in these classes of casiings since 1890 has 
ranged from 65% in the more difficult forms to 907o in the simpler ones; 
the tensile strength has been from 62,000 to 78,000 lbs., elongation from 
15% to 25%,. 

The first steel castings of which anything is generally known were 
crossing-frogs made for the Philadelphia & Reading R. R. in July, 1867, by 
the William Butcher Steel Works, now the Midvale Steel Co. The molds 
were made of a mixture of ground fire-brick, black-lead crucible-pots 
ground fine, and fire-clay, and washed with a black-lead wash. The steel 
was melted in crucibles, and was about as hard as tool steel. The surface 
of these castings was very smooth, but the interior was very much honey- 
combed. This was before the days when the use of silicon was known for 
solidifying steel. The sponginess, which was almost universal, was a great 
obstacle to their general adoption. 

The next step was to leave the ground pots out of the molding mixture 
and to wash the mold with finely ground fire-brick. This was a great im- 
provement, especially in very heavy castings; but this mixture still clung so 
stronglj^ to the casting that only comparatively simple shapes could be 
made with certainty. A mold made of such a mixture became almost as 
hard as fire-brick, and was such an obstacle to the proper shrinkage of 
castings that, when at all complicated in shape, they had so great a 
tendency to crack as to make their successful manufacture almost impos- 
sible. By this time the use of silicon had been discovered, and the only 
obstacle in the way of making good castings was a suitable molding 
mixture. This was ultimately found in mixtures having the various kinds 
of silica sand as the principal constituent. 

One of the most fertile sources of defects in castings is a bad design. 
Very intricate shapes can be cast successfully if they are so designed as to 
cool uniformly. Mr. Cramp says while he is not yet prepared to state that 
anything that can be cast successfully in iron can be cast in steel, indica- 
tions seem to point that way in all cases where it is possible to put on suit- 
able sinking-heads for feeding the casting. 

H. L. Gantt {Trans. A. S. M, £"., xii, 710) says: Steel castings not only 
shrink much more than iron ones, but with less regularity. The amount of 
shrinkage varies with the composition and the heat of the metal; the hotter 
the metal the greater the shrinkage; and, as we get smoother castings from 
hot metal, it is better to make allowance for large shrinkage and pour the 
metal as hot as possible. Allow 3/i6 or 1/4 in. per ft. in length for shrinkage, 
and 1/4 in. for finish on machined surfaces, except such as are cast "up. 
Cope surfaces which are to be machined should, in large or hard castings, 
haveanallowanceoffrom%to3^in. for finish, as a large mass of metal 



490 STEEL. 

slowly rising in a mold is apt to beccrne crusty on the surface, and such a 
crust is sure to be full of imperfections. On small, soft castings i/g in. on 
drag side and 1/4 in. on cope side will be sufiRcient. No core should have 
less than 1/4 in. finish on aside and very large ones should have as much as 
1/2 in. on a side. Blow-holes can be entirely prevented in castings by the 
addition of manganese and silicon in sufficient quantities: but both of 
these cause brittleness, and it is the object of the conscientious steel- 
maker to put no more manganese and silicon in his steel than is just suffi- 
cient to make it solid. The best results are arrived at when all portions of 
the castings are of a uniform thickness, or very neariy so. 

The following table will illustrate the effect of annealing on tensile 
strength and elongation of steel castings: 





Tensile Strength. 


Elongation. 


Carbon. 


Unannealed. 


Annealed. 


Unannealed. 


Annealed. 


0.23% 

0.37 

0.53 


68.738 
85.540 
90.121 


67.210 22.40% 
82.228 8.20 
106.415 ; 2.35 


31.40% 

21.80% 

9.80 



The proper annealing of large castings takes nearly a week. 

The proper steel for roll pinions, hammer dies, etc., seems to be that 
containing about 0.60 % of carbon. Such castings, properly annealed, have 
worn well and seldom broken. IMiscellaneous gearing should contain 
carbon 0.40% to 0.60%, gears larger in diameter being softest. General 
machinery castings should, as a rule, contain less than 0.40% of carbon, 
those exposed to great shocks containing as low as 0.20% of carbon. Such 
castings will give a tensile strength of from 60,000 to 80,000 lbs. per sq. 
in. and at least 15% extension in 2 in. Machinery and hull castings for 
war-vessels for the United States Navy, as well as carriages for naval 
guns, contain from 0.20% to 0.30% of carbon. 

For description of methods of manufacture of steel castings by the Besse- 
mer, open-hearth, and crucible processes, see paper by P. G, Salom, Trans^ 
A. I. M, E., xiv. 118. 

CRUCIBLE STEEL. 

Selection of Grades by the Eye, and Effect of Heat Treatment. 

(J. W. Langley, Amer. Chemist, Nov., 1876.) — In the early days of steel 
making the grades were determined by inspection of the fractured surfaces 
of the cast ingots. The method of selection is described as follows: 

The steel when thoroughly fluid is poured into cast-iron molds, and 
when cold the top of the ingot is broken off, exposing a freshly fractured 
surface. The appearance presented is that of confused groups of crystals, 
all appearing to have started from the outside and to have met in the 
center; this general form is common to all ingots of whatever composition, 
but to the trained eye, and only to one long and critically exercised, a 
minute but indescribable difference is perceived between varying samples 
of steel, and this difference is now known to be owing almost wholly to 
variations in the amount of combined carbon, as the following table wilt 
show. Twelve samples selected by the eye alone, and analyses of drillings 
taken direct from the ingot before it had been heated or hammered, gave 
results as below: 

Ingot Nos. 1 2 3456789 10 11 12 

C 0.302 .490 .529 .649 .801 .841 .867 .871 .955 1.005 1.058 1.079 

Diff. of C 0.188 .039 .120 .152 .040 .026 .004 .084 .050 .053 .021 

The C is seen to increase in quantity in the order of the numbers. The 
other elements, with the exception of total iron, bear no relation to the 
number on the samples. The mean difference of Cis 0.071. 

In mild steels the discrimination is less perfect. 

The appearance of the fracture by which the above twelve selections 
were made can only be seen in the cold ingot before any operation, except 
the original one of casting, has been performed upon it. As soon as it is 
hammered, the structure changes, .so that all trace of the primitive con- 
dition appears to be lost. 

The specific gravity of steel is Influenced not only by its chemical analy- 
sis but by the heat to which it is subjected. 
The sp. gr. of the ingots in the above list ranged from 7.855 for No. 1 



CRUCIBLE STEEL. 491 

down to 7.803 for No. 12. Rolling into bars produced a very slight dif- 
ference, — 0.005 in Nos. 5 and 6 and +0.020 in No. 12, but overheating 
reduced the sp. gr. of the bar 0.023 in No. 3 to 0.135 in No. 12, the sp. gr. of 
the burnt sample of No. 12 being only 7.690. 

Effect of Heat on the Grain of Steel. (W. Metcalf, — Jeans on 
Steel, p. 642.) — A simple experiment will show the alteration produced 
in a high-carbon steel by different methods of hardening. If a bar of such 
steel be nicked at about 9 or 10 places, and about half an inch apart, a 
suitable specimen is obtained for the experiment. Place one end of the 
bar in a good fire, so that the first nicked piece is heated to whiteness, 
while the rest of the bar, being out of the fire, is heated up less and less 
as we approach the other end. As soon as the first piece is at a good 
white heat, which of course burns a high-carbon steel, and the temperature 
of the rest of the bar gradually passes down to a very dull red, the metal 
should be taken out of the fire and suddenly plunged in cold water, in 
which it should be left till quite cold. It should then be taken out and 
carefully dried. An examination with a file will show that the first piece 
has the greatest hardness, while the last piece is the softest, the inter- 
mediate pieces gradually passing from one condition to the other. On 
now breaking off the pieces at each nick it will be seen that very consider- 
able and characteristic changes have been produced in the appearance of 
the metal. The first burnt piece is very open or crystalline in fracture; 
the succeeding pieces become closer and closer in the grain until one piece 
is found to possess that perfectly even grain and velvet-like appearance 
which is so much prized by experienced steel users. The first pieces also, 
which have been too much hardened, will probably be cracked; those at 
the other end will not be hardened through. Hence if it be desired to 
make the steel hard and strong, the temperature used must be high 
enough to harden the metal through, but not sufficient to open the grain. 

Heating Tool Steel. (Crescent Steel Co., Pittsburg, Pa.) — There are 
three distinct stages or times of heating: First, for forging; second, for 
hardening; third, for tempering. 

The first requisite for a good heat for forging is a clean fire and plenty of 
fuel, so that jets of hot air will not strike the corners of the piece; next, 
the fire should be regular, and give a good uniform heat to the whole part 
to be forged. It should be keen enough to heat. the piece as rapidly as 
may be, and allow it to be thoroughly heated through, without being 
so fierce as to overheat the corners. Steel should not be left in the fire 
any longer than is necessary to heat it clear through, as "soaking" in 
fire is injurious; on the other hand, it is necessary that it should be hot 
through, to prevent surface cracks. By observing these precautions a 
piece of steel maj^ always be heated safely, up to even a bright yellow 
heat, when there is much forging to be done on it. 

The best and most economical of welding fluxes is clean, crude borax, 
which should be first thoroughly melted and then ground to fine powder. 

After the steel is properly heated, it should be forged to shape as quickly 
as possible; and just as the red heat is leaving the parts intended for cutting 
edges, these parts should be refined by rapid, light blows, continued until 
the red disappears. 

For the second stage of heating, for hardening, great care should be used: 
first, to protect the cutting edges and working parts from heating more 
rapidly than the body of the piece; next, that the whole part to be hardened 
be heated uniformly through, without any part becoming visibly hotter 
than the other. A uniform heat, as low as will give the required hardness, 
is the best for hardening. 

For everjr variation of heat which is great enough to be seen there will 
result a variation in grain, which may be seen by breaking the piece; and 
for every such variation in temperature there is a very good chance for a 
crack to be seen. Many a costly tool is ruined by inattention to this point. 

The effect of too high heat is to open the grain; to make the steel coarse. 
The effect of an irregular heat is to cause irregular grain, irregular strains, 
and cracks. 

As soon as the piece is properly heated for hardening, it should be 
promptly and thoroughly quenched in plenty of the cooling medium, water, 
brine, or oil, as the case may be. An abundance of cooling bath, to do 
the work quickly and uniformly all over, is necessary to good and safe 
work. 

To harden a large piece safely a running stream should be used. 

Much uneven hardening is caused by the use of too small baths. 



492 STEEL. 

For the third stage of heating, to temper, the first important requisite is 
again uniformity. The next is time; the more slowly a piece is Drought 
down to its temper, the better and safer is the operation. 

When expensive tools are to be made it is a wise precaution to try small 

Eieces of the steel at different temperatures, so as to find out how low a 
eat will dve the necessary hardness. The lowest heat is the best for any 
steel. [This is true of carbon steel but not of " high speed " alloy steels.] 

Heating in a Lead Bath. — A good method of heating steel to a 
uniform temperature is by means of a bath of lead kept at a red heat by 
a gas furnace. See Heat Treatment by the Taylor-White Process, under 
Machine Shop. 

Heating Steel in 3Ielted Salts by Electric Current. — L. M. Cohn 
(Eledrof. Z., Aug., 1906, Mach'y, Dec, 1906) describes a furnace pat- 
ented bv Gebr. Korting, Berlin, in which steel may be heated uniformly 
to any desired temperature up to 1300° C. (2372° F.) without danger of 
oxidizing. 

The furnace consists mainly of a cast-iron box, lined inside with fire- 
clay, a second lining of fire-bricks, lined again with asbestos, and 
inclosing the crucible made of one piece of fireproof material. Two 
electrodes lead into the crucible, through which alternating current is 
sent. The crucible is filled with metal salts. For temperatures above 
1000° C. pure chloride of barium is used, the melting-point of which is 
at about 950° C. (1742 F.) : for lower temperatures a mixture of chloride 
of barium and chloride of potassium, 2 to 1, is used, melting at about 
G70° C. (123S F.). Any other suitable salts may be used. A regulating 
transformer regulates the current, and thus also the temperature. 

A test was made with a furnace, the bath of which was 61 /2 X 61 /2 X 7 
in. A 50-period alternating current of 190- volt primary tension was 
used. This tension had to be reduced to from 50 to 55 volts by the 
regulating transformer for starting the furnace, and lowered later on. 
The heating lasted about half an hour. For temperatures from 750 to 
1300° C, the secondary tension amounted to from 13 to 18 volts. The 
consumption of energy was as follows: 880° C 5.4 Kw.; 1140° C, 8.5 
Kw.; 1300° C, 12.25 Kw. A milling cutter 5 in. diam., li/4in. bore, 1 in. 
thick, was heated in 62 seconds to 1300° C. A bushing of tool steel 23 4 
in. diam., 23/4 in. long, 5/8 m. bore, was heated in 243 seconds to 850°C. 

Heating to Forge. (Crescent Steel Co.) — The trouble in the forge 
fire is usually uneven heat, and not too high heat. Suppose the piece to 
be forged has been put into a very hot fire, and forced as quickly as possible 
to a high yellow heat, so that it is almost up to the scintillating point. If 
this be done, in a few minutes the outside will be quite soft and in a nice 
condition for forging, while the middle parts will not be more than red-hot. 
Now let the piece be placed under the hammer and forged, and the soft 
outside \\ill yield so much more readily than the hard inside, that the 
outer particles will be torn asunder, while the inside will remain sound. 

Suppose the case to be reversed and the inside to be much hotter than the 
outside; that is, that the inside shall be in a state of semi-fusion, while the 
outside is hard and firm. Now let the piece be forged, and the outside will 
be all sound and the whole piece will appear perfectly good until it is 
cropped, and then it is found to be hollow inside. 

In either case, if the piece had been heated soft all through, or if it had 
been only red-hot all through, it would have forged perfectly sound. 

In some cases a high heat is more desirable to save heavy labor, but in 
every case where a fine steel is to be used for cutting purposes it must be 
borne in mind that very heavy forging refines the bars as they slowly cool, 
and if the smith heats such refined bars until they are soft, he raises the 
grain, makes them coarse, and he cannot get them fine again unless he has 
a very heavy steam-hammer at command and knows how to use it well. 

Annealing. (Crescent Steel Co.) — Annealing or softening is accom- 
plished by heating steel to a red heat and then cooling it very slowly, 
to prevent it from getting hard again. 

The higher the degree of heat, the more will steel be softened, until the 
limit of softness is reached, when the steel is melted. 

It does not follow that the higher a piece of steel is heated the softer it 
will be when cooled, no matter how slowly it may be cooled; this is proved 
by the fact that an ingot is always harder than a rolled or hammered t)ar 
made from it. 

Therefore there is nothing gained by heating a piece of steel hotter than 



CRUCIBLE STEEL. 493 

a good, bright, cherry-red; on the contrary, a higher heat has several dis- 
advantages: First. If carried too far, it may leave the steel actually 
harder than a good red heat would leave it. Second. If a scale is raised 
on the steel, this scale will be harsh, granular oxide of iron, and will spoil 
the tools used to cut it. Third. A high scaling heat continued for a little 
time changes the structure of the steel, makes it brittle, liable to crack in 
hardening, and impossible to refine. 

To anneal any piece of steel, heat it red-hot; heat it uniformly and heat it 
through, taking care not to let the ends and corners get too hot. As 
soon as it is hot, take it out of the fire, the sooner the better, and cool it 
as slowly as possible. A good rule for heating is to heat it at so low a red 
that when the piece is cold it will still show the blue gloss of the oxide 
that was put there by the hammer or the rolls. Steel annealed in this 
way will cut very soft; it will harden very hard, without cracking, and 
when tempered it will be strong, nicely refined, and will hold a keen, 
strong edge. 

Tempering. — Tempering steel is the act of giving it, after it has been 
shaped, the hardness necessary for the work it has to do. This is done by 
first hardening the piece, generally a good deal harder than is necessary, 
and then toughening it by slow heating and gradual softening until it is 
just right for work. 

A piece of steel properly tempered should always be finer in grain than 
the bar from which it is made. If it is necessary, in order to make the 
piece as hard as is required, to heat it so hot that after being hardened the 
grain will be as coarse as or coarser than the grain in the original bar, then 
the steel itself is of too low carbon for the desired work. 

If a great degree of hardness is not desired, as in the case of tap? and 
most tools of complicated form, and it is found that at a moderate heat the 
tools are too hard and are liable to crack, the smith should first use a lower 
heat in order to save the tools already made, and then notify the steel- 
maker that his steel is too high, so as to prevent a recurrence of the 
trouble. 

For descriptions of various methods of tempering steel, see "Tempering 
of Metals," by Joshua Rose, in App. Cyc. Mech., vol. ii, p. 863: also, 
" Wrinkles and Recipes," from the Scientific American. In both of these 
works Mr. Rose gives a "color scale," lithographed in colors, by which the 
following is a list of the tools in their order on the color scale, together 
with the approximate color and the temperature at which the color 
appears on brightened steel when heated in the air: 

Scrapers for brass; very pale yellow, Hand-plane irons. 

430° F. Twist-drills. 

Steel-engraving tools. Flat drills for brass. 

SUght turning tools. Wood-boring cutters. 

Hammer faces. Drifts. 

Planer tools for steel. Coopers' tools. 

Ivory-cutting tools. Edging cutters; light purple, 530° F. 

Planer tools for iron. Augers. 

Paper-cutters. Dental and surgical instruments. 

W^ood-engraving tools. Cold chisels for steel. 

Bone-cutting tools. Axes; dark purple^ 550° F. 
Milling-cutters; straw yellow, 460° F. Gimlets. 

Wire-drawing dies. Cold chisels for cast iron. 

Boring-cutters. Saws for bone and ivory. 

Leather-cutting dies. Needles. 

Screw-cutting dies. Firmer-chisels. 

Inserted saw-teeth. Hack-saws. 

Taps. Framing-chisels. 

Rock-drills. Cold chisels for wrought iron. 

Chasers. Molding and planing cutters to be 
Punches and dies. filed. 

Penknives. Circular saws for metal. 

Reamers. Screw-drivers. 

Half-round bits. Springs. 

Planing and molding cutters. Saws for wood. 
Stone-cutting tools; brown yellow. Dark blue, 570° F. 

500^ F. Pale blue. 610°. 

Gouges. Blue, tinged with green, 630°. 



494 



STEEL. 



Uses of Crucible Steel of Different Carbons. (Metcalf on Steel.)—- 
0.50 to 0.60 C, for hot work and tor battering tools. 
0.60 to 0.70 C, ditto, and for tools of dull edge. 
0.70 to 0.80 C, battering tools, cold-sets, and some forms of reamers and 

taps. 
0.80 to 0.90 C, cold-sets, hand-chisels, drills, taps, reamers and dies. 
0.90 to 1.00 C, chisels, drills, dies, axes, knives, etc. 
1.00 to 1.10 C, axes, hatchets, knives, large lathe-tools, and many kinds 

of dies and drills if care be used in tempering them. 
1.10 to 1.50 C, lathe-tools, graving tools, scribers. scrapers, little drills. 

and many similar purposes. 

The best all-around tool steel is found between 0.90 and 1.10 C; steel 
that can be adapted safely and successfully to more uses than any 
other. 

High-speed Tool Steel. (A. L. Valentine. Am. Mach.. July 2. 1908.) — 
Eight brands of high-speed steel were analyzed with the following 
results: 



Steel. 


C. 


W. 


Cr. 


Mn. 


Si. 


Mo. 


P. 


s. 




0.70 
0.25 
0.75 
0.49 
0.65 
0.60 
0.55 
0.66 


14.91 
17.27 
14.83 
17.60 


2.95 
2.69 
2.90 
5.11 


0.01 

Trace 

0.08 






0.013 

0.035 

0.02 

0.01 

0.016 

0.019 


0.008 


b 
c 

d 


0.179 


■'5:i9' 


Trace 
0.01 
0.007 


0.19 


0.039 


9.60 


0.005 


f 


13.00 
17.81 
19.03 


2.88 
2.48 


0.01 


0.11 


0.090 
0.036 






h 




0.015 











W, Wolfram, symbol for tungsten. 

Where blanks appear in the table, the steel was not analyzed for these 
ingredients. 

Many different brands of high-speed steel are being made. Some that 
have been marketed are almost worthless. From some of these steels a 
tool can be made from one end of a bar that is easily forged, machined 
and hardened, while the other end of the bar would resist almost any 
cutting tool and would invariably crack in hardening. Different bars of 
the same make also give very different results. These faults are some- 
times caused by non-uniform annealing in the steels which are sent out as 
thoroughly annealed, and in many cases they are caused by the use of 
impure ingredients. A good high-speed steel will stand a temperature 
as high as 1200° F., or over double that of carbon steel, without losing its 
hardness, and experience has proven that the higher the temperature is 
raised over the white-heat point, the higher a temperature caused by 
friction the tool will withstand, before losing its intense hardness. The 
higher the percentage of carbon is, the more brittle and hard to work the 
steel will be, especially to forge. The steel which has given the best all- 
around results has contained about 0.40 C. The analysis of this same 
steel showed nearly 3% of chromium. The higher the percentage of 
tungsten in the steel, the better has been its cutting qualities. (See Best 
High-Speed Tool Steel, and description of the Taylor-White process of 
heat treatment, under "The Machine-Shop." 

MANGANESE, NICKEL, AJVD OTHER "ALLOY" STEELS. 

Manganese Steel. (H. M. Howe, Trans. A, S, M, E., vol. xii.) — 
Manganese steel is an alloy of iron and manganese, incidentally, and 
probably unavoidably, containing a considerable proportion of carbon. 

The effect of small proportions of manganese on the hardness, strength, 
and ductility of iron is probably slight. The point at which manganese 
begins to have a predominant effect is not known; it may be somewhere 
about 2.5%. 

Manganese steel is very free from blow-holes; it welds with great diffi- 
culty; its toughness is increased by quenching from a yellow heat; its elec- 
tric resistance is enormous, and very constant with changing temperature; 
it is low in thermal conductivity. Its remarkable combination of great 
hardness, which cannot be materially lessened by annealing, and great 
tensile strength, with astonishing toughness and ductility, at once creates 
and limits its usefulness. 



I 



''alloy'' steels. 495 

The hardness of manganese steel seems to be of an anomalous kind. 
The alloy is hard, but under some conditions not rigid. It is very hard in 
its resistance to abrasion; it is not always hard in its resistance to impact. 

Manganese steel forges readily at a yellow heat, though at a bright white 
heat it crumbles under the hammer. But it offers greater resistance to 
deformation, i.e., it is harder when hot, than carbon steel. 

The most important single use for manganese steel is for the pins which 
hold the buckets of elevator dredges. Here abrasion chiefly is to be 
resisted. Another important use is for the links of common chain- 
"elevators. As a material for stamp-shoes, for horse-shoes, for the knuckles 
of an automatic car-coupler, it has not met expectations. 

Manganese steel has been regularly adopted for the blades of the Cyclone 
pulverizer. Some manganese-steel wheels are reported to have run over 
300,000 miles each without turning, on a New England railroad. 

Manganese Steel and its Uses. (E. F. Lake, Am. Mach., May 16, 
1907.) — When more than 2% and less than 6% of Mn is added, with C 
less than 0.5%, it makes steel very brittle, so that it can be powdered 
under a hand hammer. From 6 % Mn up, this brittleness gradually dis- 
appears until 12% is reached, when the former strength returns and 
reaches its maximum at 15 %. After this, a decrease in toughness, but 
not in transverse strength, takes place until 20% is reached, after which 
a rapid decrease in strength again takes place. 

Steel with from 12 to 15 % Mn and less than 0.5% of C is very hard 
and cannot be machined or drilled in the ordinary way ; yet it is so tough 
that it can be twisted and bent into pecuhar shapes without breaking. 
It is malleable enough to be used for rivets that are to be headed cold-. 

This hardness, toughness and malleability make manganese steel the 
most durable metal known, in its ability to resist wear, for such parts 
as the teeth on steam-shovel dippers, where they will outwear about three 
teeth made of the best tool steel; for plow points on road-building work; 
for frogs, switches and crossings in railroad construction; for fluted or 
toothed crushing rolls used on ore, coal and stone crushers; for gears, 
sprockets, link belts, etc., when used in places where they are subjected 
to the grinding wear of gritty particles of dust. 

The higher the percentage of C in the steel, the less percentage of Mn 
will be required to produce brittleness. Si, however, neutralizes the 
injurious tendencies of Mn, and in Europe the Si-Mn alloy is used for 
automobile springs and gears. This steel is not high in Mn and can be 
rolled, while the peculiar properties given to steel by the addition of from 
12 to 15 % of manganese make such steel impossible to roll; therefore all 
parts made of this steel have to be cast, after which it can be forged and 
rendered tougher by quenching from a white heat. 

One of its peculiarities is that it is softened by rapid cooling and can be 
restored to its former hardness by heating to a bright red. 

It is more difficult to mold in the foundry than the ordinary cast steel, 
as it must be poured at a very high temperature, and in cooling it shrinks 
nearly twice as much. The shrinkage allowed for patterns to be cast of 
the ordinary cast steel is s/ig in. per foot, and for manganese-steel cast- 
ings 5/i6 in. per foot. 

This enormous shrinkage makes it impossible to cast in any intricate 
or delicate shapes, and as it is too hard to machine or drill successfully, 
all holes must be cored in the casting. If a close fit is desired in these 
they must be ground out with an emery wheel. These properties limit 
its use to a large extent. * 

The composition that seems to give the best results is: Mn, from 12 
to 15%; C, not over 0.5%; P, not over 0.04% ; S, not over 0.04%. 

Manganese-steel castings should be annealed in order to remove any 
internal strains which may be caused by its high shrinkage and the fact 
that the outer surface cools so much quicker than the core, which leaves 
the center of the casting strained. This can be done by heating to 1500° 
F. and quenching in water, after which it can be hardened by heating to 
900° and allowed to cool slowly. Manganese-steel castings, when 
tested in a 7/8-inch round bar, shoTild show : 

T. S. per sq. in., not less than 140,000 lb.; E. L., not less than 90,000 
lb. ; Red. of area, not less than 50% ; Elong. in 2 in., not less than 20%. 

A new manganese steel containing between 5 and 9 % of manganese, 
with carbon ranging from about 0.7 to about 1.3%, is described in U. S. 
Patent 1,113,539, Oct. 13, 1914, assigned to Taylor- Wharton Iron & 



496 STEEL. 

Steel Co. It is said to possess the characteristic hardness of regular 
manganese steel, while being cheaper. 

Chrome Steel. (F. L. Garrison, Jour. F. I., Sept., 1891.) — Chromium 
increases the hardness of iron, perhaps also the tensile strength and 
elastic limit, but it lessens its weldability. 

Chromium does not appear to give steel the power of becoming harder 
when quenched or cliilled. Howe states that chrome steels forge more 
readily than tungsten steels, and when not containing over 0.5 of chro- 
miiun nearly as well as ordinary carbon s.teelsof hke percentage of carbon.. 
On the whole, the status of chrome steel is not satisfactory. There are 
other steel alloys coming into use, which are so much better that it would 
seem to be only a question of time when it will drop entirely out of the 
race. Howe states that many experienced chemists have found no 
chromium, or but the merest traces, in chrome steel sold in the markets. 

J.W. Langley (Trans. A. S.C.E., 1892) says: Chromium, like manganese, 
is a true hardener of iron even in the absence of carbon. The addition of 
1 % or 2 % of chromium to a carbon steel will make a metal which gets 
excessively hard. Hitherto its principal employment has been in the 
production of chiUed shot and shell. Powerful molecular stresses result 
during coohng, and the shells frequently break spontaneously months 
after they are made. 

Tungsten Steel — Mushet Steel. (J. B. Nau, Iron Age, Feb. 11, 
1892.) — By incorporating simultan:^ously carbon and tungsten in iron, 
it is possible to obtain a much harder steel than with carbon alone, with- 
out danger of an extraordinary brittleness in the cold metal or an in- 
creased difficulty in the working of the heated metal. 

When a special grade of hardness is required, it is frequently the 
custom to use a high tungsten steel, known in England as special steel. 
A specimen from Sheffield, used for chisels, contained 9.3% of tungsten, 
0.7% of silver, and 0.6% of carbon. This steel, though used with ad- 
vantage in its imtempered state to turn chilled rolls, was not brittle; 
nevertheless it was hard enough to scratch glass. 

A sample of Mushet's special steel contained 8.3% of tungsten and 
1.73 % of manganese. 

According to analyses made by the Due de Luynes of ten specimens 
of the celebrated Oriental damasked steel, eight contained tungsten, two 
of them in notable quantities (0.518 % to 1 %) , while in all of the samples 
analyzed nickel was discovered ranging from traces to nearly 4%. 

Stein & Schwartz, of Philadelphia, in a circular say: It is stated that 
tungsten steel is suitable for the manufacture of steel magnets, since it 
retains its magnetism longer than ordinary steel. Cast steel to which 
tungsten has been added needs a higher temperature for tempering than 
ordinary steel, and should be hardened only between yellow, red, and 
white. Chisels made of timgsten steel should be drawn between cherry- 
red and blue, and stand well on iron and steel. Tempering is best done 
in a mixture of 5 parts of yellow rosin, 3 parts of tar, and 2 parts of 
taUow, and then the article is once more heated and then tempered as 
usual in water of about 15° C. 

Aluminum Steel. (Aluminum Co. of America, 1909.) — Aluminum is 
added to steel: To increase the soundness of tops of ingots, and conse- 
quently decrease the scrap losses; to quiet the ebullition in molten 
steel, permitting the successful pouring of "wild" steel; to prevent 
oxidation and increase- the homogeneity of the steel ; to increase tensile 
strength without decreasing ductiUty; to remove oxygen or oxides, the 
aluminum acting as a deoxidizer; to reduce the hability of the steel to 
oxidation; to produce smoother siufaced castings and ingots than is 
possible without the use of aluminum. 

Aluminum is not a hardener of steel, and none of its alloys with steel 
have proved advantageous. Strictly speaking, there is no aliuninum- 
steel in the sense that there is nickel-steel or chromium-steel. Alumi- 
nimi is the principal deoxidizer of steel; 100 parts by weight of oxygen 
will combine with 114 parts of aluminum, 140 parts of sihcon or 350 parts 
of manganese. The aluminum will entirely disappear if there is any 
oxygen present, and it only appears in completely deoxidized steel. If 
too much aluminum be added, the metal is Uable to form deep pipes in 
the ingots. To add the correct quantity requires experience, but suc- 
cessful results have been obtained by adding from one-eighth to three- 
fourth pound of aluminum to the ton of steel. Steel ingots which are 



"alloy" steels. 



m 



to be hammered or rolled have been improved by the addition of 
two to four ounces of aluminum per ton of steel. For steel castings, to 
insure soundness and absence of blowholes, 16 to 32 ounces per ton may- 
be advantageously added. The aluminum may be added by throwing 
the metal in smaU pieces into the ladle as the metal is poured into it, or 
by the use of ferro-aluminum placed in the ladle before pouring the steel. 
The metal is more commonly used in America, and the alloy in England. 

Nickel Steel. — The remarkable tensile strength and ductihty of nickel 
steel, as shown by the test-bars and the behavior of nickel-steel armor- 
plate under shot tests, are witness of the valuable quaUties conferred 
upon steel by the addition of a few per cent of nickel. 

Nickel steel has shown itself to be possessed of some exceedingly valuable 
properties; these are, resistance to cracking, high elastic Umit, and homo- 
geneity. Resistance to cracking, aproperty to which thenameof non-fissi- 
bility has been given is shown more remarkably as the percentage of nickel 
increases. Bars of 27 % nickel illustrate this property. A 1 K-in. square 
bar was nicked 1/4 in. deep and bent double on itself without further fracture 
than the splintering off, as it were, of the nicked portion. Sudden failure 
or rupture of this steel would be impossible; it seems to possess the tough- 
ness of rawhide with the strength of steel. With this percentage of nickel 
the steel is practically non-corrodible and non-magnetic. The resistance 
to cracking shown by the lower percentages of nickel is best illustrated in 
the many trials of nickel-steel armor. 

In such places (shafts, axles, etc.) where failure is the result of the fatigue 
of the metal this higher elastic limit of nickel steel will tend to prolong in- 
definitely the life of the piece, and at the same time, through its superior 
toughness, offer greater resistance to the sudden strains of shock. 

Howe states that the hardness of nickel steel depends on the proportion 
of nickel and carbon jointly, nickel up to a certain percentage increasing 
the hardness, beyond this lessening it. Thus while steel with 2% of nickel 
and 0.90% of carbon cannot be machined, with less than 5% nickel it can 
be worked cold readily, provided the proportion of carbon be low. As the 
proportion of nickel rises higher, cold-working becomes less easy. It forges 
easily whether it contain much or little nickel. 

The presence of manganese in nickel steel is most important, as it 
appears that without the aid of manganese in proper proportions the 
conditions of treatment would not be successful. 

Properties of Nickel Steel. — D. H. Browne, in Proc. A. I. M. E., 
1899, gives a paper of 79 pages, entitled "Nickel Steel: a synopsis of 
experim.ent and opinion," including a bibliography containing 50 titles. 
Some extracts from this paper are here given. 

Commercially pure nickel, containing 98.13 Ni, 1.15 Co, 0.43 Fe, 
0.08 Si, 0.11 Mn, showed the following physical properties: 





L. P.* 


E. L. 


T.S. 


M.E.* 


El % 
in 2 m. 


Cast bars 


5,119 
9,243 
17.064 


12.557 
21.045 
18.059 
16.921 


40.669 
72.522 
72.806 
71.860 


23.989.140 
29.506.500 
26.870.800 


18.2 


-^ ( Raw 


43.9 


~ < Annealed 


48.6 


f§ ( Quenched 


45.0 



* Limit of Proportionahty. * Modulus of Elasticity. 

Annealed Cast Bars of Nickel Steel with C 0.15 to 0.20. (Had- 
field.) The proportion of Ni used in soft steels for armor and for engine- 
forgings is from 3 to 3.5%. With 0.25 C this produces an E. L. and T. 
S. equal to open-hearth steel of 0.45 C without Ni, with a ductihty 
equal to that of the lower-carbon steel. 

Nickel Steel, 3.25 Ni, and Simple Steel Forgings Compared. 
(Bethlehem Steel Co.) 













Red. 












Red. 


c. 


Ni. 


T.S. 


E. L. 


EL, 

%. 


Area, 

%. 
60 


C. 
0.20 


Ni. 


T.S. 


E. L. 


EL, 

%. 


Area, 

%. 


0.20 





55000 


28000 


34 


3.5 


85000 


48000 


26 


55 


0.30 





75000 


37000 


30 


50 


0.30 


3.5 


95000 


60000 


22 


48 


0.40 





85000 


43000 


25 


45 


0.40 


3.5 


110000 


72000 


18 


40 


0.50 





95000 


48000 


21 


40 


0.53 


3.5 


125C00 


85000 


13 


32 



498 STEEL, 

As compared ^Ith simple steels of the same tensile strength, a 3% 
nickel steel will have from 10 to 20% higher E. L. and from 20 to 30% 
greater elongation, while as compared with simple steels of the same 
carbon, the nickel steel, up to 5% Ni, will have about 40% greater tensile 
strength, with practically the same elongation and reduction of area 

Cholat and Harmet found with 0.30 C and 15% Ni a T. S. of 213,400 lbs 
per sq. in.; when oil-tempered a T. S. of 277,290 and an E. L. of 166,300! 

Riley states that steel of 25% Ni and 0.27 C gave a T. S. of 102 600 
and elong. 29%, while steel of 25% Ni gave 94,300 T. S. and 40% elong. 
Steels high in Ni are entirely different in physical properties from low- 
nickel steels. 

Effect of Ni on Haedness. — Gun barrels with 4.5% Ni and 0.30 C are 
soft and very ductile; T. S. 80,000, elong. 25%, red. of area 45%. Rolls 
with 5% Ni and 1 % C turned easier than simple steel of 1 % C. If a steel 
contains less than 6% Ni the influence of the C present on the hardness 
produced by water quenching is strongly marked. Above 8% Ni the effect 
of the C seems to be masked by the Ni; steel with 18% Ni is as hard and 
elastic with 0.30 as ^\ith 0.75 C. If steel with 18% Ni and 0.60 C be heated 
and plunged in water it will be perceptibly softened, and if the Ni is 
raised to 25% this softening is very noticeable. 

Compression Tests of Low-Carbon Nickel Steels. (Hadfield.) 



Carbon . . ... 


0.13 
0.95 

20 

49 


0.14 
1.92 

27 

47 


0.19 
3.82 

28 

41 


0.18 
5.81 

40 

37 


0.17 
7.65 

40 

33 


0.16 
9.51 
70 
3 


0.18 
11.39 
100 

1 


0.23 
13.48 
80 

1 


0.19 
19.64 
80 

3 


0.16 
24.51 
50 
16 


0.14 


Nickel 


29.07 


E. L., tons 

Shortening* ... 


24 
41 



* Shortening by 100-ton load, %. 

Specific Gravity. — The sp. gr. of low-carbon nickel steels containing 
up to 15% Ni is about the same as that of carbon steel, from 7.86 to 7.90; 
from 19 to 39% Ni it is from 7.91 to 8.08; one sample of wire of 29% Ni, 
however, being reported at 8.4. A 44% Ni steel, according to Guillaume, 
has a sp. gr. of 8.12. 

The Resistance of Corrosion of nickel steel increases with the per- 
centage of Ni up to 18. "This alloy is practically non-corrodible." 
"Tico " resistance wire, 27.5% Ni, was very slightly rusted after a year's 
exposure in a wet cellar; iron wire under the same conditions was entirely 
changed to oxide. With the ordinary nickel steels, 3 to 3.5% Ni, corrosion 
is slightly less than in simple steels. 

Electrical Resistance. — All nickel steels have a high electrical resist- 
ance which does not seem to vary much with the percentage of Ni. The 
resistance wires, "Tico," "Superior," and "Climax," containing from 25 
to 30% Ni, have about 48 times, while German silver has about 18 times 
the resistance of copper. 

Magnetic Properties. — According to Guillaume all nickel steels below 
25.7% Ni can be, at the same temperature, either magnetic or non- 
magnetic, according to their previous heat-treatment, and they show 
different properties at ascending and at descending temperatures. The 
low-nickel steels, 3 to 5% Ni, possess a magnetic permeability greater than 
that of wrought iron. 

Nickel Steel for Bridges. — J. A. L. Waddell, Trans. A.S.C. E., 1908, 
presents at length an argument in favor of the use of nickel steel in long- 
span bridges. 

Some Uses of Nickel Steel. (F. L. Sperry, A.I.M. E., xxv, 51.) — The 
propeller shaft of the U. S. cruiser Brooklyn was made of hollow-forged, 
oil-tempered nickel steel, 17 in. outside, 11 in. inside diam., length 38 ft. 11 
in., weight per foot, 449 lbs. Test bars cut from the tube gave T. S., 90,350 
to 94,245; E. L., 56,470 to 60,770; El. in 2 in., 25.5 to 28.0%; Red. of area, 
59.8 to 61.3%. A solid shaft of the same elastic strength of simple steel, 
having anE.L. of3/5 of that of the nickel steel, would be 18.9 in. diam., and 
would have weighed 920 lbs. per foot. 

The rotating field of the 5000 H.P. electric generators of the Niagara 
Falls Power Co. is inclosed in a ring of forged nickel steel, outside diam. 
1393/8 in.; inside, 130 in.; width, 503/4 in.; weight, 28,840 lbs. It travels 
at the rate of nearly two miles per minute. 

Nickel steel wire with 27.7% Ni and 0.40 C used for torpedo defense 
netting, 0.116 in. diam., gave a T. S. of 198,700; El. in 2 in., 6.25%; Red. 
of area, 16.5%. 



"alloy'' steels. 499 

Flange plate of soft nickel steel, NL 2.69; C, 0.08; Mn, 0.36; P, 0.045; S. 
0.038, gave, average of 6 tests, T. S., 65,760; E. L., 47,080; El. in 8 in., 
24 8%- Red. of area, 52.0%. For comparison: Soft carbon steel, C, 
0.10; Mn, 0.27; P, 0.048; S, 0.039; T. S., 54,450; E. L., 35.240; El., 27.4%; 
Red. of area, 55.3%. 

Coefficients of Expansion of Nickel Steel. (D. H. Browne, 
A.I. M. B., 1899.) — Per degree C. (Prefix 0.0000 to the figures here given.) 
% Ni. 26. 28. 28.7 30.4 31.4 34.6 35.6 37.3 39.4 44.4 
Coeff. 1312 1131 1041 0458 0340 0137 0087 0356 0537 0856 

For comparison: Brass, 1878; Hard steel, 1239; Soft steel, 1078: 
Platinum, 0884; Glass, 0861; Nickel, 1252. Ordinary commercial nickel 
steels, containing 3 to 4% Ni, have coefficients about the same as carbon 
steel. See also page 567. 

Invar is a nickel-iron alloy, which is characterized by an extraordinarily 
low coefficient of expansion at ordinary temperatures. The analysis is 
about as follows: — carbon, 0.18; nickel, 35.5%; manganese, 0.42, — the 
other elements being low. Guillaume gives the mean coefficient of 
expansion for an alloy containing 35.6% nickel as (0.877 + 0.00117 0^*^"* 
between temperatures 0° C. and t° C. where t does not exceed 200° C. 
This material is used in measuring instruments and for standards of 
length, chronometers, etc. Its expansion as compared with ordinary 
steel is about as 1:11.5; with brass, as 1:17.2; with glass, as 1 : 8.5. Alloys 
either richer or poorer in nickel show much greater expansion, and the 
alloy containing 47.5% nickel, known as "Platinite," has the same 
coefficient of expansion as platinum and glass. See also page 567. 

Copper Steels. — Pierre Breuil (Jour. I. and S. /., 1907) gives an account 
of experiments on four series of copper steels containing respectively 0.15, 
0.40, 0.65, and 1% of C with Cu in each ranging from to 34%. An ab- 
stract of his principal conclusions is as follows: 

Copper steel does not yield a metal capable of being rolled in practice, 
if Cu exceeds 4%. 

When in the ingot state copper hardens steel in proportion as there is 
less C present. 

Copper steels as rolled appear to be stronger in proportion as they con- 
tain more Cu. This difference is the more manifest in proportion as the 
C is lower. 

Annealing leaves the steels with the same characteristics, but greatly 
reduces the differences observed in the case of the untreated steels. 
Quenching restores the differences encountered in the case of the steels 
as cast. 

Copper steels equal nickel steels in tensile strength and would be less 
costly than the latter. They are no more brittle than nickel steels con- 
taining equivalent percentages of Ni. The steel containing 0.16% C and 
4% Cu is remarkable in this respect. 

The presence of copper makes the constituents of the steel finer, 
approximating them to classes containing higher percentages of C. 
While hardening the steel the presence of Cu does not render it brittle. 
It confers upon it a very fair degree of elasticity, while leaving the elon- 
gation good, thus conducing to the production of a most valuable metal. 

Cutting tests were carried on with steels containing C about 1 % and 
Cu 0%, 1%, and 3% respectively. The presence of Cu in no wise altered 
the cutting properties. 

The presence of Cu was found to increase the electrical resistance, 
and a well-defined maximum was shown, coinciding with 2% Cu in 0.15 C, 
with 1.7% in 0.35% C, and with 0.5% Cu in 0.7 to 1% carbon steels. 

Nickel- Vanadium Steels. (Eng. Mag., April, 1906.) — M. Leon Guillet 
has investigated the influence of Ni and Va when used jointly. 

In steels containing 0.20 C and from 2 to 12% of Ni, the tensile strength 
and the elastic limit are both materially increased by the addition of 
small percentages of Va. In no case should the Va exceed 1%, the best 
results being secured by the use of 0.7 to 1 %. A steel containing 0.20 C, 
2% of Ni, and 0.7% Va showed a tensile strength of 91,000 lbs., an 
elastic limit of 70,000 lbs., and an elongation of 23.5%. With 1% Va, 
the T. S. increased to 119,500 lbs., and the E. L. to 91,000 lbs., the elong. 
falling to 22%. A nickel steel of 0.20%, C and 12%, Ni gave, with 
0.7 Va, a T. S. of over 200,000 lbs. and an E. L. of 172.000 lbs. per sq. in., 
the elong. being 6%. while with 1% Va theT. S. rose to 220,000 lbs. 



500 STEEL. 

and the E. L. to 176,000 lbs., the elongation remaining unchanged. 
When the Va is increased above l%the tensile strength falls off, and the 
material begins to show evidence of brittleness. Similar effects are pro- 
duced for steels of the higher carbon, but in a lesser degree. 

When the nickel-vanadium steels are subjected to a tempering process 
the beneficial effects of the Va are still further emphasized. The temper- 
ing experiments of M. Guillet were conducted by heating the steel to a 
temperature of 850° C, and cooling in water at 20° C. The T. S. and 
the E. L. were increased, being nearly doubled for the low nickel con- 
tent. Thus while the 0.20 C steel with 2% of Ni, untempered, and 
containing 0.7% of Va, gave a T. S. of 91,000 lbs., with an E. L. of 70,000 
lbs., the same steel, tempered from 850° C, showed a T. S. of 168,000 lbs. 
and an E. L. of 150,000 lbs., the resistance to shock and the hardness 
being also increased. 

Static and Dynamic Properties of Steels. (W. L. Turner, Iron Age, 
July 2, 1908.) — The term "crystallization" is a name given to designate 
phenomena due to the influences of shock and alternating stresses, 
whether pure or combined. The name has been advantageously altered 
to "intermolecular disintegration," but, whatever we choose to call it, 
there remains the evidence that some modification takes place in the 
structure of steel when the above-named forces are to be dealt with. 

Resistance to fatigue is not a function of static strength. 

An example of our knowledge of the "life" properties of ordinary steel 
is the case of the staying of a locomotive fire-box. Something is re- 
quired which will possess considerable strength combined with the 
power to withstand a moderate degree of flexure in all directions. Expe- 
rience has shown that the use of anything but the mildest steel for this 
work is prohibitive, and that wrought iron, or even copper, is still more 
satisfactory. 

The writer has completed a prehminary investigation into the relative 
dynamic properties of iron and the various ordinary and alloy steels, 
the results being given in the accompanying table. The conditions of 
the "dynamic" tests were as follows: 

A cylindrical test-piece, 6 in. long, 3/8 in. diam., finished with emery to 
remove all tool marks, is clamped at one end in a vise. A tool-steel 
head, in which there is cut a slot, is placed over the other end, the dis- 
tance from the striking center of this head to the vise line being 4 in. 
A crank and connecting rod furnished the reciprocating motion for this 
head, thereby causing the test-piece to be deflected 3/8 in. each side of 
the neutral position. In addition to this alternating flexure, the test- 
piece is also subjected, at each reversal, to an impact, due to the slot on 
the reciprocating head. The sample undergoes 650 alternations per 
minute. A deflection of 3/8 in. on each side has the effect of imparting a 
permanent set to the test-piece. 

On each class of steel a large number of dynamic tests were made, an 
average being taken of the results after elimination of those figures which 
were apparently abnormal. 

It is apparent that the action of nickel is twofold: 1. It statically 
intensifies. 2. It dynamically "poisons." As an instance of this, take 
tests Nos. 13 and 15, the former being a 3.7% nickel steel and the latter a 
chrome-vanadium steel. In the annealed condition, the elastic limits of 
the two are almost identical, but at the same time the alternations of 
stress endured by the latter are 2V4 times the number sustained by the 
nickel steel. Take again Nos. 17 and 18. The dynamic figures are more 
than three to one in favor of the chrome-vanadium product, whereas the 
difference in elastic limit is only about 3%. 

It is manifest that the static action of vanadium is similar to that of 
nickel, but that its dynamic effects are the exact converse. The differ- 
ences are markedly brought out in the quality figures, which invite 
attention as to comparison with those of ordinary carbon steel. Taking 
the latter as standard, the chrome-vanadium steels are as much above it 
as the nickel steels are below it. 

Chromium, per se, does not appear to exert appreciable influence other 
than statically, but it is possible that the effect of this metal in a ternary 
steel might be very marked. 

The dynamic attributes of plain carbon steel reach a maximum with 
about 0.25% C, falling away on both sides of this amount. 

The quality figure in the case of the chrome-vanadium steel does not 



''alloy'' steels. 



501 



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502 



STEEL. 



appear to undergo much alteration in the process of oil tempering, but 

there are considerable variations in other cases. The dynamic test may 
eventually act as a reliable guide to the correct methods for the heat 
treatment of individual steels. 

Strength for strength, the chrome-vanadium steels also have the 
advantage over all others as regards machining properties. Chrome- 
vanadium steel may be forged with the same ease as ordinary steel of simi- 
lar contents, no special precaution being necessary as to temperatures. 

Comparative Effects of Cr and Va, Sankey and J. Kent Smith, Proc. 
Inst. M.E., 1904. 



Cr. Va. 


T.S.* 


E.L.* 


El. in 
2 in. 


Red. A. 


Cr. Va. 


T.S.* 


E.L.* 


El. in 

2 in. 


Red. A. 


0.5 

1.0 

... 0.1 
... 0.15 
... 0.25 


34.0' 

38.2 

34.8 

36.5 

39.3 


22.9 
25.0 
28.5 
30.4 
34.1 


33% 

30 

31 

26 

24 


60.6% 

57.3 

60.0 

59.0 

59.0 


1.0 0.15 
1.0 0.15 
1.0 0.25 
C-Mn 
C-Mn 


48.6 

t52.6 

60.4 

27.0 

t32.2 


36.2 
34.4 
49.4 
16.0 
17.7 


24. 

25.0 

18.5 

35. 

34. 


56.6 
55.5 
46.3 
60.0 
52.6 



* Tons, of 2240 lbs., per sq. in. f Open-hearth steels; all the others 
are crucible. The last two steels in the table are ordinary carbon 
steels. 

Effect of Heat Treatment on Cr-Va Steel. (H. R. Sankey and 
J. Kent Smith, Proc. Inst. M. E., 1904, p. 1235.) — Various kinds of 
heat treatment were given to several Cr-Va steels, the results of which 
are recorded at length. The following is selected as a sample of the 
results obtained. Steel with C, 0.297; Si, 0.086; Mn, 0.29; Cr, 1.02; Va, 
0.17. gave: 



Tens. 

Str. 



Yield 
Point, 



El. in 
2 in. 



Red. 
Area. 



Im- 
pact. 



Alter- 
na- 
tions. 



As rolled , 

Annealed I/2 hr. at 800° C 

Soaked 12 hours at 800° C 

Water quenched at 800° C 

Oil quenched at 800° C 

Oil quenched at 800°, reheated to 

350° 

Water quenched at 1200° C 

Oil quenched at 1200° C 



121,200 
87,360 
86,020 
167,100 
122,080 

132,830 
209,440 
140,220 



82,650 
47,260 
68,100 
135,070 
82,880 

111,550 
191,520 
118,500 



24.0% 
34.5 
33.7 
7.5 
22.0 

23.0 
1.2 

8.5 



44.9% 

53.1 

51.5 

16.6 

35.2 

50.8 

1.5 

21.5 



3.1 
15.6 
11.2 
1.2 
2.4 

9.0 

3.0 



1906 
2237 



174 
296 



1314 



* Too hard to machine. 

The impact tests were made on a machine described in Eng*g, Sept. 25, 
1903, p. 431. The test-piece was 3/4 in. broad, notched so that 0.137 in. in 
depth remained to be broken through. The figures represent ft .-lbs. of 
energy absorbed. The piece was broken in one blow. The alternations- 
of-stress tests were made on Prof. Arnold's machine, described in The 
Engineer, Sept. 2, 1904, p. 227. The pieces were s/gin. square, one end 
was gripped in the machine and the free end, 4 in. long, was bent forwards 
and backwards about 710 times a minute, the motion of the free end being 
3/4 in. on each side of the center line. 

Tests by torsion of the same steel were made. The test-piece was 6 in. 
long, 3/4 in. diam. The results were: 





Shearing Stress 


Twist 
Angle. 






Elastic . 


Ulti- 
mate. 


No. of 

Twists. 


As rolled 


45.700 


99.900 


1410° 
1628° 


3.92 


Annealed I/2 hr. at 800° C 


38.528 


90.272 


4.52 



alloy" steels. 503 



Heat-treatment of Alloy Steels. (E. F. Lake, Am. Mach., Aug. 1, 
1907.) — In working the high-grade alloy steels it is very important that 
they be properly heat treated, as poor workmanship in this regard will 
produce working parts that are no better than ordinary steel, although 
the stock used be the highest grade procurable. By improperly heat- 
treating them it is possible to make these high-grade steels more brittle 
than ordinary carbon steels. 

The theory of heat treatment rests upon the influence of the rate of 
cooling on certain molecular changes in structure occurring at different 
temperatures. These changes are of two classes, critical and progres- 
sive; the former occur periodically between certain narrow temperature 
limits, while the latter proceed gradually with the rise in temperature, 
each change producing alterations in the physical characteristics. By 
controlling the rate of cooling, these changes can be given a permanent 
set, and the characteristics can thus be made different from those in the 
metal in its normal state. 

The results obtained are influenced by certain factors: 1. The original 
chemical and physical properties of the metal; 2. The composition of 
the ^ases and other substances which come in contact with the metal in 
heating and cooling. 3. The time in which the temperature is raised 
between certain degrees. 4. The highest temperature attained. 5. The 
length of time the metal is maintai-ned at the highest temperature. 
6. The time consumed in allowing the temperature to fall to atmos- 
pheric. 

The highest temperature that it is safe to submit a steel to for heat- 
treating is governed by the chemical composition of the steel. Thus 
pure carbon steel should be raised to about 1300° F., while some of the 
high-grade alloy steels may safely be raised to 1750°. The alloy steels 
must be handled very carefully in the processes of annealing, hardening, 
and tempering; for this reason special apparatus has been installed to 
aid in performing these operations with definite results. 

The baths for quenching are composed of a large variety of materials, 
^ome of the more commonly used are as follows, being arranged accord- 
ing to their intensity on 0.85% carbon steel: Mercury: water with sulphuric 
acid added; nitrate of potassium; sal ammoniac; common salt; carbonate 
of lime; carbonate of magnesia; pure water; water containing soap, 
sugar, dextrine or alcohol; sweet milk; various oils; beef suet; tallow; 
wax. 

With many of these alloy steels a dual quenching gives the best results, 
that is, the metal is quenched to a certain temperature in one bath and 
then immersed in the second one until completely cooled, or it may 
be cooled in the air after being quenched in the first bath. For this a 
lead bath, heated to the proper temperature, is sometimes used for the 
first quenching. 

With the exception of the oils and some of the greases, the quenching 
effect increases as the temperature of the bath lowers. Sperm and hn- 
seed oils, however, at all temperatures between 32° and 250°, act about 
the same as distilled water at 160°. 

The more common materials used for annealing are powdered char- 
coal, charred bone, charred leather, fire clay, magnesia or refractory 
earth. The piece to be annealed is usually packed in a cast-iron box 
in some of these materials or combinations of them, the whole heated 
to the proper temperature and then set aside, with the cover left on, to 
cool gradually to the atmospheric temperature. For certain grades of 
steel these materials give good results; but for all kinds of steels and for 
all grades of annealing, the slow-cooling furnace no doubt gives the 
best satisfaction, as the temperature can be easily raised to the right 
point, kept there as long as necessary, and then regulated to cool down 
as slowly as is desired. The gas furnace is the easiest to handle and 
regulate. 

A high-grade alloy steel should be annealed after every process in man- 
ufacturing which tends to throw it out of its equilibrium, such as forging, 
rolling and rough machining, so as to return it to its natural state of 
repose. It should also be annealed before quenching, case-hardening 
or carbonizing. 

The wide range of strength given to some of the alloy steels by heat 



504 



STEEL. 



treatment is shown by the table below. The composition of the alloy 
uras: Ni, 2.43; Cr, 0.42; Si, 0.26; C, 0.23; Mn, 0.43; P, 0.025; S, 0.022. 





if 
3- 


1^ 

cm 


'if 
|i 


1^ 


Tempered 
at 1025° F. 


G— 


t 

BZ 


Tensile Strength . 
E. L 


227,000 

208,000 

4 


219.000 

203,500 

6 


195,500 

150,000 

8 


172,000 

148,500 

11 


156,500 

125,000 

13 


141,000 

102,000 

15 


109,500 
70,500 


Elong.,% in 2 in. 


22 



VARIOUS SPECIFICATIONS FOR STEEL. 

Structural Steel. — There has been a change during the ten years from 
1880 to 1890, in the opinions of engineers, as to the requirements in speci- 
fications for structural steel, in the direction of a preference for metal of 
low tensile strength and great ductility. The following specifications for 
tension members at different dates are given by A. E. Hunt and G. H. 
Clapp, Trans. A. I. M. E., xix, 926: 

1879. 1881. 1882. 1885. 1887. 1888. 

Elastic limit.. . . 50.000 40 @ 45,000 40,000 40,000 40,000 38,000 

Tensile strength 80,000 70 @ 80.000 70,000 70,000 67@75,000 63 @ 70,000 
Elongation in 8 in. 12% 18% 18% 18% 20% 22% 

Reduction of area 20% 30% 45% 42% 42% 45% 

F. H. Lewis (IronAoe, Nov. 3, 1892) says: Regarding steel to be used 
under the same conditions as wrought iron, that is, to be punched without 
reaming, there seems to be a decided opinion (and a growing one) among 
engineers, that it is not safe to use steel in this way, when the ultimate 
tensile strength is above 65,000 ibs. The reason for this is not so much 
because there is any marked change in the material of this grade, but 
because all steel, especially Bessemer steel, has a tendency to segregations 
of carbon and phosphorus, producing places in the metal which are harder 
than they normally should be. As long as the percentages of carbon and 

ghosphorus are kept low, the effect of these segregations is inconsiderable; 
ut when these percentages are increased, the existence of these hard 
spots in the metal becomes more marked, and it is therefore less adapted 
to the treatment to which wTOUght iron is subjected. 

There is a wide consensus of opinion that at an ultimate of 64,000 to 
65,000 lbs. the percentages of carbon and phosphorus reach a point where 
the steel has a tendency to crack when subjected to rough treatment. 

A grade of steel, therefore, running in ultimate strength from 54,000 to 
62,000 lbs., or in some cases to 64,000 lbs., is now generally considered a 
Droper material for this class of work. 

A. E. Hunt, Trans. A.I.M.E., 1892, says: Why should the tests for steel 
be so much more rigid than for iron destined for the same purpose? Some 
of the reasons are as follows: Experience shows that the acceptable quali- 
ties of one melt of steel offer no absolute guarantee that the next melt to it, 
even though made of the same stock, will be equally satisfactory. 

It is now almost universally recognized that soft steel, if properly made 
and of good q^uality, is for many purposes a safe and satisfactory substitute 
for wrought iron, being capable of standing the same shop-treatment as 
wrought iron. But the conviction is equally general, that poor steel, or an 
unsuitable grade of steel, is a very dangerous substitute for wrought iron 
even under the same unit strains. 

For this reason it is advisable to make more rigid requirements in select- 
ing material which may range between the brittleness of glass and a duc- 
tility greater than that of wrought iron. 

Speclflcatlons for Structural Steel for Bridifes. (Proc. A. S. T. M., 
1905.) — Steel shall be made by the open-hearth process. The chcml* 
cal and physical properties shall conform to the following limits: 



VARIOUS SPECIFICATIONS FOR gTEEt. 



505 



Elements Considered. 



Phosphorus, f Basic. . . 

Max \ Acid. . . . 

Sulphur, Max 

Tensile strength, lbs. 
per sq. in 

Elong.: Min. % in 8 in. 

Elong.: Min. % in 2 in. 
Fracture 

Cold bend without 
fracture 



Structural Steel. 



0.04% 
0.08% 
0.05% 

Desired 

60,000 

1,500,000* 

tens. str. 

22 

Silky 



180° flatt 



Rivet Steel. 



0.04% 
0.04% 
0.04% 

Desired 

50,000 

1,500,000 

tens. str. 



Silky 
180° flatt 



Steel Castings 



0.05% 
0.08% 
0.05% 

Not less than 
65,000 



18 

Silky or fine 
granular 

90°, d = 3t 



* The following modifications will be allowed in the requirements for 
elongation for structural steel: For each Vie inch in thickness below 
5/i6 inch, a deduction of 2 1/2 will be allowed from the specified percent- 
age. For each Vs inch in thickness above 3/4 inch, a deduction of 1 will 
be allowed from the specified percentage. 

t Plates, shapes and bars less than 1 in. thick shall bend as called for. 
Full-sized material for eye-bars and other steel 1 in. thick and over, tested 
as rolled, shall bend cold 180° around a pin of a diameter twice the thick- 
ness of the bar, without fracture on the outside of bend. When required 
by the inspector, angles 3/4 in. and less in thickness shall open flat, and 
angles 1/2 in. and less in thickness shall bend shut, cold, under blows of 
a hammer, without sign of fracture. 

t Rivet steel, when nicked and bent around a bar of the same diam- 
eter as the rivet rod, shall give a gradual break and a fine, silky, uniform 
fracture. 

If the ultimate strength varies more than 4000 lbs. from that desired, 
a retest may be made, at the discretion of the inspector, on the same 
gauge, which, to be acceptable, shall be within 5000 lbs. of the desired 
strength. 

Chemical determinations of C, P, S, and Mn shall be made from a 
test ingot taken at the time of the pouring of each melt of steel. Check 
analyses shall be made from finished material, if caUed for by the pur- 
chaser, in which case an excess of 25% above the required limits will be 
aUowed. 

Specimens for tensile and bending tests for plates, shapes and bars 
shall be made by cutting coupons from the finished product, which shall 
have both faces rolled and both edges milled with edges parallel for at 
least 9 in.; or they may be turned 3/4 in. diam. for a length of at least 
& in., with enlarged ends. Rivet rods shall be tested as rolled. Speci- 
mens shall be cut from the finished rolled or forged bar in such manner 
that the center of the specimen shall be 1 in. from the surface of the bar. 
The specimen for tensile test shall be turned with a uniform section 2 in. 
long, with enlarged ends. The specimen for bending test shall be 1 X 1/3 
in. in section. 

Speciflcations for Steel for the Manhattan Bridge. (Eng. News, 
Aug. 3, 1905.) — 

Material for Cables. Suspenders and Hand Ropes. Open- 
hearth steel. (The wire for serving the cables shall be made of Norway 
iron of approved quality.) The ladle tests of the steel shall contain not 
more than : C, 0.85; Mn, 0.55; Si, 0.20; P, 0.04; S, 0.04; Cu, 0.02%. 
The wire shall have an ultimate strength of not less than 215,000 lbs. 
per sq. in. before galvanizing, and an elongation of not less than 2%, in 
12 in. The bright wire shall be capable of bending cold around a rod 
IV2 times its own diam. without sign of fracture. The cable wire before 
galvanizing shall be 0.192 in. ± 0.003 in. in diam.; after galvanizing, the 
wire shall have an ultimate strength of not less than 200,000 lbs. per sq. 
in. of gross section. 



506 



STEEL. 



Carbon Steel. The ladle tests as usually taken shall contain not 
more than: P, 0.04; S, 0.04; Mn, 0.60; Si, 0.10%. The ladle tests of 
the carbon rivet steel shall contain not more than: P, 0.035; S, 0.03. 
Rivet steel shall be used for all bolts and threaded rods. 

Nickel Steel. The ladle test shall contain not less than 3.25 Ni, 
and not more than: P, 0.04; S, 0.04; Mn, 0.60; Si, 0.10; nickel rivet steel 
not more than: P, 0.035; S, 0.03%. 

Nickel steel for plates and shapes in the finished material must show: 
T. S., 85,000 to 95,000 lbs. per sq. in.; E. L., 55,000 lbs. min.; elong. in 
8 ins., min., == 1,600,000 ^ T. S.; min. red. of area, 40%. 

Specimens cut from the finished material shall show the following 
physical properties: 



Material. 



T. S., lbs. per sq. 
in. 



Min.E.L., 
lbs. per 
sq. in. 



Min. 
Elong., 
% in Sin, 



Min. Red. 
of Area, 

%. 



Shapes and universal mill 
plates 

Eye-bars, pins and rollers 

Sheared plates 

Rivet rods 

High-carbon steel for 
trusses 



60,000 to 68,000 
64,000 to 72,000 
60,000 to 68,000 
50,000 to 58,000 

85,000 to 95,000 



33,000 
35,000 
33,000 
30,000 

45,000 



1,500,000 



ultimate 



44 
40 
44 
50 

35 



Nickel rivet steel: T. S., 70,000 to 80,000; E. L., min., 45,000; elong., 
min., 1,600,000 ^ T. S., % in 8 ins. 

Steel Castings. The ladle test of steel for castings shall contain 
not more than: P, 0.05; S, 0.05; Mn, 0.80; Si, 0.35%. Test-pieces taken 
from coupons on the annealed castings shall show T. S., 65,000; E. L., 
35,000: elong. 20% in 8 ins. They shall bend without cracking around a 
rod three times the thickness of the test-piece. 



Specifications for Steel. {Proc, A. S. T. M., 1905.) 



Steel Forgings. 



Solid or hollow forgings, no diam. 
or thickness of section to exceed 
10 in. 

Solid or hollow forgings, diam. 
not to exceed 20 in. or thickness 
of section 15 in. 

Solid forgings, over 20 in 

Solid forgings 

Solid or hollow forgings, diam. or 
thickness not over 3 in. 

Solid rectangular sections, thick- 
ness not over 6 in., or hollow 
with walls not over 6 in. thick. 

Solid rect. sections, thickness not 
over 10 in., or hollow with walls 
not over 10 in. thick. 

Locomotive forgings 



Kind of 
Steel. 



Tensile 
Strength. 



S. 

c. 

fC.A. 

N.A, 

C.A. 

N.A. 

C.A. 
N.A. 
CO. 
N.O. 

CO. 
N.O. 

'CO. 

:n.o. 



58,000 
75,000 
80,000 
80,000 

75 000 
80,000 

70,000 
80,000 
90,000 
95,000 

85,000 
90,000 

80,000 
85,000 

80,000 



Elast. 


El. in 
2 in., 

%. 


Limit. 


29,000* 


28 


37,500* 


18 


40,000 


22 


50,000 


25 


37,500 


23 


45,000 


25 


35,000 


24 


45,000 


24 


55,000 


20 


65,000 


21 


50.000 


22 


60,000 


22 


45,000 


23 


55,000 


24 


40,000 


20 



Red 
Area, 

%. 

35 (a) 
30(c) 
35(b) 
45(a) 

35(b) 
45(a) 

30(c) 
40(a) 



45(b) 



50 



45(b) 
50(b) 

40(b) 
45(b) 

25(d) 



* The yield point, instead of the elastic limit, is specified for soft steel 
and carbon steel not annealed. It is determined by the drop of the 
beam or halt in the gauge of the testing machine. The elastic limit, 
specified for all other steels, is determined by an extensometer, and is 
defined as that point where the proportionality changes. The standard 
l^( specimen is V2 in. turned di^m. with a gauged length oi 2 inchei. 



VARIOUS SPECIFICATIONS FOR STEEL. 



507 



Kind of steel: S., soft or low carbon. C, carbon steel, not annealed. 
C. A., carbon steel, annealed. C. O., carbon steel, oil tempered. N. A., 
nickel steel, annealed. N. O., nickel steel, oil tempered. Bending 
tests: A specimen 1 X V2 in. shall bend cold 180° without fracture on 
outside of bent portion, as follows: (a) around a diam. of 1/2 in.; (b) 
around a diam. of 1 in.; (c) around a diam. of 1/2 in.; (d) no bending 
test required. 

Chemical composition: P and S not to exceed 0.10 in low-carbon steel, 
0.06 in carbon steel not annealed, 0.04 in carbon or nickel steel oil tem- 
pered or annealed, 0.05 in locomotive forgings. Mn not to exceed 0.60 
in locomotive forgings. Ni 3 to 4% in nickel steel. 

Specifications for Steel Ship Material. (Amer. Bureau of Shipping. 
1900. Proc. A. S. T, M., 1906, p. 175.) — 



For Hull Construction. 



Tens. Strength. 



E. L. 



El. in 
8in., %. 



Plates, angles and shapes 

Castings 

Forgings 



58,000 to 60,000 
60,000 to 75,000 
55,000 to 65,000 



1/2 T. S. 



22*. 18t 
20 



* In plates 18 lbs. per sq. ft. and over. t In plates under 18 lbs. 

For Marine Boilers: Open-hearth steel ; Shell: P and S, each not over 
0.04%. Fire-box, not over 0.035%. Tensile Strength: Rivet steel, 
45,000 to 55,000; Fire-box, 52,000 to 62,000; Shell, 55,000 to 73,000; 
Braces and stays, 55,000 to 65,000; Tubes and all other steel, 52,000 to 
62,000 lbs. per sq. in. 

Elongation in 8 in.: Rivet steel, 28%; Plates 3/8 in. and under, 20%; 
3/8 to 3/4 in., 22%; 3/4 in. and over, 25%. 

Cold Bending and Quenching Tests. Rivet steel and all steel of 
52,000 to 62,000 lbs. T. S., V2 in. thick and under, must bend 180° flat on 
itself without fracture on outside of bent portion; over 1/2 in. thick, 180° 
around a mandrel II/2 times the thickness of the test-piece. For hull 
construction a specimen must stand bending on a radius of half its thick- 
ness, without fracture on the convex side, either cold or after being 
heated to cherry-red and quenched in water at 80° F. 

High-strength Steel for Shipbuilding. (Eng'g, Aug. 2, 1907, p. 137.)— 
The average tensile strength of the material selected for the Lusitania 
was 82,432 lbs. per sq. in. for normal high-tensile steel, and 81,984 lbs. 
for the same annealed, as compared with 66,304 lbs. for ordinary mild 
steel. The metal was subjected to tup tests as well as to other severe 
punishments, including the explosion of heavy charges of dynamite 
against the plates, and in every instance the results were satisfactory. 
It was not deemed prudent to adopt the high-tensile steel for the rivets. 
a point upon which there seems some difference of opinion. 



Penna. R. R. Specifications for Steel, 





6 



6 

1 


C. 


Mn. 


Si. 


P. 


S. 


Cu. 


Plates for steel cars 


(I) 


1899 
1901 
1899 
1904 
1902 
1906 
1906 


0.12 
1.00 
0.40 
0.45 
0.45 
0.18 
0.18 


0.35 
0.25 

0.50 

0.60- 

0.50 

0.40- 

0.40- 


0.05 

0.15- 

0.05 

0.05- 

0.05 

0.05- 

0.02- 


0.04- 
0.03- 
0.05- 
0.03- 
0.03- 
0.04- 
0.03- 


0.03- 
0.03- 
0.04- 
0.04- 
0.02- 
0.03- 
0.02- 




Bar spring steel 


0,03- 


Steel for axles 


(2) 
(3) 
(4) 
(5) 
(6) 




Steel for crank pins 




Billets or blooms for forging 
Boiler-shell sheets 


0.03- 
0.03- 


Fire-box sheets 


0.03- 







508 STEEL. 

The minus sign after a figure means "or less." The figures without 
the minus sign represent the composition desired. 

Steel castings. Desired T. S.. 70,000 lbs. per sq. in.; elong. in 2 in., 
15%. Will be rejected if T. S. is below 60,000, or elong. below 12%, or if 
the castings show blow-holes or shrinkage cracks on machining. 

Notes. (1) Tensile strength, 52,000 lbs. per sq. in.; elong. in 8 ins. 
= 1,500,000 -^ T. S. (2) Axles are also subjected to a drop test, similar 
to that of the A. S. T. M. specifications. Axles will be rejected if they 
contain C below 0.35 or above 0.50, Mn above 0.60, P above 0.07%. 
(3) T. S. desired, 85,000 lbs. per sq. in.; elong. in 8 ins. 18%. Pins will 
be rejected if the T. S. is below 80,000 or above 95,000, if the elongation 
is less than 12%, or if the P is above 0.05%). (4) The steel will be re- 

iected if the C is below 0.35 or above 0.50, Si above 0.25, S above 0.05, 
^ above 0.05, or Mn above 0.60%. (5) T. S. desired, 60.000; elong. in 
8 ins. 26%. Sheets will be rejected if the T. S. is less than 55,000 or 
over 65,000, or if the elongation is less than the quotient of 1,400,000 
divided by the T. S., or if P is over 0.05%o. (6) T. S. desired, 60,000, 
with elong. of 28% in 8 in. Sheets will be rejected if the T. S. is less 
than 55,000 or above 65,000 (but if the elong. is 30% or over plates will 
not be rejected for high T. S.),if the elongation is less than 1,450,000 -i- 
T. S., if a single seam or cavity more than 1/4 in. long is shown in either 
one of the three fractures obtained in the test for homogeneity, described 
below, or if on analysis C is found below 0.15 or over 0.25, P over 0.035, 
Mn over 0.45, Si over 0.03, S over 0.045, or Cu over 0.a5%. 

Homogeneity Test for Fire-box Steel. — This test is made on one of the 
broken tensile-test specimens, as follows: 

A portion of the test-piece is nicked \^ith a chisel, or grooved on a ma- 
chine, transversely about a sixteenth of an inch deep, in three places 
about 2 in. apart. The first groove should be made on one side, 2 in. from 
the square end of the piece; the second, 2 in. from it on the opposite side; 
and the third, 2 in. from the last, and on the opposite side from it. The 
test-piece is then put in a vise, with the first groove about 1/4 in. above 
the jaws, care being taken to hold it firmly. The projecting end of the 
test-piece is then broken off by means of a hammer, a number of light 
blows being used, and the bending being away from the groove. The 
piece is broken at the other two grooves in the same way. The object 
of this treatment is to open and .render visible to the eye any seams due 
to failure to weld up, or to foreign interposed matter, or cavities due 
to gas bubbles in the ingot. After rupture, one side of each fracture is 
examined, a pocket lens being used if necessary, and the length of the 
seams and cavities is determined. The sample shall not show any single 
seam or cavity more than 1/4 in. long in either of the three fractures. 

Dr. Chas. B. Dudley, chemist of the P. R. R. (Trajis. A. I. M. E., 1892), 
referring to tests of crank-pins, says: In testing a recent shipment, the 
piece from one side of the pin showed 88,000 lbs. strength and 22% elon- 
gation, and the piece from the opposite side showed 106,000 lbs. strength 
and 14% elongation. Each piece was above the specified strength and 
ductility, but the lack of uniformity between the two sides of the pin was 
so marked that it was finally determined not to put the lot of 50 pins in 
use. To guard against trouble of this sort in future, the specifications 
are to be amended to require that the difference in ultimate strength of 
the two specimens shall not be more than 3000 lbs. 

Speciflcations for Steel Rails. (Adopted by the manufacturers of the 
U. S. and Canada. In effect Jan. 1, 1909.)— Bessemer rails: 
Wt. per yard, lbs. 50 to 60 61 to 70 71 to 80 81 to 90 91 to 100 

Carbon, % 0.35-0.45 0.35-0.45 0.40-0.50 0.43-0.53 0.45-0.55 

Manganese, %... .0.70-1 .00 0.70-1.00 0.75-1.05 0.80-1.10 0.84-1.14 

Phosphorus not over 0.10%; silicon not over 0.20%. Drop Test: A 
piece of rail 4 to 6 ft. long, selected from each blow, is placed head up- 
wards on supports 3 ft. apart. The anvil weighs at least 20,000 lbs., 
and the tup, or falling weight, 2000 lbs. The rail should not break when 
the drop is as follows: 

Weight per yard, lbs 71 to 80 81 to 90 91 to 100 

Height of drop, feet 16 17 18 

If any rail breaks when subjected to the drop test, two additional tests 
will be made of other rails from the same blow of steel, and if either ol 



VARIOUS SPECIFICATIONS FOR STEEL. 



509 



these latter tests fail, all the rails of the blow which they represent will 
be rejected; but if both of these additional test-pieces meet the require- 
ments, all the rails of the blow which they represent will be accepted. 

Shrinkage: Tae number ot passes and the speed oT the roll train shall 
be so regulated that for sef'tions 75 lbs. per yard nnd heavier the temper- 
ature on leaving the rolls will not exceed that which requires a shrinkage 
allowance at the hot sa^-s of 611/16 in^'hes for a 33-ft. 75-lb. rail, with an 
increase of Vie ' ^. for each increase of 5 lbs. in the weight of the section. 

Open-hearth rails; chemical specifications: 

Weight per yard, lbs. . 60 to 60 61 to 70 71 to 80 81 to 90 90 to 100 
Carbon, % 0.46-0.59 0.46-0.59 0.52-0.65 0.59-0.72 0.62-0.75 

Manganese, 0.60 to 0.90; Phosphorus, not over 0.04; Silicon, not over 
0.20. Drop Tests : 50 to 60-lb., 15 ft.; 61 to 70-lb., 16 ft.; heavier sec- 
tions same as Bessemer. 

Specifications for Steel Axles. (Proc. A. S. T. M., 1905 p. 56.) — 





P.'& 


Tens. 

Str. 


Yield 
Pt. 


El. in 
2 in. 


Red. 
Area. 


Car and tender truck 


0.06 
0.06 
0.04 










Driving and engine truck, C. S.* 

Driving and engine truck, N. S.f 


80,000 
80,000 


40,000 
50,000 


il 


25% 
45% 



* Carbon steel. 

t Nickel steel, 3 to 4 % Ni. 

i Each not to exceed. Mn in carbon steel not over 0.60 %. 

Drop Tests. — One drop test to be made from each melt. The axle 
rests on supports 3 ft. apart, the tup weighs 1640 lbs., the anvil supported 
on springs, 17,500 lbs.; the radius of the striking face of the. tup is 5 in. 
The axle is turned over after the first, third and fifth blows. It must 
stand the number of blows named below without rupture and without 
exceeding, as the result of the first blow, the deflection given. 



Diam. axle at center, in 

Number of blows 

Height of drop, ft 

Deflection, in 



41/4- 


43/8 


4^7/16 

281/2 
81/4 


45/8 

31 

8 


43/4 

34 
8 


5 3/8 

43 

7 


24 
81/41 


26 
81/4 



57/8 

43 
51/2 



Speclflcations for Tires. (A. S. T. Af., 1901.) — Physical require- 
ments of test-piece 1/2 in. diam. Tires for passenger engines: T. S., 100,000; 
El. in 2 in., 12%. Tires for freight engines and car wheels: T. S., 110,000; 
El., 10%. Tires for switching engines: T. S., 120,000; El., 8%. 

Drop Test. — If a drop test is called for, a selected tire shall be placed 
vertically under the drop on a foundation at least 10 tons in weight and 
subjected to successive blows from a tup weighing 2240 lbs. falling from 
increasing heights until the required deflection is obtained, without break- 
ing or cracking. The minimum deflection must equal D^ -*• "(407^ 4- 
2D), D being internal diameter and T thickness of tire at center ol 
tread. 

Splice-bars. (A. S. T. M., 1901.) — Tensile strength of a specimen 
cut from the head of the bar, 54,000 to 64,000 lbs.; yield point, 32,000 
lbs. Elongation in 8 in., not less than 25 per cent. A test specimen 
cut from the head of the bar shall bend 180° flat on itself without fracture 
on the outside of the bent portion. If preferred, the bending test may 
be made on an unpunched splice-bar, which shall be first flattened and 
then bent. One tensile test and one bending test to be made from each 
blow or melt of steel. 



510 



STEEIi, 



Specifications for Steel Used in Automobile Construction* 

(E. F. Lake, Am. Mach., March 14, 1907.) — 



(1) 
(2) 
(3) 
(4) 

(7) 



40-0.55 

20-0.35 

25 

25-0.35 

45-0.55 
28-0.36 
85-1.00 
50 



Mn. 



0.40- 

0.40- 

0.40 

0.60 

1.1-1.3 
0.3-0.6 
0.25-0.5 
1.50- 



Cr. 



0.80 + 

0.80 + 
1.50 



Ni. 



1.50 + 

1.50 + 
3.50 
1.50 + 



30.0 



P. 



0.04- 

0.04- 

0.015 

0.03 

0.065- 
0.05- 
0.03- 
0.04- 



S. 



0.04- 

0.04- 

0.025 

0.04 

0.06- 
0.06- 
0.03- 
0.06- 



T. S. 



f 90000 + 
1180000 + 
/ 85000 + 
1130000 + 

120000 

f 85000 + 

I1OOOOO + 

85000 + 

75000 + 



E. L. 



65000 + 
140000 + 
65000 + 
100000 + 
105000 
60000 + 
70000 + 
55000 + 
40000 + 



El. in 
2 in. 



18 + 
8 + 
20 + 
12 + 
20 
25 + 
20 + 
15 + 
25 + 



R.of 
A. 



35 + a 
20 +b 
50+a 
30+b 
58c 
50+a 
50 + b 
45 + c 
40+c 



The plus sign means "or over"; the minus sign "or less.'* 
a, fully annealed; b, heat-treated, that is oil-quenched and partly 
annealed; c, as rolled. 

(1) 45% carbon chrome-nickel steel, for gears of high-grade cars. 
When annealed this steel can be machined with a high-speed tool at the 
rate of 35 ft. per min., with a Vl6-in. feed and a s/iQ-in. cut. It is annealed 
at 1400° F. 4 or 5 hours, and cooled slowly. In heat-treating it is heated 
to 1500°, quenched in oil or water and drawn at 500° F. 

(2) 25% carbon chrome-nickel steel, for shafts, axles, pivots, etc. 
This steel may be machined at the same rate as (1), and it forges more 
easily. 

(3) A foreign steel used for forgings that have to withstand severe 
alternating shocks, such as differential shafts, transmission parts, universal 
joints, axles, etc. 

(4) Nickel steel, used instead of (1) in medium and low-priced cars. 

(5) "Gun-barrel " steel, used extensively for rifle barrels, also in low- 
priced automobiles, for shafts, axles, etc. It is used as it comes from 
the maker, without heat-treating. 

(6) Machine steel. Used for parts that do not require any special 
strength. 

(7) Spring steel used in automobiles. 

(8) Nickel steel for valves. Used for its heat-resisting qualities in 
valves of internal-combustion engines. 

Carbonizing or Case-hardening. — Some makers carbonize the surface 
of gears made from steel (1) above. They are packed in cast-iron boxes 
with a mixture of bone and powdered charcoal and heated four hours 
at nearly the melting-point of the boxes, then cooled slowly in the boxes. 
They are then taken out, heated to 1400° F. for four hours to break up the 
coarse grain produced by the carbonizing temperature. After this the 
work is heat-treated as above described. 

The machine steel (6) case-hardens well by the use of this process. 

Specifications for Steel Castings. (Proc. A. S. T. M., 1905, p. 53.) — 
Open-hearth, Bessemer, or crucible. Castings to be annealed unless 
otherwise specified. Ordinary castings, in which no physical require- 
ments are specified, shall contain not over 0.04 C and not over 0.08 P. 
Castings subject to physical test shall contain not over 0.05 P and not 
over 0.05 S. The minimum requirements are: 





T. S. 


Y. P. 


El. in 2 

in. 


Red. 
Area. 


Hard castings 


85.000 
70,000 
60.000 


38.250 
31.500 
27,000 


15^- 
18 % 
22% 


20% 


Medium castings 


25% 


Soft castings 


30% 







' FORCE, STATICAL MOMENT, EQUILIBRIUM, ETC. 511 

For small or unimportant castings a test to destruction may be sub- 
stituted. Three samples are selected from each melt or blow, annealed 
in the same furnace charge, and shall show the material to be ductile 
and free from injurious defects, and suitable for the purpose intended. 
Large castings are to be suspended and hammered all over. No cracks, 
flaws, defects nor weakness shall appear after such treatment. A speci- 
men 1 X V2 in. shall bend cold around a diam. of 1 in. without fracture 
on outside of bent portion, through an angle of 120° for soft and 90° for 
medium castings. 

Specifications for steel castings issued by the U. S. Navy Department, 
1889 (abridged): Steel for castings must be made by either the open- 
hearth or the crucible process, and must not show- more than 0.06% of 
phosphorus. All castings must be annealed, unless otherwise directed. 
The tensile strength of steel castings shall be at least 60,000 lbs., with an 
elongation of at least 15% in 8 in. for all castings for moving parts of 
machinery, and at least 10% in 8 in. for other castings. Bars 1 in. sq. 
shaU be capable of bending cold, without fracture, through an angle of 
90°, over a radius not greater than IV2 in. All castings must be sound, 
free from injurious roughness, sponginess, pitting, shrinkage, or other 
cracks, cavities, etc. 

Pennsylvania Railroad specifications, 1888: Steel castings should have a 
tensile strength of 70,000 lbs. per sq. in. and an elongation of 15% in 
section originally 2 in. long. Steel castings will not be accepted if tensile 
strength falls below 60,000 lbs., nor if the elongation is less than 12%, nor 
if castings have blow-holes and shrinkage cracks. Castings weighing 80 
lbs. or more must have cast with them a strip to be used as a test-piece. 
The dimensions of this strip must be 3/4 in. sq. by 12 in. long. 



MECHANICS. 

FORCE, STATICAL M03IENT, EQUILIBRIUM, ETC. 

Mechanics is the science that treats of the action of force upon bodies. 
Statics is the mechanics of bodies at rest relatively to the earth's surface. 
Dynamics is the mechanics of bodies in motion. Hydrostatics and hydro- 
dynamics are the mechanics of liquids, and Pneumatics the mechanics 
or air and other gases. These are treated in other chapters. 

There are four elementary quantities considered in Mechanics: Matter, 
Force, Space, Time. 

Matter. — Any substance or material that can be weighed or measured. 
It exists in three forms: solid, liquid, and gaseous. A definite portion 
of matter is called a body. 

The Quantity of 3Iatter in a body may be determined either by 
measuring its bulk or by weighing it, but as the bulk varies with temper- 
ature, with porosity, with size, shape and method of piling its particles, 
etc., weighing is generally the more accurate method of determining its 
quantity. 

Weight. 3Iass. — The word "weight" is commonly used in two 
senses: 1. As the measure of quantity of matter in a body, as deter- 
mined by weighing it in an even balance scale or on a lever'^or platform 
scale, and thus comparing its quantity with that of certain pieces of metal 
called standard weights, such as the pound avoirdupois. 2. As the 
measure of the force which the attraction of gravitation of the earth 
exerts on the body, as determined by measuring that force with a spring 
balance. As the force of gravity varies with the latitude and elevation 
above sea level of different parts of the earth's surface, the weight deter- 
mined in this second method is a variable, while that determined by 
the first method is a constant. For this reason, and also because spring 
balances are generally not as accurate instruments as even balances, or 
lever or platform scales, the word "weight," in engineering, unless other- 
wise specified, means the quantity of matter as determined by weigh- 
ing it by the first method. The standard unit of weight is the pound. 

The word "mass" is used in three senses bj^ writers on physics and 
engineering: 1. As a general expression of an indefinite quantity, syn- 
onymous with lump, piece, portion, etc., as in the expression "a mass 
whose weight is one pound." 2. As the quotient of the weight, ai 



512 MECHANICS. 

determined by the first method of weighing given above, by 32.174, the 
standard value of g, the acceleration due to gravity, expressed by 
the formula M = W/g. This value is merely the arithmetical ratio of 
the weight in pounds to the acceleration in feet per second per second, 
and it has no unit. 3. As a measure of the quantity of matter, ex- 
actly synonymous with the first meaning of the word "weight," given 
above. In this sense the word is used in many books on physics and 
theoretical mechanics, but it is not so used by engineers. The state- 
ment in such books that the engineers' unit of mass is 32.2 lbs. is an 
error. There is no such unit. Whenever the term "mass" is repre- 
sented by M in engineering calculations it is equivalent to W/g, in 
which Wis the quantity of matter in pounds, and g = 32.1740 (or 32.2 
approximate) . 

Local Weight. — The force, measured in standard pounds of force 
(see Unit of Force, below), with which gravity attracts a body at a 
locality other than one where g = 32.174 is sometimes caUed the 
"local weight" of the body. It is the weight that would be indicated 
if the body was weighed on a spring balance calibrated for standard 
pounds of force. If the balance was calibrated for the particular lo- 
cality, it would indicate not the local weight, but the true or standard 
weight, that is, the quantity of matter in pounds or the force that 
gravity would exert on the body at the standard locality, these being 
numerically identical. The difference between standard and local 
weight is rarely large enough to be of importance in engineering 
problems. In the United States (exclusive of Alaska), the range of 
the value of g is only from 0.9973 (at lat. 25°, 10,000 ft. above the sea) 
to 1.0004 (lat. 49° at the sea level) of the standard value (lat. 45° at 
the sea level) of 32.1740. 

A Force is anything that tends to change the state of a body with 
respect to rest or motion. If a body is at rest, anything that tends to 
put it in motion is a force; if a body is in motion, anything that tends to 
change either its direction or its rate of motion is a force. 

A force should always mean the pull, pressure, rub, attraction (or re- 
pulsion) of one body upon another, and always implies the existence of a 
simultaneous equal and opposite force exerted by that other body on th3 
first body, i.e., the reaction. In no case should we call anything a forco 
imless we can conceive of it as capable of measurement by a sprin<? 
balance, and are able to say from what other body it comes. (I. P. 
Church.) 

Forces may be divided into two classes, extraneous and molecular; 
extraneous forces act on bodies from without; molecular forces arc 
exerted between the neighboring particles of bodies. 

Extraneous forces are of two kinds, pressures and moving forces: pres- 
sures simply tend to produce motion; moving forces actually produc3 
motion. Thus, if gravity act on a fixed body, it creates pressure; if on a 
free body, it produces motion. 

Molecular forces are of two kinds, attractive and repellent: attractive 
forces tend to bind the particles of a body together ; repellent forces tend 
to thrust them asunder. Both kinds of molecular forces are continu- 
ally exerted between the molecules of bodies, and on the predominanca 
of one or the other depends the physical state of a body, as solid, liquid, 
o^ gaseous. 

The Unit of Force used in engineering, by English writers, is the 
pound avoirdupois. Strictly, it is the force which would give to a 
pound of matter an acceleration of 32.1740 feet per sec. per sec, or the 
force with which gravity attracts a pound of matter at 45° latitude at 
the sea level. In the French C. G. S. or centimeter-gram-second system, 
the unit of force is the force which acting on a mass of one gram will 
produce in one second a velocity of one centimeter per second. This 
unit is called a "dyne" = 1/980-665 gram. 

An attempt has been made by some writers on physics to introduce 
the so-called "absolute system" into English weights and measures, and 
to define the "absolute unit" of force as that force which acting on the 
mass whose weight is one pound at London will in one second produce a 
velocity of one foot per second, and they have given this unit the name 
"poundal." The use of this unit only makes confusion for students, 
and it is to be hoped that it will soon be abandoned in high-school text- 
books. Professor Perry, in his "Calculus for Engineers," p. 26, says. 



FOKCE, STATICAL MOMENT, EQUILIBRIUM, ETC. 513 



" One might as well talk Choctaw in the shops as to speak about ... so 
many poundals of force and so many foot-poundals of work."* 

Inertia is that property of a body by virtue of which it tends to con- 
tinue in the state of rest or motion in which it may.be placed, until acted 
on by some force 

Newton's Laws of Motion. — 1st Law. If a body be at rest, it will 
remain at rest, or if in motion it will move uniformly in a straight line till 
acted on by some force. 

2d Law. If a body be acted on by several forces, it will obey each as 
though the others did not exist, and this whether the body be at rest or in 
motion. (This law is expressed in different forms by various authors. 
One of these forms is: Change of the motion of a body is proportional 
to the force and to the time during which the force acts, and is in the 
same direction as the force.) 

3d Law. If a force act to change the state of a body with respect to rest 
or motion, the body will offer a resistance equal and directly opposed to the 
force. Or, to every action there is opposed an equal and opposite reaction. 

Graphic Representation of a Force. — Forces may be represented 
geometrically by straight Unes, proportional to the forces. A force is 
given when we know its intensity, its point of application, and the direc- 
tion in which it acts. When a force is represented by a •ine, the length of 
the hne represents Its intensity; one extremity represents the point of 
apphcation; and an arrow-head at the other extremity shows the direc- 
tion of the force. 

Composition of Forces is the operation of finding a single force whose 
effect is the same as that of two or more given forces. The required 
force is called the resultant of the given forces. 

Resolution of Forces is the operation of finding two or more forces 
whose combined effect is equivalent to that of a given force. The required 
forces are called components of the given force. 

The resultant of two forces applied at a point, and acting in the same di- 
rection, is equal to the sum of the forces. If two forces act in opposite 
directions, their resultant is equal to their difference, and it acts in the 
direction of the greater. 

If any number of forces be applied at a point, some in one direction and 
others in a contrary direction, their resultant is equal to the sum of those 
that act in one direction, diminished by the sum of those that act in the 
opposite direction; or, the resultant is equal to the algebraic sum of the 
components. 

Parallelogram of Forces. — If two forces acting on a point be rep- 
resented in direction and intensity by adjacent sides of a parallelogram, 
their resultant will be represented by that diagonal of the parallelogram 
which passes through the point. Thus OR, Fig. 99, is the resultant of 
OQ and OP, 

#5 




Fig. 99. 



Fig. 100. 




Polygon of Forces. — If several forces are applied at a point and act 
in a single plane, their resultant is found as follows: 

Through the point draw a line representing the first force; through the 

* Professor Perry himself, however, makes a slip on the same page in 
saying : " Force in pounds is the space-rate at which work in foot-pounds 
is done; it is also the time-rate at which momentum is produced or de- 
stroyed." He gets this idea, no doubt, from the equations FT = MV, 
F = MV/T, F = }4 MV^ -r- 5. Force is not these things: it is merely 
numerically equivalent, when certain units are chosen, to these last two 
quotients. We might as well say, since T = MV/F, that time is the 
force-rate of momentum. 



514 



MECHANICS. 



extremity of this draw a line representing the second force; and so on, 
throughout the system; finally, draw a line from the starting-point to the 
extremity of the last line drawn, and this will be the resultant required. 
Suppose the body A, Fig. 100, to be urged in the directions ^1, A2, A3, 
A4i, and A5 by forces which are to each other as the lengths of those lines. 
Suppose these forces to act successively and the body to first move from A 



all the forces considered. If there had been an additional force. Ax, in 
the group, the body would be returned by that force to its original position, 
supposing the forces to act successively, but if they had acted simul- 
taneously the body would never have moved at all; the tendencies to 
motion balancing each other. 

It follows, therefore, that if the several forces which tend to move a 
body can be represented in magnitude and direction by the sides of a 
closed polygon taken in order, the body will remain at rest; but if the 
forces are represented by the sides of an open polygon, the body will moye 
and the direction will be represented by the straight line which closes the 
polygon. 

Twisted Polygon. — The rule of the polygon of forces holds true even 
when the forces are not in one plane. In this case the lines Al, 1-2', 2'-3', 
etc.. form a twisted polygon, that is, one whose sides are not in one plane. 

Parallelopipedon of Forces. — If three forces acting on a point be 
represented by three edges of a parallelopipedon which meet in a common 
point, their resultant will be represented by the diagonal of the parallelo- 
pipedon that passes through their common point. 

Thus OT^.Fig. 101 ,is the resultant of OQ, OS and OP. OM is the result- 
ant of OP and OQ, and OR is the resultant of OM and OS. 





Fig. 102. 

3Ioment of a Force. — The moment of a force (sometimes called 
statical moment), with respect to a point, is the product of the force by 
the perpendicular distance from the point to the direction of the force. 
The fixed point is called the center of moments; the perpendicular distance 
is the lever-arm of the force; and the moment itself measures the tendency 
of the force to produce rotation about the center of moments. 

If the force is expressed in pounds and the distance in feet, the moment 
is expressed in foot-pounds. It is necessary to observe the distinction be- 
tween foot-pounds of statical moment and foot-pounds of work or energy. 
(See Work.) 

In the bent lever. Fig. 102 (from Trautwine), if the weights n and m 
represent forces, their moments about the point / are respectively nX af 
and m X fc. If instead of the weight m a pulling force to balance the 
weight n is applied in the direction bs, or b7j or bd, s, y, and d being the 
amounts of these forces, their respective moments are sXft,yX fb, 
dXfh. 

If the forces acting on the lever are in equilibrium it remains at rest, and 
the moments on each side of / are equal, that is, n X a/ = m X fc, or s X 
ft. or yX fb. or d X hf. 

The moment of the resultant of any number of forces acting together in 



FORCE, STATICAL MOMENT, EQUILIBRIUM, ETC. 515 

the same plane is equal to the algebraic sum of the moments of the forces 
taken separately. 

Statical 3Ioment. Stability. — The statical moment of a body is 
the product of its weight by the distance of its line of gravity from some 
assumed line of rotation. The line of gravity is a vertical line drawn from 
its center of gravity through the body. The stability of a body is that 
resistance which its weight alone enables it to oppose against forces tend- 
ing to overturn it or to slide it along its foundation. 

To be safe against turning on an edge the moment of the forces tending 
to overturn it, taken with reference to that edge, must be less than the 
statical moment. When a body rests on an inclined plane, the line of 
gravity, being vertical, falls toward the lower edge of the body, and the 
condition of its not being overturned by its own weight is that the line of 
gravity must fall within this edge. In the case of an inclined tower 
resting on a plane the same condition holds — the line of gravity must 
fall within the base. The condition of stability against sliding along a 
horizontal plane is that the horizontal component of the force exerted 
tending to cause it to slide shall be less than the product of the weight of 
the body into the coefficient of friction between the base of the body and 
its supporting plane. This coefficient of friction is the tangent of the 
angle of repose, or the maximum angle at which the supporting plane 
might be raised from the horizontal before the body would begin to slide. 
(See Friction.) 

The Stability of a Dam against overturning about its lower edge 
is calculated by comparing its statical moment referred to that edge with 
the resultant pressure of the water against its upper side. The horizontal 
pressure on a square foot at the bottom of the dam is equal to the weight of 
a column of water of one square foot in section, and of a height equal to the 
distance of the bottom below water-level; or, if H is the height, the pressure 
at the bottom per square foot = 62.4 X H ll5s. At the water-level the 
pressure is zero, and it increases uniformly to the bottom, so that the sum 
of the pressures on a vertical strip one foot in breadth may be represented 
by the area of a triangle whose base is 62.4 X H and whose altitude is H, 
or 62.4 //2 -T- 2.. The center of gravity of a triangle being i/a of its altitude, 
the resultant of all the horizontal pressures may be taken as equivalent 
to the sum of the pressures acting at 1/3 H, and the moment of the sum of 
the pressures is therefore 62.4 X H^ -v- 6. 

Parallel Forces. — If two forces are parallel and act in the same direc- 
tion, their resultant is parallel to both, and lies bet^yeen them, and the 
intensity of the resultant is equal to the sum of the intensities of the two 
forces. Thus in Fig. 102 the resultant of the forces n and m^acts verti- 
cally downward at /, and is equal to n ■\- m. 

If two parallel forces act at the extremities of a straight line and in 
the same direction, the resultant divides the line joining the points of 



N 



N 



p^ ^-^Q Q< -^ 

y-^ — >R ¥^. >p 



I Fig. 104. 



Md^ 1 >P Fig. 103. ^^ 1 ^r 

c 

application of the components, inversely as the components. Thus in 
Fig. 102 m: n:: af:fc'' and in Fig. 103, P: Q:: SN: SM. 

The resultant of two parallel forces acting in opposite directions is 
parallel to both, lies without both, on the side and in the direction of the 
greater, and its intensity is equal to the diflereiicc of the intensities of 
the two forces. 

Thus the resultant of the tw^o forces Q and P, Fig. 104, is equal to 
Q — P = R. Of any two parallel forces and their resultant each is pro- 
portional to the distance between the other two; this in both Figs. 103 
and 104, P:Q: R:: SN: SM: MN. 

Couples. — If P and Q be equal and act in opposite directions, R = Q; 
that is, they have no resultant. Two such forces constitute a couple. 

The tendency of a counle is to produce rotation; the measure of this 
tendency, called the moment of the couple, is the product of one of the 
forces by the distance between the two. 



616 MECHANICS. 



[ 



^ "S Since a couple has no single resultant, no 

single force can balance a couple. To prevent 
the rotation of a body acted on by a couple the 
apphcation of two other forces is required, 
forming a second couple. Thus in Fig. 105, 
P and Q, forming a couple, may be balanced 
by a second couple formed by R and 5. The 
point of application of either R or S may be a 
Fig 105. fixed pivot or axis. 

r^y f :Moment of the couple PQ = P{c-\-h + a) = 
I ^' moment of RS = Rb. Also, P + R = Q -{- S. 

^ rs The forces R and S need not be parallel to P 

and Q, but if not, then their components par- 
allel to PQ are to be taken instead of the forces themselves. 

Equilibrium of Forces. — A system of forces applied at points of a 
solid body will be equilibrium when they have no tendency to produce 
motion, either of translation or of rotation. 

The conditions of equilibrium are: 1. The algebraic sum of the com- 
ponents of the forces in the direction of any three rectangular axes must 
separately equal 0. 2. The algebraic sum of the moments of the forces, 
with respect to any three rectangular axes, must separately equal 0. 

If the forces lie in a plane: 1. The algebraic sum of the components 
of the forces, in the direction of any two rectangular axes, must be 
separately equal to 0. 2. The algebraic sum of the moments of the 
forces, with respect to any point in the plane, must be equal to 0. 

If a body is restrained by a fixed axis, as in case of a pulley, or wheel 
and axle, the forces will be in equilibrium when the algebraic sum of 
the moments of the forces with respect to the axis is equal to 0. 

CENTER OF GRAVITY. 

The center of gravity of a body, or of a system of bodies rigidly con- 
nected together, is that point about which, if suspended, all jthe parts will 
be in equilibrium, that is, there wdll be no tendency to rotation. It is 
the point through which passes the resultant of the efforts of gravitation 
on each of the elementary particles of a body. In bodies of equal heavi- 
ness throughout, the center of gravity is the center of magnitude. 

(The center of magnitude of a figure is a point such that if the figure 
be divided into equal parts the distance of the center of magnitude of 
the whole figure from any given plane is the mean of the distances of 
the centers of magnitude of the several equal parts from that plane.) 

A body suspended at its center of gravity is in equilibrium in all 
positions. If suspended at a point outside of its center of gravity, it 
will take a position so that its center of gravity is vertically below its 
point of suspension. 

To find the center of gravity of any plane figure mechanically, sus- 
pend the figure by any point near its edge, and mark on it the direction 
of a plumb-line hung from that point; then suspend it from some other 
point, and again mark the direction of the plumb-line in like manner. 
The center of gravity will be at the intersection of the two marks. 

Tlie Center of Gravity of Regular Figures, whether plane or solid, 
is the same as their geometrical center; for instance, a straight Une, 
parallelogram, regular polygon, circle, circular ring, prism, cylinder, 
sphere, spheroid, middle frustums of spheroid, etc. 

Of a triangle: On a line drawn from any angle to the middle of the 
opposite side, at a distance of one-third of the line from the side; or at 
the intersection of such lines dra^vn from any two angles. 

Of a trapezium or trapezoid: Draw a diagonal, dividing it into two tri- 
angles. Draw a Une joining their centers of gravity. Draw the other 
diagonal, making two other triangles, and a line joining their centers 
of gravity. The intersection of the two lines is the center of gravity. 

Of a sector of a circle: On the radius which bisects the arc, 2 cr -i- S I 
from thn center, c being the chord, r the radius, and I the arc. 

Of a semicircle: On the middle radius, 0.4244 r from the center. 

Of a quadrant: On the middle radius, 0.600 r from the center. 

Of a segment of a circle: c^ ^ ^ 2a from the center, c = chord, a =area. 

Of a paraboic surface: In the axis, 3/5 of its length from the vertex. 

Of a semi-parabola (surface): 3/5 length of the axis from the vertex, 
and 3/8 of the semi-base from the axis. 



MOMENT OF INERTIA. 517 

Of a cone or pyramid: In the axis, 1/4 of its length from the base. 

Of a paraboloid: In the axis, 2/3 or its length from the vertex. 

Of a cylinder, or regular prism: In the middle point of the axis. 

Of a frustum of a cone or pyramid' Let a = length of a line drawn from 
the vertex of the cone when complete to the center of gravity of the base, 
and a' that portion of it between the vertex and the top of the frustum; 
then distance of center of gravity of the frustum from center of gravity of 

its base =- ? - ^, , ^^^? . ,,, - 
4 4(a2 + aa' + a'2) 

For two bodies, fixed one at each end of a straight bar, the common 
center of gravity is in the bar, at that point which divides the distance 
between their respective centers of gravity in the inverse ratio of the 
weights. In this solution the weight of the bar is neglected. But it may 
be taken as a third body, and allowed for as in the following directions: 

For more than two bodies connected in one system: Find the common 
center of gravity of two of them; and find the common center of these two 
jointly with a third body, and so on to the last body of the group. 

Another method, by the principle of moments: To find the center of 
gravity of a system of bodies, or a body consisting of several parts, whose 
several centers are known. If the bodies are in a plane, refer their several 
centers to two rectangular coordinate axes. Multiply each weight by ita 
distance from one of the axes, add the products, and divide the sum by the 
sum of the weights; the result is the distance of the center of gravity from 
that axis. Do the same with regard to the other axis. If the bodies are 
not in a plane, refer them to three planes at right angles to each other, and 
determine the mean distance of the sum of the weights from each plane. 

MOMENT OF INERTIA. 

The moment of inertia of the weight of a body with respect to an axis 
is the algebraic sum of the products of the weight of each elementary 
particle by the square of its distance from the axis. If the moment of 
inertia with respect to any axis = /, the weight of any element of the 
body = w, and its distance from the axis = r, we have I = ^{wr^)» 

The moment of inertia varies, in the same body, according to the 
position of the axis. It is the least possible when the axis passes through 
the center of gravity. To find the moment of inertia of a body, referred 
to a given axis, divide the body into small parts of regular figure. Multi- 
ply the weight of each part by the square of the distance of its center of 
gravity from the axis. The sum of the products is the moment of inertia. 
The value of the moment of inertia thus obtained will be more nearly 
exact, the smaller and more numerous the divisions of the body. 

Moments of Inertia of Regular Solids. — Rod, or bar, of uniform 
thickness, with respect to an axis perpendicular to the length of the rod, 

/=Tf(| -{-d^y (1) 

W = weight of rod, 21 = length, d = distance of center of gravity from 

axis. 

Thin circular plate, axis in its ) i'_ w /?f . ^2 \ (o\ 

own plane, J U / ^^ 

r = radius of plate. 

Circular plate, axis perpendicular to ) r_ ^,7 /^^ •_ W2 \ ffi\ 

the plate, T "- ^^ V 2* "^ / ^ ' 

Circular ring, axis perpendicular to) r_Trr (r^ + r^ , ^2\ iA\ 

its own plane, ^i-w y — + a j, . . . k^) 

r and r' are the exterior and interior radii of the ring. 

Cyhnder, axis perpendicular to the) t_tt7 /^^ ,^^ . W2\ {k\ 

axis of the cylinder. T ~ ^ U "^ 3 "^ ^ j* * ' ' ^^' 

r = radius of base. 2 1 = length of the cylinder. 

By making d = in any of the above formulae, we find the moment of 
inertia for a parallel axis through the center of gravity. 

The moment of inertia, ^wr'^, numerically equals the weight of a body 
which, if concentrated at the distance unity from the axis of rotation, 
would require the same work to produce a given increase of angular 
velocity that the actual body requires. It bears the same relation to 
angular acceleration which weight does to linear acceleration (Rankine). 
The term moment of inertia is also used in regard to areas, as the cross- 



518 MECHANICS. 

sections of) beams under strain. In this case I ='^ar^, a being any ele- 
mentary area, and r its distance from the center. (See Strength of Ma- 
terials, p. 293. ) Some writers call 27??r2 = 2ut2-t- g the moment of inertia. 

CENTERS OF OSCILLATION AND OF PERCUSSION. 

Center of Oscillation. — If a body oscillate about a fixed horizontal 
axis, not passing through its center of gravity, there is a point in the line 
drawn from the center of gravity perpendicular to the axis whose motion 
is the same as it would be if the whole mass were collected at that point 
and allowed to vibrate as a pendulum about the fixed axis. This point is 
called the center of oscillation. 

The Radius of Oscillation, or distance of the center of oscillation 
from the point of suspension = the square of the radius of gyration -r- dis- 
tance of the center of gravity from the point of suspension or axis. The 
centers of oscillation and suspension are convertible. 

If a straight line, or uniform thin bar or cylinder, be suspended at one 
end, oscillating about it as an axis, the center of oscillation is at 2/3 the 
length of the rod from the axis. If the point of suspension is at 1/3 the 
length from the end, the center of oscillation is also at 2/3 the length from 
the axis, that is, it is at the other end. In both cases the oscillation will 
be performed in the same time. If the point of suspension is at the 
center of gravity, the length of the equivalent simple pendulum is infinite, 
and therefore the time of vibration is infinite. 

For a sphere suspended by a cord, r = radius, h == distance of axis of 
motion from the center of the sphere, h' = distance of center of oscillation 
from center of sphere, I = radius of oscillation = /i + /i' = ^ + 2/5 (r2-i- h). 

If the sphere vibrate about an axis tangent to its surface, h = r, and 
l = r+ 2 sr. If h = 10 r, I = 10 r + (r-^25). 

Lengths of the radius of oscillation of a few regular plane figures or 
thin plates, suspended by the vertex or uppermost point. 

1st. When the vibrations are perpendicular to the plane of the figure: 

In an isosceles triangle the radius of oscillation is equal to 3/4 of the 
height of the triangle. 

In a circle, Ws of the diameter. 

In a parabola, 5/7 of the height. 

2d. When the vibrations are edgewise, or in the plane of the figure: 

In a circle the radius of oscillation is 3/4 of the diameter. 

In a rectangle suspended by one angle, 2/3 of the diagonal. 

In a parabola, suspended by the vertex, 5/7 of the height plus 1/3 of 
the parameter. 

In a parabola, suspended by the middle of the base, 4/7 of the height plus 
1/2 the parameter. 

Center of Percussion. — The center of percussion of a body oscillat- 
ing about a fixed axis is the point at which, if a blovv is struck by the body, 
the percussive action is the same as if the whole mass of the bodv were 
concentrated at the point. It is identical with the center of oscillation. 

CENTER AND RADIUS OF GYRATION. 

The center of gyration, with reference to an axis, is a point at which, if 
the entire weight of a body be concentrated, its moment of inertia will re- 
main unchanged; or, in a revolving body, the point in which the whole 
weight of the body may be conceived to be concentrated, as if a pound of 
platinum were substituted for a pound of revolving feathers, the angular 
velocity and the accumulated work remaining the same. The distance of 
this point from the axis is the radius of gyration. If W = the weight of a 
body, / = 221^2 = its moment of inertia, and k = its radius of gyration, 

The moment of inertia = the weight X the square of the radius of gyration. 
To find the radius of gyration divide the body into a considerable 
number of equal small parts, — the more numerous the more nearly exact 
is the result, — then take the mean of all the squares of the distances of the 
parts from the axis of revolution, and find the square root of the mean 
square. Or, if the moment of inertia is known, divide it by the weight 
and extract the square root. For radius of gyration of an area, divide 
the moment of inertia of the area by the area and extract the square 
root. 



CENTER AND RADIUS OF GYRATION. 



519 



The radius of gyration is the least possible when the axis passes through 
the center of gravity. This minimum radius is called the principal radius 
of gyration. If we denote it by k and any other radius of gj^ration by k' , 
we have for the five cases given under the head of moment of inertia above 
the following values: 



(1) Rod, axis perpen. to ) 7. 
length, S 



A^'-yll- 



d\ 



(2) Circular plate, axis in) 7. _ ^, 1., _ K hi 
Its plane, T 2' ~ V 4 



(3) 



+ cP. 



Circular plate, axis per- ) 7. _ _ 4 / 1 . 7., _ 4 /!!! . ^ 
pen. to plane, ]'^~^\ 2' ~ \ 2^ ' 



(4) Circular ring, axis per- ) j^ _ J LL±J2.- i-^ - Jll±j2 4. tn 

pen. to plane, p-V 2 •'^-V 2 ^' 

(5) Cylinder, axis per- K _ Jt+l • k' = J^T^T^ 

pen. to length, ] V43' V43' 

Principal Radii of Gyration and Squares of Radii of Gyration. 

(For radii of gyration of sections of columns, see page 295.) 



Surface or Solid. 



Parallelogram: ) axis at its base 

height^ J " mid-height 

^^^^i.l}^ r^l ih-.r. I axis at end 

Rectangular prism: 

axes 2 a, 2 b, 2c, referred to axis 2 a... . 
Parallelopiped: length I, base b, axis at j 

one end, at mid-breadth ( 

Hollow square tube: 

out. side h, inner h\ axis mid-length . . . 

very thin, side = h, axis mid-length . . . 

Thin rectangular tube: sides 5, h, axis j 
mid-length j 

Thin circ. plate: rad. r, diam. h, ax. diam. 
Flat circ. ring: diams. h, h', axis diam.. . 
Solid circular cylinder: length I, axis di- ] 

ameter at mid-length 1 

Circular plate: solid wheel of uniform 

thickness, or cylinder of any length, 

referred to axis of cyl 

Hollow circ. cylinder, or flat ring: 

I, length; R, r, outer and inner radii. 

Axis, I, longitudinal axis; 2, diam. at 

mid-length 

Same: very thin, axis its diameter 

" radius r; axis, longitudinal axis . . . 

Circumf . of circle, axis its center 

*' ^ " " " diam 

Sphere: radius r, axis its diam 

Spheroid: equatorial radius r, revolving) 

polar axis a ) 

Paraboloid: r=rad. of base, rev. on axis. 
Ellipsoid: semi-axes a,b,c; revolving on ) 

axis 2 a J 

Spherical shell: radii R, r, revolving on ) 

its diam ) 

Sarne: very thin, radius r 

Solid cone; r = rad. of base, rev. on axis. . 



Rad. of Gyration. 



0.5773 ;i 
0.2886/1 

0.5773 Z 
0.2886 i 



Square of R. 
of Gyration. 



0.577 V62 + c^ 



0.289 V4i2 +1^ 



0.289 Vh'^ +h'2 
.408 h 



0.289A 



1/4 V A2 + h'2 



0.289 Vz2 + 3j.2 



0.7071 : 



0.7071 \//?2 + ^2 



■289V^2+3(^2+^2) 

0.289 V^2T6lF^ 
r 

0.7071 r 
0.6325 r 
0.6325 r 
0.5773 r 
0.4472^62 + c2 



0.6325 



\ R^-r^ 



0.8165 r 
0.5477 r 



1/3 /i2 
V3/2 

(62 + C2) ^ 3 

4^2 + &2 
12 

(/l2 + /l'2)^12 

/l2-6 
h^ h + 3b 

12* h+b 
l/4r2 = ;i2- 16 
ih^ + h'^)^ 16 

12 4 
1/2 r2 

(R^ + r^) -2 
12 4 

ii + ^ 

12 2 

r2 

r2 

1/2 r2 
2/5 r2 

2/5 r^ 

1/8 r2 

5 
2 i^s - r« 



5 R3 -1^ 
2/3 r2 
0.3 r2 



520 MECHANICS. 

THE PENDULUM. 

A body of any form suspended from a fixed axis about which it oscil- 
lates by the force of gravity is called a compound pendulum. The ideal 
body concentrated at the center of oscillation, suspended from the cen- 
ter of suspension by a string without weight, is caUed a simple pendulum. 
This equivalent simple pendulum has the same weight as the given body, 
and also the same moment of inertia, referred to an axis passing through 
the point of suspension, and it oscillates in the same time. 

The ordinary pendulum of a given length vibrates in equal times when 
the angle of the vibrations does not exceed 4 or 5 degrees, that is, 2° or 
2 32° each side of the vertical. This property of a pendulum is called its 
isochronism. 

The time of vibration of a pendulum varies directly as the square root 
of the length, and inversely as the square root of the acceleration due to 
gravity at the given latitude and elevation above the earth's surface. 

If r = the time of vibration, I = length of the simple pendulum, g = 

\T VT 

the acceleration, then T = ir \ —-, since n is constant Too —7=. At a 

^ 9 Vg 

given location g is constant and T 00 \/~L If I be constant, then for any 

1 7r2/ 

location T 00 —;=. If Tbe constant, g T^- = n^l; Iqc g; g ^ -=-. From this 

\/g T^ 

equation the force of gravity at any place may be determined if the 
length of the simple pendulum, vibrating seconds, at that place is 
known. At New York this length is 39.1017 inches = 3.2585 ft., 
whence g = 32.16 ft. 

Time of vibration of a pendulum of a given length at New York 



"=aj; 



I \fr 



/ 39.1017 6.253 

t being in seconds and I in inches. Length of a pendulum having a given 
time of vibration, 1 = PX 39.1017 inches. 

The time of vibration of a pendulum may be varied by the addition of 
a weight at a point above the center of suspension, which counteracts 
the lower weight, and lengthens the period of vibration. By varying the 
height of the upper weight the time is varied. 

To find the weight of the upper bob of a compound pendulum, vi- 
brating seconds, when the weight of the lower bob and the distances of 
the weights from the point of suspension are given: 

^ _ w ^^^-^ X D) - D^ 
•^ (39.1 X d) + d2 • 

W = the weight of the lower bob, w = the weight of the upper bob; 
D = the distance of the lower bob, and d = the distance of the upper 
bob from the point of suspension, in inches. 

Thus, by means of a second bob, short pendulums may be constructed 
to vibrate as slowly as longer pendulums. 

By increasing w or d until the lower weight is entirely counterbalanced 
the time of vibration may be made infinite. 

Conical Pendulum. — A weight suspended by a cord and revolving 
at a uniform speed in the circumference of a circular horizontal plane 
whose radius is r, the distance of the plane below the point of suspension 
being h, is held in equiUbrium by three forces — the tension in the cord, 
the centrifugal force, which tends to increase the radius r, and the force 
of gravity acting downward. If v = the velocity in feet per second of 
the center of gravity of the weight, as it describes the circimiference, g 
= 32.16, and r and h are taken in feet, the time in seconds of performing 
one revolution is (at New York or other place where g = 32.16) 



t==^ = 2n\l]L, 71 = ^=0.8146^2. 



V \g ' 4 772 

If t= 1 second, h = 0.8146 foot =9.775 inches. 
The principle of the conical pendulum is used in the ordinary fly-ball 
governor for steam-engines. (See Governors.) 



VELOCITY, ACCELERATION, FALLING BODIES. 521 

CENTRIFUGAL FORCE. 

A body revolving in a curved path of radius = R in feet exerts a force, 
called centrifugal force, F, upon the arm or cord which restrains it from 
moving in a straight line, or " flying off at a tangent." If W = weight of 
the body in pounds, N = number of revolutions per minute, v == unear 
velocity of the center of gravity of the body, in feet per second, g = 32.174, 
then 

"=-60- • ^= ^ = 32a7i^ = -^600F =^^^^-'000S40S4WBNnbS. 

If n = number of revolutions per second, F = 1.2270 WRn"^, 
(For centrifugal force in fiy-wheels, see Fly-wheels.) 

VELOCITY, ACCELERATION, FALLING BODIES. 

Velocity is the rate of motion, or the speed of a body at any instant. 
If s = space in feet i)assed over in t seconds, and i; = velocity in feet per 
second, if the velocity is uniform, 

V = r', s = vt; C = — 

t V 

If the velocity varies uniformly, the mean velocity v^ = V2 (^'i + ^2) . in which 
Vi is the velocity at the beginning and V2 the velocity at the end of the time t. 

S = V2(Vl +V2)t (1) 

If Vt = 0, then 5 = I/2 ^2^. '?;2 = 2 s/t. 

If the velocity varies, but not uniformly, v for an exceedingly short 
interval of time = s/t, or in calculus v = ds/dt. 

Acceleration is the change in velocity which takes place in a unit of 
time. Unit of acceleration = a = 1 foot per second in one second. For 
uniformly varying velocity, the acceleration is a constant quantity, and 

a=''-2^;V2 = v^ + at;v^==V2-at-,t==^^^^^' . . . (2) 

If the body start from rest, Vi = 0; then if t?^ = mean velocity 

v^= ^; V2=2i;^; a= y; V2=cU; V2-cit=0; ^= ■^' 

g 32.16 \ g =^Tm = T' 
u = space fallen through in the Tth second = g {T - l^). 

It Vi = 0, 5=1/2 V2t. 

Retarded Motion. — If the body start with a velocity Vi and come to 

rest, V2= 0; then s = y2V\t. 

In any case, if the change in velocity is v, 

V . v^ a .. 

For a body starting from or ending at rest, we have the equations 

V = at; s = -t; s = -^•, v^ = 2 as. 

Falling Bodies. — In the case of falling bodies the acceleration due 
to gravity, at 40° latitude, is 32.16 feet per second in one second, =* g. 
Then if v = velocity acquired at the end of t seconds, or final velocity, 
and h = height or space in feet passed over in the same time, 

v=gt = 32.16^ = ^2^= S.02^h = ^ : 
;i = --_16.08(2=- ____ __ 

t=L=--l—= 1^ = \/~h ^ 2 h^ 
g a2.16 \ g 4.01 ~ v ' 
u = space fallen tlirough in the Tth second = g {T — ^2)* 



522 



MECHANICS. 



1 
1 

1 


2 
1 

2 


3 

1 
3 


4 

1 
4 


6 

1 
5 


6 

1 
6 


1 


3 


6 


7 


9 


11 


1 


4 


9 


16 


25 


36 



From the above formulae tor falling bodies we obtain the following: 
During the first second the body starting from a state of rest (resistance 
of the air neglected) falls g ^ 2 = 16.08 feet; the acquired velocity is f/ = 

32.16 ft. per sec; the distance fallen in two seconds is /i = ~ = 16.08 X 4 

= 64.32 ft.; and the acquired velocity is v = p^ = 64.32 ft. The acceler- 
ation, or increase of velocity in each second, is constant, and is 32.16 ft. 
per second. Solving the equations for different times, we find for 

Seconds, t 

Acceleration, g 32.16 X 

Velocity acquired at end of time, u . . . . 32.16 X 

32 16 
Height of fall in each second, u — - — X 

Total height of fall, /i 32.16-4-2 x 

Value of g. — The value of g increases with the latitude, and decreases 
with the elevation. At the latitude of Philadelphia, 40°, its value is 
32.16. At the sea-level, Everett gives g = 32.173 - .082 cos 2 lat. - 
.000003 height in feet. 

At lat. 45° Everett's formula gives g = 32.173. The value given by the 
International Conference on Weights and Measures, Paris, 1901, is 32.1740. 

Values of ^2g, calculated by an equation given by C. S. Pierce, are 
given in a table in Smith's Hydraulics, from which we take the following: 

Latitude 0° 10** 20° 30° 40° 50° 60° 

Value of V2^.. 8.0112 8.0118 8.0137 8.0165 8.0199 8.0235 8.0269 
Value of ^ 32.090 32.094 32.105 32.132 32.160 32.189 32.216 

The value of ^^2^ decreases about .0004 for every 1000 feet increase in 
elevation above the sea-level. 

For all ordinary calculations for the United States, g is generally taken 
at 32.16. and \/2g at 8.02. In England g = 32.2. V2g = 8.025. Practi- 
cal limiting values of g for the United States, according to Pierce, are: 

Latitude 49° at sea-level g = 32. 186 

25° 10,000 feet above the sea g = 32 .089 

Local values of g are used in tjie calculation of problems that involve 
local gravitational force, such as those of falling bodies, lifting loads, 
and power of waterfalls. In all cases in wliich g appears in an equation 
as a di\isor of w (standard weight in pounds), as in the equation for 
centrifugal force on the preceding page, the value 32.174 should be used. 

Fig. 106 represents graphically the velocity, space, etc., of a body falling 
for six seconds. The vertical line at the left is the time in seconds, the 
horizontal lines represent the acquired 
velocities at the end of each second = 
32.16 i. The area of the small triangle 
at the top represents the height fallen 
through in the first second = 1/2 ^= 16.08 
feet, and each of the other triangles is an 
equal space. The number of triangles 
between each pair of horizontal lines rep-^ 
resents the height of fall in each second, 
and the number of triangles between any 
horizontal line and the top is the total 
height fallen during thetime. The figures 
under h, u and v adioining the cut are to 
be multiplied by 1 6.08 to obtain the actual 
velocities and heights for the given times. 16 7 8 4" 

Anerular and Linear Velocity of a 
Turnine Body. - Let r = radius of a 
turning body in feet, n = number of revo- 25 9 10 5" 
lutions per minute, v^ linear velocity of 
a point on the circumference in feet per 
second, and 60 ^ « velocity in feet per 36 U 12 6- 
zniQute. 

^, 27rrn ^_ ^ Fig. 106. 

t; •= -Q^; 60i; = 2irrn. 



h u V t 



1 .1. 2 \" 



3 4 2" 



5 6 r 




K 



K 



PARALLELOGRAM OF VELOCITIES. 



523 



Angular velocity is a term used to denote the angle through which any 
radius of a body turns in a second, or the rate at which any point in it 
having a radius equal to unity is moving, expressed in feet per second. 
The unit of angular velocity is the angle which at a distance = radius 
from the center is subtended by an arc equal to the radius. This unit 

1 or) 

angle = ^^^ degrees = 57.3°. 2nX 57.3° = 360°, or the circumference. 



If A = angular velocity, v ■ 
called a radian. 



Ar, 



J, _ V _ 2irn 
~ r ~ 60 



180 
The unit angle — is 



Height Corresponding to a Given Acquired Velocity. 



i 




>i 




>» 




>> 




>. 




>> 




-♦.> 






-1-5 
















•*i 


o 


-c 


'2 


-fl 


*o 


^ 


'S 


-d 


■— 


-a 


'3 


•9. 





M 


^ 


bJO 


3, 


W) 


o^ 


bC 


o 


bfl 


o^ 


.Sf 


% 


"S 


"flS 


2 


"o 


"2 


% 


'S 


13 


'5 


"3 


<0 


> 


w 


> 


w 


> 


S 


>' 


!--( 


> 


2^ 


> 


ffl 


feet 




feet 




feet 




feet 




feet 




feet 




per 


feet. 


per 


feet. 


per 


feet. 


per 


feet. 


per 


feet. 


per 


feet. 


sec. 




sec. 




• sec. 




sec. 




sec. 




sec 




.25 


0.0010 


13 


2.62 


34 


17.9 


55 


47.0 


76 


89.8 


97 


146 


.50 


0.0039 


14 


3.04 


35 


19.0 


56 


48.8 


77 


92.2 


98 


149 


.75 


0.0087 


15 


3.49 


36 


20.1 


57 


50.5 


78 


94.6 


99 


152 


1.00 


0.016 


16 


3.98 


37 


21.3 


58 


52.3 


79 


97.0 


100 


155 


1.25 


0.024 


17 


4.49 


38 


22.4 


59 


54.1 


80 


99.5 


105 


171 


1.50 


0.035 


18 


5.03 


39 


23.6 


60 


56.0 


81 


102.0 


110 


188 


1.75 


0.048 


19 


5.61 


40 


24.9 


61 


57.9 


82 


104.5 


115 


203 


2 


0.062 


20 


6.22 


41 


26.1 


62 


59.8 


83 


107.1 


120 


224 


2.5 


0.097 


21 


6.85 


42 


27.4 


63 


61.7 


84 


109.7 


130 


263 


3 


0.140 


22 


7.52 


43 


28.7 


64 


63.7 


85 


112.3 


140 


304 


3.5 


0.190 


23 


8.21 


44 


30.1 


65 


65.7 


86 


115.0 


150 


350 


4 


0.248 


24 


8.94 


45 


31.4 


66 


67.7 


87 


117.7 


175 


476 


4.5 


0.314 


25 


9.7! 


46 


32.9 


67 


69.8 


88 


120.4 


200 


622 


5 


0.38S 


26 


10.5 


47 


34.3 


68 


71.9 


89 


123.2 


300 


1399 


6 


0.559 


27 


11.3 


48 


35.8 


69 


74.0 


90 


125.9 


400 


2488 


7 


0.761 


28 


12.2 


49 


37.3 


70 


76.2 


91 


128.7 


500 


3887 


8 


0.994 


29 


13.1 


50 


38.9 


71 


78.4 


92 


131.6 


600 


5597 


9 


1.26 


30 


14.0 


51 


40.4 


72 


80.6 


93 


134.5 


700 


7618 


10 


1.55 


31 


14.9 


52 


42.0 


73 


82.9 


94 


137.4 


800 


9952 


11 


1.88 


32 


15.9 


53 


43.7 


74 


85.1 


95 


140.3 


900 


12.593 


12 


2.24 


33 


16.9 


54 


45.3 


75 


87.5 


96 


143.3 


1000 


15,547 



Parallelogram of Velocities. — The principle of the composition 
and resolution of forces may also be applied to velocities or to distances 
moved in given Intervals of time. Referring 

to Fig. 99, page 513, if a body at O has a A 1 2 3 B 
force appUed to it which acting alone would ^ \^^ ~\ 
give it a velocity represented by OQ per A ^i"M 
second, and at the same time it is acted on 
by another force which acting alone would 
give it a velocity OP per second, the result 
of the two forces acting together for one sec- 
ond will carry it to R, OR being the diagonal 
of the parallelogram of OQ and OP, and the 
resultant velocitv. If the two component 
velocities are uniform, the resultant will be 
uniform and the line Off will be a straight 
hne: but if either velocity is a varying one, 
the line will be a curve. Fig. 107 shows the 

resultant velocities, also the path traversed .^ , „ ,.r.\fr.y,r^ 

Dy a body acted on by two forces, one of which would carry it at a unitorm 
velocity over the intervals 1. 2. 3. B and the other of which would carry it 
by an accelerated motion over the i ntervals a.b.c. D in the same times. Ai 




Fig. 107. 



524 



MECHANICS. 



Falling Bodies: 



Velocity Acquired by a Body Falling a Given 
Height. 





>> 




>j 




>> 




>> 




>» 




>i 


■tJ 








-1^ 














-^ 


X 


•s 


s: 


'S 


^ 


S 


j3 


o 


-€5 


'o 


•£ 


•3 


bC 


^ 


fcf 


o 


bC 


^ 


bl3 


O^ 


b£ 


o 


M 





'S 


"oj 


"S 


"o 


"S 


'S 


'53 


"O) 


"S 


-o 


'S 


13 


s 


> 


a^ 


> 


H 


> 


l-H 


> 


H-( 


> 


W 


> 


feet. 


feet 


feet. 


feet 


feet. 


feet 


feet. 


feet 


feet. 


feet 


feet. 


feet 




p. sec. 




p. sec. 




p. sec. 




p. sec. 




p.sec. 




p.sec. 


0.005 


.57 


0.39 


5.01 


1.20 


8.79 


5. 


17.9 


23. 


38.5 


72 


68.1 


i.ClO 


.80 


0.40 


5.07 


1.22 


8.87 


.2 


18.3 


.5 


38.9 


73 


68.5 


0.015 


.98 


0.41 


5.14 


1.24 


8.94 


.4 


18.7 


24. 


39.3 


74 


69.0 


0.020 


1.13 


0.42 


5.20 


1.26 


9.01 


.6 


19.0 


.5 


39.7 


75 


69.5 


0.025 


1.27 


0.43 


5.26 


1.28 


9.08 


.8 


19.3 


25 


40.1 


76 


69.9 


0.030 


1.39 


0.44 


5.32 


1.30 


9.15 


6. 


19.7 


26 


40.9 


77 


70.4 


0.035 


1.50 


0.45 


5.38 


1.32 


9.21 


.2 


20.0 


27 


41.7 


78 


70.9 


0.040 


1.60 


0.46 


5.44 


1.34 


9.29 


.4 


20.3 


28 


42.5 


79 


71.3 


0.045 


1.70 


0.47 


5.50 


1.36 


9.36 


.6 


20.6 


29 


43.2 


80 


71.8 


0.050 


1.79 


0.48 


5.56 


1.38 


9.43 


.8 


20.9 


30 


43.9 


81 


72.2 


0.055 


1.88 


0.49 


5.61 


1.40 


9.49 


7. 


21.2 


31 


44.7 


82 


72.6 


0.060 


1.97 


0.50 


5.67 


1.42 


9.57 


.2 


21.5 


32 


45.4 


83 


73.1 


0.065 


2.04 


0.51 


5.73 


1.44 


9.62 


.4 


21.8 


33 


46.1 


84 


73.5 


0.070 


2.12 


0.52 


5.78 


1.46 


9.70 


.6 


22.1 


34 


46.8 


85 


74.0 


0.075 


2.20 


0.53 


5.84 


1.48 


9.77 


.8 


22.4 


35 


47.4 


86 


74.4 


0.080 


2.27 


0.54 


5.90 


1.50 


9.82 


8. 


22.7 


36 


48.1 


87 


74.8 


0.085 


2.34 


0.55 


5.95 


1.52 


9.90 


.2 


23.0 


37 


48.8 


88 


75.3 


0.090 


2.41 


0.56 


6.00 


1.54 


9.96 


.4 


23.3 


38 


49.4 


89 


75.7 


0.095 


2.47 


0,57 


6.06 


1.56 


10.0 


.6 


23.5 


39 


50.1 


90 


76.1 


0.100 


2.54 


0.58 


6.11 


1.58 


10.1 


.8 


23.8 


40 


50.7 


91 


76.5 


0.105 


2.60 


0.59 


6.16 


1.60 


)0.2 


9. 


24.1 


41 


51.4 


92 


76.9 


0.110 


2.66 


0.60 


6.21 


1.65 


10.3 


.2 


24.3 


42 


52.0 


93 


77.4 


0.115 


2.72 


0.62 


6.32 


1.70 


10.5 


.4 


24.6 


43 


52.6 


94 


77.8 


0.120 


2.78 


0.64 


6.42 


1.75 


10.6 


.6 


24.8 


44 


53.2 


95 


78.2 


0.125 


2.84 


0.66 


6.52 


1.80 


10.8 


.8 


25.1 


45 


53.8 


96 


78.6 


C.130 


2.89 


0.68 


6.61 


1.90 


11.1 


10. 


25.4 


46 


54.4 


97 


79.0 


C.I4 


3.00 


0.70 


6.71 


2. 


11.4 


.5 


26.0 


47 


55.0 


98 


79.4 


0.15 


3.11 


0.72 


6.81 


2.1 


11.7 


11. 


26.6 


48 


55.6 


99 


79.8 


0.16 


3.21 


0.74 


6.90 


2.2 


11.9 


.5 


27.2 


49 


56.1 


100 


80.2 


C.!7 


3.31 


0.76 


6.99 


2.3 


12.2 


12. 


27.8 


50 


56.7 


125 


89.7 


C.18 


3.40 


0.78 


7.09 


2.4 


12.4 


.5 


28.4 


51 


57.3 


150 


98.3 


0.19 


3.50 


0.80 


7.18 


2.5 


12.6 


13. 


28.9 


52 


57.8 


175 


106 


0.20 


3.59 


0.82 


7.26 


2.6 


12.0 


.5 


29.5 


53 


58.4 


200 


114 


0.21 


3.68 


0.84 


7.35 


2.7 


13.2 


14. 


30.0 


54 


59.0 


225 


120 


0.22 


3.76 


0.86 


7.44 


2.8 


13.4 


.5 


30.5 


55 


59.5 


250 


126 


0.23 


3.85 


0.88 


7.53 


2.9 


13.7 


15. 


31.1 


56 


60.0 


275 


133 


0.24 


3.93 


0.90 


7.61 


3. 


13.9 


.5 


31.6 


57 


60.6 


300 


139 


0.25 


4.01 


0.92 


7.69 


3.1 


14.1 


16. 


32.1 


58 


61.1 


350 


150 


0.26 


4.09 


0.94 


7.78 


3.2 


14.3 


.5 


32.6 


59 


61.6 


400 


160 


0.27 


4.17 


0.96 


7.86 


3.3 


14.5 


17. 


33.1 


60 


62.1 


450 


170 


0.28 


4.25 


0.98 


7.94 


3.4 


14.8 


.5 


33.6 


61 


62.7 


500 


179 


29 


4.32 


1.00 


8.02 


3.5 


15.0 


18. 


34.0 


62 


63.2 


550 


188 


0.30 


4.39 


1.02 


8.10 


3.6 


15.2 


.5 


34.5 


63 


63.7 


600 


197 


0.31 


4.47 


1.04 


8.18 


3.7 


15.4 


19. 


35.0 


64 


64.2 


700 


212 


032 


4.54 


1.06 


8.26 


3.8 


15.6 


.5 


35.4 


65 


64.7 


800 


227 


0.33 


4.61 


1.08 


8.34 


3.9 


15.8 


20. 


35.9 


66 


65.2 


900 


241 


0.34 


4.68 


1.10 


8.41 


4. 


16.0 


.5 


36.3 


67 


65.7 


1000 


254 


0.35 


4.74 


1.12 


8.49 


.2 


16.4 


21. 


36.8 


68 


66.1 


2000 


359 


36 


4.81 


1.14 


8.57 


.4 


16.8 


.5 


37.2 


69 


66.6 


3000 


439 


37 


4.88 


1.16 


8.64 


.6 


17.2 


22. 


37.6 


70 


67.1 


4000 


507 


0.38 


4.94 


1.18 


8.72 


.8 


17.6 


.5 


38.1 


71 


67.6 


5000 


567 



FORCE OF ACCELERATION. 525 

the end of the respective intervals the body will be found at Ci, C2, C3, C, 
and the mean velocity during each interval is represented by the dis- 
tances between these points. Such a curved path is traversed by a shot, 
the impelling force from the gun giving it a uniform velocity in the 
direction the gun is aimed, and gravity giving it an accelerated velocity 
downward. The path of a projectile is a parabola. The distance it will 
travel is greatest when its initial direction is at an angle 45° above the 
horizontal. 

FUNDAMENTAL EQUATIONS IN DYNAMICS. 

(Uniformly Accelerated Motion) 

Much difficulty to students of Mechanics has resulted from the use 
in various text-books of such terms as "poundal" as a unit of force 
(see page 512), "gee-pound," "slug," or "engineers' unit of mass" 
(= 32.2 lbs. of matter), and by the various definitions given to the 
words "mass" and "weight." The following elementary treatment of 
the subject, in which all of these troublesome words are avoided, is 
taken from an article by the author in Science, March 19, 1915. It 
is urgently commended to the attention of text-book writers and 
teachers, and constructive criticism of it is solicited. 

The fundamental problem is: Given a constant force F lbs. acting 
for T seconds on a quantity of matter W lbs., at rest at the beginning 
of the time, but free to move, what are the results, assuming that there 
is no frictional resistance? 

The first result is motion, at a gradually increasing velocity. The 
relation between the elapsed time and the velocity is determined by 
experiment. The velocity varies directly as the time and as the force, 
and inversely as the quantity of matter, and the equation is V 00 FT/W 
or V= KFT/W, K being a constant whose value is approximately 32, 
provided V is in feet per second, F and W in pounds and T in seconds. 

Accurate determinations, involving precise measurements of both F 
and W, and of S, the distance traversed during the time T, from which 
Vis determined, and precautions to ehminate resistance due to friction, 
give K = 32.1740. This figure is twice the number of feet that the 
body would fall in vacuo in one second at or near latitude 45° at the sea 
level. It is commonly represented by g, or by go, to distinguish it from 
other values of g that may be obtained by experiments on falling 
bodies (or on pendulums) at other latitudes and elevations. The 
fundamental equation then is 

V=FTg/W (1) 

The quantity g is commonly caUed the acceleration due to gravity, 
but it also may be considered either as an abstract figure, the constant 
g in equation (1), or as the velocity acquired at the end of 1 second by 
a falling body, or as the distance a body would travel in 1 second at 
that same velocity if the force ceased to act and the velocity remained 
constant. 

If the velocity varies directly as the time (imiformly accelerated 
motion) , then the distance is the product of the mean velocity and the 
time. As the body starts from rest when the velocity is 0, and the 
velocity is V at the end of the time T, the mean velocity is 1/2 V and the 
distance is 1/2 VT, whence V= 2S/T and T = 2S/V. 

The velocity V in feet per second, at the end of the time T is numer- 
ically equal to the nimaber of feet the body would travel in one second 
after the expiration of the time T if the force had then ceased to act 
and the body continued to move at a uniform velocity. 

In equation (1) substitute for V its value 2S/T and we obtain 

^~2lV ^^^ 

We have four elementary quantities F, T, S, W, one derived quan- 
tity V, and one constant figure 32.1740. It is understood that F is 
measured in standard pounds of force, one pound of force being the 
force that gravity exerts on a pound of matter at the standard loca- 
tion where g = 32.1740. 

Each equation contains four variables, V, F, T, W, or S, F, T, W, and 
in either equation if values be given to any three the fourth may be 
found. By transposition, or by giving new symbols to the product or 



526 MECHANICS. 

quotient of two of the variables, many different equations may be 
derived from them, the most important of which are given below. 

From (1), let F = W, the case of a body faUing at latitude 45° at the 
sea level: then V = gT. U T also = 1, then V = g, that is the velocity 
at the end of 1 second is (7. . _. , ^,,r , 

In the equation V = gT substitute for T its value 25/ V and we have 
V = 2gS/ V, whence V^ = 2gS. In the case of falling bodies, the height 
of fall H is usually substituted for S, and we obtain 

y=V2^ (3) 

Equation (2) with F == W gives V= t/2gT2. 
From (1), by transposition we obtain 

FT =WX V/g, or FT = VxW/g (4) 

The product FT is sometimes called impulse, and the expression 
W X V/g is called momentum. It is convenient to use the letter M 
instead of W/g, so that the equation becomes 

FT = MV (5) 

Impulse = Momentum 
In (4) we mav substitute for T its value in terms of 5 and V above 
given, viz., T = 25/ V and obtain F2S/V = MV; 

whence FS = 1/2 MV^ (6) 

Work expended = Kinetic energy. 

Acceleration. — The quotient V/T is called the acceleration. It is 
defined as the rate of increase of velocity. In the problem under con- 
sideration, the action of a force on a body free to move, with no retarda- 
tion by friction, the acceleration is a constant, V/T = A. Equation 
(5) then may be written 

F = MA (7) 

Force = M times the acceleration.* 

If a given body is acted on at two different times by two forces F 
and Fi, and if A and Ai are the corresponding accelerations, then 

F = MA 

y^-~~^ whence F/Fi ^ A/Ax (8) 

By the use of these eight equations and their transformations all 
problems relating to uniformly accelerated motion may be solved. 

Force of Acceleration. — Force has been defined as that which causes, 
or tends to cause, or to destroy, motion. It may also be defined as the 
cause of acceleration; and the unit of force, the pound, as the force re- 
quired to produce an acceleration of 32.174 ft. per second per second of 
one pound of matter free to move. 

Force equals the product of the mass by the acceleration,* or/ = ma. 

Also, if 1; = the velocity acquired in the time t, ft = mv; '^= mv -i- 1; 
the acceleration being uniform. 

The force required to produce an acceleration of g (that is, 32.174 ft. 

per sec. in one second) is/ =mg = — g = w,ov the weight of the body. 

Also, / = ma = m — , in which V2 is the velocity at the end. and vi 

the velocity at the beginning of the time t, and f = mg = - " ~ =» 

- a: — = -; or, the force required to give any acceleration to a body is 

to the weight of the body as that acceleration is to the acceleration pro- 

* Equation (7) is sometimes read "force equals mass times acceler- 
ation," which is strictly true in the dyne-centimeter-gram-second, or 
"absolute" system of measurements, in which force is measured in 
dynes, but it is not true in the pound-foot-second system, nor in the 
metric system where the kilogram is used as a unit of both force and 
quantity of matter, unless it is understood that the word "mass" means 
tne quotient of W divided by 32.174. 



FORCE OF ACCELERATION. 527 

duced by gravity. In problems in which the local attraction of gravity 
is a factor the local value of g must be used if great accuracy is desired. 
Example. — Tension in a cord hfting a weight. A weight of 100 lbs. 
is lifted vertically by a cord a distance of 80 feet in 4 seconds, the velocity 
uniformly increasing from to the end of the time. What tension must 
be maintained in the cord, assuming the local value of g to be 32.108 or 
0.998 of the standard value? Mean velocity = v^ =20 ft. per sec.; 

V2 40 
final velocity = v-i = 2Vjyi - ^^' acceleration 0' — y=~T^ 1^- Force 

f =ma = — = S^lTi X 1^ = ^^-^^ ^^^' '^^^ standard value of g, 
32.174 must be used here, for the force required for acceleration is 
independent of local gravitation. This is the force required to pro- 
duce the acceleration only ; to it must be added the force required to lift 
the weight without acceleration, or 100 lbs. X 0.998 = 99.8 lbs., 
making a total of 130.88 lbs. (The factor 0.998 is used here because the 
force of gravity at the given locality is 0.002 less than at the standard 
locality) . 

The Resistance to Acceleration is the same as the force required to pro- 
duce the acceleration = — -^-7 — -, 
Q t 

Formulae for Accelerated Motion. — For cases of uniformity accel- 
erated motion other than those of falling bodies, we have the formulae 

already given, / = — a, = -- - — 7—. If the body starts from rest, Vi = 
9 Q t, 
W V vt 

0, t;2 = r and/ = - jlfgt — wv. We also have s = — . Transforming 

and substituting for g its value 32.174, we obtain 

wV' ^ wv ^ ws ^ ^ S2.17ft ^ 64.35/5 . 

'■" 64.35 s 32.17 f 16.09^2' ^' '^ ^2 ' 

„_ wv^ _ 16.09/^2^1^^^ t; = 8 02 \\(^- ^2.17/^. 



wv 



64.35/ w 2 • • \ w; w 

01 \ / 



32.17/ 4,01 
For any change in velocity,/ = w ( qa 3 ^ \ ) • 



(See also Work of Acceleration, under Work.) 

Motion on Inclined Planes. — The velocity acquired by a body de- 
scending an inclined plane by the force of gravity (friction neglected) is 
equal to that acquired by a body falling freely from the height of the 
plane. 

The times of descent down different inclined planes of the same height 
vary as the length of the planes. 

The riiles for uniformly accelerated motion apply to inclined planes. 
If a is the angle of the plane with the horizontal, sin a = the ratio of the 

height to the length = y, and the constant accelerating force is g sin a. 

The final velocity at the end of t seconds is v = gt sin a. The distance 
passed over in t seconds is Z = 1/2 gt^ sin a. The time of descent is 



\ ^ sin a 4.01 



LOl ^h 
Momentum, in many books erroneously defined as the quantity of 
motion in a body, is the product of the mass by the velocity at any 

w 
instant, = mv = — v. By "mass" is meant the quotient w/g. 

Since ft = mv, the product of a constant force into the time in which 
it acts equals numerically the momentum. 

Momentmn may be defined as numerically equivalent to the nmnber 
of pounds of force that will stop a moving body in 1 second, or the num- 
ber of poimds of force which acting during 1 second will give it the given 
velocity. 



528 MECHANICS. 

Vis-viva, or living force, is a term used by early writers on Mechanics 
to denote the energy stored in a moving body. The term is now obso- 
lete, its place being taken by the word energy. 

WORK, ENERGY, POWER. 

The fundamental conceptions in Mechanics are: 

Matter, Force, Time, Space, represented by W, F, T, S. 

In EngUsh miits W and F are measured in pounds, T in seconds, S 
in feet. 

Velocity = space di\dded by time, V = S -r- T, if V he uniform. V 
at end of time T (uniformly accelerated motion) = 2S -J- T. 

Resistance is that which is opposite to an acting force. It is equal 
and opposite to force. 

Work is the overcoming of resistance through a certain distance. It 
is measured by the product of the resistance into the space through 
wliich it is overcome. It is also measured by the product of the moving 
force into the distance through which the force acts in overcoming the 
resistance. Thus in Ufting a body from the earth against the attraction 
of gravity, the resistance is the weight of the body, and the product of 
this weight into the height the body is lifted is the work done. 

The Unit of Work, in British measures, is the foot-pound, or the 
amount of work done in overcoming a pressure or weight equal to one 
pound through one foot of space. 

The work performed by a piston in drl\^ng a fluid before It, or by a 
fluid in driving a piston before it, may be expressed in either of the fol- 
lowing ways: 

Resistance X distance traversed 
= intensity of pressure X area X distance traversed ; 
= intensity of pressure X volvmie traversed. 

By intensity of pressure is meant pressure per unit of area, as lbs. per 
sq. in. 

The work performed in lifting a body is the product of the weight of 
the body into the height through which its center of gra\ity is Ufted. 

If a machine hfts the centers of gravity of several bodies at once to 
heights either the same or different, the whole quantity of work per- 
formed in so doing is the simi of the several products of the weights and 
heights ; but that quantity can also be computed by multiplying the sum 
of all the weights into the height through which th^ir common center of 
gravity is hfted. (Rankine.) 

Power is the rate at which work is done, and is expressed by the quo- 
tient of the work divided by the time in which it is done, or by units of 
work per second, per minute, etc., as foot-pounds per second. The most 
common unit of power is the horse-power, estabUshed by James Watt as 
the power of a strong London draught-horse to do work during a short 
interval, and used by him to measure the power of his steam-engines. 
This unit is 33,000 foot-pounds per muiute = 550 foot-pounds per sec- 
ond = 1,980,000 foot-pounds per hour. 

Power exerted for a certain time produces work; FT = FS = FVT, 
if V be uniform. 

Horse-power Hours, an expression for work measured as the product 
of a power into the time during which it acts, = FT. Sometimas it is 
the summation of a variable power for a given time, or the average 
power multiphed by the time. 

Energy, or stored work, is the capacity for performing work. It is 
measured by the same unit as work, that is, in foot-pounds. It may be 
either potential, as in the case of a body of water stored in a reservoir, 
capable of doing work by means of a water-wheel, or actual, sometimes 
called kinetic, which is the energy of a moving body. Potential energy 
is measured by the product of the weight of the stored body into the dis- 
tance t hrough which it is capable of acting, or by the product of the 
pressur(3 it exerts into the distance tlirough which that pressure is cap- 
able of acting. Potential energy may also exist as stored heat, or as 
stored chemical energy, as in fuel, gunpowder, etc., or as electrical en- 
ergy, the measure of these energies being the amount of work that they 
are capabl(^ of performing. Actual energy of a moving body is the work 
which It is capable of performing against a retarding resistance before 
bemg brought to rest, and is equal to the work which must be done 
upon it to bring it from a state of rest to its actual velocity. 



WORK OF ACCELERATION, 529 

The measure of actual energy is the product of the weight of the b<)dy 
Into the height from which it must fall to acquire its actual velocity. If' 
V = the velocity in feet per second, according to the principle of falling 

bodies, h, the height due to the velocity, = ^^—i and if w = the weight, : 

the energy = 1/2 mv'^ = wv^ ■- 2g = wh. Since energy is the capacity for 
performing work, the units of work and energy are equivalent, or FS = 
1/2 mV^ = wh. Energy exerted = work done. 

The actual energy of a rotating body whose angular velocity is A and 
moment of inertia SitT^ = I is — — , that is, the product of the moment 
of inertia into the height due to tne velocity, A, of a point whose distance 
from the axis of rotation is unity ; or it is equal to -^, in which w is the 
weight of the body and v is the velocity of the center of gyration. 

Work of Acceleration.— The work done in giving acceleration to a 
body is equal to the product of the force producing the acceleration, or 
of the resistance to acceleration, into the distance moved in a given time. 
This force, as already stated, equals product of the mass into the acceler- 
ation, or f ~ ma = — '■. If the distance traversed in the time t = s, 

. W V2 - Vl 

then work =/s = ^ s. 

Q f 

Example. — What work is required to move a body weighing 100 lbs. 
horizontally a distance of 80 ft. in 4 seconds, the velocity uniformly 
increasing, friction neglected? 

Mean velocity v^ = 20 ft. per second; final velocity = 2;2 = 2 i?^ =40; 

V2 — Vl 40 
initial velocity vi = 0; acceleration, a = — - — = — - = 10; force = 

— a = -^jf X 10 = 31.1 lbs.; distance 80 ft.; work = /s = 31.1 X 80 
= 2488 foot-poimds. 

The energy stored in the body moving at the final velocity of 40 ft. 
per second is 

1/2 mt;2 = i y v2 = l^^^^^^^ = 2488 foot-pounds, 
which equals the work of acceleration, 

g t g t 2 2 g 

If a body of the weight W falls from a height H, the work of accelera- 
tion is simply WH, or the same as the work required to raise the body 
to the same height. 

Work of Accelerated Rotation. — Let A = angular velocity of a 
solid body rotating about an axis, that is, the velocity of a particle 
whose radius is unity. Then the velocity of a particle whose radius is r 
is V = Ar. If the angular velocity is accelerated from Ai to A2, the in- 
crease of the velocity of the particle is ?;2 — ?;i = r (Ai — A2), and the 
work of accelerating it is 

w_ V2^ = vi"^ _ wr^ A2^ — Ai^ 
g ^ 2~" ~ g 2 ' 

in which w is the weight of the particle. A is measured in radians. 
The work of acceleration of the whole body is 

The term 2ut2 is the moment of inertia of the body. 

" Force of the Blow " of a Steam Hammer or Other Falling 
Weight. — The question is often asked: " With what force does a fall- 
ing hammer strike? " The question cannot be answered directly, and it 
is based upon a misconception or ignorance of fundamental mechanical 



530 MECHANICS. 

laws. The energy, or capacity for doing work, of a body raised to a given 
height and let tali cannot be expressed in pounds, simply, but only in foot- 
pounds, vvliich is the product of the weight into the height through which 
It falls, or the product of its weight -^ 64.32 into the square of the velocity, 
in feet per second, which it acquires after falling through the given height. 
Xf F = weight of the body, M its mass, g the acceleration due to gravity, 
S the height of fall, and v the velocity at the end of the fall, the energy in 
the body just before striking is FS = 1/2 Mv^=Wv^ ^ 2g = Wv"^ ^ 64.32, 
which is the general equation of energy of a moving body. Just as the 
energy of the body is a product of a force into a distance, so the work it 
does when it strikes is not the manifestation of a force, which can be ex- 
pressed simply in pounds, but it is the overcoming of a resistance through 
a certain distance, which is expressed as the product of the average resist- 
ance into the distance through which it is exerted. If a hammer weighing 
100 lbs. falls 10 ft., its energy is 1000 foot-pounds. Before being brought 
to rest it must do 1000 foot-pounds of work against one or more resistances. 
These are of various kinds, such as that due to motion imparted to the 
body struck, penetration against friction, or against resistance to shearing 
or other deformation, and crushing and heating of both the falling body 
and the body struck. The distance through which these resisting forces 
act is generally indeterminate, and therefore the average of the resisting 
forces, which themselves generally vary with the distance, is also indeter- 
minate. 

Impact of Bodies. — If two inelastic bodies collide, they will move on 
together as one mass, with a common velocity. The momentum of the 
combined mass is equal to the sum of the momenta of the two bodies 
before impact. If mj and m2 are the masses of the two bodies and V\ and V2 
their respective velocities before impact, and v their common velocity 
after impact, (mi -H m2)v = niiVi + m2V2, 

rriiVi 4- m2t'2 

V = ; 

If the bodies move in opposite directions, v = ^ ^ , — ^ , or the velocity 

fni -p 1712 
of two inelastic bodies after impact is equal to the algebraic sum of their 
momenta before impact, divided by the sum of their masses. 

If two inelastic bodies of equal rnomenta impinge directly upon one an- 
other from opposite directions they will be brought to rest. 

Impact of Inelastic Bodies Causes a Loss of Energy, and this loss 
is equal to the sum of the energies due to the velocities lost and gained 
by the bodies, respectively. 

1/2 niiVt^ 4- 1/2 ^21^2^ — V2 (Wi + m2) v^ = 1/2 mi (vi — v)"^ + 1/2 ^2 {vi — vy-, 
in which t^i — 1; is the velocity lost by m\ and v — V2 the velocity gained 
by ma. 

Example. — Let mi = 10, m2 = 8, t'l = 12, V2 = 15. 

iQ v/ 19 8 vi5 

If the bodies collide they will come to rest, for v= ^- , ^ = 0. 

10+0 

The energy loss is 

1/2 10 X 144+ 1/2 8 X 225 -I/2I8X = 1/2 10(12 - 0)2 4-1/2 8(15- 0)« = 
1620 ft.-lbs. 

What becomes of the energy lost? Ans. It is used doing intei-nai work 
on the bodies themselves, changing their shape and heating them. 

For imperfectly elastic bodies, let e = the elasticity, that is, the ratio 
which the force of restitution, or the internal force tending to restore the 
shape of a body after it has been compressed, bears to the force of com- 
pression; and let mi and m2 be the masses, Vi and V2 their velocities before 
impact, and Vx, V2 their velocities after impact; then 

, ^ mxVx 4- mivi __ m2e {vx — ^2) 
* mi 4- m2 mi -H mt * 

, ^ m\v\ + rrtiVi m\e {vx — Vi) 
mi 4- ma mi 4- rrn 



ENERGY. 531 

If the bodies are perfectly elastic, their relative velocities before and 
after impact are the same. That is, v\' — vi' = V2 - vi. 

In the impact of bodies, the sum of their momenta after impact is the 
same as the sum of their momenta before impact. 

ruiVi + m2V2 = rriiVi + 7^12^2. 

For demonstration of these and other laws of impact, see Smith's Me- 
chanics; also, Weisbach's Mechanics. 

Energy of Recoil of Guns. (Eng'g, Jan. 25, 1884, p. 72.) -- 

Let W = the weight of the gun and carriage; 

V == the maximum velocity of recoil; 
w = the weight of the projectile; 

V = the muzzle velocity of the projectile. 

Then, since the momentum of the gun and carriage is equal to the 
rromentum of the projectile (because both are acted on by equal force, 
tne pressure of the gases in the gun, for equal time), we have WV = wv, 
or F = ivv -^ W. 

Taking the case of a 10-inch gun firing a 400-lb. projectile with a muzzle 
velocity of 2000 feet per second, the weight of the gun and carriage being 
22 tons = 50,000 lbs., we find the velocity of recoil = 

y = '°^onnr - 16 feet per second. 
50,000 

Now the energy of a body in motion is WV^ -^ 2g. 

Therefore the energy of recoil = ' — = 198,800 foot-pownds. 

400 X 2000^ 
The energy of the projectile is ^ = 24,844,000 foot-pounds. 

Conservation of Energy. — No form of energy can ever be pro- 
duced except by the expenditure of some other form, nor annihilated ex- 
cept by being reproduced in another form. Consequently the sum total of 
energy in the universe, like the sum total of matter, must always remain 
the same. (S. Newcomb.) Energy can never be destroyed or lost; it can 
be transformed, can be transferred from one body to another, but no 
matter what transformations are undergone, when the total effects of the 
exertion of a given amount of energy are summed up the result will be 
exactly equal to the amount originally expended from the source. This 
law is called the Conservation of Energy. (Cotterili and Slade.) 

A heavy body sustained at an elevated position has potential energy. 
When it falls, just before it reaches the earth's surface it has actual or 
kinetic energy, due to its velocity. When it strikes, it may penetrate the 
earth a certain distance or may be crushed. In either case friction results 
by which the energy is converted into heat, which is gradually radiated 
into the earth or into the atmosphere, or both. Mechanical energy and 
heat are mutually convertible. Electric energy is also convertible into 
heat or mechanical energy, and either kind of energy may be converted 
into the other. 

Sources of Energy. — The principal sources of energy on the earth's 
surface are the muscular energy of men and animals, the energy of the 
wind, of flowing water, and of fuel. These sources derive their energy 
from the rays of the sun. Under the influence of the sun's rays vegetation 
grows and wood is formed. The wood may be used as fuel under a steam- 
boiler, its carbon being burned to carbon dioxide. Three-tenths of its heat 
energy escapes in the chimney and by radiation, and seven-tenths appears 
as potential energy in the steam. In the steam-engine, of this seven-tenths 
six parts are dissipated in heating the condensing water and are wasted; 
the remaining one-tenth of the original heat energy of the wood is con- 
verted into mechanical work in the steam-engine, which may be used to 
drive machinery. This work is finally, by friction of various kinds, or pos- 
sibly after transformation into electric currents, transformed into heat 
which is radiated into the atmosphere, increasing its temperature. Thus 



532 



MECHANICS. 



all the potential heat energy of the wood is, after various transformations, 
converted into heat, which, mingling with the store of heat in the atmos- 
phere, apparently is lost. But the carbon dioxide generated by the com- 
Bustion of the wood is, again, under the influence of the sun's rays, 
absorbed by vegetation, and more wood may thus be formed having poten- 
tial energy equal to the original. 

Perpetual 3Iotion. — The law of the conservation of energy, than 
which no law of mechanics is more firmly established, is an absolute barrier 
to all schemes for obtaining by mechanical means what is called " perpetual 
motion," or a machine which will do an amount of work greater than the 
equivalent of the energy, whether of heat, of chemical combination, of elec- 
tricity, or mechanical energy, that is put into it. Such a result would be 
the creation of an additional store of energy in the universe, which is not 
possible by any human agency. 

The Efficiency of a Machine is a fraction expressing the ratio of 
the useful work to the whole work performed, which is equal to the energy 
expended. The limit to the efficiencj^ of a machine is unitj% denoting the 
efficiency of a perfect machine in which no work is lost. The difference 
between the energy expended and the useful work done, or the loss, is 
usually expended either in overcoming friction or in doing work on bodies 
surrounding the machine from which no useful work is received. Thus 
in an engine propelling a vessel part of the energy exerted in the cylinder 
does the useful work of giving motion to the vessel, and the remainder is 
spent in overcoming the friction of the machinery and in making currents 
and eddies in the surrounding water. 

A common and useful definition of efficiency is ** output divided by 
input." 



ANIMAL POWER. 

Work of a Man against Known Resistances. 



(Rankine.) 



Kind of Exertion. 


R, 
lbs. 


F. 

ft. per 

sec. 


T" 

3600 

(hours 

per 

day). 


RV, 
ft.-lbs. 
per sec. 


RVT, 
ft.-lbs. 
per day. 


1. Raising his own weight up 
stair or ladder 


143 

40 
44 

143 

6 

132 

26.5 
(12.5 
\ 18.0 
(20.0 

13.2 

15 


0.5 

0.75 
0.55 

0.13 

1.3 

0.075 

2.0 
5.0 
2.5 
14.4 
2.5 
? 


8 

6 
6 

6 

10 

10 

8 
? 
8 
2 min. 
10 
8? 


71.5 

30 

24.2 

18.5 
7.8 

9.9 

53 

62.5 
45 
288 
33 
? 


2,059.200 

648.000 
522,720 

399.600 

280,800 


2. Hauling up weights with rope, 
and lowering the rope un- 
loaded 


3. Lifting weights by hand 

4. Carrying weights up-stairs 

and returning unloaded 

5. Shoveling up earth to a 

height of 5 ft. 3 in 


6. Wheeling earth in barrow up 
slope of 1 in 12, 1/2 horiz. 
veloc. 0.9 ft. per sec, and re- 
turning unloaded 


356.400 
1,526,400 


7. Pushing or pulling horizon- 
tally (capstan or oar) 


8. Turning a crank or winch 


1,296.000 


9. Working pump 


1 188 000 


10. Hammering 


480.000 







Explanation. — R, resistance; V, effective velocity = distance 
through which R is overcome ^ total time occupied, including the time 
of moving unloaded, if any; T'\ time of working, in seconds per day; 
T" -h 3600, same time, in hours per day; RV, effective power, in foot- 
pounds per second; RVT, daily work. 



ANIMAL POWER. 



533 



Performance of a Man in Transporting Loads Horizontally. 

(Rankine.) 



Kind of Exertion. 



11. Walking unloaded, trans- 

porting his own weight 

12. \\^eeling load L in 2-whld 

barrow, return unloaded . 

13. Ditto in 1-wh. barrow, ditto. . 

14. Traveling with burden. ..,.. , 

15. Carrying burden, returning 

unloaded 

16. Carrying burden, for 30 sec- 

onds only 







rptf 


LV, 


L 


V 


3600 


lbs. 


lbs. 


ft. -sec. 


(hours 
per 


con- 
veyed 






day). 


1 foot. 


140 


5 


10 


700 


224 


12/3 


10 


373 


132 


12/3 


10 


220 


90 


21/2 


7 


225 


140 


12/3 


6 


233 


( 252 










\ 126 


11.7 




1474.2 


( 


23.1 








lbs. con- 
veyed 
1 foot. 



25,200,000 

13,428,000 
7,920,000 
5,670,000 

5,032,800 



Explanation. — L, load; V, effective velocity, computed as before; 

T", time of working, in seconds per day; T" ^ 3600, same time in hours 

per day; LV, transport per second, in lbs. conveyed one foot; LVT^ 

daily transport. 

In the first line only of each of the two tables above is the weight of 

the man taken into account in computing the work done. 

Clark says that the average net 
daily work of an ordinary laborer 
at a pump, a winch, or a crane may 
be taken at 3300 foot-pounds per 
minute, or one-tenth of a horse- 
power, for 8 hours a day; but for 
shorter periods from four to five 
times this rate ma,y be exerted. 

Mr. Glynn says that a man may 
exert a force of 25 lbs. at the 
handle of a crane for short periods ; 
but that for continuous work a 
force of 15 lbs. is all that should 
be assumed, moving through 220 
feet per minute. 

Man-wheel. — Fig. 108 is a sketch 
of a very efficient man-power hoist- 
ing-machine which the author saw 
in Berne, Switzerland, in 1889. 
The face of the wheel was wide 

enough for three men to walk abreast, so that nine men could work in it 

at one time. 




Fig. 108. 



Work of a Horse against 


a Known Resistance. 


(Rankine.) 


Kind of Exertion. 


R. 


V. 


rptt 

3'600 


RY. 


RYT. 


1. Cantering and trotting, draw- 
ing a light railway carriage 
(thoroughbred) 


(min. 221/2 
mean 301/2 
max. 50 

120 

100 

66 


1 142/3 

3.6 

3.0 
6.5 


4 

8 

8 
41/2 


4471/2 

432 

300 
429 


6,444,000 


2. Horse drawing cart or boat, 
walking (draught-horse) . . . 

5. Horse drawing a gin or mill, 
walking 


12,441,600 
8,640,000 


4. Ditto, trotting 


6,950,000 







534 



MECHANICS. 



Explanation. — R, resistance, in lbs.; F, velocity, in feet per second; 
T" -^ 3600, hours work per day; RV, work per second; RVT^ work per 
day. 

The average power of a draught-horse, as given in line 2 of the above 
table, being 432 foot-pounds per second, is 432/550 = 0.785 of the con- 
ventional value assigned by Watt to the ordinary unit of the rate of 
work of prime movers. It is the mean of several results of experiments, 
and may be considered the average of ordinary performance under favor- 
able circumstances. 

Performance of a Horse in Transporting Loads Horizontally. 

(Rankine.) 



Kind of Exertion. 



5. Walking with cart, always 

loaded 

6. Trotting, ditto 

7. Walking with cart, going 

loaded, returning empty; 
y, mean velocity 

8. Carrying burden, walking. . 

9. Ditto, trotting 



L. 


7. 


T. 


LV. 


1500 


3.6 


10 


5400 


750 


7.2 


41/2 


5400 


1500 


2.0 


10 


3000 


270 


3.6 


10 


972 


180 


7.2 


7 


1296 



LVT. 



194,400,000 
87,480,000 



108,000,000 
34,992,000 
32,659,200 



Explanation. — L, load in lbs. ; V, velocity in feet per second ; T, work- 
ing hours per day; LV, transport per second; LVT, transport per day. 

This table has reference to conveyance on common roads only, and 
those evidently in bad order as respects the resistance to traction upon 
them. 

Horse-Gin. — In this machine a horse works less advantageously 
than in drawing a carriage along a straight track. In order that the best 
possible results may be realized with a horse-gin, the diameter of the cir- 
cular track in which the horse walks should not be less than about forty 
feet. 

Oxen, 3Iules, Asses. — Authorities differ considerably as to the power 
of these animals. The following may be taken as an approximative com- 
parison between them and draught-horses (Rankine): 

Ox. — Load, the same as that of average draught-horse; best velocity 
and work, two-thirds of horse. 

Mule. — Load, one-half of that of average draught-horse; best velocity, 
the same as horse; work, one-half. 

Ass. — Load, one-quarter that of average draught-horse; best velocity, 
the same; work, one-quarter. 

Reduction of Draught of Horses by Increase of Grade of Roads. 
{Engineering Record, Prize Essays on Roads, 1892.) — Experiments on 
Enghsh roads by Gayffier & Parnell: 

Calling load that can be drawn on a level 100: 

On a rise of 1 in 100. 1 in 50. 1 in 40. 1 in 30. 1 in 26. 1 in 20. 1 in 10. 

A horse can draw only 90 81 72 64 54 40 25 

^ The Resistance of Carriages on Roads is (according to Gen. Morin) 
given approximately by the following empirical formula: 

W 

R = lL[a -{-h {u - 3.28)1. 

In this formula R = total resistance; r = radius of wheel in inches; 
W = gross load; u = velocity in feet per second; while a and b are 
constants, whose values are: For good broken-stone road, a = 0.4to0.55, 
b = 0.024 to 0.026; for paved roads, a = 0.27, b = 0.0684. 

Rankine states that on gravel the resistance is about double, and on 
sand five times, the resistance on good broken-stone roads. 



ELEMENTS OF MACHINES. 



535 



B 



b 



Qw' 



Fig. 109. 



B 



Ow 



Fig. 110. 



B 



Ow 



ELE3IENTS OF MACHINES. 

The object of a machine is usually to transform the work or mechanical 
energy exerted at the point where the machine receives its motion into 
work at the point where the final resistance 
is overcome. The specific result may be to 
change the character or direction of mo- 
tion, as from circular to rectilinear, or vice 
versa, to change the velocity, or to overcome 
a great resistance by the application of a 
moderate force. In all cases the total energy 
exerted equals the total work done, the latter 
including the overcoming of aU the frictional 
resistances of the machine as well as the use- 
ful work performed. No increase of power 
cran be obtained from any machine, since this 
is impossible according to the law of conser- 
vation of energy. In africtionless machine the 
product of the force exerted at the driving- 
point into the velocity of the driving-point, 
cr the distance it moves in a given interval 
of time, equals the product of the resistance 
into the distance through which the resist- 
ance is overcome in the same time. 

The most simple machines, or elementary 
machines, are reducible to three classes, viz., 
the Lever, the Cord, and the Inclined Plane. 

The first class includes every machine con- 
sisting of a solid body capable of revolving 
on an axis, as the Wheel and Axle. 

The second class includes every machine in 
which force is transmitted by means of flexi- 
ble threads, ropes, etc., as the Pulley. 

The third class includes every machine in -piQ 111. 

which a hard surface inclined to the direc- 
tion of motion is introduced, as the Wedge and the Screw. 

A Lever is an inflexible rod capable of motion about a fixed point, 
called a fulcrum. The rod may be straight or bent at any angle, or 
curved. 

It is generally regarded, at first, as without weight, but its weight may 
be considered as another force applied in a vertical direction at its center 
of gravity. 

The arms of a lever arS the portions of it intercepted between the force, 
P, and fulcrum, C, and between the weight or load, W, and fulcrum. 

Levers are divided into three kinds or orders, according to the relative 
positions of the applied force, load, and fulcrum. 

In a lever of the first order, the fulcrum hes between the points at which 
the force and load act. (Fig. 109.) 

In a lever of the second order, the load acts at a point between the 
fulcrum and the point of action of the force. (Fig. 110.) 

In a lever of the third order, the point of action of the force is between 
that of the load and the fulcrum. (Fig. 111.) 

In all cases of levers the relation between the force exerted or the pull, 
P, and the load lifted, or resistance overcome, W, is expressed by the 
equation P X AC = W X BC, in which AC is the lever-arm of P, and 
BC is the lever-arm of W, or moment of the force = the moment of the 
resistance. (See Moment.) 

In cases in which the direction of the force (or of the resistance) is not 
at right angles to the arm of the lever on which it acts, the "lever-arm" 
is the length of a perpendicular from the fulcrum to the line of direction 
of the force (or of the resistance). W : P : : AC : BC, or, the ratio of 
the resistance to the applied force is the inverse ratio of their lever-arms. 
Also, if Vwis the velocity of W, and Vp is the velocity of P, W : P : : Vp: 
Vw, and Px Vp = WX Vw. 

If Sp is the distance through which the applied force acts, and Sw is 
the distance the load is lifted or through which the resistance is over- 
come, W :P :;Sp:Sw:WX Sw = PXSp, OT the load into the dis- 



536 



MECHANICS. 



tance it is lifted equals the force into the distance through which it is. 
exerted. 

These equations are general for all classes of machines as well as for 
levers, it being understood that friction, which in actual machines in- 
creases the resistance, is not at present considered. 

The Bent JLever. — In the bent lever (see Fig. 102, p. 614), the lever- 
arm of the weight m is cf instead of hf. The lever is in equiUbrium when 
^ X a/ = w X c/", but it is to be observed that the action of a bent lever 
may be very different from that of a straight lever. In the latter, so 
long as the force and the resistance act in lines parallel to each other, the 
ratio of the lever-arms remains constant, although the lever itself changes 
its inclination with the horizontal. In the bent lever, however, this 
ratio changes: thus, in the cut, if the arm 6/ is depressed to a horizontal 
direction, the distance cf lengthens while the horizontal projection of 
af shortens, the latter becoming zero when the direction of af becomes 
vertical. As the arm af approaches the vertical, the weight n which 
may be Ufted with a given force s is very great, but the distance through 
which it may be hfted is very small. In all cases the ratio of the weight 
m to the weight n is the inverse ratio of the horizontal projection of their 
respective lever-arms. 

The Moving Strut (Fig. 112 ) is similar to the bent lever, except that 
one of the arms is missing, ana that the force and the resistance to be 
overcome act at the same end of the 
single arm. The resistance in the 
case shown in the cut is not the load 
W, but its resistance to being 
moved, R, which may be simply 
that due to its friction on the hori- 
zontal plane, or some other oppos- 
ing force. When the angle between 
the strut and the horizontal plane 
changes, the ratio of the resistance 
to the applied force changes. When 
the angle becomes very small, a 
moderate force will overcome a 
very great resistance, which tends 
to become infinite as the angle ap- 
proaches zero. If a =the angl^, P X cos a = i2 X sin a. 
cos a = 0.99619, sin a = 0.08716, R = 11.44 P. 

The stone-crusher (Fig. 113) shows a practical example of the use of 
two moving struts. 

The Toggle-joint is an elbow or knee-joint consisting of two bars so 
connected that they^ may be brought into a straight line and made to 
produce great endwise pressure when a force is applied to bring thera 
into this position. It is a case of two moving struts placed end to end, 




Fig. 112. 



If a = 5 degrees. 





Fig. 113. 



Fig. 114. 



the moving force being applied at their point of junction, in a direction 
at right angles to the direction of the resistance, the other end of one of 
the struts resting against a fixed abutment, and that of the other against 
the body to be moved. If a = the angle each strut makes with the straight 
line joining the points about which their outer ends rotate, the ratio of 
the resistance to the applied force is i? : P : : cos a : 2 sin a; 2 i? sin a 
« P cos a. The ratio varies when the angle varies, becoming infinite 
when the angle becomes zero. 



ELEMENTS OF MACHINES. 



ii37 



The toggle-joint is used where great resistances are to be overcome 
through very small distances, as in stone-crushers (Fig. 114). 

The Inclined Plane, as a mechanical element, is supposed perfectly 
hard and smooth, unless friction be considered. It assists in sustaining 
a heavy body by its reaction. This reaction, however, being normal to 
the plane, cannot entirely counteract the weight of the body, which acts 
vertically downward. Some other force must 
therefore be made to act upon the body, in order 
that it may be sustained. 

If the sustaining force act parallel to the plane 
(Fig. 115 ), the force is to the weight as the height 
of the plane is to its length, measured on the 
incline. 

If the force act parallel to the base of the 
plane, the force is to the weight as the height is 
to the base. 

If the force act at any other angle, let i = the 
angle of the plane with the horizon, and 6= the 
angle of the direction of the applied force with the angle of the plane. 
P : TT : : sin i : cos e\ P X cos e = W sin i. 

Problems of the inclined plane may be solved by the parallelogram of 
forces thus: 

Let the weight W be kept at rest on the incline by the force P, acting 
in the line bP\ parallel to the plane. Draw the vertical line ba to repre- 
sent the weight; also bb' perpendicular to the plane, and complete the 
parallelogram b'c. Then the vertical weight 6a is the resultant of bb\ the 
measure of support given by the plane to the weight, and be, the force of 
gravity tending to draw the weight down the plane. The force required 
to maintain the weight in equilibrium is represented by this force be. 
Thus the force and the weight are in the ratio of be to ba. Since the 
triangle of forces abe is similar to the triangle of the incline ABC, the 
latter may be substituted for the former in determining the relative 




Fig. 115. 



magnitude of the forces, and 
P :W : 



be : ab : : BC : AB. 



The Wedge is a pair of inclined planes united by their bases. In the 
application of pressure to the head or butt end of the wedge, to cause it to 
penetrate a resisting body, the applied force is to the resistance as the 
thickness of the wedge is to its length. Let t be the thickness, I the length, 
W the resistance, and P the applied force or pressure on the head of the 

wedge. Then, friction neglected, P:W : :t :l; P == ■^; W = y- 

The Screw is an inclined plane wrapped around a cylinder in such a 
way that the height of the plane is parallel to the axis of the cylinder. If 
the screw is formed upon the internal surface of a hollow cylinder, it is 
usually called a nut. When force is applied to raise a weight or overcome 
a resistance by means of a screw and nut, either the screw or the nut may 
be fixed, the other being movable. The force is generally applied at the 
end of a wrench or lever-arm, or at the circumference of a wheel. If r = 
radius of the wheel or lever-arm, and p = pitch 
of the screw, or distance between threads, that 
is, the height of the inclined plane for one revo- 
lution of the screw, P = the applied force, and 
W = the resistance overcome, then, neglecting 
resistance due to friction, 2 Trr X P = Wp; \V 
= 6.283 Pr -^ p. The ratio of P to IF is thus 
independent of the diameter of the screw. In 
actual screws, much of 
the power transmitted is 
lost through friction. 

The Cam is a revolv- 
ing inclined plane. It 
may be either an in- 
clined plane wrapped 
around a cylinder in such 
a way that the height of 
the plane is radial to the 




Fig. 116. 




Fig. 117. 
cylinder, such as the ordinary lifting-cam, used in stamp-mills (Fig. 116), 



538 



MECHANICS. 



or it may be an inclined plane curved edgewise, and rotating in a plane 
parallel to its base (Fig. 117). The relation of the weight to the applied 
force is calculated in the same manner as in the case of the screw. 

EflBciency of a Screw. — Let a = angle of the thread, that is, the 
angle whose tangent is the pitch of the screw divided by the circum- 
ference of a circle whose diameter is the mean of the diameters at the 
top and bottom of the thread. Then for a square thread 
Efficiency = (1 - /tan a) ^ (1 +/cotan a), 
in which/ is the coefficient of friction. (For demonstration, see Cotterill 
and Slade, Apphed Mechanics.) Since cotan = 1 -f- tan, we may sub- 
stitute for cotan a the reciprocal of the tangent, or if p = pitch, and 
c = mean circumference of the screw, 

Efficiency = (1 -fp/c) -i- (1 +/c/p). 

Example. — Efficiency of square-threaded screws of 1/2 inch pitch. 
Diameter at bottom of thread, in. . . 1 2 3 4 

Diameter at top of thread, in IV2 21/2 31/2 41/2 

Mean circumference of thread, in.. . . 3.927 7.069 10.21 13.35 

Cotangent a = c -i- p =7.854 14.14 20.42 26.70 

Tangent a = p -^ c =0.1273 .0707 .0490 .0375 

Efficiency if/ = 0.10 =55.3% 41.2% 32.7% 27.2% 

Efficiency if / = 0.15 =45% 31.7% 24.4% 19.9% 

The efficiency thus increases with the steepness of the pitch. 

The above formulae and examples are for square-threaded screws, and 
consider the friction of the screw-thread only, and not the friction of the 
collar or step by which end thrust is resisted, and which further reduces 
the efficiency. The efficiency is also further reduced by giving an inclina- 
tion to the side of the thread, as in the V-threaded screw. For discussion 
of this subject, see paper by Wilfred Lewis, Jour. Frank. Inst. 1880; also 
Trans. A. S. M. E., vol. xii, 784. „ ^ . . , . „ . 

Efficiency of Screw-bolts. — Mr. Lewis gives the following approxi- 
mate formula for ordinary screw-bolts (V-threads, with collars): p= pitch 
of screw, d = outside diameter of screw, F — force applied at circum- 
ference to Hft a unit of weight, E = efficiency of screw. For an average 
case, in which the coefficient of friction may be assumed at 0.15, 
F = {p + d) ^ M, E = p-i- (p + d). 

For bolts of the dimensions given above, 1/2-inch pitch, and outside 
diameters II/2, 21/2, 31/2, and 41/2 inches, the efficiencies according to this 
formula would be, respectively, 0.25, 0.167, 0.125, and 0.10. 

James McBride (Trans. A. S. M. E., xii, 781) describes an experiment 
with an ordinary 2-inch screw-bolt, with a V-thread, 41/2 threads per inch, 
raising a weight of 7500 pounds, the force being applied by turning the 
nut. Of the power applied 89.8 per cent was absorbed by friction of the 
nut on its supporting washer and of the threads of the bolt in the nut. 
The nut was not faced, and had the flat side to the washer. 

Professor Ball in his "Experimental Mechanics" says: "Experiments 
showed in two cases respectively about 2/3 and 3/4 of the power was lost. " 

Weisbach says: "The efficiency is from 19 per cent to 30 per cent." 





ELEMENTS OF MACHINES. 



639 



Pulleys or Blocks. — P = force applied, or pull; W= load lifted, 
or resistance. In the simple pulley A (Fig. 118) the point F on the 
pulling rope descends the same amount that the load is lilted, therefore 
P=W. In B and C the point P moves twice as far as the load is lifted, 
therefore W = 2P. In B and C there is one movable block, and two 
phes of the rope engage with it. In D there are three sheaves in the 
movable block, each with two plies engaged, or six in all. Six plies of 
the rope are therefore shortened by the same amount that the load is 
lifted and the point P moves six times as far as the load, consequently 
W = 6 P. In general, the ratio of W to P is equal to the number of plies 
of the rope that are shortened, and also is equal to the number of plies that 
engage the lower block. If the lower block has 2 sheaves and the upper 
3, the end of the rope is fastened to a hook in the top of the lower block, 
and then there are 5 plies sliortened instead of 6, and W= 5 P. If F = 
velocity of W, and v = velocity of P, then in all cases FTF= vP, whatever 
the number of sheaves or their arrangement. If the hauling rope, at the 
pulling end, passes first around a sheave in the upper or stationary block, 
it makes no difference in what direction the rope is led 
from this block to the point at wliich the pull on the 
rope is applied ; but if it first passes around the movable 
block, it is necessary that the pull be exerted in a direc- 
tion parallel to the line of action of the resistance, or a 
line joining the centers of the two blocks, in order to 
obtain the maximum effect. If the rope pulls on the 
lower block at an angle, the block will be pulled out of 
the line drawn between the load and the upper block, 
and the effective pull will be less than the actual pull 
on the rope in the ratio of the cosine of the angle the 
pulling rope makes with the vertical, or line of action of 
the resistance, to unity. 

Differential Pulley. (Fig. 119. ) — Two pulleys, B 
and C, of different radii, rotate as one piece about a 
fixed axis, A. An endless chain, BDECLKH, passes 
over both pulleys. The rims of the pulleys are shaped 
so as to hold the chain and prevent it from shpping. 
One of the bights or loops in which the chain hangs, DE, 
passes under and supports the running block F. The 
other loop or bight, HKL, hangs freely, and is called the 
hauling part. It is evident that the velocity of the haul- 
ing part is equal to that of the pitch-circle of the pulley B. 

In order that the velocity-ratio may be exactly 
uniform, the radius of the sheave F should be an exact 
mean between the radii of B and C. 

Consider that the point B of the cord BD moves through an arc whose 
length = AB^ during the same time the point C or the cord CE will 
move downward a distance = ^C. The length of the bight or loop 
BDEC will be shortened by AB — AC, which will cause the pulley F to 
be raised half of this amount. If P = the pulling force on the cord HK, 
and W the weight Ufted at P, then P X vl5 = IF X V2 {AB - AC). 

To calculate the length of chain required for a differential pulley, take 
the following sum: Half the circumference of A + half the circumference 
of jB + half the circumference of P + twice the greatest distance of P 
from A + the least, length of loop HKL, The last quantity is fixed 
according to convenience. 

A Wheel and Axle, or Windlass, resembles two pulleys on one axis, 
having different diameters. If a weight be lifted by means of a rope 
wound over the axle, the force being applied at the rim of the wheel, 
the action is like that of a lever of which the shorter arm is equal to the 
radius of the axle plus half the thickness of the rope, and the longer 
arm is equal to the radius of the wheel. A wheel and axle is therefore 
sometimes classed as a perpetual lever. If P = the apphed force, D = 
diameter of the wheel, W = the weight lifted, and d the diameter of the 
axle + the diameter of the rope, PD = Wd. 

Toothed-wheel Gearing is a combination of two or more wheels and 
axles (Fig. 120 ). If a series of wheels and pinions gear into each other, 
as in the cut, friction neglected, the weight lifted, or resistance over- 
come, is to the force applied inversely as the distances through which 




Fig. 119. 



540 



MECHANICS. 



thev act in a given time. If R, Ri, R2 be the radii of the successive wheels, 
measured to the pitch-line of the teeth, and r, n, 7*2 the radii of the cor- 
responding pinions, P the applied force, and W the weight lifted, P X 
RX RiX R2 = W XrXriXr2, or the applied force is to the weight 
as the product of the radii of the pinions is to the product of the radii of 
the wheels; or, as the product of the numbers expressing the teeth in 
each pinion is to the product of the numbers expressing the teeth in each 
wJieel. 





Fig. 120. 



Fig. 121. 



Endless Screw, or Worm-gear. (Fig. 121.) — This gear is com- 
monly used to convert motion at high speed into motion at very slow 
speed. When the handle P describes a complete circumference, the pitch- 
line of the cog-wheel moves through a distance equal to the pitch of the 
screw, and the weight W is lifted a distance equal to the pitch of the screw 
multiplied by the ratio of the diameter of the axle to the diameter of the 

J)itch-circle of the wheel. The ratio of the applied force to the weight 
ifted is inversely as their velocities, friction not being considered ; but the 
friction in the worm-gear is usually very great, amounting sometimes to 
three or four times the useful work done. 

If V •= the distance through which the force P acts in a given time, say 
1 second, and V = distance the .weight W is lifted in the same time, r=« 
radius of the crank or wheel through which P acts, t = pitch of the screw, 
and also of the teeth on the cog-wheel, d = diameter of the axle, and 



D = diameter of the pitch-line of the cog-wheel,] v = 
6.283 rD. Pv = W^V-f friction. 



6.283 r D 



X V; 



t d 

V = vXtd- 

The Differential Windlass (Fig. 122) is identical in principle with the 
differential pulley, the difference in construction being that in the dif- 
ferential windlass the running block hangs in the 
bight of a rope whose two parts are wound round, 
and have their ends respectively made fast to two 
barrels of different radii, which rotate as one piece 
about the axis A. The differential windlass is 
little used in practice, because of the great length 
of rope which it requires. 

The Differential Screw (Fig. 123) is a com- 
pound screw of different pitches, in which the 
threads wind the same way. A^i and N2 are the 

two nuts; aSi>Si, 
S2 the longer-pitched 

thread; S2S2. the 

short er-pi t ched 

thread: in the figure 

both these threads Fig. 122. 

^ ^ are left-handed. At 

each turn of the screw the nut A^2 advances relatively to Ni through a 
distance equal to the difference of the pitches. The use of the differential 
screw IS to combine the slowness of advance due to a fine pitch with 
the strength of thread which can be obtained by means of a coarse 
pitch only. 





Fig. 123. 



STRESSES IN FRAMED STRUCTURES. 



541 



Efficiency of a Differential Screw. — A correspondent of the 
American Machinist describes an experiment with a differential screw- 
punch, consisting of an outer screw 2 inch diameter, 3 threads per 
inch, and an inner screw 13/8 inch diameter, 31/2 threads per inch. The 
pitch of the outer screw being 1/3 inch and that of the inner screw 2/7 inch 
the punch would advance in one revolution 1/3 — Vi = V21 inch. 
Experiments were made to determine the force required to punch an 
u/i6-inch hole in iron 1/4 inch thick, the force being applied at the end 
of a lever-arm of 473/4 inch. The leverage would be 47 3/4 x 27r x 21 => 
6300. The mean force applied at the end of the lever was 95 pounds, 
and the force at the punch, if there was no friction, would be 6300 X 
95 = 598,500 pounds. The force required to punch the iron, assuming 
a shearing resistance of 50,000 pounds per square inch, would be 50,000 X 
IV16 X Ti" X 1/4 = 27,000 pounds, and the efficiency of the punch would 
be 27,000 -J- 598,500 = only 4.5 per cent. With the larger screw only 
used as a punch the mean force at the end of the lever was only 82 pounds. 
The leverage in this case was 473/4 X 27r X 3 = 900, the total force 
referred to the punch, including friction, 900 X 82 = 73,800, and tha 
efficiency 27,000 -i- 73,800 = 36.7 per cent. The screws were of tool- 
steel, well fitted, and lubricated with lard-oil and plumbago. 



STRESSES IN FRAMED STRUCTURES. 

Framed structures in general consist of one or more triangles, for the 
reason that the triangle is the one polygonal form whose shape cannot be 
changed without distorting one of its sides. Problems in stresses of 
simple framed structures m.ay generally be solved either by the applica- 
tion of the triangle, parallellogram, or polygon of forces, by the principle 
of the lever, or by the method of moments. We shall give a few ex- 
amples, referring the student to the works of Burr, Dubois, Johnson, and 
others for more elaborate treatment of the subject. 

1. A Simple Crane. (Figs. 124 and 125.^ — A is a fixed mast, B a 
brace or boom, T a tie, and P the load. Required the strains in B and T. 
The weight P, considered as acting at the end of the boom, is held in 
equihbrium by three forces: first, gravity acting dow^nwards; second, the 
tension in T; and third, the thrust of B. Let the length of the line p 
represent the magnitude of the downward force exerted by the load, and 
draw a parallelogram with sides bt parallel, respectively, to B and T, 
such that p is the diagonal of the parallelogram. Then b and t are the 
components drawn to the same scale as p, p being the resultant. Then 
if the length p represents the load, t is the tension in the tie, and b is the 
compression in the brace. 

Or, more simply, T, B, and that portion of the mast included between 
them or A' may represent a triangle of forces, and the forces are propor- 
tional to the length of the sides of the triangle; that is, if the height of the 




Fig. 124. 



Fig. 125. 



Fig. 126. 



triangle A' = the load, then B = the compression in the brace, and T = 
the tension in the tie; or if P = the load in pounds, the tension in T = 

jP X ^» and the compression in B = P X -j;- Also, if a = the angle 

the inclined member makes withthemast, the other member being 



542 



MECHANICS. 



horizontal, and the triangle being right-angled, then the length of the 
inclined member = height of the triangle X secant a, and the strain in the 
inclined member = P secant a. Also, the strain in the horizontal 
member = P tan a. 

The solution by the triangle or parallelogram of forces, and the equa- 
tions Tension in T = P X T/A\ and Compression in B = P X B/A\ hold true 
even if the triangle is not right-angled, as in Fig. 126 ; but the trigono- 
metrical relations above given do not hold, except in the case of a right- 
angled triangle. It is evident that as A' decreases, the strain in both T 
and B increases, tending to become infinite as A' approaches zero. If 
the tie T is not attached to the mast, but is extended to the ground, as 
shown in the dotted line, the tension in it remains the same. 

2. A Guyed Crane or Derrick. (Fig. 127. ) — The strain in B is, as 
before, P X B/A\ A' being that portion of the vertical included between 
B and T, wherever T may be attached to A, If, however, the tie T is 
attached to B beneath its extremity, there may be in addition a bending 
strain in B due to a tendency to turn about the point of attachment of T 
as a fulcrum. 

The strain in T may be calculated by the principle of moments. The 
moment of P is Pc, that is, its weight X its perpendicular distance from 
the point of rotation of B on the mast. The moment of the strain on T 
is the product of the strain into the perpendicular distance from the line 

-'- f .. , 




Fig. 127. 

of its direction to the same point of rotation of B, or Td. The strain in 
T therefore = Pc -r- d. As d decreases, the strain on T increases, tending 
to infinity as d approaches zero. 

The strain on the guy-rope is also calculated by the method of moments. 
The moment of the load about the bottom of the mast O is, as before, Pc. 
If the guy is horizontal, the strain in it is F and its moment is Ff, and F = 
Pc -7- /. If it is inclined, the moment is the strain G X the perpendicular 
distance of the line of its direction from O, or Gg, and G = Pc -^ g. 

The guy-rope having the least strain is the horizontal one F, and the 
strain in G = the strain in F X the secant of the angle between F and 
G. As G is made more neariy vertical g decreases, and the strain increases, 
becoming infinite when ^7 = 0. 

3. Shear-poles with Guys. 
(Fig. 128.) — First assume that 
the two masts act as one placed 
at BD, and the two guys as 
oneat^J5. Calculate the strain 
in BD and AB as in Fig. 126. 
Multiply half the strain in BD 
(or AB) by the secant of half 
the angle the two masts (or 
guys) make with each other to 
find the strain in each mast (or 
guy). 

Two Diagonal Braces and 
a Tie-rod. (Fig. 129.) — Sup- 
pose the braces are used to 
Compressive stress on AD = 1/2 P X AD 
This is true only if CB and BD 




sustain 
-I- AB\ 



Fig. 128. 
single load P. 

1/2 P X CA - AB, 



on CA 



STRESSES IN FRAMED STRUCTURES. 



543 



are of equal length, in which case 1/2 of P is supported by each abutment 
C and D. If they are unequal in length (Fig. 130), then, by the principle 
of the lever, find the reactions of the abutments R\ and R2. If P is the 
load applied at the point B on the lever CD, the fulcrum being D, 
then RiX CD = PX BD 3ind RiX CD = PX BC]Ri = PX BD -^ CD; 
^2 = p X BC -V- CD. 

"The strain ori AC '= RiX AC -^ AB, and on AD = R2X AD + AB. 

The strain on the tie = RiX CB -ir AB = R2X BD -r- AB. 

When CB = BD, Ri = R2, and the strain on the tie is equal to 
MP X HCD ~ AB. 





Fig. 130. 




Fig. 131. 



If the braces support a uniform load, as a pair of rafters, the strains 
caused by such a load are equivalent to that caused by one-half of the 
load applied at the center. The horizontal thrust of the braces against 
each other at the apex equals the tensile strain in the tie. 

King-post Truss or Bridge. (Fig. 131. ) — If the load is distributed 
over the whole length of the truss, the effect is the same as if half the 

load were placed at the center, the other 
half being carried by the abutments. Let 
P = one-half the load on the truss, then 
tension in the vertical tie AB = P. Com- 
pression in each of the inclined braces 
= 1/2 P X AD -T- AB. Tension in the tie 
CD = 1/2 P X BD -T- AB. Horizontal 
thrust of inclined brace AD at D = the 
tension in the tie. If IF = the total 
load on one truss uniformly distributed, 
I = its length and d = its depth, then 
the tension on the horizontal tie = Wl -^ 8 d. 

Inverted King-post Truss, (Fig. 132 ) — If P = a load applied at B, 
or one-half of a uniformly distributed load, then compression on. AB = P 
(the floor-beam CD not being considered 
to have any resistance to a slight bend- 
ing). Tension on AC or AD = 1/2 P 
X AD -^ AB. Compression on CD = 
1/2 P X BD -^ AB. 

Queen-post Truss. (Fig. 133.) — If 
uniformly loaded, and the queen-posts 
divide the length into three equal bays, 
the load may be considered to be divided 
into three equal parts, two parts of 
which, Pi and P2, are concentrated at the panel joints and the remainder 

is equally divided between the 

abutments and supported by them 

directly. The two parts Pi and P2 

only are considered to affect the 

members of the truss. Strain in 

the vertical ties BE and CF each 

equals Pi or P2. Strain on AB and 

CD each = PiXCD -^ CF. Strain 

on the tie AE or EF or ED-^PiX 

FD-^CF. Thrust on BC= tension 

Fig. 133. on EF. 

For stability to resist heavy unequal loads the queen-post truss should 

have diagonal braces frorn B to F and froni C to E, 




Fig. 132. 




544 



MECHANICS, 



Inverted Queen-post Truss. (Fig. 134.) — Compression on EB and 
FC each = Pi or P2. Compression on AB or BC or CD = PiX AB -i-EB, 

Tension on AE or FD = Pi X AE-i- 
EB. Tension on EF = compression 
on BC. For stability to resist 
unequal loads, ties should be run 
from C to E and from B to F. 

Burr Truss of Five Panels. 
(Fig. 135. ) — Four-fifths of the load 
may be taken as concentrated at the 
points E, K, L and F, the other fifth 
being supported directly by the two 
J ^r^ .1- X 1, .. , abutments. For the strains in 5A 

and CD the truss may be considered as a queen-post truss, with the loads 
Pi, P2 concentrated at E, and the loads P3, P4 concentrated at F. Then 
compressive strain on AB = (Pi -}- P2) X AB -r- BE. The strain on 
CD is the same if the loads and panel lengths^ are equal. The tensile 




Fig. 134 




Fig. 135. 

strain on BE or CF = Pi -h P2. That portion of the truss between E 
and F may be considered as a smaller queen-post truss, supporting the 
loads P2, P3 at K and L. The strain on EG or HF = P2 X EG -r- GK. 
The diagonals GL and KH receive no strain unless the truss is unequally 
loaded. The verticals GK and HL each receive a tensile strain equal to 
P2 or P3. 

For the strain in the horizontal members: BG and CH receive a thrust 
equal to the horizontal component of the thrust in AB or CD, = (Pi + Pi) 
X tan angle ABE, or (Pi + P2) X AE -¥■ BE. GH receives this thrust, 
and also, in addition, a thrust equal to the horizontal component of the 
thrust in EG or HF, or, in all, (Pi -f- P2 + P3) X AE -i- BE. 

The tension in AE or FD equals the thrust in BG or HC, and the ten- 
sion in EK, KL, and LF equals the thrust in GH. 

, Pratt or Whipple Truss. (Fig. 136.) — In this truss the diagonals are 
ties, and the verticals are struts or columns. 

Calculation by the method of distribution of strains: Consider first the 
load Pi. The truss having six bays or panels, s/g of the load is trans- 
mitted to the abutment H, and 1/6 to the abutment O, on the principle 
of the lever. As the five-sixths must be transmitted through JA and 
AH, write on these members the figure 5. The one-sixth is transmitted 
successively through JC, CK, KD, DL, etc., passing alternately through 
a tie and a strut. Write on these members, up to the strut GO inclusive, 
the figure 1. Then consider the load P2, of which ^q goes to AH and 
2/6 to GO. Write on KB, BJ, J A, and AH the figure 4, and on KD, 
DL, LE, etc., the figure 2. The load P3 transmits S/g in each direction; 
wnte 3 on each of the members through which this stress passes, and so 
on for all the loads, when the figures on the several members will appear 
as on the cut. Adding them up, we have the following totals: 

Tension on diagonals {^^ ^ f^^ (^( CL DK DM EL EN FM FO GN 

Compression on verticals {4f f/ ^f ^^ ^^ \^ ^^ 

Each of the figures in the first line is to be multiplied by Ve P X secant 
of angle HAJ, or i/a P X AJ -h AH, to obtain the tension, and each 



STRESSES IN FRAMED STRUCTURES. 



545 



figure in the lower line is to be multiplied by 1/6 P to obtain the com- 
pression. The diagonals HB and FO receive no strain. 

It is common to build tliis truss with a diagonal strut at HB instead 
of the post HA and the diagonal AJ; in which case s/e of the load P is 
carried through JB and the strut BH, which latter then receives a strain 
= 15/6 P X secant of HBJ, 




06600 ^ 



Pg P3 

Fig. 136. 

The strains in the upper and lower horizontal members or chords in- 
crease from the ends to the center, as shown in the case of the Burr 
truss. AB receives a thrust equal to the horizontal component of the 
tension in AJ, or 15/6 P X tan AJB. BC receives the same thrust + 
the horizontal component of the tension in BK, and so on. The tension 
in the lower chord of each panel is the same as the thrust in the upper 
chord of the same panel. (For calculation of the chord strains by the 
method of moments, see below.) 

The maximum thrust or tension is at the center of the chords and is 
WL 
equal to —jr-^ in which W is the total load supported by the truss, L is 

the length, and D the depth. This is the formula for maximum stress in 
the chords of a truss of any form whatever. 

The above calculation is based on the assumption that all the loads 
Pi, P2, etc., are equal. If they are unequal, the value of each has to be 
taken into account in distributing the strains. Thus the tension in AJ, 
with unequal loads, instead of being 15 X VqP secant 9 would be seed 
X (5/6 Pi + 4/6 P2 + 3/6 P3 + 2/6 P4 4- 1/6 P5). Each panel load, Pi, etc., 
includes its fraction of the weight of the truss. 

General Formula for Strains in Diagonals and Verticals. — I^et 
n = total number of panels, x == number of any vertical considered from 
the nearest end, counting the end as 1, r = rolling load for each panel, 
P = total load for each panel, 

Stram on verticals = — 



-l) + (a;-l)2]P ^ r(x-l) + (x-l)2 



2n 2 n 

For a uniformly distributed load, leave out the last term, 

[r (X - 1)+ (X - 1)2J --- 2n. 
Strain on principal diagonals (AJ, GN, etc.) = strain on verticals 
X secant 0, that is secant of the angle the diagonal makes with the 
vertical. 

Strain on the counterbraces (BH, CJ, FO, etc.): The strain on the 
counterbrace in the first panel is 0, if the load is uniform. On the 2d, 

3d, 4th, etc., it is P secant ^ X - . ^-^ . ^-i^-^^, etc., P being the total 

n n n 

load in one panel. 

Strain in the Chords — Method of Moments. — Let the truss be 
uniformly loaded, the total load acting on it = W. Weight supported at 
each end, or reaction of the abutment = W/2. Length of the truss = L. 
Weight on a unit of length = W/L. Horizontal distance from the nearest 
abutment to the point (say M in Fig. 136) in the chord where the strain 
is to be determined = x. Horizontal strain at that point (tension on the 
lower chord, compression in the upper) == H. Depth of the truss = D, 



546 



MECHANICS. 



By the method of moments we take the differeace of the moments, about 
the point M, of the reaction of the abutment and of the load between 
M and the abutments, and equate that difference with the moment of 
the resistance, or of the strain in the horizontal chord, considered with 
reference to a point in the opposite chord, about which the truss would 
turn if the first chord were severed at M. 

The moment of the reaction of the abutment is Wx/2. The moment of 
the load from the abutment to M is (W/Lx) X the distance of its center of 
sravitv from M, which is x/2, or moment = Wx^ -r- 2 L. Moment of the 

Wx Wx"^ W / x\ 

stress in the chord = HD = —^ ^Z' whence H == 2D V " XJ' 

WL 

U X = or L, H = 0. It x = L/2, H = -5-7^ • which is the horizontal 

Strain at the middle of the chords, as before given. 




Fig. 137. 

The Howe Truss. (Fig. 137.) — In the Howe truss the diagonals are 
struts, and the verticals are ties. The calculation of strains may be made 
in the same method as described above for the Pratt truss. 

The Warren Girder. (Fig. 138. ) — In the Warren girder, or triangu- 
lar truss, there are no vertical struts, and the diagonals may transmit either 
tension or compression. The strains in the diagonals may be calculated by 
the method of distribution of strains as in the case of the rectangular truss. 




Fig. 138. 

On the principle of the lever, the load Pi being Vio of the length of the 
span from the Une of the nearest support a, transmits 9/ioof its weight to 
a and Vio to g. Write 9 on the right hand of the strut la, to represent the 
compression, and 1 on the right hand of lb, 2c, Sd, etc., to represent com- 
pression, and on the left hand of 62, c3, etc., to represent tension. The 
foad P2 transmits 7/io of its weight to a and 3/io to g. Write 7 on each 
member from 2 to a, and 3 on each member from 2 to g, placing the figures 
representing compression on the right hand of the member, and those 
representing tension on the left. Proceed in the same manner with all 
the loads, then sum up the figures on each side of each diagonal, and 
write the difference of each sum beneath, and on the side of the greater 
Bum, to show whether the difference represents tension or compression. 
The results are as follows: Compression, la, 25; 26, 15; 3c, 5; 3rf, 5; 4^, 15; 
5g, 25. Tension, lb, 15; 2c, 5; 4rf, 5;5e, 15. Each of these figures is to 



STRESSES IN FRAMED STRUCTURES. 



547 



be multiplied by Vio of one of the loads as Pi, and by the secant of the 
angle the diagonals make with a vertical line. 

The strains in the horizontal chords may be determined by the method 
of moments as in the case of rectangular trusses. 

Roof-truss. — Solution by Method of Moments. — The calculation of 
strains in structures by the method of statical moments consists in taking 
a cross-section of the structure at a point where there are not more than 
three members (struts, braces, or chords). 

To find the strain in either one of these members take the moment about 
the intersection of the other two as an axis of rotation. The sum of the 
moments of these members must be if the structure is in equilibrium. 
But the moments of the two members that pass through the point of ref- 
erence or axis are both 0, hence one equation containing one unknown 
quantity can be found for each cross-section. 







/ 

/ 


\ 
\ 


=3 




yy ,^2 


€^ 


*^^r\ 




3 

> 




"> 


J^^^;^^^ 


\ 


\ 
\ 

\ V 


30 






>s^ z 


15 


\\'^ 
j\\\ 


/ 


r^^ 25 ^-^-^ 


12.5 ^\ 




lis \ 


L 




A 


V 


^ > F 




If n 


I ■ 



,'X 



Fig. 139. 

In the truss shown in Fig. 139 take a cross-section at fs, and determine 
the strain in the three members cut by it, viz., CE, ED, and DF. Let 
X = force exerted in direction CE, Y = force exerted in direction DE, 
Z = force exerted in direction FD. 

For X take its moment about the intersection of Y and Z at D = Xx, 
For Y take its moment about the intersection of X and Z at A = Yy. 
For Z take its moment about the intersection of X and F at ^ = Zz, 
Let z = 15, X = 18.6, y = 38.4, AD = 50, CD = 20 ft. Let Pi, P2, 
P3, P4 be equal loads, as shown, and 31/2 P the reaction of the abutment A, 

The sum of all the moments taken about D or A or ^ will be when the 
structure is at rest. Then - Za; + 3.5P X 50 - P3 X 12.5 - P2 X 25 

- Pi X 37.5 = 0. 

The + signs are for moments in the direction of the hands of a watch or 
" clockwise " and — signs for the reverse direction or anti-clockwise. Since 
P = Pi = P2 = P3, - 18.6 X + 175 P - 75 P = 0; - 18.6 X = - 100 P; 
X = 100 P-^ 18.6 = 5.376 P. 

- Yy -h P3 X 37.5 + P2 X 25 -^ Pi X 12.5 = 0; 38.4 F = 75 ; F = 

75 P -^ 38.4 = 1.953 P. 

- Z2 + 3.5 P X 37.5 - Pi X 25 - P2 X 12.5 - P3 X = 0; 15 Z = 

93.75 P;Z = 6.25 P. 
In the same manner the forces exerted in the other members have been 
found as follows: EG = 6.7S P',GJ = 8.07 P; J A = 9A2P;JH = 1.35 P; 
GF = 1.59 P; AH = 8.75 P; HF = 7.50 P. 

The Fink Roof-truss. (Fig. 140.) — An analysis by Prof. 
Philbrick {Van N. Mag., Aug., 1880) gives the following results: 
W= total load on roof; 
N= No. of panels on both rafters; 
W/N= P = load at each joint h, d, /, etc.; 
V= reaction at A = 1/2 W = 1/2 ^VP = 4P; 
AD= S; AC = L; CD = D; 
ti,t2, t3= tension on De, eg, gA, respectively; 
ci, ca, cj, C4= compression on Cb, bd, df, and /A. 



P. H. 



548 



MECHANICS. 



Strains in 

l,oTDe - ti= 2PS -i- D; 

2, ''eg = <2 = 3P5 -T- /); 

3, •♦ gA = ts=7/2PS -r- D; 

4, *' Af =ca=V2PL -^ D; 

6, V fd = C3 = V2PL/D-PD/L', 
6, •• db =C2=y2PL/D-'2PD/L; 



7, or bC^Cx = V2PL/D-3PDfL; 

8, •* bcoTfg= PS -t- L; 

9, •• rfe =2P*S-f- L; 

10, •• cdoTdg^lhPS -^ D; 

11. "ec =PS -i- D; 
12," cC =3/2P^ -r D. 




Fig. 140. 

Example. — Given a Fink roof-truss of span 64 ft., depth 16 ft., with 
four panels on each side, as in hecut; total load 32 tons, or 4 tons 
each at the points /, d, b, C, etc. (and 2 tons each at A and B, which trans- 
mit no strain to the truss me mbers). Here W = 32tons, jP = 4 tons, 
^=32 ft., D = 16 ft., L = V^2 + 2)2 = 2.236 XT). L -i- D = 2.236, 
D + L = 0.4472, S -ir D = 2, S -i- L = 0.8944. The strains on the 
numbered members then are as follows: 



1, 2X4X2 =16 tons; 

2, 3X4X2 =24 

3, 7/2X4X2 =28 " 

4, 7/2X4X2.236=31.3 " 

5, 31.3-4X0.447 = 29.52 " 

6, 31.3-8X0.447 = 27.72 " 



7, 31.3-12X0.447 =25.94 tons. 

8, 4X0.8944= 3.58 " 

9, 8X0.8944= 7.16 " 

10, 2X2 =4 

11, 4X2 =8 

12, 6X2 =12 " 



The Economical Angle. — A structure of tri- 
angular form, Fig. 141, is supported at a and b. It 
sustains any load L, the elements cc being in com- 
pression and t in tension. Required the angle so 
that the total weight of the structure shall be a 
minimum. F. R. Honey (Sci. Am, Supp., Jan. 17, 
1891) gives a solution of this problem, with the 



result tan = 



v/ 



(7+ T 



in which C and T represent 




the crushing and the tensile strength respectively of 

the material employed. It is applicable to any 

material. For C = T, = 543/4°. For C = OAT ^^ 

493/4°. For C = 0.8 r (soft steel), 9 = 53V4°. For C = 6 T (cast iron), 

««= 691/4°. 



Fig. 141. 
(yellow pine), 



PYROMETRY. 549 

HEAT. 

THER3I03IETERS. 

The Fahrenheit thermometer is generally used in English-speaking 
countries, and the Centigrade, or Celsius, thermometer in countries that 
use the metric system. In many scientific treatises in English, however, 
the Centigrade temperatures are also used, either with or without their 
Fahrenheit equivalents. The Reaumur thermometer is used to some 
extent on the Continent of Europe and in breweries in this country. 

In the Fahrenheit thermometer the freezing-point of water is taken at 
32°, and the boiling-point of water at mean atmospheric pressure at the 
sea-level, 14.7 lbs. per sq. in., is taken at 212^, the distance between these 
two points being divided into 180°. In the Centigrade and Reaumur 
thermometers the freezing-point is taken at 0°. The boiling-point is 
100° in the Centigrade scale, and 80° in the Reaumur. 

1 Fahrenheit degree = s/g deg. Centigrade =4/9 deg. Reaumur. 

1 Centigrade degree = ^/sdeg. Fahrenheit =4/5 deg. Rdaumur. 

1 Reaumur degree = 9/4 deg. Fahrenheit =5/4 deg. Centigrade. 

Temperature Fahrenheit = 9/5 X temp. C. + 32° =9/4 R. + 32°. 
Temperature Centigrade = 5/9 (temp. F. - 32°) =5/4 R. 
Temperature Reaumur = 4/5 temp. C. =4/9 (F. - 32°). 

Handy Rule for Converting Centigrade Temperature to Fah- 
renheit. — Multiply by 2, subtract a tenth, add 32, 

Example. — 100° C. X 2 = 200, ~ 20 = 180, + 32= 212° F. 

Mercurial Thermometer. (Rankine, S. E., p. 234.) — The rate of 
expansion of mercury with rise of temperature increases as the temperature 
becomes higher; from which it follows, that if a thermometer showing the 
dilatation of mercury simply were made to agree with an air thermometer 
at 32° and 212°, the mercurial thermometer would show lower temperatures 
than the air thermometer between those standard points, and higher tem- 
peratures beyond them. 

For example, according to Regnault, when the air thermometer marked 
350° C. (= 662° F.), the mercurial thermometer would mark 362.16° C. 
(= 683.89° F.), the error of the latter being in excess 12.16° C. (= 21.89° 
F.). 

Actual mercurial thermometers indicate intervals of temperature pro- 
portional to the difference between the expansion of mercury and that of 
glass. 

The inequalities in the rate of expansion of the glass (which are very 
different for different kinds of glass) correct, to a greater or less extent, the 
errors arising from the inequalities in the rate of expansion of the mercury. 

For practical purposes connected with heat engines, the mercurial ther- 
mometer made of common glass may be considered as sensibly coinciding 
with the air-thermometer at all temperatures not exceeding 500° F. 

If the mercury is not throughout its whole length at the same tempera- 
ture as that being measured, a correction, k, must be added to the tem- 
perature t in Fahrenheit degrees; k = 95 D (t-f) -^ 1,000,000, where D is 
the length of the mercury column exposed, measured in Fahrenheit 
degrees, and t is the temperature of the exposed part of the thermometer. 
When long thermometers are used in shallow wells in high-pressure steam 
pipes this correction is often 5° to 10° F. (Moyer on Steam Turbines.) 

PYR03IETRY. 

Principles Used in Various Pyrometers. 

Pyrometers may be classified according to the principles upon which 
they operate, as follows: 

1. Expansion of mercury in a glass tube. When the space above the 
mercury is filled with compressed nitrogen, and a specially hard glass is 
used for the tube, mercury thermometers may be made to indicate tem- 
Deratures as high as 1000° F. 





TEMPERAXrRES, 


CENTIGRADE 


JLSJy FAHRENHEIT 




c. 


F. 


C. 


F. 


C. 


F. 


C. 


F. 


C. 


F. 


C. 


F. 


C. 


F. 


-40 


-40. 


26 


78.8 


92 


197.6 


158 


316.4 


224 


435.2 


290 


554 


950 


1742 


-39 


-38.2 


27 


80.6 


93 


199.4 


159 


318.2 


2251437. 


300 


572 


960 


1760 


-38 


-36.4 


28 


82.4 


94 


201.2 


160 


320. 


226438.8 


310 


590 


970 


1778 


-37 


-34.6 


29 


84.2 


95 


203. 


161 


321.8 


2271440.6 


320 


608 


980 


1796 


-36 


-32.8 


30 


86. 


96 


204.8 


162 


323.6 


228442.4 


330 


626 


990 


1814 


-35 


-31. 


31 


87.8 


97 


206.6 


163 


325.4 


229 444.2 


340 


644 


1000 


1832 


-34 


-29.2 


32 


89.6 


98 


203.4 


164 


327.2 


230 446. 


350 


662 


1010 


1850 


-33 


-27.4 


33 


91.4 


99 


210.2 


165 


329. 


231 '447.8 


360 


680 


1020 


1868 


-32 


-25.6 


34 


93.2 


100 


212. 


166 


330.8 


232 449.6 


370 


698 


1030 


1886 


-31 


-23.8 


35 


95. 


101 


213.8 


167 


332.6 


233,451.4 


380 


716 


1040 


1904 


-30 


-22. 


36 


96.8 


102 


215.6 


168 


334.4 


2341453.2 


390 


734 


1050 


1922 


-29 


-20.2 


37 


98.6 


103 


217.4 


169 


336.2 


235455. 


400 


752 


1060 


1940 


-28 


-18.4 


38 


100.4 


104 


219.2 


170 


338. 


236:456.8 


410 


770 


1070 


1958 


-27 


-16.6 


39 


102.2 


105 


221. 


171 


339.8 


237|458.6 


420 


788 


1080 


1976 


-26 


-14.8 


40 


104. 


106 


222.8 


172 


341.6 


2381460.4 


430 


806 


1090 


1994 


-25 


-13. 


41 


105.8 


107 


224.6 


173 


343.4 


2391462.2 


440 


824 


1100 


2012 


-24 


-11.2 


42 


107.6 


108 


226.4 


174 


345.2 


2401464. 


450 


842 


1110 


2030 


-23 


- 9.4 


43 


109.4 


109 


228.2 


175 


347. 


241 


465.8 


460 


860 


1120 


2048 


-22 


- 7.6 


44 


111.2 


110 


230. 


176 


348.8 


242 


467.6 


470 


878 


1130 


2066 


-21 


- 5.8 


45 


113. 


111 


231.8 


177 


350.6 


243 


469.4 


480 


896 


1140 


2084 


-20 


- 4. 


46 


114.8 


112 


233.6 


178 


352.4 


244 


471.2 


490 


914 


1150 


2102 


-19 


- 2.2 


47 


116.6 


113 


235.4 


179 


354.2 


245 


473. 


500 


932 


1160 


2120 


-18 


- 0.4 


48 


118.4 


114 


237.2 


180 


356. 


246 


474.8 


510 


950 


1170 


2138 


-17 


+ 1.4 


49 


120.2 


115 


239. 


181 


357.8 


2471476.6 


520 


968 


1180 


2156 


-16 


3.2 


50 


122. 


116 


240 8 


182 


359.6 


2481478.4 


530 986 


1190 


2174 


-15 


5. 


51 


123.8 


117 


242.6 


183 


361.4 


249 


480.2 


540;i004 


1200 


2192 


-14 


6.8 


52 


125.6 


118 


244.4 


184 


363.2 


250 


482. 


550-1022 


1210 


2210 


-13 


8.6 


53 


127.4 


119 


246.2 


185 


365. 


251 


483.8 


560 1040 


1220 


2228 


-12 


10.4 


54 


129.2 


120 


248. 


186 


366.8 


252 


485.6 


570 1058 


1230 


2246 


-11 


12.2 


55 


131. 


121 


249.8 


187 


368.6 


253 


487.4 


580 1076 


1240 


2264 


-10 


14. 


56 


132.8 


122 


251.6 


188 


370.4 


254 


489.2 


590 1094 


1250 


2282 


- 9 


15.8 


57 


134.6 


123 


253.4 


189 


372.2 


255 


491. 


600 


1112 


1260 


2300 


- 8 


17.6 


58 


136.4 


124 


255.2 


190 


374. 


256 


492.8 


610 


1130 


1270 2318 


- 7 


19.4 


59 


138.2 


125 


257. 


191 


375.8 


257 


494.6 


620 


1148 


12802336 


- 6 


21.2 


60 


140. 


126 


258.8 


192 


377.6 


258 


496.4 


630 1166 


12902354 


- 5 


23. 


61 


141.8 


127 


260:6 


193 


379.4 


259 


498.2 


640 1184 


1300;2372 


- 4 


24.8 


62 


143.6 


128 


262.4 


194 


381.2 


260 


500. 


650 1202 


13102390 


- 3 


26.6 


63 


145.4 


129 


264.2 


195 


383. 


261 


501.8 


660 1220 


1320|2403 


- 2 


28.4 


64 


147.2 


130 


266. 


196 


384.8 


262 503.6 


67011238 


13302426 


- 1 


30.2 


65 


149. 


131 


267.r 


197 


386.6 


2631505.4 


680 1256 


1340 2444 





32. 


66 


150.8 


132 


269.6 


198 


388.4 


264 507.2 


69011274 


1350 2462 


4- 1 


33.8 


67 


152.6 


133 


271.4 


199 


390.2 


265 509. 


700,1292 


1360 2480 


2 


35.6 


68 


154.4 


134 


273.2 


200 


392. 


266 510.8 


710 1310 


1370 2498 


3 


37.4 


69 


156.2 


135 


275. 


201 


393.8 


267i512.6 


720,1328 


1380,2516 


4 


39.2 


70 


158. 


136 


276.8 


202 


395.6 


268 514.4 


730 1346 


1390 2534 


5 


41. 


71 


159.8 


137 


278.6 


203 


397.4 


269,516.2 


74011364 


14002552 


6 


42.8 


72 


161.6 


138 


280.4 


204 


399.2 


270,518. 


750 1382 


14102570 


7 


44.6 


73 


163.4 


139 


282.2 


205 


401. 


27ll519.8 


760 1400 


1420 2588 


8 


46.4 


74 


165.2 


140 


284. 


206 


402.8 


272 521.6 


770 1418 


143012606 


9 


48.2 


75 


167. 


141 


285.8 


207 


404.6 


273,523.4 


780 1436 


1440,2624 


10 


50. 


76 


168.8 


142 


287.6 


208 


406.4 


274 525.2 


79011454 


14:^02642 


11 


51.8 


77 


170.6 


143 


289.4 


209 


408.2 


275 527. 


800ll472 


1460 2660 


12 


53.6 


78 


172.4 


144 


291.2 


210 


410. 


276 528.8 


810 1490 


1470 2678 


13 


55.4 


79 


174.2 


145 


293. 


211 


411.8 


277 530.6 


320 1508 


1480 2696 


14 


57.2 


80 


176. 


146 


294.8 


212 


413.6 


278 532.4 


330 1526 


1490 2714 


15 


59. 


81 


177.8 


147 


296.6 


213 


415.4 


279 534.2 


840 1544 


1500 2732 


16 


60.8 


82 


179.6 


148 


298.4 


214 


417.2 


280,536. 


850 1562 


1510|2750 


^7 


62.6 


83 


181.4 


149 


300.2 


215 


419. 


28l'537.8 


360 1580 


1520,2768 


18 


64.4 


84 


183.2 


150 


302. 


216 


420.8 


282,539.6 


870,1598 


1530l2786 


19 


66.2 


85 


185. 


151 


303.8 


217 


422.6 


283 541.4 


8S0M616 


1540|2804 


20 


68. 


86 


186.8 


152 


305.6 


218 


424.4 


284 543.2 


890,1634 


155012822 


21 


69.8 


87 


188.6 


153 


307.4 


219 


426.2 


285 545. 


900 1652 


16007912 


22 


71.6 


88 


190.4 


154 


309.2 


220 


428. 


286! 546.8 


910 1670 


1650 3002 


23 


73.4 


89 


192.2 


155 


311. 


221 


429.8 


287 548.6 9201 16881 


1700 3092 


24 


75.2 


90 


194. 


156 


312.8 


222 


431.6 288 550.4 930 1706 


1750 3182 


25 


77. 


91 


195.8 


157 


314.6 


223 


433.4 289|552.2 940 1724 


1800 3272 



550 



TEMPERATURES, FAHRENHEIT AXD CENTIGRADE. 



F. 


C. 


F. 


C. 


F. 


C. 


F. 


C. 


F. 

224 


C. 


F. 


C. 


F. 


C. 


^ 


-40. 


26 


-3.3 


92 


333 


158 


70. 


106.7 


29C 


) 143.3 


36C 


182.2 


-39 


-39.4 


27 


-2.8 


93 


33.9 


159 


70.6 


225 


107.2 


291 


143.9 


370 


187.8 


-38 


-38 9 


28 


-2.2 


94 


34.4 


160 


71.1 


226 


107.8 


292 


144.4 


380 


193.3 


-37 


-38.3 


29 


-1.7 


95 


35. 


161 


71.7 


227 


108.3 


293 


145. 


390 


198.9 


-36 


-37.8 


30 


-1.1 


96 


35.6 


162 


72.2 


228 


108.9 


294 


145.6 


400 


204.4 


-35 


-37.2 


31 


-0.6 


97 


36.1 


163 


72.8 


229 


109.4 


295 


146.1 


410 


210. 


-34 


-36.7 


32 


0. 


98 


36.7 


164 


73.3 


230 


110. 


296 


146.7 


420 


215.6 


-33 


-36.1 


33 


+ 0.6 


99 


37.2 


165 


73.9 


231 


110.6 


297 


147.2 


430 


221.1 


-32 


-35.6 


34 


1.1 


100 


37.8 


166 


74.4 


232 


111.1 


298 


147.8 


440 


226.7 


-31 


-35. 


35 


1.7 


101 


38.3 


167 


75. 


233 


111.7 


299 


148.3 


450 


232.2 


-30 


-34.4 


36 


2.2 


102 


38.9 


168 


75.6 


234 


112.2 


300 


148.9 


460 


237.8 


-29 


-33.9 


37 


2.8 


103 


39.4 


169 


76.1 


235 


112.8 


301 


149.4 


470 


243.3 


-28 


-33.3 


38 


3.3 


104 


40. 


170 


76.7 


236 


113.3 


302 


150. 


480 


248.9 


-27 


-32.8 


39 


3.9 


105 


40.6 


171 


77.2 


237 


113.9 


303 


150.6 


490 


254.4 


-26 


-32.2 


40 


4.4 


106 


41.1 


172 


77.8 


238 


114.4 


304 


151.1 


500 


260. 


-25 


-31.7 


41 


5. 


107 


41.7 


173 


78.3 


239 


115. 


305 


151.7 


510 


265.6 


-24 


-31.1 


42 


5.6 


108 


42.2 


174 


78.9 


240 


115.6 


306 


152.2 


520 


271.1 


-23 


-30.6 


43 


6.1 


109 


42.8 


175 


79.4 


241 


116.1 


307 


152.8 


530 


276.7 


-22 


-30. 


44 


6.7 


no 


43.3 


176 


80. 


242 


116.7 


308 


153.3 


540 


282.2 


-21 


-29.4 


45 


7.2 


111 


43.9 


177 


80.6 


243 


117.2 


309 


153.9 


550 


287.8 


-20 


-28.9 


46 


7.8 


112 


44.4 


178 


81.1 


244 


117.8 


310 


154.4 


560 


293.3 


-19 


-28.3 


47 


8.3 


113 


45. 


179 


81.7 


245 


118.3 


311 


155. 


570 


298.9 


-18 


-27.8 


48 


8.9 


114 


45.6 


180 


82.2 


246 


118.9 


312 


155.6 


580 


304.4 


-17 


-27.2 


49 


9.4 


115 


46.1 


181 


82.8 


247 


119.4 


313 


156.1 


590 


310. 


-16 


-26.7 


50 


10. 


116 


46.7 


182 


83.3 


248 


120. 


314 


156.7 


600 


315.6 


-15 


-26.1 


51 


10.6 


1 17 


47.2 


183 


83.9 


249 


120.6 


315 


157.2 


610 


321.1 


-14 


-25.6 


52 


11.1 


118 


47.8 


184 


84.4 


250 


121.1 


316 


157.8 


620 


326.7 


-13 


-25. 


53 


11.7 


119 


48.3 


185 


85. 


251 


121.7 


317 


158.3 


630 


332.2 


-12 


-24.4 


54 


12.2 


120 


48.9 


186 


85.6 


252 


122.2 


318 


158.9 


640 


337.8 


-11 


-23.9 


55 


12.8 


121 


49.4 


187 


86.1 


253 


122.8 


319 


159.4 


650 


343.3 


-10 


-23.3 


56 


13.3 


122 


50. 


188 


86.7 


254 


123.3 


320 


160. 


660 


348.9 


- 9 


-22.8 


57 


13.9 


123 


50.6 


189 


87.2 


255 


123.9 


321 


160.6 


670 


354.4 


- 8 


-22.2 


58 


14.4 


124 


51.1 


190 


87.8 


256 


124.4 


322 


161.1 


680 


360. 


- 7 


-21.7 


59 


15. 


125 


51.7 


191 


88.3 


257 


125. 


323 


161.7 


690 


365.6 


- 6 


-21.1 


60 


15.6 


126 


52.2 


192 


88.9 


258 


125.6 


324 


162.2 


700 


371.1 


- 5 


-20.6 


61 


16.1 


127 


52.8 


193 


89.4 


259 


126.1 


325 


162.8 


710 


376.7 


- 4 


-20. 


62 


16.7 


128 


53.3 


194 


90. 


260 


126.7 


326 


163.3 


720 


382.2 


- 3 


-19.4 


63 


17.2 


129 


53.9 


195 


90.6 


261 


127.2 


327 


163.9 


730 


387.8 


- 2 


-18.9 


64 


17.8 


130 


54.4 


196 


91.1 


262 


127.8 


328 


164.4 


740 


393.3 


- 1 


-18.3 


65 


18.3 


131 


55. 


197 


91.7 


263 


128.3 


329 


165. 


750 


'398.9 





-17.8 


66 


18.9 


132 


55.6 


198 


92.2 


264 


128.9 


330 


165.6 


760 


404.4 


+ 1 


-17.2 


67 


19.4 


133 


56.1 


199 


92.8 


265 


129.4 


331 


166.1 


770 


410. 


2 


-16.7 


68 


20. 


134 56.7 


200 


93.3 


266 


130. 


332 


166.7 


780 


415.6 


3 


-16.1 


69 


20.6 


135|57.2 


201 


93.9 


267 


130.6 


333 


167.2 


790 


421.1 


4 


-15.6 


70 


21.1 


136 


57.8 


202 


94.4 


268 


131.1 


334 


167.8 


800 


426.7 


5 


-15. 


71 


21.7 


137 


58.3 


203 


95. 


269 


131.7 


335 


168.3 


810 


432.2 


6 


-14.4 


72 


22.2 


138 


58.9 


204 


95.6 


270 


132.2 


336 


168.9 


820 


437.8 


7 


-13.9 


73 


22.8 


139 


59.4 


205 


96.1 


271 


132.8 


337 


169.4 


830 


443.3 


8 


-13.3 


74 


23.3 


140 


60. 


206 


96.7 


272 


133.3 


338 


170. 


840 


448.9 


9 


-12.8 


75 


23.9 


14l! 


60.6 


207 


97.2 


273 


133.9 


339 


170.6 


850 


454.4 


10 


-12.2 


76 


24.4 


142 


61.1 


208 


97.8 


274 


134.4 


340 


171.1 


860 


460. 


11 


-11.7 


77 


25. 


143 


61.7 


209 


98.3 


275 


135. 


341 


171.7 


870 


465.6 


12 


-11.1 


78 


25.6 


144 


62.2 


210 


98.9 


276 


135.6 


342 


172.2 


880 


471.1 


13 


-10.6 


79 


26.1 


145 


62.8 


211 


99.4 


277 


136.1 


343 


172.8 


890 


476.7 


14 


-10. 


80 


26.7 


146 


63.3 


212 


100. 


278 


136.7 


344 


173.3 


900 


482.2 


15 


- 9.4 


81 


27.2 


147 


63.9 


213 


100.6 


279 


137.2 


345 


173.9 


910 


487.8 


16 


- 8.9 


82 


27.8 


148 


64 4 


214 


101.1 


280 


137.8 


346 


174.4 


920 


493.3 


17 


- 8.3 


83 


28.3 


149 


65. 


215 


101.7 


281 


138.3 


347 


175. 


930 


498.9 


18 


- 7.8 


84 


28.9 


150 


65.6 


216 


102.2 


282 


138.9 


348 


175.6 


940 


504.4 


19 


- 7.2 


85 


29.4 


151 


66.1 


217 


102.8 


283 


139.4 


349 


176.1 


950 


510. 


20 


- 6.7 


86 


30. 


152 66.7 


218 


103.3 


284 


140. 


350 


176.7 


960 


515.6 


21 


- 6.1 


87 


30.6 


153j67.2 


219 


103.9 


285 


140.6 


351 


177.2 


970 


521.1 


22 


- 5.6 


88 


31.1 


154 67.8 


220 


104.4 


286 


141.1 


352 


177.8 


980 


526.7 


23 


- 5. 


89 


31.7 


155 68.3 


221 


105. 


287 


141.7 


353 


178.3 


990 


532.2 


24 


- 4.4 


90 


32.2 


156 68.9 


222 


• 05.6 


288 


142.2 


354 


178.9 


1000 


537.8 


25 


- 3.9 


91 


32.8 


157 69.4 


223 


106.1 


289 


142.8 


355 


179.4 


1010 


543.3 



551 



552 



HEAT. 



Temperature Conversion Table. 

(By Dr. Leonard Waldo.) 
Reprint from Metallurgical and Chemical Engineering. 



c« 





10 


20 


30 


40 


50 


60 


70 

F 

-454 

-274 

-94 


80 


90 

F 

-310 
-130 


-200 

-100 

-0 


F 

-328 
-148 

+32 


F 

-346 
-166 
+ 14 


F 

-364 

-184 

-4 


F 

-382 

-202 

-22 


F 

-400 

-220 

-40 


F 

-418 

-238 

-58 


F 

-436 

-256 

-76 


F 

-292 
-112 





32 


50 


68 


86 


104 


122 


140 


158 


176 


194 


100 
200 
300 

400 
500 
600 

700 
800 
900 


212 
392 
572 

752 
932 
1112 

1292 
1472 
1652 


230 
410 
590 

770 
950 
1130 

1310 
1490 
1670 


248 
428 
608 

788 
968 
1148 

1328 
1508 
1688 


266 
446 
626 

806 
986 
1166 

1346 
1526 
1706 


284 
464 
644 

824 
1004 
1184 

1364 
1544 
1724 


302 
482 
662 

842 
1022 
1202 

1382 
1562 
1742 


320 
500 
680 

860 
1040 
1220 

1400 
1580 
1760 


338 
518 
698 

878 
1058 
1238 

1418 
1598 
1778 


356 
536 
716 

896 
1076 
1256 

1436 
1616 
1796 


374 
554 
734 

914 
1094 
1274 

1454 
1634 
1814 


1000 


1832 


1850 


1868 


1886 


1904 


1922 


1940 


1958 


1976 


1994 


1100 
1200 
1300 

1400 
1500 
1600 

1700 
1800 
1900 


2012 
2192 
2372 

2552 
2732 
2912 

3092 
3272 
3452 


2030 
2210 
2390 

2570 
2750 
2930 

3110 
3290 
3470 


2048 
2228 
2408 

2588 
2768 
2948 

3128 
3308 
3488 


2066 
2246 
2426 

2606 
2786 
2966 

3146 
3326 
3506 


2084 
2264 
2444 

2624 
2804 
2984 

3164 
3344 
3524 


2102 
2282 
2462 

2642 
2822 
3002 

3182 
3362 
3542 


2120 
2300 
2480 

2660 
2840 
3020 

3200 
3380 
3560 


2138 
2318 
2498 

2678 
2858 
3038 

3218 
3398 
3578 


2156 
2336 
2516 

2696 
2876 
3056 

3236 
3416 
3596 


2174 
2354 
2534 

2714 
2894 
3074 

3254 
3434 
3614 


2000 


3632 


3650 


3668 


3686 


3704 


3722 


3740 


3758 


3776 


3794 


2100 
2200 
2300 

2400 
2500 
2600 

2700 
2800 
2900 


3812 
3992 
4172 

4352 
4532 
4712 

4892 
5072 
5252 


3830 
4010 
4190 

4370 
4550 
4730 

4910 
5090 
5270 


3848 
4028 
4208 

4388 
4568 
4748 

4928 
5108 
5288 


3866 
4046 
4226 

4406 
4586 
4766 

4946 
5126 
5306 


3884 
4064 
4244 

4424 
4604 
4784 

4964 
5144 
5324 


3902 
4082 
4262 

4442 
4622 
4802 

4982 
5162 
5342 


3920 
4100 
4280 

4460 
4640 
4820 

5000 
5180 
5360 


3938 
4118 
4298 

4478 
4658 
4838 

5018 
5198 
5378 


3956 
4136 
4316 

4496 
4676 
4856 

5036 
5216 
5396 


3974 
4154 
4334 

4514 
4694 
4874 

5054 
5234 
5414 


3000 


5432 


5450 


5468 


5486 


5504 


5522 


5540 


5558 


5576 


5594 


3100 
3200 
3300 

3400 
3500 
3600 

3700 
3800 
3900 


5612 
5792 
5972 

6152 
6332 
6512 

6692 
6872 
7052 


5630 
5810 
5990 

6170 
6350 
6530 

6710 
6890 
7070 


5648 
5828 
6008 

6188 
6368 
6548 

6728 
6908 
7088 


5666 
5846 
6026 

6206 
6386 
6566 

6746 
6926 
7106 


5684 
5864 
6044 

6224 
6404 
6584 

6764 
6944 
7124 


5702 
5882 
6062 

6242 
6422 
6602 

6782 
6962 
7142 


5720 
5900 
6080 

6260 
6440 
6620 

6800 
6980 
7160 


5738 
5918 
6098 

6278 
6458 
6638 

6818 
6998 
7178 


5756 
5936 
6116 

6296 
6476 
6656 

6836 
7016 
7196 


5774 
5954 
6134 

6314 
6494 
6674 

6854 
7034 
7214 


C 


10 


20 


30 


40 


50 60 


70 


80 


90 



Examples: 1347°. C = 2444° F+ 12°.6 F = 2456°.6 F: 3367° F=1850*'C + 2°.78C= 
J852°.78 C. For other tables of temperatures, see pages 550 and 551. 



PYROMETRT. 553 

2. Contraction of clay, as in the old Wedgwood pyrometer, at one time 
used by potters. This instrument was very inaccurate, as the contraction 
of clay varied with its nature. 

3. Expansion of air, as in the air-thermometer, Wiborgh's pyrometer. 
Uehling and Steinbart's pyrometer, etc. 

4. Pressure of vapors, as in some forms of Bristol's recording pyrometer. 

5. Relative expansion of two metals or other substances, as in Brown's, 
Bulkley's and other metallic pyrometers, consisting of a copper rod or 
tube inside of an iron tube, or vice versa, with the difference of expansion 
multiplied by gearing and indicated on a dial. 

6. Specific heat of solids, as in the copper-ball and platinum-ball 
pyrometers. 

7. Melting-points of metals, alloys, or other substances, as in approxi- 
mate determination of temperature by melting pieces of zinc, lead, etc., 
or as in Seger's fire-clay pyrometer. 

8. Time required to heat a weighed quantity of water inclosed in a 
vessel, as in one form of water pyrometer. 

9. Increase in temperature of a stream of water or other liquid flow- 
ing at a given rate through a tube inserted into the heated chamber. 

10. Changes in the electric resistance of platinum or other metal, as 
in the Siemens pyrometer. 

11. Measurement of an electric current produced by heating the 
junction of two metals, as in the Le Chatelier pyrometer. 

12. Dilution by cold air of a stream of hot air or gas flomng from a 
heated chamber and determination of the temperature of the mixture by 
a mercury thermometer, as in Hobson's hot-blast pyrometer. 

13. Polarization and refraction by prisms and plates of light radiated 
from heated surfaces, as in Mesur^ and Nouel's pyrometric telescope or 
optical pyrometer, and Wanner's pyrometer. 

14. Heating the filament of an electric lamp to the same color as that 
of an incandescent body, so that when the latter is observed through a 
telescope containing the lamp the filament becomes invisible, as in Hol- 
born and Kurlbaum's and Morse's optical pyrometers. The current 
required to heat the filament is a measure of the temperature. 

15. The radiation pyrometer. The radiation from an incandescent 
surface is received in a telescope containing a thermo-couple, and the 
electric current generated therein is measured, as in Fury's radiation 
pyrometer. 

(See "Optical Pyrometry '* by C. W. W. Waidner and G. K. Burgess, 
Bulletin No. 2. Bureau of Standards, Department of Commerce and 
Labor; also Eng'g, Mar. 1, 1907.) 

The "Veritas" Pyrometer (called Buller's Rings in England) is an 
improvement on the Wedgewood pyrometer. It is based on the con- 
traction of a flat ring of a special clay mixture, which is made with 
great care to secure uniformity of composition. The contraction is 
found to be directly proportional to the increase of temperature^above 
800° C. (1472° F.) and its amount is measured by a multiplying index. 
The rings are 21/2 in. external and 3/4 in. internal diam., s/ie in. thick. 
They are made by Veritas Firing System Co., Trenton, N. J., and are 
largely used by potters. 

Platinum or Copper Ball Pyrometer. — A weighed piece of platinum, 
copper, or iron is allowed to remain in the furnace or heated chamber till 
it has attained the temperature of its surroundings. It is then suddenly 
taken out and dropped into a vessel containing water of a known weight 
and temperature. The water is stirred rapidly and its maximum tem- 
perature taken. Let W = weight of the water, w the weight of the ball, 
t = the original and T the final heat of the water, and S the specific heat of 
the metal; then the temperature of fire may be found from the formula 

W(T - t) 

wS 

The mean specific heat of platinum between 32° and 446® F. is 0.03333 or 
1/30 that of water, and it increases with the temperature about 0.000305 
for each 100° F. For a fuller description, by J. C. Hoadley, see Trans. 
A. S. M. E„ vi, 702. Compare also Henry M. Howe, Trans. A. I. M. E., 
xviii. 728. 

For accuracy corrections are requu-ed for variations in the specific heat 



554 



HEAT. 



of tiie water and of the metal at different temperatures, for loss of heat by 
radiation from the metal during the transfer from the furnace to the water, 
and from the apparatus during the heating of the water; also for the heat- 
absorbing capacity of the vessel containing the water. 

Fire-clay or fire-brick may be used instead of the metal ball. 

Le Chatelier's Thermo-electric Pyrometer. — For a very full 
description, see paper by .Joseph Struthers, School of Mines Quarterly, 
vol. xii, 1891; also, paper read by Prof. Roberts- Austen before the Iron 
and Steel Institute, May 7, 1891. 

The principle upon which this pyrometer is constructed is the measure- 
ment of a current of electricity produced by heating a couple composed of 
two wires, one platinum and the other platinum with 10% rhodium — 
the current produced being measured by a galvanometer. 

The composition of the gas which surrounds the couple has no influence 
on the indications. 

When temperatures above 2500° F. are to be studied, the wires must 
have an isolating support and must be of good length, so that all parts 
of a furnace can be reached. The wires are supported in an iron tube 1/2 
inch interior diameter and held in place by a cylinder of refractory clay 
having two holes bored through, in which the wires are placed. The 
shortness of time (five seconds) allows the temperature to be taken with- 
out deteriorating the tube. 

Tests made by this pyrometer in measuring furnace temperatures under 
a great variety of conditions show that the readings of the scale uncorrected 
are always within 45° F. of the correct temperature, and in the majority 
of industrial measurements this is sufficiently accurate. 

Graduation of Le Chatelier's Pyrometer. — W, C. Roberts- Austen 
in his Researches on the Properties of Alloys, Proc. Inst. M. E., 1892, 
says: The electromotive force produced by beating the thermo-junction 
to any given temperature is measured by themovementof the spot ©flight 
on the scale graduated in millimeters. The scale is calibrated by heating 
the thermo-junction to temperatures which have been carefully deter- 
mined by the aid of the air-thermometer, and plotting the curve from 
the data so obtained. Many fusion and boiling-points have been estab- 
lished by concurrent evidence of various kinds, and are now generally 
accepted. The following table contains certain of these: 



Deg. F. 


Deg. 


c. 


Deg. F. 


Deg. C. 


212 


100 


Water boils. 


1733 


945 


Sliver melts. 


618 


326 


Lead melts. 


1859 


1015 


Potassium sulphate 


676 


358 


Mercury boils. 






melts. 


779 


415 


Zinc melts. 


1913 


1045 


Gold melts. 


838 


448 


Sulphur boils. 


1929 


1054 


Copper melts. 


1157 


625 


Aluminum melts. 


2732 


1500 


Palladium melts. 


1229 


665 


Selenium boils. 


3227 


1775 


Platinum melts. 



The Temperatures Developed in Industrial Furnaces. — M. Le 

Chatelier states that by means of his pyrometer he has discovered that 
the temperatures which occur in melting steel and in other industrial 
operations have been hitherto overestimated. He finds the melting 
heat of white cast iron 1135° (2075° F.), and that of gray cast iron 1220^ 
(2228° F.). Mild steel melts at 1475° (2687° F.), and hard steel at 1410° 
(2570-* F.). The furnace for hard porcelain at the end of the baking has a 
heat of 1370° (2498° F.). The heat of a normal incandescent lamp is 
1800° (3272° F.), but it may be pushed to beyond 2100° (3812° F.). 

Prof. Roberts-Austen (Recent Advances in Pyrometry, Trans. A.I.M.E., 
Chicago Meeting, 1893) gives an excellent description of modern forms of 
pyrometers. The following are some of his temperature determinations. 

Ten-ton Open-hearth Furnace, Woolwich Arsenal. 

Degrees Degrees 
Centigrade. Fahr. 
Temperature of steel, 0.3% carbon, pouring into ladle. 1645 2993 

Steel, 0.3% carbon, pouring into large mold 1580 2876 

Reheating furnace, interior 930 1706 

Cupola furnace, No. 2 cast iron, pouring into ladle 1600 2912 

The following determinations have been effected by M. Le Chatelier: 



PYROMETRY. 555 

Bessemee Pkocess. Six-ton Converter. Deg. C. Deg F.. 

A. Bath of Slag 1580 2876 

B. Metal m ladle 1640 2984 

C. Metal in ingot mold 1580 2876 

D. Ingot in reheating furnace 1200 2192 

E. Ingot under the hammer 1080 1976 

Open-hearth Furnace (Semi-mild Steel). 

A. Fuel gas near gas generator 720 1328 

B. Fuel gas entering into bottom of regenerator chamber 400 752 

C. Fuel gas issuing from regenerator chamber 1200 2192 

Air issuing from regenerator chamber 1000 1832 

Chimney gases. Furnace in perfect condition 300 590 

End of the melting of pig charge 1420 2588 

Completion of conversion 1500 2732 

Molten steel. In the ladle — Commencement of casting . 1580 2876 

End of casting 1490 2714 

In the molds 1520 2768 

For very mild (soft) steel the temperatures are higher by 50° C. 
Blast-furnace (Gray-Bessemer Pig). 

Opening in face of tuyere 1930 3506 

Molten metal — Commencement of fusion 1400 2552 

End, or prior to tapping 1570 2858 

Hoffman Red-brick Kiln 
Burning temperatures 1100 2012 

R. Moldenke {The Foundry, Nov., 1898) determined with a Le 
Chatelier pyrometer the melting-point of 42 samples of pig iron of 
different grades. The range was from 2030° F. for pig containing 
3.98% combined carbon to 2280 for pig containing 0.13 combined car- 
bon and 3.43% graphite. The results of the whole series may be ex- 
pressed within 30° F. by the formula Temp. = 2300° - 70 X % of 
combined carbon. 

Hobson's Hot-blast Pyrometer consists of a brass chamber having 
three hollow arms and a handle. The hot blast enters one of the arms 
and induces a current of atmospheric air to flow into the second arm. 
The two currents mix in the chamber and flow out through the third 
arm, in which the temperature of the mixture is taken by a mercury 
thermometer. The openings in the arms are adjusted so that the pro- 
portion of hot blast to the atmospheric air remains the same. 

The Wiborgh Air-pyrometer. (E. Trotz, Trans. AJ.M.E., 1892.) — 
The inventor using the expansion-coefficient of air, as determined by 
Gay-Lussac, Dulon, Rudberg, and Regnault, bases his construction on 
the following theory: If an air- volume, V, inclosed in a porcelain globe 
and connected through a capillary pipe with the outside air, be heated 
to the temperature T (which is to be determined) and thereupon the 
connection be discontinued, and there be then forced into the globe 
containing V another volume of air V of known temperature t, which 
was previously under atmospheric pressure H, the additional pressure 
h, due to the addition of the air- volume V to the air- volume V, can be 
measured by a manometer. But this pressure is of course a function 
of the temperature T. Before the introduction of V\ we have the two 
separate air-volumes, V at the temperature T, and V at the tempera- 
ture t, both under the atmospheric pressure H. After the forcing in 
of V into the globe, we have, on the contrary, only the volmne V of 
the temperature T, but under the pressure H -\- h. 

Seger Cones. (Stowe-Fuller Co., Cleveland, 1914). Seger Cones 
were developed in 1886 in Germany, by Dr. Herman A. Seger. They 
comprise a series of triangular cones, of pyramidal shape, of differing 
mineral compositions, each one of which requires a different amount of 
heat work to soften and deform it. They are used principally in the 
clay, pottery, and allied industries to determine the proper heat con- 
ditions of kilns, furnaces, etc. The difference in softening point 
between any two adjoining member of the series, is kept as nearly 
equal as possible, so that the cones form a sort of pyrometric scale. 
The softening or fusion is not altogether a matter of temperature, the 
element of time entering in also. A longer exposure at a slightly lower 
temperature will accomplish the same amount of heat work in clay- 
working as a shorter exposure at a somewhat higher temperature, pro- 



556 



HEAT. 



vided it is always above the critical temperature at which chemical 
reactions take place in the clay. Although the time element must be 
considered, a melting point in degrees F. has been assigned to each cone 
number for convenience. For rapid burning, this temperature is 
fairly accurate, but in commercial clay-burning, the cones melt at 
lower temperatures than those given in the table. In extremely long 
firings the difference between the actual and assigned temperatures 
may be as much as 100° or 150° C. (212° to 297° F.) 

Dr. Seger's original series consisted of twenty different mixtures, 
and covered a relatively narrow range of temperatures. Several other 
series have since been devised, as follows: Hecht series, used by 
china and glass decorators, consisting of fusible lead-soda borate glass 
and kaolin, the glass alone making the softest cone, successive addi- 
tions of kaolin raising the fusing point. The Cremer series, used for 
red burning clays and for soft glazes, sewer pipe, drain tiles, roof tiles, 
etc., consisting of a lime-soda borate glass, oxide of iron, feldspar, 
carbonate of hme, potters flint and kaolin, it begins with a large 
amount of glass for the softest cone, and decreasing to almost none at 
the upper end. The Seger series, used for harder red burning wares of 
vitrified variety, and for all buff burning and white burning clay wares 
consisting of potters flint, feldspar, carbonate of hme and feldspar, 
oxide of iron appearing in the three lowest temperature cones; no glass 
is used and the proportion of kaolin and flint increases with the fusion 
temperature. High temperature series, used for testing refractory 
materials only, consisting except in the two lowest numbers of kaolin 
potters flint, and oxide of alumina; the highest cone consists of pure 
oxide of alumina. No temperatures can be assigned to this series, 
although 1850° C. (3362° F.) has been set as the melting point of 
No. 36. The table gives the approximate fusion points of the various 
cones. 

Fusion Points of Seger Cones. 



Symbol 


Melting Point 


Sym- 
bol 
or 

Cone 
No. 


Melting 


I Point 


or 
Cone 

No. 


Melting Point 


or 
Cone 
No. 


Deg.C 


Deg.F 


Deg.C 


Deg.F 


Deg.C 


Deg.F 


HECHT 


















SERIES 






04 


1070 


1958 


13 


1390 


2534 


022 


590 


1094 


03 


1090 


1994 


14 


1410 


2570 


021 


620 


1148 


02 


1110 


2030 


15 


1430 


2606 


020 


650 


1202 


01 


1130 


2066 


16 


1450 


2642 


019 


680 


1256 


SEGER 
SERIES 






17 


1470 


2678 


018 


710 


1310 


1 


1150 


2102 


18 


1490 


2714 


017 


740 


1364 


2 


1170 


2138 


19 


1510 


2750 


016 


770 


1418 


3 


1190 


2174 


20 


1530 


2786 


015 


800 


1472 


4 


1210 


2210 


HIGH 

TEMP. 






0121/2 


875 


1607 


5 


1230 


2246 


SERIES 






CREMER 
















SERIES 






6 


1250 


2282 


26 


Lowest Grade for No. 2 Refractories. 


010 


950 


1742 


7 


1270 


2318 


30 


Lowest Grade for No. 1 Refractories. 


09 


970 


1778 


8 


1290 


2334 


32 


Good Qual. No. 1 Firebrick. 


08 


990 


1814 


9 


1310 


2390 


34 


Excellent Qual. No. 1 Firebrick. 


07 


1010 


1850 


10 


1330 


2426 


36 


Melting point pure Kaolin. 


06 


1030 


1886 


11 


1350 


2462 


38 


Melting point good qual. Bauxite. 


05 


1050 


1922 


12 


1370 


2498 


42 


Melting point pure Alumina. 



The German cones are manufactured by the German Government 
at the Royal Porcelain Factory, Charlottenburg, and can be obtained 
in the United States through Elmer and Amend, New York, and other 
chemical supply houses. In 1896, Prof. Edw. Orton, Jr., of the Oliio 
State University, Columbus, Ohio, began their manufacture in Amer- 
ica. The American cones agree with the German cones in all re- 
pects, and have come into general use in America. They are not sold 
through dealers, but must be obtained direct from the maker. 

MesuTv and Nouel's Pyrometric Telescope. (H. M. Howe, E. and 
M. oA., June 7, 1890) — Mesuro and Nouel's telescope gives an immediate 



PYROMETRY. 657 

determination of the temperature of incandescent bodies, and is there- 
fore better adapted to cases where a great number of observations aro 
to be made, and at short intervals, than Seger's. The little telescope, 
carried in the pocket or hung from the neck, can be used by foreman 
or heater at any moment. 

It is based on the fact that a plate of quartz, cut at right angles to the 
axis, rotates the plane of polarization of polarized light to a degree nearly 
inversely proportional to the square of the length of the waves; and, 
further, on the fact that while a body at dull redness merely emits red 
light, as the temperature rises, the orange, yellow, green, and blue waves 
successively appear. 

If, now, such a plate of quartz is placed between two Nicol prisms at 
right angles, "a ray of monochromatic light which passes the first, or 
polarizer, and is watched through the second, or analyzer, is not extin- 
guished as it was before interposing the quartz. Part of the Ught passes 
the analyzer, and, to again extinguish it, we must turn one of the Nicols a 
certain angle," depending on the length of the waves of light, and hence on 
the temperature of the incandescent object which emits this light. Hence 
the angle through which we must turn the analyzer to extinguish the light 
is a measure of the temperature of the object observed. 

The Uehling and Steinbart Pyrometer. (For illustrated descrip- 
tion see Engineering, Aug. 24, 1894.) — The action of the pyrometer is 
based on a principle wliich involves the law of the flow of gas through 
minute apertures in the following manner: If a closed tube or chamber be 
supplied with a minute inlet and a minute outlet aperture, and air be 
caused by a constant suction to flow in through one and out through the 
other of these apertures, the tension in the chamber between the apertures 
will vary with the difference of temperature between the inflowing and 
outflowing air. If the inflowing air be made to vary with the tem- 
perature to be measured, and the outflowing air be kept at a certain con- 
stant temperature, then the tension in the space or chamber between the 
two apertures will be an exact measure of the temperature of the inflow- 
ing air, and hence of the temperature to be measured. 

In operation it is necessary that the air be sucked into it through the 
first minute aperture at the temperature to be measured, through the 
second aperture at a lower but constant temperature, and that the suc- 
tion be of a constant tension. The first aperture is therefore located 
in the end of a platinum tube in the bulb of a porcelain tube over which 
the hot blast sweeps, or inserted into the pipe or chamber containing 
the gas whose temperature is to be ascertained. 

The second aperture is located in a coupling, surrounded by boiling 
water, and the suction is obtained by an aspirator and regulated by a 
column of water of constant height. 

The tension in the chamber between the apertures is indicated by a 
manometer. 

The Air-thermometer. (Prof. R. C. Carpenter, Eng^g News, Jan. 5, 
1893.) — Air is a perfect thermometric substance, and if a given mass of 
air be considered, the product of its pressure and volume divided by its 
absolute temperature is in every case constant. If the volume of air 
remain constant, the temperature will vary with the pressure; if the 
pressure remain constant, the temperature will vary with the volume. As 
the former condition is more easily attained, air-thermometers are usually 
constructed of constant volume, in which case the absolute temperature 
will vary with the pressure. 

If we denote pressures by p and p', and the corresponding absolute 
temperatures by T and T\ we should have 

T 
p :%>' ::T '.T and T' = p' - • 

The absolute temperature T is to be considered in every case 460 higher 
than the thermometer-reading expressed in Fahrenheit degrees. From 
the form of the above equation, if the pressure p corresponding to a 
known absolute temperature T be known, T can be found. The quotient 
T/p is a constant which may be used in all determinations with the 
instrument. The pressure on the instrument can be expressed in inches 
of mercury, and is evidently the atmospheric pressure h as shown by a 
barometer, plus or minus an additional amount h shown by a manometer 
attached to the air-thermometer. That is, in general, p = h ±.h. 



558 



HEAT, 



The temperature of 32° F. is fixed as the point of melting ice, inwhich 
case r = 460 4- 32 = 492° F. This temperature can be produced by sur- 
roundrng the bulb in meltmgiceand leaving: it several minutes, so that the 
temperature of the confined air shall acquire that of the surrounding ice 
When the air is at that temperature, note the reading of the attached* 
manometer h, and that of a barometer; the sum will be the value of v 
corresponding to the absolute temperature of 492° F. The constant or 
the instrument, K = 492 -i- j), on^e obtained, can be used in all future 
determinations. 

High Temperatures judged by Color. — The temperature of a body 
can be approximately judged by the experienced eye unaided. M. 
Pomllet in 1836 constructed a table, which has been generally quoted in 
the text-books, giving the colors and their corresponding temperature, 
but which is now replaced by the tables of H. M. Howe and of Maunsel 
White and F. W. Taylor {Trans. A. S. M. E., 1899), which are given 
below. 



Howe. ° C. ° F. 
Lowest red vis- 
ible in dark., 470 878 
Lowest red vis- 
ible in day- 
light 475 887 

Dull red 550 to 625 1022 to 1 157 

Full cherry.... 700 1292 

Light red 850 1562 



White and Taylor. ° C. ° F. 
Dark blood-red, black- 
red 

Dark red, blood- red, low 

red 556 

Dark cherry-red 635 

Medium cherrv-red 

Cherry, full red 746 

Light cherry, light red*. 843 



Full yellow 950 to 1000 1742 to 1832 Orange, free scaUng heat 899 



Light yellow 
White 



1050 
1150 



1922 
2102 



* Heat at which scale forms and 



Light orange 941 

Yellow 996 

Light yellow 1079 

White 1205 

adheres on iron and steel, i.e., 



990 

1050 
1175 
1250 
1375 
1550 
1650 
1725 
1825 
1975 
2200 
does 



not fall away from the piece when allowed to cool in air. 

Skilled observers may vary 100° F. or more in their estimation of 
relatively low temperatures by color, and beyond 2200° F. it is practically 
impossible to make estimations with any certainty whatever. (Bulletin 
No. 2, Bureau of Standards, 1905.)' 

In confirmation of the above paragraph we have the following, in a 
booklet published by the Halcomb Steel Co., 1908. 
°C. 

400 

474 

525 

581 

700 
800 
900 

Different substances heated to the same temperature give out the 
same color tints. Objects which emit the same tint and intensity of light 
cannot be distinguished from each other, no matter how different their 
texture, surface, or shape may be. When the temperature at all parts of 
a furnace at a low yellow heat is the same, different objects inside the 
furnace (firebrick, sand, platinum, iron) become absolutely invisible. 
(H. M. Howe.) 

A bright bar of iron, slowly heated in contact with air, assumes the fol- 
lowing tints at annexed temperatures (Claudel): 



°F. 


Colors. 


°C. 


°F. 


Colors. 


752 


Red, visible in the dark. 


1000 


1832 


Bright cherry- red. 


885 


Red, visible in the twilight. 


1100 


2012 


Orange-red. 


9;5 


Red, visible in the day- 


1200 


2192 


Orange-yellow. 




light. 


1300 


2372 


Yellow-white. 


1077 


Red, visible in the sun- 


1400 


2552 


W^hite welding heat. 




light. 


1500 


2732 


Brilliant white. 


1292 


Dark red. 


1600 


2912 


Dazzling white (bluish 


1472 


Dull cherry-red. 






white). 


1652 


Cherry- red. 









Cent. Fahr. 

Yellow at 225 437 

Orange at 243 473 

Red at 265 509 

Violet at 277 531 



Cent. Fahr. 

Indigo at 288 5 3G 

Blue at 293 559 

Green at 332 630 

"Oxide-gray"... 400 752 



The Halcomb Steel Co. (1908) gives the following heats and temi:er 
colors of steel: 



MELTING POINTS OF METALS. 



559 



Cent. Fahr. 


Colors. 


Cent. Fahr. 


221. 1 


430 


Very pale yellow. 


265.6 


510 


226.7 


440 


Light yellow. 


271.1 


520 


232.2 


450 


Pale straw-yellow. 


276.7 


530 


237.8 


460 


Straw-yellow. 


282.2 


540 


243.3 


470 


Deep straw-yellow. 


287.8 


550 


248.9 


480 


Dark' yellow. 


293.3 


560 


254.4 


490 


Yellow-brown. 


298.9 


570 


260.0 


500 


Brown-yellow. 


315.6 


600 



Colors. 
Spotted red-brown. 
Brown-purple. 
Light purple. 
Full purple. 
Dark purple. 
Full blue. 
Dark blue. 
Very dark blue. 

ATMOSPHERIC PBESSUKE. 

per square inch. 

' F. Saturated brine 226** F. 

Nitric acid 248 

Oil of turpentine 315 

Aniline 363 

Naphthaline 428 

Phosphorus 554 

Sulphur 800 

Sulphuric acid 590 

Linseed oil ; 597 

.2 Mercury 676 

increase as the pressure increases. 

MELTING-POINTS OF VARIOUS SUBSTANCES. 

The following figures are given by Clark (on the authority of Pouillett 
Claudel, and Wilson), except those marked *, which are given by Prof. 
Roberts-Austen, and those marked t, which are given by Dr. J. A. Harker. 
These latter are probably the most reliable figures. 



BOILING-POINT AT 

14.7 lb. 

Ether, sulphuric 100' 

Carbon bisulphide 118 

Chloroform 140 

Bromine 145 

Aqua ammonia, sp.gr. 0.95. 146 

Wood spirit 150 

Alcohol 173 

Benzine 176 

Water 212 

Average sea- water 213 

The boiling-points of liquids 



Sulphurous acid — 148° 

Carbonic acid — 108 

Mercury -39, - 38t 

Bromine + 9.5 

Turpentine 14 

Hyponitric acid 16 

Ice 32 

Nitro-glycerine 45 

Tallow 92 

Phosphorus 112 

Acetic acid 113 

Stearine 109 to 120 

Spermaceti 120 

Margaric acid .... 131 to 140 

Potassium 136 to 144 

Wax 142 to 154 

Stearic acid 158 

Sodium 194 to 208 

Iodine 225 

Sulphur 239 

Alloy, 11/2 tin, 1 lead 334, 367t 
Tin 446, 449t 



Cadmium 442° F. 

Bismuth 504 to 507 

Lead 618*, 620t 

Zinc 779*, 786t . 

Antimony 1150, 1169t 

Aluminum 1157*, 1214t 

Magnesium 1200 

NaCl, common salt 1472t 

Calcium Full red heat. 

Bronze 1692 

Silver 1733*, 1751t 

Potassium sulphate.. 1859*, 1958t 

Gold 1913*, 1947t 

Copper 1929*, 1943t 

Nickel 2600t 

Cast iron, white 1922, 2075t 

gray 2012 to 2786, 2228* 

Steel 2372 to 2532* 

" hard . .. 2570*; mild, 2687 
Wrought iron 2732 to 2912, 2737* 

Palladium 2732* 

Platinum 3227*, 3110t 



Cobalt and manganese, fusible in highest heat of a forge. Tungsten 
and chromium, not fusible in forge, but soften and agglomerate. Plati- 
num and iridium, fusible only before the oxyhydrogen blowpipe, or in an 
electrical furnace. For melting-point of fusible alloys see Alloys. For 
boiling and freezing points of air and other gases see p. 606. 

Melting Points of Bare Metals. — H. Von Wartenberg has deter- 
mined the melting points of some rare metals. The temperature was 
measured by a Wanner pyrometer. The following melting points were 
thus obtained: 

Vanadium 1710° C. = 3110° F. 

Rhodium 1970° C. = 3578° F. 

Iridium 2360° C. = 4280° F. 

Molybdenum over 2550° C. = 4622° F. 

Tungsten 2900° C. = 5252° F. 

The metals were as pure as possible. It is stated that the vanadixmi 



560 



HEAT. 



used was of 97% purity. The results were published in a German 
periodical. — Brass World, June, 1910. 

QUANTITATIVE MEASUREMENT OF HEAT. 

Unit of Heat. — The British thermal unit, or heat unit (B.T.U.), is the 
quantity of heat required to raise tlie temperature of 1 lb. of pure water 
from 62° to 63° F. (Peabody), or i/iso of the heat required to raise the 
temperature of 1 lb. of water from 32° to 212° F. (Marks and Davis, 
see Steam, p. 867). 

The French thermal unit, or calorie, is the quantity of heat required 
to raise the temperature of 1 kilogram of pure water from 15° to 16° C. 

1 French calorie = 3.968 British thermal units; 1 B.T.U. = 0.252 
calorie. The "pound calorie" is sometimes used by English writers; 
it is the quantity of heat required to raise the temperature of 1 lb. of 
water 1° C. 1 lb. calorie = 9/5 B.T.U. = 0.4536 calorie. The heat of 
combustion of carbon to CO2 is said to be 8080 calories. This figure is 
used either for French calories or for poimd calories, as it is the number 
of pounds of water that can be raised 1° C. by the complete combustion 
of 1 lb. of carbon, or the number of kilograms of water that can be 
raised 1° C. by the combustion of 1 kilo, of carbon; assummg in each 
case that all the heat generated is transferred to the water. 

The Mechanical Equivalent of Heat is the number of foot-pounds 
of mechanical energy equivalent to one British thermal unit, heat and 
mechanical energy being mutually convertible. Joule's experiments, 
1843-50, gave the figure 772, which is known as Joule's equivalent. 
More recent experiments by Prof. Rowland (1880) and others give higher 
figures; 778 is generally accepted, but 777.6 is probably more nearly 
correct. (Goodenough's " Properties of Steam and Ammonia," 1915.) 

1 heat-unit is equivalent to 778 ft.-lbs. of energy. 1 ft.-lb. = 1/778 = 
0.0012852 heat-unit. 1 horse-power = 33,000 ft.-lbs. per minute = 
2545 heat-units per hour = 42.416 + per minute = 0.70694 per second. 
1 lb. carbon burned to CO2 = 14,600 heat-units. 1 lb. C per H.P. per 
hoxir = 2545 -^ 14,600 = 17.43% efficiency. 

Heat of Combustion of Various Substances in Oxygen. 



Heat-units. 



Cent. Fahr, 



Authority. 



Hydrogen to liquid water at 0° C. 

to steam at 100<^ C 

Carbon (wood charcoal) to car- 
bonic acid, CO2; ordinary tem- 
peratures 

Carbon, diamond to (302 

black diamond to CO2 ... . 

" graphite to CO2 

Carbon to carbonic oxide, CO 

Carbonic oxide to CO2 per unit of 
CO 

CO to CO2 per unit of C=21/3X2403 

Marsh-gas, Me thane, CH4,to water 
and CO2 

Olefiant gas, Ethylene, C2H4, to 
water and CO2 

Beneole gas,C6H«,to water and CO2 
Sulphur to sulphur dioxide, SO2. 



34,462 
33,808 
34,342 
28,732 
8,080 
7,900 
8,137 
7,859 
7,861 
7,901 
2,473 
2,403 
2,431 
2,385 
5,607 
13,120 
13,108 
13,063 
11,858 
11,942 
11,957 
10,102 
9.915 
2,250 



62,032 

60,854 

61,816 

51,717 

14,544 

14,220 

14,647 

14,146 

14,150 

14,222 

4,451 

4,325 

4,376 

4,293 

10,093 

23,616 

23,594 

23,513 

21,344 

21,496 

21,523 

18,184 

17.847 

4,050 



Favre and Silbermann. 

Andrews. 

Thomsen. 

Favre and Silbermann. 

Andrews. 
Berthelot. 



Favre and Silbermann. 

Andrews. 

Thomsen. 

Favre and Silbermann. 

Thomsen. 

Andrews. 

Favre and Silbermann. 

Andrews. 
Thomsen. 

Favre and Silbermann. 
N. W. Lord. 



HEAT OF COMBUSTION. 561 

In calculations of the heating value of mixed fuels the value for carbon 
is commonly taken at 14,600 B.T.U., and that of hydrogen at 62,000. 
Taking the heating value of C burned to CO2 at 14,600, and that of C to 
CO at 4450, the difference, 10,150 B.T.U., is the heat lost by the imperfect 
combustion of each lb. of C burned to CO instead of to CO2. If the CO 
formed by this imperfect combustion is afterwards burned to CO2 the lost 
hp8it is rPErained 

In burning 1 pound of hydrogen with 8 pounds of oxygen to forni D 
pounds of water, the units of heat evolved are 62,000; but if the resulting 
product is not cooled to the initial temperature of the gases, part of the 
heat is rendered latent in the steam. The total heat of 1 lb. of steam at 
212° F. is 1150.0 heat-units above that of water at 32°, and 9 X 1150 = 
10,350 heat-units, which deducted from 62,000 gives 51,650 as the heat 
evolved by the combustion of 1 lb. of hydrogen and 8 lbs. of oxygen at 
32° F. to form steam at 212° F. 

Some writers subtract from the total heating value of hydrogen only 
the latent heat of the 9 lbs. of steam, or 9 X 970.4 = 8734 B.T.U., leavmg 
as the " low " heating value 53,266 B.T.U. . _ „ •« «^«„^„ 

The use of heating values of hydrogen "burned to steam, in compu- 
tations relating to combustion of fuel, is inconvenient, smc® it necessi- 
tates a statement of the conditions upon which the figures are based ; and 
it is, moreover, misleading, if not inaccurate, since hydrogen in fuel is no. 
often burned in pure oxygen, but in air; the temperature of the gases 
before burning is not often the assumed standard temperature, and tne 
S?oductso7 combustion are not often discharged at 212°. In steam- 
boiler practice the chimney gases are usually discharged above 300 but 
if econSmizers are used, and the water supplied to tbem is cold the gases 
mav be cooled to below 212°, in wliich case the steam in the gases is con- 
dSfsed and its latent heat of evaporation is utilized If there is any need 
at all of using figures of the -available" heating value of hydrogen, or its 
heating valul when "burned to steam," the fact.that the gas is burned m 
air and not in pure oxygen should be taken into consideration. The 
resulting figures will then be much lower than those above given, and they 
vdll vaiy with different conditions. (Kent. '♦ Steam Boiler Economy," 

^'lupDOse that 1 lb. of H is burned in twice the quantity of air required 
for complete combustion, or 2 X (8 O + 26 56 N) = 69.12 lbs. air 
supplied at 62° F., and that the products of combustion escape at 562 H . 
The heat lost in the products of combustion will be , or^ -d rp tt 

lbs. water heated from 62° to 212° . . 1352 B.T.U. 

Latent heat of 9 lbs. H2O at 212°. 9 X 9^9.7. .... ... . 8727 

Superheated steam, 9 lbs. X (562° - 212°) X 0.48 (sp. ht.) 1512 ^. 

Nitrogen, 26.56 X (562° - 62°) X 0.2438 3238 ^^ 

Excess air, 34.56 X (562° - 62°) X 0.2375 ^104^ 

Total 1^'^^^ " 

which subtracted from 62,000 .gives 43,067 B.T.U. as the net available 
heatine value under the conditions named. rr^, . x- 1 

Heating Value of Compound or Mixed Fuels. — The heating value 
of a solif clm^^ound or mixe^ fuel is the sum of its elementary constituents, 
and is calculated as follows by Dulong s formula: 

3 X.U.- f^f 14.600 C + 62.000 (h - ^) 4- 4500 sj ; 

in which C H, O; and S are respectively the percentages of the several 
elements. The term H - Vs O is called the ; available", or'' disposable'' 
hydrogen or that which is not combined with oxygen in the fuel. For 
all the common varieties of coal, cannel coal and some lignites excepted 
the forSTs accurate within the limits of error of chemical analyses and 



^^He't^Absorb^^^^^ the decomposition of a 

chemkal compound as much heat is absorbed or rendered latent as was 
evolved when the compound was formed. If 1 lb. of carbon s burned to 
OO2 generating 14,600 B.T.U.. and the CO2 thus formed is immediately 
reduced to CO in the presence of glowing carbon, by the reaction CO2 4- 
C= 2 CO the result is the same as if the ? lbs. Chadf been burned directly 
to 2 CO, generating 2X4450 = 8900 B.T.U. The 2 lbs. C burned to CO2 



562 



HEAT. 



would generate 2 X 14,600 = 29,200 B.T.U., the difference, 29,200 - 
8900 = 20,300 B.T.U., being absorbed or rendered latent in the 2 CO, or 
10,150 B.T.U. for each pound of carbon. 

In Uke manner if 9 lbs. of water be injected into a large bed of glowing 
coal, it will be decomposed into 1 lb. H and 8 lbs. O. The decomposition 
will absorb 62,000 B.T.U. , cooling the bed of coal this amount, and the 
same quantity of heat will again be evolved if the H is subsequently 
burned with a fresh supply of O. The 8 lbs. of O will combine with 6 lbs. 
C, forming 14 lbs. CO (since CO is composed of 12 parts C to 16 parts O), 
generating 6 X 4450 = 26,700 B.T.U., and 6 X 10,150 = 60,900 B.T.U. 
will be latent in this 14 lbs. CO, to be evolved later if it is burned to CO2 
with an additional supply of 8 lbs. O. 

SPECIFIC HEAT. 

Thermal Capacity. — The thermal capacity of a body between two 
temperatures To and Ti is the quantity of heat required to raise the tem- 
perature from To to Ti. The ratio of the heat required to raise the temper- 
ature of a certain weight of a given substance one degree to that required 
to raise the temperature of the same weight of water from 62° to 63° F. 
is commonly called the specific heat of the substance. Some writers 
object to the term as being an inaccurate use of the words *' specific " 
and *' heat." A more correct name would be '* coefficient of thermal 
capacity." 

Determination of Specific Heat. — Method by Mixture. — The body 
whose specific heat is to be determined is raised to a known temperature, 
and is then immersed in a mass of liquid of which the weight. sDecific 
heat, and temperature are known. TVnen both the body and the liquid 
have attained the same temperature, this is carefully ascertained. 

Now the quantity of heat lost by the body is the same as the quantity of 
heat absorbed by the hquid. 

Let c, w, and t be the specific heat, weight, and temperature of the hot 
body, and c', w\ and t' of the liquid. Let T be the temperature the miX' 
ture assumes. 

Then, by the definition of specific heat, c X w X (t — T) = heat-units: 
lost by the hot body, and c' X w^ X {T — V) = heat-units gained by the 
cold hquid. If there is no heat lost by radiation or conduction, these 
must be equal, and 

c^ti/ (T — /'> 
cw {t~T)= dw' (T-t) or c == ^.^^ _ T) 

Elecirical Method. This method is believed to be more accurate in 
many cases than the method by mixture. It consists in measuring the 
quantity of current in watts required to heat a unit weight of a substance 
one degree in one minute, and translating the result into heat-units. 
1 Watt = 0.0569 B.T.U. per minute. 

Specific Heats of Various Substances. 

The specific heats of substances, as given by different authorities show 
considerable lack of agreement, especially in the case of gases. 

The following tables give the mean specific heats of the substances 
named according to Regnault. (From Rontgen's Thermodynamics, p. 
134.) These specific heats are average values, taken at temperatures 
which usually come under observation in technical application. The 
actual specific heats of all substances, in the solid or liquid state, increase 
slowly as the body expands or as the temperature rises. It is probable 
that the specific heat of a body when hquid is greater than when solid. 
For many bodies this has been verified by experiment. 



Solids. 



Antimony . 0508 

Copper . 0951 

Gold 0.0324 

Wrought iron 0.1138 

Glass 0.1937 

Cast iron 0.1298 

Lead 0.0314 

Platinum . 0324 

Silver 0,0570 

^Crn 0.0562 



Steel (soft) 0.1165 

Steel (hard) 0.1175 

Zinc 0.0956 

Brass 0.0939 

Ice 0.5040 

Sulphur 0.2026 

Charcoal 0.2410 

Alumina 0.1970 

Phosphorus - . 0.1887 



SPECIFIC HEAT. 



563 



Liquids. 



Mercury . 0333 

Alcohol (absolute) . 7000 

Fusel oil 0.5640 

Benzine . 4500 

Ether 0.5034 



Water 1.0000 

Lead rmelted) 0.0402 

Sulphur " 0.2340 

Bismuth " 0.0308 

Tin *' 0.0637 

Sulphuric acid 0.3350 

Gases. 
Constant Pressure, 

Air . 23751 

OTVcen. ... 0. 21751 

HySogen..*.-.'. ' 3.40900 

Nitrogen S'?t^|^ 

Superheated steam* X* n?S 

Carbonic acid . 217 

; . Olefiant gas C2H4 (ethylene) . 404 

I Carbonic oxide . 2479 
Ammonia • 508 
Ether 0.4797 
Alcohol 0.4534 
Acetic acid 0. 4125 

Chloroform 0. 1567 

In addition to the above, the following are given by other authorities. 
(Selected from various sources.) 

Metals. 

Wrought iron (Petit & Dulong). 

32° to 212°.. 0.109S 
32° to 392°.. 0.115 



Constant Volume. 
0.16847 
0.15507 
2.41226 
0.17273 
0.346 
0.171 
0.332 
0.1758 
0.299 
0.3411 
0.399 



32° to 572°. . 0.1218 
32° to 662°. . 0.1255 
Iron at high temperatures. 
(Pionchon, Comptes Rendus, 1887.) 

1382^ to 1832° F 0.213 

1749' to 1843° F 0.218 

1922" to 2192° F 0.199 



Platinum, 32° to 446° F.. . . 0.0333 
(increased .000305 for each 100° F.) 

Cadmium 0.0567 

Brass 0.0939 

Copper, 32° to 212° F 0.094 

'' 32° to 572° F 0.1013 

Zinc, 32° to 212° F 0.0927 

32° to 572° F 0.1015 

Nickel 0.1086 

Aluminum, 0° F. to melting- ^ ^^^^ 

point (A. E. Hunt) 0.2185 

Dr -Ing P. Oberhoffer, in Zeit. des Vereines Deutscher Ingemeure iEng 
Diaest Sept., 1908), describes some experiments on the specific heat of 
nearly pure iron. The following mean specific heats were obtained: 
TPTTin F ^00 600 800 1000 1200 1300 

Sp Ht 0.1228 0.1266 0.1324 0.1388 0.1462 0.1601 

Temp F 1500 1800 2100 2400 2700 

Sp Ht 0.1698 0.1682 0.1667 0.1662 0.1666 

The specific heat increases steadily between 500 and 1200 F. Then It 
Increases rapidly to 1400, after which it remains nearly constant. 
Other Solids. 

Coal 0.20 to 0.241 

Coke 0.203 

Graphite 0.202 

Sulphate of lime 0. 197 

Magnesia 0.22" 



Brickwork and masonry, about . 20 

Marble 0.210 

Chalk 0.215 

Quicklime 0.217 

Magnesian limestone 0. 217 



Silica 0.191 

Corundum 0.198 

Stones generally 0.2 to 0.22 



Oven dried, 
0.327. (U. S. 



Soda 0.231 

Quartz 0.188 

River sand 0. 195 

Woods. 

20 varieties, sp. ht. nearly the same for all, average 
Forest Service, 1911.) 

Liquids. 

Olive oil 0.310 

Benzine 0.393 

Turpentine, density 0.872 . . . 472 
Bromine 1.111 



Alcohol, density 0.793 0. 622 

Sulphuric acid, density 1.87. . 0.335 

•' " 1.30. . 0.661 

Hydrochloric acid . 600 



* See Superheated Steam, page 869. 



564 



HEAT. 






Gases. 



At Constant At Constant 
Pressure. Volume. 



Sulphurous acid 0. 1553 0. 1246 

Light carbureted hydrogen, marsh gas (CH4) . . 5929 . 4683 
Bhist-furnace gases . 2277 



Specific Heat of Water. 



(Peabody's Steam Tables, from Barnes and 
Regnault.) 



°c. 


op 


Sp. Ht. 


°,c. 


°F. 


Sp. Ht. 


°c. 


°F. 


Sp. Ht. 


120 


op 

248 


Sp. Ht. 





1.0094 


35 


95 


0.99735 


70 


153 


1.00150 


1 .01620 


s 


41 


1.00530 


40 


104 


0.99735 


75 


167 


1.00275 


140 


284 


1 .02230 


10 


50 


1.00230 


45 


113 


0.99760 


80 


176 


1.00415 


160 


320 


1.02850 


15 


5Q 


1.00030 


50 


122 


0.99800 


85 


188 


1.00557 


180 


356 


1.03475 


?o 


6« 


0.99895 


55 


131 


0.99850 


90 


194 


1.00705 


200 


392 


1.04100 


?'> 


77 


0.99806 


60 


140 


0.99940 


95 


203 


1.00855 


220 


428 


1.04760 


30 


86 


0.99759 


65 


149 


1 .00040 


100 


212 


1.01010 









Specific Heat of Salt Solution. (Schuller.) 
Per cent salt in solution .... 5 10 15 20 25 

Specific heat 0.9306 0.8909 0.8606 0.8490 0.8073 

Specific Heat of Air. — Regnault gives for the mean value at constant 

pressure 

Between - 30° C. and + 10° C 0.23771 

0°C. " 100° C 0.23741 

0° C. " 200° C 0.23751 

Hanssen uses 0.16S6 for the specific heat of tir at constant volume. 
The value of this constant has never been found to any degree of accuracy 
by direct experiment. Prof. Wood gives 0.2375 -i- 1.406 = 0.1689. The 
ratio of the specific heat of a fixed gas at constant pressure to the sp. ht. 
at constant volume is given as follows by different writers {Eng'g, July 12, 
1889): Regnault, 1.3953; Moll and Beck, 1.4085; Szathmari, 1.4027; J, 
Macfarlane Gray, 1.4. The first three are obtained from the velocity of 
sound in air. The fourth is derived from theory. Prof. Wood says: 
The value of the ratio for air, as found in the days of La Place, was 1.41, 
and we have 0.2377 -^ 1.41 = 0.1686, the value used by Clausius, Hanssen, 
and many others. But this ratio is not definitely known. Rankine in 
his later writings used 1.408, and Tait in a recent work gives 1.404, while 
some experiments give less than 1.4, and others more than 1.41. Prof. 
.Wood uses 1,406. 

Specific Heat of Gases. — Experiments by Mallard and Le Chatelier 
indicate a continuous increase in the specific heat at constant volume of 
steam, CO2, and even of the perfect gases, with rise of temperature. The 
variation is inappreciable at 100° C, but increases rapidly at the high tem- 
peratures of the gas-engine cylinder. (Robinson's Gas and Petroleum 
Engines.) 

Thermal Capacity and Specific Heat of Gases. (From Damour*s 
•' Industrial Furnaces.") — The specific heat of a gas at any temperature is 
the first derivative of the function expressing the thermal capacity. It 
is not possible to derive from the specific heat of a gas at a given temper- 
ature, or even from the mean specific heat between 0° and 100° C, the 
thermal capacity at a temperature above 100° C. The specific heats of 
gases under constant pressure between 0° and 100° C., given by Regnault, 
are not sufficient to calculate the quantity of heat absorbed by a gas in 
heating or radiated in cooling, hence all calculations based on these 
figures are subject to a more or less grave error. 

The thermal capacities of a molecular volume (22.32 liters) of gases 
from absolute 0° (- 273° C.) to a temperature T (= 273° 4- may be 
expressed by the formula Q == 0.001 aT + 0.000,001 ftjT^ in which a is a 
constant. 6.5, for all gases, and h has the following values for different 
gases: O2, N2. H2. CO, 0.6; H2O vapor, 2.9; CO2, 3.7; CH4, 6.0. The 
tables on pagci 505 give the thermal capacities of different gases under 
varying conditions of pressure, temperature and volume. 



EXPANSION BY HEAT. 



565 



Specific Heats of Gases per Kilogram. 



Gases. 


Under Constant 
Pressure. 


Under Constant 
Volume. 


Oxygen 


0.213+ 38XlO-6f 
0.243+ 42X10 -H 
3.400+600X10 -H 
0.447+324X10 'H 
0.193 + 168X10 -H 
0.608+748X10 ^H 


0.150+ 38X10-6^ 


Nitrogen and Carbon Monoxide. . 
Hydrogen 


0.171+ 42XlO-«i 
2.400+600X10 -«« 


Water Vapor 


0.335+324X10 -H 


Carbon Dioxide 


0.150 + 168XlO-«« 


Methane 


0.491 +748X10 -^i 



Thermal Capacities of Gases per Kilogram in Centigrade Degs. 



Gases. 



Under Constant 
Pressure. 



Under Constant 
Volume. 



Oxygen 

Nitrogen and Carbon Monoxide. 

Hydrogen 

Water Vapor 

Carbon Dioxide 

Methane or Marsh Gas 



0.213/+ 19X10-6^2 
0.243^+ 21X10-61(2 
3.400 ^+300XlO-n2 
0.447^ + 162x10-6^2 
0.193^+ 84X10-6^2 
0.608^+374X10-^2 



0.150^+ 19X10-6^2 
0.171 <+ 21 XlO-6^2 
2.400 <+300XlO-6«2 
0.335^ + 162X10-6^2 
0.150<+ 84X10-6^2 
0.491 ^+374X10-6^2 



Thermal Capacities of Gases per Kilogram. 



Temperatures. 


0. 


N2,C0 


H2 


H2O 


CO2 


CH4 


Degrees Centigrade. 
200 




47.0 
88.0 
134.0 
181.0 
232.0 
284.0 
334.0 
391.0 
444.0 
503.0 
558.0 
670.0 
681.0 
735.0 
810.0 



50 
100 
154 
207 
264 
325 
383 
445 
508 
575 
637 
708 
777 
850 
921 




700 

1400 

2150 

2900 

3700 

4550 

5350 

6250 

7100 

8050 

8950 

9900 

10900 

11900 

12950 




100 

203 

326 

461 

609 

770 

943 

1130 

1330 

1542 

1751 

1985 

2241 

2520 

2799 




43.1 

91.0 

145.0 

208.0 

277.0 

354.0 

435.0 

523.0 

618.0 

728.0 

840.0 

950.0 

1070.0 

1200.0 

1355.0 



136.6 


400 

600 


303.0 
499.0 


800 


726.0 


1000 


982.0 


1200 


1269 


1400 


1584.0 


1600 

1800 


1931.0 
2307.0 


2000 


2712.0 


2200 


3148.0 


2400 


3614.0 


2600 


4109.0 


2800 


4635.0 


3000 


5190.0 







EXPANSION BY HEAT. 

In the centigrade scale the coefficient of expansion of air per degree 
is 0.003665 = 1/273; that is, the pressure being constant, the volume 
of a perfect gas increases 1/273 of its volume at 0° C. for every in- 
crease in temperature of 1° C. In Fahrenheit units it increases 1/491.6 
= 0.002034 of its volume at 32° F. for every increase of 1° F. 
Expansion of Gases by Heat from 33° to 212° F. (Kegnault.) 



Increase 


in Volume, 


Increase 


in Pressure, 


Pressure Constant. 


Volume Constant. 


Volume at 32° Fahr. 


Pressure at 32° 


= 1.0, for 


Fahr. = 1.0, for 


100° C. 


1°F. 


100° C. 


1°F. 


0.3661 


0.002034 


0.3667 


0.002037 


0.3670 


0.002039 


0.3665 


0.002036 


0.3670 


0.002039 


0.3668 


0.002039 


0.3669 


0.002038 


0.3667 


0.002037 


0.3710 


0.002061 


0.3688 


0.002039 


0.3903 


0.002168 


0.3845 


0.002136 



Hydrogen 

Atmospheric air . . 

Nitrogen 

Carbon monoxide. 
Carbon dioxide . . . 
Sulphur dioxide . . . 



If the volume is kept constant, the pressure varies directly as the 
absolute temperature. 



566 



HEAT. 



Lineal Expansion of Solids at Ordinary Temperatures. 

(Mostly British Board of Trade; from Clark.) 



For 
PFahr. 
Length 



For 
l°Cent. 
Length 



Expan- 
sion 
from 
32° to 
212° F. 



Accord- 
ing to 
Other 

Author^ 
ities. 



Aluminum (drawn) 

Aluminum (cast). 

Antimony (cryst.) 

Brass, cast 

Brass, plate 

Brick 

Brick (fire) 

Bronze (Copper, 17; Tin, 21/2; Zinc, 1).. 

Bismuth 

Cem.ent, Portland (mixed), pure 

Concrete: cement-mortar and pebbles.. 

Copper 

Ebonite 

Glass, English flint 

Glass, thermometer 

Glass, hard 

Granite, gray, dry 

Granite, red, dry 

Gold, pure 

Iridium, pure 

Iron, wrought 

Iron, cast 

Lead. 

Magnesium 

Marbles, various | ^^^^^' "" : ' • 

[ from 

: to 

Mercury (cubic expansion) 

Nickel 

Pewter 

Plaster, white 

Platinum 

Platinum, 85 %, Iridium, 15 % 

Porcelain 

Quartz, parallel to maj. axis, 0° to 40° C. 
Quartz, perpend, to maj. axis, 0° to 40°C, 

Silver, pure 

Slate 

Steel, cast 

Steel, tempered 

Stone (sandstone), dry 

Stone (sandstone), Rauville 

Tin 

Wedgwood ware 

Wood, pine 

Zinc 

Zinc, 8, Tin, I 



0.00001360,0.00002450 



Masonry, brick j 



00001234 
0.00000627 
0.00000957 
0.00001052 
0.00000306 
0.00000300 
0.00000986 
0.00000975 
0.00000594 
0.00000795 
0.00000887 
0.00004278 
0.00000451 
0.00000499 
0.00000397 
0.00000438 
0.00000498 
0.00000786 
0.00000356 
0.00000648 
0.00000556 
0.00001571 



00002221 
0.00001129 
0.00001722 
0.00001894 
0.00000550 
0. 000005 40 
0.00001774 
0.00001755 
0.00001070 
0.00001430 
0.00001596 
0.00007700 
0.00000812 
0.00000897 
0. 00000714 
.00000789 
0.00000897 
0.00001415 



0.002450 
002221 
001129 
0.001722 
0.001894 
0.000550 
0.005400 
0.001774 
0.001755 
0.001070 
0.001430 
0.001596 
0.007700 
0.000812 
0.000897 
0.000714 
0.000789 
0. 000897 
0.001415 



a. 001083 
O.OOI808 



0.001392 



0.001718 



0.00000641 0.000641 
0.00001166 0.001166 



0.00001001 
0.00002828 



0.00000308 
0.00000786 
0.00000256 
0.00000494 
0.00009984 
0.00000695 
0.00001129 
0.00000922 
0.00000479 
0.00000453 
0.00000200 
0.00000434 
0.00000788 
0.00001079 
0.00000577 
0.00000636 
0.00000689 
0.00000652 
0.00000417 
0.00001163 
0.00000489 
0.00000276 
0.00001407 
0.00001496 



0.001001 
0.002828 



0.00000554 
0.00001415 
0.00000460 
0.00000890 
0.00017971 
0.00001251 
0.00002033 
0.00001660 
0.00000863 
0.00000815 
0.00000360 
00000781 
00001419 
00001943 
00001038 
0.00001144 
0.00001240 
0.00001174 
0.00000750 
0.00002094 
0.00000881 
0.00000496 
0.00002532 
0.00002692 



0.000554 
0.001415 
0.000460 
0.000890 
0.017971 
0.001251 
0.002033 
0.001660 
0.000863 
0.000815 
0.000360 
0.000781 
0.001419 
0.001943 
0.001038 
0.001144 
0.001240 
0.001174 
0.000750 
0.002094 
0.000881 
0.000496 
0.002532 
0.002692 



0.001235 
O.COlllO 



0.002694 



0.018018 
0.001279 



0.000884 



0.001908 



0.001079 



0.001938 



0.002942 



Invar (see next page), .000,000,374 to 0.000,000,44 for 1° C. 

Cubical expansion, or expansion of volume = linear expansion X 3. 

Expan.sion of Steel at Hisrh Temperatures. (Charpv and Grenet, 
Comptes Rendut, 1902.) — Coefficients of expansion (for 1° C.) of annealed 
carbon and nickel steels at temperatures at which there is no transforma* 



ABSOLUTE TEMPERATURE. 



567 



tion of the steel. The results seem to show that iron and carbide of iron 
have appreciabiy the same coefficient of expansion. [See aiso p. 449.1 



Composition 
of Steels. 


Mean Coefficients of Expansion 
from 


Coeffs. betwe«n 


r, 


Mn 


Si 


P 


1.5° to 200° 


200° to 500° 


500° to 650° 






03 


01 


0.03 


0.013 


11.8x10-6 


14.3X10-6 


17.0X10^ 


24.5x10-6 


880° & 950*' 


73 


04 


05 


010 


11.5 


14.5 


17.5 


23.3 


800° & 950° 


64 


12 


14 


009 


12.1 


14.1 


16.5 


23.3 


720° & 950° 


93 


10 


05 


0,005 


11.6 


14.9 


16.0 


27.5 


" " 


1 23 


10 


08 


0.005 


11.9 


14.3 


16.5 


33.8 


«( «( 


1 50 


04 


09 


O.OIO 11.5 


14.9 


16.5 


36.7 


«( ti 


3.50 


0.03 


0.07 


0.005 11.2 


14.2 


18.0 


33.3 





Nickel Steels. 


Mean Coefficients of Expansion from 


Ni 


C 


Mn 


I5« to 100« 


100° to 200« 


200° to 400° 


400° to 600° 


600° to 900° 


26.9 


0.35 


0.30 


ii.oxia-« 


18.0xl0-« 


I8.7xl0-« 


22.0xl0-« 


23.0x10-* 


28.9 


0.35 


0.36 


10.0 


21.5 


19.0 


20.0 


22.7 


30.1 


0.35 


0.34 


9.5 


14.0 


19.5 


19.0 


21.3 


34.7 


0.36 


0.36 


2.0 


2.5 


11.75 


19.5 


20.7 


36.1 


0.39 


0.39 


1.5 


1.5 


11.75 


17.0 


20.3 


32.8 


0.29 


0.66 


8.0 


14.0 


18.0 


21.5 


22.3 


35.8 


0.31 


0.69 


2.5 


2.5 


12.5 


18.75 


19.3 


37.4 


0.30 


0.69 


2.5 


1.5 


8.5 


19.75 


18.3 


25.4 


1.01 


0.79 


12.5 


18.9 


19.75 


21.0 


35.0 


29.4 


0.99 


0.89 


11.0 


12.5 


19.0 


20.5 


31.7 


34.5 


0.97 


0.84 


3.0 


3.5 


13.0 


18.75 


26.7 



Invar, an alloy of iron with 36 per cent of nickel, has a smaller coeffi- 
cient of expansion with the ordinary atmospheric changes of temperature 
than any other metal or alloy known. This alloy is sold under the name 
of ** Invar, " and is used for scientific instruments, pendulums of clocks, 
steel tape-measures for accurate survey work, "etc. The Bureau of Stand- 
ards found its coefficient of expansion to range from 0.000,000,374 to 
0.000,000,44 for 1° C, or about V28 of that of steel. For all surveys except 
in the most precise geodetic work a tape of invar may be used without 
correction for temperature. (Eng. News, Aug. 13, 1908.) 

Platinite, an alloy of iron with 42 per cent of nickel, has the same 
coefficient of expansion and contraction at atmospheric temperatures as 
has glass. It can, therefore, be used for the manufacture of armored 
glass, thai is, a plate of glass into which a network of steel wire has been 
rolled, and which is used for fire-proofing, etc. It can also be used instead 
of platinum for the electric connections passing through the glass plugs in 
the base of incandescent electric lights. (Stoughton's " Metallurgy oi 
Steel.") 

Expansion of Liquids from 32° to 213° F. — Apparent expansion 
in glass (Clark). Volume at 212°, volume at 32° being 1: 



Water 1.0466 

Water saturated with salt . 1.05 

Mercury 1.0182 

Alcohol 1.11 



Nitric acid 1.11 

Olive and linseed oils 1 . 08 

Turpentine and ether 1 . 07 

Hydrochloric and sulphuric 
acids 1.06 

For water at various temperatures, see Water. 

For air at various temperatures, see Air. 

ABSOLUTE TEMPERATURE — ABSOLUTE ZERO. 

The absolute zero of a gas is a theoretical consequence of the law of 
expansion by heat, assuming that it is possible to continue the cooling of 
a perfect gas until its volume is diminished to nothing. 



568 HEAT. 

The volume of a perfect gas increases 1/273.1 of its volume at 0° C. for 
every increase of temperature of 1° C, and decreases 1/273.1 of its 
voluine at 0° C. for every decrease of temperature of 1° C. At - 273. 1° C. 
the volume would then be reduced to nothing. This point, - 273. 1° C. = 
- 459.6° F., or 491.6° F. below the temperature of melting ice, is called 
the absolute zero, and absolute temperatures are measured on either the 
Centigrade or the Fahrenheit scale, from this zero. The freezing-point, 
32° F., corresponds to 491.6° F. absolute. If po be the pressure and vo 
the volimie of a perfect gas at 32° F. = 491.6° absolute, = To, and p the 
pressure and v the volume of the same weight of gas at any other 
absolute temperature T, then 

pv __T__ t + 459.6 . pv ^ j!?o?;o ^ -^ 
PqVo ~ To~ 491.6 ' T ~ To ~ * 
A cubic foot of dry air at 32° F. at the sea level (barometer = 29.921 
in. of mercury) weighs 0.080728 lb. The volume of one pound is 
1/0.080728 = 12.387 cu. ft. The pressure is 2116.3 lb. per sq. ft. 
^ _ povo _ 2116.3 X 12.387 _ 26,214 _ _ ._ 
^ - "r7 " 49176 " ~ 491.6 ~ ^^-"^^ 

LATENT HEATS OF FUSION AND EVAPORATION. 

Latent Heat means a quantity of heat which has disappeared, having 
been employed to produce some change other than elevation of tempera- 
ture. By exactly reversing that change, the quantity of heat which 
has disappeared is reproduced. IVIaxwell defines it as the quantity of 
heat which must be commimicated to a body in a given state in order to 
convert it into another state without changing its temperature. 

Latent Heat of Fusion. — When a body passes from the solid to the 
liquid state, its temperature remains stationary, or nearly stationary, at 
a certain melting-point during the whole operation of melting; and in 
order to make that operation go on, a quantity of heat must be trans- 
ferred to the substance melted, being a certain amount for each unit 
of weight of the substance. This quantity is called the latent heat of 
fusion. 

When a body passes from the liquid to the solid state, its temperature 
remains stationary or nearly stationary during the whole operation of 
freezing; a quantity of heat equal to the latent heat of fusion is pro- 
duced in the body and rejected into the atmosphere or other surround- 
ing bodies. 

The following are examples in British thermal units per pound, as 
given in Landolt and Bernstein's " Physikalische-Chemische Tabellen " 
(Berlin, 1894). 

Snb«;tancp^ Latent Heat qnh«tnnf>P«3 Latent Heat 

buDstances. ^^ Fusion. Substances. ^^ Fusion. 

Bismuth 22.75 Silver 37.93 

Cast iron, gray. . . 41.4 Beeswax 76.14 

Cast iron, white. . . 59.4 Paraffine 63.27 

Lead 9.66 Spermaceti 66.56 

Tin 25.65 Phosphorus 9.06 

Zinc 50.63 Sulphur 16.86 

The latent heat of fusion of ice is generally taken at 144 B.T.U. per 
lb. The U. S. Bureau of Standards (1915) gives it as 79.76 20°-calories 
per gram = 143.57 B.T.U. per lb. 

Latent Heat of Evaporation. — When a body passes from the 
sohd or Uquid to the gaseous state, its temperature during the operation 
remams stationary at a certain boiUng-point, depending on the pressure of 
the vapor produced; and in order to make the evaporation go on, a 
quantity of heat must be transferred to the substance evaporated, whose 
amount for each unit of weight of the substance evaporated depends on 
the temperature. That heat does not raise the temperature of the sub- 
stance, but disappears in causing it to assume the gaseous state, and it is 
called the latent heat of evaporation. 

When a body passes from the gaseous state to the liquid or solid state, 
its temperature remains stationary, during that operation, at the boiling- 
point corresponding to the pressure of the vapor: a quantity of heat 
equal to the latent heat of evaporation at that temoerature is produced 



EVAPORATION AND DRYING. 569 

in the body; and in order that the operation of condensation may go on, 
that heat must be transferred from the body condensed to some other 
body. 

The following are examples of the latent heat of evaporation in British 
thermal units, of one pound of certain substances, when the pressure of 
the vapor is one atmosphere of 14.7 lbs. on the square inch: 

Q„Kofov,/.ri Boiling-point under Latent Heat in 

bUDstance. ^^^ ^^^^ ^^^^^ British units. 

Water 212.0 965.7 (Regnault). 

Alcohol 172.2 364.3 (Andrews). 

Ether 95.0 162.8 

Bisulphide of carbon 114.8 156.0 

The latent heat of evaporation of water at a series of boiling-points ex- 
tending from a few degrees below its freezing-point up to about 375 
degrees Fahrenheit has been determined experimentally by M. Regnault. 
The results of those experiments are represented approximately by the 
formula, in British thermal units per pound, 

I nearly = 1091.7 - 0.7 (t - 32°) = 965.7 - 0.7 (t - 212°). 

Henning (Ann. der Physik, 1906) gives for t from 0° to 100° C. 

Fori kg., ^= 94.210 (365-^° C.) 0.31249. 

Fori lb., Z = 141.124 (689-^° F.) 0.31249. 

The last formula gives for the latent heat at 212° F.. 969.7 B.T.U. 

The Total Heat of Evaporation is the sum of the heat which dis- 
appears in evaporating one pound of a given substance at a given tem- 
perature (or latent heat of evaporation) and of the heat required to raise its 
temperature, before evaporation, from some fixed temperature up to the 
temperature of evaporation. The latter part of the total heat is called the 
sensible heat. 

In the case of water, the experiments of M. Regnault show that the 
total heat of steam from the temperature of melting ice increases at a 
uniform rate as the temperature of evaporation rises. The following is 
the formula in British thermal units per pound: 

h = 1091.7 + 0.305 (t - 32°). 

H. N. Davis (Trans. A. S. M. E., 1908) gives, in British units, 
71 = 1150 + 0.3745 (^-21 2) -0.000550 (^-212)2. 

For the total heat, latent heat, etc., of steam at different pressures, see 
table of the Properties of Saturated Steam. For tables of total heat, 
latent heat, and other properties of steams of ether, alcohol, acetone, 
chloroform, chloride of carbon, and bisulphide of carbon, see Rontgen's 
Thermodynamics (Dubois's translation). For ammonia and sulphur 
dioxide, see Wood's Thermodynamics; also, tables under Refrigerating 
Machinery, in this book. 

EVAPORATION AND DRYING. 

In evaporation, the formation of vapor takes place on the surface; in 
boiling, within the liquid: the former is a slow, the latter a quick, method 
of evaporation. 

If we bring an open vessel with water under the receiver of an air-pump 
and exhaust the air, the w^ater in the vessel will commence to boil, and if we 
keep up the vacuum the water will actually boil near its freezing-point. 
The formation of steam in this case is due to the heat which the water 
takes out of the surroundings. 

Steam formed under pressure has the same temperature as the liquid in 
which it was formed, provided the steam is kept under the same pressure. 

By properiy cooling the rising steam from boiling water, as in the mul- 
tiple-effect evaporating systems, we can regulate the pressure so that the 
water boils at low temperatures. 

Evaporation of Water in Reservoirs. — Experiments at the Mount 
Hope Reservoir, Rochester, N. Y., in 1891, gave the following results: 

July. Aug. Sept. Oct. 

Mean temperature of air in shade 70.5 70.3 68.7 53.3 

" water in reservoir. . . 68.2 70.2 66.1 54.4 

" humidity of air, per cent 67.0 74.6 75.2 74.7 

Evaporation in inches during month 5.59 4.93 4.05 3.23 

Rainfall in inches during month 3.44 2.95 1.44 2.16 



570 ' HEAT. 

Evaporation of Water from Open Channels.— (Flynn's Irrigation 
Canals and Flow of Water.) — Experiments from 1881 to 1885 in Tulare 
County, California, showed an evaporation from a pan in the river 
equal to an average depth of Vs in. per day throughout the year. 

When the pan was in the air the average evaporation was less than 
3/i6 in. per day. The average for the month of August was 1/3 in. per 
day, and for March and April 1/12 in. per day. Experiments in Colorado 
show that evaporation ranges from 0.088 to 0.16 in. per day during 
the irrigating season. 

In Northern Italy the evaporation was from 1/12 to 1/9 inch per day 
while in the south, under the influence of hot winds, it was from i/e 
to V5 inch per day. 

In the hot season in Northern India, with a decidedly hot wind blow- 
ing, the average evaporation was 1/2 inch per day. The evaporation 
increases with the temperature of the water. 

Evaporation by the Multiple System. — A multiple effect is a series 
of evaporating vessels each having a steam chamber, so connected that 
the heat of the steam or vapor produced in the first vessel heats the 
second, the vapor or steam produced in the second heats the third, and 
so on. The vapor from the last vessel is condensed in a condenser. 
Three vessels are generally used, in which case the apparatus is called 
a Triple Effect. In evaporating in a triple effect the vacuum is gradu- 
ated so that the liquid is boiled at a constant and low temperature. 

A series distilling apparatus of high efficiency is described by W.F. 
M. Goss in Trans. A. S. M. E., 1903. It has seven chambers in series, 
and is designed to distill 500 gallons of water per hour with an eflQ- 
ciency of approximately 60 lbs. of water per pound of coal. 

Tests of Yaryan six-effect machines have shown as high as 44 lbs. of 
water evaporated per pound of fuel consumed. — Mach'y, April, 1905. 
A description of a large distilling apparatus, using three 125-H.P. boilers 
and a Lillie triple effect, with record of tests, is given in Eng. News, 
Mar. 29, 1900, and in Jour. Am. Soc'y of Naval Engineers, Feb., 1900. 

Tests of heating and evaporating apparatus used in sugar houses, 
including calandrias, multiple effects, vacuum pahs, and condensers, 
are described by E. W. Kerr in a 178-page pamplilet, Bulletin 149 of 
the Agricultural Experiment Station of the Louisiana State University, 
August, 1914. 

Resistance to Boiling. — Brine. (Rankine.) — The presence in a 
liquid of a substance dissolved in it (as salt in water) resists ebullition, and 
raises the temperature at which the liquid boils, under a given pressure; but 
unless the dissolved substance enters into the composition of the vapor, 
the relation between the temperature and pressure of saturation of the 
vapor remains unchanged. A resistance to ebullition is also offered by a 
vessel of a material which attracts the liquid (as when water boils in a 
glass vessel), and the boiling take place by starts. To avoid the errors 
which causes of this kind produce m the measurement of boiling-points, 
it is advisable to place the thermometer, not in the liquid, but in the 
vapor, which shows the true boiling-point, freed from the disturbing 
effect of the attractive nature of the vessel. The boiling-point of saturated 
brine under one atmosphere is 226° F., and that of weaker brine is higher 
than the boiling-point of pure water by 1.2° F., for each 1/32 of salt that 
the water contains. Average sea- water contains I/32; and the brine in 
marine boilers is not suffered to contain more than from 2/32 to 3/32. 
,„^^!^thods of Evaporation Employed in the Manufacture of Salt. 
(F. E. Engelhardt, Chemist Onondaga Salt Springs; Report for 1889.) — 
1. Solar heat — solar evaporation. 2. Direct fire, applied to the heat- 
»n& surface of the vessels containing brine — kettle and pan methods. 
3. The steam-grainer system — steam-pans, steam-kettles, etc. 4. Use 
of steam and a reduction of the atmospheric pressure over the boiling 
brine — vacuum system. 

When a saturated salt solution boils, it is immaterial whether it is done 
under ordinary atmospheric pressure at 228° F., or under four atmospheres 
with a temperature of 320° F., or in a vacuum under VlO atmosphere, the 
result will always be a fine-grained salt. 

The fuel consumption is stated to be as follows: By the kettle method, 
40 to 45 bu. of salt evaporated per ton of fuel, anthracite dust burned on 
perforated grates; evaporation, 5.53 lbs. of water per pound of coal. By 



EVAPORATION AND DRYING. 



571 



the pan method, 70 to 75 bu. per ton of fuel. By vacuum pans, single 
effect, 86 bu. per ton of anthracite dust (2000 lbs.). With a double 
effect nearly double that amount can be produced. 



Solubility of Common Salt in Pure Water. 

Temp, of brine, F. 32 50 



(Andrese.) 



86 104 140 176 
100 parts water dissolve parts. . 35.63 35.69 36.03 36.32 37.06 38.00 
100 parts brine contain salt 26.27 26.30 26.49 26.64 27.04 27.54 

According to Poggial, 100 parts of water dissolve at 229.66° F., 40.35 
parts of salt, or in per cent of brine, 28.749. Gay-Lussac found that at 
229.72° F., 100 parts of pure water would dissolve 40.38 parts of salt, in 
per cent of brine, 28.764 parts. 

The solubiUty of salt at 229° F. is only 2.5% greater than at 32°. Hence 
we cannot, as in the case of alum, separate the salt from the water by 
allowing a saturated solution at the boiling-point to cool to a lower 
temperature. 

Strength of Salt Brines. — The following table is condensed from 
one given in U. S. Mineral Resources for 1888, on the authority of Dr. 
Engelhardt. 

Relations between Salinometer Strength, Specific Gravity, Solid 
Contents, etc., of Brines of Different Strengths. 











V4 


■« w 


'd 


dj © 


0'*i X 


c^ 













-A 


t 


^§ 


-°a.- 


s" 


•S 


1 


1 


1 

-4^ 


« a 


1^ 


H 

•si 


■si- 


coal requirec 

e a bushel 

lb. coal eva 

6 lbs. of wate 


of salt that 
de with a ton 
2000 pounds. 


a 








1^ 


m 


O 53 




-or,^ 




.a 


« 


02 






3 o 




3 ^^ 


^iii 


l^i 


1 


0.26 


1.002 


0.265 


8.347 


0.022 


2,531 


21,076 


3,513 


0.569 


2 


0.52 


1.003 


0.530 


8.356 


0.044 


1,264 


10,510 


1,752 


1.141 


4 


1.04 


1.007 


1.060 


8.389 


0.088 


629.7 


5,227 


871.2 


2.295 


6 


1.56 


1.010 


1.590 


8.414 


0.133 


418.6 


3,466 


577./ 


3.462 


8 


2. OS 


1.014 


2.120 


8.447 


0.179 


312.7 


2,585 


430.9 


4.641 


10 


2.60 


1.017 


2.650 


8.472 


0.224 


249.4 


2,057 


342.9 


5.833 


12 


3.12 


1.021 


3.180 


8.506 


0.270 


207.0 


1,705 


284.2 


7.038 


14 


3.64 


1.025 


3.710 


8.539 


0.316 


176.8 


1,453 


242.2 


8.256 


16 


4.16 


1.028 


4.240 


8.564 


0.364 


154.2 


1,265 


210.8 


9.488 


18 


4.68 


1.032 


4.770 


8.597 


0.410 


136.5 


1,118 


186 3 


10.73 


20 


5.20 


1.035 


5.300 


8.622 


0.457 


122.5 


1,001 


176.8 


11.99 


30 


7.80 


1.054 


7.950 


8.781 


0.698 


80.21 


648.4 


108.1 


18.51 


40 


10.40 


1.073 


10.600 


8.939 


0.947 


59.09 


472.3 


78.71 


25.41 


50 


13.00 


1.093 


13.250 


9.105 


1.206 


46.41 


366.6 


61.10 


32.73 


60 


15.60 


1.114 


15.900 


9.280 


1.475 


37.94 


296.2 


49.36 


40.51 


70 


18.20 


1.136 


18.550 


9.454 


1.755 


31.89 


245.9 


40.98 


48.80 


80 


20.80 


1.158 


21.200 


9.647 


2.045 


27.38 


208.1 


34.69 


57.65 


90 


23.40 


1.182 


23.850 


9.847 


2.348 


23.84 


178.8 


29.80 


67.11 


100 


26.00 


1.205 


26.500 


10.039 


2.660 


21.04 


155 3 


25 88 


77 26 



Solubility of Sulphate of Lime in Pure Water. (Marignac.) 

32 64.5 89.6 100.4 105.8 127.4 186.8 212 



Temperature F. degrees.. 
Parts water to dissolve" 

1 part gypsum 
Parts water to dissolve l' 

part anhydrous CaS04 



415 
•525 



386 371 


368 


370 


375 


417 


452 


488 470 


466 


468 


474 


528 


572 



In salt brine sulphate of lime is much more soluble than in pure water. 
In the evaporation of salt brine the accumulation of sulphate of lime tends 



572 HEAT. 

to stop the operation, and it must be removed from the pans to avoid 
waste of fuel. The average strength of brine in the New York salt 
districts in 1889 was 69.38 degrees of the saUnometer. 

Concentration of Sugar Solutions.* (From "Heating and Con- 
centrating Liquids by Steam," by John G. Hudson; The Engineer, June 13, 
1890.) — In the early stages of the process, when the liquor is of low 
density, the evaporative duty will be high, say two to three (British) 
gallons per square foot of heating surface with 10 lbs. steam pressure, 
but will gradually fall to an almost nominal amount as the final stage is 
approached. As a generally safe basis for designing, Mr. Hudson takes 
an evaporation of one gallon per hour for each square foot of gross heating 
surface, with steam of the pressure of about 10 lbs. 

As examples of the evaporative duty of a vacuum pan when performing 
the earlier stages of concentration, during which all the heating surface 
can be employed, he gives the following: 

Coil Vacuum Pan. — 43/4 in. coj^per coils, 528 square feet of surface; 
steam in coils, 15 lbs.; temperature in pan, 141° to 148°; density of feed, 
25° Baume, and concentrated to 31° Baume. 

First Trial. — Evaporation at the rate of 2000 gallons per hour = 3.8 
gallons per square foot ; transmission, 376 units per degree of difference of 
temperature. 

Second Trial. — Evaporation at the rate of 1503 gallons per hour = 
2.8 gallons per square foot ; transmission, 265 units per degree. 

As regards the total time needed to work up a charge of massecuite from 
liquor of a given density, the following figures, obtained by plotting the 
results from a large number of pans, form a guide to practical working. 
The pans were all of the coil type, some with and some without jackets, 
the gross heating surface probably averaging, and not greatly differing 
from, 0.25 square foot per gallon capacity, and the steam pressure 10 lbs. 
per square inch. Both plantation and refining pans are included, making 
various grades of sugar: 

Density of feed (degs. Baume) 10° 15° 20° 25° 30° 

Evaporation required per gallon masse- 
cuite discharged 6.123 3.6 2.26 1.5 .97 

Average working hours required per charge . 12. 9. 6.5 5. 4. 

Equivalent average evaporation per hour 
per square foot of gross surface, assum- 
ing 0.25 sq. ft. per gallon capacity 2.04 1.6 1.39 1.2 0.97 

Fastest working hours required per charge . 8.5 5.5 3.8 2.75 2.0 

Equivalent average evaporation per hour 

per square foot 2.88 2.6 2.38 2.18 1.9 

The quantity of heating steam needed is practically the same in vacuum 
as in open pans. The advantages proper to the vacuum system are pri- 
marily the reduced temperature of boiling, and incidentally the possibility 
of using heating steam of low pressure. 

In a solution of sugar in water, each pound of sugar adds to the volume 
of the water to the extent of 0.061 gallon at a low density to 0.0638 gallon 
at high densities. 

A 3Iethod of Evaporatins: by Exhaust Steam is described by 
Albert Stearns in Trans. A. S. M. E., vol. viii. A pan 17' 6" X 11' X 1' 6% 
fitted with cast-iron condensing pipes of about 250 sq. ft. of surface, 
evaporated 120 gallons per hour from clear water, condensing only about 
one-half of the steam supplied by a plain slide-valve engine of 14" X 32" 
cyhnder, making 65 revs, per min., cutting off about two-thirds stroke, 
with steam at 75 lbs. boiler pressure. 

It was found that keeping the pan-room warm and letting only suffident 
air in to carry the vapor up out of a ventilator adds to its efficiency, as 
the average temperature of the water in the pan was only about 165° F. 

Experiments were made with coils of pipe in a small pan, first with no 
agitator, then with one having straight blades, and lastly with troughed 
blades; the evaporative results being about the proportions of one, two, 
and three respectively. 

In evaporating liquors whose boiling-point is 220° F.. or much above 
that of water, it is found that exhaust steam can do but little more than 

* For other sugar data, see Bagasse as Fuel, under Fuel 



EVAPORATION AND DRYING. 573 

bring them up to saturation strength, but on weak liquors, sirups, glues, 
etc., it should be very useful. 

Drying in Vacuum. — An apparatus for drying grain and other sub- 
stances in vacuum is described by Mr. Emil Passburg in Proc.Inst. Mcch. 
Engrs., 1889. The three essential lequirementc for a successful and eco- 
nomical process of drying are: 1. Cheap evaporation of the moisture; 
2. Quick drying at a low temperature; 3. Large capacity of the apparatus. 

The removal of the moisture can be effected in either of two ways: either 
by slow evaporation, or by quick evaporation — that is, by boiling. 

Slow Evaporation. — The principal idea carried into practice in machines 
acting by slow evaporation is to bring the wet substance repeatedly into 
contact with the inner surfaces of the apparatus, which are heated bv 
steam, while at the same time a current of hot air is also passing through 
the substances for carrying off the moisture. This method requires much 
heat, because the hot-air current has to move at a considerable speed in 
order to shorten the drying process as much as possible; consequently a 
great quantity of heated air passes through and escapes unused. As a 
carrier of moisture hot air cannot in practice be charged beyond half its full 
saturation; and it is in fact considered a satisfactory result if even this 
proportion be attained. A great amount of heat is here produced which is 
not used; while, with scarcely half the cost for fuel, a much quicker 
removal of the water is obtained by heating it to the boiling-point. 

Quick Evaporation by Boiling. — This does not take place until the 
water is brought up to the boiling-point and kept there, namely, 212° F., 
under atmospheric pressure. The vapor generated then escapes freely. 
Liquids are easily evaporated in this way, because by their motion conse- 
quent on boiling the heat is continuously conveyed from the heating sur- 
faces through the liquid, but it is different with solid substances, and 
many more difficulties have to be overcome, because convection of the 
heat ceases entirely in solids. The substance remains motionless, and 
consequently a much greater quantity of heat is required than with 
liquids for obtaining the same results. 

Evaporation in Vacuum. — All the foregoing disadvantages are avoided 
if the boiling-point of water is lowered, that is, if the evaporation is carried 
out under vacuum. 

This plan has been successfully applied in Mr. Passburg's vacuum drjing 
apparatus, which is designed to evaporate large quantities of water con- 
tained in solid substances. 

The drying apparatus consists of a top horizontal cylinder, surmounted 
by a charging vessel at one end, and a bottom horizontal cylinder with a 
discharging vessel beneath it at the same end. Both cylinders are 
incased in steam-jackets heated by exhaust steam. In the top cylinder 
works a revolving cast-iron screw with hollow blades, which is also heated 
by exhaust steam. The bottom cylinder contains a revolving drum of 
tubes, consisting of one large central tube surrounded by 24 smaller ones, 
all fixed in tube-plates at both ends; this drum is heated by live steam 
direct from the boiler. The substance to be dried is fed into the charg- 
ing vessel through two manholes, and is carried along the top cjdinder 
by the screw creeper to the back end, where it drops through a valve 
Into the bottom cylinder, in which it is lifted by blades attached to the 
drum and travels forward in the reverse direction; from the front end of 
the bottom cylinder it falls into a discharging vessel through another 
valve, having by this time become dried. The vapor arising during the 
process is carried off by an air-pump, through a dome and air-valve on 
the top of the upper cylinder, and also through a throttle-valve on 
the top of the lower cylinder; both of these valves are supplied with 
strainers. 

As soon as the discharging vessel is filled with dried material the valve 
connecting it with the bottom cylinder is shut, and the dried charge taken 
out without impairing the vacuum in the apparatus. When the charging 
vessel requires replenishing, the intermediate valve between the two cylin- 
ders is shut, and the charging vessel filled with a fresh supply of wet mate- 
rial; the vacuum still remains unimpaired in the bottom cylinder, and has 
to be restored only in the top cylinder after the charging vessel has been 
closed again. 

. In this vacuum the boiling-point of the water contained in the wet mate- 
rial is brought down as low as 1 iO° F. The difference between this tern- 



574 HEAT. 

perature and that of the heating surfaces is amply sufficient for obtainine: 
good results from the employment of exhaust steam for heating all the 
surfaces except the revolving drum of tubes. The water contained in 
the solid substance to be dried evaporates as soon as the latter is heated 
to about 110° F., and as long as there is any moisture to be removed the 
solid substance is not heated above this temperature. 

Wet grains from a brewery or distillery, containing from 75% to 78% of 
water, have by this drying process been converted from a worthless incum- 
brance into a valuable food-stuff. The water is removed by evaporation 
only, no previous mechanical pressing being resorted to. 

At Guinness's brewery in Dublin two of these machines are employed. 
In each of these the top cylinder is 20 ft. 4 in. long and 2 ft. 8 in. diam., 
and the screw working inside it makes 7 revs, per min.; the bottom 
cyUnder is 19 ft. 2 in. long and 5 ft. 4 in. diam., and the drum of the tubes 
inside it makes 5 revs, per min. The drying surfaces of the two cylinders 
amount together to a total area of about 1000 sq. ft., of which about 40% 
is heated by exhaust steam direct from the boiler. There is only one air- 
pump, which is made large enough for three machines; it is horj,- 
zontal, and has only one air-cylinder, which is double-acting, 17 3/4 in. 
diam. and 173/4 in. stroke; and it is driven at about 45 revs, per min. 
As the result of about eight months* experience, the two machines 
have been drying the wet grains from about 500 cwt. of malt per day of 
24 hours. 

Roughly speaking, 3 cwt. of malt gave 4 cwt. of wet grains, and the 
latter yield 1 cwt. of dried grains; 500 cwt. of malt will therefore yield 
about 670 cwt. of wet grains, or 335 cwt. per machine. The quantity of 
water to be evaporated from the wet grains is from 75% to 78% of their 
total weight, or, say, about 512 cwt. altogether, being 256 cwt. per 
machine. 

Driers and Drying. 
(Contributed by W. B. Ruggles, 1909.) 

Materials of different physical and chemical properties require different 
types of drying apparatus. It is therefore necessary to classify mate- 
rials into groups, as below, and design different machines for each 
group. 

Grouj) A: Materials which may be heated to a high temperature and 
are not injured by being in contact with products of combustion. These 
include cement rock, sand, gravel, granulated slag, clay, mari, chalk, ore, 
graphite, asbestos, phosphate rock, slacked lime, etc. 

The most simple machine for drj^ing these materials is a single revolving 
shell with lifting flights on the inside, the shell resting on bearing wheels 
and having a furnace at one end and a stack or fan at the other. The 
advantage of this style of machine is its low cost of installation and the 
small number of parts. The disadvantages are great cost of repairs and 
excessive fuel consumption, due to radiation and high temperature of the 
stack gases. If the material is fed from the stack and towards the furnace 
end, the shell near the furnace gets red-hot, causing excessive radiation and 
frequent repairs. Should the feed be reversed the exhaust temperature 
must be kept above 212° F., or recondensation will take place, wetting the 
material. 

In order to economize fuel the shell is sometimes supported at the 
ends and brickwork is erected around the shell, the hot gases passing 
under the shell and back through it. Although this method is more 
economical in the use of fuel, the cost of installation and the cost of 
repairs are greater. 

Group B: Materials such as will not be injured by the products of com- 
bustion but cannot be raised to a high temperature on account of driving 
off water of crystallization, breaking up chemical combinations, or en 
account of danger from ignition. Included in these are gypsum, fluor- 
spar, iron pyrites, coal, coke, lignite, sawdust, leather scraps, cork chips, 
tobacco stems, fish scraps, tankage, peat, etc. Some of these materials 
may be dried in a single-shell drier and some in a bricked-in machine, 
but none of them in a satisfactory way on account of the difificulty of 
regulating the temperature and, in some cases, the danger of explosion of 
dust. 

Group C: Materials which are not injured by a high temperature but 
which cannot be allowed to come into contact with products of combus- 



EVAPORATION AND DRYING. 575 

tion. These are kaolin, ocher and other pigments, fuller's earth, which is 
to be used in filtering vegetable or animal oils, whiting and similar earthy 
materials, a large proportion of which would be lost as dust in direct-heat 
drying. These may be dried by passing through a single-shell drier 
incased in brickwork and allowing heat to come into contact with the 
shell only, but this is an uneconomical machine to operate, due to the 
high temperature of the escaping gases. 

Group D: Organic materials which are used for food either by man or 
the lower animals, such as grain which has been wet, cotton seed, starch 
feed, corn germs, brewers' grains, and breakfast foods, which must be 
dried after cooking. These, of course, cannot be brought into contact 
with furnace gases and must be kept at a low tempjerature. For these 
materials a drier using either exhaust or live steam is the only practical 
one. This is generally a revolving shell in wliich are arranged steam 
pipes. Care should be exercised in selecting a steam drier which has 
perfect and automatic drainage of the pipes. The condensed steam 
always amounts to more than the water evaporated from the material. 

Group E: Materials which are composed wholly or contain a large pro- 

Eortion of soluble salts, such as nitrate of soda, nitrate of potash, car- 
onates of soda or potash, chlorates of soda or potash, etc. These in 
drying form a hard scale which adheres to the shell, and a rotary drier 
cannot be profitably used on account of frequent stops for cleaning. The 
only practical machine for such materials is a semicircular cast-iron 
trough having a shaft through the center carrying paddles that con- 
stantly^ stir up the material and feed it through the drier. This machine 
has brick side walls and an exterior furnace; the heat from the furnace 
passing under the shell and back through the drying material or out 
through a stack or fan without passing through the material, as may be 
desired. Should the material also require a low temperature, the same 
type of drier can be used by substituting steam-jacketed steel sections 
instead of cast iron. 

The efficiency of a drier is the ratio of the theoretical heat required to 
do the drying to the total heat supplied. The greatest loss is the heat 
carried out by the exhaust or waste gases; this may be as great as 40% 
of the total heat from the fuel, or with a properly designed drier may be 
as small as 8%. The radiation from the shell or walls may be as high as 
25% or as low as 4%. The heat carried away by the dried material may 
amount under conditions of careless operation to as much as 25% or may 
be as low as nothing. 

A properly designed drier of the direct-heat type for either group ** A *' 
or *'B" will give an efficiency of from 75% to 85%; a bricked-in return- 
draught single-shell drier, from 60% to 70%; and a single-shell straight- 
draught dryer, from 45% to 55%. A properly designed indirect-heat 
drier for group "C" will give an efficiency of 50% to 60%, and a poorly 
designed one may not give more than 30%; The best designed steam 
drier for group '*D," in which the losses in the boiler producing the 
steam must be considered, will not often give an efficiency of more than 
42%; and, while a poorly designed one may have an equal efficiency. 
Its capacity may be not more than one-half of a good drier of equal size. 
The drier described for group "E" will not give an efficiency of more 
than 55%. 

Perfoemance of a Steam Drier. 

Material: Starch feed. Moisture, initial 39.8%, final 0.22%. 
Dried material per hour, 831 lbs. Water evaporated per hour, 548 lbs. 
Steam consumed per hour, 793 lbs. Water evaporated per pound 
steam, 0.691 lb. Temperature of material, moist, 58°, dry, 212°. 
Steam pressure, 98 lbs. gauge. 

Total heat to evaporate 548 lbs. water at 58° Into steam, 
548 X (154.2 + 969.7) = 615,897 B.T.U. 

Heat supplied by 793 lbs. steam condensed to water at 212^ 
793 X (1188.2 - 180.3) = 799,265 B.T.U. 

Heat used to evaporate water, 

(615,897 -- 799,265) = 77.1%. 

Heat used to raise temperature of material, 

(831 X 154 X 0.492) = 62,963 = 7.9%. 

Loss by radiation . . 100 - (77.1 + 7.9) = 15%. 

Total efficiency , . 85.0%. 



576 



HEAT. 



Performance of Different Types of Driers. 

(W. B. Ruggles.) 



Type of drier 



Material ..< ..«<«««««••< • 

Moisture, initial , per cent 

Moisture, final, per cent 

Calorific value of fuel, B.T.U 

Fuel consumed per hour, lbs 

Water evaporated per hour, lbs.. 
Water evap. per pound fuel, lbs.. 

Material dried per hour, lbs 

Fuel per ton dried material, lbs. . . 
Heat lost in exhaust air, per cent 
Heat lost by radiation, etc., per 

cent 

Heat used to evaporate water, 

per cent 

Heat used to raise temperature of 

material, per cent 

Total eflaciency, per cent 



Is 



Sand. 

4.58 



12100 

398 

2196 

5.3 
36460 
21.8 
11.3 

7.6 

52.3 

28.6 
81.1 



C3t>. 



Coal. 

10.2 

12290 
213.6 
924.2 
4.3 
8300 
51.3 
42.8 

7.7 

39.4 

10.1 

49.5 



•^^-^ 

Cement 
slurry. 
61.2 
40.7 
13200 
667 
4057 

6.1 
7680 
17.3 
38.4 

12.3 

52.0 

7.1 

59,1 






Lime- 
stone. 
3.6 
0.5 
13180 
460 
1325 
2.3 
41400 
22.2 
38.2 

15.6 

24.4 

21.8 
46.2 



c3 c3 a> 
•*^ n (-1 

Nitrate 
of soda. 
7.2 
0.3 
13600 
87 
349 

4.0 
4581 
38.0 
40.7 

13.8 

33.1 

12.4 
45.5 



Water Evaporated and Heat Required for Drying. 
M = percentage of moisture in material to be dried. 
Q = lbs. water evaporated per ton (2000 lbs.) of dry material. 
H = British thermal units required for drying, per ton of dry material. 



M 


Q 


H 


M 


. Q 


H 


M 


Q 


H 


1 


20.2 


85.624 


14 


325.6 


424.884 


35 


1,077 


1,269,240 


2 


40.8 


108.696 


15 


352.9 


458.248 


40 


1.333 


1,555.960 


3 


61.9 


130.424 


16 


381.0 


489.720 


45 


1,636 


1.895,320 


4 


83.3 


156.296 


17 


409.6 


521.752 


50 


2,000 


2.303.000 


5 


105.3 


180.936 


18 


439.0 


554,680 


55 


2,444 


2.800.280 


6 


127.7 


206.024 


19 


469.1 


588,392 


60 


3,000 


3.423.000 


7 


150.5 


231.560 


20 


500.0 


623.000 


65 


3,714 


4.222,680 


8 


173.9 


257.768 


21 


531.6 


658,392 


70 


4.667 


5,290.040 


9 


197.8 


284.536 


22 


564.1 


694.792 


75 


6.000 


6,783,000 


10 


222.2 


311,864 


23 


597.4 


732.088 


80 


8,000 


9,023,000 


11 


247.2 


339.864 


24 


631.6 


770.392 


85 


11.333 


12,755,960 


12 


272.7 


368.424 


25 


666.7 


809,704 


90 


18.000 


20,223.000 


13 


298.9 


397.768 


30 


857.0 


1,022,840 


95 


38.000 


42,623,000 



Formulee: Q = 



2000 M 



H = 1120 Q + 63,000. 



100- M' 

The value of H is found on the assumption that the moisture is heated 
from 62° to 212° and evaporated at that temperature, and that the 
specific heat of the material is 0.21. [2000 X (212 - 62) X 0.211 = 63,000. 

Calculations for Design of Drying Apparatus, — A most efficient 
system of drying of moist materials consists in a continuous circulation of a 
volume of warm dry air over or through the moist material, tthen passing 
the air charged with moisture over the cold surfaces of condenser coils to 
remove the moisture, then heating the same air by steam-heating coils 
or other means, and again passing it over the material. In the design of 
apparatus to work on this system it is necessary to know the a/nount 
of moisture to be removed in a given time, and to calculate the volume of 
air that will carry that moisture at the temperature at which it leaves the 
material, making allowance for the fact that the moist, warm air on leaving 



EVAPORATION AND DRYING. 



577 



the material may not be fully saturated, and for the fact that the cooled 
air is nearly or fully saturated at the temperature at which it leaves the 
cooling coils. A paper by Wm. M. Grosvenor, read before the Am. Inst. 
of Chemical Engineers {Heating and Ventilating Mag., May, 1909) con- 
tains a "humidity table" and a "humidity chart" which greatly facilitate 
the calculations required. The table is given in a condensed form below. 
It is based on the following data: Density of air + 0.04% COo = 

0.001293052 ,. ^^ s r^ -^ ^ . " 

1 + 0.00367 X Temp. C. ^^^ ^^' P^' ^"- '^'^' ^^^'^^^ ^^ ^'^^^^ ^^P^" 
= 0.62186 X density of air. Density at partial pressure -^ density at 760 
m.m. =partial pressure -^ 760 m.m. Specific heat of water vapor = 0.475; 
gp. ht. of air = 0.2373. Kg. per cu. meter X 0.062428 = lbs. per cu. ft. 
The results given in the table agree within 1/4% with the figures of the 
U. S. Weather Bureau. (Compare also the tables of H. M. Prevost 
Murphy, given under "Air," page 586.) The term "humid heat" in 
the heading of the table is defined as ihe, B.T.U. required to raise 
1° F. one pound of air plus the vapor it may carry when saturated at 
the given temperature and pressure; and '''humid volume" is the 
volume of one pound of air when saturated at the given temperature 
i,nd pressure. 

Humidity Table. 





Vapor 


Lbs. 






Density, lbs. 

per cu.ft. at 760 

Millimeters. 


Volume in cu. 


Temp. 


Tension, 

Milli- 
meters of 
Mercury. 


Water 

Vapor 

per lb. 

Air. 


Humid 

Heat, 

B.T.U. 


Humid 

Volume 

cu.ft. 


ft. per lb. of 


Dry 
Air. 


Sat'd 
Mix. 


Dry 

Air. 


Sat'd 
Mix. 


32 


4.569 


0.003761 


0.2391 


12.462 


0.080726 


0.080556 


12.388 


12.414 


35 


5.152 


.0042435 


.2393 


12.549 


.080231 


.080085 


12.464 


12.496 


40 


6.264 


.0050463 


.2398 


12.695 


.079420 


.079181 


12.590 


12.629 


45 


7.582 


.0062670 


.2403 


12.843 


.078641 


.078348 


12.718 


12.763 


50 


9.140 


.0075697 


.2409 


12.999 


.077867 


.077511 


12.842 


12.901 


55 


10.980 


.0091163 


.2416 


13.159 


.077109 


.076685 


12.968 


13.041 


60 


13.138 


.010939 


.2425 


13.326 


.076363 


.075865 


13.095 


13.180 


65 


15.660 


.013081 


.2435 


13.501 


.075635 


.075039 


13.222 


13.325 


70 


18.595 


.015597 


.2447 


13.683 


.074921 


.074219 


13.348 


13.471 


75 


22.008 


.018545 


.2461 


13.876 


.074218 


.073471 


13.474 


13.624 


80 


25.965 


.021998 


.2478 


14.081 


.073531 


.072644 


13.600 


13.777 


85 


30.573 


.026026 


.2497 


14.301 


.072852 


.071744 


13.726 


13.938 


90 


35.774 


.030718 


.2519 


14.539 


.072189 


.070894 


13.852 


14.106 


95 


41.784 


.036174 


.2545 


14.793 


.071535 


.070051 


13.979 


14.275 


100 


48.679 


.042116 


.2575 


15.071 


.070894 


.069179 


14.106 


14.455 


105 


56.534 


.049973 


.2610 


15.376 


.070264 


.068288 


14.232 


14.643 


110 


65.459 


.058613 


.2651 


15.711 


.069647 


.067383 


14.358 


14.840 


115 


75.591 


.068662 


.2699 


16.084 


.069040 


.066447 


14.484 


15.050 


120 


87.010 


.080402 


.2755 


16.499 


.068443 


.065477 


14.611 


15.272 


125 


99.024 


.094147 


.2820 


16.968 


.067857 


.064480 


14.736 


15.509 


130 


114.437 


.11022 


.2896 


17.499 


.067380 


.063449 


14.863 


15.761 


135 


130.702 


.12927 


.2987 


18.103 


.066713 


.062374 


14.989 


16.032 


140 


148.885 


.15150 


.3093 


18.800 


.066156 


.061255 


15.116 


16.325 


145 


169.227 


.17816 


.3219 


19.609 


.065601 


.060104 


15.242 


16.643 


150 


191.860 


.21005 


.3371 


20.559 


.065154 


.058865 


15.368 


16.993 


155 


216.983 


.24534 


.3553 


21.687 


.064539 


.057570 


15.494 


17.370 


160 


244.803 


.29553 


.3776 


23.045 


.064016 


.056218 


15.621 


17.788 


165 


275.592 


.35286 


.4054 


24.708 


.063502 


.054795 


15.748 


18.250 


170 


309.593 


.42756 


.4405 


26.790 


.062997 


.053305 


15.874 


18.761 


175 


347.015 


.52285 


.4856 


29.454 


.062500 


.051708 


16.000 


19.339 


180 


388.121 


.64942 


.5458 


32.967 


.062015 


.050035 


16.126 


19.987 


185 


433.194 


.82430 


.6288 


37.796 


.061529 


.048265 


16.253 


20.719 


190 


482.668 


1.00805 


.7519 


44.918 


.061053 


.046391 


16.379 


21.557 


195 


536.744 


1.4994 


.9494 


56.302 


.060588 


.044405 


16.505 


22.521 


200 


595.771 


2.2680 


1.3147 


77.304 


,060127 


.042308 


16.631 


23.638 


205 


660.116 


4.2272 


2.1562 


131.028 


.059674 


.040075 


16.758 


24.954 


210 


730.267 


15.8174 


15.9148 


562.054 


.059228 


.037323 


16.884 


26.796 



578 



HEAT. 



RADIATION OF HEATo 

Radiation of heat takes place between bodies at all distances apart, and 
follows the laws for the radiation of light. 

The heat rays proceed in straight lines, and the intensity of the rays 
radiated from any one source varies inversely as the square of their 
distance from the source. , , . , 

This statement has been erroneously interpreted by some writers, who 
have assumed from it that a boiler placed two feet above a fire would re- 
ceive by radiation only one-fourth as much heat as if it were only one foot 
above. In the case of boiler furnaces the side walls reflect those rays that 
are received at an angle, — following the law of optics, that the angle oi 
incidence is equal to the angle of reflection, — with the result that the 
intensity of heat two feet above the fire is practically the same as at one 
foot above, instead of only one-fourth as much. 

The rate at which a hotter body radiates heat, and a colder body 
absorbs heat, depends upon the state of the surfaces of the bodies aa 
well as on their temperatures. The rate of radiation and of absorption 
are increased by darkness and roughness of the surfaces of the bodies, 
and diminished by smoothness and polish. For this reason the covering 
01 steam pipes ana boilers snouid be smooth and of a light color: uncovered 
pipes and steam-cylinder covers should be polished. 

The quantity of heat radiated by a body is also a measure of its heat- 
absorbing power under the same circumstances. When a polished body 
is struck by a ray of heat, it absorbs part of the heat and reflects the rest. 
The reflecting power of a body is therefore the complement of its absorb- 
ing power, which latter is the same as its radiating bower. 

The relative radiating and reflecting power of different bodies has been 
determined by experiment, as shown in the table below, but as far as 
quantities of heat are concerned, says Prof. Trowbridge (Johnson's 
Cyclopaedia, art. Heat), it is doubtful whether anything further than the 
said relative determinations can, in the present state of our knowledge, 
be depended upon, the actual or absolute quantities for different tem- 
peratures being still uncertain. The authorities do not even agree on the 
relative radiating powers. Thus, Leslie gives for tin plate, gold, silver, 
and copper the figure 12, which differs considerably from the figures in 
the table below, given by Clark, stated to be on the authority of Leslie, 
De La Provostaye and Desains, and Melloni. 

Relative Radiating and Reflecting Power of DiflPerent Substances. 



u 









bD 




toa 


to 


111 


II 


^-Q O 




^<Pii 


1^ 


100 





100 





100 





98 


2 


93 to 98 


7 to 2 


90 


10 


85 


15 


72 


28 


27 


73 . 


25 


75 


23 


77 


23 


77 



Lampblack 

Water 

Carbonate of lead . . . 

Writing-paper 

Ivory, jet, marble... 

Ordinary glass 

Ice 

Gum lac 

Silver-leaf on glass . . 

Cast iron, bright pol- 
ished 

Mercury, about 

Wrought iron, pol- 
ished 



Zinc, polished 

Steel, polished 

Platinum, polished. 

Platinum in sheet . . 

Tin 

Brass, cast, dead 
polished 

Brass, bright pol- 
ished 

Copper, varnished . . 

Copper, hammered . 

Gold, plated 

Gold on polished 
steel 

Silver, polished 
bright 



19 


81 


17 


83 


24 


76 


17 


83 


15 


85 


11 


89 


7 


93 


14 


86 


7 


93 


5 


95 


3 


97 


3 


97 



Experiments of Dr. A.M. Mayer give the following: The relative radi- 
ations from Si, cube of cast iron, having faces rough, as from the foundry. 



CONDUCTION AND CONVECTION OF HEAT. 579 

planed, "drawfiled,'*and polished, and from the same surfaces oiled, are as 
below (Prof. Thurston, in Trans. A. S. M, E., vol. xvi): 





Rough. 


Planed. 


Drawfiled. 


Polished. 


Surface oiled 

Surface dry .....•.•...• 


100 

100 


60 
32 


49 
20 


45 

18 







It here appears that the oiling of smoothly polished castings, as of 
cylinder-heads of steam-engines, more than doubles the loss of heat by 
radiation, while it doer not seriously affect rough castings. 

" Black Body •• Radiation. Stefan and Boltzman's Law. {Eng*a^ 
March 1, 1907.) — Kirchhoff defined a black body as one that would absorb 
all radiations falling on it, and would neither reflect nor transmit any. 
The radiation from such a body is a function of the temperature alone, 
and is identical with the radiation inside an inclosure aU parts ot wmcn 
have the same temperature. By heating the wails of an inclosure as 
uniformly as possible, and observing the radiation through a very small 
opening, a practical reaUzation of a black body is obtained. Stefan and 
Boltzman's law is: The energy radiated by a black body is proportional 
to the fourth power of the absolute temperature, or ^' = A (2 * - 2'o*), 
where E = total energy radiated by the body at T to the body at Tq, and 
K is a constant. The total radiation from other than black bodies increases 
more rapidly than the fourth power of the absolute temperature, so that 
as the temperature is raised the radiation of all bodies approaches that of 
the black body. A confirmation of the Stefan and Boltzman law is given 
in the results of experim.ents bv Lummer and Kurlbaum, as below (To = 
290 degrees C, abs. in all cases). 

654. 795. 1108. 

108.4 109.9 109.0 
6.56 8.14 12.18 
33.1 36.6 46.9 



1761 



1481. 

110.7 

16.69 19.64 

65J 



r= 492. 

E (Blackbody 109.1 

7=7 — T=-r \ Polished platinum. . 4 .28 
^*-^o* (Iron oxide 33.1 

The Stefan-Boltzman law as applied to radiation from a given body 
may be written W = 5.7 e [(O.OOID^- (0.001 Te )Y\ W = energy in 
watts radiated per square centimeter of surface, T = temperature of 
the hot body, Tg — temperature of the surrounding space, e = relative 
emissivity, a characteristic of the radiating body, always less than 
unity. For clean poUshed metal surfaces e ranges from 0.02 to 0.20; 
for non-metallic surfaces, from about 0.3 to about 0.9. 



CONDUCTION AND CONVECTION OF HEAT. 

Conduction is the transfer of heat between two bodies or parts of a 
body which touch each other. Internal conduction takes place between 
the parts of one continuous body, and external conduction through the 
surface of contact of a pair of distinct bodies. 

The rate at which conduction, whether internal or external, goes on, 
being proportional to the area of the section or surface through which it 
takes place, may be expressed in thermal units per square foot of area per 
hour. 

Internal Conduction varies with the heat conditctivity, which depends 
upon the nature of the substance, and is directly proportional to the 
difference between the temperatures of the two faces of a layer, and in- 
versely as its thickness. The reciprocal of the conductivity is called the 
internal thermal resistance of the substance. If r represents this resist- 
ance, X the thickness of the layer in inches, T' and T the temperatures 
on the two faces, and q the quantitv in thermal units transmitted per 

7" — T* 
hour per square foot of area, q = •• (Rankine.) 



P^clet gives the following values of r: 



rx 



Gold, platinum, silver 0.0016 

Copper 0.0018 

Iron 0.0043 

Zinc 0.0045 



Lead 0.0090 

Marble 0.0716 

Brick 0.1500 



580 



HEAT. 



Relative Heat-conducting Power of Metals. 



*C.&J. tW.&F. 
1000 1000 



Metals. 

Silver 

Gold 981 

Gold,withl% of silver. 840 

Copper, rolled 845 

Copper, cast 811 

Mercury 677 

Mercury, with 1.25% of 

tin 412 

Aluminum 665 

Zinc: 

cast vertically 628 

cast horizontally. . . 608 

rolled 641 

* Calvert & Johnson, 



532 
736 



Metals. *C.&J. fW.&P. 

Cadmium 577 

Wrought iron 436 

Tin 422 

Steel 397 

Platinum 380 

Sodium 365 

Cast iron 359 

Lead 287 

Antimony: 

cast horizontally. . 215 

cast vertically. . . . 192 

Bismuth 61 



119 
145 
116 

84 



85 



18 



t Weidemann & Franz. 



Influence of a Non-metallic Substance in Combination on the 
Conducting Power of a Metal. 



Influence of carbon on iron: 

Wrought iron 436 

Steel 397 

Cast iron 359 



Cast copper 811 

Copper with 1 % of arsenic. . . . 570 

with 0.5% of arsenic. . 669 

** with 0.25% of arsenic, 771 



The Rate of External Conduction through the bounding surface 
between a solid body and a fluid is approximately proportional to the 
difference of temperature, when that is small; but when that difference is 
considerable, the rate of conduction increases faster than the simple ratio ol 
that difference. (Rankine.) 

If r, as before, is the coefficient of internal thermal resistance, e and e' 
the coefficient of external resistance of the two surfaces, x the thickness of 
the plate, and T' and T the temperatures of the two fluids in contact 

T' — T 
with the two surfaces, the rate of conduction is q = — ; — , . • Accord- 



ingtoP6clet.e+e'=3^3^j:^g-^ 
B have the following values: 



T)] 



€+ e^ + rx 
in which the constants A and 



B for polished metaUic surfaces . 0028 

B for rough metallic surfaces and for non-metallic surfaces . . 0. 0037 

A for polished metals, about 0.90 

A for glassy and varnished surfaces 1 . 34 

A for dull metallic surfaces 1 . 58 

A for lampblack 1 . 78 

When a metal plate has a liquid at each side of it, it appears from experi- 
ments by P6clet that B = 0.058, A = 8.8. 

The results of experiments on the evaporative power of boilers agree 
very well with the following approximate formula for the thermal resist- 
ance of boiler plates and tubes: 



e-\- e' = ■ 



{T - T) 
which gives for the rate of conduction, per square foot of surface per hour, 

^ a 

This formula is proposed by Rankine as a rough approximation, near 
enough to the truth for its purpose. The value of a lies between 160 and 
200. Experiments on modern boilers usually give higher values. 

Convection, or carrying of heat, means the transfer and diffusion of the 
heat in a fluid mass by means of the motion of the particles of that mass. 

The conduction, properly so called, of heat through a stagnant mass of 
fluid is very slow in hquids, and almost, if not wholly, inappreciable in 
gases. It is only by the continual circulation and mixture of the particles 
of the fluid that uniformity of temperature can be maintained in the fluid 
mass, or heat transferred between the fluid mass and a solid body. 

The free circulation of each of the fluids which touch the side of a solid 
plate is a necessary condition of the correctness of Rankine's formulae for 
the conduction of heat through that plate; and in these formulae it is 



CONDUCTION AND CONVECTION OF HEAT. 581 



fmplied that the circulation of each of the fluids by currents and eddies is 
such as to prevent any considerable difference of temperature between the 
fluid particles in contact with one side of the solid plate and those at con- 
siderable distances from it. 

When heat is to be transferred by convection from one fluid to another, 
through an intervening layer of metal, the motions of the two fluid masses 
should, if possible, be in opposite directions, in order that the hottest par- 
ticles of each fluid may be in communication with the hottest particles of 
the other, and that the minimum difference of temperature between the 
adjacent particles of the two fluids may be the greatest possible. 

Thus, in the surface condensation of steam, by passing it through metal 
tubes immersed in a current of cold water or air, the cooling fluid should 
be made to move in the opposite direction to the condensing steam. 

Coefficients of Heat Conduction of Different Materials. (W. 
Nusselt, Zeit des Ver. Deut. Ing., June, 1908. Eng. Digest, Aug., 1908.) — 
The materials were inclosed between two concentric metal vessels, the 
fnner of which contained an electric heating device. 

It was found that the materials tested all followed Fourier's law, the 
quantity of heat transmitted being directly proportional to the extent of 
surface, the duration of flow and the temperature difference between the 
inner and outer surfaces: and inversely proportional to the thickness of 
the mass of material. It was also found that the coefficient of conduction 
increased as the temperature increased. The table gives the British 
equivalents of the average coeflQcients obtained. 

Coefficients of Heat Conduction at Different Temperatures 

FOR Various Insulating Materials. 
(B.T.U. per hour = Area of surface in square feet X coefiQcient 4- thick- 
ness in inches.) 



Lb. per 
cu. ft. 


M aterials. 


32« 
F. 


212° 
F. 


392° 
F. 


572° 
F. 


752° 
F. 


to 


Ci round cork . . 


0.250 
0.266 
0.306 
0.314 
0.379 

0.403 


0.387 
0.403 
0.411 
0.419 
0.476 

0.508 


0.443 






8 5 


Sheep's wool'*' 






6 3 


Silk waste 








9 18 


Silk tufted . 








5 06 


Cotton wool .... 








11.86 


Charcoal (carbonized cabbage 
leaves) 








13 42 


Sawdust CO 443 at 1 12° F ) 








10 


Peat refuset CO 443 at 77° F.) . 












2^85 


Kieselguhr (infusorial earth), 
loose 


3.419 


0.532 


).596 


0.629 




12.49 


Asphalt-cork composition (0.492 
at65°F.). 




25 28 


CoTTiDOsition 1 loose 


0.484 
0.516 


0.613 
0.629 


0.653 
0.742 






12.49 


Kieselguhr stone § 


J. 854 


0.961 


12 17 


Peat refuset (0.564 at 68° F.) 




36.2 


Kieselguhr, dry and compacted 
(0.669 at 302° F.- 0.991 at 662° F.) . 












43.07 


Composition, §§ compacted (0.806 
at 302° F • 967 at 428° F.) . 













22.47 


Porous blast-furnace slag (0.766 
at 112° F ) 












35.96 
34 33 


Asbestos (1.644 at 1112° F.) 

Slac- conrretell (] 532 at 112° F > 


1.048 


1.346 


1.451 


1.499 


1.548 


18.23 


Pumice stone gravel (1.612 at 
112° F.). 












128.5 


Portland cement, neat (6.287 at 
95° F.) 













* Tufted, oily, and containing foreign matter. Used in Linde's 
apparatus, t Hygroscopic; measurements made in moist zones. % Cork, 
asbestos, kieselguhr and chopped straw, mixed with a binder and made 
in sheets for application to steam pipes in successive layers, the whole 
being wrapped in canvas and painted. § Kieselguhr, mixed with a binder 
and burned; very porous and hygroscopic. §§ Ingredients of (t) mixed 
with water and compacted. |l 1 part cement, 9 parts porous blast-furnace 
slag, by volume. 



682 HEAT. 

Heat Resistance* the Reciprocal of Heat Conductivity. (W. 

Kent, Trans. A. S. M. E., xxi^, 278.) — The resistance to the passage of 
heat through a plate consists of three separate resistances; viz., the 
resistances of the two surfaces and the resistance of the body of the plate, 
wliich latter is proportional to the thickness of the plate. It is probable 
also that the resistance of the surface differs with the nature of the body 
or medium with which it is in contact. 

A complete set of experiments on the heat-resisting power of heat- 
insulating substances should include an investigation into the difference 
in surface resistance when a surface is in contact with air and when it is 
in contact with another solid body. Suppose we find that the total resist- 
ance of a certain non-conductor may be represented by the figure 10, and 
that similar pieces all give the same figure. Two pieces in contact give 16. 
One piece of half the thickness of the others gives 8. What is the resist- 
ance of the surface exposed to the air in either piece, of the surface in 
contact with another surface, and of the interior of the body itself? Let 
the resistance of the material itself, of the regular thickness, be rep- 
resented by A^ that of the surface exposed to the air by a, and that of the 
surface in contact with another surface by c. 

We then have for the three cases, 

Resistance of one piece A + 2a =» 10 

** of two pieces in contact .... 2A+2c+2a = 16 
of the thin piece 1/2 A + 2 a = 8 

These three equations contain three unknown quantities. Solving the 
equations w^e find A = 4, a = 3, and c = 1. Suppose that another 
experiment be made with the two pieces separated by an air space, and 
that the total resistance is then 22. If the resistance of the air space be 
represented by s we have the two equations: Resistance of one piece, 
A + 2a = 10;resistanceof two pieces and air space, 2 A 4- 4 a + 5 = 22, 
from which we find s = 2. Having these results we can easily estimate 
what will be the resistance to heat transfer of any number of layers of the 
material, w^hether in contact or separated by air spaces. 

The writer has computed the figures for heat resistance of several 
insulating substances from the figures of conducting power given in a table 
published by John E. Starr, in Ice and Refrigeration, Nov., 1901. Mr. 
Starr's figures are given in terms of the B.T.U. transmitted per sq. ft. of 
surface per day per degree of difference of temperatures of the air adjacent 
to each surface. The writer's figures, those in the last column of the table 
given on p. 583, are calculated by dividing Mr. Starr's figures by 24, to 
obtain the hourly rate, and then taking their reciprocals. They may be 
called "coefficients of heat resistance" and defined as the reciprocals of 
the B.T.U. per sq. ft. per hour per degree of difference of temperature. 

Analyzing some of the results given in the last column of the table, we 
observe that, comparing Nos. 2 and 3, 1 in. added thickness of pitch 
increased the coefficient 0.74; comparing Nos. 4 and 5, lV2in. of mineral 
wool increased the coefficient 1.11. If we assume that the 1 in. of mineral 
wool in No. 4 was equal in heat resistance to the additional IV2 in. added 
in No. 5, or 1.11 reciprocal units, and subtract this from 5.22, we get 4.11 
as the resistance of two 7/8-in. boards and two sheets of paper. This 
would indicate that one //s-in. board and one sheet of paper give nearly 
twice as much resistance as 1 in. of mineral wool. In like manner any 
number of deductions may be drawn from the table, and some of them 
will be rather questionable, such as the comparison of No. 15 and No. 16, 
showing that 1 in. additional sheet cork increased the resistance given by 
four sheets 6.67 reciprocal units, or one-third the total resistance of No. 15. 
This result is extraordinary, and indicates that there must have been 
considerable differences of conditions during the two tests. 

For comparison with the coefficients of heat resistance computed from 
Mr. Starr's results we may take the reciprocals of the figures given by 
Mr. Alfred R. Wolff as the result of German experiments on the heat 
transmitted through various building materials, as below: 

K= B.T.U. transmitted per hour per sq. ft. of surface, per degree 
F. differenco of temperature. 

C = co(^fTicient of heat resistance = reciprocal of K. 

The irregularity of the differences of C computed from the original 
values of K for each increase of 4 inches in thickness of the brick walls 
indicates a difference in the conditions of the experiments. The average 



CONDUCTION AND CONVECTION OF HEAT. 



583 



Heat Conducting and Resisting Values of Different Materiai^. 



Insulating Material. 



Conductance, 
B.T.U. per 
Sq. Ft. per 
Day per Deg., 
Difference of 
Temperature. 



Coefficient 

of Heat 

Resistance. 

C. 



2. 
3. 
4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

13. 
11. 
15. 

16. 
17. 
18. 
19. 

20. 

21. 



5/8-in. oak board, 1 in. lampblack, V/g-m. pme 

board (ordinary family refrigerator).. . 

7/8-in. board, 1 in. pitch, 7/8-in. board 

7/8-in. board, 2 in. pitch, 7/8-in. board 

7/8-in. board, paper, 1 in. mineral wool, paper, 

7/8-in. board 

7/8-in. board, paper, 21/2 in. mineral wool, 

paper, 7/8-in. board 

7/8-in. board, paper, 21/2 in. calcined pumice, 

7/8-in. board , 

Same as above, when wet 

7/8-in. board, paper, 3 in. sheet cork, 7/8-in. 

board 

Two 7/8-in. boards, paper, solid, no air space, 

paper, two 7/o-in. boards 

Two 7/8-in. boards, paper, 1 in. air space, 

paper, two 7/8-in. boards 

Two 7/8-in. boards, paper, 1 in. hair felt, 

paper, two 7/8-in. boards 

Two 7/8-in. boards, paper, 8 in. mill shav- 
ings, paper, two 7/8-in. boards 

The same, slightly moist 

The same, damp 

Two 7/8-in. boards, paper, 3 in. air, 4 in. 

sheet cork, paper, two 7/8-in. boards 

Same, with 5 in. sheet cork 

Same, with 4 in. granulated cork 

Same, with 1 in. sheet cork 

Four double 7/8-in. boards (8 boards), with 

paper between, three 8-in. air spaces ..... 
Four 7/8-in. boards, with three quilts of V4-in 

hair between, papers separating boards . . .1 

- ■- board, 6 in. patented silicated strawH 
■ " t...l 



5.7 

4.89 
4.25 

4.6 

3.62 

3.38 
3.90 

2.10 

4.28 

3.71 

3.32 

1.35 

1.80 
2.10 

1.20 
0.90 
1.70 
3.30 



4.21 

4.91 
5.65 

5.22 

6.63 

7.10 
6.15 

11.43 

5.61 
6.47 

7.23 

17.78 
13.33 
11.43 

20.00 

26.67 

14.12 

7.27 



7/8-in, 
board 



finished inside with thin cement 



2.70 


8.89 


2.52 


9.52 


2.48 


9.68 



difference of C for each 4 inches of thickness is about 0.80. Using this 
average difference to even up the figures we find the value of C is ex- 
pressed by the approximate formula C = 0.70 + 0.20 t, in which t is the 
thickness in inches. The revised values of C, computed by this formula, 
and the corresponding revised values of K, are as follows: 



Thick., In. 


4 


8 


12 


16 


20 


24 


28 


32 


36 


40 


C 


1.50 
0.667 
0.68 
0.013 


2.30 
0.435 
0.46 
0.025 


3.10 
0.323 
0.32 
0.003 


3.90 
0.256 
0.26 
0.004 


4.70 
0.213 
0.23 
0.017 


5.50 
0.182 
0.20 
0.018 


6.30 
0.159 
0.174 
0.015 


7.10 
0.141 
0.15 
0.009 


7.90 
0.127 
0.129 
0.002 


8.70 


K, revised. . 
K, original . 
Difference. . 


0.115 
0.115 
0.0 



The following additional values of C are computed from Mr. Wolff's 
figures for K: 

Wooden beams planked over or ceiled : K C 

As flooring 0.083 12.05 

As ceiUng 0.104 9.71 

Fireproof construction, floored over: 

As flooring 0.124 8.06 

As ceiling . 145 6 . 90 

Single window 1 . 030 . 97 

Single skylight 1.118 . 89 

Double window 0.518 1.93 

Double skylight 0.621 1.61 

Door..., , 0.414 2.42 



I 



584 



HEAT. 



It should be noted that the coefficient of resistance thus defined will be 
approximately a constant quantity for a given substance under certain 
fixed conditions, only when the difference of temperature of the air on its 
two sides is small — say less than 100° F. When the range of tem- 
perature is great, experiments on heat transmission indicate that the 
quantity of heat transmitted varies, not directly as the difference of tem- 
perature, but as the square of that difference. In this case a coefficient 
of resistance with a different definition may be found — viz., that ob- 
tained from the formula a = (T — t)"^ ^ q, in which a is the coefficient, 
T — t the range of temperature, and q the quantity of heat transmitted, 
in British thermal miits per square foot per hour. 

Steam-pipe Coverings. 

Experiments by Prof. Ordway, Trans. A. S. M. E., vi, 168; also Circular 
No. 27 of Boston Mfrs. Mutual Fire Ins. Co., 1890. 



Substance 1 In. Thick. 
Applied, 310° F. 



Heat 



Pounds of 
Water 
Heated 

10° F., per 

Hour, 
Through 
I Sq. Ft. 



British 

Thermal 

Units per 

Sq. Ft. per 

Minute. 



Solid Mat- 
ter in I Sq. 
Ft., 1 In. 
Thick, 
Parts in 
1000. 






1 . Loose wool 

2. Live-geese feathers , 

3. Carded cotton wool 

4. Hair felt 

5. Loose lampblack , 

6. Compressed lampblack , 

7. Cork charcoal 

8. White-pine charcoal 

9. Anthracite-coal powder 

10. Loose calcined niagnesia 

1 1. Compressed calcined magnesia. . 

12. Light carbonate of magnesia. . . . 

13. Compressed carb. of magnesia.. . 

14. Loose fossil-meal '. . 

15. Crowded fossil-meal 

16. Ground chalk (Paris white). . . „ . 

1 7. Dry plaster of Paris 

18. Fine asbestos 

1 9. Air alone 

20. Sand 

2 1 . Best slag-wool 

22. Paper 

23. Blotting-paper wound tight 

24. Asbestos paper wound tight 

25. Cork strips bound on 

26. Straw rope wound spirally 

27. Loose rice chaff 

28. Paste of fossil-meal with hair . . . 

29. Paste of fossil-meal with asbestos 

30. Loose bituminous-coal ashes. . . . 

31. Loose anthracite-coal ashes 

32. Paste of clay and vegetable fiber 



8.1 
9.6 
10.4 
10.3 
9.8 
10.6 
11.9 
13.9 
35.7 
12.4 
42.6 
13.7 
15.4 
14.5 
15.7 
20.6 
30.9 
49.0 
48.0 
62.1 
13. 
14. 
21. 
21.7 
14.6 
18. 
18.7 
16.7 
22. 
21. 
27. 
30.9 



1.35 
1.60 
1.73 
1.72 
1.63 
1.77 
1.98 
2.32 
5.95 
2.07 
7.10 
2.28 
2.57 
2.42 
2.62 
3.43 
5.15 
8.17 
8.00 
10.35 
2.17 
2.33 



3.50 
4.50 
5.15 



56 
50 
20 

185 
56 

244 
53 

119 

506 
23 

285 

150 

60 

112 

253 

368 

81 



529 



944 
950 
980 
815 
944 
756 
947 
881 
494 
977 
715 
940 
850 
940 
888 
747 
632 
919 
1000 
471 



It will be observed that several of the incombustible materials are 
nearly as efficient as wool, cotton, and feathers, with which they may be 
compared in the preceding table. The materials which may be con- 
sidered wholly free from the danger of being carbonized or ignited by 
slow contact with pipes or boilers are printed in Roman type. Those 
which are more or less liable to be carbonized are printed in italics. 

The results Nos. 1 to 20 inclusive were from experiments with the 
various non-conductors each used in a mass one inch thick, placed on a 
flat surface of iron kept heated by steam to 310° F. The substances 



CONDUCTION AND CONVECTION OF HEAT. 



585 



Nos. 21 to 32 were tried as coverings for two-inch steam-pipe; the 
results being reduced to the same terms as the others for convenience 
of comparison. 

Experiments on still air gave results which differ little from those of 
Nos. 3, 4, and 6. The bulk of matter in the best non-conductors is 
relatively too small to have any specific effect except to trap the air and 
keep it stagnant. These substances keep the air still by virtue of the 
roughness of their fibers or particles. The asbestos, No. 18, had smooth 
fibers. Asbestos with exceedingly fine fiber made a somewhat better 
showing, but asbestos is really one of the poorest non-conductors. It 
may be used advantageously to hold together other incombustible sub- 
stances, but the less of it the better. A "magnesia" covering, made of 
carbonate of magnesia with a small percentage of good asbestos fiber 
and containing 0.25 of sohd matter, transmitted 2.5 B.T.U, per square 
foot per minute, and one containing 0.396 of solid matter transmitted 
3.33 B.T.U. 

Any suitable substance which is used to prevent the escape of steam 
heat should not be less than one inch thick. 

Any covering should be kept perfectly dry, for not only is water a good 
carrier of heat, but it has been found that still water conducts heat about 
eight times as rapidly as still air. 

Tests of Commercial Coverings were made by Mr. Geo. M. Brill 
and reported in Trans, A. S. M. E., xvi, 827. A length of 60 feet of 8-inch 
steam-pipe was used in the tests, and the heat loss was determined by the 
condensation. The steam pressure was from 109 to 117 lbs. gauge, and 
the temperature of the air from 58° to 81° F. The difference between the 
temperature of steam and air ranged from 263° to 286°, averaging 
272°. 

The following are the principal results: 



Kind of Covering. 



a 



03 



8 <x» 






o <u 

CO 



too 

c a 

> o 

~ (U 



"'d 


I2 

4) 


^ > 





■S" 


<0 


w 







" ^ 


« oT 


'^'^a 


|«p^ 



^ TO 



Bare pipe 

Magnesia 

Rock wool 

Mineral wool 

Fire-felt .- 

Manville sectional 

Manv. sect and hair-felt 
Manville wool-cement . . . 
Champion mineral wool . 

Hair-felt 

Riley cement 

Fossil-meal 



1.25 
1.60 
1.30 
1.30 
1.70 
2.40 
2.20 
1.44 
0.82 
0.75 
0.75 



0.846 
0.120 
0.080 
0.089 
0.157 
0.109 
0.066 
0.108 
0.099 
0.132 
0.298 
0.275 



12.27 
1.74 
1.16 
1.29 
2.28 
1.59 
0.96 
1.56 
1.44 
1.91 
4.32 
3.99 



2.706 
0.384 
0.256 
0.285 
0.502 
0.350 
0.212 
0.345 
0.317 
0.422 
0.953 
0.879 



0.726 
0.766 
0.757 
0.689 
0.737 
0.780 
0.738 
0.747 
0.714 
0.548 
0.571 



100. 


14.2 


9.5 


10.5 


18.6 


12.9 


7.8 


12.7 


11.7 


15.6 


35.2 


32.5 



2.819 
0.400 
0.267 
0.297 
0.523 
0.364 
0.221 
0.359 
0.330 
0.439 
0.993 
0.919 



Tests of Pipe Coverings by an Electrical Method. (H. G. Stott, 
Power, 1902.) — A length of about 200 ft. of 2-in. pipe was heated to a 
known temperature by an electrical current. The pipe was covered with 
different materials, and the heat radiated by each covering was deter- 
mined by measuring the current required to keep the pipe at a constant 
temperature. A brief description of the various coverings is given below. 

No. 2. Solid sectional covering, I1/3 in. thick, of granulated cork 
molded under pressure and then baked at a temperature of 500° F,; 
Vs in. asbestos paper next to pipe. 

No. 3. Solid l-in. molded sectional, 85% carbonate of magnesia. 



586 SEAT. 

No. 4. Solid 1-in. sectional, granulated cork molded under pressure 
and baked at 500° F.; Vs in. asbestos next to pipe. 

No. 5. Solid 1-in. molded sectional, 85% carbonate of magnesia; out- 
side of sections covered with canvas pasted on. 

No. 6. Laminated 1-in. sectional, nine layers of asbestos paper with 
granulated cork between; outside of sections covered with canvas, i/s in. 
asbestos paper next to pipe. 

No. 7. Solid 1-in. molded sectional, of 85% carbonate of magnesia; 
outside of sections covered with light canvas. 

No. 8. Laminated 1-in. sectional, seven layers of asbestos paper 
indented with i/4-in. square indentations, which serve to keep the asbestos 
layers from coming in close contact with one another; Vs in. asbestos 
paper next to pipe. 

No. 9. Laminated 1-in. sectional, 64 layers of asbestos paper, in which 
were embedded small pieces of sponge; outside covered with canvas. 

No. 10. Laminated 1 1/2-in. sectional, 12 plain layers of asbestos paper 
with corrugated layers between, forming longitudinal air cells; 1/8 in. 
asbestos paper next to pipe; sections wired on. 

No. 11. Laminated 1-in. sectional, 8 layers of asbestos paper with 
corrugated layers betw^een, forming small air ducts radially around the 
covering. 

No. 12. Laminated lV4-in. sectional, 6 layers of asbestos paper 
with corrugated layers; outside of sections covered with two layers of 
canvas. 

No. 15. "Remanit," composed of 2 layers wound in reverse direction 
with ropes of carbonized silk. Inner layer 21/2 in. wide and 1/2 in. thick; 
outer layer 2 in. wide and 3/4 in. thick, over w^hich was wound a network 
of fine wire; Vsin. asbestos next to pipe. Made in Germany. 

No. 16. 2V2-in. covering, 85% carbonate of magnesia, 1/2-in. blocks 
about 3 in. wide and 18 in. long next to pipe and wired on; over these 
blocks were placed solid 2-in. molded sectional covering. 

No. 17. 2V2-in. covering, 85% magnesia. Put on in a 2-in. molded 
section wired on; next to the pipe and over this a 1/2-in. layer of magnesia 
plaster. 

No. 18. 2 1/2-in. covering, 85% carbonate of magnesia. Put on in two 
solid 1-in. molded sections with 1/2-in. layer of magnesia plaster between; 
two 1-in. coverings wired on and placed so as to break joints. 

No. 19. 2-in. covering, of 85% carbonate of magnesia, put on in two 
1-in. layers so as to break joints. 

No. 20. Solid 2-in. molded sectional, 85% magnesia. 

No. 21. Solid 2-in. molded sectional, 85% magnesia. 

Two samples covered with the same thickness of similar material give 
different results; for example, Nos. 3 and 5, and also Nos. 20 and 21. 
The cause of this difference was found to be in the care with which the 
joints between sections were made. A comparison between Nos. 19 and 
20, having the same total thickness, but one applied in a solid 2-in. section, 
and the other in two 1-in. sections, proved the desirability of breaking 
joints. 

An attempt was made to determine the law governing the effect of 
increasing the thickness of the insulating material, and for all the 85% 
magnesia coverings the efficiency varied directly as the square root of the 
thickness, but the other materials tested did not follow this simple law 
closely, each one involving a different constant. 

To determine which covering is the most economical the following 
quantities must be considered: (1) Investment in covering. (2) Cost 
of coal required to supply lost heat. (3) Five per cent interest on 
capital invested in boilers and stokers rendered idle through having to 
supply lost heat. (4) Guaranteed life of covering. (5) Thickness of 
covenng. 

The coverings Nos. 2 to 15 were finished on the outside with resin paper 
and 8-ounce canvas; the others had canvas pasted on outside of the sec- 
tions, and an 8-oz. canvas finish. The following is a condensed statement 
of the results with the temperature of the pipe corresponding to 160 lb. 
fiteam pressure. 



CONDUCTION AND CONVECTION OF HEAT. 



587 



Electrical Test op Steam-Pipe Coverings. 



No. 



CJovering. 



Solid cork 

85 % magnesia 

Solid cork 

85% magnesia 

Laminated asbestos cork 

85% magnesia 

Asbestos air cell [indent] 

Asbestos sponge felted 

Asbestos air cell [long] 

" Asbestoscel " [radial] 

Asbestos air cell [long] 

" Remanit" [silk] wrapped 

85 % magnesia, 1" sectional and 1/2' 

block 

85 % magnesia, 1" sectional and 1/2' 

plaster 

85% magnesia, two T' sectional 

85% magnesia, two \" sectional 

85% magnesia, 2" sectional 

85% magnesia, 1" sectional 

Bare pipe [from outside tests] 



Aver. 
Thick- 
ness. 



1.68 
1.18 
1.20 
1.19 
1.48 
1.12 
1.26 
1.24 
1.70 
1.22 
1.29 
1.51 

2.71 

2.45 
2.50 
2.24 
2.34 
2.20 



B.T.U. 
Loss 

per 
Min. 

persq. 
ft. at 

1601b. 
Pres. 



1.672 
2.008 
2.048 
2.130 
2.123 
2.190 
2.333 
2.552 
2.750 
2.801 
2.812 
1.452 

1.381 

1.387 
1.412 
1.465 
1.555 
1.568 
13. 



B.T.U. 
persq. 

ft. per 
Hr. per 

Deg. 
Diff. of 
Temp. 



0.348 
0.418 
0.427 
0.444 
0.442 
0.456 
0.486 
0.532 
0.573 
0.584 
0.580 
0.302 

0.288 

0.289 
0.294 
0.305 
0.324 
0.314 
2.708 



Per 

cent 
Heat 

Saved 
by 

Cover- 
ing. 



87.1 
84.5 
84.2 
83.6 
83.7 
83.2 
83.1 
80.3 
78.8 
78.5 
78.4 
88.8 

89.4 

88.7 
89.0 
88.7 
88.0 
87.9 



Transmission of Heat, through Solid Plates, from Water to Water. 

(Clark, S. E.) — M. Peclet found, from experiments made with plates of 
wrought iron, cast iron, copper, lead, zinc, and tin, that when the fluid 
in contact with the surface of the plate was not circulated by artificial 
means, the rate of conduction was the same for different metals and for 
plates of the same metal of different thicknesses. But when the w^ater 
was thoroughly circulated over the surfaces, and when these were perfectly 
clean, the quantity of transmitted heat was inversely proportional to the 
thickness, and directly as the difference in temperature of the two faces 
of the plate. When the metal surface became dull, the rate of trans- 
mission of heat through all the metals was very nearly the same. 

It follows, says Clark, that the absorption of heat through metal plates 
is more active whilst evaporation is in progress — when the circulation of 
the water is more active — than while the water is being heated up to the 
boiling-point. 

Transmission from Steam to Water. — M. Peclet's principle is 
supported by the results of experiments made in 1867 by Mr. Isherwood on 
the conductivity^ of different metals. Cylindrical pots, 10 inches in 
diameter, 211/4 inches deep inside, and Vs inch, 1/4 inch, and 3/3 inch 
thick, turned and bored, were formed of pure copper, brass (60 copper 
and 40 zinc), rolled wrought iron, and remelted cast iron. They were 
immersed in a steam bath, which was varied from 220° to 320° F. Water 
at 212° was supplied to the pots, which were kept filled. It was ascer- 
tained that the rate of evaporation was in the direct ratio of the difference 
of the temperatures inside and outside of the pots; that is, that the rate 
of evaporation per degree of difference of temperatures was the same for 
all temperatures; and that the rate of evaporation was exactly the same 
for different thicknesses of the metal. The respective rates of conductiv- 
ity of the several metals were as follows, expressed in weight of water 
evaporated from and at 212° F. per square foot of the interior surface of 
the pots per degree of difference of temperature per hour, together with 
the equivalent quantities of heat-units: 



588 



HEAT. 



Water at 212°. 

Copper o . 665 lb. 

Brass 577 " 

Wrought iron 387 ** 

Cast iron 327 " 



Heat-units. 


Ratio, 


642.5 


1.00 


556.8 


0.87 


373.6 


.58 


315.7 


.49 



Whitham, "Steam Engine Design," p. 283, also Trans. A. S. M. E., ix, 
425, in using these data in deriving a formula for surface condensers, calls 
these figures those of perfect conductivity, and multiplies them by a 
coefficient C, which he takes at 0.323, to obtain the efficiency of con- 
denser surface in ordinary use, i.e., coated with saline and greasy deposits. 

Transmission of Heat from Steam to Water through Coils of Iron 
Pipe. — H. G. C. Kopp and F. J. Meystre (Stevens Indicator, Jan., 1894) 
give an account of some experiments on transmission of heat through 
coils of pipe. They collate the results of earlier experiments as follows, 
for comparison: 







Steam con- 


Heat trans- 








densed per 


mitted per 






6 


square foot 


square foot 








per degree 


per degree 






1 


difference of 


difference of 




, 


rS 


temperature 


temperature 




0) 




per hour. 


per hour. 


Remarks. 


g 


b£ » 


► M 


hC . 








c3 








0^ 






6 


£^ 


^^- 


W« 


H^« 




Laurens . 


Copper coils . . 
2 Copper coils 


0.292 


0.981 
1.20 


315 


974 
1120 




Havrez . . 


Copper coil . . . 


0.268 


1.'26 


280 


1200 




Perkins. . 


Iron coil 




0.24 




215 


Steam pressure 
= 100. 








4< 


a 




0.22 




208.2 


1 Steam pressure 
\ =10. 








Box 


Iron tube 


0.235 
0.196 
0.206 




230 
207 
210 






Havrez . . 


Cast-iron boiler 


0.077 


6.i05 


82 


100 





From the above it would appear that the efficiency of iron surfaces is 
less than that of copper coils, plate surfaces being far inferior. 

In all experiments made up to the present time, it appears that the 
temperature of the condensing water was allowed to rise, a mean between 
the initial and final temperatures being accepted as the effective tempera- 
ture. But as water becomes warmer it circulates more rapidly, thereby 
causing the water surrounding the coil to become agitated and replaced 
by cooler water, which allows more heat to be transmitted. 

A^ain, in accepting the mean temperature as that of the condensing 
medium, the assumption is made that the rate of condensation is in direct 
proportion to the temperature of the condensing water. 

In order to correct and avoid any error arising from these assumptions 
and approximations, experiments were undertaken, in which all the condi- 
tions were constant during each test. 

The pressure was maintained uniform throughout the coil, and pro- 
\nsion was made for the free outflow of the condensed steam, in order to 
obtain at all times the full efficiency of the condensing surface. The con- 
densing water was continually stirred to secure uniformity of temperature, 
which was regulated by means of a steam-pipe and a cold-water pipe 
entering the tank in which the coil was placed. 



CONDUCTION AND CONVECTION OF HEAT. 



689 



The following is a condensed statement of the results. 

Heat Transmitted per Square Foot of Cooling Surface, per Hour, 
PER Degree of Difference of Temperature. (British Thermal Units.) 



Temperature 
of Condens- 
ing Water. 


1-in. Iron Pipe; 

Steam inside, 

60 lbs. Gauge 

Pressure. 


1 V2-in. Pipe; 

Steam inside, 

10 lbs. 

Pressure. 


1 V2-in. Pipe; 

Steam outside, 

10 lbs. 

Pressure. 


lV2-in. Pipe; 

Steam inside, 

60 lbs 

Pressure. 


80 


265 
269 
272 
277 
281 
299 
313 


128 
130 
137 
145 
158 
174 


200 
230 
260 
267 
271 
270 




100 
120 
140 
160 
180 
200 


239 
247 
276 
306 
349 
419 











The results indicate that the heat transmitted per degree of difference of 
temperature in general increases as the temperature of the condensing 
water is increased. 

The amount transmitted is much larger with the steam on the outside of 
the coil than with the steam inside the coil. This may be explained in 
part by the fact that the condensing water when inside the coil flows over 
the surface of conduction very rapidly, and is more efficient for cooling 
than when contained in a tank outside of the coil. 

This result is in accordance with that found by Mr. Thomas Craddock, 
which indicated that the rate of cooling by transmission of heat through 
metallic surfaces was almost wholly dependent on the rate of circulation of 
the cooling medium over the surface to be cooled. 

Transmission of Heat in Condenser Tubes. (Eng'g, Dec. 10, 1875, 
p. 449.) — In 1874 B. C. Nichol made experiments for determining the 
rate at w^hich heat was transmitted through a condenser tube. The 
results went to show that the amount of heat transmitted through the 
walls of the tube per estimated degree of mean difference of temperature 
increased considerably with this difference. For example: 



Estimated mean difference of 
temperature between inside and 
outside of tube, degrees Fahr. . . . 

Heat-units transmitted per hour 
per square foot of surface per 
degree of mean diff. of temp 



Vertical Tube. Horizontal Tube. 



128 151.9 152.9 111.6 146.2 150.4 



422 531 561 610 737 823 



These results seem to throw doubt upon Mr. Isherwood's statement that 
the rate of evaporation per degree of difference of temperature is the same 
for all temperatures. 

Mr. Thomas Craddock found that water was enormously more efficient 
than air for the abstraction of heat through metallic surfaces in the process 
of cooUng. He proved that the rate of cooling by transmission of heat 
through metallic surfaces depends upon the rate of circulation of the cool- 
ing medium over the surface to be cooled. A tube filled with hot water, 
moved by rapid rotation at the rate of 59 ft. per second, through air, lost as 
much heat in one minute as it did in still air in 12 minutes. In water, at a 
velocity of 3 ft. per second, as much heat was abstracted in half a minute 
as was abstracted in one minute when it was at rest in the water. Mr. 
Craddock concluded, further, that the circulation of the cooling fluid 
became of greater importance as the difference of temperature on the 
two sides of the plate became less. (Clark, R. T. D., p. 461.) 

G. A. Orrok (Power, Aug. 11, 1908) gives a diagram showing the relation 
of the B.T.U. transmitted per hour per sq. ft. of surface per degree of 
difference of temperature to the velocity of the water in the condenser 
tubes, in feet per second, as obtained by different experimenters. Approx- 
imate figures taken from the several curves are given below. 



590 



HEAT. 



Authority. 



1. Stanton.. 

2. Stanton., 



Tubes. 



1/2-in. vert, copper. 
1/2-in. vert, copper. 



3. Nichols I 3/4-in. vert, brass 



4. Nichol 

5. Hepburn... 

6. Hepburn. . 

7. Richter. . . . 

8. Weighton.. 

9. Allen 



3/4-in. horiz. brass 

1 1/4-in. horiz. copper. . . . 
1 1/4-in. horiz. corrugated 
1 1/2-iii. horiz. corrugated 

5/8-in. plain tubes 

5/8-in. horizontal 



Velocity of Water. Feet per 

Second. 



0.5 



B.T.U. per sq. ft. per hr. per 
deg. diff. 



250 
360 
^60 



325 
420 
340 
500 
365 
560 



380 

225 



400 
470 
370 
530 
590 



615 
290 



465 
525 
405 
560 



760 
365 



520 
560 
435 
585 



865 



550 
585 
460 
615 



940 



470 
650 



No. 1, water flowing up. Nos. 2 and 3, water flowing down. 

Transmission of Heat in Feed-water Heaters. (W. R. Billings, 
The National Engineer, June, 1907.) — Experiments show that the rate of 
transmission of heat through metal surfaces from steam to w^ater increases 
rapidly with the increased rate of flow of the water. Mr. Billings there- 
fore recommends the use of small tubes in heaters in which the water is 
inside of the tubes. He says: A high velocity through the tubes causes 
friction between the water and the walls of the tubes; this friction is not 
the same as the friction between the particles of water themselves, and it 
tends to break up the column of w^ater and bring fresh and cooler particles 
against the hot walls of the tubes. 

The following results were obtained in tests: 

1 1/4-in. smooth tubes \Jj Z iH^ 570 670 

1 1/2-in. corrugated tubes [JjZ^lt 444 465 735 

V = velocity of the water, ft. per min. U = B.T.U. transmitted per 
sq. ft. per hour per degree difference of temperature. (See Condensers.) 

In calculations of heat transmission in heaters it is customary to take 
as the mean difference of temperature the difference between the tem- 
perature of the steam and the arithmetical mean of the initial and final 
temperatures of the water; thus if >S = steam temperature, / = initial 
and F = final temperature of the water, and D = mean difference, then 
D = *S — 1/2 {I + F). Mr. Billings shows that this is incorrect, and on 
the assumption that the rate of transmission through any portion of the 
surface is directly proportional to the difference he finds the true mean 
F — I 

to be D = -r \ — TTEi T^ 77i i^i * (Tliis formula was derived by 

hyp. log [{S - I) -^ (S - F)] ^ 
Cecil P. Poole in 1899, Power, Dec, 1906.) 

The following table is calculated from the formula: 

Degrees of Difference Between Steam Temperature and Actual 
Average Temperature of Water. 



Initial 

Temperature 

of Water. 



40 
50 
60 
70 



Vacuum Heaters Between Engine and Condenser. 



26" Vac. Temp. 126° F. 



Final Temp, of Water. 



105 110 115 120 



46.1 
42.8 
39.3 
35.6 
31.8 



41.6 
38.4 
35.3 
31.9 
28.3 



36.9 
33.6 
30.7 
27.6 
24.5 



30.1 
27.6 
25.0 
22.4 
19.6 



24'' Vac. 



Temp. 141° F. 



Final Temp, of Water. 



105 


110 


115 


120 


125 


62.9 


60.2 


55.3 


50.9 


46.1 


59.2 


56.6 


51.8 


47.7 


43.2 


55.5 


52.1 


48.4 


44.4 


40.1 


51.6 


48.2 


45.0 


41.0 


36.9 


47.6 


44.2 


41.2 


37.5 


33.6 



130 

40.6 
37.9 
35.0 
32.2 
29.2 



CONDUCTION AND CONVECTION OF HEAT. 



591 





Atmospheric Heaters. 




Atmos. Press. Temp. 


'o 


Atmos. Press. Temp. 


Initial Temp. 


212° F. 




212° F. 


of Water. 








Final Temp, of Water. 


•a 

105 


Final Temp, of Water. 




192 
70.6 


196 
65.7 


200 
60.1 


204 
53.5 


208 
44.8 


210 
38.0 


192 
51.9 


196 
47.9 


200 
43.4 


204 
38.2 


208 
31.4 


210 


40 


26.4 


50 


67.9 


63.1 


57.6 


51.2 


42.8 


36.4 


110 


50.3 


46.4 


42.1 


36.9 


30.2 


25.5 


60 


65.1 


60.4 


55.2 


48.9 


40.7 


34.7 


115 


48.8 


45.0 


40.6 


35.7 


29.2 


24.5 


70 


62.2 


57.7 


52.6 


46.6 


38.7 


32.9 


120 


47.2 


43.5 


39.2 


34.4 


28.0 


23.5 


80 


59.4 


54.9 


50.0 


44.2 


36.6 


31.0 


125 


45.6 


41.9 


37.8 


33.1 


26.9 


22.5 



The error in using the arithmetic mean for the value of D is not impor- 
tant if F is very much lower than S, but if it is within 10° of S then the 
error may be a large one. With S = 212, I = 40, F = 110, the arith- 
metic mean difference is 137, and the value by the logarithmic formula 
131, an error of less than 5% ; but if F is 204, the arithmetic mean is 90, 
and the value by the formula 53.5. 

It should be observed, however, that the formula is based on an assump- 
tion that is probabljr greatly in error for high temperature differences, 
i.e., that the transmission of heat is directly proportional to the tem- 
perature difference. It may be more nearly proportional to the square 
of the difference, as stated by Rankine. This seems to be indicated by 
the results of heating water by steam coils, given below. 

Heating Water by Steam Coils. — A catalogue of the American 
Radiator Co. (1908) gives a chart showing the pounds of steam condensed 
per hour per sq. ft. of iron, brass and copper pipe surface, for different 
mean or average differences of temperature between the steam and the 
water. Taking the latent heat of the steam at 966 B.T.U. per lb., the fol- 
lowing figures are derived from the table. 





Lb. Steam Condensed 


Lb. Steam Condensed 


B.T.U. per Sq. 


Mean 


per Hour per Sq. Ft. 


per Hour per Sq. Ft. 


Ft. per Hour 


of Pipe. 


per Deg. Diff . 


per Deg. Diff. 


Diflf. 


















Iron. 


Brass. 


Copper 


Iron. 


Brass. 


Copper 


Iron. 


Brass 


Cop. 


50 


7.5 


12.5 


14.5 


0.150 


0.250 


0.290 


101 


198 


280 


100 


18.5 


38 


43.5 


0.185 


0.380 


0.435 


179 


367 


415 


150 


32.2 


76.5 


87.8 


0.215 


0.510 


0.585 


208 


493 


565 


200 


48 


128 


144 


0.240 


0.640 


0.720 


232 


618 


696 



The chart is said to be plotted from a large number of tests with pipes 
placed vertically in a tank of water, about 20 per cent being deducted 
from the actual results as a margin of safety. 

W. R. Billings (Eng. Rec, Feb., 1898) gives as the results of one set of 
expenments with a closed feed-water heater: 

Diff. bet. temp, of steam and final temp, of 

water, deg. F 5 6 8 11 15 18 

B.T.U. per sq.ft. per hr. per deg. mean diff.. . 67 79 89 114 129 139 

Heat Transmission through Cast-iron Plates Pickled in Nitric 
Acid. — Experiments by R. C. Carpenter (Trans. A. S. M. E., xii, 179) 
show a marked change in the conducting power of the plates (from 
steam to water), due to prolonged treatment with dilute nitnc acid. 



592 



HEAT. 



The action of the nitric acid, by dissolving the free iron and not attack- 
ing the carbon, forms a protecting surface to the iron, which is largely 
composed of carbon. The following is a summary of results: 





Increase 


Proportionate 






in Tem- 


Thermal Units 


Rela- 




perature 


Transmitted for 


tive 


Character of Plates, each plate 8.4 in. 


of 3.125 


each Degree of 


Trans- 


by 5.4 in., exposed surface 27 sq. ft. 


lbs. of 


Difference of 


mission 




Water 


Temperature per 


of 




each 


Square Foot per 


Heat. 




Minute. 


Hour. 




Cast iron — untreated skin on, but 








clean, free from rust 


13.90 
11.5 


113.2 
97.7 


100 


Cast iron — nitric acid, 1 % sol., 9 days . . 


86.3 


1% sol., 18 days 


9.7 


80.08 


70.7 


1% sol., 40 days 


9.6 


77.8 


68.7 


5% sol., 9 days.. 


9.93 


87.0 


76. 8 


5% sol., 40 days 


10.6 


77.4 


68. 5 


Plate of pine wood, same dimensions as 








the plate of cast iron 


0.33 


1.9 


1.6 







The effect of covering cast-iron surfaces with varnish has been investi- 
gated by P. M. Chamberlain. He subjected the plate to the action of strong 
acid for a few hours, and then applied a non-conducting varnish. One 
surface only was treated. Some of his results are as follows: 



erg 


r 170. 




152. 


o) q cy 


169. 


^o^V 


162. 


00.1: bjo 




"Sfc-^ ' 


166. 


^ft^b 






113. 


Qi'^ <U 




w 


117. 



As finished — greasy. 

washed with benzine and dried. 
Oiled with lubricating oil. 
After exposure to nitric acid ^xteen hours, then oiled 

(linseed oil). 
After exposure to hydrochloric acid twelve hours, then 
oiled (linseed oil). 
After exposure to sulphuric acid 1, water 2, for 48 
hours, then oiled, varnished, and allowed to dry for 
24 hours. 



Transmission of Heat through Solid Plates from Air or other Dry- 
Gases to Water. (From Clark on the Steam Engine.) — The law of the 
transmission of heat from hot air or other gases to water, through metallic 
plates, has not been exactly determined by experiment. The general 
results of experiments on the evaporative action of different portions of 
the heating surface of a steam-boiler point to the general law that the 
quantity of heat transmitted per degree difference of temperature is 
practically uniform for various differences of temperature. 

The communication of heat from the gas to the plate surface is much 
accelerated by mechanical impingement of the gaseous products upon the 
surface. 

Clark says that when the surfaces are perfectly clean, the rate of trans- 
mission of heat through plates of metal from air or gas to water is greater 
for copper, next for brass, and next for wrought iron. But when the 
surfaces are dimmed or coated, the rate is the same for the different 
metals. 

With raspect to the influence of the conductivity of metals and of the 
thickness of the plate on the transmission of heat from burnt gases to 
water, Mr. Napier made experiments with small boilers of iron and copper 
placed over a gas-flame. The vessels were 5 inches in diameter and 2 1/2 
Inches deep. From three vessels, one of iron, one of copper, and one 
of iron sides and copper bottom, each of them 1/30 inch in thickness, 



CONDUCTION AND CONVECTION OF HEAT. 593 

equal quantities of water were evaporated to dryness, in the times as 
follows: 

Water. Iron Vessel. Copper Vessel. ^^^^ v'ws^el.^^^" 

4 ounces 19 minutes 18.5 minutes 

11 " 33 " 30.75 " 

5V2 " 50 " 44 " 

4 " 35.7 " 36.83 minutes 

Two other vessels of iron sides Vao inch thick, one having a V4-inch 
copper bottom and the other a i/4-inch lead bottom, were tested against 
the iron and copper vessel, V30 inch thick. Equal quantities of water were 
evaporated in 54, 55, and 531/2 minutes respectively. Taken generally, 
the results of these experiments show that there are practically but slight 
differences between iron, copper, and lead in evaporative activity, and 
that the activity is not affected by the thickness of the bottom. 

Mr. W. B. Johnson formed a hke conclusion from the results of his 
observations of two boilers of 160 horse-power each, made exactly ahke, 
except that one had iron flue-tubes and the other copper flue-tubes. No 
difference could be detected between the performances of these boilers. 

Divergencies between the results of different experimenters are attrib- 
utable probably to the difference of conditions under which the heat was 
transmitted, as between water or steam and water, and between gaseous 
matter and water. On one point the divergence is extreme: the rate of 
transmission of heat per degree of difference of temperature. Whilst from 
400 to 600 units of heat are transmitted from water to water through iron 
plates, per degree of difference per square foot per hour, the quantity of 
heat transmitted between water and air, or other dry gas, is only about 
from 2 to 5 units, according as the surrounding air is at rest or in move- 
ment. In a locomotive boiler, where radiant heat was brought into play, 
17 units of heat were transmitted through the plates of the fire-box per 
degree of difference of temperature per square foot per hour. 

Transmission of Heat through Plates from Flame to Water. — 
Much controversy has arisen over the assertion by some makers of hve- 
steam feed-water heaters that if the water fed to a boiler was first heated to 
the boiling point before being fed into the boiler, by means of steam taken 
from the boiler, an economy of fuel would result; the theory being that 
the rate of transmission through a plate to water was very much greater 
when the water was boiUng than when it was being heated to the boihng 
point, on account of the greatly increased rapidity of circulation of the 
water when boiUng. (See Eng'g, Nov. 16, 1906, and Eng. Review [Londonl, 
Jan., 1908.) Two experiments by Sir Wm. Anderson (1872), with a steam- 
jacketed pan, are quoted, one of which showed an increased transmission 
when boiling of 133%, and the other of 80%; also an experiment by 
Sir F. Bramwell, with a steam-heated copper pan, which showed a gain of 
164% with boiUng water. On the other hand, experiments by S. B. Bil- 
brough (Transvaal Inst. Mining Engineers, Feb., 1908) showed in tests 
with a flame-heated pan that there was no difference in the rate of trans- 
mission whether the water was cold or boiUng. W. M. Sawdon (Pouer, 
Jan. 12, 1909) objects to Mr. Bilbrough's conclusions on the ground that 
no corrections for radiation were made, and finds by a similar experiment, 
with corrections, that the increased rate of transmission with boiling water 
is at least 38%. All of these experiments were on a small scale, and in 
view of their conflict no conclusions can be drawn from them as to the 
value of live-steam feed-water heating in improving the economy of a 
steam boiler. 

A. Blechynden's Tests. — A series of steel plates from 0.125 in. to 
1.187 in. thick were tested with hot gas on one side and water on the other 
with differences of temperature ranging from 373° to 1318° F. Trails.) 
Inst, Naval Architects, 1894.) Mr. Blechynden found that the heat 
transmitted is proportional to the square of the difference between the 
temperatures at the two sides of the plate, or: Heat transmitted per sq. 
ft. -^ (diff. of temp.)2 = a constant. A study of the results of these 
tests is made in Kent's " Steam Boiler Economy," p. 325, and it is shown 
that the value of a in Rankine's formula g =(7"!— T)"^ -^a, which a is the 
reciprocal of Mr. Blechynden's constant and is a function of the thickness 
of the plate. One of the plates, A, originally 1.1S7 in. thick, was reduced 



594 



HEAT. 



in four successive operations, by machining to 0.125 in. Another, B, was 
tested in four thicknesses. The other plates were tested in one or two 
thicknesses. Each plate was found to nave a law of transmission of its 
own. For plate A the value of a is represented closely by the formula 
a = 40 -I- 20 t, in which t is the thickness in inches. The formula a ■= 
40 + 20 t ih 10 covers the whole range of the experiments. The whole 
range of values is 38.6 to 71.9, which are very low when compared with 
values of a computed from the results of boiler tests, which are usually 
from 200 to 400, the low values obtained by Blechynden no doubt being 
due to the exceptionally favorable conditions of his tests as compared 
with those of boiler tests. Rankine says the value of a lies between 160 
and 200, but values below 200 are rarely found in tests of modern types 
of boilers. (See Steam-Boilers.) 

Cooling of Air. — H. F. Benson {Am. Mach., Aug. 31, 1905) derives 
the following formula for transmission of heat from air to water through 
copper tubes. It is assumed that the rate of transmission at any point of 
the surface is directly proportional to the difference of temperature 
between the air and water. 

Let A = cooling surface, sq. ft.; K = lb. of air per hour; Sa = specific 
heat of air; Ta^ = temp, of hot inlet air; Ta^ =temp. of cooled outlet air; 
d = actual average diff. of temp, between the air and the water; V = 
B.T.U. absorbed by the water per degree of diff. of temp, per sq. ft. per 



hour. W 



orbed by 
= lb. of 



water per hour; T^, = temp, of inlet water; r^» = 



temp, of outlet water. Then 

AdU = KSaiTa, - T^^); A = X5«(r«^ - T^,) -^ dU, 
d = KTa, - To,) -(T^,- T^,)] -log [(r«, - T^^) -^{Ta,- T^,), 
KS^W 



AU = 



W- 






The more cooling water used, the lower is the temperature T^^^. Also 
the less Tip^ is, the larger d becomes and the less surface is needed. About 
10 is the largest value of W/K that it is economical to use, as there is a 
saving of less than 0,5% in increasing it from 10 to 15. When desirable 
to save water it will be advisable to make W/K = 5. Values of U 
obtained by experiment with a Wainwright cooler made with corrugated 
copper tubes are given in the following table. K and W are in lb. per 
mmute, B^ = B.T.U. from air per min., B^= B.T.U. from water per 
nun., Vw = velocity of water, ft. per min. 



^«. 


^-. 


^-. 


T., 


K 


W 


^a 


Bu, 


Vu; 


U 


221.0 


76.3 


50.0 


169.0 


125.2 


28.50 


4303 


3392 


2.20 


6.75 


217.0 


64.3 


45.8 


146.4 


122.8 


36.73 


4452 


3695 


2.84 


7.12 


224.0 


63.3 


45.7 


149.2 


126.3 


40.30 


4819 


4171 


3.11 


7.91 


209.6 


54.0 


43.8 


125.9 


122.1 


50.00 


4511 


4105 


3.86 


8.81 


214.5 


46.3 


43.0 


106.2 


124.6 


68.95 


4976 


4357 


5.32 


10.55 


234.6 


63.6 


52.6 


120.2 


124.4 


73.25 


5051 


4852 


5.65 


8.41 


214.2 


43.5 


43.0 


94.7 


117.3 


79.84 


4753 


4128 


6.16 


14.32 


242.9 


61.7 


55.3 


114.0 


133.6 


92.72 


5649 


5443 


7.15 


10.01 


223.0 


46.0 


40.1 


79.1 


130.5 


114.80 


5484 


4477 


8.86 


7.86 


239.3 


57.5 


51.0 


95.2 


130.0 


125.70 


5612 


5556 


9.70 


9.38 


246 


58.0 


52.3 


95.1 


133.8 


145.90 


5977 


6244 


11.26 


10.57 



Sixteen other tests were made besides those given above, and their 
plotted results all come within the field covered by those in the table. 



CONDUCTION AND CONVECTION OF HEAT. 



595 



There is apparently an error in the last line of the table, for the heat 
gained by the water could not be greater than that lost by the air. The 
excess lost by the air may be due to radiation, but it shows a great irregu- 
larity. It appears that for velocities of water between 2.2 and 5.3 ft. per 
min. the value of U increases with the velocity, but for higher velocities 
the value of U is very irregular, and the cause of the irregularity is not 
explained. 

Chas. L. Hubbard {The Engineer, Chicago, May 18, 1902) made some 
tests by blowing air through a tight wooden box which contained a nest 
of 30 lV2-in. tin tubes, of a total surface of about 20 sq. ft., through 
which cold water flowed. The results were as follows: 



Cu. ft. of air per minute 

Velocity over cooling surface 

Initial temperature of air 

Drop in temperature 

Average temp, of water 

Average temp, of air 

Difference 

B.T.U. per hour per sq. ft. per degree 
difference 



268 


268 


469 


469 


636 


638 


638 


1116 


1116 


1514 


72° 


72° 


72° 


74° 


74° 


8° 


12° 


8° 


10° 


8° 


50° 


43° 


48° 


48° 


50° 


68° 


66° 


68° 


69° 


70° 


18° 


23° 


20° 


21° 


20° 


6.5 


7.6 


10.2 


12.1 


13.8 



636 

1514 
740 

10* 
440 

68<» 
24» 

14.4 



Transmission of Heat through Plates and Tubes from Steam or 
Hot Water to Air. — The transfer of heat from steam or water through 
a plate or tube into the surrounding air is a complex operation, in which 
the internal and external conductivity of the metal, the radiating power 
of the surface, and the convection of heat in the surrounding air, are all 
concerned. Since the quantity of heat radiated from a surface varies with 
the condition of the surface and with the surroundings, according to laws 
not yet determined, and since the heat carried away by convection varies 
with the rate of the flow of the air over the surface, it is evident that no 
general law can be laid down for the total quantity of heat emitted. 

The following is condensed from an article on "Loss of Heat from 
Steampipes," in The Locomotive, Sept. and Oct., 1892. 

A hot steam-pipe is radiating heat constantly off into space, but at the 
same time it is cooling also by convection. Experimental data on which 
to base calculations of the heat radiated and otherwise lost by steam-pipes 
are neither numerous nor satisfactory. 

In Box's " Practical Treatise on Heat" a number of results are given for 
the amount of heat radiated by different substances when the temperature 
of the air is 1° Fahr. lower than the temperature of the radiating body. A 
portion of this table is given below. It is said to be based on P^clet's 
experiments. 



Heat Units Radiated per Hour, per Square Foot op Surface, 
FOR 1° Fahrenheit Excess in Temperature. 



Copper, pohshed 0.0327 

Tin, pohshed 0.0440 

Zinc and brass, polished. . . 0.0491 

Tinned iron, pohshed 0.0858 

Sheet iron, polished 0.0920 

Sheet lead 0.1329 

Sheet iron, ordinary 0.5662 



Glass 0.5948 

Cast iron, new 0.6480 

Common steam-pipe, in- 
ferred 0.6400 

Cast and sheet iron, rusted . . 0.6868 
Wood, building stone, and 

brick 0.7358 



When the temperature of the air is about 50° or 60° Fahr., and the radiat- 
ing body is not more than about 30° hotter than the air, we may calculate 
the radiation of a given surface by assuming the amount of heat given off 
by it in a given time to be proportional to the difference in temperature 
between the radiating body and the air. This is '* Newton's law of cooling. " 
But when the difference in temperature is great, Newton's law does not 
hold good; the radiation is no longer proportional to the difference in tem- 
perature, but must be calculated by a complex formula established experi- 
mentally by Dulong and Petit. Box has computed a table from thli 



596 



HEAT. 



formula, which greatly facilitates its application, and which is given 
below: 

Factors for Reduction to Dulonq's Law of Radiation. 



Differences in Tem- 


Temperature of the Air < 


3n the Fahrenheit Scale. 


perature between 

Radiating Body 

and the Air. 




32° 


50° 
1,07 


590 
1.12 


68° 
1.16 


86° 
1.25 


1Q4° 
1.36 


122° 
1.47 


140° 
1.58 


158° 
1.70 


176° 
1.85 


194° 
1.99 


212' 


Deg. Fahr. 
18 


1 00 


2.15 


36 


1 03 


1,11 


1.16 


1.21 


1.30 


1.40 


1.52 


1.68 


1.76 


1.91 


2.06 


2.23 


54 


1 07 


1.16 


1.20 


1.25 


1.35 


1.45 


1.58 


1.70 


1.83 


1.99 


2.14 


2.31 


72 


1,12 


1.20 


1.25 


1.30 


1.40 


1.52 


1.64 


1.76 


1.90 


2.07 


2.23 


2 40 


90 


1.16 


1.25 


1.31 


1.36 


1.46 


1.58 


1.71 


1.84 


1.98 


2.15 


2.33 


2.51 


108 


1 21 


1,31 


1.36 


1.42 


1.52 


1.65 


1.78 


1.92 


2.07 


2.28 


2.42 


2,62 


126 


1.26 


1.36 


1.42 


1.48 


1.60 


1.72 


1.86 


2.00 


2.16 


2.34 


2.52 


2.72 


144 


1 32 


1.42 


1.48 


1.54 


1.65 


1.79 


1.94 


2.08 


2.24 


2.44 


2.64 


2 83 


162 


1.37 


1.48 


1.54 


1.60 


1.73 


1.86 


2.02 


2.17 


2.34 


2.54 


2.74 


2.96 


180 


1.44 


1.55 


1.61 


1.68 


1.81 


1.95 


2.11 


2.27 


2.46 


2.66 


2.87 


3.10 


198 


1 50 


1.62 


1.69 


1.75 


1.89 


2.04 


2.21 


2.38 


2.56 


2.78 


3.00 


3,24 


216 


1 58 


1.69 


1.76 


1.83 


1.97 


2.13 


2.32 


2.48 


2.68 


2.91 


3 13 


3 38 


234 


1.64 


1.77 


1.84 


1.90 


2.06 


2.23 


2.43 


2.52 


2.80 


3.03 


3.28 


3 46 


252 


1,71 


1.85 


1.92 


2.00 


2.15 


2.33 


2.52 


2.71 


2.92 


3.18 


3.43 


3.70 


270 


1,79 


1.93 


2.01 


2.09 


2.26 


2.44 


2.64 


2.84 


3.06 


3.32 


3.58 


3 87 


288 


1 89 


2,03 


2.12 


2.20 


2.37 


2.56 


2.78 


2.99 


3.22 


3.50 


3.77 


407 


306 


1.98 


2.13 


2.22 


2.31 


2.49 


2.69 


2.90 


3.12 


3.37 


3.66 


3 95 


4.26 


324 


2,07 


2.23 


2.33 


2.42 


2.62 


2.81 


3.04 


3.28 


3.53 


3.84 


4.14 


4.46 


342 


2.17 


2.34 


2.44 


2.54 


2.73 


2.95 


3.19 


3.44 


3.70 


4.02 


4.34 


4.68 


360 


2.27 


2.45 


2.56 


2.66 


2.86 


3.09 


3.35 


3.60 


3.88 


4.22 


4.55 


4.91 


378 


2.39 


2.57 


2.68 


2.79 


3.00 


3.24 


3.51 


3.78 


4.08 


4.42 


4.77 


5.15 


396 


2.50 


2.70 


2.81 


2.93 


3.15 


3.40 


3.68 


3.97 


4.28 


4.64 


5.01 


5.40 


414 


2 63 


2,84 


2.95 


3.07 


3.31 


3.56 


3.87 


4.12 


4.48 


4.87 


5.26 


5.67 


432 


2.76 


2.98 


3.10 


3.23 


3.47 


3.76 


4.10 


4.32 


4.61 


5.12 


5.53 


6.04 



The loss of heat by convection appears to be independent of the nature 
of the surface, that is, it is the same for iron, stone, wood, and other 
materials. It is different for bodies of different shape, however, and it 
varies with the position of the body. Thus a vertical steam-pipe will not 
lose so much heat by convection as a horizontal one will; for the air 
heated at the lower part of the vertical pipe will rise along the surface of 
the pipe, protecting it to some extent from the chilling action of the sur- 
rounding cooler air. For a similar reason the shape of a body has an 
important influence on the result, those bodies losing most heat whose 
forms are such as to allow the cool air free access to every part of their 
surface. The following table from Box gives the number of heat units 
that horizontal cyUnders or pipes lose by convection per square foot of 
surface per hour, for one degree difference in temperature between the 
pipe and the air. 

Heat Units Lost by Convection from Horizontal Pipes, per Square 
Foot of Surface per Hour, for a Temperature 
Difference of 1° Fahr. 



External 

Diameter 

of Pipe 

in Inches. 


Heat 
Units 
Lost. 


External 
Diameter 

of Pipe 
in Inches. 


Heat 

Units 
Lost. 


External 

Diameter 

of Pipe 

in Inches. 


Heat 
Units 
Lost. 


2 
3 
4 
5 
6 


0.728 
0.626 
0.574 
0.544 
0.523 


7 

8 
9 
10 
12 


0.509 
0.498 
0.489 
482 
0.472 


18 
24 
36 
48 


0.455 
0.447 
438 
434 









THERMODYNAMICS. 



597 



The loss of heat by convection is nearly proportional to the difference 
In temperature between the hot body and the air, but the experiments of 
Dulong and P6ciet show that this is not exactly true, and we may here also 
resort to a table of factors for. correcting the results obtained by sample 
proportion. 

Factors for Reduction to Dulong's Law of Convection. 



Difference 




Difference 




Difference 




in Temp. 




in Temp. 




in Temp. 




between Hot 


Factor. 


between Hot 


Factor. 


between Hot 


Factor. 


Body and 




Body and 




Body and 




Air. 




Air. 




Air. 




IS^F. 


0.94 


180° F. 


1.62 


342° F. 


1.87 


36<» 


1.11 


198° 


1.65 


360° 


1.90 


54° 


1.22 


216° 


1.68 


378° 


1.92 


72° 


1.30 


234° 


1.72 


396° 


1.94 


90° 


1.37 


252° 


1.74 


414° 


1.96 


108° 


1.43 


270° 


1.77 


432° 


1.98 


126° 


1.49 


288° 


1.80 


450° 


2.00 


144° 


1.53 


306° 


1.83 


468° 


2.02 


162° 


1.58 


324° 


1.85 













Example in the Use of the Tables. — Required the total loss of heat 
by both radiation and convection, per foot of length of a steam-pipe 211/32 
In. external diameter, steam pressure 60 lbs., temperature of the air in the 
room 68° Fahr. 

Temperature corresponding to 60 lbs. equals 307°; temperature dif- 
ference = 307° - 68 = 239°. 

Area of one foot length of steam-pipe = 211/32 X 3.1416 -f- 12 =» 
0.614 sq. ft. 

Heat radiated per hour per square foot per degree of difference, from 
table, 0.64. 

Radiation loss per hour by Newton's law = 239° X 0.614 ft. X 0.64 = 
93.9 heat units. Same reduced to conform with Dulong's law of radiation: 
factor from table for temperature difference of 239° and temperature of 
air 68° = 1.93. 93.9 X 1.93 = 181.2 heat units, total loss by radiation. 

Convection loss per square foot per hour from a 211/32-inch pipe: by 
interpolation from table, 2" = 0.728, 3" = 0.626, 211/32" = 0.693. 

Area. 0.614 X 0.693 X 239° = 101.7 heat units. Same reduced to 
conform with Dulong's law of convection: 101.7 X 1.73 (from table) = 
175.9 heat units per hour. Total loss by radiation and convection =« 
181.2 + 175.9 = 357.1 heat units per hour. Loss per degree of difference 
of temperature per Unear foot of pipe per hour = 357.1 -^ 239 = 1.494 
heat units = 2.433 per sq. ft. 

It is not claimed, says The Locomotive, that the results obtained by this 
method of calculation are strictly accurate. The experimental data are 
not sufficient to allow us to compute the heat-loss from steam-pipes wdth 
any great degree of refinement: yet it is believed that the results obtained 
as indicated above will be sufficiently near the truth for most purposes. 
An experiment by Prof. Ordway, in a pipe 211/32 in. diam. under the above 
conditions (Trans. A. S. M. E., v. 73), showed a condensation of steam of 
181 grams per hour, which is equivalent to a loss of heat of 358.7 heat 
units per hour, or within half of one per cent of that given by the above 
calculation. 

The quantity of heat given off by steam and hot-water radiators in 
ordinary practice of heating buildings by direct radiation varies from 1.25 
to about 3.25 heat units per hour per square foot per degree of difference 
of temperature. (See Heating and Ventilation.) 

THERMODYNA3IICS. 

Thermodynamics, the science of heat considered as a form of energy, 
is useful in advanced studies of the theory of steam, gas, and air engines, 
refrigerating machines, compressed air, etc. The method of treatment 
adopted by the standard writers is severely mathematical, involving 
constant application of the calculus. The student will find the subject 



598 HEAT. 

thoroughly treated in the works by Rontgen (Dubois's translation), Wood, 
Peabody, and Zeuner. 

First Law of Thermodynamics. — Heat and mechanical energy are 
mutually convertible in the ratio of about 778 foot-pounds for the British 
thermal unit. (Wood.) 

Second Law of Thermodynamics. — The second law has by different 
writers been stated in a variety of ways, and apparently with ideas so 
diverse as not to cover a common principle. (Wood, Therm., p. 389.) 

It is impossible for a self-acting machine, unaided by any external 
agency, to convert heat from one body to another at a higher temperature. 
(Clausius.) 

If all the heat absorbed be at one temperature, and that rejected be at 
one lower temperature, then will the heat which is transmuted into work 
be to the entire heat absorbed in the same ratio as the difference between 
the absolute temperature of the source and refrigerator is to the absolute 
temperature of the source. In other words, the second law is an expression 
for the efficiency of the perfect elementary engine. (Wood.) 

The expression ^^^^ — - = ^ ^ — ^ may be called the symbolical or 
Qi 1 1 

algebraic enunciation of the second law, — the law which limits the 
efficiency of heat engines, and which does not depend on the nature of the 
working medium employed. (Trowbridge.) Qi and Ti = quantity and 
absolute temperature of the heat received; Q2 and T2 = quantity and 
absolute temperature of the heat rejected. 
T\ — T2 
The expression — -^ represents the efficiency of a perfect heat 

engine which receives all its heat at the absolute temperature Ti, and 
rejects heat at the temperature T2, converting into work the difference 
between the quantity received and rejected. 

Example. — What is the efficiency of a perfect heat engine which 
receives heat at 388° F. (the temperature of steam of 200 lbs. gauge 
pressure) and rejects heat at 100° F. (temperature of a condenser, pressure 
1 lb. above vacuum)? 

388+ 459.2 - (100+ 459.2) ..^ , 
383^^,9, -^ = 34%, nearly. 

In the actual engine this efficiency can never be attained, for the difference 
between the quantity of heat received into the cyhnder and that rejected 
into the condenser is not all converted into work, much of it being lost by 
radiation, leakage, etc. In the steam engine the phenomenon of cyhnder 
condensation also tends to reduce the efficiency. 

The Carnot Cycle. — Let one pound of gas of a pressure pi, volume v\ 
and absolute temperature T\ be enclosed in an ideal cylinder, having non- 
conducting walls but the bottom a perfect con- 
ductor, and having a moving non-conducting 
frictionless piston. Let the pressure and volume 
of the gas be represented by the point A on the 
Vv or pressure-volume diagram. Fig. 142, and 
let it pass through foUr operations, as follows: 

1. Apply heat at a temperature of T\ to the 
bottom of the cyhnder and let the gas expand, 
doing work against the piston, at the constant 

temperature Ti, or isothermally, to jhvi, or B. 

T^-^ i^r> 2. Remove the source of heat and put a non- 

r iG. 14^. conducting cover on the bottom, and let the gas 

expand adiabatically, or without transmission of heat, to vzvz, or C, while 
Its temperature is being reduced to Ti. 

3. Apply to the bottom of the cyhnder a cold body, or refrigerator, of 
the temperature Ti, and let the gas be compressed by the piston isother- 
maUy to the pomt D, or va^, rejecting heat into the cold body. 

4. Remove the cold body, restore the non-conducting bottom, and 
compress the gas adiabatically to ^, or the original pwi, while its tempera- 
ture is being raised to the original T\. The point D on the isothermal 
line CD is chosen so that an adiabatic hne passing through it will also pass 
through A, and so that va/v\= 'm/vi. 

The area aABCc represents the work done by the gas on the piston; 




THERMODYNAMICS. 599 

the area CDAac the negative work, or the work done by the piston on the 
gas; the difference, ABCD, is the net work. 

la. The area aABb represents the work done during isothermal expan- 
sion. It is equal in foot-pounds to Wi = pivi logg {v2/v\), where pi = the 
initial absolute pressure in lbs. per sq. ft. and vi = the initial volume in 
cubic feet. It is also equal to the quantity of heat supplied to the gas,= 
Ui = RTi logg (i;2/?'i). R is Sb constant for a given gas, =- 53.35 for air. 

2a. The area bBCc is the work done during adiabatic expansion, = Wt 

= ^^ { 1 — (^) J , y being the ratio of the specific heat at constant 

pressure to the specific heat at constant volume. For air y = 1.406. 
The loss of intrinsic energy = K^{Ti — Ti) ft. -lbs. K^= specific heat 
at constant volume X 778. 

3a. CDdc is the work of isothermal compression, = Wi = PiVi log^ 
(vsM) = heat rejected = JJi = RTilog^ {vi/vC). 

4a. DAad is the work of adiabatic compression 



=^«=^{-(Dn- 



which is the same as TF2 and therefore, being negative, cancels it, and the 

net work ABCD = Wi- W3. The gain of intrinsic energy is K^iTi- T2). 

Comparing la and 3a, we have pivi= P2V2; pzvz = P4V4; V2/vz = vi/Vi — r. 

Wi = pwi logg r = RTi logg r\ Wz = PiVi logg r = RT2 logg r. 

W1-W3 R(Ti^T2)\oger T1-T2 , T2 
Efficiency —^^ = ^^^^^g^, = -^^ = 1 - j^ 



=-0 



V2\Y-1 U1-U2 



Ui 



Entropy. — In the pv or pressure- volume diagram, energy exerted or 
expended is represented by an area the lines of which show the changes 
of the values of p and v. In the Carnot cycle the^e changes are shown 
by curved lines. If a given quantity of heat Q is added to a substance 
at a constant temperature, we may represent it by a rectangular area 
in which the temperature is represented by a vertical line, and the base 
is the quotient of the area divided by the length of the vertical line. To 
this quotient is given the name entropy. When the temperature at 
which the heat is added is not constant a more general definition is 
needed, vi^.: Entropy is length on a diagram thQ area of which represents 
a quantity of heat, and the height at any point represents absolute tempera- 
ture. The value of the increase of entropy is given in the language of 

r^^dO 
calculus, E= I —-, which may be interpreted thus: increase of entropy 

•J T2 ■'■ 
between the temperatures T2 and Ti equals the summation of all the 
quotients arising by dividing each small quantity of heat added by 
the absolute temperature at which it is added. It is evident that if 
the several small quantities of heat added are equal, while the values of 
T constantly increase, the quotients are not equal, but are constantly 
decreasing. The diagram, called the temperature-entropy diagram, or 
the 6(f), theta-phi, diagram, is one in which the abscissas, or horizontal 
distances, represent entropy, and vertical distances absolute temperature. 
The horizontal distances are measured from an arbitrary vertical line 
representing entropy at 32° F., and values of entropy are given as values 
beyond that point, while the temperatures are measured above absolute 
zero. Horizontal fines are isothermals, vertical lines adiabatics. The use- 
fulness of entropy in thermodynamic studies is due to the fact that in 
many cases it simplifies calculations and makes it possible to use alge- 
braic or graphical methods instead of the more difiBcult methods of the 
calculus. 



T 


^ Ti 


B 


D 





c 


Ta 

a e 






600 HEAT. 

Tlie Carnot Cycle in the Temperature-Entropy Diagram. — Let a 

pound of gas having a temperature Ti and entropy E be subjected to the 
four operations described above. (1) Ti being 
constant, heat (area aABc, Fig. 143) is added and 
the entropy increases from A to B: isothermal 
expansion. (2) No heat is transferred, as heat, 
but the temperature is reduced from Ti to T2; 
entropy constant; adiabatic expansion. (3) Heat 
is rejected at the constant temperature T2, the 
area CcaD being subtracted; entropy decreases 
from C to D; isothermal compression. (4) En- 
tropy constant, temperature increases from D to 
A, or from T2 to Ti; no heat transferred as heat; 
adiabatic compression. The area aABc repre- 
sents the total heat added during the cycle, the 
area cCDa the heat rejected ; the difference, or the 
•p-p 1 ^o area ABCD, is the heat utilized or converted into 

work. The ratio of this area to the whole area 
aABc is the efficiency; it is the same as the ratio (Ti- T2) -^ Ti. It 
appears from this diagram that the efficiency may be increased by in- 
creasing jTi or by decreasing T2; also that since T2 cannot be lowered by 
any self-acting engine below the temperature of the surrounding atmos- 
phere, say 460°+ 62° F.= 522° F., it is not possible even in a perfect 
engine to obtain an efficiency of 50 per cent unless the temperature of 
the source of heat is above 1000° F. It is shown also by this diagram 
that the Carnot cycle gives the highest possible efficiency of a heat engine 
working between any given temperatures Ti and T2, and that the admis- 
sion and rejection of heat each at a constant temperature gives a higher 
efficiency than the admission or rejection at any variable temperatures 
within the range Ti — T2. 

The Reversed Carnot Cycle — Refrigeration. — Let a pound of cool 
gas whose temperature and entropy are represented by the "state- 
point" D on the diagram (1) receive heat at a constant temperature T2 
(the temperature of a refrigerating room) until its entropy is C; (2) then 
let it be compressed adiabatically (no heat transmission, CB) to a high 
temperature Ti; (3) then let it reject heat into the atmosphere at this 
temperature Ti (isothermal compression); (4) then let it expand adia- 
batically, doing work, as through a throttled expansion cock, or by 
pushing a piston, it will then cool to a temperature which may be far 
below that of the atmosphere and be used to absorb heat from the 
atmosphere. (See Refrigeration.) 

Principal Equations of a Perfect Gas. — Notation: P = pressure in 
lb. per sq. ft. V= volume in cu. ft. PoVo, pressure and volume at 
32° F. r, absolute temperature = ^° F. + 459.6. Cp, specific heat at 
constant pressure. C^, specific heat at constant volume. Kp = 
CpX 777.6; Ky = C^ X-777.6; specific heats taken in foot-pounds of 
energy. R, a constant, = Kp - K^. y = Cp/Cy. r = ratio of iso- 
thermal expansion or compression = P2/P1 or Vi/ V2. 

For air: Cp = 0.2375; Cy = 0.1689; Kp = 184.8; Ky = 131.4; 
R = 53.32; y = 1.406. 

Boyle's Law, PV= constant when T is constant. PiVi = P2V2. 
For 1 lb. air PoVo = 2116.3 X 12.387 = 26,215 ft.-lb. 

Charles's Law, PiVi/Ti = P2V2/T2; PiVi = PoVo X Ti/To; To = 32 
+ 459.6 = 491.6; Pi Vi for air = 26,215 -^ 491.6 = 53.32. 

General Equation, PV = RT. R is sl constant which is different for 
different gases. 

Internal or Intrinsic Energy Ky {Ti- To) = R (Ti - To) -^ (y - 1) 
= PiVi 4- (7 — 1) = amount of heat in a body, measured above abso- 
lute zero. For air at 32° F., KyiTi - To) = 131.4 X 491.6 = 64,600 
ft.-lb. When air is expanded or compressed isothermally, PV = con- 
stant, and the internal energy remains constant, the work done in 
expansion = the heat added, and the work done in compression = the 
heat rejected. 



THERMODYNAMICS. 601 

Work done by Adiabatic Expansion, no transmission of heat, from PiVi to 
P2F2 = PiFi \l - (Vi/V2)^~'l -^ (y - 1). = (PiFi - P2V2) - (y - 1) 

- PiFi{ 1 ~(P2/Pi) y } - (y - 1). 

Work of Adiabatic Compression from PiVi to P2V2 (P2 here being the 
higher pressure) = Pi Fi {(7i/F2)'^~^ -l} -^ (y- 1) = (P2F2-PiFi)^ y-1 

= PiFi {(P2/P1) y -l}^(y-l). 

Loss of Intrinsic Energy in adiabatic expansion, or gain in compression 
= K^(Ti— T2), Ti being the higher temperature. 

Work of Isothermal Expansion, temperature constant, = heat expended 
= PiFi logg F2/Fi= PiFi loggr= RT log^r. 

Work of Isothermal Compression from Pi to P2 = PiFi log^ Pi/Pa 
= RT\oggr= heat discharged. 

Relation between Pressure, Volume and Temperature: 

y-i 

7^2 = 7^1 (^') Y = r 1 (-f ')^"\ Pi FiV = P, F2Y. 

For air, y = 1,406; y - 1 = 0.406; 1/y = 0.711; l/(y - 1) = 2.463; 
y/(y-l) = 3.463; (y - l)/y = 0.289. 

Differential Equations of a Perfect Gas. Q = quantity of heat. ^ = 
entropy. 

dQ = C^dT+(Cj,-C^)^dV, d<j> = C„^-\-{Cj,-C^)^^ 

dQ = CpdT+iC^-Cp)^dV. d^=Cp^-h(C^-Cp)~-' 

T T dP dV 

dQ=Cy ^dP+Cj, ^ dV. d4>= C^ ^+ Cp ^ . 

^- ^i = (7^ logg ^^ +(Cp-C^) log^ ^^ . 

^ - ^1 = Cp log^ Y^-^iC^- Cp) logg ^^ 

4>2-4>l = C^ logg p^ +Cp logg :p^ . 

Work of Isothermal Expansion, TF = Pi Fi f ^ ^ = Pi Fi log^ 77^ • 

JVi ^ ^i 

I^eat supplied during isothermal expansion, 

J'F2 (jy y„ 

^^ ^=(Cp-e^) Tiiog^ f^ 

Heat added= work done= ARTi log^ F2/Fi= ^PiFi log^ F2/Fi; (A- 
1/778). 

Work of adiabatic expansion. 



602 



HEAT. 



A(Pi'Wi) 



Construction of the Curve P V* = C. (Am. Mach., June 21, 1900.)— 
Referring to Fig. 144, on a system of rectangular coordinates YOX lay 

o£E OB = pi and BA — ri. 
Draw off extended, at 
any convenient angle a, 
say 15°, with OX, and OC 
at an angle ^ with OF. /3 
is found from the equation 
1 + tan ^ =[1 +tanap. 
Draw AJ parallel to YO. 
From B draw BC at 45° 
with J50, and draw CE 
parallel to OX. From J 
draw JH at 45'' with ^ J, 
and draw HE and HJi 
parallel to YO. The inter- 
section of CE and H-E is 
the second point on the 
curve, or P2V2. From Ji 
draw JiHi at 45° to HJi 
and draw the vertical 
J2H1R. Draw DX at 45° 
to DOi and KT? parallel 
to OX. R is the third 
point on the curve, and 
so on. 

Conversely, if we have 
a curve for which we wish 




Fig. 144. 



r.° Abs. . 



392 



212 



•460 



852 



672 



492 



CTl 



B/ 



To 



C 



J 



to derive an exponent, we can, by working backward, locate the hues 
OC and OJ, measure the angles a and /3, and solve for n. 

The smaller the angle a is taken the more closely the points of the 
curve may be located. If a = /3 the curve is the isothermal curve, 
pv = constant. If a = 15° and jB = 21° 30' the curve is the adiabatic 
for air, n = 1.41. (See Index of the Curve of an Air Diagram, p. 636.) 

Temperature-Entropy Diagram of Water and Steam. — The line 
OA, Fig. 145, is the origin from which entropy is measured on horizontal 
lines, and the line Og is the line of zero ^ 

temperature, absolute. The diagram 
represents the changes in the state 
of one pound of water due to the 
addition or subtraction of heat or to 
changes in temperature. Any point on 
the diagram is called a ** state point." 
A is the state of 1 lb. of water at, 
32° F. or 492° abs., B the state at 
212°, and C at 392° F., correspond- 
ing to about 226 lbs. absolute pres- 
sure. At 212° F. the area OABb is 
the heat added, and Ob is the increase 
of entropy. At 392° F., bBcC is the 
further addition of heat, and the 
entropy, measured from OA, is Oc. 
The two quantities added are nearly 
the same, but the second increase 
of entropy is the smaller, since the 
mean temperature at which it is 
added is higher. If Q = the quantity 
of heat added, and Ti and T2 are 
respectively the lower and the 
higher temperatures, the addition of 
entropy, <}>, is approximately Q -i- 1/2 (T2+ Ti) = 180 -^ 1/2 (672 + 492) 
= 0.3093. More accurately it is 6 = log e {T2/T1) = 0.3119. In both of 
these expressions it is assumed tnat the specific heat of water = 1 at all 
temperatures, which is not strictly true. Accurate values of the entropy 
of water, taking into account the variation in specific heat, will be found 
ia Marks and Davis's Steam Tables. 

J^t the 1 lb. pf water at the state B have heat added to it at the con-. 



9 



Entropy - 



-n 



Fig. 145. 



?HtSICAL PROPEKTIES OF GASES. 603 

stant temperature of 212® P. until it is evaporated. The quantity of 
heat added will be the latent heat of evaporation at 212'^ (see Steam 
Table) or L = 970.4 B.T.U., and it will be represented on the diagram by 
the rectangle hBFf. Dividing by Ti = 672, the absolute temperature, 
gives <|>2 - 01 = 1.444 = 5F. Adding <^i = 0.312 gives c^2 = 1.756, the 
entropy of 1 lb. steam at 212° F. measured from water at 32° F. 

In like manner if we take L = 834.4 for steam at 852° abs.. <^2 — <^i =3 
0.980 = CE, and <Ai = entropy of water at 852° = 0.556, the sum (^a^ 
1.536 = Oe on the diagram. 

E is the state point of dry saturated steam at 852° abs, and F the 
state point at 672°. The line EFG is the line of saturated steam and the 
line ABC the water line. The line CE represents the increase of entropy 
m the evaporation of water at 852° abs. If entropy CD only is added, 
or cCDd of heat, then a part of the water wiU remain unevaporated, 
viz.: the fraction DE/CE of 1 lb. The state point D thus represents wet 
steam having a dryness fraction of CD/DE. 

If steam having a state point E is expanded adiabatically to 672* 
abs. its state point is then ei, having the same entropy as at E, a total 
heat less by the amount represented by the area BCEei, and a dryness 
fraction Bei/BF. If it is expanded while remaining saturated, heat 
must be added equal to eEFf, and the entropy increases by ef. 

If heat is added to the steam at E, the temperature and the entropy 
both increase, the line EH representing the superheating, and the area 
EH, down to the Hne Og, is the heat added. If from the state point H 
the steam is expended adiabatically, the state point follows the MneHJ 
until it cuts the Une EFG, when the steam is dry saturated, and if it 
crosses this line the steam becomes wet. 

If the state point follows a horizontal line to the left, it represents 
condensation at a constant temperature, the amount of heat rejected 
being shown by the area under the horizontal line. If heat is rejected 
at a decreasing temperature, corresponding vvith the decreasing pressure 
at release in a steam engine, or condensation in a cylinder at a decreasing 
pressure, the state point follows a curved line to the left, as shown in 
the dotted curved line on the diagram. 

In practical calculations with the entropy-temperature diagram it is 
necessary to have at hand tables or charts of entropy, total heat, etc., 
sucn as are given in Peabody's or Marks and Davis's Steam Tables, 
and other works. The diagram is of especial service in the study of 
steam turbines, and an excellent chart for this purpose will be found in 
Moyer's Steam Turbine. It gives for all pressures of steam from 0.5 
to 300 lbs. absolute, and for different degrees of dryness up to 300° of 
superheating, the total heat contents in B.T.U. per pound, the entropy, 
and the velocity of steam through nozzles. 

PHYSICAL PROPERTIES OP GASES. 

(Additional matter on this subject will be found under Heat, Air, Gas 
and Steam.) 

When a mass of gas is inclosed in a vessel it exerts a pressure against the 
walls. This pressure is uniform on every square inch of the surface of the 
vessel; also, at any point in the fluid mass the pressure is the same in every 
direction. 

In small vessels containing gases the increase of pressure due to weight 
may be neglected, since all gases are very light; but where liquids are 
concerned, the increase in pressure due to their weight must always be 
taken into account. 

Expansion of Gases, Mariotte's Law. — The volume of a gas dimin- 
ishes in the same ratio as the pressure upon it is increased, if the tem- 
perature is unchanged. 

This law is by experiment found to be very nearly true for all gases, and 
is known as Boyle's or Mariotte's law. 

If p = pressure at a volume v, and pi = pressure at a volume Pi, pivi =» 

pv; pi = — p; pv = a constant. 

Vi 

The constant, C, varies with the temperature, everything else re- 
maining the same. 



604 PHYSICAL PKOPERTIES OF GASES. 

Air compressed by a pressure of seventy-five atmospheres has a 
volume about 2% less than that computed from Boyle's law, but this is 
the greatest divergence that is found below 160 atmospheres pressure. 

Law of Charles. — The volume of a perfect gas at a constant pressure 
is proportional to its absolute temperature. If vo be the volume of a 
gas at 32° F., and vi the volume at any other temperature, ti, then 



Vl 



= ^» (-491:^)'^ =(1 +-491:6-)^° 



Vl = Vo 1, 
Pi 



or Vl = [1 4- 0.002034 (^1 - 32 )] Vo. 
If the pressure also change from poto pi, 
po / ti + 459.6 \ 
^ ( 491.6 /' 

The Densities of the elementary gases are simply proportional to 
their atomic weights. The density of a compound gas, referred to 
hydrogen as 1, is one-half its molecular weight; thus the relative den- 
sity of CO2 is 1/2 (12 + 32) = 22. 

Avogadro's Law. — Equal volumes of all gases, under the same condi- 
tions of temperature and pressure, contain the same nimaber of molecules. 
To find the weight of a gas in pounds per cubic foot at 32° F., multiply 
half the molecular weight of the gas by 0.00559. Thus 1 cu. ft. of marsh- 
gas, CH4. ^ j^^ ^^2 + 4) X 0.00559 = 0.0447 lb. 

When a certain volume of hydrogen combines with one-half its voliune 
of oxygen, there is produced an amount of water vapor which will 
occupy the same volume as that which was occupied by the hydrogen 
gas when at the same temperature and pressure. 

Physical Laws of Methane Gas. — (P. F. Walker, Trans. A. S. M. E., 
1914.) The specific heat of CHa under constant pressure at tempera- 
tures from 18° to 218° C. is 0.5929 according to Landolt and Bomstein's 
Tables. The same tables, on the authority of Lussana, give values of 
0.5915 at a pressure of 1 atmosphere and 0.6919 at 30 atmospheres. The 
ratio of specific heats at constant pressure and constant volume is given 
variously at from 1.235 to 1.315. The gas shows a considerable varia- 
tion from Boyle's law. PV = constant, or PV = PiVi. The variation 
amounts to as much as 4% in the case of CHa gas at 300 lb. per square 
inch reduced to the equivalent volume at atmospheric pressure. The 
difference is of commercial importance when natural gas is sold measured 
at high pressures and the price based on the equivalent volume at 
atmospheric pressure. The relation of pressure and volume is ex- 
pressed by Pyw = a constant and the value of n for CHa ranges from 
0.98 to 0.995, varying with pressure and temperature, averaging 0.99. 
SuflBcient data are not yet available for the construction of tables 
showing the variation of the pressure-volume relation from that given 
by Boyle's law. 

Saturation Point of Vapors. — A vapor that is not near the satura- 
tion point behaves like a gas under changes of temperature and pressure; 
but if it is sufficiently compressed or cooled, it reaches a point where it 
begins to condense: it then no longer obeys the same laws as a gas, but 
its pressure cannot be increased by diminishing the size of the vessel con- 
taining it, but remains constant, except when the temperature is changed. 
The only gas that can prevent a liquid evaporating seems to be its own 
vapor. 

Dalton's Law of Gaseous Pressures. — Every portion of a mass of 
gas inclosed in a vessel contributes to the pressure against the sides of the 
vessel the same amount that it would have exerted by itself had no other 
gas been present. 

3Iixtures of Vapors and Gases. — The pressure exerted against the 
interior of a vessel by a given quantity of a perfect gas inclosed in it is the 
sum of the pressures which any number of parts into which such quan- 
tity might be divided would exert separately, if each were inclosed in a 
vessel of the same bulk alone, at the same temperature. Although this 
law is not exactly true for any actual gas, it is very nearly true for many. 
Thus if 0.080728 lb. of air at 32° F., being inclosed in a vessel of one cubic 
foot capacity, exerts a pressure of one atmosphere, or 14.7 pounds, on each 



PHYSICAL PROPERTIES OF GASES. 603 

square inch of the interior of the vessel, then will each additional 0.080728 
lb. of air which is inclosed, at 32°, in the same vessel, produce very nearly 
an additional atmosphere of pressure. The same law is applicable to 
mixtures of gases of different kinds. For example, 0.1 2344 lb. of carbonic- 
acid gas, at 32°, being inclosed in a vessel of one cubic foot in capacity, 
exerts a pressure of one atmosphere: consequently, if 0.080728 lb. of air 
and 0.12344 lb. of carbonic acid, mixed, be inclosed at the temperature 
of 32°, in a vessel of one cubic foot of capacity, the mixture will exert a 
pressure of two atmospheres. As a second example: Let 0.080728 lb. 
of air, at 212°, be inclosed in a vessel of one cubic foot; It will exert a 
pressure of 

Let 0.03797 lb. of steam, at 212°, be inclosed in a vessel of one cubic 
foot ; it will exert a pressure of one atmosphere. Consequently, if 0.080728 
lb. of air and 0.03797 lb. of steam be mixed and inclosed together, at 212°, 
in a vessel of one cubic foot, the mixture will exert a pressure of 2.366 
atmospheres. It is a common but erroneous practice, in elementary 
books on physics, to describe this law as constituting a difference between 
mixed and homogeneous gases; whereas it is obvious that for mixed and 
homogeneous gases the law of pressure is exactly the same, viz., that the 
pressure of the whole of a gaseous mass is the sum of the pressures of all 
its parts. This is one of the laws of mixture of gases and vapors. 

A second law is that the presence of a foreign gaseous substance in con- 
tact with the surface of a solid or liquid does not affect the density of the 
vapor of that sohd or liquid unless there is a tendency to chemical com- 
bination between the two substances, in which case the density of the 
vapor is shghtly increased. (Rankine, S. E., p. 239.) 

If 0.0591 lb. of air, = 1 cu. ft. at 212° and atmospheric pressure, is con- 
tained in a vessel of 1 cu. ft. capacity, and water at 212° is introduced, 
heat at 212° being furnished by a steam jacket, the pressure will rise to 
two atmospheres. 

If air is present in a condenser along with water vapor, the pressure is 
that due to the temperature of the vapor plus that due to the quantity of 
air present. 

Flow of Gases. — By the principle of the conservation of energy, it 
may be shown that the velocity with which a gas under pressure will 
escape into a vacuum is inversely proportional to the square root of its 
density; that is, oxygen, which is sixteen times as heavy as hydrogen, 
would, under exactly the same circumstances, escape through an opening 
only one fourth as fast as the latter gas. 

Absorption of Gases by Liquids. — Many gases are readily absorbed 
by water. Other liquids also possess this power in a greater or less 
degree. Water will, for example, absorb its own volume of carbonic-acid 
gas, 800 times its volume of ammonia, 2V3 times its volume of chlorine, 
and only about V20 of its volume of oxygen. 

The weight of gas that is absorbed by a given volume of liquid is pro- 
portional to the pressure. But as the volume of a mass of gas is less as 
the pressure is greater, the volume which a given amount of liquid can 
absorb at a certain temperature will be constant, whatever the pressure. 
Water, for example, can absorb its own volume of carbonic-acid gas at 
atmospheric pressure; it will also dissolve its own volume if the pressure 
is twice as great, but in that case the gas will be twice as dense, and con- 
sequently twice the weight of gas is dissolved. 

Liquefaction of Gases. — Liquid Air. (A. L. Rice, Trans. A.S.M. E., 
xxi, 156.)— Oxygen was first liquefied in 1877 by Cailletet and Pictet, 
working independently. In 1884 Dewar liquefied air, and in 1898 he 
liquefied hydrogen at a temperature of - 396.4° F., or only 65° above the 
absolute zero. The method of obtaining the low temperatures required 
for liquefying gases was suggested by Sir W. Siemens, in 1857. It consists 
in expanding a compressed gas in a cylinder doing work, or through a 
small orifice, to a lower pressure, and using the cold gas thereby produced 
to cool, before expansion, the gas coming to the apparatus. Hampson 
claims to have condensed about 1.2 quarts of liquid air per hour at an 



606 



Atn. 



expenditure of 3.6 H.P. for compression, using a pressure of 120 atmos- 
pheres expanded to 1, and getting 6.6 per cent of the air handled as 
liquid. 

The follo^i^nng table gives some physical constants of the principal gases 
that have been liquefied. The critical temi^erature is that at which the 
properties of a liquid and its vapor are indistinguishable, and above wnich 
the vapor cannot be liquefied by compression. The critical pressure is 
the pressure of the vapor at the critical temperature. 







Criti- 
cal 
Temp. 
Deg. F. 


Criti- 
cal 

Pres- 
sure in 

Atmo- 
spheres 


Temp. 

of 
Satu- 
rated 
Vapor 

at 
Atmos. 
Pres- 
sure 
Deg. F. 


Freez- 
ing 
Point. 
Deg. F. 


Density of 

Liquid at 

Temperature 

Given. 


Water.. 


NH4 

C2H2 

CO2 

C2H4 

CH4 

C2 

A 
CO 

N2 
H2 


689 
266 

98.6 

88 

50 

—115.2 

—182 

—185.8 
-219.1 
-220 

-231 
—389 


200 

115 

........ 

51.7 
54.9 

50.8 

50.6 
35.5 
39 

35 
20 


212 
— 27 
—121 
—112 
—150 

-263.4 

—294.5 

—304.6 

—310 

—312.6 

—318 
—405 


32 
—107 
—113.8 
— 69 

—272 

—302.4 

—309.3 
—340.6 

—353.2 


1 at 39° F. 


Ammonia 


0.6364 at 32° F. 






Carbon Dioxide 


0.83 at 32° F. 


Methane 


0.415 \ 

at -263° F. ( 

1.124 \ 

\ at -294° F. f 

( about 1.5 

(at -305° F. . 


Oxygen 


Argon 


Carbon Monoxide.. 
Air 


( 0.933 ) 
iat-313°F.( 
0.885 ) 
Iat-318°F. 


Nitroffcn 


Hydrogen 



AIR. 

Properties of Air. — Air is a mechanical mixture of the gases oxygen 
and nitrogen, with about 1 % by volume of argon. Atmospheric air of 
ordinary purity contains about 0.04% of carbon dioxide. The com- 
position ofairjsvariously given as follows : 





By Volume. 


By Weight. 




N 





Ar 


N 





Ar 


1 


79.3 
79.09 
78.122 
78.06 


20.7 
20.91 
20.941 
21. 




77 

76.85 
75.539 
75.5 


23 

23.15 
23.024 
23.2 




2 


" 6:937' ■ 
0.94 




3 


1.437 


4 


1.3 



(1) Values formerly given in works on physics. (2) Average results 
of several determinations, Hempel's Gas Analysis. (3) Sir. Wm. Ram- 
say, Bull. U. S. Geol. Survey, No. 3.30. (4) A. Leduc, Comptes Rendus, 
1896. Jour. F. /., .Tan., 1898. Leduc gives for the density of oxygen 
relatively to air 1.10523; for nitrogen 0.9671; for argon, 1.376. 

The weight of pure air at 32° F. and a barometric pressure of 29.92 
inches of mercury, or 14.6963 lbs. per sq. in., or 2116.3 lbs. per sq. ft., is 
0.080728 lb. per cubic foot. Volume of 1 lb. = 12.387 cu. ft. At any 
other temperature and barometric pressure its weight in lbs. per cubic 

1 QpKO Ny' D 

foot is W= 459 6 4- r ' where B = height of the barometer, T = tem- 
perature Fahr., and 1.3253 = weight in lb. of 459.6 cu. ft. of air at 0° F. 
and one inch barometric pressure. Air expands 1 /49 1.6 of its volume at 



AIB. 



607 



32° P. for every increase of 1° F., and its volume varies inversely as the 
pressure. 

Conversion Table for Air Pressures. 



















^S 




li 


4 


M 










ki 




d^ 


^^ 


ss 




^^ 


3^ 




li 


1 lb. per sq. ft.. 


1 


0.19245 


V9 


0.1604 


0.01414 


Vl44 


13.14 


29.1 


I in. water at 


















62° F 


5.196 


1 


0.5774 


Vn 


0.07347 


0.036085 


68.30 


66.3 


1 oz. per sq. in . . 


9 


1.732 


1 


0.1443 


0.1272 


Vl6 


118.3 


87.2 


1 ft. water at 


















62° F 


62.355 


12 


6.928 


1 


0.8816 


0.43302 


819.6 


230 


1 in. mercury at 


















32° F 


70.73 


13.612 


7.859 


1.1343 


1 


0.49117 


929.6 


245 


1 lb. per sq. in . . 


144 


27.712 


16 


2.3094 


2.036 


1 


1893 


349 


1 atmosphere. . . 


2116.3 


407.27 




33.94 


29.921 


14.6963 


27,815 


1338 


(I) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


(8) 


(9) 



The figures in column (8) show the head in feet of air of uniform 
density at atmospheric pressure and 62° F. corresponding to the pres- 
sure in the preceding columns, and those in column (9) the theoretical 
velocities corresponding to these heads, or the velocities of a j[et flowing 
from a frictionless conical orifice whose flow coeflQcient is imity. 

The Air-manometer consists of a long, vertical glass tube, closed at 
the upper end, open at the lower end, containing air, provided with a 
scale, and immersed, along with a thermometer, in a transparent hquid, 
such as water or oil, contained in a strong cylinder of glass, which com- 
municates with the vessel in which the pressure is to be ascertained. 
The scale shows the volume occupied by the air in the tube. 

Let vq be that volume, at the temperature of 32° Fahrenheit, and mean 
pressure of the atmosphere, po ; let vi be the volume of the air at the 
temperature t, and under the absolute pressm'e to be measured pi ; then 
_ At + 459.6) poVo 
^^~ 491.6 i;i 

Pressure of the Atmosphere at Different Altitudes. 

At the sea level the pressure of the air is 14.7 pounds per square inch; at 
1/4 of a mile above the sea level it is 14.02 pounds; at 1/2 mile, 13.33; at 
3/4 mile, 12.66; at 1 mile, 12.02; at 1 1/4 mile, 11.42; at II/2 mile, 10.88; and 
at 2 miles, 9.80 pounds per square inch. For a rough approximation we 
may assume that the pressure decreases 1/2 pound per square inch for 
every 1000 feet of ascent. (See table, p. 608.) 

It is calculated that at a height of about 31/2 miles above the sea level 
the weight of a cubic foot of air is only one-half what it is at the surface of 
the earth, at seven miles only one-fourth, at fourteen miles only one- 
sixteenth, at twenty-one miles only one sixty-fourth, and at a height of 
over forty-five miles it becomes so attenuated as to have no appreciable 
weight. 

The pressure of the atmosphere increases with the depth of shafts, equal 
to about one inch rise in the barometer for each 900 feet increase in depth: 
this may be taken as a rough-and-ready rule for ascertaining the depth of 
shafts. 

Leveling by the Barometer and by Boiling Water. (Trautwine.) 
— Many circumstances combine to render the results of this kind of 
leveUng unreUable where great accuracy is required. It is difficult to 
read off from an aneroid (the kind of barometer usually employed for 
engineering purposes) to within from two to five or six feet, depending on 
its size. The moisture or dryness of the air affects the results; also winds, 
the vicinity of mountains, and the daily atmospheric tides, which cause 
incessant and irregular fluctuations in the barometer. A barometer 
hanging quietly jn a room will often vary Vip of an inch within Sk few 



608 



AIB. 



hours, corresponding to a difference of elevation of nearly 100 feet. 
No formula can be devised that shall embrace these sources of error. 
Boiling Point of Water. — Temperature in degrees F., barometer in 
in. of mercury. 



In. 


.0 


.1 


.2 


.3 


.4 


.5 


.6 


.7 


.8 


.9 


28 
29 
30 


208.7 
210.5 
212.1 


208.9 
210.6 
212.3 


209.1 
210.8 
212.4 


209.2 
210.9 
212.6 


209.4 
211.1 
212.8 


209.5 
211.3 
212.9 


209.7 
211.4 
213.1 


209.9 
211.6 
213.3 


210.1 
211.8 
213.5 


210.3 
212.0 
213.6 



To Find the Difference in Altitude of Two Places. — Take from the 
table the altitudes opposite to the two boiling temperatures, or to the two 
barometer readings. Subtract the one opposite the lower reading from 
that opposite the upper reading. The remainder will be the required 
height, as a rough approximation. To correct this, add together the 
two thermometer readings, and divide the sum by 2, for their mean. 
From table of corrections for temperature, take the number under this 
mean. Multiply the approximate height just found by this number 

At 70° F. pure water will boil at 1° less of temperature for an average of 
about 550 feet of elevation above sea level, up to a height of 1/2 a mile. 
At the height of 1 mile, 1° of boiling temperature will correspond to anout 
560 feet of elevation. In the table the mean of the temperatures at the 
two stations is assumed to be 32° F., at which no correction for temperature 
is necessary in using the table. 



Boiling. 

point 
in Deg. 

Fahr. 




Altitude 
above 

Sea level. 
Feet. 


Boiling- 
point 

in Deg. 
Fahr. 


L 

PQ 


Altitude 
above 

Sea level. 
Feet. 


Boiling- 
point 

in Deg. 
Fahr. 


pq 


Altitude 
above 

Sea level. 
Feet. 


184° 


16.79 


15,221 


196 


21.71 


8.481 


208 


27.73 


2,063 


185 


17.16 


14,649 


197 


22.17 


7,932 


208.5 


28.00 


1,809 


186 


17.54 


14,075 


198 


22.64 


7,381 


209 


28.29 


1,539 


187 


17.93 


13,498 


199 


23.11 


6,843 


209.5 


28.56 


1,290 


188 


18.32 


12,934 


200 


23.59 


6,304 


210 


28.85 


1,025 


189 


18.72 


12,367 


201 


24.08 


5,764 


210.5 


29.15 


754 


190 


19.13 


11,799 


202 • 


24.58 


5,225 


211 


29.42 


512 


191 


19.54 


11,243 


203 


25.08 


4,697 


211.5 


29.71 


255 


192 


19.96 


10,685 


204 


25.59 


4,169 


212 


30.00 


S.L.= 


193 


20.39 


10.127 


205 


26.11 


3,642 


212.5 


30.30 


-261 


194 


20.82 


9,579 


206 


26.64 


3,115 


213 


30.59 


-511 


195 


21.26 


9,031 


207 


27.18 


2,589 















Corrections for Temperature. 



Mean temp. F. in shade 
Multiply by ^933 



10' 
.954 



30* 
.996 



40< 
1.016 



50° 
1.036 



60' 
1.058 



70* 
1.079 



1.100 



90° 
1.121 



100° 
1.142 



Pressure of the Atmosphere per Square Inch and per Square Foot 
at Various Readings of the Barometer. 

^ Rule. — Barometer in inches X 0.4916 = pressure per square inch; 
pressure per square inch X 144 = pressure per square foot. 



Barometer. 


Pressure 
per Sq. In. 


Pressure 
per Sq. Ft. 


Barometer. 


Pressure 
per Sq. In. 


Pressure 
per Sq. Ft. 


In. 


Lb. 


Lb.* 


In. 


Lb. 


Lb.* 


[28.00 


13.75 


1980 


29.75 


14.61 


2104 


28.25 


13.88 


1998 


30.00 


14.73 


2122 


28.50 


14.00 


2016 


30.25 


14.86 


2140 


28.75 


14.12 


2033 


30.50 


14.98 


2157 


29.00 


14.24 


2051 


30.75 


15.10 


2175 


29.25 


14.37 


2069 


31.00 


15.23 


2193 


29.50 


14.49 


2086 









„ , * Decimals omitted. 

For lower pressures see table of the Properties of Steam 



AIK. 



609 



Barometric Readings corresponding witli Different 
Altitudes, in Frencli and Englisli Measures. 



Alti- 
tude, 


Read- 




Reading 




Reading 




Reading 


ing of 


Altitude. 


of 


Alti- 


of 


Altitude. 


of 


Barom- 




Barom- 


tude, 


Barom- 




Barom- 




eter. 




eter. 




eter. 




eter. 


meters 


mm. 


feet. 


inches. 


meters. 


mm. 


feet. 


inches. 





762 


0. 


30. 


1147 


660 


3763.2 


25.98 


21 


760 


68.9 


29.92 


1269 


650 


4163.3 


25.59 


127 


750 


416.7 


29.52 


1393 


640 


4568.3 


25.19 


234 


740 


767.7 


29.13 


1519 


630 


4983 . 1 


24.80 


342 


730 


1122.1 


28.74 


1647 


620 


5403.2 


24.41 


453 


720 


1486.2 


28.35 


1777 


610 


5830.2 


24.01 


564 


710 


1850.4 


27.95 


1909 


600 


6243. 


23.62 


678 


700 


2224.5 


27.55 


2043 


590 


6702.9 


23.22 


793 


690 


2599.7 


27.16 


2180 


580 


7152.4 


22.83 


909 


680 


2962.1 


26.77 


2318 


570 


7605.1 


22.44 


1027 


670 


3369.5 


26.38 


2460 


560 


8071. 


22.04 



Weight of Air per Cubic Foot at Different Pressures and 
Temperatures. 

Formula: W = 0.080728 X ^j^g X y|^ 



Tempera- 
ture 



Beg. 
F. Ab. 



459, 
491, 
501. 
511. 
521. 
529. 
539. 
549 



Gage. 



P = 

14.6963 



086349 

080728 

6.079119: 

6.077572 



I 

P= 
15.696 



2 

P = 
16.696 



5 

P = 
19.696 



100 559. 

120 579 

140 599 

160 619 

180 I 639 

200 i 659 

250 709 

300 759. 6|. 032245 

350 ! 809.6.049019 



076085 
074936 
073547 
072209 
070918 
6|. 068471 
6.066187 
6.064051 
6.062048 
6.060167 
61.055927 



400 
450 
500 
550 
600 
650 
700 
800 
900 
1000 



859 
909 
959 
1009 
1059 
1109 
1159 
1259. 
1359 
1459 



.046168 

043630 

041357 

039309 

61.037454 

6.035766 

6.034224 

6.031507 

6.029190' 

61.027190' 



.09222 
.08622 
, 08450 
, 08285 
08126 
08004 
07855 
07712 
07574 
07313 
07069 
06841 
06627 
06426 
05973 
05580 
05236 
04931 
04660 
04417 
04198 
04000 
03820 
03655 
03365 
03118 
,02904 



09810 
09171! 
08989 
08813 
.08644 
.08513 
.08356 
.08204 
.08057 
.07779 
.075^19 
.07277 
.07049 
. 06835 
.06354 
.05936 
.05569 
. 05245 
.04957 
.04699 
. 04466 
. 04255 
.04063 
. 03888 
.03579 
.03316 
.03089 



.11573 
.10819 
.10604 
.10396 
.10197 
. 10043 
.09857 
.09678 
.09504 
.09177 
.08871 
.08584 
.08316 
.08064 
.07496 
.07002 
.06570 
.06188 
.05847 
.05543 
.05268 
.05020 
.04793 
.04587 
.04223 
.03912 
.03644 



10 

P = 
24.696 



.14511 
.13566 
13295 
13035 
12786 
12592 
12359 
12134 
11937 
11506 
11122 
10763 
10427 
10111 
09398 
08779 
08237 
07758 
07332 
06950 
06606 
06294 
06010 
05751 
05294 
04905 
04569 



20 

P = 
34.696 



.20385 
.19059 
.18679 
.18314 
.17963 
.17691 
.17364 
.17048 
.16743 
.16165 
.15626 
.15122 
.14649 
.14205 
.13204 
.12335 
.11573 
. 10900 
.10301 
.09764 
.09280 
.08842 
. 08444 
.08080 
.07438 
.06891 
.06419 



40 

P = 

54.696 



32137 
30045 
29446 
28871 
28317 
27887 
27372 
26874 
26394 
25483 
24633 
23838 
23093 
22393 
20815 
19445 
18244 
17183 
16238 
15392 
14630 
13939 
13311 
12737 
11726 
10864 
10119 



60 80 100 

P= I p= p = 
74.69694.696114.696 



43888 
41031 
40213 
39427 
38671 
38087 
37381 
36701 
36045 
34802 
33641 
32555 
31537 
30581 
28426 
26555 
24915 
23466 
22176 
21020 
19979 
19037 
18179 
17395 
16014 
14836 
13830 



55639 
52017 
50980 
49984 
49026 
48285 
47390 
46528 
45697 
44120 
42648 
41272 
39981 
38769 
36037 
33665 
31586 
29748 
28113 
26648 
25329 
24133 
23046 
22052 
20301 
18808 
17519 



.67391 
.63004 
.61748 
.60541 
.59380 
.58483 
.57399 
.56355 
.55348 
.53438 
.51656 
.49988 
.48425 
.46957 
.43649 
.40775 
.38257 
.36032 
.34051 
.32277 
.30678 
.2923C 
.27913 
.26710 
.24589 
.22781 
.21220 



120 

P = 

134.696 



.79141 
.73990 
.72515 
.71097 
.69734 
.68681 
.67408 
.66182 
.64999 
.62756 
.60663 
.58705 
.56869 
.55145 
.51259 
.47885 
.44925 
.42314 
.39988 
.37905 
.36028 
.34327 
.32781 
.31367 
.28877 
.26753 
.24920 



Moisture in the Atmosphere. — Atmospheric air always contains a 
small quantity of carbonic acid (see Ventilation), and a varying quantity 
of aqueous vapor or moisture. The relative humidity of the air at any time 
is the percentage of moisture contained in it as compared with the amount 
it is capable of holding at the same temperature. 

The degree of saturation or relative humidity of the air is determined 
bv the use of the dry and wet bulb thermometer. The degree of satura- 
tion for a number of different readings of the thermometer is given in 



610 



AIR. 



the following table, condensed from the Hygrometric Tables of the 
U. S. Weather Bureau: 

Relative Humidity, Per Cent. 



H c bo 



Difference between the Dry and Wet Thermometers, Deg. F. 

I| 2| 3| 4| 5| 6| 71 81 9|I0|1 1| 121l3H4il5|16|l7[18|l9|20|21|22|23|24|26|28|30 

Relative Humidity, Saturation being 100. (Barometer = 30 in.) 



32 
40 
50 
60 
70 
80 
90 
100 
110 
120 
140 



89179 6959 49 39 30 20 II 2 1 

92,83 75 68 60 52 45 37 29'23| 151 71 0! | 

93 87 80 74 67 6155 49 43 38 32 27 21 16 111 5 

94 89 83 78 73 68 63 58 53 48 43 39 34 30 26 21117 13 9 5 1 
95|90 86 81 77 72 68 64 59 55 51 48 44 40 36 33 29 25 22 19 15|12 
96 91 87 83 79 75 72 68 64 61 57 54 50 47 44 41 38 35 32 29 26 23 20 18 12 
96 92 89 85 81 78 74 71 68 65 61 58 55 52 49 47 44 41 39 36 34 31 29 26 22 17 13 

96 93 89 86 83 80 77 73 70 68 65 62 59 56 54 51 49 46 44 41 39 37 35 33 28 24:21 

97 93 90 87 84 81 78 75 7370 67 65 62 60 57 55 52 50 48 46 44 42 40 38 34 30 26 
9794 91 88 85 82 80 77 74 72 69 67 65 62 60 58 55 53 51 ,49 47i45i43j41 38 34|3I 
97195,92,89 87 84 82 79 77175 7370 68 66 64,62 60 58,56,54:53151 |49|47i44:4l|38 



Mixtures of Air and Saturated Vapor, 

(From Goodenough's Tables.) 




10 
20 
32 
35 
40 
45 
50 
55 
60 
65 
70 
75 
80 
85 
90 
95 
100 
105 

no 

115 
120 
130 
140 
150 
160 
170 
180 
190 
200 



Pressure of 

Saturated 

Vapor. 



In., 

Mer- 
cury. 



Lb. per 

Sq. In. 



Weight of 

Saturated 

Vapor. 



Per Cu. 
Ft. 



Per Lb. 
of 

Dry Air. 



Volume 
in Cu. Ft. 



0.0375 


0.0184 


.0628 


.0308 


.1027 


.0504 


.1806 


.0887 


.2036 


.1000 


.2478 


.1217 


.3003 


.1475 


.3624 


.1780 


.4356 


.2140 


.5214 


.2561 


.6218 


.3054 


.7386 


.3628 


.8744 


.4295 


1.0314 


.5066 


1.212 


.5955 


1.421 


.6977 


1.659 


.8148 


1.931 


.9486 


2.241 


1.1010 


2.594 


1.274 


2.994 


1.470 


3.444 


1.692 


4.523 


2.221 


5.878 


2.887 


7.566 


3716 


9.649 


4.739 


12.20 


5.990 


15.29 


7.51 


19.01 


9.34 


23.46 


11.53 



0.0000674 
.0001103 
.000177 
.000303 
.000340 
.000410 
.000492 
.000588 
.000699 
.000829 
.000979 
.001153 
.001352 
.001580 
.001841 
.002137 
.002474 
.002855 
.003285 
.003769 
.004312 
.004920 
.006356 
.008130 
.01030 
.01294 
.01611 
.01991 
.02441 
.02972 



0.000781 
.001309 
.002144 
.003782 
.004268 
.005202 
.00632 
.00764 
.00920 
.01105 
.01323 
.01578 
.01877 
.02226 
.02634 
.03109 
.03662 
.04305 
.0505 
.0593 
.0694 
.0813 
.1114 
.1532 
.2122 
.2987 
.4324 
.6577 

1.0985 

2.2953 



1 Lb. Ib.Dryb^p^ 
Dry Air + H5o 
Air. Vapor, (r^ 



11.58 
11.83 
12.09 
12.39 
12.47 
12.59 
12.72 
12.84 
12.97 
13.10 
13.22 
13.35 
13.48 
13.60 
13.73 
13.86 
13.98 
14.11 
14.24 
14.36 
14.49 
14.62 
14.88 
15.13 
15.39 
15.64 
15.90 
16.16 
16.41 
16.67 



Of one 



5" 

h-3 o 



11.59 
11.86 
12.13 
12.47 
12.55 
12.70 
12.85 
13.00 
13.16 
13.33 
13.50 
13.69 
13.88 
14.09 
14.31 
14.55 
14.80 
15.08 
15.39 
15.73 
16.10 
16.52 
17.53 



0.0 
2.411 
4.823 
7.716 
8.44 
9.65 
10.86 
12.07 
13.28 
14.48 
15.69 
16.90 
18.11 
19.32 
20.53 
21.74 
22.95 
24.16 
25.37 
26.58 
27.79 
29.00 
31.42 
18.8433.85 
20.601 36.27 
23.09 38.69 



26.84 
33.04 
45.00 



41.12 
43.55 
45.97 



77.24:48.40 



op 



S> 



0.964 
1.608 
2.623 
4.058 
4.57 
5.56 
6.73 
8.12 
9.76 
11.69 
13.96 
16.61 
19.71 
23.31 
27.51 
32.39 
38.06 
44.63 
52.26 
61.11 
71.40 
83.37 
113.64 
155.37 
214.03 
299.55 
431.2 
651.9 
1082.3 
2247.5 






Q>2 



0.964 
4.019 
7.446 
11.783 
13.02 
15.21 
17.59 
20.19 
23.04 
26.18 
29.65 
33.51 
37.81 
42.64 
48.04 
54.13 
61.01 
68.79 
77.63 
87.69 
99.10 

112.37 

145.06 

189.22 

250.3 

338.2 

472.3 

695.5 
1128.3 
2296 



^iRy\? ^ F. the pressure of saturated vapor in contact with ice is 
rJw QoX^i^^l^V^^.^^s^ce P"in do not include the heat of the liquid, 
ueiow ,i2 b . the heat of sublimation of ice rather than the latent heat of 
vaporization is used. 



AIR. 611 

Moisture In Afr at Different Pressures and Temperatures. (H. M, 

Prevost Murphy, Eng. News, June 18, 1908.) — 1. The maximum amount 
of moisture that pure air can contain depends only on its temperature 
and pressure, and has an unvarying value for each condition. 

2. The higher the temperature of the air, the greater is the amount 
of moisture that it can contain. 

3. The higher the pressure of the air, the smaller is the amount of 
moisture that it can contain. 

4. When air is compressed, the rise of temperature due to the com- 
pression, in all cases found in practice, far more than offsets the opposite 
effect of the rise of pressure on the moisture-carrying capacity of the air. 
Water is deposited, therefore, by compressed air as it passes from the com- 
pressor to the various portions of the system. 

Suppose that a certain amount of atmospheric air enters a compressor 
and that it contains all the moisture possible at the existing outside tem- 
perature and pressure. As this air is compressed its moisture-carrying 
capacity rapidly increases, consequently all the moisture is retained by 
the air and passes with it into the main or storage reservoir. Now if 
this air is permitted to pass from the reservoir into the various parts of 
the system before being cooled to the outside temperature, it will carry 
more moisture than it is capable of holding when the temperature 
finally drops to the normal point, and this excess quantity will be de- 
posited, because, the pressure being high, the air cannot hold as much 
moisture as it did at the same temperature and only atmospheric pressure. 

In order to reduce the moisture to a minimum, it is desirable to cool 
the air to the outside temperature before it leaves the reservoir, thereby 
causing it to deposit all of its excess moisture, which may be easily removed 
by drain cocks. 

Although compressed air may be properly dried before leaving the 
main reservoirs, some moisture may be temporarily deposited when the 
air is subsequently expanded to lower pressures, as its moisture-carry- 
ing capacity is usually affected more by the drop in temperature, result- 
ing from the expansion, than by the drop in pressure, but when the air 
again attains the outside temperature, the moisture thus deposited will 
be re-absorbed if it is freely exposed to the compressed air. 

In order to determine what percentage of moisture pure air can contain 
at various pressures and temperatures, to ascertain how low the "rela- 
tive humidity" of the atmosphere must be in order that no water will be 
deposited in any part of a compressed-air system and also to find to what 
temperature air drawn from a saturated atmosphere must be cooled in 
order to cause the deposition of moisture to commence, the follo\ving 
formulae and tables are used, based on Dalton's law of gaseous pressures, 
which may be stated as follows: 

The total pressure exerted against the interior of a vessel by a given 
quantity of a mixed gas enclosed in it is the sum of the pressures which 
each of the component gases, or vapors, would exert separately if it were 
enclosed alone in a vessel of the same bulk, at the same temperature. 
[The derivation of the formulae is given at length in the original paper.] 

Formulae for the Weight, in Lbs., of 1 Cu. Ft. of Dry Air, of 1 Cu. 
Ft. of Saturated Steam or Water Vapor and the Maximum Weight 
of Water Vapor that 1 Lb. of Pure Air Can Carry at Any Pressure 
and Temperature. (Copyright, 1908, by H. M. Prevost Murphy.) 
The values K and H being given in the table for various temperatures, 

f, in Fahrenheit degrees, the formulae are: 

Weight of 1 cu. ft. saturated steam = ^'459^2+^^ ' 

H = elastic force or tension of water vapor or saturated steam, in in. of 
mercury corresponding to the temperature t (Fahr.) = 2.036 X (gauge pres- 
sure 4- atmospheric pressure, in pounds per square inch). 

K = the ratio of the weight of a volume of saturated steam to an equal 
volume of pure dry air at the same temperature and pressure, 

Values of K and H corresponding to the various temperatures t ar« 
given in the table on p. 612. 



612 



AIR. 



^.,. <.. r.. -J— • 1.325271 M 2.698192 P 

Weight of 1 cu. ft. pure dry air = ^gg^ + f = 459.2 + f 

i\/ = absolute pressure in inches of mercury. 

P = absolute pressure in pounds per square inch. 

W = maximum weight, in lbs., of water vapor, that 1 lb. of pure air 
can contain, when the temperature of the mixture is t, and the total, 
or observed, absolute pressure in pounds per square inch is P, 

KH 
2.036 P- H' 

Note. — The results obtained by the use of any of the above formulae 
agree exactly with the average data for air and steam weights as given 
by the most reliable authorities and careful experiments, for all pres- 
sures and temperatures; the value of K being correct for all tempera- 
tures up to the critical steam temperature of 689° F. 

Values of "K" and "H" Corresponding to Tempeeatures t 
FROM - 30° TO 434° F. 



t 


K 


H 


t 


K 1 H 


t 


K H 


t 


K 


H 


t 


K 1 H 


-30 


.6082 


.0099 


64 


.61 88. 5962 


158 


.6323 9.177 


252 


.6501 


62.97 


344 


.6739' 254. 2 


-28 


.6084 


.0111 


66 


..6190 .6393 


160 


.6326,9.628 


254 


.6505 


65.21 


346 


.6745 261.0 


-26 


.6086 


.0123 


68 


.6193'. 6848 


162 


.6330 10.10 


256 


.6510 


67.49 


348 


.6751268.0 


-24 


.6088 


.0137 


70 


.61961.7332 


164 


.6333,10.59 


258 


.6514 


69.85 


350 


.6757 275.0 


-22 


.6090 


.0152 


72 


.6198'. 7846 


166 


.6336' 11. 10 


260 


.6518 


72.26 


352 


.6763 282.2 


-20 


.6092 


.0168 


74 


.6201 1.8391 


168|.6340;il.63 


262 


.6523 


74.75 


354 


.6770 289.6 


-18 


.6094 


.0186 


76 


.6203 .8969 


170 .6343 12.18 


264 


.6528 


77.30 


356 


.6776 297.1 


-16 


.6096 


.0206 


78 


.6206'. 9585 


172 .6346:12.75 


266 


.6532 


79.93 


358 


.6783 304.8 


-14 


.6098 


.0227 


80 


.6209 1.024 


174 .6350!l3.34 


268 


.6537 


82.62 


360 


.6789 312.6 


-12 


.6100 


.0250 


82 


.6211 1.092 


176 .6353 


13.96 


270 


.6541 


85.39 


362 


.6795 320.6 


-10 


.6102 


.0275 


84 


.6214-1.165 


1781.6357 


14.60 


272 


.6546 


88.26 


364 


.6803 328.7 


- 8 


.6104 


.0303 


86 


.6217 1.242 


180 '6360 


15.27 


274 


.6551 


91.18 


366 


.6809 337.0 


- 6 


.6107 


.0332 


88 


.6219 1.324 


182 .6364 


15.97 


276 


.6555 


94.18 


368 


.6816345.4 


- 4 


.6109 


.0365 


90 


.6222 1.410 


184 .6367 


16.68 


278 


.6560 


97.26 


370 


.68221354.0 


- 2 


.6111 


.0400 


92 


.62251. 501 


186 .6371 


17.43 


280 


.6565 


100.4 


372 


.6829 362.8 





.6113 


.0439 


94 .622711.597 


188 


.6374 


18.20 


282 


.6570 


103.7 


374 


.6836'371.8 


2 


.6115 


.0481 


96 .6230 1.698 


190 


.6377 


19.00 


284 


.6575 


107.0 


376 


.6843380.9 


4 


.6117 


.0526 


98 


.6233,1.805 


192 


.6381 


19.83 


286 


.6580 


110.4 


378 


.6850 390.2 


6 


.6120 


.0576 


100 


.6236 1.918 


194 


.6385 


20.69 


288 


.6584 


113.9 


380 


.6857 399.6 


8 


.6122 


.0630 


102 


.62382.036 


196 


.6389 


21.58 


290 


.6590 


117.5 


382 


.6865 409.3 


10 


.6124 


.0690 


104 


.6241:2. 161 


198 


.6393 


22.50 


292 


.6594 


121.2 


384 


.6871 419.1 


12 


.6126 


.0754 


106 


.6244 2.294 


200 


.6396123.46 


294 


.66C0 


125.0 


386 


.6879 429.1 


14 


.6128 


.0824 


108 


.6247 2.432 


202 


.640024.44 


296 


.6604 


128.8 


388 


.6886 439.3 


16 


.6131 


.0900 


110 


.62502.578 


204 


.6404 25.47 


298 


.6610 


132.8 


390 


.6893 449.6 


18 


.6133 


.0983 


112 


.62532.731 


206 


.640726.53 


300 


.6615 


136.8 


392 


.6901 460.2 


20 


.6135 


.1074 


114 


.6256,2.892 


208 


.6411 27.62 


302 


.6620 


141.0 


394 


.6908 470.9 


22 


.6137 


.1172 


116 


.62583.061 


210 


.6415:28.75 


304 


.6625 


145.3 


396 


.6915481.9 


24 


.6140 


.1279 


118 


.6261 3.239 


212 


.6419,29.92 


306 


.6631 


149.6 


398 


.6923:493.0 


26 


.6142 


.1396 


120 


.62643.425 


214 


.6423,31.14 


308 


.6636 


154.1 


403 


.6931504. 4 


28 


.6144 


.1523 


122 


.62673.621 


216 


.6426 32.38 


310 


.6641 


158.7 


402 


.6939515.9 


30 


.6147 


.1661 


124 


.6270 3.826 


218 


.6430 33.67 


312 


.6647 


163.3 


404 


.69471527.6 


32 


.6149 


.1811 


126 


.627314.042 


220 


.6434 35.01 


314 


.6652 


168.1 


406 


.6955 539.5 


34 


.6151 


.1960 


128 


.627614.267 


222 


.6438 36.38 


316 


.6658 


173.0 


408 


.6962*551.6 


36 


.6154 


.2120 


130 


.627914.503 


224 


.6442 37.80 


318 


.6663 


178.0 


410 


.6970 564.0 


38 


.6156 


.2292 


132 


.62824.750 


226 


.6446 


39.27 


320 


.6669 


183.1 


412 


.6979 576.5 


40 


.6158 


.2476 


134 


.6285; 5.008 


228 


.6451 


40.78 


322 


.6674 


188.3 


414 


.6987 589.3 


42 


.6161 


.2673 


136 .6288 5.280 


230 


.6455 


42.34 


324 


.6680 


193.7 


416 


.6995 602.2 


44 


.6163 


.2883 


138 


.6291] 5. 563 


232 


.6458 


43.95 


326 


.6686 


199.2 


418 


.7003615.4 


46 


.6166 


.3109 


140 


.6294 5.859 


234 


.6463 


45.61 


528 


.6691 


204.8 


420 


.7012628.8 


48 


.6168 


.3350 


142 


.6298 6.167 


236 


.6467 


47.32 


330 


.6697 


210.5 


422 


.7021 642.5 


50 


.6170 


.3608 


144 


.630116.490 


238 


.6471 


49.08 


332 


.6703 


216.4 


424 


.7029 656.3 


52 


.6173 


.3883 


146. 6304 6.827 


240 


.6475!50.89 


334 


.6709 


222.4 


426 


.7037 670.4 


54 


.6175 


.4176 


148 .63077.178 


242 


.6479152.77 


336 


.6715 


228.5 


428 


.7046 684.7 


56 


.6178 


.4490 


150 .6310 7.545 


244 


.6484 54.69 


3^8 


.6721 


234.7 


430 


.7055 699.2 


58 


.6180 


.4824 


152 .6313 7.929 


246 


.6488 56.67 


340 


.6727 


241.1 


432 


.7064713.9 


60 


.6183 


.5180 


154 .6317 8.328 


248|. 6492 58.71 


342 


.6733 


247.6 


434 


.7073 728.9 


62 


.6185 


.5559 


1561.6320 8.744 


2501.6496 60.81 













AIR. 



613 



Weights in Pounds, of Pure Dry Air, Water Vapor and Saturated 

Mixtures of Air and Water Vapor at Various Temperatures, at 

Atmosptieric Pressure, 29.921 In. of Mercury or 14.6963 

Lb. per Sq. In. Also tlie Elastic Force or Pressure 

of the Air and Vapor Present in Saturated 

Mixtures. 

(Copyright, 1908, by H. M. Prevost Murphy.) 





Weight of One 
Cubic Foot of 
PureDry Air, Lb. 


Saturated Mixtures of Air and Water Vapor. 


Temperatures 

in Fahrenheit 

Degrees. 


Elastic Force 
of the Vapor, 
In. of Mercury. 


Elastic Force 
of the Air 

alone, when 
Saturated, Ins. 

of Mercury. 


Weight of the 
Vapor in I Cu. 
Ft. of the Mix- 
ture, or Wt. of 1 
Cu. Ft. of Satu- 
rated Steam. 











0.086354 


0.0439 


29.877 


0.000077 


0.086226 


0.086303 


0.000898 


12 


0.084154 


0.0754 


29.846 


0.000130 


0.083943 


0.084073 


0.001548 


22 


0.082405 


0.1172 


29.804 


0.000198 


0.082083 


0.082281 


0.002413 


32 


0.080728 


0.1811 


29.740 


0.000300 


0.080239 


0.080539 


0.003744 


42 


0.079117 


0.2673 


29.654 


0.000435 


0.078411 


0.078846 


0.005554 


52 


0.077569 


0.3883 


29.533 


0.000621 


0.076563 


0.077184 


0.008116 


62 


0.076081 


0.5559 


29.365 


0.000874 


0.074667 


0.075541 


0.011709 


72 


0.074649 


0.7846 


29.136 


0.001213 


0.072690 


0.073903 


0.016691 


82 


0.073270 


1.092 


28.829 


0.001661 


0.070595 


0.072256 


0.023526 


92 


0.071940 


1.501 


28.420 


0.002247 


0.068331 


0.070578 


0.032877 


102 


0.070658 


2.036 


27.885 


0.002999 


0.065850 


0.068849 


0.045546 


112 


0.069421 


2.731 


27.190 


0.003962 


0.063085 


0.067047 


0.062806 


122 


0.068227 


3.621 


26.300 


0.005175 


0.059970 


0.065145 


0.086285 


132 


0.067073 


4.750 


25.171 


0.006689 


0.056425 


0.063114 


0.118548 


142 


0.065957 


6.167 


23.754 


0.008562 


0.052363 


0.060925 


0.163508 


152 


0.064878 


7.929 


21.992 


0.010854 


0.047686 


0.058540 


0.227609 


162 


0.063834 


10.097 


19.824 


0.013636 


0.042293 


0.055929 


0.322407 


172 


0.062822 


12.749 


17.172 


0.016987 


0.036055 


0.053042 


0.471146 


182 


0.061843 


15.965 


13.956 


0.021000 


0.028845 


0.049845 


0.728012 


192 


0.060893 


19.826 


10.095 


0.025746 


0.020545 


0.046291 


1.25319 


202 


0.059972 


24.442 


5.479 


0.031354 


0.010982 


0.042336 


2.85507 


2I^ 


0.059079 


29.921 


0.000 


0.037922 


0.000000 


0.037922 


Infinite 



Applications of the Formulae and Tables. 

Example 1. — How low must the relative humidity be, when the at- 
mospheric pressure is 14.7 lb. per sq. in. and the outside temperature is 
60°, in order that no moisture may be deposited in any part of a com- 
pressed air system carrying a constant gauge pressure of 90 lb. per sq. in? 

Ans. — The maximum amount of moisture that 1 lb. of pure air can 
contain at 90 lb. gauge, = 104.7 lb. (absolute pressure) and 60° F., is 
w ^g 0.6183 X 0.5180 n nm ^.n^ IH 

^ = 2.036P-H = 2.036X104.7-0.5180 = ^'^^^^^^ ^^' 

The maximum weight of moisture that 1 lb. of air can contain at 60° 
F. and 14.7 lb. (absolute pressure) is 

In order that no moisture may be deposited, the relative humidity 
must not be above 

(0.001506 -f- 0.01089) X 100 = 13.83%. 

Note. — Air is said to be saturated with water vapor when it contains 
the maximum amount possible at the existing temperature and pressure. 

Example 2. — When compressing air into a reservoir carrying a con- 
stant gauge pressure of 75 lb., from a saturated atmosphere of 14.7 lb. 
abs. press, and 70° F., to what temperature must the air be cooled after 
compression in order to cause the deposition of moisture to commence? 

Ans. — First find the maximum weight of moisture contained in 
1 lb. of pure air at 14.7 lb. pressure and 70° F. 



614 AIR. 

TTT gg 0.6196 X 0.7332 _nni^^ftiK 

^ = 2.036 P- if = 2.036 X 14.7 - 0.7332 " 0.015561b. 
The temperature to which the air must be cooled in order to cause 
the deposition of moisture may be found by placing this value of 0.01556 
together with P equal to 75 + 14.7 in the equation thus: 

n m "^f^fi = ^^ =: ^^ 

u.uiooQ 2.036 X 89.7 -if 182.63 - H 

2 842 
ov H — 7r-;TT-r^ — r— ^ . and the temperature which satisfies this equation 
O.Olooo + K 

is found by aid of the table [by trial and error] to be approximately 
129° F. 

Example 3, — When the outside temperature is 82° F., and the 
pressure of the atmosphere is 14.6963 lb. per sq. in., the relative humid- 
ity being 100%, how many cu. ft. of free air must be compressed 
and delivered into a reservoir at 100 lb. gauge in order to cause 1 lb. of 
water to be deposited when the air is cooled to 82° F.? 

Ans. — Weight of moisture mixed with 1 lb. of air at 82° F., and 
atmospheric pressure = 0.023526 lb. For 100 lb. gauge pressure, 
TTT _ KH _ 0.6211 X 1.092 _nnn9Qisih 

^ " 2.036 P-H ~ 2.036 X 114.6963 - 1.092 " ^'^^^^^^ ^^' 

Weight of moisture deposited by each lb. of compressed air = 0.023526 
— 0.002918 = 0.020608 lb. Each cu. ft. of the moist atmosphere con- 
tains 0.070595 lb. of pure air, therefore the number of cu. ft. that must 
be delivered to cause 1 lb. of water to be deposited is 

^ X ^ ^i,^no = 687.37 cu. ft. 



0.070595 ^ 0.020608 

Example 4. — Under the same conditions as stated in Example 3, 
what is the loss in volumetric efficiency of the plant when the excess 
moisture is properly trapped in the main reservoirs? 

Ans. — Before compression, each pound of air is mixed with 0.023526 
lb. of water vapor and the weight of 1 cu. ft. of the mixture is 0.072256 lb., 
consequently the volume of the mixture is 

1.023526 -f- 0.072256 = 14.165 cu. ft. 

For 100 lb. gauge pressure and 82° F. as shown in Example 3, 1 lb. 
of air can hold 0.002918 lb. of water in suspension, having deposited 
0.020608 lb. in the reservoir. The weight of 1 cu. ft. of water vapor at 
82° is 0.001661 lb., consequently by Dalton's law the volume of the mix- 
ture of 1 lb. of air and 0.002918 lb. of water vapor at 1001b. gauge press- 
ure is the same as that of the vapor or saturated steam alone; that is, 
0.002918 H- 0.001661 = 1.757 cu. ft. 

By Mariotte's law, the volume of the 1.757 cu. ft. of mixed gas at 
114.6963 lb. absolute when expanded to atmospheric pressure will be 

(114.6963 -5- 14.6963) X 1.757 = 13.712 cu. ft.; 
consequently the decrease of volume, that is, the loss of volumetric 
efiQciency, is 

14.165 - 13.712 = 0.453 cu. ft., or (0.453 -^ 14.165) X 100 = 3.2%. 

This example shows that, particularly in warm, moist climates, there 
Is a very appreciable loss in the efficiency of compressors, due to the 
condensation of water vapor. 

Specific Heat of Air at Constant Volume and at Constant Pressure. 

— Volume of 1 lb. of air at 32° F. and pressure of 14.7 lbs. per sq. in. = 
12.387 cu. ft. =a column 1 sq. ft. area X 12.387 ft. high. Raising tem- 
perature 1° F. expands it 1/492, or to 12.4122 ft. high, a rise of 0.02522 ft. 

Work done = 2116 lbs. per sq. ft. X .02522 = 53.37 foot-pounds, or 
53.37 -i- 778 = 0.0686 heat units. 

The specific heat of air at constant pressure, according to Regnault, is 
0.2375; but this includes the work of expansion, or 0.0686 heat units; hence 
the specific heat at constant volume = 0.2375 - 0.0686 = 0.1689. 

Ratio of specific heat at constant pressure to specific heat at constant 
volume = 0.2375 -r 0.1689 = 1.406. (See Specific Heat, p. 562.) 



FLOW OF AIR THROUGH ORIFICES. 615 

Flow of Air through Orifices. — 'ine ineoreiicai velocity in fee t per 
second of Jow of any fluid, liquid, or gas through an orifice is v = "^2 gh 
= 8.02 V/i, in which h = the " head " or height of the fluid in feet required 
to produce the pressure of the fluid at the level of the orifice. (For gases 
the formula holds good only for smali difference of pressure on the two 
sides of the orifice.) The quantity of flow in cubic feet per second is equal 
to the product of this velocity by the area of the orifice, in square feet, 
multiplied by a "coefficient of flow," which takes into account the con- 
traction of the vein or flowing stream, the friction of the orifice, etc. 

For air flowing through an orifice or short tube, from a reservoir of the 
pressure pi into a reservoir of the pressure p2, Weisbach gives the following 
values for the coefficient of flow, obtained from his experiments. 

Flow of Air through an Orifice. 
Coefficient c in formula v= c \/2gh 
Diam. 1 cm. = 0.394 in.: 

Ratio of pressures .. . 1.05 1.09 1.43 1.65 1.89 2.15 

Coefficient 555 .589 .692 .724 .754 . 788 

Diam. 2.14 cm. = 0.843 in.: 

Ratio of pressures .. . 1.05 1.09 1.36 1.67 2.01 

Coefficient 558 .573 .634 .678 .723 

Flow of Air through a Short Tube. 
Diam. 1 cm*, = 0.394 in., length 3 cm. = 1.181 in. 

Ratio of pressures pi -^p2. . . 1.05 1.10 1.30 

Coefficient 730 .771 .830 

Diam. 1.414 cm. = 0.557 in., length 4.242 cm. = 1.670 in.: 

Ratio of pressures 1.41 1 . 69 

Coefficient 813 .822 

Diam. 1 cm. = 0.394 in., length 1.6 cm. = 0.630 in. Orifice rounded: 

Ratio of pressures 1.24 1.38 1.59 1.85 2.14 ... 

Coefficient .979 .986 .965 .971 .978 ... 

Clark (Rules, Tables, and Data, p. 891) gives, for the velocity of flow 
of air through an orifice due to small differences of pressure, 

7 = cv/2ifx773.2x(:^4^^)x2^ 

in which V = velocity in feet per second; 2g = 64.4; h = height of the 
column of water in inches, measuring the difference of pressure; t = the 
temperature Fahr.; and p = barometric pressure in inches of mercury. 
773.2 is the volume of air at 32° under a pressure of 29.92 inches of mercury 
when that of an equal weight of water is taken as 1. 

For 62° F., the form_ula becomes V = 363 C ^h/p, and if p = 29.92 
inches, V = 66.35 C \^h. 

The coefficient of efflux C, according to Weisbach, is: 
For conoidal mouthpiece, of form of the contracted vein, 

with pressures of from 0.23 to 1.1 atmospheres C = 0.97 to 0.99 

Circular orifices in thin plates C = 0.56 to 79 

Short cylindrical mouthpieces C = 0.81 to 84 

Thesame rounded at the inner end C = 0.92 to 0.93 

Conical converging mouthpieces C = 0.90 to 0.99 

R. J. Durley, Trans. A. S. M. E., xxvii, 193, gives the following: 

Ine consideration of the adiabatic flow of a perfect gas through a 
rnctionless orifice leads to the equation 



= a/: 






W = weight of gas discharged per second in pounds. 
A = area of cross section of jet in square feet. 
Pi = pressure inside orifice in pounds per square foot. 
F2 = pressure outside orifice. 

Vi = specific volume of gas inside orifice in cu. ft. per lb. 
y — ratio of the specific heat at constant pressure to that at constant 
yolurqe. 



616 



AIR. 



For air, where y = 1.404, we have for a circular orifice of diameter d 
inches, the initial temperature of the air being 60° Fahr. (or 521° abs.), 



W= 0.000491 rf2Pi 



<{9r 



/P_2y.712 



KPJ 



(2) 



In practice the flow is not frictionless, nor is it perfectly adiabatic, 
and the amomit of heat entering or leaving the gas is not known. Hence 
the weight actually discharged is to be found from the formulas by in- 
troducing a coeflQcient of discharge (generally less than unity) depend- 
ing on the conditions of the experiment and on the construction of 
the particular form of orifice employed. 

If we neglect the changes of density and temperature occurring as 
the air passes through the orifice, we may obtain a simpler though 
approximate formula for the ideal discharge: 



W= 0.01369 rf 



o hp 



(3) 



in which d = diam. in inches, i = difference of pressures measured in 
inches of water, P = mean absolute pressure in lbs. per sq. ft., and T = 
absolute temperature on the Fahrenheit scale = degrees F. -F 461. In 
the usual case, in which the discharge takes place into the atmosphere, 
F is approximately 2117 pounds per square foot and 



W = 0.6299 



a^^[i 



(4) 



To obtain the actual discharge the values found by the formula are to be 
multipUed by an experimental coefiQcient C, values of which are given in 
the table below. 

Up to a pressure of about 20 ins. of water (or 0.722 lbs. per sq. in.) above 
the atmospheric pressure, the results of formulae (2) and (4) agree very 
closely. At higher differences of pressure divergence becomes noticeable. 

They hold good only for orifices of the particular form experimented 
with, and bored in plates of the same thickness, viz.: iron plates 0.057 in. 
thick. 

The experiments and curves plotted from them Indicate that: — 

(1) The coeflQcient for small orifices increases as the head increases, but 
at a lesser rate the larger the orjfices, till for the 2-in. orifice it is almost 
constant. For orifices larger than 2 ins. it decreases as the head increases, 
and at a greater rate the larger the orifice. 

(2) The coeflflcient decreases as the diameter of the orifice increases, and 
at a greater rate the higher the head. 

(3) The coeflBcient does not change appreciably with temperature 
(between 40° and 100° F.). 

(4) The coeflficient (at heads under 6 ins.) is not appreciably affected 
by the size of the box in which the orifice is placed if the ratio of the areas 
of the box and orifice is at least 20 : 1 . 

Mean Discharge in Pounds per Square Foot of Orifice per Second 
AS Found from Experiments. 



Diameter 
Orifice, 
Inches. 


1-inch 

Head 

Discharge 

per Sq. Ft. 


2-inch Head 
Discharge 
per Sq. Ft. 


3-inch Head 
Discharge 
per Sq. Ft. 


4-inch 

Head 

Discharge 

per Sq. Ft. 


5-inch 

Head 

Discharge 

per Sq. Ft. 


0.3125 


3.060 


4.336 


5.395 


6.188 


7.024 


0.5005 


3.012 


4.297 


5.242 


6.129 


6.821 


1.002 


3.058 


4.341 


5.348 


6.214 


6.838 


1.505 


3.050 


4.257 


5.222 


6.071 


6.775 


2.002 


2.983 


4.286 


5.284 


6.107 


6.788 


2.502 


3.041 


4.303 


5.224 


5.991 


6.762 


3.001 


3.078 


4.297 


5.219 


6.033 


6.802 


3.497 


3.051 


4.258 


5.202 


, 5.966 


6.814 


4.002 


3.046 


4.325 


5.264 


5.951 


6.774 


4.506 


3.075 


4.383 


5.508 


6.260 


7.028 



FLOW OF AIR IN PIPES. 



6W 



Coefficients of Dischaegb for Various Heads and Diameters of 

Orifice. 



Diameter 

of Orifice, 

Inches. 


1-inch 


2-inch 


3-inch 


4-inch 


5-inch 


Head. 


Head. 


Head. 


Head. 


Head. 


5/16 


0.603 


0.606 


0.610 


0.613 


0.616 


V2 


0.602 


0.605 


0.608 


0.610 


0.613 


1 


0.601 


0.603 


0.605 


0.606 


0.607 


IV2 


0.601 


0.601 


0.602 


0.603 


0.603 


2 


0.600 


0.600 


0.600 


0.600 


0.600 


21/2 


0.599 


0.599 


0.599 


0.598 


0.598 


3 


0.599 


0.598 


0.597 


0.596 


0.596 


31/2 


0.599 


0.597 


0.596 


0.595 


0.594 


4 


0.598 


0.597 


0.595 


0.594 


0.593 


41/2 


0.598 


0.596 


0.594 


0.593 


0.592 



Corrected Actual Discharge in Pounds per Secont) at 60° F. and 

14.7 Lbs. Barometric Pressure for Circular Orifices in 

Plate 0.057 In. Thick. 











Diameter of Orifice 


in Inches. 








si* 


0.3125 


0.500 


1.000 


1.500 


2.000 


2.500 


3.000 


3.500 


4.000 


4.500 


5.000 


^l2 


0.00114 0.00293 


0.01170.0263,0.0468 0.0732 


0.105 


0.143 


0.187 


0.237 


0.292 


1 


0.0C162 


0.00416 


0.0166 


0.0373 0.0663,0.103 


0.149 


0.202 


0.264 


0.334 


0.413 


IV? 


0.00199 


0.00510 


0.0203 


0.0457 


0.0811 0.127 


0.182 


0.248 


0.323 


0.409 


0.505 


2 


0.00231 


C. 00590 


0.0235 


0.0528 


0.0937 0.146 


0.210 


0.285 


0.373 


0.471 


0.582 


ZVo 


0.00259 


0.00662 


0.0263 


0.1591 


0.105 


0.163 


0.235 


0.319 


0.416 


0.526 


0.649 


3 


0.00285 


0.00726 


0.02890.0648 


0.115 


0.179 


0.257 


0.349 


0.455 


0.575 


0.710 


31/2 0.00308 


0.00786 


0.03120.0700 


0.124 


0.193 


0.277 


0.377 


0.491 


0.621 


0.766 


4 


0.00330 


0.00842 


0.0334 0.0749 


0.133 


0.206 


0.296 


0.402 


0.525 


0.663 


0.817 


4V? 


0.00351 


0.00695 


0.0355 0.0794 


0.141 


0.219 


0.314 


0.426 


0.556 


0.702 


0.865 


5 


0.00371 


0.00945 


0.0375 0.0838 


0.148 


0.231 


0.331 


0.449 


0.586 


0.739 


0.912 


51/2 0.00390 


0.00993 


0.0393:0.0879 


0.155 


0.242 


0.347 


0.471 


0.613 


0.774 


0.953 


6 10.00408 


0.01049 


0.041110.0918 


0.162 


0.252 


0.362 


0.492 


0.640 


0.808 


0.995 



Fliegner's Equation for Flow of Air tlirough an Orifice. — (Peabody's 
"Thermodynamics," also Trans. A. S. M. E., vol. 27, p. 194.) 

W = 0.53 A -^• 

W = flow in poirnds per second : A = area of the orifice (or sum of the 

areas of all the orifices) in square inches; P = absolute pressure in the 
orifice chamber lb. per sq. in.; T = absolute temperature, deg. F., of thQ 
air in the chamber. The formula applies only when the absolute 
pressure in the reservoir is greater than twice the atmospheric pressure, 
and for orifices properly made. The orifices are in hardened steel 
plates 3/8 in. to 1/2 in. thick, accurately ground, with the inside orifice 
rounded to a radius i/ie in. less than the thickness of the plate, leaving 
V16 in. of the hole straight. 

FLOW OF Am TS PIPES. 

In the steady flow of any liquid or gas, without friction, the sum of 
the velocity head, V^ -i- 2 g, pressure head p/u\ and potential head, z, 
(that is the distance in feet above an assumed datum) at any section of 

2g w 
statement is known as Bernoulli's theorem. 

V = velocity in ft. per sec; 2 g = 64.35; p = absolute pressure in 
pounds per square feet; w = density, pounds per cubic feet; z = height 
of the section above a given datum level. When the pipe is level we 
may take its axis as datum, and then z = 0. 

When "fluid friction" or "skin friction" is taken into account there 



the pipe is a constant quantity. 



-\- z = B, constant. This 



618 AIR. 

is a "loss of head*' or "friction head" between any two selected points, 

Ij v^ 
such as the two ends of the pipe, H = fLv^ ~- R 2 g ; or H = 4:f ~ —■; 

U JfQ 

H is the loss of head, or head causing the flow, measured in feet of the 
fluid, / is a coefficient of friction and R the mean hydraulic radius, 
which in circular pipes = 1/4 D. L is the length of the pipe and D the 
diameter, both in feet. By transposition the velocity in feet per 

second is ^ ='\Tf ~J~^ = 4.0103 a/ ^ ^ . 

The value off in this formula varies through a considerable range 
with the roughness of the pipe, with the diameter, and probably to 
some extent with the velocity. For a rough approximation its value 
for air and other gases may be taken as 0.005. 

For convenience in calculation, the loss of head in feet of H may be 
replaced by the difference in pressure in lb. per sq. in., H = 144 (pi — P2) 
-7- W, and the diameter d may be taken in inches. We thus obtain 

„ = 4.0103-Ji^P^p^ = 13.892 -Ji JME?^. 
\ f W L 12 \/\w?L 

The quantity of ^ow in cubic feet per minute, = 60 A V. A being 
the area in sq. ft. =60 X 0.7854 X tZ2 -j- 144, whence we have (by multi- 



plying 60 X 0.7854 X 13.89 -5- 144), Q = 4.546 -J-y- X a/— 



— P2 6> 



w L 

(vi — V2) d^ 
— y — which is the common formula for flow of any liquid or 

gas when Q is in cubic feet per minute measured at the density w cor- 
responding to the higher pressure pi. To reduce this to the equivalent 

volume of "free air" at atmospheric pressure, Qa = Q X :[x^. 



.004 .0045 


.005 .0055 


.006 .0065 .007 .0075 


71.9 67.8 


64.3 61.3 


58.7 56.4 54.7 52.4 



'■ The weight flowing per minute is Qw = W = c-d ~ — . Values 

of c corresponding to different values off are as follows: 

/.. . 0.003 .0035 
C... 83.0 76.9 

The experimental data from which the values of c and / for air and 
gas may be determined are few in number and of doubtful accuracy. 
Probably the most reliable are those obtained by Stockalper at the 
St. Gothard tunnel. Unwin found from these data that the value off 
varied with the diameter and that it might be expressed by the formula 
/= 0.0028 (1 + 3.6/d), d being taken in inches. 

Ford= 1 2 3 4 6 12 24 48 In. 

/ = 0.013 .0078 .0062 .0053 .0045 .0036 .0032 .0030 
c= 40.0 51.3 57.9 62.3 67.9 75.3 80.1 82.8 



TJnwin's formula may be given the form Q = K\ — r /, 1^0 ^/^x » 
\t/; jL (1 + o.o/a) 

in which K = 4.546 V 1 -^ .0028 = 85.9. This is practically the 
same as Babcock's formula for steam, in which / is taken at 0.0027, 
giving K = 87.5. 

Formulae for Flow with Large Drop in Pressure.— The above for- 
mulae are based on the assumption that the drop in pressure is small, 
and that, therefore, the density remains practically constant during 
the flow. When the drop is large the density decreases with the pres- 
sure and the velocity increases. Church ("Mechanics of Engineering," 
7. 791) and Unwin (Ency. Brit., 11th ed., vol. xiv., p. 67), develop 
ormulae for compressible fluids with large drop of pressure and in- 
creasmg velocity. The temperature is assumed to be constant, the 
heat generated by friction balancing the cooUng due to the work done 
m expansion. 



Fc 



FLOW OF AIR IN PIPES. ' 619 



Church's formula: Q = l/itv d^ A^-Tfi ^P^^ ~ P^^). 

x^ . , i. 1 T7 \g RT d (pi2 - P22) 
Unwin's formula: V = \ r . . , — r^— ^. 

V= velocity, ft. per sec; Q = volume, cu. ft. per sec. at the pressure 
P\\g = 32.2; R = the constant in the formula PV = RT (see Thermody- 
namics) = 53.32 for air; d = diam., and L = length, in feet; pi, p2 = 
absolutelpressures in lb. per sq. ft. ; w = density, lb. per cu. ft. ; T = 
temperature F. + 459.6. The value of / is given by Church as from 
0.004 to 0.005. Unwin makes it vary with the diameter as stated 
above. 

These two formulae give identical results when the value of/ is taken 
the same in both, for RT/pi^ = 1 -j- wpi. 

J. E. Johnson, Jr. (Am. Mach., July 27, 1899) gives Church's formula 
in a simpler form as follows: pi"^ — p%^ = KQ'^L 4- d^, in which pi and 
P2 are the initial and final pressures in lb. per sq. in., Q the volume of 
free air (that is the volume reduced to atmospheric pressure) in cubic 
feet per minute, d the diameter of the pipe in inches, L the length in feet, 
and K a numerical coefficient which from the Mt. Cenis and St. Gothard 
experiments has a value of about 0.0006. E. A. Rix, in a paper on the 
Compression and Transmission of Illuminating Gas, read before the 
Pacific Coast Gas Ass'n, 1905, says he uses Johnson's formula, with a 
coeflacient of 0.0005, which he considers more nearly correct than 0.0006. 
For gas the velocity varies inversely as the square root of the density, 
and for gas of a density G, relative to air as 1, Rix gives the formula 
pi2 - P22 = 0.0005 \/G X Q'^L/dK 

If Church's formula is translated into the same form as Johnson's, 
taking/ = 0.005, w = 0.07608 for air at 62° F., and atmospheric pressure, 
14.7 lbs. per sq. in., the value of K is 0.00054. A more convenient 

form is Q^ = Ci J^Pllzi^fLll in ^luch Ci = VlW- With K in 

Johnson's formula taken at 0.0006, Ci = 40.8. With / in Church's 
formula taken at 0.005, Ci = 43.0. 

Note that Church's formula gives Q in cubic feet per second meas- 
ured at the pressure pi, while Johnson's Qa is in cubic feet per minute 
reduced to atmospheric pressure. 

Both Church and Johnson assume that the flow varies as \/d^, the 
coeflScients/ and K being independent of the diameter. In this respect 
their formulae are faulty, for, as Unwin shows, the coeflQcient of friction 
is a function of the diameter. 

The relation between the results given by these formu lae and t hose 
gi ven b3^ the common formula is the relation between \/pi^ — pz^ and 
\/pi - p2. Taking pi (in any unit) as 100, and different drops in 
pressure, the relative results are as follows: 

Pressure drop 1 10 20 40 60 80 

V alues of p2. . 99 90 80 60 40 20 

Vpi^-p^^^Vpi -P2 14.1 13.8 13.4 12.2 11.8 10.8 

Ratio, 14.1 = 100 100 97.6 95.0 86.5 83.7 76.6 

It thus appears that the calculated result by Johnson's formula is 
not more than 5 per cent less than that calculated by the common 
formula, when the same value of / is used, if the drop in pressure is 
not greater than 20 per cent of pi. 

Comparison of Different Formulae. — We may compare the several 
formulae given above by applying them to the data of the St. Gothard 
experiments, as in table p. 620. 

The value of Q is given as reduced to atmospheric pressure, 14.7 lb. 
per sq. in. and 62° F. The length of the pipe 7.87 in. diam. was 15,092 
ft., and that of the pipe 5.91 in diam., 1712.6 ft. The mean tempera- 
ture of the air in the large pipe was 70° F. and in the small pipe 80° F. 



620 



AIR. 



In the table, Formula (1) is the commonlformula, Qi = c-W 



w L 



Formula (2) is Un win's, Qi = K 



■V 



(pi - Pi) rfs 
wL{l-\- 3.6/d) • 

- P22) d5 



V(i9j2 7J2' 
_*^ ^ 

Q\ — cubic ft. per min. at pressure pi. 

Ofl = cubic ft. per min. reduced to atmospheric pressure =Q pi -^14.7. 



Di- 
am- 


Mean 
Vel. 
Ft. 
Per 
Sec. 


Cu. 

Ft. 
Per 

Min. 

Q 


Lb. 
Per 
Sec. 


Absolute 

Pressures. 

lb. per sq. in. 


Coefficient in 
Formula. 


Ratio of 

Coefficient to 

Average Value. 


eter, 




(1) 
c 


(2) 
K 


F> 




In.' 


Vi 


V2 


(1) 


(2) 


(3) 


7.87 
7.87 
7.87 
5.91 
5.91 


19.3 
16.3 
15.6 
37.1 
29.3 


2105 
1401 
1169 
2105 
1169 


2.669 
1.776 

1.483 
2.669 
1.483 


82.32 
63.95 
56.45 
77.03 
53.66 


77.03 
60.71 
53.66 
73.50 
52.04 


76.0 
73.5 

70.2 
74.8 
65.5 


89.6 
86.5 
82.8 
94.9 
83.1 


51.3 

49.3 
46.0 
44.5 
43.6 


1.06 
1.02 
0.98 
1.04 
0.91 


1.03 
0.99 
0.95 
1.09 
0.95 


1.09 
1.05 
0.98 
0.95 
0.93 


Av( 


jrage. 










72.0 


87.4 


46.9 









The above comparison shows that no one of three formulae fits the 
St. Gothard experiments better than any other; each one when apphed 
with the average value of its coefficient may give a result that differs 
as much as 9 per cent from the observed result. 

Arson's Experiments. — Unwin quotes some experiments by A. Arson 
on the fiow of air through cast-iron pipes which showed that the co- 
efficient of friction varied with the velocity. For a velocity of 100 ft. 
per sec, and without much error for higher velocities, Unwin finds 
that the values of / agree fairly with the formula / = 0.005 (1 -}-3.6/fZ). 
Translating the figures given by him for the varying values of / into 
values of c for use in the common formula, we have the following: 

Diameter of pipe, inches 1.97 3.19 4.06 10 12.8 19.7 

Vnin^c ( ^= 10 ft), persec. 35.7 39.4 39.8 49.2 52.8 64.7 
nfr \ 50 " " " 38.6 42.5 45.0 51.5 55.7 65.2 

"^*" I 100 '• " •• 41.3 45.5 46.0 53.6 56.4 65.4 

The values of c for the same diameter with/ = 0.0028 (1 +3.6/d), as 
deduced by Unwin from Stockalper's experiments are: 51.4, 57.9, 
62.3, 73.7, 75.9, 79.1. 

Unwin says that Stockalper's pipes were probably less rough than 
Arson's. The values of c according to Stockalper's experiments range 
from 21 to 37 per cent higher than those calculated from the formula 
derived from Arson's experiments. 

Use of the Formulae. — It is evident from the above comparisons 
that any formula for the flow of air or gas must be considered as only 
a rough approximation to the actual fiow, and that an observed result 
may differ as much as 40 per cent from that calculated by a formula. 
Part of this error is due to variations in the roughness of pipes, part 
due to error in measurements of the actual flow, and part due to the 
fact that the coefficients of the several formulae are based on too few 
experiments. In the light of our present knowledge, Unwin's formula 



for moderate drop. Q 



= 87 \\~ 



(pi — Pi) d^ 



is probably the best one 



, „ L (1 + 3.6/d) 
to use for all cases in which the drop in pressure does not exceed 20 
per cent of the absolute initial pressure, and Johnson's formula, 



Qa= 47 



V 



(Pl"^- P22) t/5 



for cases in which the drop is larger and the pipes 



FLOW OF AIR AT LOW PRESSURES. 



621 



are not less than 12 inches diameter. For smaller pipes the term 
(1 4- 3.6/rf) had better be used after L in the denominator. These 
formulae with the coefficients given apply only to straight pipes with a 
fairly smooth interior surface. For crooked or rough pipes it may be 
well to use the common formula with the coefficients derived from 
Arson's experiments, given above. 

Another comparison of the three formulae may be made by applying 
them to some extreme cases, as follows: The initial pressure is taken 
at 100 lb. absolute per sq. in., the corresponding density is 0.5176 lb. 
per cu. ft.; diameters are assumed at 1 in. and 48 in., the drop in pres- 
sure 1 lb. and 40 lb. and the length 100 ft. and 40,000 ft., making 
eight cases in all. A ninth case is taken with intermediate values: 
diameter, 10 in.; length, 1,000 ft.; and drop, 1 lb. The results are 
given in the following table. The results obtained by Johnson's for- 
mula have been reduced by dividing them by the ratio (100 -^ 14.7) 
to obtain Q. The value of c in the common formula is taken at 72, the 
average figure from the St. Gothard experiments. 



Diam., In. 


1 


48 


10 


Vi- P2, lb. 


1 


40 


1 40 


1 


L, ft 


100 |40,000 


100 1 40,000 


100 1 40,000 100 1 40,000 


1,000 


Formula 


Cubic feet of air per minute at the pressure pi. 


Common 

Unwin 

Johnson 


10.08 
5.64 
9.75 


0.50 
0.28 
0.49 


63.3 
35.7 
55.3 


3.16 
1.78 
2.76 


159,800 
186,200 
155,600 


7,990 l,010,000i50,500[l,008 
9,310 1,178,000 58,900 1,037 
7,778 882,300 44,110 974 


Ratio of results to Un win's = 1 . 


Common 

Johnson 


1.79 
1.73 


1.79 
1.75 


1.78 
1.55 


1.78 
1.55 


0.86 
0.84 


0.86 
0.84 


0.86 
0.75 


0.86 
0.75 


0.96 
0.94 



These figures show that while the three formulae agree fairly well for 
the 10-in. pipe with 1-lb. drop in 1,000 ft., they show wide disagreements 
when a great range of diameters, lengths, and drops in pressure are 
taken. For the 1-in. pipe Unwin's figures are from 35 to 45 per cent 
lower than those given by the common formula or by Johnson's, but 
they are not therefore certainly too low. We have a check on them 
in CuUey and Sabine's experiments on 2 V4-in. lead pipes, 2000 to 
nearly 6000 ft. long, quoted by Unwin, which gave a value of f = 0.07. 
Unwin's formula, / = 0.0028 (1 + 3.6/(Z) gives / = 0.0073. The cor- 
responding values of c in the common formula are 54.7 and 53.2. 

Formula for Flow of Air at Low Pressures. — For ventilating and 
similar purposes, air is usually carried at pressures, but slightly above 
that of the atmosphere. Pressures are measured in inches of water 
column or in ounces per square inch above atmospheric pressure. 
For smooth and straight circular pipes, probably the best formula to 

use is Unwin's, Q = 87 ^/ ^ ^^(]~^^3 g^L > the coefficient 87 being de- 

rived from the St. Gothard experiments on compressed air. In 
order to put the formula into a more convenient form for low pres- 
sures, let h = head or difference in pressures measured in inches of 
water column, = 27.712 (pi - po), and take w = 0.07493 = density 
of air, lb. per cu. ft. at 70° and atmospheric pressure, then Q = 



87 X 



V. 



d^ 



= 60.37 



v; 



h d^ 



or Q 



/.27.71 .07493 L (1 + 3.6/(?) ""•"' \L (1 + 3.6/fZ)' 

Vhd^ 
-J-, in which C is a coefficient varying with the diameter, values 

for different diameters being given in the table below. For other 
temperatures and pressures, the flow varying inversely as the square 
root of the density, the figure 0.07493 in the above equation should be 

replaced by 0.07493 x ~ X ^^^^ in which p = absolute pressure. 



622 



AIR. 



lb. per sq. in., and T = degrees F. ^ is the quantity in cubic feet per 
minute measured at the given pressure and temperature. 
Flow of Air at Low Pressures. 



Q = cubic feet per minute = C 






drop in pressure, inches of 



water column, d = diameter in inches. L = length of pipe in feet. C, a 
coefficient varying with the diameter. The values of C in the table 
are based on air at atmospheric pressure and 70° F., and the values of 
Q are calculated for the same pressure and temperature and for a drop 
of 1-inch water column in 100 ft. 



d. 


C. 


Q. 


d. 


C. 


Q. 


d. 


C. 


Q. 


d. 


C. 


Q. 


4 


43.9 


140 


10 


51.8 


1,637 


22 


56.0 


12,700 


42 


57.9 


66,240 


5 


46.1 


257 


12 


53.0 


2,642 


24 


56.3 


15,880 


48 


58.2 


92,930 


6 


47.7 


421 


14 


53.9 


3,950 


26 


56.6 


19,500 


54 


58.4 


125,200 


7 


49.1 


636 


16 


54.6 


5,585 


28 


56.8 


23,580 


60 


58.6 


163,500 


8 


50.1 


908 


18 


55.1 


7,579 


30 


57.1 


28,130 


66 


58.8 


208,000 


9 


51.0 


1,240 


20 


55.6 


9,946 


36 


57.6 


44,760 1 


72 


58.9 


259,200 



For any other pressure drop than 1-inch water column per 100 ft., 
multiply Q by the square root of the drop, or by the factor given below: 
Drop, /i.... 0.5 2 3 4 6 8 10 12 14 16 18 20 
Factor. ... 0.71 1.41 1.73 2 2.45 2.83 3.16 3.46 3.74 4 4.24 4.47 

For drop in ounces per square inch (1 oz. = 1.732 in. of water) the 
factors are: 

Drop. oz. . 0.5 1 2 3 4 5 6 7 8 9 10 12 
Factor. . . . 0.93 1.32 1.86 2.28 2.63 2.94 3.22 3.48 3.72 3.95 4.16 4.56 

Loss of Pressure in Ounces per Square Inch. — B. F. Sturtevant Co. 
gives the following formula: 

L v^- /25.000 dpi , 

vi = 5T7^7^?7^ ; ^ = ^ — z — ' ^ " 



0.0000025 Lv2 



25,000 d' 



P 



p\ = loss of pressure, ounces per sq. in. ; v = velocity, ft. per sec. ; 
d = diameter, inches; L = length, ft. From the value of v we obtain 
the flow in cubic feet per minute. Q = 60 av = 60X 0. 7854^2 4- 144 x 



V 



25,000 d pi 



= 51.74 



column, h, then Q = 39.24 




If the drop is taken in inches of water 

This formula gives a value of Q 9 per 

cent less than that given in the above table for a 4-inch pipe, and 33 per 
cent less for a 72-inch pipe. 

Flow in Rectangular Pipes. — It is common practice to make air 
pipes for ventilating purposes rectangular instead of circular section 
in order to economize space. No records of experiments on the flow 
of air in such pipes are available, but a fair estimate of their capacity 
as compared with that of circular pipes of the same area may be made 
on the assumption that they follow the law of Chezy's formula for flow 
of water, viz.: that the flow is proportional to the square root of the 
mean hydraulic radius r, wliich is defined as the quotient of the area 
divided by the perimeter of the wetted surface. For a circular pipe 
r = 1/4 diameter in feet, and for a square pipe of the same area, r = 
0.222d. For rectangles of the same area r will decrease as the ratio 
of the longer to the shorter side increases. For different proportions 
of sides, the values of r and the ratio of \/r"to the value of \/n, the 
hydrauHc radius of a circular pipe having the same area, are as below: 

Ratio of sides .. (circle) l(sq.) 1.5 2 3 4 5 6 

r= ^0.25 0.222 0.217 0.209 0.192 0.177 0.165 0.155 

Ratio \/rV\/ri. 1 0.942 0.932 0.914 0.875 0.842 0.813 0.787 

That is, a square pipe will have 94 per cent of the carrying capacity of 
a circular pipe of the same area, and a rectangular pipe whose sides are 
in the ratio of 6 to 1 will have only 79 per cent of the capacity of a 
circular pipe of the same area, 



FLOW OF AIR. 



623 



•2 .B 



o 


8 


fA — CT^ 

— — (N<Nrs|cr\crMA\D0O 


§ 


mt>.Oc<>vO — mOm — m» — — 
— fN(Nmc<^Tj-mt^av 


i 


O^m 

mt»sOrAr^fN\0<Nr^r<^oomNO 
— ^ — (N<Nri^cnTrmr^a^ 


g 


Ooo — t>«.oOfAm(NO^T}-c(^Tj-rs| 
rsir^^c*^-^ — m>Tra^r^fSTt-o^r^ 
vOoO — -^oOcooOf^^O^^O — O^O 


s 


00 en 

0<Ntj- — vOvOa>'<Nr^fnO<N'^ 
vOoOfSm>ONmO\OfNO^mim.oO 

— — — <Ncncn'<r'«rNOooo 


Actual 

Internal 

Diam., 

In. 


oo-^fNOOmmmi — oooomimi 


h*iOOO — <Nfn'^mivOr>.0^'— m 


Nomi- 
nal 

Size, 
In. 


PQQQQ 

coao-fsj en 2: If^ddddd 

t^OOOtNTj- 




1 


ooooom-^ 
Tj-asaNrsima^^O'NOmvOCNotfn 


oO'-'<rsO<NO^o^o^'^^vomav 
— — mmioO'— m>mii^ 


o 


t^fNOrsioO 

mo^oocnmm>o^-^0 

Tfa^O'^oooomt>*Trcnomcno 


00<N-^\OcnO — (NoOOmr^r^ 

'-(N^sO00<N^OvOO^ 


§ 


o-^moo — 

vO'TOfNO^r^.O'^vOm 


O — fS-^t^-^ — cnm(N\0 — — t^ 

— — (NTt- 


s 


vO -* CO ""iJ- "^ 

ooorsia^oomvomoo 


0»-(NTft^m<NvoavoOfn — r^ — 
»-<NTrvoaNcnoooN'<r 

— — (NTT 


s 


oOvOr^ — vO 

m — cncNO^ — -^O^mommo 


o — <NmoovO'^a^fn^<Ncovoo 


Actual 

Internal 

Diam., 

In. 


<N'^O^OOt>.O^OOoOvOvOt^iAfn 
(NCNtToo — vOvOvOn-(NOTj-vO<N 
vOoOOpr^^OO■«rOlr^OmlOOO 


OO — — '-<N<Nfnfn'^'«J-m\Ot>* 


1 







©• 



~^ 



II 
o 

a 

u 
O 






T3 



=« .2 



lO o* 









> • l> 

CO 
CO 

. OOfN 



; c« o 

X2 



Q fi 



624 



AIR. 



Volume of Air Transmitted in Cubic Feet per Minute In 
Pipes of Various Diametersc 

Formula Q= — ^ d^vXQO. 
144 



h 


Actual Diameter of Pipe in I 


nches. 








11 




















*is ^ 


























o *= 


1 


2 


3 


4 


5 


6 


8 


10 


12 


16 


20 


24 


^ 


























1 


0.327 


I.3I 


2.95 


5.24 


8.18 


1K78 


20.94 


32.73 


47.12 


83.77 


130.9 


188.5 


2 


0.655 


2.62 


5.89 


10.47 


16.36 


23.56 


4K89 


65.45 


94.25 


167.5 


261.8 


377.0 


3 


0.982 


3.93 


8.84 


15.7 


24.5 


35.3 


62.8 


98„2 


141.4 


251.3 


392.7 


565.5 


4 


I.3I 


5.24 


11.78 


20.9 


32.7 


47.1 


83.8 


131 


188 


335 


523 


754 


5 


1.64 


6.54 


14.7 


26.2 


41.0 


59.0 


104 


163 


235 


419 


654 


942 


6 


1.96 


7.85 


17.7 


31.4 


49.1 


70.7 


125 


196 


283 


502 


785 


1131 


7 


2.29 


9.16 


20.6 


36.6 


57.2 


82.4 


146 


229 


330 


586 


916 


1319 


8 


2.62 


10.5 


23.5 


41.9 


65.4 


94 


167 


262 


377 


670 


1047 


1508 


9 


2.95 


11.78 


26.5 


47 


73 


106 


188 


294 


424 


754 


1178 


1696 


10 


3.27 


13.1 


29.4 


52 


82 


118 


209 


327 


471 


838 


1309 


1885 


12 


3.93 


15.7 


35 3 


63 


98 


141 


251 


393 


565 


1005 


1571 


2262 


15 


4.91 


19.6 


44,2 


78 


122 


177 


314 


491 


707 


1256 


1963 


2827 


18 


5.89 


23.5 


53 


94 


147 


212 


377 


589 


848 


1508 


2356 


3393 


20 


6.54 


26.2 


59 


105 


164 


235 


419 


654 


942 


1675 


2618 


3770 


24 


7.85 


31.4 


7] 


125 


196 


283 


502 


785 


1131 


2010 


3141 


4524 


25 


8.18 


32.7 


73 


131 


204 


294 


523 


818 


1178 


2094 


3272 


4712 


28 


9.16 


36.6 


82 


146 


229 


330 


586 


916 


1319 


2346 


3665 


5278 


30 


9.8 


39.3 


88 


157 


245 


353 


628 


982 


1414 


2513 


3927 


5655 



Effect of Bends In Pipes. (Norwalk Iron Works Co.) 
Radius of elbow, in diameter 

of pipe = 5 3 2 11/2 11/4 1 3/4 i/j 

Equivalent lengths of straight 

pipe, diams. 7.85 8.24 9.03 10.36 12.72 3 7.5135.09 121.2 

E. A. Rix and A. E. Chodzko, in their treatise on Compressed Air 
(1896), give the following as the loss in pressure through 90° bends. 
Rad. of bend ^ internal 

diam. of pipe 1 2 3 4 5 

Loss in lb. per sq. in O.OOSr^ .0022r2 .0016i)2 .0013^2 .00121)2 

V is the velocity of air at entrance, in feet per second. 

Friction of Air in Passing tlirougli Valves and Elbows. W. L. 
Saunders, Compressed Air, Dec, 1902. — The following figures give the 
length in feet of straight pipe which will cause a reduction in pressure equal 
to that caused by globe valves, elbows, and tees in different diameters of 
pipe. 
Diam. of pipe, in.. 1 II/2 2 21/2 3 31/2 4 5 6 7 8 10 

Globe Valves 2 4 7 10 13 16 20 28 36 44 53 70 

Elbows and Tees .23 5 7 911 13 19 24 30 35 47 

Measurement of the Velocity of Air in Pipes by an Anemometer. 
— Tests were made by B. Donkin, Jr. (Inst. Civil Engrs., 1892), to com- 
pare the velocity of air in pipes from 8 in. to 24 in. diam., as shown by an 
anemometer 23/4 in. diam. with the true velocity as measured by the time 
of descent of a gas-holder holding 1622 cubic feet. A table of the results 
with discussion is given in Eng'g News, Dec. 22, 1892. In pipes from 8 in. 
to 20 in. diam. with air velocities of from 140 to 690 feet per minute the 
anemometer showed errors varying from 14.5% fast to 10% slow. With 
a 24-inch pipe and a velocity of 73 ft. per minute, the anemometer gave 
from 44 to 63 feet, or from 13.6 to 39.6% slow. The practical conclusion 
drawn from these experiments is that anemometers for the measurement 
of velocities of air in pipes of these diameters should be used with great 
caution. The percentage of error is not constant, and varies considerably 
with the diameter of the T)ipes and the speeds of air. The use of a baffle 
consisting of a perforated plate, which tended to equalize the velocity in 
the center and at the sides in some cases diminished the error. 



FLOW OF AIR. 



625' 



The impossibility of measuring the true quantity of air by an anemometer 
held stationary in one position is shown by the following figures, given by 
Wm. Daniel {Proc. Inst. M, E.j 1875), of the velocities of air found at 
different points in the cross-sections of two different airways in a mine. 

Differences of Anemometer Readings in Airways. 

8 ft. square. 

5 X 8ft. 



1712 


1795 


1859 


1329 


1622 


1685 


1782 


1091 


1477 


1344 


1524 


1049 


1262 


1356 


1293 


1333 



1170 


1209 


1288 


948 


1104 


1177 


1134 


1049 


1106 



Average 1132. 



Average 1469. 



Equalization of Pipes. — It is frequently desired to know what nurpber 
of pipes of a given size are equal in carrying capacity to one pipe of a 
larger size. At the same velocity of flow the volume delivered by two 
pipes of different sizes is proportional to the squares of their diameters; 
thus, one 4-inch pipe will deliver ihe same volume as four 2-inch pipes. 
With the same head, however, the velocity is less in the smaller pipe, and 
the volume delivered varies about as the square root of the fifth power 
(i.e., as the 2.5 power). The following table has been calculated on this 
basis. The figures opposite the intersection of any tw^o sizes is the num- 
ber of the smaller-sized pipes required to equal one of the larger. Thua 
one 4-inch pipe is equal to 5.7 two-inch pipes. 



li 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


12 


14 


16 


18 


20 


24 


2 
3 


5.7 
15.6 


1 
2.8 


1 




























4 


32.0 


5.7 


2.1 


1 


























5 


55.9 


9.9 


3.6 


1.7 


1 
























6 


88.2 


15.6 


5.7 


2.8 


1.6 


1 






















7 


130 


22.9 


8.3 


4.1 


2.3 


1.5 


1 




















8 


181 


32.0 


11.7 


5.7 


3.2 


2.1 


1.4 


1 


















9 


243 


43.0 


15.6 


7.6 


4.3 


2.8 


1.9 


1.3 


1 
















10 


316 


S5.9 


20.3 


9.9 


5.7 


3.6 


2.4 


1.7 


1.3 


1 














11 


401 


70.9 


25.7 


12.5 


7.2 


4.6 


3.1 


2.2 


1.7 


1.3 














12 


499 


88.2 


32.0 


15.6 


8.9 


5.7 


3.8 


2.8 


2.1 


1.6 


1 












13 


609 


108 


39.1 


19.0 


10.9 


7.1 


4.7 


3.4 


2.5 


1.9 


1.2 












14 


733 


130 


47.0 


22.9 


13.1 


8.3 


5.7 


4.1 


3.0 


2.3 


1.5 


I 










15 


871 


154 


55.9 


27.2 


15.6 


9.9 


6.7 


4.8 


3.6 


2.8 


1.7 


1.2 










16 




181 


65.7 


32.0 


18.3 


11.7 


7.9 


5.7 


4.2 


3.2 


2.1 


1.4 


1 








17 




211 


76.4 


37.2 


21.3 


13.5 


9.2 


6.6 


4.9 


3.8 


2.4 


1.6 


1.2 








18 




243 


88.2 


43.0 


24.6 


15.6 


10.6 


7.6 


5.7 


4.3 


2.8 


1.9 


1.3 


1 






19 




278 


101 


49.1 


28.1 


17.8 


12.1 


8.7 


6.5 


5.0 


3.2 


2.1 


1.5 


1.1 






20 




316 


115 


53.9 


32.0 


20.3 


13.8 


9.9 


7.4 


5.7 


3.6 


2.4 


1.7 


1.3 


1 




22 




401 


146 


70.9 


40.6 


25.7 


17.5 


12.5 


9.3 


7.2 


4.6 


3.1 


2.2 


1.7 


1.3 




24 




499 


181 


88.2 


50.5 


32.0 


21.8 


15.6 


11.6 


8.9 


5.7 


3.8 


2.8 


2.1 


1.6 


J 


26 




609 


221 


108 


61.7 


39.1 


26.6 


19.0 


14.2 


10.9 


7.1 


4.7 


3.4 


2.5 


1.9 


1.2 


28 




733 


266 


130 


74.2 


47.0 


32.0 


22.9 


17.1 


13.1 


8.3 


5.7 


4.1 


3.0 


2.3 


1.5 


30 




871 


316 


154 


88.2 


55.9 


38.0 


27.2 


20.3 


15.6 


9.9 


6.7 


4.8 


3.6 


2.8 


1.7 


36 






499 
733 


243 
357 
499 
670 
871 


130 
203 
286 
383 
499 


88.2 

130 

181 

243 

316 


60.0 

88.2 

123 

165 

215 


43.0 

63.2 

88.2 

118 

154 


32.0 
47.0 
62.7 
88.2 
115 


24.6 
36.2 
50.5 
67.8 
88.2 


15.6 
19.0 
32.0 
43.0 
55.9 


10.6 
15.6 
21.8 
29.2 
38.0 


7.6 
11.2 
15.6 
20.9 
27.2 


5.7 

8.3 
11.6 
15.6 
20.3 


4.3 
6.4 
8.9 
12.0 
15.6 


? 3 


47 






4 1 


48 






•> 7 


M 








7 6 


60 




.... 




9.9 



626 



AIR. 



WEVD. 

Force of the Wind. — Smeaton in 1759 publishecf a table of the 

velocity and pressure of wind, as follows: 

Velocity and Force of Wind, in Pounds per Square Inch. 



Of- 


!1 


O . 3 


Common Appella- 
tion of the 


AC 






Common Appella- 
tion of the 


1- 

1.47 


1-^ 

0.005 


Force of Wind. 


r 


£s 




Force of Wind. 


1 


Hardly perceptible. 


18 


26.4 


1.55 




2 

3 


2.93 
4.4 


0.020 
0.044 


1 Just perceptible. 


20 
25 


29.34 
36.67 


1.968 
3.075 


[Very brisk. 


4 


5.87 


0.079 




30 


44.00 


4.429 


[ High wind. 


5 


7.33 


0.123 


Gentle, pleasant 


35 


51.34 


6.027 


6 


8.8 


0.177 


wind. 


40 


58.68 


7.873 




7 
8 


10.25 
11.75 


0.241 
0.315 




45 
50 


66.01 
73.35 


9.963 
12.30 


>Very high storm. 


9 


13.2 


0.400 




55 


80.7 


14.9 




10 


14.67 


0,492 




60 


88.00 


17.71 




12 


17.6 


0.708 


• Pleasant, brisk gale 


65 


95.3 


20.85 


Great storm. 


14 


20.5 


0.964 




;o 


102.5 


24.1 




15 


22.00 


1.107 




75 


110.00 


27.7 


[ Hurricane. 


16 


23.45 


1.25 




80 


117.36 


31.49 










100 


146.67 


49.2 


) Immense hurri- 
cane. 













The pressures per square foot in the above table correspond to the 
formula P = 0.005 V^, in which V is the velocity in miles per hour. 
Eng'g News, Feb. 9, 1893, says that the formula was never well established, 
and has floated chiefly on Smeaton's name and for lack of a better. It 
was put forward only for surfaces for use in windmill practice. The 
trend of modern evidence is that it is approximately correct only for such 
surfaces, and that for large, solid bodies it often gives greatly too large 
results. ^Observations by others are thus compared with Smeaton's 
formula: 

Old Smeaton formula .P = 0.005 V^ 

As determined by Prof. Martin P = 0.004 F* 

" Whipple and Dines P = 0.0029 V^ 

At 60 miles per hour these formulas give for the pressure per square foot, 
18, 14.4, and 10.44 lbs., respectively, the pressure varying by all of them as 
the square of the velocity. Lieut. Crosby's experiments (Eng'g, June 13, 
1890), claiming to prove that P = fV instead of P = fV^, are discredited. 

Experiments by M. Eiffel on plates let fall from the Eiffel tower in Paris 
gave coefficients of V^ ranging from 0.0027 for small plates to 0.0032 for 
plates 10 sq. ft. area. For plates larger than 10 sq. ft. the coefficient 
remained constant at 0.0032. — Eng'g, May 8, 1908. 

A. R. Wolff (" The Windmill as a Prime Mover," p. 9) gives as the theo- 
retical pressure per sq. ft. of surface, P = dQv/g, in which d = density of 
0.018743 (p + P) 



air in pounds per cu. ft. = 



t 



; p being the barometric pres- 



sure per square foot at any level, and temperature of 32° F., t any 
absolute temperature, Q = volume of air carried along per square foot in 
onesecond, i; = velocity of the wind in feet per second, gf = 32.16. Since 
Q = V cu. ft. per sec, P=dv^/g. Multiplying this by a coefficient 0.93 
found by experiment, and substituting the above value of d, he obtains 

P == / ..^o!!V^^^^ ^ ^ — ■ , and when p = 2116.5 lb. per sq. ft., or average 



t X 32.16 

V2 



0.018743 



atmospheric pressure at the sea-level, P 



36.8929 



t X 32.16 



-0.018743 



pression in which the pressure is shown to vary with the temperature : 
and he gives a table showing the relation between velocity and pressure 



WINDMILLS. 627 

for temperatures i'rom 0° to 100° F., and velocities from 1 to 80 miles per 
hour. For a temperature of 45° F. the pressures agree with those in 
Smeaton's table, for 0° F. they are about 10 per cent greater, and for 100°, 
10 per cent less. 

Prof. H. Allen Hazen, Eng'g News, July 5, 1890, says that experiments 
with whirling arms, by exposing plates to direct wind, and on locomotives 
with velocities running up to 40 miles per hour, have invariably shown the 
resistance to vary with V"^. The coefficient of V^ has been found in some 
experiments with very short whirling arms and low velocities to vary with 
the perimeter of the plate, but this entirely disappears ^dth longer arms 
or straight line motion, and the only quertion now to be determined is 
the value of the coefficient. Perhaps some of the best experiments for 
determining this value were tried in France in 1886 by carrying flat 
boards on trains. The resulting formula in this case was, for 44.5 miles 
per nour, p = 0.00535 SV^. 

Prof. Kernot, of Melbourne {Eng. Rec, Feb. 20, 1894), states that 
experiments at the Forth Bridge showed that the average pressure on sur- 
faces as iarge as railway carriages, houses, or bridges never exceeded two- 
thirds of that upon email surfaces of one or two square feet, and also that 
an inertia effect, which is frequently overiooked, may cause some forms 
of anemometer to give false results enormously exceeding the correct 
indication. Experiments made by Prof. Kernot at speeds varying from 
2 to 15 miles per hour agreed with the eariier authorities. The pressure 
upon one side of a cube, or of a block proportioned like an ordinary 
carriage, was found to be 0.9 of that upon a thin plate of the same area. 
The same result was obtained for a square tower. A square pyramid, 
whose height was three times its base, experienced 0.8 of the pressure 
upon a thin plate equal to one of its sides, but if an angle was turned to 
the wind the pressure was increased by fully 20%. A bridge consisting 
of two plate-girders connected by a deck at the top was found to expe- 
rience 0.9 or the pressure on a thin plate equal in size to one girder, when 
the distance between the girders was equal to their depth, and this was 
increased by one-fifth when the distance between the girders was double 
the depth. A lattice- work in which the area of the openings was 55% of 
the whole area experienced a pressure of 80% of that upon a plate of the 
same area. The pressure upon cyUnders and cones was proved to be equal 
to half that upon the diametral planes, and that upon an octagonal prism 
to be 20% greater than upon the circumscribing cylinder. A sphere was 
subject to a pressure of 0.36 of that upon a thin circular plate of equal 
diameter. A hemispherical cup gave the same result as the sphere; when 
its concavity was turned to the wind the pressure was 1.15 of that on a 
flat plate of equal diameter. When a plane surface parallel to the direc- 
tion of the wind was brought nearly into contact with a cylinder or sphere, 
the pressure on the latter bodies was augmented by about 20%, owing to 
the lateral escape of the air being checked. Thus it is possible for the 
security of a tower or chimney to be impaired by the erection of a building 
nearly touching it on one side. 

Pressures of Wind Registered in Storms. — Mr. Frizell has examined 
the published records of Greenwich Observatory from 1849 to 1869, and 
reports that the highest pressure of wind he finds recorded is 41 lb. per 
sq. ft., and there are numerous instances in which it was between 30 and 
40 lb. per sq. ft. Prof. Henry says that on Mount Washington, N. H., a 
velocity of 150 miles per hour has been observed, and at New York City 
60 miles an hour, and that the highest winds observed in 1870 were of 72 
and 63 miles per hour, respectively. Lieut. Dunwoody, U. S. A., says, 
in substance, that the New England coast is exposed to storms which 
produce a pressure of 50 lb. per sq. ft. — Eng, News, Aug. 20, 1880. 

WINDMILLS. 

Power and EflHciency of Windmills. — Rankine, S. E., p. 215, gives 
the following: Let Q — volume of air which acts on the sail, or part of a 
Bail, in cubic feet per second, v = velocity of the wind in feet per second, 
s = sectional area of the cyUnder, or annular cylinder of wind, through 
which the sail, or part of the sail, sweeps in one revolution, i? = a coeffi- 
cient to be found by experience: then Q = cvs. Rankine, from experi- 
mental data given by Smeaton, and taking c to include an allowance for 



628 AIR. 

friction, gives for a wtieel with four sails, proportioned in the best manner, 
c = 0.75. Let A = weather angle of the sail at any distance from the 
axis, i.e., the angle the portion of the sail considered makes with its plane 
of revolution. This angle gradually diminishes from the inner end of the 
sail to the tip; w = the velocity of the same portion of the sail, and E = 
the efficiency. The efficiency is the ratio of the useful work performed to 
the whole energy of the stream of wind acting on the surface s of the wheel, 
which energy is Dsv^ -^ 2 g, D being the weight of a cubic foot of air* 
Rankine's formula for efficiency is 

in which c = 0.75 and /is a coefficient of friction found from Smeaton's 
data = 0.016. Rankine gives the following from Smeaton's data: 

A = weather-angle =7° 13° 19° 

r 4- V = ratio of speed of greatest 
efficiency, for a given 
weather-angle, to that 

ofthewind =2.63 1.86 1.41 

^ = efficiency =0.24 0.29 0.31 

Rankine gives the following as the best values for the angle of weather 
at different distances from the axis: 

Distance in sixths of total radius 12 3 4 5 6 

Weather angle 18° 19° 18° 16° 121/2*^ 7° 

But Wolff (p. 125) shows that Smeaton did not term these the best 
angles but simply says they "answer as well as any," possibly any that 
were m existence innis time. Wolff says tnat tney '^ cannot in tne nature 
of things be the most desirable angles." Mathematical considerations, 
he says, conclusively show that the angle of impulse depends on the 
relative velocity of each point of the sail and the wind, the angle growing 
larger as the ratio becomes greater. Smeaton's angles do not fulfil this 
condition. Wolff develops a theoretical formula for the best angle of 
weather, and from it calculates a table of the best angles for different 
relative velocities of the blades and the wind, which differ widely from 
those given by Rankine. 

A. R. Wolff, in an article in the American Engineer, gives the following 
(see also his treatise on Windmills) : 

Let c = velocity of wind in feet per second; 

n = number of revolutions of the windmill per minute; 

&0i ^1. ^2, b^ be the breadth of the sail or blade at distances Iq, li, h^ 
Is, and Z, respectively, from the axis of the shaft; 

lo = distance from axis of shaft to beginning of sail or blade proper, 

I = distance from axis of shaft to extremity of sail proper; 

Vo. 'i^h "^2, Vs, v^ = the velocity of the sail in feet per second at dis- 
tances Iq, li, h, h, I, respectively, from the axis of the shaft; 

Co, ai, a2, as, a^ = the angles of impulse for maximum effect at dis- 
tances Iq, l\, h, h, I, respectively, from the axis of the shaft; 

a = the angle of impulse when the sails or blocks are plane surfaces 

so that there is but one angle to be considered; 
N = number of sails or blades of windmill; 

K = 0.93; 

d = density of wind (weight of a cubic foot of air at average tem- 
perature and barometric pressure where mill is erected) ; 
W = weight of wind-wheel in pounds; 

/ = coefficient of friction of shaft and bearings; 

D = diameter of bearing of windmill in feet. 



The effective horse-power of a windmill with plane sails will equal 
'^'muj X mean of < vq (sm a cos ajoo cos a 



v^{sin a - ^cos a\ b^cos a | - - ^^^^ 



05236 nP 
550 



WINDMILLS. 



629 



The effective horse-power of a windmill of shape of sail for maximum 
effect equals 



2200^7 



Xmean of 



/ 2 sin' 
\ si 



ao — 1 



sin2 ao 



&o. 



2 sin^ ai — 1 . 
sin" ai 



2 sin2 a^. - 1 
' sin2 a^ 



0- 



/TF X 0.05236 nP 
550 



The mean value of quantities in brackets is to be found according" to 
Simpson's rule. Dividing I into 7 parts, finding the angles and breadths 
corresponding to these divisions by substituting them in quantities within 
brackets will be found satisfactory. Comparison of these formulae with 
the only fairly reliable experiments in windmills (Coulomb's) showed a 
close agreement of results. 

Approximate formulae of simpler form for windmills of present con- 
struction can be based upon the above, substituting actual average values 
for a, c, d, and e, but since improvement in the present angles is possible, 
It is better to give the formulae in their general and accurate form. 

Wolff gives the following table, based on the practice of an American 
manufacturer. Since its preparation, he says, over 1500 \vindmills have 
been sold on its guaranty (1885), and in all cases the results obtained did 
not vary sufficiently from those presented to cause any complaint. The 
actual results obtained are in close agreement \\ith those obtained by 
theoretical analysis of the impulse of wind upon windmill blades. 









Capacity of 


the WindrailL 








1 

a 

o 


fi 

> 


1 

ti 

TO c 


Gallons of Water raised per Minute 
to an Elevation of 


Equivalent Actual Use- 
ful Horse-power 
developed. 


Average No. of Hours 
per Day during 
which this Result 
will be obtained. 


25 

feet. 


50 
feet. 


75 

feet. 


100 

feet. 


150 
feet. 


200 
feet. 


wheel 
81/2 ft. 
10 " 


16 
16 
16 
16 
16 
16 
16 
16 


70 to 75 
60 to 65 
55 to 60 
50 to 55 
45 to 50 
40 to 45 
35 to 40 
30 to 35 


6.162 
19.179 
33.941 
45.139 
64.600 
97.682 
124.950 
212.381 


3.016 
9.563 
17.952 
22.569 
31.654 
52.165 
63.750 
106.964 










0.04 
0.12 
0.21 
0.28 
0.41 
0.61 
0.78 
1.34 


8 


6.638 
11.851 
15.304 
19.542 
32.513 
40.800 
71.604 


4.750 
8.485 
11.246 
16.150 

24.421 
31.248 
49.725 






8 


12 •• 
14 •• 
16 •• 
18 •* 
20 •• 
23 " 


5.680 
7.807 
9.771 
17.485 
19.284 
37.349 


'4;998 
8.075 
12.211 
15.938 
26.741 


8 
8 
8 
8 
8 
8 



These windmills are made in regular sizes, as high as sixty feet diameter 
of wheel; but the experience with the larger class of mills is too limited to 
enable the presentation of precise data as to their performance. 

If the wind can be relied upon in exceptional localities to average a 
higher velocity for eight hours a day than that stated in the above table, 
the performance or horse-power of the mill will be increased, and can be 
obtained by multiplying the figures in the table by the ratio of the cube 
of the higher average velocity of wind to the cube of the velocity above 
recorded. 

He also gives the following table showing the economy of the windmill. 
All the items of expense, including both interest and repairs, are reduced 
to the hour by dividing the costs per annum by 365 X 8 = 2920; the 
Interest, etc., for the twenty-four hours being charged to the eight hours of 
actual work. By multiplying the figures in the 5th column by 584, the 
first cost of the windmill, in dollars, is obtained. 



G30 



AIB. 









Economy of the Windmill. 










CO 


Equivalent Actual Use- 
ful Horse-power de- 
veloped. 


^11 


Expense of Actual Useful Power 






Developed, in Cents, per Hour. 


Is 


Designa- 
tion of 
Mill. 


2^ 


Average Number 
Hours per Day du 
which this Quan 
will be raised. 


For Interest on 
First Cost (First 
Cost, including 
Cost of Windmill, 
Pump, and Tower, 
5% per Annum) 


For Repairs and 
Depreciation (5% 
of First Cost per 
Annum). 


6 
o 

a 

< 

u 




3 


K 

III 


wheel 
















81/2 ft. 


370 


0.04 


8 


0.25 


0.25 


0.06 


0.04 


0.60 


15.0 


10 '• 


1151 


0.12 


8 


0.30 


0.30 


0.06 


0.04 


0.70 


S 8 


12 •• 


2036 


0.21 


8 


0.36 


0.36 


0.06 


0.04 


0.82 


5 9 


14 " 


2708 


0.28 


8 


0.75 


0.75 


0.06 


0.07 


1.63 


5 8 


16 •• 


3876 


0.41 


8 


1.15 


1.15 


0.06 


0.07 


2.43 


5 9 


18 •• 


5861 


0.61 


8 


1.35 


1.35 


0.06 


07 


2.83 


4 6 


20 " 


7497 


0.79 


8 


1.70 


1.70 


0.06 


0.10 


3,56 


4,5 


25 " 


12743 


1.34 


a 


2.05 


2.05 


0.06 


0.10 


4.26 


3.2 



Prof. De Volson Wood (Am. Mach., Oct. 29, 1896) quotes some results 
by Thos. O. Perry on three wheels, each 5 ft. diam.: A, a good "stock" 
wheel, B and C, improved wheels. Each wheel was tested with a dyna- 
mometer placed 1 ft. from the axis of the wheel, and it registered a 
constant load at that point of 1.9 lbs. The velocity of the wind in each 
test was 8.45 miles per hour = 12.4 ft. per second. The number of turns 
per minute was: A, 30.67; B, 38.13; C, 56.50. The efficiency was: A, 
0.142; B, 0.176; C, 0.261. The work of wheel C was 674.5 ft. lb. per 
min. = 0.020 H.P. Assuming that the power increases as the square 
of the diameter and as the cube of the velocity, a wheel of the quality of 
C, 121/2 ft. diam., with a wind velocity of 17 miles per hour, would be re- 
quired for 1 H.P.; but wheel C had an exceptionally high efficiency, and 
such a high delivery would not likely be obtained in practice. 

Prof. O. P. Hood (Am. Mach., April 22, 1897) quotes the following 
results of experiments by E. C. Murphy; the mills were tested by pumping 
water : 

Wind, miles per hour 8 12. 

Strokes per min., Mill No. 1, 8-ft. wheel . . 10.2 
Strokes per min., Mill No. 2, 8-ft. wheel 8 20.2 
Strokes per min., Mill No. 3, 12-ft. wheel . . 4.8 
Strokes per min., Mill No. 4, 12-ft. wheel . . 6.2 



16. 

19.3 

26.1 

12.7 

11.9 



25. 

28.1 

27.5 

23.3 

16. 



30 

25 



25 



20. 
25.3 

28. 

18.8 

. .. ^.^ 14.7 

Mill No. 3 was loaded nearly 90% heavier than mill No. 4. 
In a 25-mile wind, seven 12-ft. mills developed, respectively, 0.379, 
0.291, 0.309, 0.6, 0.247, 0.219, and 0.184 H.P.: and five 8-ft. mills, 0.043, 
0.099, 0.059, 0.099, and 0.005 H.P. These effects include the effects of 
pumps of unknown and variable efficiency. The variations are largely 
due to the variable relation of the fixed load on the mill to the most 
favorable load which that mill might carry at each wind velocity. With 
each mill the efficiency is a maximum only for a certain load and a certain 
velocity, and for different loads and velocities the efficiency varies greatly. 
The useful work of mill No. 3 was equal to 0.6 H.P. in a 25-mile wind, 
and its efficiency was 5.8%. In a 16-mile wind the efficiency rose to 12.1 %, 
and in a 12-mile wind it fell to 10.9%). The rule of the power developed, 
varying as the cube of the velocity, is far from true for a single wheel 
fitted with a single non-adjustable pump, and can only be true when the 
work of the pump per stroke is adjusted by varying the stroke of the 
pump, or by other means, for each change of velocity. 

. R. M. Dyer (The Iowa Engineer, July, 1906: also Mach'y, Aug., 1907) 
gives a brief review of the history of \Aind mills, and quotes experiments 
^H ^^^- ?erry, E. C. Murphy, Prof. F. H. King, and the Aermotor Co. 
Mr. Perry s experiments are reported in pamphlet No. 20 of the W^ater 



WINDMILLS. 631 

Supply and Irrigation Papers of the U. 8. Geological Survey, Mr. Murphy's 
In pamphlets Nos. 41 and 42 of the same Papers, and Prof. King's, in 
Bulletin No. 82 of the Agricultural Experiment Station of the University 
of Wisconsin. The Aermotor Co .'s experiments are described in catalogues 
of that company. Some of Mr. Dyer's conclusions are as follows: 

Experiments showed that 7/8 of the zone of interruption could be covered 
with sails ; that the gain in power in from 3/4 to 7/8 of the surface was so small 
that the use of the additional material was not justifiable; that the sail 
surface should extend only two-thirds the distance from the outer diam- 
eter to the center; that a wheel running behind the carrying mast is not 
neariy as efficient as one running in front of the mast; that there should 
be the least possible obstruction behind the wheel; that to be efficient 
the velocity of the travel of the vertical circumference of the wheel 
should be from 1 to IV4 times the velocity of the wind, hence the 
necessity of back gearing to reduce the pump speed to 40 strokes per 
minute as a maximum, which is the limit of safety at which ordinary 
pumps can be operated. 

I hold that no manufacturer will be able to produce a marketable 
motor which will absorb and deliver, when acted upon by an elastic fluid, 
like air, in which it is entirely surrounded and submerged, more than 
35% of the kinetic energy of the impinging current. 

Theoretical demonstrations show that the kinetic energy of the air, 
impinging on the intercepted area of a wheel, varies as the cube of the 
wind velocity; consequently, the power of windmills of the same type 
varies theoretically as the square of the diameter and as the cube of the 
wind velocity; but as a wheel is designed to give its best efficiency in low 
winds, say 10 to 15 miles per hour, we cannot expect that the same 
angle of sail would obtain the same percentage of efficiency in winds of 
considerably higher velocity. 

The ordinary wheel works most efficiently under wind velocities of from 
10 to 12 miles per hour; such wheels will give reasonable efficiency in from 
5- to 6-mile winds, while, if the wind blows more than 12 miles per hour, 
there will be power to spare. Our wheel must work in light winds, such 
being nearly always present, while the higher velocities only occur at 
intervals. Mills built for grinding purposes, or geared mills, will develop 
power almost approaching to the cube of the wind velocity, within reason- 
able limits, as their speed need not be kept down to a certain number of 
revolutions per minute, as in the case of the pumping mill. 

Should this theoretic condition hold, the following table, showing the 
amount of power for different sizes of mills at different wind velocities, 
would apply; Figures show Horse Power, 

5 10 15 20 25 30 35 40 

Size mile. mile. mile. mile. mile. mile. mile. mile. 

8 ft 0.011 0.088 0.297 0.704 1.375 2.176 

12 ft 0.025 0.20 0.675 1.6 3.125 5.4 8.57 12.8 

16 ft 0.045 0.36 1.215 2.88 5.52 9.75 15.3 21.04 

These figures have been proven by laboratory tests at velocities 
ranging from 10 to 25 miles per hour and more practically by the 
Murphy tests on miUs actually in use, which show very close relation 
at the wind velocities at which the mills are best adapted. 

The Murphy figures are as follows: 

Size of mill. 10 mile. 15 mile. 20 mile. 
12 ft. 0.21 H.P. 0.58 H.P. 1.05 H.P. 

16 ft. 0.29 0.82 1.55 

For higher wind velocities the Murphy values fall much under the 
theoretical values, but the range of velocities over which his experi- 
ments extend does not justify any change in the general law except 
inasmuch as common sense teaches us that theoretic conditions can 
rarely be attained in actual practice. 

In view of the fact that a windmill does not work as efficiently in 
high winds as in winds under 20 miles per hour my experience would 
lead me to believe that the following figures (H.P.) would be the 
probable extension of the Murphy tests: 

Size of mill. 25 mile. 30 mile. 35 mile. 40 mile. 
12 ft. 2.5 4 5 6 

16 ft. 4. 6 8 10 

A 20-ft. mill would deliver approximately 50% greater than a 16-ft 



632 AIR. 

riie foregoing table must be translated with reasonable allowances for 
conditions under which wind wheels must work and which cannot well 
be avoided, e.g: Pumping mills must be made to regulate off at a certain 
maximum speed to prevent damage to the attached pumping devices. 
The regulating point is usually; between 20- and 25-mile wind velocities, 
so that no matter how much higher the wind velocity may be the power 
absorbed and deUvered by the wheel will be no greater than that indicated 
at the regulating point. 

Electric storage and lighting from the power of a windmill has been 
tested on a large scale for several years by Charles F. Brush, at Cleveland, 
Ohio. In 1887 he erected on the grounds of his dwelling a windmill 56 ft. 
in diameter, that operates with ordinary wind a dynamo at 500 revolutions 
per minute, with an output of 12,000 watts — 16 electric horse-power — 
charging a storage system that gives a constant lighting capacity of 100 
16 to 20 candle-power lamps. The current from the dynamo is auto- 
matically regulated to commence charging at 330 revolutions and 70 volts, 
and cutting the circuit at 75 volts. Thus, by its 24 hours' work, the 
Storage system of 408 cells in 12 parallel series, each cell having a capacity 
of 100 ampere-hours, is kept in constant readiness for all the requirements 
of the estabhshment, it being fitted up with 350 incandescent lamps, 
about 100 being in use each evening. The plant runs at a mere nominal 
expense for oil, repairs, and attention. (For a fuUer description of this 

£lant, and of a more recent one at Marblehead Neck, Mass., see Lieut, 
lewis's paper in Engineering Magazine, Dec, 1894, p. 475.) 

COMPRESSED AIR. 

Heating of Air by Compression. — Kimball, in his treatise on Physic 
cal Proi)erties of Gases, says: When air is compressed, all the work which 
Is done in the compression is converted into heat, and shows itself in the 
rise in temperature of the compressed gas. In practice many devices are 
employed to carry off the heat as fast as it is developed, and keep the tem- 
perature down. But it is not possible in any way to totally remove tliis 
difficulty. But, it may be objected, if all the work done in compression is 
converted into heat, and if tliis heat is got rid of as soon as possible, then 
the work may be virtually thrown away, and the compressed air can have 
no more energy than it had before compression. It is true that the com- 
pressed gas has no more energy than the gas had before compression, if 
Its temperature is no higher, but the advantage of the compression lies in 
bringing its energy into more available form. 

The total energy of the compressed and uncompressed gas is the same 
at the same temperature, but the available energy is much greater in the 
former. 

When the compressed air is used in driving a rock-drill, or any other 
piece of machinery, it gives up energy equal in amount to the work it does, 
and its temperature is accordingly greatly reduced. 

Causes of Loss of Energy in Use of Compressed Air. (Zahner, on 
Transmission of Power by Compressed Air.) — 1. The compression of 
air always develops heat, and as the compressed air always cools down to 
the temperature of the surrounding atmosphere before it is used, the 
mechanical equivalent of this dissipated heat is work lost. 

2. The heat of compression increases the volume of the air, and hence 
it is necessary to carry the air to a higher pressure in the compressor in 
order that we may finally have a given volume of air at a given pressure, 
and at the temperature of the surrounding atmosphere. The work spent 
in effecting this excess of pressure is work lost. 

3. Friction of the air in the pipes, leakage, dead spaces, the resistance 
offered by the valves, insufficiency of valve-area, inferior workmanship, 
and slovenly attendance, are all more or less serious causes of loss of 
power. 

The first cause of loss of work, namely, the heat developed by compres- 
sion, is entirely unavoidable. The whole of the mechanical energy which 
the compressor-piston spends upon the air is converted into heat. This 
heat is dissipated by conduction and radiation, and its mechanical equiva- 
lent is work lost. The compressed air, having again reached thermal 



COMPRESSED AIR. 633 

equilibrium with the surrounding atmosphere, expands and does work in 
an air motor, losing temperature and intrinsic energy in proportion to 
the work done. 

A large, fall in temperature will cause any moisture in the air to 
freeze, and, unless the air is pre-heated before use in the motor, per- 
mitting it to expand to more than two volumes will cause difficulties. 
It is for this reason, and also because of the heat-losses in the compressor, 
that the lower the pressure at which compressed air is used for power 
transmission the more efficient is the system. Against the increased 
efficiencies of the lower pressures must be balanced the higher cost of 
the mechanisms, on account of size, to utilize the lower pressures. 

The intrinsic energy of any gas is the energy which it is capable of 
exerting against a piston in changing from a given state as to temper- 
ature and volume to a total privation of heat and indefinite expansion. 
The intrinsic energy of i lb. of gas at any pressure and volume is the 
product of its absolute temperature and its specific heat at constant 
volume. (See Thermodynamics.) 

Loss due to Excess of Pressure caused by Heating in the Com- 
pression-cylinderc — If the air during compression were kept at a con- 
stant temperature, the compression-curve of an indicator-diagram taken 
from the cylinder would be an isothermal curve, arid would follow the law 

of Boyle and Mariotte, pv = a constant, or pivi — PoVo, or pi = po. — ,poi'o 

being the pressure and volume at the beginning of compression, and 
Pivi the pressure and volume at the end, or at any intermediate point. 
But as the air is heated during compression the pressure increases faster 
than the volume decreases, causing the work required for any given pres- 
sure to be increased. If none of the heat were abstracted by radiation or 
by injection of water, the curve of the diagram would be an adiabatic 

/-ys 1.405 

curve, with the equation pi = po ( — ) • CooUng the air during com- 
pression, or compressing it in two cylinders, called compounding, and 
cooling the air as it passes from one cyhnder to the other, reduces the 
exponent of this equation, and reduces the quantity of work necessary to 
effect a given compression. F. T. Gause (Am. Mach., Oct. 20, 1892), 
describing the operations of the Popp air-compressors in Paris, says: 
The greatest saving realized in compressing in a single cylinder was 33 per 
cent of that theoretically possible. In cards taken from the 2000 H.P. 
compound compressor at Quai De La Gare, Paris, the saving realized is 
85 per cent of the theoretical amount. Of this amount only 8 per cent is 
due to cooling during compression, so that the increase of economy in the 
compound compressor is mainly due to cooling the air between the two 
stages of compression. A compression-curve with exponent 1.25 is the 
best result that was obtained for compression in a single cylinder and 
cooling with a very fine spray. The curve with exponent 1.15 is that 
which must be realized in a single cyhnder to equal the present economy 
of the compound compressor at Quai De La Gare. 

Adiabatic and Isotliermal Compression. — Theoretically, air may 
be compressed adiabatically, in which case all the heat of compression 
is retained in the air, or isothermally, in which case the heat of com- 
pression is removed as rapidly as it is generated, by some refrigerating 
process. Adiabatic compression is impossible as some of the heat will 
be radiated into the compressor walls, and isothermal compression is 
practically impossible, as the heat must be generated before it can be 
absorbed. The best practical results that have been obtained by 
compressing air in a single stage compressor make it possible to save 
approximately one-third of the loss due to the heat generated in the 
compressor. 

Formulae for Adiabatic Compression or Expansion of Air (or 
Other Sensibly Perfect Gas). 

Let air at an absolute temperature Tu absolute pressure pi, and volume 
vi be compressed to an absolute pressure P2 and corresponding volume vz 
and absolute temperature T2\ or let compressed air of an initial pressure, 
volume, and temperature P2, vi, and T2 be expanded to p\, v\, and T'l, there 
being no transmission of heat from or into the air during the ofjeration 



634 AIR. 

Then the following equations express the relations between pressure, 
volume, and temperature (see works on Thermodynamics): 

V2 \pJ ' pi \V2/ ' V2 \tJ * 
T2^(vi\^'*\ l2^(Pl\^'^. V2^(T^'^^ 

The exponents are derived from the ratio c^ ■*• c^ = A; of the specific 
heats of air at constant pressure and constant volume. Taking k = 
1.406, 1 -i- k = 0.711; A - 1 = 0.406; 1 -^ (A; - 1) = 2.463; A: -f- 
(A: - 1) = 3.463; {k - 1) -^ k == 0.289. 

Work of Adiabatic Compression of Air. — If air is compressed in a 
cylinder without clearance from a volume ^i and pressure pi to a smaller 
volume V2 and higher pressure p2, work equal to pivi is done by the external 
air on the piston while the air is drawn into the cylinder. Work is then 
done by the piston on the air, first, in compressing it to the pressure pa 
and volume V2, and then in expelling the volume V2 from the cylinder 

against the pressure P2. If the compression is adiabatic, PiVi = P2V3 = 
constant, k = 1.406. . 

The work of compression of a given quantity of air is, in foot-pounds, 



k-l 



jPtVl 

k 



2.463 p,v, { {^'■" - 1 } = 2.463 p.., { g)°"- 1 } • 

/7),\ 0.29 

The work of expulsion is P2V2 ~ PiVi ( — ) 

I work is the sum of the work of co 
one on the piston during admissio 

!^i(^r-! -.463...|gr-.i- 

n effective pressure during the stroke is 



The total work is the sum of the work of compression and expulsion less 
the work done on the piston during admission, and it equals" 
x—i 
I h f /7)<) 
pm I 

The mean effective pressure during the stroke is 
k-l 



Pi and Pa are absolute pressures above a vacuum, in pounds per square 
foot. 

Example. — Required the work done in compressing 1 cubic foot of 
air per second from 1 to 6 atmospheres, including the work of expulsion 
from the cylinder. 

^.Kt ^1 = ^: ^^'^ ~ 1 = 0.681; 3.463 X 0.681 = 2.358 atmospheres 
X 14.7 = 34.661b. per sq. in. mean effective pressure, X 144 = 4991 lb. 
per sq.ft., XI ft. stroke=4991 ft.-lb.,-;- 550 f t .-lb. per second = 9.08 H.P. 

If i? = ratio of pressures = P2 -^ pi, and if i;i = 1 cubic foot, the work 
done in compressing 1 cubic foot from pi to p2 is, in foot-pounds, 

3.463 pi (i?o-29_ 1), 
Pi being taken in lb. per sq. ft. For compression at the sea level p, may 
be taken at 14 lbs. per sq. in. = 2016 lb. per sq. ft., as there is some loss 
or pressure due to friction of valves and passages. 

Horse-power required to compress and deliver 100 cubic feet of free air 
per minute = 1.511 Pi (RO'29 - i); P^ being the pressure of the free air in 
pounds per sq. in., absolute. 

Example. To compress 100 cu. ft. from 1 to 6 atmospheres. Pj = 14.7; 
R - 6: 1.511 X 14.7 X 0.681 = 15.13 H.P. 

Indicator-cards from compressors in good condition and under working- 
speeds usually follow the adiabatic line closely. A low curve indicates 
piston leakage. Such cooling as there may be from the cylinder-jacket 
and the re-expansion of the air in clearance-spaces tends to reduce the 



COMPRESSED AIR. 



635 



mean eflPective pressure, while the "camel-backs" in the expulsion-line, 
due to resistance to opening of the discharge-valve, tend to increase it. 

Work of one stroke of a compressor, with adiabatic compression, in 
foot-pounds, 

W= 3.463 PiVi (R 0-29- 1). 
in which Pi = initial absolute pressure in lb. per sq. ft. and Vi = volume 
traversed by piston in cubic feet. 

The work done during adiabatic compression (or expansion) of 1 pound 
of air from a volume vi and pressure pi to another volume V2 and pressure 
P2 is equal to the mechanical equivalent of the heating (or cooling). If 
ti is the higher and t2 the lower temperature, Fahr., the work done is 
c^J (h - ^2) foot-pounds, c^ being the specific heat of air at constant 
volume = 0.1689, and J = 778, c^J = 131.4. 

The work during compression also equals 

l:~[(9""'-]- "•""[©•■'■-]• 

Ba being the value of pv -^ absolute temperature for 1 lb. of air = 53.32. 
The work during expansion is 

2.463 p... [l -(!)""] = 2.463 nv. [g)"-" - l]. 

in which piVi are the initial and P2V2 the final pressures and volumes. 

Compound Compression, with Air Cooled between the Two Cyl- 
inders. {Am. Mach., March 10 and 31, 1898.) — Work in low-pressure 
cyUnder = Wi, in high-pressure cylinder W2. Total work 

TFi + W2 = 3.46 PiVi [riO-29 + 7^0.29 x n -029 _ 2]. 
ri = ratio of joressures in I. p. cyl., r2 = ratio in h.p. cyl., R = rir2. When 
ri = r2 = ^R, the sum Wi + 1^2 is a minimum. Hence for a given total 
ratio of pressures, R, the work of compression, will be least when the ratios 
of the pressures in each of the two cylinders are equal. 

The equation may be simplified, when ri = ^R, to the following: 
TFi 4- TF2 = 6.92 PiVi [i?oi45 _ 1], 

Dividing by Vi gives the mean effective pressure reduced to the low- 
pressure cylinder M.E.P. = 6.92 Pi [i^o-i^a _ 1], 

In the above equation the compression in each cylinder is supposed to 
be adiabatic, but the intercooler is supposed to reduce the temperature 
of the air to that at which compression began. 

Horse-power required to compress adiabatically 100 cu. ft. of free air 
per minute in two stages with intercooling, and with equal ratio of com- 
pression in each cyhnder, = 3.022 Pi (Ro ^^3- 1); Pi being the pressure in 
lbs. per sq. in. , absolute, of the free air, and R the total ratio of compression. 

Example. To compress 100 cu. ft. per min. from 1 to 6 atmospheres. 
P = 14.7; R = 6; 3.022 X 14.7 X 0.2964 = 13.17 H.P. 

Mean Effective Pressures of Air Compressed in Two Stages, assum- 
ing the Intercooler to Reduce the Temperature to that at which 
Compression Began. (F. A. Halsey, Am. Mach., Mar. 31, 1898.) 



R. 


7^0.145, 


M.E.P. 
from 
14 lbs. 
Initial. 


Ultimate 
Saving 

by Com- 
pound- 
ing,%. 


R, 


2^0.145. 


M.E.P. 

from 
14 lbs. 
Initial. 


Ultimate 
Saving 

by Com 
pound- 
ing,%. 


5.0 


1.263 


25.4 


11.5 


9.0 


1.375 


36.3 


15.8 


5.5 


1.280 


27.0 


12.3 


9.5 


1.386 


37.3 


16.2 


6.0 


1.296 


28.6 


12.8 


10 


1.396 


38.3 


16.6 


6.5 


1.312 


30.1 


13.2 


11 


1.416 


40.2 


17.2 


7.0 


1.326 


31.5 


13.7 


12 


1.434 


41.9 


17.8 


7.5 


1.336 


32.8 


14.3 


13 


1.451 


43.5 


18.4 


8.0 


1.352 


34.0 


14.8 


14 


1.466 


45.0 


19.0 


8.5 


1.364 


35.2 


15.3 


15 


1.481 


46.4 


19.4 



R = final -^ initial absolute pressure. 
M.E.P. = mean effective pressure, lb. per sq. in., based on 14 lb. 
absolute initial pressure reduced to the low-pressure cylinder. 



636 



AIR. 



To find the Index of the Curve of an Air-diagram. If PiVi be 

pressure and volume at one point on the curve, and P V the pressure and 

P /Vi\^ 
volume at another point, then p- = (r— J , in which x is the index to be 

found. Let P •^_Pi = R, and Fi -J- 7 = r; then R = r^; log R =rc log r. 
whence x = log R 4- log r. (See also graphic method on page 602.) 

Pressures, Volumes, Mean Effective Pressures, and Final Temper- 
atures, in Single-stage Compression from 1 Atmosphere and 60° Fahr. 

(Contributed by M. C. Wilkinson, San Pedro, Cal., 1914.) 















M. E. P. of 


Final Tem- 




Pressure* 


Volume 




Stroke 


perature. 


a; 


1 


i 


2 


onent 

= 1.25 (best 

actice). 


lonent 
= 1.41 
diabatic). 




12 
§11 


§ II 


§ II 


^ 


2 


s 


Sh 


r1^^ 


S^^ 


&^ 


&^ 


&^ 


&^ 


O 


< 


<; 


o 


H 


^ 


w 


W^ 


H 


H 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 





14.7 


1.0 


I .0000 


1.000 


1.000 


0.000 


0.000 


60.0 


60.0 


1 


15.7 


1.068 


0.9363 


0.948 


0.954 


0.974 


0.982 


66.3 


70.0 


2 


16.7 


1.136 


.8803 


.903 


.910 


1 .896 


1.913 


73.4 


79.6 


3 


17.7 


1.204 


.8305 


.862 


.876 


2.778 


2.810 


79.7 


88.8 


4 


18.7 


1.272 


.7862 


.825 


.841 


3.624 


3.681 


85.6 


97.6 


5 


19.7 


1.340 


.7463 


.791 


.812 


4.432 


4.510 


91.7 


106.1 


10 


24.7 


1.680 


.5952 


.660 


.692 


8.041 


8.267 


116.9 


144.5 


15 


29.7 


2.020 


.4950 


.570 


.607 


11.099 


11.515 


.138.5 


177.7 


20 


34.7 


2.360 


.4237 


.503 


.544 


13.774 


14.396 


157.5 


207.1 


25 


39.7 


2.701 


.3702 


.452 


.494 


16.155 


16.998 


174.3 


233.6 


30 


44.7 


3.041 


.3288 


.411 


.454 


18.309 


19.375 


189.5 


257.9 


35 


49.7 


3.381 


.2955 


.377 


.421 


20 259 


21 .569 


203.5 


280.3 


• 40 


54.7 


3.721 


.2687 


..349 


.393 


22.101 


23.610 


216.3 


301.2 


45 


59.7 


4.061 


.2462 


.326 


.370 


23.777 


25.529 


228.2 


320 8 


50 


64.7 


4.401 


.2272 


.303 


.349 


25.358 


27.331 


239.4 


339.2 


55 


69.7 


4.742 


.2109 


.288 


.329 


26 842 


29.037 


249.9 


356.7 


60 


74.7 


5.082 


.1968 


.272 


.315 


28.239 


30.661 


259.8 


373.2 


65 


79.7 


5.422 


.1844 


.258 


.301 


29.562 


32.808 


269.2 


388.9 


70 


84.7 


5.762 


.1736 


.247 


.288 


30.826 


33.680 


278.1 


404.0 


75 


89.7 


6.102 


.1639 


.235 


.277 


32.031 


35.105 


286.6 


418.6 


80 


94.7 


6.442 


.1552 


.225 


.266 


33.185 


36.469 


294.8 


432.5 


85 


99.7 


6.782 


.1474 


.216 


.257 


34.288 


37.782 


302.6 


446.0 


90 


104.7 


7.122 


.1404 


.208 


.248 


35.346 


39.050 


310.1 


458.9 


95 


109.7 


7.463 


.1340 


.200 


.240 


36.368 


40.277 


317.3 


471.4 


100 


114.7 


7.803 


.1282 


.192 


.233 


37.354 


41 .463 


324.3 


483.5 


105 


119.7 


8.143 


.1228 


.186 


.226 


38.401 


42.613 


331.0 


495.3 


110 


124.7 


8.483 


.1179 


.181 


.219 


39.220 


43 . 728 


337.5 


506.7 


115 


129.7 


8.823 


.1133 


.175 


.213 


40.109 


44.813 


343.8 


517.8 


120 


134.7 


9.163 


.1091 


.170 


.207 


40.969 


45.866 


349.9 


528.6 


125 


139.7 


9.503 


.1052 


.165 


.202 


41.807 


46.900 


355.8 


539.1 


130 


144.7 


9.844 


.1015 


.160 


.197 


42.623 


47.898 


361.6 


549.3 


135 


149.7 


10.184 


.0982 


.156 


.192 


43.416 


48.880: 367.2 


559.3 


140 


154.7 


10.524 


.0950 


.152 


.188 


44.189 


49.832 372.6 


569.0 


145 


159.7 


10.864 


.0921 


.148 


.184 


44.938 


50.769 


377.9 


578.6 


150 


164.7 


11.204 


.0893 


.145 


.180 


45 . 766 


51.681 


383.1 


587.9 


160 


174.7 


11.884 


.0841 


.138 


.172 


47.084 


53.451 


393.1 


606.0 


170 


184.7 


12.565 


.0796 


.132 


.166 


48.429 


55.147 


402.7 


623.3 


180 


194.7 


13.245 


.0755 


.126 


.160 


49.723 


56.781 


411.8 


641.0 


190 


204.7 


13.295 


.0718 


.121 


.154 


50.968 


58.359 


420.6 


656.1 


200 


214.7 


14.605 


.0685 


.117 


.147 


52.156 


59.881 


429.0 


671.7 



Columns 1, 2 and 3 give the relative pressure readings in gage, 
aDsolute and atmospheric pressures. 



COMPRESSED AIR. 



637 



Column 4 gives the relative volumes of the air after compression and 
with the temperature reduced to 60° F. These are the volumes that 
are available for use in the operation of the driven mechanisms. 

Column 5 gives the relative volumes of the air as the compressor 
has to deal with it. 

Column 7 gives the mean effective pressures of a single stroke of the 
compressor, including the compression and expulsion of air from the 
cylinder. In computing the power required to operate the com- 
pressor a certain percentage (usually from 5 to 20) must be added 
for mechanical friction and valve resistance and other compressor 
characteristics. 

Column 9 gives the temperature of the air as it leaves the com- 
pressor. 

Columns 6, '8 and 10 give the theoretical, final volumes, mean effec- 
tive pressures and final temperatures of air compressed adiabatically. 

Mean Effective Pressures of Air Compressed Adiabatically. 

(F. A. Halsey, Am. Mach., Mar. 10, 1898.) 







M.E.P. from 






M.E.P. from 


R. 


720-29. 


14 lbs. 
Initial. 


R, 


720-29. 


14 lbs. 
Initial. 


1.25 


1.067 


3.24 


4.75 


1.570 


27.5 


1.50 


1.125 


6.04 


5 


1.594 


28.7 


1.75 


1.176 


8.51 


5.25 


1.617 


29.8 


2 


1.223 


10.8 


5.5 


1.639 


30.8 


2.25 


1.265 


12.8 


5.75 


1.660 


31.8 


2.5 


1.304 


14.7 


6 


1.681 


32.8 


2.75 


1.341 


16.4 


6.25 


1.701 


33.8 


3 


1.375 


18.1 


6.5 


1.720 


34.7 


3.25 


1.407 


19.6 


6.75 


1.739 


35.6 


3.5 


1.438 


21.1 


7 


1.757 


36.5 


3.75 


1.467 


22.5 


7.25 


1.775 


37.4 


4 


1.495 


23.9 


7.5 


1.793 


38.3 


4.25 


1.521 


25.2 


8 


1.827 


39.9 


4.5 


1.546 


26.4 









R = final 4- initial absolute pressure. 

M.E.P. =mean effective pressure, lb. per sq. in., based on 14 lb. initial. 



Horse-power required to com- 
press and deliver One Cubic Foot 
of Free Air per minute to a given 
pressure with no cooling of the air 
during the compression; also the 
horse power required, supposing the 
air to 'be maintained at constant 
temperature during the compression. 



Air constant 
temperature. 

0.0188 

0.0333 

0.0551 

0.0713 

0.0843 

0,0946 

0.1036 

0.1120 

0.1195 

0.1261 

0.1318 



Gauge- 


Air not 


pressure. 


cooled. 


5 


0.0196 


10 


0.0361 


20 


0.0628 


30 


0.0846 


40 


0.1032 


50 


0.1195 


60 


0. 1342 


70 


0.1476 


80 


0.1599 


90 


0.1710 


100 


0.1815 



n.P. required to compress and 
deliver One Cubic Foot of Com- 
pressed Air per minute at a given 
pressure (the air being measured at 
the atmospheric temperature) with 
no cooling of the air during the 
compression; also supposing the air 
to be maintained at constant tem- 
perature during the compression. 



Gauge- 


Air not 


Air constant 


pressure. 


cooled. 


temperature. 


5 


0.0263 


0.0251 


10 


0.0606 


0.0559 


20 


0.1483 


0.1300 


30 


0.2573 


0.2168 


40 


0.3842 


0.3138 


50 


0.5261 


0.4166 


60 


0.6818 


0.5266 


70 


0.8508 


0.6456 


80 


1.0302 


0.7700 


90 


1.2177 


0.8979 


100 


1.4171 


1.0291 



The horse-power given above is the theoretical power, no allowance 
being made for friction of the compressor or other losses, wliich may 
amount to 10 per cent or more. 



638 



AIR. 



Compressed-air Engines, Adiabatic Expansion. — Let the initial 
pressure and volume taken into the cylinder be pi lb. per sq. ft. and Vi 
cubic feet; let expansion take place to p2 and V2 according to the adiabatic 
law pivi^*^ = P2V2^-*^; then at the end of the stroke let the pressure drop 
to the back-pressure Ps, at which the air is exhausted. Assuming no 
clearance, the work done by one pound of air during admission, measured 

above vacuum, is pivi, the work during expansion is 2.463 PiVi 1 — 

f — j I, and the negative or back pressure work is —P2V2. The total 

work is PiVt + 2.463 PiVt 1 — (— ) — P3V2, and the mean effective pres- 
sure is the total work divided by V2. 

If the air is expanded down to the back-pressure ps the total work is 

3.463 p...{l-g)°^'}. 
or, in terms of the final pressure and volume, 

3.463P3.^{(D°"-1}. 
and the mean effective pressure is 

3.463 .3{(f-f»-l}. 

The actual work is reduced by clearance. When this is considered, the 
product of the initial pressure pi by the clearance volume is to be sub- 
tracted from the total work calculated from the initial volume vi, including 
clearance. (See p. 961 under " Steam-engine. *') 

Mean and Terminal Pressures of Compressed Air used Expansively 
for Gauge Pressures from 60 to 100 lb. 

(Frank Richards, Am. Mack., April 13, 1893.) 



d 

5 

3 










Initial Pressure. 








60 


70 


80 


90 


100 





C CO 


Terminal 

Air- 
pressure. 




Terminal 

Air- 
pressure. 


n 


Terminal 

Air- 
pressure. 


6 

ft 


Terminal 

Air- 
pressure. 


ft 


Terminal 

Air- 
pressure. 


.25 


23.6 


10.65 


28.74 


12.07 


33.89 


13.49 


39.04 


14.91 


44.19 


1.33 


.30 


28.9 


13.77 


34.75 


0.6 


40.61 


2.44 


46.46 


4.27 


53.32 


6.!l 


i 


32.13 


0.96 


38.41 


3.09 


44.69 


5.22 


50.98 


7.35 


57.26 


9.48 


.35 


33.66 


2.33 


40.15 


4.38 


46.64 


6.66 


53.13 


8.95 


59.62 


11.23 


f 


35.85 


3.85 


42.63 


6.36 


49.41 


7.88 


56.2 


11.39 


62.98 


13.89 


.40 


37.93 


5.64 


44.99 


8.39 


52.05 


11.14 


59.11 


13.88 


66.16 


16.64 


.45 


41.75 


10.71 


49.31 


12.61 


56.9 


15.86 


64.45 


19.11 


72.02 


22.36 


.50 


45.14 


13.26 


53.16 


17. 


61.18 


20.81 


69.19 


24.56 


77.21 


28.33 


.60 


50.75 


21.53 


59.51 


26.4 


68.28 


31.27 


77.05 


36.14 


85.82 


41.01 


i 


51.92 


23.69 


60.84 


28.85 


69.76 


34.01 


78.69 


39.16 


87.61 


44.32 


Jo 


53.67 


27.94 


62.83 


33.03 


71.99 


38.68 


81.14 


44.33 


90.32 


49.97 


54.93 


30.39 


64.25 


36.44 


73.57 


42.49 


82.9 


48.54 


92.22 


54.59 


.75 


56.52 


35.01 


66.05 


41.68 


75.59 


48.35 


85.12 


55.02 


94.66 


61.69 


.80 


57.79 


39.78 


67.5 


47.08 


77.2 


54.38 


86.91 


61.69 


96.61 


68.99 


i 


59.15 


47.14 


69.03 


55.43 


78.92 


63.81 


88.81 


72. 


98.7 


80.28 


.90 


59.46 


49.65 


69.38 


58.27 


79.31 


66.89 


89.24 


75.52 


99.17 


87.82 



Pressures in italics are absolute; all others are gage pressures 



AIR COMPRESSION AT ALTITUDES. 



639 



AIR COMPRESSION AT ALTITUDES. 

(Ingersoll-Rand Co. Copyright, 1906, by F. M. Hitchcock.) 
Multipliers to Determine the Volume of Free Air which., when 
Compressed, is Equivalent in Effect to a Given Volume of Free 
Air at Sea Level. 



Alti- 


Barometric 
Pressure. 


( 


jauge Pressure (Pounds). 




tude, 
Feet. 












In. of 
Mercury. 


Lb. per 

Sq. In. 


60 


80 


100 


125 


150 


1,000 


28.88 


14.20 


1.032 


1.033 


1.034 


1.035 


1.036 


2,000 


27.80 


13.67 


1.064 


1.066 


1.068 


1.071 


1.072 


3,000 


26.76 


13.16 


1.097 


1.102 


1.105 


1.107 


1.109 


4,000 


25.76 


12.67 


1.132 


1.139 


1.142 


1.147 


1.149 


5,000 


24.79 


12.20 


1.168 


1.178 


1.182 


1.187 


1.190 


6,000 


23.86 


11.73 


1.206 


1.218 


1.224 


1.231 


1.234 


7,000 


22.97 


11.30 


1.245 


1.258 


1.267 


1.274 


1.278 


8,000 


22.11 


10.87 


1.287 


1.300 


1.310 


1.319 


1.326 


9,000 


21.29 


10.46 


1.329 


1.346 


1.356 


1.366 


1.374 


10,000 


20.49 


10.07 


1.373 


1.394 


1.404 


1,416 


1.424 



Horse-power Developed in Compressing One Cubic Foot of Free Air 
at Various Altitudes from Atmospheric to Various Pressures. 

Initial Temperature of the Air in Each CyHnder Taken as 60° F.; Jacket 
CooUng not Considered ; Allowance made for usual losses. 





Simph 


3 Compression. 


Two Stage Compression. 


Altitude, 
Feet. 


Gauge Pressure 
(Pounds). 


Gauge Pressure (Pounds). 




60 


80 


100 


60 


80 


100 


125 


150 





0.1533 


0.1824 


0.2075 


0.1354 


0.1580 


0.1765 


0.1964 


0.2138 


1,000 


0.1511 


0.1795 


0.2040 


0.1332 


0.1553 


0.1734 


0.1926 


0.2093 


2,000 


0.1489 


0.1766 


0.2006 


0.1310 


0.1524 


0.1700 


0.1887 


0.2048 


3,000 


0.1469 


0.1739 


0.1971 


0.1286 


0.1493 


0.1666 


0.1848 


0.2003 


4,000 


0.1448 


0.1712 


0.1939 


0.1263 


0.1464 


0.1635 


0.I8I0 


0.1963 


5,000 


0.1425 


0.1685 


0.1906 


0.1241 


0.1438 


0.1600 


0.1772 


0.1921 


6,000 


0.1402 


0.1656 


0.1872 


0.1218 


0.1409 


0.1566 


0.1737 


0.1879 


7,000 


0.1379 


0.1628 


0.1839 


0.1197 


0.1383 


0.1536 


0.1700 


0.1838 


8,000 


0.1358 


0.1600 


0.1807 


0.1173 


0.1358 


0.1504 


0.1662 


0.1797 


9,000 


0.1337 


0.1572 


0.1774 


0.1I5I 


0.1329 


0.1473 


0.1627 


0.1758 


10.000 


0.1316 


0.1547 


0.1743 


0.1132 


0.1303 


0.1442 


0.1592 


0.1717 



Example. — Required the volume of free air which when compressed 
to 100 lb. gauge at 9,000 ft. altitude will be equivalent to 1,000 cu. ft. 
of free air at sea level; also the power developed in compressing this 
volume to 100 lb. gauge in two stage compression at this altitude. 

From first table the multipUeris 1.356. Equivalent free air = 1,000 X 
1.356 = 1,356 cu, ft. 

From second table, power developed in compressing 1 cu. ft. of free air 
is 0.1473 H.P.; 1,356 X 0.1473 = 199.73 H.P. 

The Popp Compressed-air System in Paris. — A most extensive 
system of distribution of power by means of compressed air is that of 
M. Popp, in Paris. One of the central stations is laid out for 24,000 
horse-power. For a very complete description of the system, see Engineer- 
ing, Feb. 15, June 7, 21, and 28, 1889, and March 13 and 20, April 10, and 
May 1, 1891. Also Proc, Inst. M. E., July, 1889. A condensed descrip- 
tion will be found in Modern Mechanism, p. 12. 

Utilization of Compressed Air in Small 3Iotors. — In the earliest 
stages of the Popp system in Paris it was recognized that no good results 



640 AIR. 

could be obtained if the air were allowed to expand direct into the motor; 
not only did the formation of ice due to the expansion of the air rapidly 
accumulate and choke the exhaust, but the percentage of useful work 
obtained, compared with that put into the air at the central station, was 
so small as to render commercial results hopeless. 

After a number of experiments M. Popp adopted a simple form of 
cast-iron stove lined with fire-clay, heated either by a gas jet or by a 
small coke fire. Tliis apparatus answered the desired purpose until a 
better arrangement was perfected, and the tj^pawas accordingly adopted 
throughout the whole system. The economy resulting from the use of 
the improved form was very marked. 

It was found that more than 70% of the total heating value of the fuel 
employed was absorbed by the air and transformed into useful work. 
The efficiency of fuel consumed in this way is at least six times greater 
than when utilized in a boiler and steam-engine. According to Prof. 
Riedler, from 15% to 20% above the power at the central station can be 
obtained by means at the disposal of the power users. By heating the 
air to 480° F. an increased efficiency of 30% can be obtained. 

A large number of motors in use among the subscribers to the Com- 
pressed Air Company of Paris are rotary engines developing 1 H.P. and 
less, and these in the early times of the industry were very extravagant 
in their consumption. Small rotary engines, working cold air without 
expansion, used as high as 2330 cu. ft. of air per brake H.P. per hour, 
and with heated air 1624 cu. ft. Working expansively, a 1-H.P. rotary 
engine used 1469 cu. ft. of cold air, or 960 cu. ft. of heated air. and a 
2-H.P. rotary engine 1059 cu. ft. of cold air, or 847 cu. ft. of air, heated 
to about 122° F. 

The efficiency of this type of rotary motors, with air heated to 122° F., 
may now be assumed at 43%. 

Tests of a small Riedinger rotary engine, used for driving sewing- 
machines and indicating about 0.1 H.P., showed an air-consumption of 
1377 cu. ft. per H.P. per hour when the initial pressure of the air was 
86 lb. per sq. in. and its temperature 54° F., and 988 cu. ft. when the air 
was heated to 338° F., its pressure being 72 lb. With a V2-H.P. variable- 
expansion rotary engine the air-consumption was from 800 to 900 cu. ft. 
per H.P. per hour for initial pressures of 54 to 85 lb. per sq. in. with the 
air heated from 336° to 388° F., and 1148 cu. ft. with cold air, 46° F., and 
an initial pressure of 72 lb. The volumes of air were all taken at atmos- 
pheric pressure. 

Trials made with an old single-cylinder 80-horse-power Farcot steam° 
engine, indicating 72 H.P., gave a consumption of air per brake H.P. as 
low as 465 cu. ft. per hour. The temperature of admission was 320° F., 
and of exhaust 95° F. 

Prof. Elliott gives the following as typical results of efficiency for 
various systems of compressors and air-motors: 

Simple compressor and simple motor, efliciency 39.1% 

Compound compressor and simple motor, " 44.9 

" compound motor, efficiency. . 50.7 
Triple compressor and triple motor, efficiency 55.3 

The efficiency is the ratio of the I. H.P. in the motor cylinders to the 
I. H.P. in the steam-cylinders of the compressor. The pressure as- 
sumed is 6 atmospheres absolute, and the losses are equal to those 
found in Paris over a distance of 4 miles. 
Summary of Efficiencies of Compressed-air Transmission at Paris, 

between the Central Station at St. Fargeau and a 10-horse-power 

Motor Working with Pressure Reduced to 41/2 Atmospheres. 

(The figures below correspond to mean results of two experiments cold and 
two heated.) 

One indicated horse-power at central station gives 0.845 1.H.P. in com- 
pressors, and corresponds to the compression of 348 cu. ft. of air per hour 
from atmospheric pressure to 6 atmospheres absolute. 

0.845 I. H.P. in compressors delivers as much air as will do 0.52 I.H.P. 
in adiabatic expansion after it has fallen to the normal temperature of the 
mains. 

The fall of pressure in mains between central station and Paris (say 5 
kilometres) reduces the possibility of work from 0.52 to 0.51 I.H.P. 



AIK COMPRESSORS. 



641 



The further fall of pressure through the reducing valve to 41/2 atmos- 
pheres (absolute) reduces the possibility of work from 0.51 to 0.50. 

Incomplete expansion, wire-drawing, and other such causes reduce the 
actual I.H.P. of the motor from 0.50 to 0.39. 

By heating the air before it enters the motor to about 320° F., the 
actual I.H.P. at the motor is, however, increased to 0.54. The ratio of 
gain by heating the air is, therefore, 0.54 -^ 0.39 = 1.38. 

In this process additional heat is suppUed by the combustion of about 
0.39 lb. of coke per I.H.P. per hour, and if this be taken into account, the 
real indicated efficiency of the whole process becomes 0.47 instead of 0.54. 

Working with cold air the work spent in driving the motor itself reduces 
the available horse-power from 0.39 to 0.26. 

Working with heated air the work spent in driving the motor itself 
reduces the available horse-power from 0.54 to 0.44. 

A summary of the efficiencies is as follows: 

Efficiency of main engines 0.845. 

Efficiency of compressors 0.52 -^ 0.845 = 0.61. 

Efficiency of transmission through mains 0.51 -r- 0.52 = 0.98. 

Efficiency of reducing valve 0.50 -^ 0.51 -= 0.98. 

The combined efficiency of the mains and reducing valve between 5 and 
41/2 atmospheres is thus 0,98 X 0.98 = 0.96. If the reduction had been 
to 4, 31/2, or 3 atmospheres, the corresponding efficiencies would have 
been 0.93, 0.89, and 0.85 respectively. 

Indicated efficiency of motor 0.39 -^ 0.50 = 0.78. 

Indicated efficiency of whole process with cold air 0.39. Apparent 
indicated efficiency of whole process with heated air 0.54. 

Real indicated efficiency of whole process with heated air 0.47. 

Mechanical efficiency of motor, cold, 0.67. 

Mechanical efficiency of motor, hot, 0.81. 



IngersoU-Band Co.'s Air Compressors.* 

Straight Line Power-Driven Compressors, Class ' 
Air Pressure 10 to 125 Poimds per sq. in. 



ER-1.' 



Cylinders, 


Piston 


Air 


Brake 


Cylinders, 


Piston 


Air 


Brake 


Inches. 


Dis- 


Pres. 


H.P. at 


Inches. 


Dis- 


Pres. 


H.P. at 






place- 
ment 


De- 
signed 


Motor, 
includ- 






place- 
ment 


De- 
signed 


Motor, 
includ- 




c3 




6 


J^ 


-^ 


Cu.ft. 


for 


ing 


g 


-^ 


Cu.ft. 


for 


ing 


.i!i 


f=! 


per 


Lb. 


Belt 


.2 


f1 


per 


Lb. 


Belt 


Q 


C/i 


Min. 


Gage. 


Loss. 


Q 


ai 


Min. 


Gage. 


Loss. 


6 


6 


52 


80-125 


8 -10 


10 


10 


210 


80-125 


33-38 


7 


6 


72 


50-100 


91/2-12 


12 


10 


304 


50-100 


38-50 


8 


6 


94 


25- 50 


91/2-12 


14 


10 


415 


20-50 


32-50 


9 


6 


121 


10- 25 


10 -121/4 


17 


10 


615 


10- 20 


27-48 


12 


6 


215 


10- 


15 - 












8 


8 


113 


80-125 


17 -22 


12 


12 


340 


80-125 


54-61 


9 


8 


145 


60-100 


191/2-24 


14 


12 


464 


45-100 


5^73 


10 


8 


179 


25- 60 


18 -25 


17 


12 


688 


30- 45 


55-73 


12 


8 


258 


15- 25 


201/2-25 


20 


12 


955 


15- 30 


35-70 


14 


8 


354 


10- 15 


21 -25 













Stroke, inches 6 8 10 12 

Revolutions per minute. . 275 250 235 220 

Belt wheel 36 X 51/2 45 X 8I/2 58 X IOI/2 72 X 141/2 

These machines are also built for steam-drive. 



* These tables are considerably abridged from the originals, and show 
only the small and medium-sized machines. Large machines up to 
8,500 cu. ft. capacity are made, usually of special designs. 



642 








AIR. 










4 


•Imperial XB-1" Duplex 


Power-Driven Compressors. 






Air Pressure 


15 to 100 Pounds per sq. in. 






i 




^a 


Pklc-oj 


Is 


1 


||d 


2S 

3 **"" 


^1^-3 


0< !^ 
Si} 

.3 f- 


a 
1 


IS? 

w 5^ 






3 

OS 

5^ 


1 


iston Displ 
ent Cu. Ft 
Air per M 






Q< 


^ 


Kg 










OhS 






7 


10 


198 


60-100 


27-37 


14 


14 


916 


35-40 


93-102 


8 


10 


258 


40-55 


29-35 


16 


14 


1198 


25-30 


99-112 


9 


10 


327 


27-35 


27-34 


18 


14 


1518 


15-20 


87-108 


10 


10 


405 


22-25 


29-33 












11 


10 


, 491 


15-20 


28-35 


13 


16 


826 


80-100 


135-154 












14 


16 


959 


65-75 


142-155 


8 


12 


289 


75-100 


47-55 


15 


16 


1103 


45-60 


129-155 


9 


12 


367 


55-70 


50-58 


17 


16 


1419 


30-40 


129-158 


10 


12 


454 


40-50 


51-58 


19 


16 


1775 


20-25 


123-145 


11 


12 


549 


27-35 


46-57 


21 


16 


2171 


15-20 


126-157 


12 


12 


655 


22-25 


47-54 












13 


12 


770 


15-20 


44-55 


15 


16a 


1100 


80-100 


181-206 












16 


16a 


1253 


55-75 


188-202 


9 


12a 


365 


85-100 


62-69 


18 


16a 


1592 


35-50 


161-205 


10 


12a 


453 


60-80 


64-75 


21 


16a 


2168 


25-30 


177-202 


11 


12a 


549 


47-55 


66-74 


24 


16a 


2836 


15-20 


162-202 


12 


12a 


654 


37-45 


67-78 












13 


12a 


769 


25-35 


63-80 


15 


20 


1254 


75-100 


197-232 


15 


12a 


1025 


15-20 


58-72 


17 


20 


1615 


50-70 


204-251 












19 


20 


2020 


35-45 


214-242 


11 


14 


563 


80-100 


94-106 


22 


20 


2714 


25-30 


223-255 


12 


14 


671 


60-75 


95-108 


25 


20 


3508 


15-20 


203-253 


13 


14 


789 ! 45-55 


94-106 













Stroke of cylinder, in. . 10 12 12a 14 16 16a 20 
Revolutions per min . . 225 210 210 185 170 170 155 
Belt wheel, diameter in. 54 ' 60 72 84 96 96 108 
Belt wheel, face in 8 1/2 10 1/2 12 1/2 16 1/2 20 1/2 28 1/2 311/2 

"Imperial XB-2" Two-Stage Power-Drr^en Air Compressors. 
For air pressure of 80 to 100 pounds per sq. in. — For sea level. 



Diameter of Air 
Cylinders, Inches 


Rev. 
per 
Min. 


Piston 
Dis- 
place- 
ment, 
Cu. Ft. 
Free Air 
per Min. 


Brake H.P. 
Required at 
Belt Wheel. 


Belt 
Wheel. 


Low 


High 
Press. 


Stroke. 


Air Pressure. 


Diam., 
Inches. 


Face, 


Press. 


80 


100 


Inches. 


10 
12 
14 
16 
19 
22 
23 


6V2 

10 
12 
13 
14 


10 
12 
12 
14 
16 
16 
20 


225 
210 
210 
185 
170 
170 
155 


203 
327 
446 
599 
888 
1190 
1482 


32 
50 
68 
92 
135 
183 
225 


36 

57 
76 
104 
152 
206 
254 


54 
60 
72 
84 
96 
96 
108 


81 

101 ; 

121 .; 
161 

20^ :. 
281 ; 

311/; 



For 5,000 feet altitude the low-pressure cvlinders are made 1 inch 
larger diameter, and for 10,000 feet altitude 2 inches larger. 

"Imperial X-2" Duplex Steam-Driven Two-Stage Air Compressors. 

Air cylinders of the same dimensions as the XB-2 compressors. 
The duplex steam cyhnders have diameters 7, 8, 9, 10. 12, and 14 
inches. The 14 X 20-inch cyUnder is designed for 150 r. p. m, 



TESTS OF AIR COMPRESSORS. 



643 



Duplex Steam-Drwen "Imperial X-1" Compressors. 
For air pressures of 15 to 100 lb. per sq. in. — Steam, 80 to 120 lb. 



Cylinder 




Piston Displace- 
ment Cu.Ft. Free 
Air per Min. 


0) fe 


g 


Cylinder 


\^i 






Diam., In. 


Ph* 
P^ 




Is 


Diam., In. 


P^ 




a 






o 


^72 


Q 


i 

o 


Ph'>» 
1— 1 




7 


10 


225 


198 


60-100 


28-38 


10 


14 


14 


185 


916 


35-40 


96-105 




8 


10 


225 


258 


40-55 


30-36 


10 


16 


14 


185 


1198 


25-30 


103^116 




9 


10 


225 


327 


27-35 


27-34 


10 


18 


14 


185 


1518 


15-20 


90-112 




iO 


10 


225 


405 


22-25 


29-34 


















11 


10 


225 


491 


15-20 


29-36 


12 


13 


16 


170 


826 


80-100 


141-161 
















12 


14 


16 


170 


959 


65-75 


149-162 


8 


8 


12 


210 


289 


75-100 


48-57 


12 


15 


16 


170 


1103 


45-60 


135-163 


8 


9 


12 


210 


367 


55-70 


51-60 


12 


17 


16 


170 


1419 


30-40 


135-165 


8 


10 


12 


210 


454 


40-50 


53-61 


12 


19 


16 


170 


1775 


20-25 


128^151 


8 


11 


12 


210 


549 


27-35 


46-59 


12 


21 


16 


170 


2171 


15-20 


131-164 


8 


12 


12 


210 


655 


22-25 


47-56 
















8 


13 


12 


210 


770 


15-20 


46-57 


14 


15 


16 


170 


1100 


80-100 


186-212 
















14 


16 


16 


170 


1253 


55-75 


173-209 


9 


9 


12 


210 


365 


85-100 


65-72 


14 


18 


16 


170 


1592 


35-50 


166-212 


9 


10 


12 


210 


453 


60-80 


67-79 


14 


21 


16 


170 


2168 


25-30 


183-208 


9 


11 


12 


210 


549 


47-55 


69-78 


14 


24 


16 


170 


2836 


15-20 


168-209 


9 


12 


12 


210 


654 


37-45 


69-81 
















9 


13 


12 


210 


769 


25-35 


66-84 


14 


15 


20 


150 


1213 


75-100 


196-232 


9 


15 


12 


210 


1025 


15-20 


61-76 


14 


17 


20 


150 


1562 


50-70 


204-251 
















14 


19 


20 


150 


1955 


35-45 


204-242 


10 


11 


14 


185 


563 


80-100 


98-110 


14 


22 


20 


150 


2626 


25-30 


224-255 


10 


12 


14 


185 


671 


60-75 


98-112 


14 


25 


20 


150 


3395 


15-20 


203-253 


10 


13 


14 


185 


789 


45-55 


97-110 

















Compound Steam Cylinders for "Imperial X" Compressors. 

For substituting in place of Duplex Steam Cylinders in the "Imperial 

X-1 and X-2" Tables for Steam-Pressures of 100 to 120 Lbs. 

Condensing or Non-Condensing. 



Compound Engines with Plain "D" 
Steam Valves. 


Compound Engines with Meyer 
Cut-off Valves. 


Standard 

Duplex 

Steam 

Cylinders. 


Standard 
Compound 

Steam 
Cylinders. 


Stroke. 


Standard 
Duplex 
Steam 

Cylinders. 


Standard 
Compound 

Steam 
Cylinders. 


Stroke. 


7& 7 
8«&8 
9&9 


7& 11 
8& 13 
10& 16 


10 
12 
12 


10& 10 
12& 12 
14& 14 
14& 14 


12& 19 
14&22 
16&25 
16&25 


14 
16 
16 
20 



Tests of Power-driven Air Compressors. — R. L. Webb, Portland, Ore., 
has furnished the author with a copy of a complete report of a test 
made by him in 1912, of tliree air compressors, two of them 18 in. diam. 
X 12 in. stroke, rated at 1000 cu. ft. per min. displacement, and the 
third 22 X 12 in., rated at 1500 cu. ft. Nos. 1 and 3 were designed for 
35 to 45 lb. gage-pressure and No. 2 for 15 to 20 lb. The compres- 
sors were driven by 500 volt d.c. shunt, commutating pole motors, with 
a speed range of 2 to 1, through Link-Belt silent chain drives, 2 in. pitch, 
9 in. wide, chain speed, 1600 ft. per min., pinions 17 and 64 teeth, chain 
gear eflaciency about 98%; gear submerged in oil. The speed control 
was regulated by the air pressure. The air delivered was measured 



644 



AIR. 



by the orifice method, using Fliegner's equation. 
tests are summarized in the table below: 



The results of the 







Tests 


OF Air Compressors. 










1^ 


Displace- 
ment, Cu. 
Ft. per 
Min. 


Output, 
Cu. Ft. 
per Min. 


a; S 0) 




Electrical 
Horse- 
power. 


Indicated 
Horse- 
power. 




5^ 



Compressor No. 1, 18 X 12 in. 



71.6 
102.0 
143.0 



502.1 
715.3 
1002.8 



412.3 


82.11 


45.6 


597.4 


83.2 


67.7 


873.3 


87.1 


87.1 



61.2 
90.7 
133.4 



51.75 


84.5 


75.28 


83.0 


06.73 


80.0 



44.6 
44.5 
44.2 



Compressor No. 2, 22 X 12 in. 



70.7 
103.8 
141.0 



749.8 
1100.8 
1495.3 



657.1 


85.6 


42.1 


986.0 


89.5 


65.0 


1333.9 


89.2 


97.6 



56.4 
87.1 
130.8 



48.3 
73.1 
106.5 



85.7 
83.0 
80.0 



19.6 
19.2 
19.5 



Compressor No. 3, 18 X 12 in. 



70.2 
101.0 
145.0 



492.3 
708.3 
1016.9 



371.1 


75.4 


43.9 


567.2 


80.1 


65.8 


837.1 


82.3 


100.7 



58.8 
88.3 
135.0 



50.0 
73.4 
109.1 



85.0 
84.0 
80.7 



44.8 
44.7 
44.4 



Steam Required to Compress 100 Cu. Ft. of Free Air. (O. S. 

Shantz, Power, Feb. 4, 1908.) — The fonowing tables show the number of 
pounds of steam required to compress 100 cu. ft. of free air to different 
gauge pressures, by means of steam engines using from 12 to 40 lbs. of 
steam per I.H.P. per hour. The figures assume adiabatic compression 
in the air cyhnders, with intercooling to atmospheric temperature in the 
case of two-stage compression, and 90% mechanical efficiency of the 
compressor. 

Steam Consumption of Air Compressors — Single-Stage Compression. 



Air 
Gage 


Steam per I.H.P. Hour. Lb. 


Pres- 
sure. 


12 1 14 1 16 1 18 1 20 1 22 


24 1 26 1 28 1 30 1 32 1 36 


40 


20 


1.36 


1.5811.82 


2.041 2.261 2.49 


2.721 2.941 3.171 3.40 


3.611 4.08 


4.54 


30 


1.84 


2.14 


2.45 


2.76 


3.06 


3.37 


3.68 


3.98 


4.29 


4.60 


4.90 


5.51 


6.12 


40 


2.26 


2.64 


3.02 


3.39 


3.77 


4.15 


4.52 


4.90 


5.26 


5.65 


6 03 


6 78 


7.50 


50 


2.62 


3.06 


3.50 


3.93 


4.36 


4.80 


5.25 


5.68 


6.10 


6.55 


7.00 


8.86 


8.71 


60 


2.92 


3.41 


3.90 


4.38 


4.80 


5.36 


5.85 


6.32 


6,80 


7.30 


7,80 


8 76 


9.71 


70 


3.22 


3.76 


4.30 


4.83 


5.36 


5.90 


6.45 


6,97 


7.50 


8 05 


8 60 


9 66 


10.70 


80 


3.50 


4.08 


4.67 


5.25 


5.84 


6.42 


7.00 


7,59 


8.15 


8,75 


9 34 


10.50 


11.61 


90 


3.72 


4.34 


4.96 


5.58 


6.20 


6.82 


7.45 


8 05 


8,66 


9 ^0 


9 94 


11.15 


12.35 


100 


3.96 


4.61 


5.29 


5.95 


6.60 


7.25 


7,92 


8 58 


9 22 


9 90 


10 56 


11 88 


13.15 


110 


4.18 


4.87 


5.58 


6.26 


6.96 


7.66 


8,36 


9 05 


9 75 


10 45 


11 15 


12 52 


13.90 


120 


4.38 


5.11 


5.85 


6.57 


7.30 


8.04 


8.76 


9.50 


10.20 


10.95 


11.66 


13.13 


14.55 



Two-Stage Compression. 



70 


2.82 


3.25 


3.76 


4.23 


4.69 


5.16 


5,63 


6,10 


6,56 


7.04 


7.50 


8.45 


9.35 


80 


3.01 


3.51 


4.03 


4.52 


5.02 


5.53 


6,03 


6,53 


7.03 


7.53 


8.03 


9.05 


10.01 


90 


3.19 


3.72 


4.26 


4.79 


5.32 


5.85 


6,38 


6.91 


7.44 


7.98 


8.50 


9.57 


10.60 


100 


3.37 


3.93 


4.50 


5.05 


5.61 


6 19 


6 74 


7 30 


7 85 


8 42 


8 99 


10.10 


11.20 


110 


3.54 


4.14 


4.74 


5.32 


5.91 


6.51 


7.10 


7 70 


8 27 


8.86 


9.46 


10.64 


11.80 


120 


3.69 


4.30 


4.93 


5.54 


6.15 


6.78 


7.38 


8,00 


8.61 


9.24 


9.85 


11.05 


12.27 


130 


3.83 


4.46 


5.11 


5.75 


6.38 


7.03 


7.66 


8.30 


8.92 


9.57 


10.20 


11,48 


12.72 


140 


3.96 


4.62 


5.29 


5.94 


6.60 


7.26 


7 92 


8 60 


9 23 


9,90 


10.56 


11 88 


13 15 


150 


4.10 


4.76 


5.46 


6.14 


6.81 


7.50 


6.74 


8.86 


9.55 


10.20 


10.90 


12.26 


13.60 



COMPRESSED AIR FOR PUMPING. 



645 



Cubic Feet of Air Required to Run Rock Drills at Various Pressures 
and Altitudes. 

(IngersoU-Rand Co., 1908.) 





Table I. - 


- CUBIC FEET OF FREE AIR REQUIRED TO RUN ONE DRILL. 






Size and Cylinder Diameter of Drill. 


cu ^ 


A 35 


A 32 
A 86 


B 


C 


D 


D 


D 


E 


F 


F 


G 


H 


H9 


6^ 


2" 


21// 


21/2'' 


23// 


3// 


31/8" 


33/16'' 


31// 


31/2" 


35/8" 


41// 


5" 


51/2'' 


60 


50 


60 


68 


82 


90 


95 


97 


100 


108 


113 


130 


150 


164 


70 


56 


68 


77 


93 


102 


108 


110 


113 


124 


129 


147 


170 


181 


80 


63 


76 


86 


104 


114 


120 


123 


127 


131 


143 


164 


190 


207 


90 


70 


84 


95 


115 


126 


133 


136 


141 


152 


159 


182 


210 


230 


100 


77 


92 


104 


126 


138 


146 


149 


154 


166 


174 


199 


240 


252 



Table II. — multipliers to give capacity of compressor to operate 
FROM 1 to 70 rock drills at various altitudes. 

















Number oi Drills. 












< 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


15 


20 


25 


30 


40 


50 


oL 1.8 '2.7 


3.4 4.1 


4.8 


5.4 


6.0 


6.5 


7.1 


9.5 11.7 


13.7 


15.8 


21.4 25.5 


1030 1.03 1.85 2.78 


3.5 4.22 4.94 5.5616. 18 


6.69 


7.3 


9.78 12.05 


14.1 


16.3 


22.0 26.26 


2300 1.0711.92 2.89 


3.64 4.3915.14 5. 78i6.42 


6.95 


7.60 


10.17 12.52 


14.66116.9 


22.9 27.28 


3000,1.10 


1.98 2.97 


3.74 4.5115.285.94:6.6 


7.15 


7.81 


10.45 12.87 


15.07 17.38 


23.54 28.05 


5300,1.17 


2.10 


3.16 


3.98 4.8 


5.626.327.02 


7.61 


8.31 


11.12 13.69 


16.03 18.49 


25.04 29.84 


8000 1 .26 


2.27 


3.40 


4.28 5.17 


6.05 6.8 7.56 


8.19 


8.95 


11.97 14.74 


17.26 19.9 


26.96 32.13 


10000 1.32 


2.38 


3.56 


4.495.41 


6.347.13 7.92 


8.58 


9.37 12.54 


15.44 


18.08 20.86 


28.25 


33.66 


15000,1.43 


2.57 


3.86 


4.865.86 

1 


6.8617.72 8.58 


9.3 


10.15 13.58 


16.73 


19.59 22.59 


30.6 


36.49 



Example. — Required the amount of free air to operate thirty 5-inch 
"H" drills at 8,000 ft. altitude, using air at a gauge pressure of 80 lb. per 
sq. in. From Table I, we find that one 5-inch " H " drill operating at 80 lb. 
gauge pressure requires 190 cu. ft. of free air per minute. From Table 
II, the factor for 30 drills at 8,000 feet altitude is 19.9; 190 X 19.9 = 
3781 = the displacement of a compressor under average conditions, to 
which must be added pioe line losses. 

The tables above are for fair conditions in ordinary hard rock. In 
soft material, where the drilling time is short more drills can be run with 
a given compressor than when working in hard material. In tunnel 
work, more rapid progress can be made if the drills are run at high air 
pressure, and it is advisable to have an excess of compressor capacity 
of about 25%. No allowance has been made in the tables for friction 
of pipe line losses. 

Compressed-air Table for Pumping Plants^ 
(IngersoU-Rand Co., 1908.) 

The following table shows the pressure and volume of air required for 
any size pump for pumping by compressed air. Reasonable allowances 
have been made for loss due to clearances in pump and friction in pipe. 

To find the amount of air and pressure required to pump a given quan- 
tity of water a given height, find the ratio of diameters between water 
and air cyUnders, and multiply the number of gallons of water by the 



646 



AIR. 



figure found in the column for the required Uft. The result is the number 
of cubic feet of free air. The pressure required on the pump will be foimd 
directly above in the same column, l^or examnle: The ratio between 
cylinders being 2 to 1, required to pump 100 gallons, height of lift 250 
leet. We find under 250 teet at ratio 2 to 1 the figures 2.11 ; 2.11 X 100 = 
211 cubic feet of free air. The pressure required is 34.38 pounds deliv- 
ered at the pump piston. 



Ratio of 
Diameters. 




Perpendicular Height, in Feet, to which the Water 
is to be Pumped. 


25 


50 


75 


100 


125 


150 


175 


200 


250 


300 


400 


1 to 1 
1 1/2 to 1 
1 3/4 to 1 


A 
B 
A 
B 
A 
B 
A 
B 
A 
B 
A 
B 


13.75 
0.21 


27.5 
0.45 

12.22 
0.65 


41.25 
0.60 

18.33 
0.80 

13.75 
0.94 


55.0 

0.75 
24.44 

0.95 
19.8 

1.14 
13.75 

1.23 


68.25 

0.89 
30.33 

1.09 
22.8 

1.24 
17.19 

1.37 
13.75 

1.53 


82.5 

1.04 
36.66 

1.24 
27.5 

1.30 
20.63 

1.52 
16.5 

1.68 
13.2 

1.79 


96.25 

1.20 
42.76 

1.39 
32.1 

1.54 
24.06 

1.66 
19.25 

1.83 
15.4 

1.98 


110.0 

1.34 
48.88 

1.53 
36.66 

1.69 
27.5 

1.81 
22.0 

1.97 
17.6 

2.06 












61.11 

1.83 
45.83 

1.99 
34.38 

2.11 
27.5 

2.26 
22.0 

2.34 


73.32 

2.12 
55.0 

2.39 
41.25 

2.40 
33.0 

2.56 
26.4 

2.62 


97.66 

2.70 

73.33 






2.88 


2 to 1 






55.0 








2.98 


21/4 to 1 








44.0 










3.15 


21/2 to 1 { 










35.2 












3 18 

















A = air-pressure at pump. B = cubic feet of free air per gallon of water. 

Compressed-air Table for Hoisting-engines. 

(IngersoU-Rand Co., 1908.) 

The following table gives an approximate idea of the volume of free air 
required for operating hoisting-engines, the air being delivered to the 
engine at 60 lbs. gauge. There are so many variable conditions to the 
operation of hoisting-engines in common use that accurate computations 
can only be offered when fixed data are given. In the table the engine is 
assumed to actually run but one-half of the time for hoisting, while the 
compressor runs continuously. If the engine runs less than one-half the 
time, the volume of air required will be proportionately less, and vice 
versa. The table is computed for maximum loads, which also in practice 
may vary \Aidely. From the intermittent character of the work of a 
hoisting-engine the parts are able to resume their normal temperature 
between the hoists, and there is little probability of freezing up the 
exhEiust-passages. 

Volume of Free Air Required for Operating Hoisting-engines, the 
Air Compressed to 60 Pounds Gauge Pressure. 

Single-cylinder Hoisting-engine. 



Diam. of 

Cylinder, 

Inches. 


Stroke, 
Inches. 


Revolu- 
tions per 
Minute. 


Normal 
Horse- 
power. 


Actual 
Horse- 
power. 


Weight 
Lifted, 
Single 
Rope. 


Cubic Ft. 
of Free Air 
Required. 


5 

5 

61/4 

81/4 


6 

8 
8 
10 
10 
12 
12 


200 
160 
160 
125 
125 
110 
110 


3 
4 
6 
10 
15 
20 
25 


5.9 
6.3 
9.9 
12.1 

16.8 
18.9 
26.2 


600 
1.000 
1,503 
2,000 
3 GOO 
5,000 
6 000 


75 

80 
125 
151 
170 

238 
330 



COMPRESSED AIR, 



647 



DOUBLE-CYLIXDER HoiSTING-EN'GINE. 



Diam. of 


Stroke, 
Inches. 


Revolu- 


Normal 


Actual 


Weight 
Lifted, 
Single 
Rope. 


Cubic Ft. 


Cylinder, 


tions per 


horse- 


Horse- 


of Free Air 


Inches. 


Minute. 


power. 


power. 


Required. 


5 


6 


200 


6 


11.8 


1,000 


150 


5 


8 


160 


8 


12.6 


1,650 


160 


61/4 


8 


160 


12 


19.8 


2,500 


250 


7 


10 


125 


20 


24.2 


3,500 


302 


81/4 


10 


125 


30 


33.6 


6,000 


340 


81/2 


12 


110 


40 


37.8 


8.000 


476 


10 


12 


no 


50 


52.4 


10,000 


660 


121/4 


15 


100 


75 


89.2 




1,125 


14 


18 


90 


100 


125. 




1,587 



Practical Results with Compressed Air. — Compressed-air System 
at the tharin Mines, Iron Mountain, Mich. — These mines are three miles 
from the falls which supply the power. There are four turbines at the 
falls, one of 1000 horse-power and three of 900 horse-power each. The 
pressure is 60 pounds at i.0° Fahr. Each turbine runs a pair of compress- 
or-. The pipe to the mines is 24 ins. diameter. The power is applied at 
the mines to Corliss engines, running pumps, hoists, etc., and direct to 
rock-drills. 

A test made in 1888 gave 1430.27 H.P. at the compressors, and 390.17 
H.P. as the sum of the horse-power of the engines at the mines. There- 
fore, only 27% of the power generated was recovered at the mines. This 
includes the loss due to leakage and the loss of energy in heat, but not the 
friction in the engines or compressors. (F. A. Pocock, Trans. A. I. M. E., 
1890.) 

W. L. Saunders (/owr. F./., 1892) says: "There is not a properly designed 
compressed-air installation in operation to-day that loses over 5% by 
transmission alone. The question is altogether one of the size of pipe; 
and if the pipe is large enough, the friction loss is a small item. 

" The loss of power in common practice, where compressed air is used 
to drive machinery in mines and tunnels, is about 70 % . In the best prac- 
tice, with the best air-compressors, and without reheating, the loss is about 
60%. These losses may be reduced to a point as low as 20% by combin- 
ing the best systems of reheating with the best air-compressors." 

Gain due to Reheatinq-. — Prof. Kennedy says compressed-air trans- 
mission system is now being carried on, on a large commercial scale, 
in such a fashion that a small motor four miles away from the central 
station can indicate in round numbers 10 horse-power, for 20 horse- 
power at the station itself, allowing for the value of the coke used in heat- 
ing the air. 

The limit to successful reheating lies in the fact that air-engines can- 
not work to advantage at temperatures over 350°. 

The efficiency of the common system of reheating is shown by the re- 
sults obtained v ith the Popp system in Paris. Air is admitted to the 
reheater at about 83°, and passes to the engine at about 315°, thus being 
increased in volume about 42%. The air used in Paris is about 11 cubic 
feet of free air per minute per horse-power. The ordinary practice in 
America ^^-ith cold air is from 15 to 25 cubic feet per minute per horse- 
power. When the Paris engines were worked without reheating the air 
consumption was increased to about 15 cubic feet per horse-power per 
minute. The amount of fuel consumed during reheating is trifling. 

Effect of Temperature of Intake upon the Discharge of a Com- 
pressor. — Air should be drawn from outside the engine-room, and 
from as cool a place as possible. The gain in efficiency amounts to one 
per cent for every five degrees that the air is taken in lower than the 
temperature of the engine-room. The inlet conduit should have an area 
at least 50% of the area of the air-piston, and should be made of wood, 
brick, or other non-conductor of heat. 

Discharge of a compressor haviner an intake capacity of 1000 cubic feet 
per minute, and volumes of the discharge reduced to cubic feet at atmos- 
pheric pressure and at temperature of 62 degrees Fahrenheit: 
Temperature of Intake. F. .. . 0° 32° 62° 75° 80° 90° 100° 110" 
Volume discharged, cubic ft. 1135 1060 1000 975 966 949 932 916 



648 



AIR. 



Compressed -Air Motors with a Return Air Circuit. — In the ordinary 
use of motors, such as rock-drills, the air, after doing its work in the 
motor, is allowed to escape into the atmosphere. In some systems, 
however, notably in the electric air-drill, the air exhausted from the 
cyhnder of the motor is returned to the air compressor. A marked 
increase in economy is claimed to have been effected m tliis w^ay {Cass. 
Mag., 1907). 

Iiitercoolers for Air Compressors. — H. V. Haight (Am. Mach., 
Aug. 30, 1906). In multi-stage air compressors, the efficiency is greater 
the more nearly the tempera tm*e of the air leaving the mtercooler ap- 
proaches that of the water entering it. The difference of these tem- 
peratures for given temperatures of the entermg water and air is 
diminished by increasing the surface of the intercooler and thereby 
decreasing the ratio of the quantity of air cooled to the area of cooling 
surface. Numerous tests of intercoolers with different ratios of quan- 
tity of air to area of surface, on being plotted, approximate to a straight- 
line diagram, from which the following figures are taken. 
Cu. ft. of free air per min. per sq. ft. of air cooling surface 5 10 15 
Difl.of temp. F°. between water entering and air leaving 12.5° 25° 37.5° 

Centrifugal Air Compressors. — The General Electric Company has 
placed on the market a line of single stage centrifugal air compressors 
with pressure ratings from 0.75 to 4 lb. per sq. in., and capacity from 
500 to 10,000 cu. ft. of free air per min. The compressor consists 
essentially of a rotating impeller smTounded by a rigid cast-iron casing 
and suitable conversion nozzles to convert velocity of the air into 
pressure. It is similar to the centrifugal pump, efficiency depending 
entirely upon the design of the passages throughout the machine. 

The compressors are driven by Ciu-tis steam-turbines or by electric 
motors specially designed for them. The induction motors used are of 
the squirrel-cage type w^hich do not permit any variation in the speed 
and care must be taken to specify a pressure sufficiently high to cover 
the operating requirements, because the pressure cannot be varied 
at constant speed without altering the design of the impeller. The 
pressure of the D. C. motor-driven imit can be changed by changing 
the speed of the motor by means of the field rheostat. 





Standard 


Off-Standard 


Off-Standard 






Designs, 


Designs, 


Designs, 




Motor 


3450 r.p.m. 


3450 r.p.m. 


3850 r.p.m. 


Pipe 


Rating 
H.P. 


Lb. 


Cu. Ft. 


Lb. 


Cu. Ft. 


Lb. 


Cu. Ft. 


Diam.. 
Inches. 




per 


per 


per 


per 


per 


per 






Sq. In. 


Min. 


Sq. In. 


Min. 


Sq. In. 


Min. 




5 




800 


0.75 


1,100 


1.25 


600 


10 


10 




1,600 


0.75 


2,100 


1.25 


1,300 


12 


20 




3,200 


0.75 


4,100 


1.25 


2,600 


16 


30 




4,500 


0.75 


5,900 


1.25 


3,800 


20 


50 




7,200 


0.75 


8,800 


1 25 


6,000 


20 


75 




10,200 


0.75 


12,000 


1.25 


8,700 


26 


10 


2 


750 


1.5 


1,000 


2.50 


500 


8 


20 


2 


1,600 


1.5 


2,100 


2.50 


1,200 


10 


30 


2 


2,500 


1.5 


3,300 


2.50 


1,900 


12 


50 


2 


4,200 


1.5 


5,400 


2.50 


3,300 


16 


75 


2 


6,200 


1.5 


8,000 


2.50 


5,000 


20 


30 


3.25 


1,250 


2.5 


1,800 


4.00 


900 


8 


50 


3.25 


2,400 


2.5 


3,200 


4.00 


1,900 


12 


75 


3.25 


3,800 


2.5 


5,000 


4.00 


3,000 


14 



Multi-stage compressors have been built in the following sizes: 
Cubic feet free air 

per minute 4,500 9,000 16,000 25,000 40,000 50,000. 

Pressure, pounds 

per square inch. . to 35 6 to 25 8 to 25 12 to 30 12 to 30 12 to 30 

As in the case of centrifugal pumps, the pressure depends upon the 



HIGH PRESSURE CENTRIFUGAL FANS. 649 

periijheral velocity of the impeUer. The volume of free air delivered 
is limited, however, by the capacity of the driver. It must never be 
operated without being piped to a load sufficient to restrict the flow of 
air to the rated value, otherwise the driver will become seriously 
overloaded. 

The power required to drive the centrifugal compressor varies ap- 
proximately with the volume of air dehvered whan operating at a 
constant speed, between the limits of 50 per cent and 125 per cent of 
the rated load. This gives flexibihty and economy to the centrifugal 
type where variable volumetric loads are required. 

When the compressor is operating as an exhauster discharging against 
atmospheric pressure, the rated pressure P, in lb. per sq. in., must 
be muUipliei by 14.7 and then divided by 14.7 plus P to obtain the 
vacuum in lbs. per sq. in. below atmosphere. The rated pressures are 
?iven for an atmospheric pressure of 14.7 lb. per sq. in. and a tempera- 
ture of 60° F. When the compressors are operated at an altitude, the 
pressure will be reduced directly in proportion to the barometric 
pressure. For other temperatui es, the pressures will be inversely 
proportioned to the absolute temperature, or P X 520 -=- (400+ r°). 
When operated on gas the rated pressure is co be corrected by multiply- 
ing it by the relative density of the gas, taking air = 1. A large 
aumber of machines have been installed to operate on illuminating 
?as, by-product coke oven gas, or producer gas. Constant suction 
governors controlling the speed of the turbine drivers are employed 
where close control of the suction head is desired, as in the case of gas 
sxhausters. 

Ten large machines (2000 to 5000 H.P.) for blowing blast furnaces 
have also been installed. These have steam turbines for drivers and 
are controlled by constant volume governors, giving a constant speed, 
so that a definite volume of air per minute is delivered, regardless of 
bhe resistance of the furnace. 

High-Pressure Centrifugal Fans. — (A. Rateau, Engg., Aug, 16, 1907.) 
In 1900, a single wheel fan driven by a steam turbine at 20,200 revs, per 
min. gave an air pressure of 81/4 lbs. per sq. in.; an output of 26.7 cu. ft. 
free air per second: useful work in H.P. adiabatic compression, 45.5; 
theoretical work in H.P. of steam-f5ow, 182; efficiency of the set, fan and 
turbine, 28%. An efficiency of 30.7% was obtained with an output of 
23 cu. ft. per sec. and 132 theoretical H.P. of steam. The pressure 
obtained with a fan is — all things being equal — proportional to the 
specific weight of the gas which flows through it ; therefore, if, instead of 
air at atmospheric pressure, air, the pressure of which has already been 
raised, or a gas of higher density, such as carbonic acid, be used, com* 
paratively higher pressures still will be obtained, or the engine can run at 
lower speeds for the same increase of pressure. 

Multiple Wheel Fans. — The apparatus having a single impeller gives 
satisfaction only when the duty and speed are sufficiently high. The 
speed is limited by the resistance of the metal of which the impeller is 
made, and also by the speed of the motor driving the fan. But by con- 
necting several fans in series, as is done with high-lift centrifugal pumps, 
it is possible to obtain as high a pressure as may be desired. 

Turbo-Compressor, Bethune Mines, 1906. — This machine compresses air 
to 6 and 7 atmospheres by utilizing the exhaust steam from the winding- 
engines. It consists of four sets of multi-cellular fans through which the 
air flows in succession. They are fitted on two parallel shafts, and each 
shaft is driven by a low-pressure turbine. A high-pressure turbine is 
also mounted on one of the shafts, but supplies no work in ordinary times. 
An automatic device divides the load equally between the two shafts. 
Between the two compressors are fitted refrigerators, in which cold water 
is made to circulate by the action of a small centrifugal pump keyed at 
the end of the shaft. In tests at a speed of 5000 r.p.m., the volume of 
air drawn per second was 31.7 cu. ft. and the discharge pressure 119.5 lb. 
per sq. in. absolute. These conditions of working correspond to an effect- 
ive work in isothermal compression of 252 H.P. The efficiency of the 
compressor has been as high as 70%. The results of two tests of the 
compressor are given below. In the first test the air discharged, reduced 
to atmospheric pressure, was 26 cu. ft. per sec; in the second test it was 
46 cu. ft. 



650 AIR. 

First Test. 

Stages. 1st. 2d. 3d. 4th. 

Abs. pressure at inlet, lbs. per sq. in. ... 15.18 23.37 38.69 66.44 

Abs. pressure at discharge 24.10 39.98 66.44 102.60 

Speed, revs, per min 4660 4660 4660 4660 

Temperature of air at inlet, deg. F. ... 57.2 67.8 63. 66. 

Temperature of air at discharge, deg. F. 171. 205. 216. 215.6 

Adiabatic rise in temp., deg. F 106. 122. 114.8 105.8 

Actual rise in temperature, deg. F. ... 113.8 137.2 153. 149.6 

Efficiency, per cent 60.5 60.5 54. 46.2 

Second Test. 

Stages. 1st. 2d. 3d. 4th. 

Abs. pressure at inlet, lbs. per sq. in. ... 15.18 21.31 37.33 65.12 

Abs. pressure at discharge 23.52 38.22 65.12 99.66 

Speed, revs, per min 5000 5000 4840 4840 

Temp, of air at inlet, deg. F 55. 69.8 64.4 68.5 

Temp, of air at discharge, deg. F 160.7 208.4 208.4 199.6 

Adiabatic rise in temp., deg. F 102.2 131. 123.8 100.4 

Efficiency, per cent 62.3 66.6 58.7 48.6 

The Gutehoffnungshiitte Co. in Germany have in course of construc- 
tion several centrifugal blowing-machines to be driven by an electric 
motor, and up to 2000 H.P. Several machines are now being designed 
for Bessemer converters, some of which will develop uj) to 4000 H.P. 
The multicellular centrifugal compressors are identical in every point 
with centrifugal pumps. In the new machines cooling water is intro- 
duced inside the diaphragms, wliich are built hollow for this purpose, 
and also inside the diffuser vanes. By this means it is hoped to reduce 
proportionally the heating of the air: thus approaching isothermal com- 
pression much more nearly than is done in the case of reciprocating 
compressors. 

Test of a Hydraulic Air Compressor. — (W. O. Webber, Trans. 
A. S. M. E., xxii, 599.) The compressor embodies the principles of 
the old trompe used in connection. with the Catalan forges some centuries 
ago, modified according to principles first described by J. P. Frizell, in 
Jour. F. I., Sept., 1880, and improved by Charles H. Taylor, of Montreal. 
(Patent July 23, 1895.) It consists principally of a down-flow passage 
having an enlarged chamber at the bottom and an enlarged tank at 
the top. A series of smah air pipes project into the mouth of the water 
inlet and the large chamber at the upper end of the vertically descending 
passage, so as to cause a number of small jets of air to be entrained by the 
water. At the lower end of the apparatus, deflector plates in connection 
with a gradually enlarging section of the lower end of the down-flow pipe 
are used to decrease the velocity of the air and water, and cause a partial 
separation to take place. The deflector plates change the direction of 
the flow of the water and are intended to facilitate the escape of the air, 
the water then passing out at the bottom of the enlarged chamber into an 
ascending shaft, maintaining upon the air a pressure due to the height of 
the water in the uptake, the compressed air being led on from the top 
of the enlarged chamber by means of a pipe. The general dimensions of 
the compressor plant are: 

^ Supply penstock, 60 ins. diam.; supply tank at top, 8 ft. diam. X 10 ft. 
high; air inlets (feeding numerous small tubes), 34 2-in. pipes: down tube, 
44 ins. diam.: down tube, at lower end, 60 ins. diam.; length of taper in 
down tube, 20 ft.: air chamber in lower end of shaft, 16 ft. diam.: total 
depth of shaft below normal level of head water, about 150 ft.; normal 
head and fall, about 22 ft.; air discharge pipe, 7 ins. diam. 

It is used to supply power to engines for operatiner the printing depart- 
ment of the Dominion Cotton Mills, Maerog, P. Q., Canada. 

There were three series of tests, viz.: (1) Three tests at different rates 
of flow of water, the compressor being as orieinally constructed. (2) Four 
tests at different rates of flow of water, the compressor inlet tubes for air 
being increased by 30 3/4-in. pipes. (3) Four tests at different rates of 
flow of water, the compressor inlet tubes for air being increased by 15 3/4-in. 



HYDRAULIC AIR COMPRESSION. 



651 



The water used was measured by a weir, and the compressed air by air 
meters. The table on p. 623 shows the principal results: 

Test 1, when the flow was about 3800 cu. ft. per min., showed a decided 
advantage by the use of 30 3/4-in. extra air inlet pipes. Test 5 shows, 
when the flow of water is about 4200 cu. ft. per min., that the economy 
is highest when only 15 extra air tubes are employed. Tests 8 and 9 show, 
when the flow is about 4600 cu. ft. per min., ttiat there is no advantage in 
increasing the air-inlet area. Tests 10 and 11 show that a flow of 5000 
or more cu. ft. of water is in excess of the capacity of the plant. These 
four tests may be summarized as follows: 

The tests show: (1) That the most economic rate of flow of water with 
this particular instaUation is about 4300 cu. ft. per min. (2) That this 
plant has shown an efficiency of 70.7 % under such a flow, which is ex- 
ceUent for a first installation. (3) That the compressed air contains only 
from 30 to 20% as much moisture as does the atmosphere. (4) That the 
air is compressed at the temperature of the water. 

Using an old CorUss engine without any changes in the valve gear 
as a motor there was recovered 81 H.P. This would represent a total 
efficiency of work recovered from the falling water, of 51.2%. When 
the compressed air was preheated to 267° F. before being used in the 
engine, 111 H.P. was recovered, using 115 lbs. coke per hour, which would 
equal about 23 H.P. The efficiency of work recovered from the falling 
water and the fuel burned would be, therefore, about 611/2%. On the basis 
of Prof. Riedler's experiments, which require only about 425 cu. ft. of air 
per B.H.P. per hour, when preheated to 300° F. and used in a hot-air 
jacketed cyUnder, the total efficiency secured would have been about 
871/2%. 



Test No 

Flow of water, cu. ft. per min.. . 

Available head in ft 

Gross v/ater, H.P 

Cu. ft. air, at atmos. press., per 

minute 

Pressure of air at comp., lbs 

Effective work in compressing, 

H.P 

Efficiency of compressor, % 

Temp, of external air, deg. F — 
Temp, of water and comp. air, 

deg. F 

Ratio of water to air, volumes... 
Moisture in external air, p. c. of 

saturation 

Moisture in comp. air, p. c. of 

saturation 



1 



3772 
20.54 
146.3 

864 
51.9 

83.3 
56.8 
68.3 

66 
4.37 

61 

51.5 



3628 
20.00 
136.9 

901 
53.7 

88.2 
64.4 
57.7 

65.5 
.4.03 

77.5 

44 



4066 
20.35 
156.2 



4.292 
19.51 
158.1 



967 1148 
53.2 53.3 



94.3 
60.3 
66.4 

66.4 
4.20 

71 

38.5 



111.74 
70.7 
65.2 

66.5 
3.74 

68 

35 



7 


8 


4408 
19.93 
165.8 


4700 

19.31 

171.4 


1091 
53.7 


1103 
52.9 


107 
64.5 
59.7 


106.8 
62.2 
65 


67 
4.04 


66.5 
4.26 


90 


60.5 


29 


31.2 



10 



5058 
18.75 
179.1 

1165 
53.3 

113.4 
63.3 
64.2 

66 
4.34 

63 

30 



Tests 1, 4, and 7 were made with the original air inlets; 2, 5, 8 and 10 
with the inlets increased by 153/4-in. pipes, and 3, 6, 9 and 11 with the 
inlets increased by 303/4-in. pipes. Tests 2, 6,9 and 11 are omitted here. 
They gave, respectively, 55.5, 61.3, 62, and 55.4% efficiency. 

Three other hydraulic air-compressor plants are mentioned in Mr. 
Webber's paper, some of the principal data of which are given below: 

Peterboro, Norwich, Cascade 

Ont. Conn. Range, 
Wash. 

Head of water 14 ft. 18Ht. 45 ft. 

Gauge pressure 25 lbs. 85 lbs. 85 lbs. 

Diam. of shaft 42 in. 24 ft. 

Diam. of compressor pipe 18 ft. 13 ft. 3 ft. 

Depth below tailrace 64 ft. 215 ft. 

Horse-power 1365 200 

In the Cascade Range plant there is no shaft, as the apparatus is con- 
structed against the vertical walls of a canyoa. The diameter of the up- 
flow pipe is 4 ft. 9 in. 



652 AIR. 

A description of the Norwich plant is given by J. Herbert Shedd in a 
paper read before the New England Water Works Assn., 1905 (Compressed 
Air, April, 1906). The shaft, 24 ft. diam., is enlarged at the bottom into 
a chamber 52 ft. diam., from which leads an air reservoir 100 ft. long, 18 ft. 
wide and 15 to 20 ft. high. Suspended in the shaft is a downflow pipe 
14 ft. diam. connected at the top with a head tank, and at the bottom with 
the air-chamber, from which a 16-in. main conveys the air four miles to 
Norwich, where it is used in engines in several estabhshments. 

The ^Fekarski Compressed-air Tramway at Berne, Switzerland. 
(Eng'Q News, April 20, 1893.) — The Mekarski system has been intro- 
duced in Berne. Switzerland, on a line about two miles long, with grades 
of 0.25% to 3.7% and 5.2%. The air is heated by passing it through 
superheated water at 330° F. It thus becomes saturated with steam, 
which subseauently partlv condenses, its latent heat being absorbed by 
the expanding air. The pressure in the car reservoirs is 440 lb. per sq. in. 

The engine is constructed like an ordinary steam tramway locomotive, 
and drives two coupled axles, the wheel-base being 5.2 ft. It has a 
pair of outside horizontal cylinders, 5.1 X 8.6 in.; four coupled wheels, 
27.5 in. diameter. The total weight of the car, including compressed 
air, is 7.25 tons, and with 30 passengers, including the driver and 
conductor, about 9.5 tons. The authorized speed is about 7 miles 
per hour. 

Theaisadvantages of this system consist in the extremely delicate adjust- 
ment of the different parts of the system, in the comparatively small 
supply of air carried by oie motor car, which necessitates the car return- 
ing to the depot for refilling after a run of only four miles or 40 minutes, 
although on the Nogent and Paris lines the cars, which are, moreover, 
larger, and carry outside passengers on the top, run seven miles, and the 
loading pressure is 547 lb. per sq. in. as against only 440 lb. at Berne. 

For description of the Mekarski system as used at Nantes, France, see 
paper by Prof. D. S. Jacobus, Trans. A. S. M. E., xix. 553. 

American Experiments on Compressed Air for Street Railways. 
— Experiments have been made in Wasliington, D. C, and in New York 
City on the use of compressed air for street-railw^ay traction. The air 
was compressed to 2000 lb. per sq. in. and passed through a reducing- 
valve and a heater before being admitted to the engine. The system has 
since been abandoned. For an extended discussion of the relative merits 
of compressed air and electric traction, with an account of a test of a 
four-stage compressor giving a pressure of 2500 lb. per sq. in., see Eng'g 
News, Oct. 7 and Nov. 4, 1897. A summarized statement of the probable 
efficiency of compressed-air traction is given as follows: Efficiency of com- 
pression to 2000 lb. per sq. in. 65%. Bv wire-drawing to 100 lbs. 57.5% 
of theavailable energy of the air will be lost, leading 65 X 0.425 = 27.625% 
as the net efficiency of the air. This may be doubled by heating, making 
55.25%, and if the motor has an efficiency of 80% the net efficiency of 
traction by compressed air will be 55.25 X 0.80 = 44.2%. For a descrip- 
tion of the Hardie compressed-air locomotive, designed for street-railway 
work, see Eng'g News, June 24, 1897. For use of compressed air in mine 
haulage, see Eng'g News, Feb. 10, 1898. 

Operation of 3Iine Pumps by Compressed Air. — The advantages 
of compressed air over steam for the operation of mine pumps are: Absence 
of condensation and radiation losses in pipe lines; high efficiency of com- 
pressed-air transmission; ease of disposal of exhaust; absence of danger 
from broken pipes. The disadvantage is that, at a given initial pressure 
without reheating, a cylinder full of air develops less power than steam. 
The power end of the pump should be designed for the use of air, with 
low clearances and with proper proportions of air and water ends, with 
regard to the head under which the pump is to operate. Wm. Cox (Comp. 
Air Mag., Feb., 1899) states the relations of simple or single-cyUnder 
pumps to be A/W = V2 /i/p, where A = area of air cylinder, sq. in., W 
= area of water cyUnder, sq. in., h = head, ft., and p = air pressure, lb. 
per sq. in. Mr. Cox gives the volume V of free air in cu. ft. per minute 
to operate a direct-acting, single-cylinder pump, working without cut off, 
to be 

V = 0.093 W2hG/P. 

Where W2 = volume of 1 cu. ft. of free air correspond! ner to 1 cu. ft. of 
free air at pre.ssure P, G= gallons of water to be raised per minute, P = 



FANS AND BLOWERS. 653 

receiver-gauge pressure of air to be used, and h = head in feet under 
which pump works. This formula is based on a piston speed of 100 ft. 
per minute and 15% has been added to the volume oi air to cover losses. 
The useful work done in a pump using air at full pressure is greater at 
low pressures than at high, and the efficiency is increased. High pressures 
are not so economical for simple pumps as low pressures. As high-pressure 
air is required for drills, etc., and as the air for pumps is drawn from the 
same main, the air must either be wire-drawn into the pumps, or a reducing 
valve be inserted between the pump and main. Wire-drawing causes a 
low efficiency in the pump. If a reducing valve is used, the increase of 
volume will be accompanied with a drop in temperature, so that the full 
value of the increase is not realized. Part of the lost heat may be regained 
by friction, and from external sources. The efficiency of the system may 
be increased by the use of underground receivers for the expanded air 
before it passes to the pump. If the receiver be of ample size, the air 
will regain nearly its normal temperature, the entrained moisture will be 
deposited and freezing troubles avoided. By compounding the pumps, 
the efficiency may be increased to about 25 per cent. In simple pumps it 
ranges from 7 to 16 per cent. For much further information on this sub- 
ject see Peele's " Compressed- Air Plant for Mines," 1908. 

FANS AND BLOWERS. 

Centrifugal Fans. — The ordinary centrifugal fan consists of a number 
of blades fixed to arms revolving at high speed. The width of the blade 
is parallel to the shaft. The experiments of W. Buckle {Proc. Inst. M. E., 
1847) are often quoted as still standard. IMr. Buckle's con elusions, how- 
ever, do not agree with those of modern experimenters, nor do the propor- 
tions of fans as determined by him have any similarity to those of modem 
fans. The experiments were made on fans of the " paddle-wheel" 
type, and have no bearing on the more modern multiblade fans of the 
" Sirocco " type. 

The rules laid down by Buckle do not give a fan the highest volu- 
metric efficiency without loss of mechanical efficiency. By volumetric 
efficiency is meant the ratio of the volume of air delivered per revo- 
lution to the cubical contents of the wheel, if the wheel be considered 
a solid whose dimensions are those of the wheel. Inasmuch as the 
loss due to friction of the air entering the fan will be less with a large 
inlet than with a small one, in a wheel of given diameter, more power 
will be consumed in delivering a given volume of air with a small 
inlet than with a larger one. 

In the ordinary fan the number of blades varies from 4 to 8, while 
with multiblade fans it is from 48 to 64. The number of blades has 
a direct relation to the size of the inlet. This is made as large as 
possible for the reason given above. Any increase in the diameter 
of the inlet necessarily decreases the depth of the blade, thus di- 
minishing the capacity and pressure. To overcome this decrease, 
the number of blades is increased to the limit placed by construc- 
tional considerations. A properly proportioned fan is one in which 
a balance is obtained between these two features of maximum inlet 
and maximum number of blades. 

In some cases two fans mounted on one shaft may be more useful than 
a single wide one, as in such an arrangement twice the area of inlet opening 
is obtained, as compared with a single wide fan. Such an arrangement 
may be adopted where occasionally half the full quantity of air is required, 
as one of the fans may be put out of gear and thus save power. 

Rules for Fan Design. — It is impossible to give any general rules 
or formulae covering the proportions of parts of fans and blowers. There 
are no less than 14 variables involved in the construction and operation of 
fans, a slight change in any one producing wide variations in the perform- 
ance. The design of a new fan by manufacturers is largely a matter of 
trial and error, based on experiments, until a compromise with all the 
variables is obtained which most nearly conforms to the given conditions. 

Pressure Due to Velocity of the Fan Blades. — The pressure of the 
air due to the velocity of the fan blades may be determined by the formula 

H = — , deduced from the law of falling bodies, in which H is the *' head " 

or height of a homogeneous column of air one inch square whose weight is 



654 



AIK. 



equal to the pressure per square inch of the air leaving the fan, v is the 
velocity of the air leaving the fan in feet per second, and g the acceleration 
due to gravity. The pressure of the air is increased by increasing the 
number of revolutions per minute of the fan. Wolff, in his "The Wind- 
mill as a Prime Mover," p. 17, argues that it is an error to take // = v^ 
■^ 2g, the formula according to him being H = v^ ^ g. See also Trow- 
bridge (Trans. A. S. M. E., vii., 536). This law is analogous to that of 
the pressure of a fluid jet striking a plane surface perpendicularly and 
escaping at right anp'les to its orierinal path, this pressure beinsr twice that 
due the height calculated from the formula h= v^ -^ 2 g. (See Hawksley, 
Proc. Inst. M. E., 1882.) Buckle says: " From the experiments 
it appears that the velocity of the tips of the fan is equal to nine- 
tenths of the velocity a body would acquire in falling the height of a 
homogeneous column of air equivalent to the density." 

To convert the head H expressed in feet to pressure .in lb. per sq. in. 
multiply it by the weight of a cubic foot of air at the pressure and tem- 
perature of the air expelled from the fan (about 0.08 lb. usually) 
and divide by 144. Multiply this by 16 to obtain pressure in ounces 
per sq. in. or by 2.035 to obtain inches of mercury, or by 27.71 to 
obtain pressure in inches of w^ater column. Taking 0.08 as the weight 
of 1 cu. ft. of air, and v =0.9 ^'YgH, __ 

= 0.00001066 i;2; ^ =310 ^p_ nearly; 
= 0.0001706 V-\ v= 80 Vj9i " 
= 0.00002169 t;2; v =220 ^P2 " 
= 0.0002954 ?;2; i; = 60 v^s 
in which u = velocity of tips of blades in feet per second. 

Testing the above formula by one of Buckle's experiments with a 
vane 14 inches long, we have p =0.00001066 v- =9.56 oz. The experi- 
ment gave 9.4 oz. 

Taking the formula v =80 Vpl, we have for different pressures in 
ounces per square inch the following velocities of the tips of the blades 
in feet per second: 
Pi = ounces per square inch 2 3 4 5 6 7 8 10 12 14 

V =feet per second 113 139 160 179 196 212 226 253 277 299 

Commenting on the statements and formulae given above, the 
B. F. Sturtevant Co., in a letter to the author, says: " Let us assume 
that the fan considered is of the centrifugal type, which is a wheel 
in a spiral casing. In any case of centrifugal fan the pressure at the 



p lb. per sq. in. 
pi ounces per sq. in. 
P2 inches of mercury 
I inches of water 




Straight 

Fig. 146. 



Forward Backward 

Types of Fan Blowers. 



fan outlet is wholly dependent 'ipon the load on the fan, and, there- 
fore, the pressure cannot well be expressed by a formula, unless it 
includes some term which is an expression in some way of the load 
upon the fan. The actual pressure depends upon the design of both 
wheel and housing, upon the blade area and also upon the form of the 
blades. With a curved blade running with the concave side forward 
it is possible to obtain a much higher pressure than if the blade is run- 
ning with the convex side forward. This can only be shown by tests, 
and can be figured out by blade-velocity diagrams." 

It should be noted, however, that while the fan with a blade con- 
caved in the direction of rotation has the highest eflaciency, all other 



PRESSURE CHARACTERISTICS OF FANS. 655' 

things being equal, the noise of operation is increased. A blade con- 
vex in the direction of rotation runs more quietly, and in most situa- 
tions it is necessary to sacrifice eflficiency in order to obtain quiet 
operation. 

Fig. 146 shows the relation of the velocity of air leaving a fan to 
the velocity of the tips of the blades for radial, bent forward, and 
bent backward blades. V represents the direction and amount of 
the velocity relative to the blade as the air leaves the blade, U the 
tangential velocity of the tip of the blade, and R the component of 
U and V, the velocity of the air relative to the fan casing. 

The kinetic energy of the air due to its velocity as it leaves the 
blades is partially converted into pressure energy as the velocity 
is reduced in the expanding scroll casing of the fan, and in the 
diverging outlet of the fan if such an outlet is used. The total or 
dynamic pressure is the sum of the static pressure and the velocity 
pressure. 

Quantity of Air of a Given Density Delivered by a Fan. 

Total area of nozzles in square feet X velocity in feet per minute corre- 
sponding to density (see, table) = air delivered in cubic feet per minute, 
discharging freely into the atmosphere (approximate). See p. 670. 



Density, Velocity, 

ounces feet per 

per sq. in. minute. 

5 11,000 

6 12,250 

7 13,200 

8 14,150 



Density, Velocity, 

ounces feet per 

per sq. in. minute. 

9 15,000 

10 15,800 

11 16,500 

12 17.300 



Density, Velocity, 

ounces feet per 

per sq. in. minute. 

1 5,000 

2 7,000 

3 8,600 

4 10,000 

"Blast Area,*' or "Capacity Area»" When the fan outlet is small 
the velocity of the outflow is equal to the peripheral velocity of the fan. 

&tart with the outlet closed; then if the opening be slowly increased 
while the speed of the fan remains constant the air will continue to flow 
with the same velocity as the fan tips until a certain size of outlet is 
reached. If the outlet is still further increased the pressure within the 
casing will drop, and the velocity of outflow will become less than the 
tip velocity. The size of the outlet at which this change takes place is 
called the blast area, or capacity area, of the fan. This varies somewhat 
mth different types and makes of fans, but for the common form of 
blower it is approximately, DW -^ 3, in wliich D is the diameter of the 
fan wheel and W its width at the circumference. — (C. L. Hubbard.) 

This established capacity area has no relation to the area of the outlet 
in the casing, which may be of any size, but is usually about twice the 
capacity area. The velocity of the air discharged through this latter 
area is practically that of the circumference of the wheel, and the pressure 
created is that corresponding thereto. — W. B. Snojv. 

Pressure Characteristics of Fans. — Figs. 147 and 148 show 
the relation of the static and total pressures, the efficiency and the 
horse-power, to the capacity of two fans, one a radial blade fan, and 
the other a multi-blade (conoidal) as determined by tests by the 
Buffalo Forge Co. In the test the fan was run at a uniform speed 
and the capacity was varied by varying the area of outlet. The 
characteristics of the two fans differ greatly. In the case of the 
radial fan the highest pressure corresponds to zero capacity, while 
with the multi-blade fan the static pressure increases as the capacity 
increases up to 100 per cent, or rated capacity, w^hich is the point of 
maximum efficiency. 

If a forward-curved blade fan is intended to operate at a certain 
pressure and capacity, and if for any reason, such as resistance greater 
than expected, the quantity of air handled is less than the fan's 
rating for the speed maintained, the total pressure will also be less 
than that specified. With the straight-blade fan the opposite holds 
true, for as the capacity is reduced the pressure will increase, at con- 
stant speed. 

Care should be taken in the selection of a fan with forward-curved 
blades in case it is to be driven by a motor. If for any reason there 



656 



AIR. 



should be a tendency to operate above rated capacity, both the air 
quantity and the pressure will increase, which may overload the 
motor in case suflQcient margin of motor capacity has not been pro- 
vided. (Buffalo Forge Co.) 

For a given fan area of outlet, piping system, and air density, the 




20 .40 60 80 100 

Per Cent of Rated Capacity 
Fig. 147. Characteristics of a Radial Blade Fan. 

relations of volume delivered, pressure at the fan outlet, speed and 
horse-power theoretically vary as follows: 

Volume dehvered varies directly as speed of the fan. 
Pressure varies as the square of the speed. 
Horse-power varies as the cube of the speed. 
For a given volume the horse-power varies as the square of the 
speed, showing the great advantage of large fans at slow speeds over 
*^00 




20 



Fig. 148. 



.40 



140 



60 80 100 120 

Per Cent- of Rated Capacity 
Characteristics of a Multi-blade Fan. 



small fans at high speeds delivering the same volume, the type of fan 
being the same. The theoretical values are greatly modified by vari- 
ations in practical conditions. For every fan running at constant speed 
there is a pressure and corresponding volume at which a fan will 
operate at its maximum efiBciency (see characteristic curves), and a 



FANS AND BLOWERS. 



657 



wide variation in these conditions will give a great drop in eflficiency. 
In selecting a fan for any purpose the catalogues and bulletins issued 
by manufacturers should be examined, and a tabular comparison 
made of the sizes, speed, etc., of different fans which may be used for 
the given purpose and conditions. The following is an example of 
such a comparison of three multi-blade fans (Sturtevant) which may be 
used to deliver approxim.ately 15,000 cu. ft. of air against a resistance 
of 5 in. of water column. 



Fan. 


Wheel 
Diam. 
Inches. 


Resistance, 5 


in. 


Size. 


R.P.M. 


H.P. 


Vol. 


R.P.M. 


H.P. 


Turbovane.. 

Supervane. . 
Multivane. . 


221/2 

25 

26 


15.500 
15,400 
15.900 


2210 
1033 
1103 


25 

23.5 
26 


Smallest 
Medium 
Largest 


Highest 
Lowest 
Medium 


Medium 

Lowest 

Highest 



Experiments on a Fan with Constant Discharge-opening and 
Varying Speed. — The first four columns are given by Mr. Snell, the 
others are calculated by the author. 





in 
01 


«4-l 




*ss 




• 4i 


5 « 
a3 . 


^ 


^ 


.s 


o 

o 




u 


fl 






<«2 


& 




a 

t 




-3^ 


o 




hi 

3:? *- 3 


add 


• - 2 <i^ 


1 . 
So 


P. 

•3 


P4 


PU 


> 


w 


> 


> 


o 


> 


H 


W 


600 


0.50 


1336 


0.25 


60.2 


56.6 


85.1 


3,630 


0.182 


73 


800 


0.88 


1787 


0.70 


80.3 


75.0 


85.6 


4,856 


0.429 


61 


1000 


1.38 


2245 


1.35 


100.4 


94 


85.4 


6,100 


0.845 


63 


1200 


2.00 


2712 


2.20 


120.4 


113 


85.1 


7,370 


1.479 


67 


1400 


2.75 


3177 


3.45 


140.5 


133 


84.8 


8,633 


2.283 


66 


1600 


3.80 


3670 


5.10 


160.6 


156 


82.4 


9,973 


3.803 


74 


1800 


4.80 


4172 


8.00 


180.6 


175 


82.4 


11,337 


5.462 


68 


2000 


5.95 


4674 


11.40 


200.7 


195 


85.6 


12,701 


7.586 


67 



Mr. Snell has not found any practical difference between the mechanical 
efficiencies of blowers with curved blades and those with straight radial 
ones. From these experiments, says Mr. Snell, it appears that we may 
expect to receive back 65% to 75% of the power expended, and no more. 
The great amount of power often used to run a fan is not due to the fan 
itself, but to the method of selecting, erecting, and piping it. (For opin- 
ions on the relative merits of fans and positive rotary blowers, see discus- 
sion of Mr. Snell's paper, Trans. A. S. M. E., ix. 66, etc.) 

Comparative Efficiency of Fans and Positive Blowers. (H. M. 

Howe, Trans. A. I. M. E., x. 482.) — Experiments with fans and positive 
(Baker) blowers working at moderately low pressures, under 20 ounces, 
show that they work more efficiently at a given pressure when delivering 
large volumes (i.e., when working nearly up to their maximum capacity) 
than when delivering comparati v^ely small volumes. Therefore, when 
great variations in the quantity and pressure of blast required are liable 
to arise, the highest efficiency would be obtained by having a number of 
blowers, always driving them up to their full capacity, and regulating the 
amount of blast by altering the number of blowers at work, instead of 
having one or two very large blowers and regulating the amount of blast 
by the speed of the blowers. 

There appears to be little difference between the efficiency of fans and 
of Baker blowers when each works under favorable conditions as regards 
quantity of work, and when each is in good order. 

For a given speed of fan, any diminution in the size of the blast-orifice 
decreases the consumption of power and at the same time raises the pres- 



658 



AIR. 



sure ot the blast; but it increases the consumption of power per unit of 
orifice for a given pressure of blast. When the orifice has been reduced to 
the normal size for any given fan, further diminishing it causes but slight 
elevation of the blast pressure: and, when the orifice becomes compara- 
tively small, further diminishing it causes no sensible elevation of the 
blast pressure, which remains practically constant, even when the orifice is 
entirely closed. 

Many ot the failures of fans have been due to too low speed, to too small 
pulleys, to improper fastening of belts, or to the belts being too nearly ver- 
tical- in brief, to bad mechanical arrangement, rather than to inherent 
defects in the principles of the machine. 

If several fans are used, it is probably essential to high efficiency to pro- 
vide a separate blast pipe for each (at least if the fans are of different size 
or speed), while any number of positive blowers may deliver into the same 
pipe without lowering their efficiency. 

The Sturtevant Multi-blade Fans.— The B. F. Sturtevant Co. 
has developed three styles of fans w^ith numerous blades which have 
been given the trade names Multivane, Supervane, and Turbovane. 
The Multivane and Supervane fans are used for the same kind of 
service, that is, mostly for heating, ventilating, and mechanical 
draught. For a given diameter, the Supervane operates at lower speed 
and requires less power than the Multivane. The Turbovane fan 
is designed for high-speed direct-connected drives, such as steam 
turbines. It is a very wide fan, made double inlet, and for a given 
volume and pressure will be smaller in diameter and operate at about 
twice the speed of the Multivane and require about the same power. 
The Turbovane and Supervane fans have blades considerably deeper 
than the Multivane. The curvature is also radically different in 
all three types. The spiral or housing is considerably different in the 
three types. 



Sturtevant Multivane Fan. 







Resist 


ance 1/2 in. 


Resistance 2 in. 


Resistance 5 in. 






i 




6^' 


g 




3|. 


S 




irt 


a3 

N3 




-i^H 


p^ 


Pu 


•i^B 


P^ 


pin' 


od S 


Pk 


Ph* 


|55 


m 


W 


> 


p^ 


K 


> 


P^' 


a 


> 


pi 


ffi 


^ 


2 


21 


1,300 


705 


0.220 


2,850 


1471 


2.15 


3,980 


2205 


6.6 


13 


3 


26l'2 


2,030 


565 


0.345 


4,440 


1178 


3.3 


6,210 


1764 


10.0 


161/2 


4 


31 1/2 


2,920 


470 


0.495 


6,400 


980 


4.8 


8.940 


1471 


14.5 


191/2 


5 


37 


3,980 


404 


0.67 


8.720 


840 


6.5 


12,200 


1260 


20 


23 


6 


42 


5,200 : 


353 


0.88 


11,400 


735 


8.5 


15,900 


1103 


26 


26 


61/2 


47 


6,570 


314 


1.10 


14,400 


654 


11.0 


20,100 


980 


33 


291/2 


7 


521/2 


8,110 


282 


1.40 


17,800 


588 


13.5 


24,800 


882 


41 


321/2 


8 


63 


11.700 


235 


2.00 


25.600 


490 


19 


35,800 


735 


60 


39 


9 


731/2 


15.900 


202 


2.70 


34,800 


420 


26 


48.700 


631 


80 


451/2 


10 


831/2 


20,800 1 


176 


3.50 


45.500 


368 


34 


63,600 


552 


105 


52 


11 


94 


26.300 i 


157 


4.45 


57.600 


327 


43 


80.500 


490 


135 


58 1/2 


12 


1041/2 


32,500 : 


141 


5.5 


71.000 


294 


54 


99.400 


441 


165 


65 


13 


115 


39,400 


128 6.7 


86.100 


268 


64 


121.000 


401 


200 


711/2 


14 


1251/2 


46.800 


118 


7.9 


102.000 


245 


76 


143.000 


368 


235 


78 


15 


136 


54.800 


109 


9.3 


120.000 


226 


90 


168.000 


340 


275 


841/2 


16 


1461/2 


63.500 


101 


11.0 


139.000 


210 


105 


195.000 


315 


320 


91 


17 


157 


73.000 


94 12.5 


160.000 


196 


120 


224.000 


294 


370 


97 1/2 


18 


167 


83.100 


88 


14 


182.000 


184 


135 


255.000 


276 


420 


104 


20 


188 


105.000 


78 


18 


230.000 


163 


170 


322.000 


245 


530 


117 


22 


209 


130.000 


71 


22 


285.000 


147 


215 


398.000 


221 


655 


130 


24 


230 


157.000 


64 


27 


344.000 


134 


260 


481.000 


200 


795 


143 


26 


2501/2 


187,000 


55 


32 


410,000 


115 


305 


573.000 


173 


945 


156 



FANS AND BLOWEES. 



659 



Sturtevant Supervane Fan. 





SI'S 


Resistance 1/2 in. 


Resistance 


2 in. 


Resistance 5 in. 








i 




^.s, 


^ 




s^. 


i 








"o^Om 


-BdS 


^ 


Pk 


o«:^S 


^ 


Pk 


'o«t^ S 


^ 


Ph 




XJl 


ffi 


> 


^ 


W 


> 


rt 


W 


> 


rt 


W 


A 


26 


1.470 


645 


0.235 


2,940 


1290 


1.90 


4.160 


1980 


6.4 


13 


B 


32 


2.230 


525 


0.355 


4,460 


1051 


2.90 


6.320 


1610 


9.7 


16 


C 


38 


3.150 


442 


0.50 


6,300 


885 


4.05 


8.910 


1358 


13.5 


19 


D 


44 


4.200 


382 


0.67 


8,420 


764 


5.4 


11,900 


1171 


18.0 


22 


E 


491/2 


5.450 


337 


0.87 


10.900 


673 


7.0 


15,400 


1033 


23.5 


25 


F 


551/2 


6.820 


300 


1.10 


13.600 


600 


8.8 


19,300 


921 


30 


28 


G 


631/2 


8.900 


262 


1.40 


17,800 


525 


11.5 


25,200 


805 


38 


32 


H 


731/2 


11.300 


233 


1.80 


22.600 


467 


14.5 


32,000 


716 


49 


36 


J 


791/2 


13.900 


210 


2.20 


27.800 


420 


18 


39.400 


645 


60 


40 


K 


911/2 


18.500 


183 


2.90 


36,900 


365 


24 


52.300 


560 


80 


46 


L 


103 


23,500 


162 


3.75 


47,000 


323 


30 


66,600 


496 


100 


52 


M 


115 


29.300 


145 


4.65 


58,500 


290 


38 


83.000 


444 


125 


58 


N 


127 


35.600 


131 


5.7 


71,200 


263 


46 


101.000 


403 


155 


64 


P 


139 


42,700 


120 


6.8 


85,400 


240 


56 


121.000 


368 


185 


70 


Q 


1501/2 


50.300 


111 


8.0 


101.000 


221 


66 


143.000 


339 


220 


76 


R 


1661/2 


61.400 


100 


9.8 


123,000 


200 


80 


174,000 


307 


265 


84 


S 


1821/2 


73.500 


91 


11.5 


147.000 


183 


96 


208,000 


280 


320 


92 


T 


1981/2 


86.900 


84 


14.0 


174.000 


168 


110 


246.000 


258 


375 


100 


U 


2141/2 


102.000 


78 


16.0 


204.000 


1561130 


288.000 


239 


440 


108 


V 


230 


117.000 


72 


18.5 


234.000 


1451150 


332.000 


222 


505 


116 


W 


254 


143.000 


66 


23 


285.000 


13l|l85 


404,000 


202 


615 


128 


X 


2771/2 


171.000 


60 27 


341.000 


120 220 


483,000 


184 


740 


140 


Y 


3011/2 201.000 


55 32 


401.000 1 


111260 


569,000 


170 


870 


152 









Sturtevant Turbovane 


Fan. 










eight of 

^asing. 

Inches. 


Resistance 


lin. 


Resistance 3 in. 


Resistance 6 in. 




i 




i 


^ 




i 


^ 


% 


i 
^ 


^ 


OJ C6 


m W^ 


> 


tf 


W 


> 


tf 


W 


> 


tf 


w 


40 


28 


1,670 


1958 


0.53 


2.930 


3400 


2.85 


4.010 


4700 


7.8 


111/2 


45 


35 


2,610 


1563 


0.83 


4,560 


2720 


4.4 


6.250 


3800 


12.0 


141/2 


50 


42 


3.770 


1300 


1.20 


6.600 


2260 


6.5 


9.050 


3161 


17.5 


17 


55 


49 


5.100 


1118 


1.65 


8.950 


1940 


8.8 


12.300 


2719 


23.5 


20 


60 


56 


6.700 


978 


2.15 


11.700 


1700 


11.0 


16.100 


2380 


31 


221/2 


65 


63 


8.500 


868 


2.75 


14,900 


1510 


14.5 


20.400 


2115 


39 


25 1/2 


70 


70 


10.500 


781 


3.35 


18.300 


1358 


17.5 


25.100 


1900 


48 


281/2 


80 


84 


15.100 


651 


4.85 


26.300 


1131 


26 


36.100 


1582 


70 


34 


90 


97 


20.500 


558 


6.5 


35,800 


971 


35 


49.100 


1360 


92 


39 1/2 


100 


112 


26.800 


490 


8.5 


46,800 


851 


45 


64.000 


1192 


120 


45 


no 


126 


34.000 


435 


11.0 


59.500 


755 


58 


81.500 


1058 


155 


51 


120 


140 


41.800 


391 


13.5 


73.000 


679 


70 


101.000 


950 


190 


561/2 


130 


154 


50.500 


353 


16.5 


88.500 


617 


86 


122.000 


865 


230 


62 


140 


168 


60.500 


326 


19.5 


106.000 


566 


100 


145.000 


792 


280 


671/2 


150 


182 


71.000 


300 


22.5 


124,000 


521 


120 


170.000 


729 


325 


731/2 


160 


196 


82.000 


279 


26 


144,000 


485 


140 


197.000 


680 


380 


79 



660 



AIR. 



Capacity of Fans and Blowers. — The follo\\ing tables supplied (1909) 
by the American Blower Co., Detroit, show the capacities of exhaust fans 
and volume and pressure blowers. The tables are all based on curves 
established by experiment. The pressures, volumes and horse-powers 
were all actually measured with the apparatus working against maintained 
resistances formed by restrictions equivalent to those found in actual prac- 
tice, and which experience shows will produce the best results. 



Speed, Capacity and Horse-power of Steel Plate Exhaust Fans. 

(American Blower Co., Type E, 1908.) 











1/2 


oz. pres- 


3/4 


oz. pres- 


1 


3z. pres- 


2 


oz. pres- 






J 


'^ . 




sure. 




sure. 




sure. 




sure. 


























; 


'^d 


a 


^.s 










(-1 

a. 


i 




i. 


i 

2 




a. 


k 


03 

n 






II 

3-S 


^ 




Si 

Si 


^ 

^ 




Si 

St 




. (D 

I'a 


la 


^ 

^ 


• 9 


• 


iz; 


Q 


^ 


Q 


/^-» 


O 


tt 


^ 


o 


« 


« 


o 


pq 


P^ 


o 


tt 


25 


16 


6Va 


10 


985 


1,09 


0.30 


1200 


1,345 


0.56 


1390 


1,555 


0.85 


1966 


2,200 


2.40 


30 


19 


71/8 


12 


830 


1,580 


0.43 


1012 


1,940,0.80 


1170 


2,240 


1.22 


1655 


3,175 


3.46 


35 


22 


«Va 


14 


715 


2.155 


0.59 


876 


2,635 


1.08 


1010 


3,040 


1.66 


1430 


4.310 


4.70 


40 


25 


93/8 


16 


630 


2,820 


0.77 


772 


3,450 


1.41 


890 


3,980 


2.17 


1260 


5.640 


6.15 


45 


28 


107/8 


18 


563 


3,560 


0.97 


689 


4,360 


1.78 


795 


5,030 


2.74 


1125 


7,140 


7.79 


50 


31 


123/s 


20 


508 


4,400 


1.20 


622 


5,390 2.20 


719 


6,220 


3.39 


1015 


8,820 


9.63 


55 


34 


13 V? 


22 


464 


5,330 


1.45 


567 


6,525 12.66 


655 


7.530 


4.10 


927 


10.650 111. 60 


60 


38 


141/7 


24 


415 


6,350 


1.73 


509 


7,775 3.18 


587 


8,960 


4.89 


830 


12,700 JI3. 85 


70 


44 


151/8 


27 


375 


7,440 


2.0Z 


459 


9,120 3.72 


530 


10.500 


5.72 


750 


14,875 


16.20 


80 


50 


161/2 


29 


328 


10,050 


2.75 


402 


12,100 4.94 


464 


13,980 


7.62 


656 


19,800 


21.60 



Speedy Capacity and Horse-power of Volume Blowers. 

(American Blower Co., Type V, 1909.) 











1/2 OZ. pres- 


3/4 oz. pres- 


1 


oz. pres- 


1 1/2 oz. pres- 






-d 


■+5 


sure. 


sure. 




sure. 




sure. 
























tj 


*o.S 


a 


a- 




u 


k 




1. 






u 

t. 


i 

S 




u 

a . 


k 






ac 


^.^ 




. Qi 


• 




. 


• 




. Qi 


• 




. © 


* 


^ 


*— r 


^Tj 




U-i 3 






«^H 3 


•^^. 






-^Ju 






-^^ 


n 


el 

«3^ 


ii 


2"^ 
a.s 






^1 


P^ 


C 

^a 


la 


P^ 


c 

^a 




P^ 


c 

^"a 


II 


Jz; 


Q 


^ 


Q 


f^ 





m 


P^ 





pq 


P^ 





« 


P^ 





« 


1 


81/0 


2 


41/2 


1850 


223 


0.06 


2270 


273 


0.11 


2620 


315 


0.17 


3210 


386 


0.32 


2 


101/4 


23^8 


51/9 


1535 


332 


0.09 


1880 


407 


0.17 


2170 


469 


0.26 


2660 


576 


0.48 




12 


31/4 


61/9 


1310 


464 


0.13 


1600 


569 


0.23 


1850 


656 


0.36 


2275 


805 


0.66 




15 V? 


43/9 


81/2 


1015 


795 


0.22 


1240 


975 


0.40 


1435 


1122 


0.61 


1760 


1377 


1.13 




19 


51/8 


103s 


830 


1185 


0.32 


1013 


1450 


0.59 


1170 


1675 


0.92 


1435 


2055 


1.68 




221/? 


61/7 


123/8 


700 


1686 


46 


8585 2065 


0.84 


990 


2385 


1.30 


1215 


2930 


2.40 




26 


71/9 


141/4 


606 


2235 


61 


742^2740 


1.12 


858 


3160 


1.72 


1050 


3880 


3.18 


8 


291/? 


81/9 


161/4 


534 


2910 


79 


654 


3560 


1 45 


755 


4110 


2.24 


928 


5040 


4.13 


9 


33 


91/2 


181/4 


477 


3660 


1.00 


585 


4490 


1.83 


675 


5175 


2.82 


825 


6350 


5.20 



Note: This table also applies to Type V, cast-iron exhaust fans. 



FANS AND BLOWERS. 



661 



Steel Pressure Blowers for Cupolas (Average Application). 

(American Blower Co., 1909.) 



c 


1 

5 


>> 

1 
Is 




5-* 

Is 

5 


-2 
o 

< 


Oz. 


2 


3 
5.19 

1.86 


4 
6.92 

2.48 


5 
8.65 

3.10 


6 
10.38 

3.73 


7 
12.12 

4.35 


8 
13.83 

4.95 


9 


J 


In. 


3.46 
1.242 


15.56 


6 


H.P. 

const, 
at 1000 
cu. ft. 


5.58 


1 


141/2 


13/8 


3.80 


53/4 


0.18 


R.P.M. 
C.F. 
H.P. 


1960 

361 

0.45 


2400 

434 

0.81 


2770 
500 
1.24 


3095 
560 
1.74 


3390 
610 

2.28 


3666 

665 

2.89 


3915 

708 

3.51 


4150 

752 

4.20 


2 


17 


15/8 


4.45 


63/4 


0.2485 


R.P.M. 
C.F. 
H.P. 


1675 

498 

0.62 


2050 
600 
1.12 


2362 
691 
1.72 


2645 

774 

2.40 


2895 

843 

3.15 


3130 

916 

3.99 


3340 

978 

4.84 

2910 
1286 
6.36 


3540 
1038 
5.79 


3 


191/2 


17/8 


5.11 


73/4 


0.327 


R.P.M. 
C.F. 
H.P. 


1460 

655 

0.82 


1785 
789 
1.47 


2060 

910 

2.26 


2300 
1018 
3.16 


2520 
1110 
4.15 


2730 
1207 
5.25 


3085 
1365 
7.62 


4 


22 


21/8 


5.76 


83/4 


0.4176 


R.P.M. 
C.F. 
H.P. 


1292 
838 
1.04 


1582 
1006 
1.87 


1825 
1162 

2.88 


2040 
1300 
4.03 


2235 
1415. 

5.28 


2420 
1540 
6.70 


2585 
1643 
8.14 


2740 
1746 
9.74 


5 


241/2 


23/8 


6.41 


93/4 


0.519 


R.P.M. 
C.F. 
H.P. 


1162 
1040 
1.30 


1422 
1250 
2.33 


1640 
1442 
3.58 


1835 
1612 
5.00 


2010 
1760 
6.57 


2175 
1915 
8.34 


2320 
2040 
10.10 


2460 
2166 
12.10 


6 


27 


27/8 


7.06 


103/4 


0.63 


R.P.M. 
C.F. 
H.P. 


1055 
1262 
1.57 


1290 
1520 
2.83 


1490 
1750 
4.34 


1665 
1960 
6.08 


1825 
2135 
7.96 


1975 

2375 

10.10 


2105 
2475 
12.25 


2233 
2630 
14.12 


7 


32 


33/8 


8.39 


121/2 


0.852 


R.P.M. 
C.F. 
H.P. 


889 
1705 
2.12 


1087 
2055 
3.83 


1255 
2366 
5.86 


1405 
2650 
8.23 


1535 
2890 
10.78 


1660 
3140 
13.66 


1775 
3350 
16.60 


1880 
3355 
19.83 


8 


37 


37/8 
43/8 


9.70 


14 


1.069 


R.P.M. 
C.F. 
H.P. 


769 
2140 
2.66 


940 
2575 
4.79 


1085 
2970 
7.36 


1212 
3325 
10.3 


1328 
3620 
13.5 


1446 
3940 
17.15 


1533 

4200 

20.80 


1625 

4460 

24.90 


9 


42 


10.98 


16 


1.396 


R.P.M. 
C.F. 
H.P. 


679 
2800 
3.48 


830 
3370 
6.27 


958 
3880 
9.63 


1072 
4340 
13.46 


1172 
4730 
17.65 


1270 

5150 

22.40 


1355 

5500 

27.25 


1435 

5825 

32.50 


10 


47 


47/8 


12.30 


171/2 


1.67 


R.P.M. 
C.F. 
H.P. 


606 
3350 
4.17 


742 

4025 

7.5 


855 
4640 
11.5 


956 
5200 
16.12 


1048 

5660 

21.12 


1133 

6160 

26.80 


1210 

6570 

32.55 


1280 

6970 

38.90 


n 


52 


53/8 


13.6 


191/4 


2.02 


R.P.M. 
C.F. 
H.P. 


548 
4050 
5.03 


670 
4870 
9.06 


774 
5610 
13.9 


865 
6290 
19.5 


947 

6850 

25.55 


1025 

7450 

32.40 


1093 

7950 

39.33 


1160 

8440 

47.10 


12 


57 


57/8 


14.92 


21 


2.405 


R.P.M. 
C.F. 
H.P. 


500 
4820 
6.00 


611 
5800 
10.78 


705 
6700 
16.62 


789 

7490 

23.25 


863 

8160 

30.45 


934 

8870 

38.60 


996 

9460 

46.85 


1056 
10040 
56.10 



662 



AIR. 



Steel Pressure Blowers for Cupolas (Average Application).— 

Continued. 



fli 


1 

5 







Q 


< 


Oz. 


10 


11 


12 


13 


14 


15 


16 


d 


In. 


17.28 


19.02 


20.75 


22.5 


24.22 


25.95 


27.66 


H.P. 

const, 
at 1000 
cu.ft. 


6.20 


6.82 


7.44 


8.07 


8.69 


9.30 


9.92 




17 


1^/8 


4.45 


63/4 


0.2485 


R.P.M. 
C.F. 
H.P. 


3740 
1093 
6.78 


3920 
1148 
7.83 


4090 
1196 
8.9 










? 































3 


191,2 


17/8 


5.11 


73/4 


0.327 


R.P.M. 
C.F. 
H.P. 


3255 
1440 
8.93 


3415 
1510 
10.3 


3570 

1575 

11.72 


3710 

1642 

13.26 


3935 

1700 

14.75 


3985 
1762 
16.4 


4120 

1820 

18.05 


4 


22 


21/8 


5.76 


83/4 


0.4176 


R.P.M. 
C.F. 
H.P. 


2890 

1840 

11.40 


3030 

1930 

13.16 


3163 
2012 
14.96 


3290 
2095 
16.9 


3420 
2175 
18.9 


3535 
2250 
20.9 


3650 
2325 
23.1 


5 


241/2 


23/8 


6.41 


93/4 


0.519 


R.P.M. 
C.F. 
H.P. 


2595 
2280 
14.13 


2720 
2395 
16.33 


2845 
2500 
18.6 


2960 

2605 

21.05 


3075 

2700 

23.45 


3180 

2800 

26.05 


3280 

2885 

28.66 


6 


27 


27/8 


7.06 


103/4 


0.63 


R.P.M. 
C.F. 
H.P. 


2355 
2770 
17.18 


2470 
2910 
19.85 


2580 
3033 
22.6 


2683 

3165 

25.55 


2790 

3280 

28.50 


2885 

3395 

31.55 


2980 
3500 
34.7 


7 


32 


33/8 


8.39 


121/2 


0.852 


R.P.M. 
C.F. 
H.P. 


1983 

3750 

23.25 


2080 
3930 
26.80 


2170 
4110 
30.6 


2260 
4276 
34.5 


2345 
4430 
38.5 


2430 
4590 
42.7 


2510 

4730 

47. 


8 


37 


37/8 
43/8 


9.70 


14 


1.069 


R.P.M. 
C.F. 
H.P. 


1715 

4700 

29.15 


1800 

4930 

33.66 


1880 

5150 

38.33 


1955 

5360 

43.25 


2030 

5560 

48.30 


2100 

5760 

53.55 


2170 

5940 

59. 


9 


42 


10.98 


16 


1.396 


R.P.M. 
C.F. 
H.P. 


1515 

6150 

38.15 


1590 

6450 

44.00 


1660 

6730 

50.15 


1728 

7010 

56.60 


1792 
7270 
63.2 


1855 
7525 
70. 


1916 

7760 

77. 


]0 


47 


47/8 


12.30 


171/2 


1.67 


R.P.M. 
C.F. 
H.P. 


1352 

7350 

45.60 


1418 

7715 

52.66 


1480 

8055 

60. 


1540 

8390 

67.66 


1600 
8700 
75.6 


1655 
9010 
83.9 


1710 
9300 

92.25 


11 


52 


53/8 


13.6 


191/4 


2.02 


R.P.M. 
C.F. 
H.P. 


1222 
8900 
55.20 


1282 
9330 
63.6 


1340 
9750 
72.5 


1393 
10140 

82. 


1447 
10520 
91.5 


1498 
10890 
101.2 


1546 
11220 
111.33 


12 


57 


57/8 


14.92 


21 


2.405 


R.P.M. 
C.F. 
H.P. 


1113 
10580 
65.5 


1168 
11100 
75.70 


1220 
11600 
86.33 


1270 
12080 
97.5 


1318 

12520 

10. 


1363 
12960 
120.5 


1410 
13380 

132.75 



Caution in Regard to Use of Fan and Blower Tables. — Many en- 
gineers report that some manufacturers' tables overrate the capacity of 
their fans and underestimate the horse-power required to drive them. In 
some cases the complaints may be due to restricted air outlets, long and 
crooked pipes, sUpping of belts, too small engines, etc. It may also be 
due to the fact that the volumes are stated without being accompanied 
by information as to the maintained resistance, and the volumes given 



FANS AND BLOWERS. 



663 



may be those delivered with an unrestricted inlet and outlet. As this 
condition is not a practical one, the volume delivered in an installation 
is much smaller than that given in the tables. The underestimating of 
horse-power required may be due to the fact that the volumes given in 
tables are for operation against a practical resistance, and in an installa- 
tion it might be that the resistance was low, consequently the volume 
and also the horse-powei required would be greater. 

Capacity of Sturtevant High-Pressure Blowers (1908). 



Number of 
blower. 


Capacity in cubic feet 
per minute, I/2 lb. pres- 
sure. 


Revolutions per 
minute. 


Inside dia. 

of inlet 
and outlet, 

inches. 


Approx. 
weight, 
pounds.* 


000 


1 to 5 


200 to 1000 


13'8 


40 


00 


5 to 25 


375 to 800 


11/2 


80 





25 to 45 


370 to 800 


21/2 


140 


1 


45 to 130 


240 to 600 


3 


330 


2 


130 to 225 


300 to 500 


4 


550 


3 


225 to 325 


380 to 525 


4 


760 


4 


325 to 560 


350 to 565 


6 


1,080 


5 


560 to 1,030 


300 to 475 


8 


1,670 


6 


1,030 to 1,540 


290 to 415 


10 


2,500 


7 


1,540 to 2,300 


280 to 410 


10 


3,200 


8 


2,300 to 3,300 


265 to 375 


12 


4,700 


9 


3,300 to 4,700 


250 to 350 


16 


6,100 


10 


4,700 to 6,000 


260 to 330 


16 


8,000 


II 


6,000 to 8,500 


220 to 310 


20 


12,100 


12 


8,500 to 11,300 


190 to 250 


24 


18,700 


13 


11,300 to 15,500 


190 to 260 


30 


22,700 



* Of blower for 1/2 lb. pressure. 



Performance of a No. 7 Steel Pressure Blower under Varying 

Conditions of Outlet. 

Per cent of 
Rated Ca- 
pacity 20 40 60 80 100 120 140 160 180 200 220 240 

Per cent of • 

Rated H.P. 28 42 57 72 86 100 116 130 144 159 173 187 202 

Total pres- 
sure, oz 10.2 11.4 11.9 12.0 11.9 11.410.9 10.3 9.7 9.1 8.5 7.9 7.2 

Static pres- 
sure, oz ..10 2 11.2 11.6 11.411.0 10.2 9.2 8.0 6.6 5.0 3.5 1.9 0.3 

Efficiency, per 

cent 26 40 50 56 60 62 61 59 56 52 48 45 

The above figures are taken from a plotted curve of the results of 
a test by the Buffalo Forge Co. in 1905. A letter describing the test 
says : 

The object was to determine the variation of pressure, power and 
efficiency obtained at a constant speed with capacities varying from zero 
discharge to free delivery. A series of capacity conditions were secured 
by restricting the outlet of the blower by a series of converging cones, 
60 arranged as to make the convergence in each case very slight, and of 
sufficient length to avoid any noticeable inequality in velocities at the 
discharge orifice. The fan was operated as nearly at constant speed as 

Eossible. The velocity of the air at the point of discharge was measured 
y a Pitot tube and draft gauge of usual construction. Readings were 
taken over several points of the outlet and the average taken, although 



664 



AIR. 



the variation under nearly all conditions was scarcely perceptible. A 
coefficient of 93% was assumed for the discharge orifice. The pressure 
was taken as the reading given by the Pitot tube and draft gauge at 
outlet. The agreement of tliis reading with the static pressure in a 
chamber from which a nozzle was conducted had been checiced by a 
previous test in which the two readings, i.e., velocity and static pressure, 
were found to agree exactly within the limit of accuracy of the draft 
gauge, wliich was about 0.01 in., or, in tiiis case, witiiin 1% The horse- 
power was determined by means of a motor wiiich had been previously 
cahbrated by a series of brake tests. Variations in speed were assumed 
to produce variation in capacity in proportion to the soeed, variation in 
pressure to the square of the speed, and variation in H.P. in proportion to 
the cube of the speed. These relations had been previouslv shewn to 
hold true for fans in other tests. They were also checked up by oper- 
ating the fan at various speeds and plotting the capacities directly with 
the speed as abscissa, the pressure with the square of the speed as abscissa, 
and the horse power with the cube of the speed as abscissa. These were 
found, as in previous cases, to have a practically straight-line relation, in , 
which the line passed through the origin. 

Effect of Resistance upon the Capacity of a Fan. — A study of the 
figures in the above table shows the im.portance of having ample capacity 
in the air mains and delivery pipes, and of the absence of sharp bends 
or other obstructions to the' flow which may increase the resistance or 
pressure against which the fan operates. The fan delivering its rated 
capacity against a static pressure of 10.2 ounces delivers only 40 % 
of that capacity, wdth the same number of revolutions, if the pressure is 
increased to 11.6 ounces; the power is reduced only to 57%, instead of 
40%, and the efficiency drops from 60% to 40%. 



Dimensions of Sirocco Fans. 

(American Blower Co., 1909.) 













_, m 









of 

lare Out- 
sq.ft. 


of Circu- 
Evasd 
tlet sq. 




eg 


^-a 


d 




|| 


hOO 




.sS 


ui 


d t-i 3 . 


gw 


Q 


^" 


48 


H 


W 


^ 


>A 


^ 


% 


< 


< 


>A 


6 


3 


56 


IT' 


4 


W 


.23 


.123 


.11 


.12 


3" 


9 


41/2 


48 


127 


V 4" 


» 


V r 


.49 


.349 


.25 


.35 


^Vi" 


12 


6 


64 


226 


1' 9" 


8 


V 1" 


.85 


.616 


.44 


.60 


53// 


15 


71/2 


64 


353 


2' r 


10 


1' 0" 


1.46 


.957 


.69 


.92 


71/? 


18 


9 


64 


509 


71 W 


12 


2' 5'' 


1.87 


1.37 


1.00 


1.40 


8I/2'' 


21 


101/2 


64 


693 


y 4// 


14 


2' 10'' 


2.40 


1.87 


1.34 


1.87 


10" 


24 


12 


64 


904 


y gr, 


16 


y y, 


3.14 


2.46 


1.78 


2.40 


1 1 1/2'' 


27 


131/2 


64 


1144 


4/ 3// 


18 


y 7/, 


4.59 


3.11 


2.25 


3.14 


13" 


30 


15 


64 


1413 


4/ 7// 


20 


4/ 0" 


5.58 


3.83 


2.78 


3.83 


141/2'^ 


36 


18 


64 


2036 


y 6" 


24 


4' 10'' 


7.87 


5.50 


4.00 


5.58 


17" 


42 


21 


64 


2770 


6' 5" 


2S 


y y, 


10.56 


7.47 


5.44 


7.47 


20" 


48 


24 


64 


3617 


7/ y, 


32 


6' y 


13.6 


9.79 


7.11 


9.85 


23" 


54 


27 


64 


4578 


8' 1" 


36 


r r 


17.0 


12.3 


9.00 


12.3 


26" 


60 


30 


64 


5652 


9. ,// 


40 


8' 0" 


20.9 


15.2 


11.11 


15.3 


281/2'' 


66 


33 


64 


6839 


9/ 1,// 


44 


8' 10" 


25.2 


18.4 


13.41 


18.3 


311/2" 


72 


36 


64 


8144 


ly 10'^ 


43 


cy 7// 


29.8 


22.2 


16.00 


22.3 


341/2" 



Sirocco or 3Iultivane Fans. — There has recently (1909) come into use 
a fan of radically different proportions and characteristics from the ordi- 
nary centrifugal fan. This fan is composed of a great number of shallow 
vanes, ranging from 48 to 64, set close together around the periphery of 
the fan wheel. Over a large range of sizes, 64 vanes appear to give tho 



Speed, Capacities and Horse-power of Sirocco Fans. 

Blower Co., 1909.) 



(American 



The figures given represent dynamic pressures in oz. per sq. in. 
static pressure, deduct 28.8%; for velocity pressure, deduct 7k2%. 


For 


si 




N3 

o 


N3 

o 

esj 


tsj 
O 


o 


o 





§ 
■* 
«" 


O 


o 

Cs| 


o 


6 


Cu.ft. 
R.P.M. 
B.H.P. 


155 
1,145 
.0185 


220 
1,615 
.052 


270 
1,980 
.095 


310 

2,290 

.147 


350 

2,560 

.205 


380 

2,800 

.270 


410 

3,025 

.34 


440 
3,230 

.42 
1,000 
2,152 

.95 


490 
3,616 

.58 
1,110 
2,408 
1.32 
1,970 
1,808 
2.32 
3,090 
1,444 
3.65 
4,450 
1,204 
5.25 
6,060 
1,032 
7.15 
7.900 

904 

9.3 
10,050 

804 

11.8 

12,350 

722 
14.5 


540 

3,960 

.76 


9 


Cu.ft. 
R.P.M. 
B.H.P. 


350 
762 
.042 


500 
1,076 
.118 


610 
1,320 
.216 


700 
1,524 
.333 


790 
1,700 
.463 


860 
1,866 
.610 


930 

2,020 

.77 


1,220 
2,640 
1.73 


12 


Cu.ft. 
R.P.M. 
B.H.P. 


625 
572 
.074 


880 
808 
.208 


1,080 
990 
.381 


1,250 
1,145 

.588 


1,400 

1,280 

.82 


1,530 
1,400 
1.08 


1,650 
1,512 
1.36 


1,770 
1,615 
1.66 


2,170 
1,980 
3.05 


15 


Cu. ft. 
R.P.M. 
B.H.P. 


975 
456 
.115 


1,380 
645 
.326 


1,690 
790 
.600 


1,950 
912 
.923 


2,180 
1,020 
1.29 


2,400 
1,120 
1.69 


2,590 
1,210 

2.14 
3,720 
1,010 

3.07 


2,760 
1,290 

2.61 
3,980 
1,076 

3.75 


3,390 

1,58U 

4.8 


18 


Cu.ft. 
R.P.M. 
B.H.P. 


1,410 
381 
.167 


1,990 
538 
.470 


2,440 
660 
.862 


2,820 
762 
1.33 


3,160 
850 
1.85 


3,450 
933 

2.43 


4,880 

1,320 

6.9 


21 


Cu.ft. 
R.P.M. 
B.H.P. 


1,925 
326 

.227 


2,710 
462 
.640 


3,310 
565 
1.17 


3,850 
652 
1.81 


4,290 

730 

2.53 


4,700 

800 

3.33 


5,070 

864 

4.18 


5,420 

924 

5.11 


6,620 

1,130 

9.4 


24 


Cu.ft. 
R.P.M. 
B.H.P. 


2,500 
286 
.296 


3,540 
404 
.832 


4,340 
495 
1.53 


5,000 

572 

2.35 


5,600 
640 

3.28 


6,120 
700 

4.32 


6,620 

756 

5.44 


7,080 

807 

6.64 


8,680 
990 
12.2 


27 


Cu. ft. 
R.P.M. 
B.H.P. 


3,175 
254 
.373 


4,490 
359 
1.05 


5,500 
440 
1.94 


6,350 

508 

2.98 


7,100 

568 

4.16 


7,780 
622 

5.48 


8,400 

672 

6.90 


8,980 

718 

8.44 


11,000 
880 
15.5 


30 


Cu.ft. 
R.P.M. 
B.H.P. 


3,910 
228 
.460 


5,520 
322 
1.30 


6,770 

395 

2.40 


7,820 

456 

3.68 


8,750 

510 

5.15 


9,600 

560 

6.75 


10,350 

604 

8.53 


11,050 
645 
10.4 


13,550 
790 
19.1 


36 


Cu.ft. 
R.P.M. 
B.H.P. 


5,650 
190 
.665 


7,950 
269 
1.87 


9,750 
330 

3.44 


11,300 
381 
5.30 


12,640 

425 

7.40 


13,800 

466 

9.72 


14,900 

504 

12.25 


15,900 
538 
15.0 


17,800 

602 

20.9 


19,500 
660 

27.5 


42 


Cu.ft. 
R.P.M. 
B.H.P. 


7,700 

163 

.903 


10,850 

231 

2.55 


13,300 

283 

4.69 


15,400 
326 
7.24 


17,170 
365 
10.1 


18,800 
400 
13.3 


20,300 
432 
16.7 


21,700 

462 

20.4 


24,250 

516 

28.5 


26,600 

566 

37.5 


48 


Cu. ft. 
R.P.M. 
B.H.P. 


10,000 

143 

1.18 


14,150 

202 

3.32 


17,350 

248 

6.10 


20,000 

286 

9.40 


22,400 
320 
13.1 


24,500 
350 
17.2 


26,500 

378 

21.75 


28,300 

403 

26.6 


31.600 

452 

37.1 

40,200 

402 

47.1 

49,400 

361 

58.2 

60,000 

328 

70.4 

71,200 

301 

83.6 

83,500 

278 

98. 

97,100 

258 

114. 

111,200 

241 

131. 


34,700 

495 

48.8 


54 


Cu.ft. 
R.P.M. 
B.H.P. 


12,700 

127 

1.49 


17,950 

179 

4.20 


22,000 

220 

7.75 


25,400 
254 
11.9 


28,400 
284 
16.6 


31,100 

311 

21.9 


33,600 

336 

27.6 


35,900 

359 

33.7 


44,000 
440 
62. 


60 


Cu.ft. 
R.P.M. 
B.H.P. 


15,650 

114 

1.84 


22,100 

161 

5.20 


27 J 00 

198 

9.58 


31,300 

228 
14.7 


35,000 

255 

20.6 


38,400 

280 

27.0 


41,400 

302 

34.1 


44,200 

322 

41.6 


54,200 
396 
76.5 


66 


Cu. ft. 
R.P.M. 
B.H.P. 


18,950 

104 

2.23 


26,800 

147 

6.30 


32,850 

180 

11.6 


37,900 
208 
17.8 


42,300 

232 

24.9 


46,400 
254 

32.7 


50,100 

275 

41.2 


53,600 

294 

50.4 


65,700 

360 

92.6 


72 


Cu.ft. 
R.P.M. 
B.H.P. 


22,600 

95 

2.66 


31,800 
134 

7.48 


39,000 

165 

13.7 


45,200 

190 

21.2 


50,600 

212 

29.6 


55,200 

233 

38.9 


59,600 

252 

49.0 


63,600 

269 

59.8 


78,000 
330 
110. 


78 


Cu.ft. 
R.P.M 
B.H.P. 


26,400 

88 

3.10 


37,350 

124 

8.77 


45,800 

153 

16.1 


52,800 
176 

24.8 


59,100 
197 

34.7 


64,700 

215 

45.6 


70,000 

233 

57.5 


74,700 

248 

70.2 


91,600 
305 
129. 


84 


Cu.ft. 
R.P.M. 
B.H.P. 


30,800 

81 

3.61 


43,400 

115 

10.2 


53,200 

142 

18.7 


61,600 

163 

28.9 


68,700 

182 

40.4 


75,200 
200 
53.0 


81,200 

216 

66.8 


86,800 

231 

81.7 


106,400 
283 
150. 


90 


Cii.ft. 
R.P.M. 
B.H.P. 


35,250 

76 

4.14 


49,800 

107 

11.7 


61,000 

132 

21.5 


70,500 

152 

33.1 


78,800 
170 

46.2 


86,400 

186 

60.7 


93,300 
201 

76.7 


99,600 

214 

93.6 


122.000 
264 
172. 



665 



666 



AIR. 



best results. The vanes, measured radially, have a depth l/ie the fan 
diameter. Axialiy, they are much longer than those of the ordinary fan, 
being 3/5 the fan diameter. The fan occupies about 1/2 the space, and is 
about 2/3 the weight of the ordinary fan. The vanes are concaved in the. 
direction of rotation and the outer edge is set forward of the inner edge. 
The inlet area is of the same diameter as the inner edge of the blades. 
Usually the inlet is on one side of the fan only, and is unobstructed, the 
wheel being overhung from a bearing at the opposite end. A peculiarity 
of this type of fan is that the air leaves it at a velocity about 80 per: 
cent in excess of the peripheral speed of the blades. The velocity of i 
the air through the inlet is practically uniform over the entire inlet : 
area. The power consumption is relatively low. This type of fan was • 
invented by S. C. Davidson of Belfast, Ireland, and is known as the ' 
"Sirocco" fan. It is made under that name in this country by the: 
American Blower Co., to which the author in indebted for the preceding : 
tables. 

A Test of a " Sirocco " Mine Fan at Llwnypia, Wales, is reported in 
Eng'g., April 16, 1909. The fan is 11 ft. Sin. diam., double inlet, direct- 
coupled to a 3-phase motor. Average of three tests: Revs, per min., 184; 
peripheral speed, 6,705 ft. per min.; water-gauge in fan drift and in main 
drift, each 6 in.; area of drift, 184.6 sq. ft.; av. velocity of air, 1842 
ft. per min; volume of air, 340,033 cu. ft. per min.; H.P. input at motor, 
420; Brake H.P. on fan shaft, 390; Indicated H.P. in air, 321.5; efficiency 
of motor, 93%; mechanical efficiency of fan, 82.43%; combined mechan- 
ical efficiency of fan and motor. 76.6%. 

High-Pressure Centrifugal Fans. (See page 648.) 
The Conoidal Fan. — A multiblade fan in which the blades are 
not parallel to the shaft, but inchned to it, so that their tips form 
the shape of a cone, the inlet being the large diameter, is made by the 
Buffalo Forge Co. It is known as the Buffalo Niagara Conoidal 
Fan. A table of the regular sizes of these fans is given below. 

Capacities of Buffalo Niagara Conoidal Fans. 

Under Average Working Conditions at 70° F. and 30 in. Barometer. 
Static Pressure is 77.5 % of Total Pressure. Volumes in cu. ft. per min. 







.. 


1- 


in. Total 


2-in. Total 


4- 


in. Total 




.1 


(D 


Pressure, or 


Pressure 


or 


Pressure, or 






S 


0.577 oz. 


1.154 oz. 


2.307 oz. 


6 


. 


i 






i 






i 






d 






^ 





9^ 


^ 


"o 


^ 


^ 


i . 


Ph* 




% 


< 


^ 


> 


w 


^ 


> 


W 


p^ 


w 


3 


155/8 


1.31 


675 


2.440 


0.54 


955 


3.450 


1.54 


1350 


4,480 


4.35 


31/2 


181/8 


1.79 


579 


3,320 


0.74 


818 


4,690 


2.09 


1157 


6,640 


5.92 


4 


201/2 


2.33 


506 


4,340 


0.97 


716 


6,130 


2.73 


1013 


8,670 


7.73 


41/2 


231/2 


2.95 


450 


5,490 


1.22 


636 


7,760 


3.46 


900 


10.970 


9.78 


5 


261/8 


3.64 


405 


6,770 


1.51 


573 


9,580 


4.27 


810 


13.550 


12.1 


51/2 


283/4 


4.41 


368 


8,200 


1.83 


521 


11,590 


5.17 


736 


16.390 


14.6 


6 


313/8 


5.25 


338 


9,750 


2.17 


477 


13,790 


6.15 


675 


19.510 


17.4 


7 


361/2 


7.14 


289 


13,280 


2.96 


409 


18,770 


8.37 


579 


26.550 


23.7 


8 


42 


9.33 


253 


17,340 


3.87 


358 


24.520 


10.9 


506 


34,680 


30.9 


9 


47 


11.81 


225 


21,950 


4.89 


318 


31,020 


13.8 


450 


43,890 


39.1 


10 


52 


14.58 


203 


27,090 


6.04 


286 


38,310 


17.1 


405 


54,180 


48.3 


11 


58 


17.64 


184 


32.780 


7.31 


260 


46.360 


20.7 


368 


65,560 


58.5 


12 


63 


21.00 


169 


39,010 


8.70 


239 


55.170 


24.6 


338 


78,020 


69.6 


13 


68 


24.65 


156 


45,780 


10.2 


220 


64,730 


28.9 


312 


91,560 


81.6 


14 


73 


28.68 


145 


53,100 


11.8 


205 


75.090 


33.5 


289 


106.200 


94.7 


15 


78 


32.80 


135 


60.960 


13.6 


191 


86,200 


38.4 


270 


121,920 


108.7 


16 


84 


37.32 


127 


69.360 


15.5 


179 


98.060 


43.7 


253 


138,700 


123.7 


17 


89 


42.14 


119 


78.300 


17.5 


169 


110,720 


49.4 


238 


156,600 


139.6 


18 


94 


47.24 


113 


87,780 


19.6 


159 


124,110 


55.3 


225 


175.550 


156.5 


19 


99 


52.63 


107 


97,800 


21.8 


151 


138,280 


61.7 


213 


195.600 


174.4 


20 


105 


58.32 


101 


108.370 


24.2 


143 


153.250 


68.3 


202 


216.720 


193.2 



FANS AND BLOWERS. 667 

METHODS OF TESTING FANS. 

Anemometer Method. — ^Measurements by anemometers are liable to 
be very inaccurate (see page 625) and results obtained by them should 
be considered only as rough approximations. 

Water Gauge Readings at End of Tapered Cone. — This method is 
also far from accurate on accomit of variable eddies in the air column. 

Pitot Tube Readings in Center of Discharge Pipe. — This method 
gives fairly accurate results when the discharge pipe is the same size 
as the fan outlet, when the Pitot tube is placed at a distance equal to 
at least 15 diameters of the pipe from the fan outlet, when the tube is 
so made that it will give correct readings of the static pressure, and 
when the velocities computed from the readings are corrected by a 
coefficient (0.87 to 0.92 in different experiments) for the ratio between 
the average velocity and the velocity at the center of the tube. 

Pitot Tube Readings in Zones of Equal Area. — ]M ore accurate results 
may be obtained if the tube is traversed across tAvo diameters of the 
tube at right angles to each other, placing the nozzle successively at 
points which will divide the cross-sectional area into equal annular 
areas (with one central circular area). If ten such points are taken 
on each diameter, the radial distances of the points from the center . of 
the pipe will be 31, 55, 71, 84, and 95% of the radius of the pipe from 
the center. Since the velocity at any point is proportional to the 
square root of the velocity head, it is necessary for accurate results 
to take the average of the square root of the readings, and square this 
average to obtain the mean velocity head of the whole area of the pipe. 
For low pressures an inclined manometer should be used with the Pitot 
tube, and it should contain gasoline instead of water, as it keeps the 
tubes clean, has a definite meniscus and almost no capillary attraction 
for the glass. The readings of the tube are to be corrected for the 
inchnation and for the specific gravity of the gasoline to reduce them 
to equivalent inches of water column. 

The best form of Pitot tube is one made of two thin brass tubes, the 
outer one 1/4-in. and the inner one i/g-in. external diameter, each about 
4 or 5 in. long, the two being soldered together at one end and the end 
then tapered down to a sharp edged nozzle. Each tube is connected 
near the rear end to tubes at right angles to the double tube, leading 
to two manometers, one for reading the total, or dynamic or impact 
pressure, the other the static pressure. The difference between these 
two readings is the velocity head. It may be obtained in one reading 
by connecting both parts of the tube to a single manometer. The 
outer, or static, tube has two or more smooth holes drilled in it, diamet- 
rically opposite, at right angles to the axis, to receive the static pressure. 
The exact form of the nozzle of the impact tube is not of importance, 
as different forms give identical readings, but care must be taken with 
the holes of the static tube or errors will be made in the readings due 
to action of the djTiamic pressure on these holes if they are not properly 
made. A thin slot instead of the holes has been found to give in- 
accurate readings. (See papers by Chas. S. Treat, Trans. A. S. M. E., 
vol. 34, and W. C. Rowse, Jour. A. S. M. E., Sept., 1913.) 

For accurate scientific work it is well to check the static tube read- 
ings by manometer readings from a piezometer ring, which is a narrow 
annular channel encirchng the pipe and soldered to it to make it air- 
tight. Six or more smooth holes are bored into the pipe at right angles 
to its axis, to connect the interior of the pipe with the ring. The Pitot 
tube may also be caUbrated by means of a Thomas electric gas meter. 

The Thomas Electric ]\feter for air and gas consists of an enlargement 
of section of the flow pipe into a chamber of a diameter equal to about 
two diameters of the pipe, with conical ends connecting it with the 
pipe. In the interior is placed an electric heater made of bare resistance 
wire mounted on a fiber frame and equally distributed over the section 
of the chamber, and also two electric resistance thermometers, one in 
front of and the other behind the heater. An electric current, meas- 
ured by a wattmeter, is passed tlirough the heater and the temperatures 
before and after the heating are measured by the thermometers. If 
Ti and T2 are the temperatures before and after the heating, H the 
heat units corresponding to the watts delivered to the heater (1 watt = 



668 



AIR. 



3.415 B.T.U. per hour), and S the specific heat of the air, then the 
weight of air heated in lb. per min. is W = AQg(y _ ^ ) 

When the Pitot tube is correctly made and used its formula is 
V = \/2gh, in which h is the mean velocity head, measured as the height 
in feet of a cohunn of air which would produce the observed velocity 
and r the velocity in ft. per sec. 

To convert the velocity head as measured in the Pitot tube in inches 
of water cohimn into velocity of the air in feet per min. we have the 
following formulae: 

p = velocity pressure in inches of water gage. 

h = corresponding heat in feet of a column of air. 

V = velocity of air in ft. per sec. V = velocity in ft. per min. 

w = weight of 1 cu. ft. of air imder existing conditions. 



h = 



62.3 p , 

12 w ' 



1)=-^- 



64.32 X 62.3 p . 



12 w 



18.27 



aI^- 



V, ft. per min. = 1096.2 ^2. 



The average weight of 1 cu. ft. of air was found by the American 
Blower Co. in a large number of tests to be 0.0715 lb. per cu. ft., whence 
V=4101\/p: 

The velocity of flow of air at a given density produced by a pres- 
sure of 1 in. of water is called the "velocity constant" of air at that 
density. A table of such constants is given by the American Blower 
Co., from which the following table is condensed: 



Air Constants for Dry Air at Sea Level, Bar. 29.92 In. 



a . 




6 


a . 




6 


d . 




6 


a . 




6 


On 


K. 


"^ 




K. 


ui 




K. 


c^ 




K. 


•^ 


H^ 




^ 


H^ 




P^ 


H' 




en; 


H° 




f« 


-40 


3567 


0.890 


60 


3968 


0.990 


160 


4333 


1.082 


500 


5389 


1.345 


-20 


3651 


.911 


70 


4006 


1. 000 


180 


4402 


1.098 


600 


5663 


1.413 





3733 


.932 


80 


4044 


1.009 


200 


4470 


1.114 


700 


5925 


1.478 


10 


3773 


.942 


90 


4081 


1.018 


250 


4636 


1.157 


800 


6177 


1.542 


20 


3813 


.952 


100 


4118 


1.028 


300 


4796 


1.197 


900 


6418 


1.602 


30 


3852 


.961 


110 


4155 


1.037 


350 


4890 


1.236 


1000 


6650 


1.660 


40 


3891 


.971 


120 


4191 


1.046 


400 


5101 


1.273 


1100 


6873 


1.715 


50 


3930 


.981 


140 


4263 


1.064 


450 


5246 


1.310 


1200 


7090 


1.770 



Constant K 



=Vi 



2g X weight of 1 cu. ft. water at 62° F. 



1 12 X weight of 1 cu. ft. air at temp, stated. 

The values under Ratio give ratios of fan speeds necessary at the 
various temperatures to produce the same water gage indication. 

Horse-power of a Fan. — If C = cu. ft. of air deUvered per minute, 
W = weight of 1 cu. ft. of air under existing conditions, H the height 
in feet of an air coliunn equivalent to the total pressure, D the dynamic 
pressure in inches of water column = WH -^- 5.2, the horse-power 
developed by the delivery of the air is A = CWH h- 33.000 = CD ^ 6356. 
One inch water gage = 5.2 lb. per sq. ft. The total pressure D with 
which the fan should be credited is the difference between the total 
pressure in the discharge pipe and that in the inlet pipe. 

The air horse-power divided by the power required to drive the fan, 
as measured by a dynamometer, gives the mechanical efficiencv of the 
fan. 

From the above formulae the air horse-power is a function of two 
variables, volume and pressure. To obtain what is called the " static 
efficiency," the fan should be credited with the difference between 
the static pressure in the medium from which the fan is drawing 
air and the static pressure in the discharge pipe. To obtain the 



FANS AND BLOWERS. 669 

impact or total efficiency the fan should be credited with the kinetic 
energy in the air in the discharge pipe or with the difference between 
the static pressure in the medium from which the fan is drawing 
air and tlie total or impact pressure in the discharge pipe. 

The work of compression is negligible, as these metliods have to do 
with air under low pressure. When readings are taken on the suction 
side of the fan, for the purpose of determining static efficiency, the 
fan should be credited only with the difference between the static 
pressure in the discharging medium and the impact pressure in the 
inlet pipe. If the object is to determine the impact efficiency where 
readings are taken at the suction side of the fan, the pressure with 
which the fan should be credited is the difference between the impact 
reading at the fan discharge and the impact reading obtained in the 
inlet pipe. This total pressure with which the fan is credited may 
also be expressed as the difference between the static pressure in the 
discharge pipe and the static suction in the inlet pipe, plus the increase 
of the velocity pressure in the outlet pipe over the velocity pressure 
in the inlet pipe. 

Accuracy of Pitot Tube Measurements. — To obtain even approx- 
imately accurate results with Pitot tubes it is necessary both to have 
the tube properly made and to take great precautions in using it. 
W. C. Rowse, Trans. A. S. M. E., vol. 35 (1913), p. 633, tested several 
forms of tube, comparing their readings with those of a Thomas 
electric gas meter. He found the best tube to be one made of a 
i/4-in. outer and a Vs-in. inner thin brass tube, 4 or 5 in. long, soldered 
together at one end, which was tapered for 3/4 in. down to the internal 
diameter of the inner tube, which was thus given a sharp edge. The 
outer tube was perforated with a small smooth hole 0.02 in. diameter 
on each side at the middle of its length. The rear end of the small 
tube and the annular space between the two tubes were each con- 
nected to 1/4 in. upright tubes, from which rubber tubes led to two 
manometers. The inner tube received the impact pressure and the 
annular space the static pressure. The difference between the two 
is the velocity pressure, a direct reading of which could be made by 
connecting the two rubber tubes, or branches from them, to the two 
legs of a single manometer. The manometers were U tubes, of glass 
about 1/2 in. internal diameter, containing gasoline, and were inclined 
at an angle of 1 vertical to 10 horizontal in order to magnify the 
readings. The scale was graduated so as to read in hundredths of 
an inch of water column. To obtain mean velocities and pressures 
the tube was traversed across two diameters of the pipe, vertical and 
horizontal, ten readings being taken on each diameter, at points 
located at the center of five annular areas into which the total area 
of the pipe was divided. The radial distances of these points from the 
center of the pipe were 32, 55, 71, 84 and 95 per cent, respectively, 
of the radius of the pipe. (See Appendix No. 6 of the report of the 
Power Test Committee of the A. S. M. E., 1915.) The results of these 
tests showed that accuracy within 1 % could be obtained when all 
readings were obtained with a sufficient degree of refinement and 
when the Pitot tube was preceded by a length of pipe 20 to 38 times 
the pipe diameter in order to make the flow as nearly uniform across 
the section of the pipe as possible. 

When readings were taken at the center of a 12-in. galvanized iron 
pipe the mean pressure was 0.80 of the pressure at the center, corre- 
sponding to a mean velocity of V0.8O or 0.894 of the velocity at the 
center, within a limit of error of 2%. The mean velocity head was 
obtained by taking the square of the average of the square roots of 
each of the 20 readings. Tests of Pitot tubes with long narrow slots 
in the outer tube, instead of the small holes, gave results which were 
in error from 3.5 to 10%. 

The Thomas Electric Gas Meter, referred to above, is described 
in Trans. A. S. M. E., vol. 31, p. 655. It consists in an enlarged 
section of the gas or air pipe containing an electric heating device 
with electric instruments for determining both the increase of tem- 

Serature and the energy absorbed in heating. Given the specific 
eat, the rise in temperature, and the watts of energy absorbed, the 
weight of gas flowing in a given time may be computed. 



670 



AIR. 



Flow of Air through an Orifice. 

VELOCITY, VOLUME, AND H.P. REQUIRED WHEN AIR UNDER GIVEN PRESSURE 
IN OUNCES PER SQ. IN. IS ALLOWED TO ESCAPE INTO THE ATMOSPHERE. 

(B. F. Sturtevant Co.) 





cu 


Qi 
ft 


J3 J CJ £ 


! i 

^J3 O 




6" 

en 

.si 


u 
a) 
ft 


hrough 
1. effec- 
ea, cu. 
min. 


p « 
1^1 


ftS 






11 


S cr <D ft 

3 M > . 


2^ > 

en O > "^ 


ftt, 




'o d 


a 6'<o ft 




13. 
ill 


Pu 


P-i 


> 


> 


W 


w 


Ph 


> 


> 


a^ 


H 


1/8 


0.216 


1.828 


12.69 


0.00043 


0.0340 


2 


7.284 


50.59 


0.02759 


0.5454 


1/4 


0.432 


2,585 


17.95 


0.00122 


0.0680 


21/8 


7.507 


52.13 


0.03021 


0.5795 


3/8 


0.648 


3.165 


21.98 


0.00225 


0.1022 


21/4 


7.722 


53.63 


0.03291 


0.6136 


1/2 


0.864 


3.654 


25.37 


0.00346 


0.1363 


23/8 


7.932 


55.03 


0.03568 


0.6^76 


5/8 


1.080 


4.084 


28.36 


0.00483 


0.1703 


21 2 


8.136 


56.50 


0.03852 


0.6818 


3/4 


1.296 


4.473 


31.06 


0.00635 


0.2044 


25,8 


8.334 


57.88 


0.04144 


0.710.0 


7/8 


1.512 


4.830 


33.54 


0.03800 


0.2385 


23/4 


8.528 


59.22 


0.04442 


0.7500 


1 


1.728 


5.162 


35.85 


0.00978 


0.2728 


27/8 


8.718 


60.54 


0.04747 


0.7541 


11/8 


1.944 


5.473 


38.01 


0.01166 


0.3068 


3 


8.903 


61.83 


0.05058 


0.8180 


1V4 


2.160 


5.768 


40.06 


0.01366 


0.3410 


31 '8 


9.084 


63.03 


0.05376 


0.8522 


13/8 


2.376 


6.048 


42.00 


0.01575 


0.3750 


31 4 


9.262 


64.32 


0.05701 


0.8863 


11/2 


2.59? 


6.315 


43.86 


0.01794 


0.4090 


3C/8' 


9.435 


65.52 


0.06031 


0.9205 


15 8 


2.808 


6.571 


45.63 


0.02022 


0.4431 


3l2 


9.606 


66.71 


0.06368 


0.9546 


13 4 


3.024 


6.818 


47.34 


0.02260 


0.4772 


35/8 


9.773 


67.87 


0.06710 


0.9887 


17/8 


3.240 


7.055 


49.00 


0.02505 


0.5112 


374 
37/8 


9.938 
10.100 


69.01 
70.14 


0.07058 
0.07412 


1.0227 
1.0567 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(1) 


(3) 


(4) 


(5> 


(6) 



The headings of the 3d and 4^h columns in the above table have been 
abridged from the original, which read as follows: Velocity of dry air, 
50° F., escaping into the atmosphere through any shaped orifice in any 
pipe or reservoir in which the given pressure is maintained. Volume of 
air in cubic feet which may be discharged in one minute through an orifice 
having an effective area of discharge of one square inch. The 6th column, 
not in the original, has been calculated by the author. The figures repre- 
sent the horse-power theoretically required to move 1000 cu. ft. of air of 
the given pressures through an orifice, without allowance for the work of 
compression or for friction or other losses of the fan. These losses may 
amount to 60% or mo!-e of the given horse-power. 

The change in density which results from a change in pressure has been 
taken into account in the calculations of the table. The volume of air at 
a given velocity discharged through an orifice depends upon its shape, and 
is always less than that measured by its full area. For a given effective 
area the volume is proportional to the velocity. The power required to 
move air through an orifice is measured by the product of the velocity and 
the total resisting pressure. This power for a given orifice varies as the 
cube of the velocity. For a given volume it varies as the square of the 
velocity. In the movement of air by means of a fan there are unavoidable 
resistances which, in proportion to their amount, increase the actual power 
considerably above the amount here given. 

Pipe Lines for Fans and Blowers. — In installing fans and blowers 
careful consideration should be given to the pipe line conducting the air 
from the Ian or blower. Bends and turns in tne pipe, even of long radii, 
will cause considerable drop in pressure, and in straight pipe the friction of 
the moving air is a source of considerable loss. The iriction increases with 
the length of the pipe and is inversely as the diameter. It also varies as the 
square of the velocity. In long runs of pipe, the increased cost of a larger 
pipe can often be compensated by the decreased cost of the motor and 
power for operating the blower. 

The advisability of using a large pipe for conveying the air is shown by 



FANS AND BLOWEES. 



671 



the following table which gives the size of pipe which should be used for 
pressure losses not exceeding one-fourth and one-half ounce per square 
inch, for various lengths of pipe. 



Diameters of Blast Pipes. 

(B. F. Sturtevant Co., 1908.) 



ft 


h 

<u 


■s 
•si 

-a 


Length of Pipe in Feet. 


2 


20 


40 


60 


80 


100 120 


140 


C 


Diameter of Pipe with Drop of 




V4 


1/2 


1/4 


1/2 


1/4 


1/2 


1/4 


1/2 


1/4 


1/2 


1/4 


1/2 


1/4 


1/2 


c 
23 


Oz. 


Oz. 


Oz. 


Oz. 


Oz. 


Oz. 


Oz. 


Oz. 


Oz. 


Oz. 


Oz. 


Oz. 


Oz. 


Oz. 


1 


500 


6 


5 


7 


6 


7 


6 


8 


7 


9 


8 


9 


8 


9 


8 


2 


27 


1,000 


8 


7 


9 


8 


10 


9 


11 


9 


11 


10 


12 


11 


12 


11 


3 


30 


1,500 


10 


8 


11 


10 


11 


10 


12 


11 


13 


11 


13 


12 


14 


12 


4 


32 


2,000 


11 


9 


12 


11 


13 


12 


14 


12 


15 


13 


15 


14 


16 


14 


5 


36 


2,500 


12 


10 


14 


12 


15 


13 


15 


14 


16 


14 


17 


15 


17 


15 


6 


39 


3,000 


13 


11 


15 


13 


16 


14 


17 


15 


18 


15 


18 


16 


18 


16 


7 


42 


3,500 


13 


12 


15 


13 


17 


15 


17 


15 


18 


16 


19 


17 


20 


18 


8 


45 


4,000 


15 


12 


16 


15 


18 


15 


18 


16 


19 


17 


20 


18 


21 


18 


9 


48 


4,500 


15 


13 


17 


15 


18 


16 


19 


17 


20 


18 


21 


19 


22 


19 


10 


54 


5,000 


15 


13 


18 


15 


19 


17 


20 


18 


21 


18 


22 


19 


23 


20 


11 


54 


5,500 


16 


14 


18 


16 


20 


17 


21 


18 


22 


19 


23 


20 


23 


20 


12 


60 


6,000 


17 


14 


19 


17 


20 


17 


21 


19 


22 


20 


23 


21 


24 


21 


13 


60 


6,500 


17 


14 


19 


17 


21 


18 


23 


19 


23 


20 


24 


21 


25 


22 


14 


60 


7,000 


18 


15 


20 


18 


22 


19 


23 


20 


24 


21 


25 


22 


26 


23 


15 


66 


7,500 


18 


16 


21 


18 


22 


19 


24 


21 


25 


22 


26 


22 


27 


23 


16 


66 


8,000 


18 


16 


22 


18 


23 


20 


24 


22 


26 


22 


26 


23 


27 


24 


17 


66 


8.500 


18 


16 


22 


18 


23 


20 


24 


22 


26 


22 


27 


24 


28 


24 


18 


72 


9,000 


18 


17 


22 


18 


24 


21 


25 


22 


27 


23 


27 


24 


28 


25 


19 


72 


9,500 


20 


17 


23 


20 


24 


22 


26 


23 


28 


23 


28 


25 


29 


26 


20 


72 


10,000 


20 


18 


23 


20 


25 


22 


27 


23 


28 


24 


29 


25 


30 


26 


21 


78 


10,500 


21 


18 


24 


21 


26 


23 


27 


23 


29 


25 


30 


26 


30 


26 


22 


78 


11,000 


21 


18 


24 


21 


27 


23 


28 


24 


29 


26 


30 


27 


31 


27 


23 


78 


11,500 


21 


19 


25 


21 


27 


24 


28 


25 


30 


26 


30 


27 


31 


27 


24 


84 


12,000 


22 


19 


25 


22 


28 


24 


28 


25 


31 


26 


31 


27 


32 


28 


25 


84 


12,500 


22 


19 


26 


22 


28 


24 


29 


26 


31 


27 


32 


28 


33 


28 


26 


84 


13,000 


22 


19 


26 


22 


28 


24 


29 


26 


31 


27 


32 


28 


33 


28 


27 


90 


13.500 


23 


20 


26 


23 


28 


24 


30 


26 


31 


27 


32 


28 


34 


28 


28 


90 


14.000 


23 


20 


27 


23 


29 


25 


30 


27 


32 


28 


33 


29 


34 


29 


29 


90 


14,500 


23 


20 


27 


23 


29 


26 


31 


27 


32 


28 


33 


29 


34 


30 


30 


90 


15.000 


24 


21 


27 


24 


29 


26 


31 


27 


32 


28 


34 


30 


35 


30 



The minimum radius of each turn should be equal to the diameter of the 
pipe. For each turn thus made add three feet in length, when using this 
table. If the turns are of less radius, the length added should be increased 
proportionately. 

The above table has been constructed on the following basis: A loss of, 
say, 1/2 oz. pressure was allowed as a standard for the transmission of a 
given quantity of air through a given length of pipe of any diameter. The 
increased loss due to increasing the length of pipe was compensated for by 
increasing the diameter sufficiently to keep the loss still at 1/2 oz. Thus, 
if 2500 cu. ft. of air is to be delivered per minute through 100 ft. of pipe 
with a loss of not more than 1/9 oz., a 14-in. pipe wiU be required. If it \s 



672 AIR. 

necessary to increase the length of pipe to 140 ft., a pipe 15 in. diameter 

will be required if the loss in pressure is not to exceed 1/2 oz. In deciding 
the size of pipe the loss in pressure in the pipe must be added to the pres- 
sure to be maintained at the fan or blower, if the tabulated efficiency of 
the latter is to be secured at the deUvery end of the pipe. 

Centrifugal Ventilators for Mines. — Of different appUances for ven- 
tilating mines various forms of centrifugal macliines having proved their 
efficiency have now almost completely replaced aU others. Most if not all 
of the machines in use in this country are of this class, being either open- 
periphery fans, or closed, with chimney and spiral casing, of a more or less 
modified*^Guibal type. The theory of such machines has been demonstrated 
by Mr. Daniel Murguein " Theories and Practices of Centrifugal Ventilating 
Machines," translated by A. L. Stevenson, and is discussed in a paper by R. 
Van A. Norris, Trans. A. I. M. E., xx. 637. From this paper the following 
formulae are taken: 

Let a = area in sq. ft. of an orifice in a thin plate, of such area that its 
resistance to the passage of a given quantity of air equals the 
resistance of the mine; 

= orifice in a thin plate of such area that its resistance to the pas- 
sage of a given quantity of air equals that of the machine; 

Q = quantity of air passing in cubic feet per minute; 

V = velocity of air passing through a in feet per second; 
Vq = velocity of air passing through o in feet per second; 

h = head in feet air-column to produce velocity V; 

ho = head in feet air-column to produce velocity To- 

Q = 0.65aV; V = ^yjgh; Q = 0.Q5 a Vj^h; 
Q 



0.65 



= equivalent orifice of mine; 



or, reducing to water-gauge in inches and quantity in thousands of cubic 
feet per minute, 

0.403 Q . - . 

Vwg"' Q = 0.65oFo; Fo = ^2^/io; <? = 0.65 V2 gr/jo; 



/ Q^ 
= \ ^ ^^^, ^ = equivalent orifice of machine. 

The theoretical depression which can be produced by any centrifugal 
ventilator is double that due to its tangential speed. The formula 

77 = H! _ Z! 

2g 2g' 

in which T is the tangential speed, V the velocity of exit of the air from the 
space between the blades, and H the depression measured in feet of air- 
column, is an expression for the theoretical depression which can be pro- 
duced by an uncovered ventilator: this reaches a maximum when the air 
leaves the blades without speed, that is, F = 0, and H = T"^ -^ 2 g. 

Hence the theoretical depression which can be produced by any uncov- 
ered ventilator is equal to the height due to its tangential speed, and one- 
half that which can be produced by a covered ventilator with expanding 
chimney. Practical considerations in the design of the fan wheel and 
casing will probably cause the actual results obtained with fans to vary 
considerably from these formulae. 

So long as the condition of the mine remains constant: 

(1) The volume produced by any ventilator varies directly as the speed 
of rotation. 

(2) The depression produced by any ventilator varies as the square of 
the speed of rotation. 

(3) For the same tangential speed with decreased resistance the quantity 
of air increases and the depression diminishes. 



MINE VENTILATING FANS. 



673 



The following table shows a few results, selected from Mr. Norris's 
paper, giving the range of efiQciency which may be expected under dif- 
ferent circumstances. Details of these and other fans, with diagrams 
of the results, are given in the paper. 



Experiments on 3Iine-Ventilating Fans. 





(h 


i 






M 


n 




.s 


I 6 


0) 


(0 <D 


i 


•o.S 


Is 

II 




^ o 


-II 


^^ o 
oo o 


bJO tn 


I 

o S 


O bD 

it 




is 


ta 


^ 


Ph 


o 


o 


O 


o 


s 


H 


w 


1 


' 84 


5517 


236,684 


2818 


3040 


4290 


1.80 


67.13 


88.40 


75.9 


TS 


100 


6282 


336,862 


3369 


3040 


5393 


2.50 


132.70 


155.43 


85.4 


« 


111 


6973 


347,396 


3130 


3040 


5002 


3.20 


175.17 


209.64 


83.6 


ru 


123 


7727 


394,100 


3204 


3040 


5100 


3.60 


223.56 


295.21 


75,7 


h 


B{ 


' 100 


6282 


188,888 


1889 


1520 


3007 


1.40 


41.67 


97.99 


42.5 


130 


8167 


274,876 


2114 


1520 


3366 


2.00 


86.63 


194.95 


44.6 


22 


^\ 


59 


3702 


59,587 


1010 


1520 


1610 


1.20 


11.27 


16.76 


67.83 




83 


5208 


82,969 


1000 


1520 


1593 


2.15 


27.86 


48.54 


57.. 38 




d{ 


40 


3140 


49,611 


1240 


3096 


1580 


0.87 


6.80 


13.82 


49 2 


32 


70 


5495 


137,760 


1825 


3096 


2507 


2.55 


55.35 


67.44 


82.07 




( 


50 


2749 


147,232 


2944 


1522 


5356 


0.50 


11.60 


28.55 


40.63 




Hi 


69 


3793 


205,761 


2982 


1522 


5451 


1.00 


32.42 


45.98 


70.50 


83 


( 


96 


5278 


299,600 


3121 


1522 


5676 


2.15 


101.50 


120.64 


84.10 






200 


7540 


133,198 


666 


746 


1767 


3.35 


70.30 


102.79 


68.40 


26.9 


i] 


200 


7540 


180,809 


904 


746 


2398 


3.05 


86.89 


129.07 


67.30 


38.3 


( 


200 


7540 


209,150 


1046 


746 


2774 


2.80 


92.50 


150.08 


61.70 


46.3 




10 


785 


28,896 


2890 


3022 


3680 


0.10 


0.45 


1.30 


35. 






20 


1570 


57,120 


2856 


3022 


3637 


0.20 


1.80 


3.70 


49. 






25 


1962 


66,640 


2665 


3022 


3399 


0.29 


2.90 


6.10 


48. 






30 


2355 


73,080 


2436 


3022 


3103 


0.40 


4.60 


9.70 


47. 


52 


GJ 


35 


2747 


94,080 


2688 


3022 


3425 


0.50 


7.40 


15.00 


48. 




40 


3140 


112,000 


2800 


3022 


3567 


0.70 


12.30 24.90 


49. 






50 


3925 


132,700 


2654 


3022 


3381 


0.90 


18.80 38.80 


48. 






60 


4710 


173,600 


2893 


3022 


3686 


1.35 


36.90 66.40 


55. 






70 


5495 


203,280 


2904 


3022 


3718 1.80 


57.70 107.10 54. 1 






^ 


6280 


222,320 


2779 


3022 


3540 


2.25 


78.80 


152.601 


52. 1 





Type of fan. 



A. Guibal, double 

B. Same, only left hand running 

C. Guibal 

D. Guibal 

E. Guibal, double 

F. Capell..^ 

0. Guibal 



Diam. 



20 ft. 

20 

20 

25 

171/2 

12 

25 



Width. 



6 ft. 
6 
6 
8 
4 
10 
8 



No. inlets . 



Diam. 

inlets. 



8 ft. 10 In. 
8 10 



10 
6 



An examination of the detailed results of each test in Mr. Norris's table 
shows a mass of contradictions from which it is exceedingly diffiault to 
draw any satisfactory conclusions. The following, he states, appear to be 
more or less warranted by some of the figures: 

1. Influence of the Condition of the Airways on the Fan. — Mines with 
varying equivalent orifices ^ive air per 100 ft. speed of tip of fan, within 
limits as follows, the quantity depending on the resistance of the mine: 



674 



AIR. 



Equivalent 
orifice, 
sq.ft. 


Cu.ft. air 

per 100 ft. 

speed of fan. 


Average. 


Equivalent 
orifice. 

sq. ft. 


Cu.ft. air 

per 100 ft. 

speed of fan. 


Average. 


Under 20 
20 to 30 
30 to 40 
40 to 50 


1100 to 1700 
1300 to 1800 
1500 to 2500 
2300 to 3500 
2700 to 4800 


1300 
1600 
2100 
2700 
3500 


60 to 70 
70 to 80 
80 to 90 
90 to 100 
100 to 114 


3300 to 5100 
4000 to 4700 
3000 to 5600 


4000 
4400 
4800 


50 to 60 


5200 to 6200 


5700 



The influence of the mine on the efficiency of the fan does not seem to be 
very clear. Eight fans, with equivalent orifices over 50 square feet, give 
efficiencies over 70%; four, with smaller equivalent mine-orifices, give 
about the same figures; while, on the contrary, six fans, with equivalent 
orifices of over 50 square feet, give lower efficiencies, as do ten fans, all 
drawing from mines with small equivalent orifices. It would seem that, 
on the whole, large airways tend to assist somewhat in attaining high 
efficiency. 

2. Influence of the Diameter of the Fan. — This seems to be practically nil, 
the only advantage of Large fans being in their greater width and the lower 
speed required of the engines. 

3. Influence of the Width of a Fan. — This appears to be small as regards 
the efficiency of the machine; but the wider fans are, as a rule, exhausting 
more air. However, increasing the width of the fan of a given diameter 
causes an increase in the velocity of the air through the wiieel inlet, and 
this increased velocity will become at a certain point a serious loss and 
will decrease the mechanical efficiency. 

4. Influence of Shape of Blades. — Tliis appears, within reasonable limits, 
to be practically nil. Thus, six fans with tips of blades curved forward, 
three fans with flat blades, and one \\ith blades curved back to a tangent 
with the circumference, all give very high efficiencies — over 70 per cent. 
A prominent manufacturer claims, however, that his tests show a higher 
efficiency with vanes curved forward as compared with straight or back- 
wardly curved vanes. 

5. Inflxience of the Shape of the Spiral Casing. — This appears to be 
considerable. The shapes of spiral casing in use fall into two classes, 
the first presenting a large spiral, beginning ?.t or near the point of cut-off, 
and the second a circular casing reaching around three-quarters of the 
circumference of the fan, with a short spiral reaching to the evasee 
chimney. Fans having the first form of casing appear to give in 
almost every case high efficiencies. 

Fans that have a spiral belonging to the first class, but very much con- 
tracted, give only medium efficiencies. It seems probable that the proper 
shape of spiral casing would be one of such form that the air between each 
pair of blades could constantly and freely discharge into the space between 
the fan and casing, the whole being swept along to the evasee chimney. 
This would require a spiral beginning near the point of cut-off, enlarging by 
gradually increasing increments, to aUow for the slowing of the air caused 
by its friction against the casing, and reaching the chimney with an area 
such that the air could make its exit with its then existing speed — some- 
what less than the periphery-speed of the fan. 

6. Influence of the Shutter. — The shutter certainly appears to be an ad- 
vantage, as by it the exit area can be regulated to suit the varying quantity 
of air given by the fan, and in this way re-entries can be prevented. It is 
not uncommon to find shutterless fans, into the chimneys of which bits of 
paper may be dropped, which are drawn into the fan, make the circuit, and 
are again thrown out. This peculiarity has not been noticed with fans 
provided with shutters. 

7. Influence of the Speed at which a Fan is Run. — It is noticeable that 
most of the fans giving high efficiency were running at a rather high 
periphery velocity. The best speed seems to be between 5000 and 6000 
feet per minute. The fans appear to reach a maximum efficiency at some- 
where about the speed given, and to decrease rapidly in efficiency when 
this maximum point is passed. The same manufacturer mentioned in 
note 4 states that the efficiency is not affected by the tip speed, providing 
that the comparison is always made at the same point in the efficiency 
curve, 



DISK FANS. 



675 



In discussion of Mr. Norris's paper, Mr. A. H. Storrs saj^s: B'rom the '" cu- 
bic feet per revolution" and "cubical contents of fan-blades," as given in 
the table, we find that the enclosed fans empty themselves from one-half to 
twice per revolution, wliile the open fans are emptied from one and three- 
quarters to nearly three times; this for fans of both types, on mines covering 
the same range of equivalent orifices. One open fan, on a very large 
orifice, was emptied nearly four times, while a closed fan, on a still 
larger orifice, only shows one and one-half times. For the open fans the 
"cubic feet per 100 ft. motion" is greater, in proportion to the fan 
width and equivalent orifice, than for the enclosed type. Notwithstand- 
ing this apparently free discharge of the open fans, they show very low 
efficiencies. 

As illustrating the very large capacity of centrifugal fans to pass air, if 
the conditions of the mine are made favorable, a 16-ft. diam. fan, 4 ft. 6 in. 
wide, at 130 revolutions, passed 360,000 cu. ft. per min., and another, of 
same diameter, but slightly wider and with larger intake circles, passed 
500,000 cu. ft., the water-gauge in both instances being about i 2 in. 

T. D. Jones says: The efficiency reported in some cases by Mr. Norris is 
larger than I have ever been able to determine by experiment. My own 
experiments, recorded in the Pennsylvania Mine Inspectors' Reports from 
1875 to 1881, did not show more than 60% to 65%. 

DISK FANS. 

Efficiency of Disk Fans. — Prof. A. B. W. Kennedy (Industries, Jan. 
17, 1890) made a series of tests on two disk fans, 2 and 3 ft. diameter, 
known as the Verity Silent Air-propeller. The principal results and 
conclusions are condensed as below. 



Speed of fan, revolutions per minute. . 

Net H.P. to drive fan and belt 

Cubic feet of air per minute 

Mean velocity of air in 3-ft. flue, feet 

per minute 

Mean velocity of air in flue, same 

diameter as fan 

Cu. f t . of air per min. per effective H.P 
Motion given to air per rev. of fan, ft.. 
Cubic feet of air per rev, of fan 



Propeller, 
2 ft. diam. 



750 
0.42 
4,183 

593 

1,330 

9,980 

1.77 

5.58 



676 
0.32 
3,830 

543 

1,220 

11,970 

1.81 

5.66 



577 
0.227 
3,410 

482 

1,085 

15,000 

1.88 

5.90 



Propeller, 
3 ft. diam. 



576 
1.02 
7,400 

1,046 



7,250 
1.82 
12.8 



459 
0.575 
5,800 

820 



10,070 
1.79 
12.6 



373 
0.324 
4,470 

632 



13,800 
1.70 
12.0 



In each case the efficiency of the fan, that is, the quantity of air deUvered 
per effective horse-power, increases very rapidly as the speed diminishes, 
so that lov.-er speeds are much more economical than higher ones. On the 
other hand, as the quantity of air delivered per revolution is verv nearly 
constant, the actual useful work done by the fan increases almost'^directly 
with its speed. Comparing the large and small fans with about the 
same air delivery, the former (running at a much lower speed, of course) 
is much the more economical. Comparing the two fans running at the 
same speed, however, the smaller fan is very much the more economical. 
The delivery of air per revolution of fan is very neariy directly propor- 
tional to the area of the fan's diameter. 

The air delivered per minute by the 3-ft. fan is neariy 12.5 R cubic feet 
(R being the number of revolutions made by the fan per minute). For 
the 2-ft. fan the quantity is 5.7R cubic feet. For either of these or any 
other similar fans of wliich the area is A square feet, the deUvery will be 
about 1.8 AR cubic feet. Of course any change in the pitch of the blades 
might entirely change these figures. 

The net H.P, taken up is not far from proportional to the square of the 
number of revolutions above 100 per minute. Thus for the 3-ft. fan the 

"'' ^-P- '' ^mm^' -"'« ^°^ the 2-ft. fan the net H. P is ^^^- 
The denominators of these two fractions are verv nearlv proportional 
inversely to the square of the fan areas or the foiirth power of the fan 



676 



AIR. 



diameters. The net H.P. required to drive a fan of diameter. D feet or 
area A square feet, at a speed of R revolutions per minute, will therefore 

. ,, D<(^- 100)2 ^2 (72 _ 100)2 
be approximately ^^ qq^ qqq or ^q^^qq qqq • 

The 2-ft. fan was noiseless at all speeds. The 3-ft. fan was also noiseless 
up to over 450 revolutions per minute. 

Experiments made with a Blaclcman Disk Fan, 4 ft. diam. by Geo. 
A. Suter, to determine the volumes of air delivered under various con- 
ditions, and the power required; with calculations of efficiency and ratio 
of increase of power to increase of velocity, by G. H. Babcock. {Trans. 
A.S. M. E.,vn. 547): 



d 

a 

> 


Cu. ft. of Air 
delivered 
per min.. 


1' 

1 




Ratio of In- 
crease of 
Speed. 


Ratio of In- 
crease of 
Delivery 


t»H 0) CD 

O ^ ^ 

r 


1^ 


?5 
§ 8 


>> 

•-fa 


350 


25,797 
32,575 
41,929 
47,756 
For 


0.65 
2.29 
4.42 
7.41 
series 














1.682 


440 
534 
612 




1.257 
1.186 
1.146 
1.749 


1.262 
1.287 
1.139 
1.851 


3.523 

1.843 

1.677 

11.140 


5.4 
2.4 
3.97 
4. 




.9553 
1.062 
.9358 








340 


20,372 
26,660 
31,649 
36,543 
For 


0.76 
1.99 
3.86 
6.47 
series 














.7110 


453 
536 
627 





1.332 
1.183 
1.167 
1.761 


1.308 
1.187 
1.155 
1.794 


2.618 
1.940 
1.676 
8.513 


3.55 
3.86 
3.59 
3.63 




.6063 
.5205 
.4802 








340 


9,983 
13,017 
17,018 
18,649 
For 


1.12 
3.17 
6.07 
8.46 
series 


0.28 
0.47 
0.75 
0.87 












.3939 


430 
534 
570 


1.265 
1.242 
1.068 
1.676 


1.304 
1.307 
1.096 
1.704 


2.837 
1.915 
1.394 
7.554 


3.93 
2.25 
3.63 
3.24 


1.95 
1.74 
1.60 
1.81 


.3046 
.3319 
.3027 


330 


8,399 
10,071 
11,157 
For 


1.31 

3.27 

6.00 

series 


0.26 
0.45 
0.75 












.2631 


437 
516 


1.324 
1.181 
1.563 


1.199 
1.108 
1.329 


3.142 
1.457 
4.580 


6.31 
3.66 
5.35 


3.06 
4.96 
3.72 


.2188 
.2202 



Nature of the Experiments. — First Series: Drawing air through 30 ft. 
of 48-in. diam. pipe on inlet side of the fan. 

Second Series: Forcing air through 30 ft. of 484n. diam. pipe on outlet 
side of the fan. 

Third Series: Drawing air through 30 ft. of 48-in. pipe on inlet side of 
the fan — the pipe being obstructed by a diaphragm of cheese-cloth. 

Fourth Series: Forcing air through 30 ft. of 48-in. pipe on outlet side 
of fan — the pipe being obstructed by a diaphragm of cheese-cloth. 

Mr. Babcock says concerning these experiments: The first four experi- 
ments are evidently the subject of some error, because the efficiency is 
such as to prove on an average that the fan was a source of power sufficient 
to overcome all losses and help drive the engine besides. The second 
series is less questionable, but still the efficiency in the first two experi- 
ments is larger than might be expected. In the third and fourth series 
the resistance of the cheese-cloth in the pipe reduces the efficiency largely, 
as would be expected. In this case the value has been calculated from 
the height equivalent to the water-pressure, rather than the actual veloc- 
ity of the air. 

This record of experiments made with the disk fan shows that this kind 
or tan is not adapted for use where there is any material resistance to the 
flow of the air. In the centrifugal fan the power used is neariy propor- 
tioned to the amount of air moved under a given head, while in this fan 
the power required for the same number of revolutions of the fan increases 
very materially with the resistance, notwithstanding the quantity of air 
moved is at the same time considerably reduced. In fact from the inspec- 



k 



POSITIVE ROTAEY BLOWERS. 677 

tion of the third and fourth series of tests, it would appear that the power 
required is very nearly the same for a given pressure, whether more or 
less air be in motion. It would seem that the main advantage, if any, 
of the disk fan over the centrifugal fan for slight resistances consists in the 
fact that the delivery is the full area of the disk, while with centrifugal 
fans intended to move the same quantity of air the opening is much 
smaller. 

It will be seen by columns 8 and 9 of the table that the power used in- 
creased much more rapidly than the cube of the velocity, as in centrifugal 
fans. The different experiments do not agree with each other, but a 
general average may be assumed as about the cube root of the eleventh 
power. 

Capacity of Disk Fans. (C. L. Hubbard, The Metal Worker, Sept. 5, 
1908.) — The rated capacities given in catalogues are for fans revolving 
in free air — that is, mounted in an opening without being connected with 
ducts or subject to other frictional resistance. 

The following data, based upon tests, apply to fans working against a 
resistance equivalent to that of a shallow heater of open pattern, and 
connecting with ducts of medium length through which the air flows at a 
velocity not greater than 600 or 800 ft. per minute. Under these con- 
ditions a good type of fan will propel the air in a direction parallel to the 
shaft, a distance equal to about 0.7 of its diameter at each revolution. 
From this we have the equation Q = 0.7 D X R X ^, in which Q = cu. 
ft. of air discharged per minute; D = diam. of fan, in ft.; R = revs, per 
min.; A = area of fan, in sq. ft. The following table is calculated on this 
basis. 
Diam.of fan, in. 

18 24 30 36 42 48 54 60 72 84 96 
Cu. ft per rev. 

1.85 4.40 8.59 14.8 23.6 35.2 50.1 68.7 118.7 188.6 281.5 

Revolutions per min. for velocity of air through fan = 1000 ft. per min. 
952 714 571 476 408 357 317 286 238 204 179 

The velocity of the air through the fan is proportional to the number 
of revolutions. For the conditions stated the H.P. required per 1000 cu. 
ft. of air moved will be about 0.16 when the velocity through the fan is 
1000 ft. per min., 0.14 for a velocity of 800 ft., and 0.18 for 1200 ft. For 
a fan moving in free air the required speed for moving a given volume of 
air will be about 0.6 of the number of revolutions given above and the 
H.P. about 0.3 of that required when moving against the resistance stated. 

POSITIVE ROTARY BLOWERS, 

Rotary Blowers, Centrifugal Fans, and Piston Blowers. (Cata- 
logue of the Connersville Blower Co.) — In ordinary w^ork the advantage 
of a positive blower over a fan begins at about 8 oz. pressure, and the 
efficiency of the positive blower increases from 8 oz. as the pressure goes 
up to a point wiiere the ordinary centrifugal fan fails entirely. The 
highest efficiency of rotary blowers is when they are w^orking against 
pressures ranging between 1 and 8 lbs. 

Fans, when run at constant speed, cannot be made to handle a constant 
volume of fluid when the pressure is variable; and they cannot give a high 
efficiency except for low and uniform pressures. 

When a fan blow^er is used to furnish blast for a cupola it is driven at a 
constant speed, and the amount of air discharged by it varies according 
to the resistance met with in the cupola. With a positive blower running 
at a constant speed, however, there is a constant volume of air forced 
into the cupola, regardless of changing resistance. 

A. rotary blower of the two-impeller type is not an economical com- 
pressor, because the impellers are working against the full pressure t.t all 
times, w^hile in an ideal blowing engine the theoretical mean effective 
pressure on the piston, when discharging air at 15 lbs. pressure, is III/2 lbs. 
For high pressures, on account of the increase of leakage and the increase 
of power required because it does not compress gradually, the rotary 
blower must give way to the piston type of macliine. Commercially, the 
line is crossed at about 8 lbs. pressure. 

1. A fan is the cheapest in first cost, and if properly applied may be 
used economically for pressures up to 8 oz. 



678 



AIR. 



2. A rotary blower costs more than a fan, but much less than a blowing 

engine; is more economical than either between 8 oz. and 8 lbs. pressure, 
and can be arranged to give a constant pressure or a constant volume. 

3. Piston machines cost much more than rotary blowers, but should 
be used for continuous duty for pressures above 8 lbs., and may be econom- 
ical if they are properly constructed and not run at too high a piston speed. 

The horse-power required to operate rotary blowers is proportional to 
the volume and pressure of air discharged. In making estimates for 
power it is safe to assume that for each 1000 cu. ft. of free air discharged, 
at one pound pressure, 5 H.P. should be provided. 

Test of a Rotary Blower. (Connersville Blower Co.) — The test was 
made in 1904 on two 39 X 84 in. blowers coupled direct to two 12 and 24 X 
36 in. compound Corhss engines. The results given below are for the 
combined units. 



Air pressure, lbs. . . . 

Engine, I.H.P 

Displacement, cu.ft 
Efficiency 




19.30 



0.05 
23.76 
19,212 



0.5 

52.83 
18,727 
68.5 



1.0 
100.91 
18,508 

79 



1.5 2. 

132.67 176.11 

18,344 18,200 

84 85.6 



2.5 
223.20 
18,028 

86 



3. 

256.87 

17,966 

86 



3.5 

287.56 
17,863 
85.9 



In calculating the efficiency the theoretical horse-power was taken as 

the power required to compress adiabatically and to discharge the net 
amount of air at the different pressures and at the same altitude. The 
test was made up to 3.5 lbs. only. Estimated efficiencies for higher 
pressures from an extension of the plotted curve are: 6 lbs. 84%, 8 lbs. 
82%, 10 lbs. 79.5%. The theoretical discharge of the blower was 19,250 
cu= ft. 

Capacity of Rotaiiy Blowers for Cupolas. 



Cu.ft 


Revs. 


Tons 


per 


per 


per 


rev. 


min. 


hour. 


1.5 


( 200 
) 400 


1 
2 


3.3 


i 175 
1 335 


1 

2 


6 


( 185 
\ 275 


2 


3 


10 


( 200 
i 250 


4 

5 




( 150 


4 


13 


\ 190 


5 




( 175 


61/2 




( 150 


5 


17 


< 205 


61/2 




( 250 


81/2 




( 166 


8 


24 


< 200 


10 




( 240 


12 




( 150 


10 


33 


< 180 


12 




( 210 


14 



Suitable 
for cupola 
in. diam.* 



I 18 to 20 
I 24 to 27 
I 28 to 32 
[ 32 to 38 

32 to 40 
36 to 45 
42 to 54 
48 to 60 



Cu. ft. 


Revs. 


Tons 


per 


per 


per 


rev. 


mm. 


hour. 




( 135 


12 


45 


} 165 


15 




( 200 


18 




( 130 


15 


57 


1 155 


18 




( 185 


21 




( 140 


18 


65 


< 160 


21 




185 


24 




( 125 


21 


84 


< 145 


24 




( 160 


27 




( 120 


24 


100 


\ '35 


27 




( 160 


30 




C 1J5 


27 


118 


< 130 


30 




140 


33 



Suitable 
for cupola 
in. diam. 



54 to 66 
I 60 to 72 
> 66 to 84 
I 72 to 90 

[ 84 to 96 

) Two 
( cupolas 
) 60 to 66 



♦ Inside diam. The capacity in tons per hour is based on 30,000 cu. ft. 
of air per ton of iron melted. 

For smith fires: an ordinary fire requires about 60 cu. ft. per min. 

For oil furnaces : an ordinary furnace burns about 2 gallons of oil per 
hour and 1800 cu. ft. of air should be provided for each gallon of oil. For 
each 100 cu. ft. of air discharged per minute at 16 oz. pressure, 1/2 H.P. 
should be provided. 

Sizes of small blowers. 173 288 576 cu. in. per rev. 

Revs, per min 800 to 1500 500 to 900 300 to 600 

Diam. of outlet, in. . . . 21/2 21/2 3 



STEAM JET BLOWER AND EXHAUSTER. 



679 



Rotary Gas Exhausters. 



Cu. ft. per rev 

Rev. permin 

Diam. of pipe open- 
ing 

Cu. ft. per rev 

Rev. per min 

Diam. pipe opening 



2/3 


IV? 


3.3 


6 


10 


13 


17 


24 


200 


180 


170 


160 


150 


150 


140 


130 


4 


6 


8 


10 


12 


12 


16 


16 


45 


57 


65 


84 


100 


118 


155 


200 


110 


100 


95 


90 


85 


82 


80 


80 


20 


24 


24 


30 


30 


30 


36 


36 



33 

120 

20 

300 

75 

42 



There is no gradual compressing of air in a rotary machine, and the 
unbalanced areas of the impellers are working against the full difference 
of pressure at all times. The possible efficiency of such a machine under 
ordinary temperature and conditions of atmosphere, assuming no me- 
chanical friction, leakage, nor radiation of heat of compression, would be 
as follows: 

Gauge pres. lb 1 2 3 4 5 10 15 

Efficiency % 97.5 95.5 93.3 91.7 90 82.7 76.7 

The proper application of rotary positive machines when operating in 
air or gas under differences of pressures from 8 oz. to 5 lbs. is where con- 
stant quantities of fluid are required to be delivered against a variable 
resistance, or where a constant pressure is required and the volume is 
variable. These are the requirements of gas works, pneumatic-uube" 
transmission (both the vacuum and pressure systems), foundry cupolas, 
smelting furnaces, knobbling fires, sand blast, burning of fuel oil, con- 
veying granular substances, the operation of many kinds of metallurgical 
furnaces, etc. —J. T. Wilkin, Trans. A. S. M. E., Vol. xxiv. 

STEAM-JET BLOWER AND EXHAUSTER 

The Steam-Jet as a Means for Ventilation. — Between 1810 and 
1850 the steam-jet was employed to a considerable extent for ventilating 
English coUieries, and in 1852 a committee of the House of Commons 
reported that it was the most powerful and a.t the same time the cheapest 
method for the ventilation of mines; but experiments made shortly after- 
wards proved that tliis opinion was erroneous, and that furnace ventila- 
tion was less than half as expensive, and in consequence the jet was soon 
abandoned as a permanent method of ventilation. 

For an account of these experiments see- Colliery Engineer, Feb., 1890. 
The jet, however, is sometimes advantageously used as a substitute, for 
instance, in the case of a fan standing for repairs, or after an explosion, 
when the furnace may not be kept going, or in the case of the fan having 
been rendered useless. 

A Blower and Exhauster is made by Schutte & Koerting Co., Phil- 
adelphia, on the principle of the steam-jet ejector. The following is a 
table of capacities. 



Diameter of 
Pipes, Inches. 


Capacity 

per 

Hour, 

Cu. ft. 


Diameter of 
Pipes, Inches. 


Capacity 

Per 

Hour, 

Cu. ft. 


Diameter of 
Pipes, Inches. 


Capacity 

Per 

Hour, 

Cu. ft. 


Air. 


Steam. 


Air. 


Steam. 


Air. 


Steam. 


V2 
IV2 


V2 


300 

600 

1,000 

2,000 


2 
4 


//^ 

wa 


4,000 
6,000 
12,000 
18,000 


5 
6 
7 
8 


2 
2 

2V. 


27,000 
35,000 
48,000 
60,000 



When used as exhausters with a steam pressure of 45 lb., these 
machines will produce a vacuum of 20 in. mercury (23.3 ft. water 
colimin), but they can be specially constructed to produce a vacuum 
of 25 in. mercury (29.3 ft. water column). 



680 



AIR. 



When used as compressors, they will operate against a coimter-pres- 
sure equal to 1/7 of the steam pressure. 

Another steam- jet blower is used for boiler-firing, ventilation, and 
similar purposes where a low counter-pressure or rarefaction meets the 
requirements. 

The volumes as given in the following table of capacities are under the 
supposition of a steam-pressure of 60 lbs. and a counter-pressure of, 
say, from 0.5 to 2 inches of water: 



• Diameter 
in Inches. 


Capacity 

per 

Hour, 

Cubic 

Feet. 


Diameter 
in Inches. 


Capacity 

Hour, 
Cubic 
Feet. 


Diameter 
in Inches. 


Capacity 

per 

Hour, 

Cubic 

Feet. 




^5 


H 




•^1 

^5 


II 




^1 




4 
5 
8 
9 


3 
4 

5 

6 


Vs 

V2 

1/2 
V4 


10,000 
20,000 
30,000 
45,000 


11 

12 
14 
16 


7 

8 
10 
12 


V4 

V4 

1 
1 


60,000 
90,000 
120,000 
180,000 


18 
24 
32 
42 


14 
18 
24 
32 


IV4 
1 1/2 

21/2 


240,000 

500.000 

1,000,000 

2,000,000 



Maximum coal burning capacity per hour = cu. ft. air per hr. 4- 200. 

BLOWING-ENGINES. 

Blowing- engines. — The following table showing dimensions, 
capacity, etc., of Corliss horizontal cross-compound condensing 
blowing engines is condensed from a table published about 1901 by 
the Philadelphia Engineering Works. Similar engines are built by 
Wilham Tod & Co., Youngstown, Ohio, and other builders. 



Corliss 


Horizontal Cross-compound 


Condensing Blowing- 






engmes. 
















m 


rl, 




•5x5 


Indicated 


d 




^ 




^ 


<v 





P<M 


ft^ 


Horse-power. 


a 




;3 ". 

^d 
t 02 




no a 




1^: 


OS'S 
_ 




15 Exp. 


13 Exp. 





125 lb. 
Steam. 


1001b. 
Steam. 


CO 

> 




3^- 


45 


I5 


m 


Appr 
ping 
lb. 






2,280 


60 


45.600 


15 


44 


78 


(2) 84 


60 


505.000 


605.000 




2,060 


60 


45.600 


12 


42 


72 


(2) 84 


60 


475,000 


550,000 


1.596 




60 


45.600 


10 


32 


60 


(2) 84 


60 


355.000 


436.000 




1,980 


60 


39.600 


15 


40 


72 


(2) 78 


60 


445,000 


545.000 




1,702 


60 


39.600 


12 


38 


70 


(2) 78 


60 


425.000 


491.000 




1.386 


60 


39.600 


10 


36 


66 


(2) 78 


60 


415.000 


450.000 




1. 175 


60 


23.500 


15 


34 


60 


(2) 72 


60 


340.000 


430.000 




822 60 


23.500 


10 


28 


50 


(2) 72 


60 


270.000 


300.000 



Vertical engines are built of the same dimensions as above, except 
that the stroke is 48 in. instead of 60, and they are run at a higher 
number of revolutions to give the same piston-speed and the same 
I.H.P. 

The calculations of power, capacity, etc., of blowing-engines are the 
same as those for air-compressors. They are built without any provision 
for cooling the air during compression. About 400 feet per minute is the 
usual piston-speed for recent forms of engines, but with positive air-valves, 
which have been introduced to some extent, this speed may be Increased. 
The efficiency of the engine, that is, the ratio of the I.H.P. of the air- 
cylinder to that of the steam-cyhnder, is usually taken at 90 per cent, the 
losses by friction, leakage, etc.. being taken at 10 per cent. 

Horse-power of Steam Cylinders of Blowing-engines. — (Wm. 
Tod & Co., 1914.) To find the indicated horse-power to be developed 
in the steam cyhnders of a blowing-engine, multiply the number of 



HEATING AND VENTILATION. 681 

cubic feet of free air to be compressed per minute by the figures given 
below for the respective pressures named. 

Gage press, lb. 

persq. in. ... 5 10 15 20 25 30 35 40 

Factor 0.0226 .0415 .0577 .0722 .0853 .0973 .1084 .1187 

These factors are based on the theoretical horse-power required 
to compress and deliver 1 cu. ft. of air to the pressure stated, plus 
an allowance of 15%, which is stated to be about right for mechanically- 
operated air valves. With poppet air valves the loss may be about 
10%. 

HEATING AND VENTILATION. 

Ventilation. (A. R. Wolff, Stevens Indicator, April, 1890.) — The 
popular impression that the impure air falls to the bottom of a crowded 
room is erroneous. There is a constant mingling of the fresh air admitted 
with the impure air due to the law of diffusion of gases, to difference of 
temperature, etc. The process of ventilation is one of dilution of the 
impure air by the fresh, and a roomx is properly ventilated in the opinion 
of the hygienists when the dilution is such that the carbonic acid in the 
air does not exceed from 6 to 8 parts by volume in 10,000. Pure country 
air contains about 4 parts CO2 in 10,000, and badly- ventilated quarters 
as high as 80 parts. 

An ordinary man exhales 0.6 of a cubic foot of CO2 per hour. New 
York gas gives out 0.75 of a cubic feet of CO2 for each cubic foot of gas 
burnt. An ordinary lamp gives out 1 cu. ft. of CO2 per hour. An 
ordinary candle gives out 0.3 cu. ft. per hour. [The use of gashght for 
interior lighting does not affect the atmosphere deleteriously. See 
pamphlet issued by National Commercial Gas Assn., 1914.] 

To determine the quantity of air to be supplied to the inmates of an 
unhghted room, to dilute the air to a desired standard of purity, we 
can establish equations as follows: 

Let V = cubic feet of fresh air to be supplied per hour. 

r = cubic feet of CO2 in each 10,000 cu. ft. of the entering air; 
R = cubic feet of CO2 which each 10,000 cu. ft. of the air in the 

room may contain for proper health conditions; 
n = number of persons in the room ; 
0.6 = cubic feet of CO2 exhaled by one man per hour. 

Then - +0.6 n equals cubic feet of CO2 communicated to the room 

during one hour. 

This value divided by v and multiplied by 10,000 gives the proportion 
of CO2 in 10,000 parts of the air in the room, and this should equal R, the 
standard of purity desired. Therefore 



^"■Q"°["i^+°-"'^] 



^= ^^^ -.or.= |^"- 

If we place r at 4 and i^ at 6, v = 6000 n -^ (6 - 4) = 3000 n, or the 
quantity of air to be supplied per person is 3000 cubic feet per hour. 

If the original air in the room is of the purity of external air, and the 
cubic contents of the room is equal to 100 cu. ft. per inmate, only 3000 — 
100 = 2900 cu. ft. of fresh air from without will have to be supplied the 
first hour to keep the air witliin the standard purity of 6 parts of CO2 in 
10,000. If the cubic contents of the room equals 200 cu. ft. per inmate, 
only 3000 - 200 = 2800 cu. ft. will have to be suppUed the first hour to 
keep the air within the standard purity, and so on. 

Again, if we only desire to maintain a standard of purity of 8 parts 
of carbonic acid in 10,000, the equation gives as the required air-supply 
per hour 

»= g_ ^ -11 = 1500 n, or 1500 cu. ft. of fresh air per inmate per hour. 



682 



HEATING AND VENTILATION. 



Cubic feet of air containing 4 parts of carbonic acid in 10,000 necessary 
per person per hour to keep the air in room at the composition of 

6 7 8 9 10 15 20 parts of CO2 in 10,000. 

3000 2000 1500 1200 1000 545 375 cubic feet. 

If the original air in the room is of purity of external atmosphere (4 parts 
of carbonic acid in 10,000), the amount of air to be supplied the first hour, 
for given cubic spaces per inmate, to have given standards of purity not 
exceeded at the end of the hour, is obtained from the following table: 



Cubic 
Feet of 


Proportion of Carbonic Acid in 10,000 Parts of the Air, not to 
be Exceeded at End of Hour. 


Space 
in Room 


6 


7 


8 


9 


10 1 15 


20 


Individ- 
ual. 


Cubic Feet of Air, of Composition 4 Parts of Carbonic Acid in 
10,000, to be Supplied the First Hour. 


100 
200 
300 
400 
500 
600 
700 


2900 
2800 
2700 
2600 
2500 
2400 
2300 
2200 
2100 
2000 
1500 
1000 
500 


1900 
1800 
1700 
1600 
1500 
1400 
1300 
1200 
1100 
1000 
500 
None 


1400 
1300 
1200 
1100 
1000 
900 
800 
700 
600 
500 
None 


1100 
1000 
900 
800 
700 
600 
500 
400 
300 
200 
None 


900 
800 
700 
600 
500 
400 
300 
200 
100 
None 


445 
345 
245 
145 
45 
None 


275 

175 

75 

None 


800 






900 






1000 






1500 






2000 








2500 


^ 

























It is exceptional that systematic ventilation supplies the 3000 cubic 
feet per inmate per hour, which adequate health considerations demand. 
For large auditoriums in which the cubic space perindividual is great, and in 
which the atmosphere is thoroughly fresh before the rooms are occupied, 
and the occupancy is of two or three hours' duration, the systematic air- 
supply may be reduced, and 2000 to 2500 cubic feet per inmate per hour 
is a satisfactory allowance. 

In hospitals where, on account of unhealthy excretions of various kinds, 
the air-dilution must be largest, an air-supply of from 4000 to 6000 cubic 
feet per inmate per hour should be provided, and this is actually secured 
in some hospitals. A report dated March 15, 1882, by a commission ap- 
pointed to examine the pubhc schools of the District of Columbia, says: 

" In each class-room not less than 15 square feet of floor-space should be 
allotted to each pupil. In each class-room the window-space should not 
be less than one-fourth the floor-space, and the distance of desk most 
remote from the window should not be more than one and a half times the 
height of the top of the window from the floor. The height of the class- 
room should never exceed 14 feet. The provisions for ventilation should 
be such as to provide for each person in a claSs-room not less than 30 cubic 
feet of fresh air per minute (1800 per hour), which amount must be intro- 
duced and thoroughly distributed without creating unpleasant draughts, 
or causing any two parts of the room to differ in temperature more than 
2° Fahr., or the maximum temperature to exceed 70° Fahr." [The provi- 
sion of 30 cu. ft. p r minute for each person in a class-room is now (1909) 
required by law in several states.] 

When the air enters at or near the floor, it is desirable that the velocity 
of inlet should not exceed 2 feet per second, which means larger sizes of 
register openings and flues than are usually obtainable, and much higher 
velocities of inlet than two feet per second are the rule in practice. 
The velocity of current into vent-flues can safely be as high as 6 or even 
10 feet per second, without being disagreeably perceptible. 

The entrance of fresh air into a room is coincident v.'ith, or dependent 
on, the removal of an equal amount of air from the room. The ordinary 
means of removal is the vertical vent-duct, rising to the top of the build- 



HEATING AND VENTILATION. 



683 



ing. bometimes reliance for the production of the current in this vent- 
duct IS placed solely on the difference of temperature of the air in the 
room and that of the external atmosphere; sometimes a steam coil is 
placed witliin the flue near its bottom to heat the air within the duct • 
sometimes steam pipes (risers and returns) run up the duct performing 
the same functions or steam jets within the flue, or exhaust fans, driven 
by steam or electric power, act directly as exhausters; sometimes the 
heating of the air in the flue is accomphshed by gas-jets. 

The draft of such a duct is caused by the difference of weight of the 
heated air in the duct, and of a column of equal height and cross-sectional 
area of the external air. 

Let d = density, or weight in pounds, of a cubic foot of the external air. 

Let di = density, or weight in pounds, of a cubic foot of the heated air 
within the duct. 

Let h = vertical height, in feet, of the vent-duct. 

h{d - c?i)=the pressure, in pounds per square foot, with which the 
air is forced into and out of the vent-duct. 

This pressure expressed in height of a column of air of density within 
the vent-duct is h id — di)-^d. 

Or, if t = absolute temperature of external air, and ti = absolute tem- 
perature of the air in the vent-duct, then the pressure = /i (ti — t) -^ t. 

The theoretical velocity, in feet per second, with which the air would 
travel through the vent-duct under this pressure is 



v=y 



2gh{h-t) 



8.02 



^'- 



ih-t) 



t ^'"^ V t 

The actual velocity will be considerably less than this, on account of loss 
due tc friction. This friction will vary with the form and cross-sectional 
area of the vent-duct and its connections, and with the degree of smooth- 
ness of its interior surface. On this account, as well as to prevent leakage 
of air through cre\aces in the wall, tin lining of vent-flues is desirable. 

The loss by friction maybe estimated at approximately 50%, and the 
actual velocity of the air as it flows through the vent-duct is 

v = -y 2^^ — ^ — , or, approximately, v=A.\l h \ ^ • 

If y = velocity of air in vent-duct, in feet per minute, and the external 
air be at 32° Fahr., since the absolute temperature on Fahrenheit scale 
equals thermometric temperature plus 459.4, 



7 = 240 



^^% 



-0. 



491.4 



from which has been computed the following table: 

Quantity of Air, in Cubic Feet, Discharged per Minute through a 
Ventilating Duct, of which the Cross-sectional Area is One 
Square Foot (the External Temperature of Air being 33° Fahr.). 



Height of 
Vent-duct in 


Excess of Temperature of Air in Vent-duct above 
that of External Air. 


feet. 


5° 


10° 


15° 


20° 


25° 


30° 


50° 


100° 


150° 


10 


77 
94 
108 
121 
133 
143 
153 
162 
171 


108 
133 
153 
171 

188 
203 
217 
230 
242 


133 
162 

188 
210 
230 
248 
265 
282 
297 


153 
188 
217 
242 
265 
286 
306 
325 
342 


171 
210 
242 
271 
297 
320 
342 
363 
383 


188 
230 
265 
297 
325 
351 
375 
398 
419 


242 
297 
342 
383 
419 
453 
484 
514 
541 


342 
419 
484 
541 
593 
640 
683 
723 
760 


419 


15 


514 


20 


593 


25 


663 


30 


726 


35 


784 


40 


838 


45 


889 


50 


937 







684 HEATING AND VENTILATION. 



Multiplying the figures in preceding table by 60 gives the cubic feet 
of air discharged per hour per square foot of cross-section of vent-duct. 
Knowing the cross-sectional area of vent-ducts we can find the total dis- 
charge; or for a desired air-removal, we can proportion the cross-sectional 
area of vent-ducts required. 

Heating and Ventilating of Large Buildings. (A. R. Wolff, Jour, 
Frank. I?2st., 1893.) — The transmission of heat from the interior to the 
exterior of a room or building, through the walls, ceilings, windows, etc., 
is calculated as follows: 

S = amount of transmitting surface in square feet; 
t = temperature F. inside, to = temperature outside; 

K = a coefficient representing, for various materials composing build- 
ings, the loss by transmission per square foot of surface in British 
thermal units per hour, for each degree of difference of tempera- 
ture on the two sides of the material; 

Q = Xotal heat transmission = SK {t— to). 

This quantity of heat is also the amount that must be conveyed to the 
room in order to make good the loss by transmission, but it does not 
cover the additional heat to be conveyed on account of the change of 
air for purposes of ventilation. (See Wolff's coefficients below, page 
688.) 

These coefficients are to be increased respectively as follows: 10% when 
the exposure is a northerly one, and winds are to be counted on as impor- 
tant factors; 10% w^hen the building is heated during the daytime only, 
and the location of the building is not an exposed one: 30% when the 
building is heated during the daytime only, and the location of the build- 
ing is exposed; 50% w^hen the building is heated during the winter months 
intermittently, with long intervals (say days or weeks) of non-heating. 

The value of the radiating-surface is about as follows: Ordinary bronzed 

cast-iron radiating-surfaces, in American radiators (of Bundy or similar 

type), located in rooms, give out about 250 heat-units per hour for each 

. square foot of surface, with ordinary steam-pressure, say 3 to 5 lbs, per 

sq. in., and about 0.6 this amount with ordinary hot-w^ater heating. 

Non-painted radiating-surfaces, of the ordinary "indirect" type 
(Climax or pin surfaces), give out about 400 heat-units per hour for each 
square foot of heating-surface, with ordinary steam-pressure, say 3 to 
5 lbs. per sq. in.; and about 0.6 this amount with ordinary hot-water 
heating. 

A person gives out about 400 heat-units per hour; an ordinary gas- 
burner, about 4800 heat-units per hour; an incandescent electric (16 
candle-power) light, about 200 heat-units per hour. 

The following example is given by Mr. Wolff to show the application of 
the formula and coefficients: 

Lecture-room 40 X 60 ft., 20 ft. high, 48,000 cubic feet, to be heated 
to 69° F.; exposures as follows: North wall, 60 X 20 ft., with four windows, 
each 14X8 feet, outside temperature 0° F. Room beyond w^est wall and 
room overhead heated to 69°, except a double skyUght in ceiling, 14 X 24 
ft., exposed to the outside temperature of 0°. Store-room beyond east 
wall at 36°. Door 6X12 ft. in wall. Corridor beyond south wall heated 
to 59°. Two doors, 6 X 12, in wall. Cellar below, temperature 36°. 

If we assume that the lecture-room must be heated to 69° F. in the 
daytime when unoccupied, so as to be at this temperature when first 
persons arrive, there will be required, ventilation not being considered, 
and bronzed direct low-pressure steam-radiators being the heating media, 
about 113,550 -^ 250 = 455 sq. ft. of radiating-surface. 

If we assume that there are 160 persons in the lecture-room, and we 
provide 2500 cubic feet of fresh air per person per hour, we will supply 
160 X 2500 = 400,000 cubic feet of air per hour (i.e., over eight changes 
of contents of room per hour). 

To heat this air from 0° F. to 69° F. will require 400,000 X 0.01785 X 
69 = 492 660 thermal units per hour (0.01785 being the product of the 
weight of a cubic foot, 0.075, by the specific heat of air, 0.238). Accord- 
ingly there must be provided 492,660 -^ 400 = 1232 sq. ft. of indirect 



HEATING AND VENTILATION. 



685 



surface, to heat the air required for ventilation, in zero weather. If the 
room were to be warmed entirely indirectly, that is, by the air supphed 
to room (including the heat to be conveyed to cover loss by transmission 
through walls, etc.), there would have to be conveyed to the fresh-air 
suppljr 492,660 + 118,443 = 611,103 heat-units. Tliis would imply the 
provision of an amount of indirect heating-surface of the "Climax" type 
of 611,103 -9- 400 = 1527 sq. ft., and the fresh air entering the room 
would have to b3 at a temperature of about 86° F., viz., 

aqo _| ^ 118.413 69 _|_ 17 = S6° F. 

^^ ^ 400,000 X 0.01785' ^ ^'^ ^ ^' 
The above calculations do not, however, take into account that 160 
persons in the lecture-room give out 160 X 400 = 64,000 thermal units 
per hour; and that, say, 50 electric lights give out 50 X 200 = 10,000 
thermal units per hour; or, say, 50 gaslights, 50 X 4800 = 240,000 
thermal units per hour. The presence of 160 people and the gaslighting 
would diminish considerably the amount of heat required. If the 50 
gaslights give out 240,000 thermal units per hour, the air supplied for 
ventilation must enter considerably below 69° Fahr., or the room will be 
heated to an unbearably high temperature. If 400,000 cubic feet of fresh 
air per hour are supplied, and 240,000 thermal units per hour generated 
by the gas must be abstracted, it means that the air must, under these 

conditions, enter 4Q0 qoq^x 0^01735 = ^^^^* ^^° ^^^^ ^^^^ ^^°' ^^ ^* 
about 52° Fahr. Recent researches show that the increase of CO2 in 
air due to gas lighting is not detrimental to health. 

The following table shows the calculation of heat transmission (some 
figures changed from the original) : 





Kind of Transmitting 
Surface. 




Calculation 
of Area of 
Transmit- 
ting Sur- 
face. 


m 


3 


1-2 


f)^^ 


Outside wall 


36^' 
36'' 
24" 
36" 


63x22-448 

4x 8x 14 
42x22- 72 

6x12 
45x22- 72 

6x12 
17x22- 72 

6x12 

32x42-336 
14x24 


938 
448 
852 

72 
918 

72 
302 

72 

1,008 

336 


10 

83 
4 

19 
2 
5 
1 
5 

10 

35 


9,380 


6Q 


Four windows (single) . . • 


37,186 


33 


Inside wall (store-room) 


3,408 


33 


Door 


1,368 


10 


Inside wall (corridor^. 


1,836 


10 


Door ... 


360 


10 


Inside wall (corridor) 


302 


10 


Door 


360 


69 


Roof 


10,080 


6<) 


Double skylight 


11,760 


33 


Floor 

Supplementary allowance, north c 
Supplementary allowance, north c 

Exposed location and intermitteni 
Total thermal units 


mtside 
)utsid£ 


62x42 


2,604 


4 


10,416 




5 wall, 10%.. 


86,454 
938 




s •windows. 1C 


)% 


3,718 




i day or night use, . 


50% 






91,110 
27,333 












118 443 











Comfortable Temperatures and Humidities. — A. G. Woodman and 
J. F. Norton, in a work on Air, Water, and Food (1914), give, on the 
authority of Hill's Recent Advances in Physiology and Biochemistry, 
a "curve of comfort," practically a straight Une, which runs from 20% 
relative humidity at 87° F. to 75% at 55° F. It approximates 40, 50 
and 60% respectively at 75°, 70° and 65° F, showing that to secure 
comfort as temperature rises, the humidity must be decreased. The 
most comfortable conditions for indoor workers are given at 40% 
humidity at 68° and 60%. at 64° F. 

Carbon Dioxide Allowable in Factories. — Haldane and Osborne 
(London, 1902) recommend that the CO2 in the air at the breathing 



686 HEATING AND VENTILATION. 

line in factories, and away from the immediate influence of special 
sources of contamination, such as persons or gas Ughts, should not 
rise dm-ing daylight, or after dark when electric lights only are used, 
beyond 12 volumes in 10,000 of air, and when gas or oil is used for 
lighting not over 20 volumes after dark. 

A pamphlet issued by the National Commercial Gas Association 
(1914) states that the use of gas for interior hghting does not affect the 
atmosphere of interiors deleteriously. 

Heat Produced by Human Beings. — According to Landry and 
Roseman, the average man produces every 24 hours per kilogram of 
body 32 to 38 calories when at rest, 35 to 45 when in easy action, and 
50 to 70 when at hard work. Translating this into British thermal 
units per hour, and taking the weight of an average man at 140 lb., 
these figures are equivalent, approximately, to a man giving off 336 to 
400 B. T. U. per hour when at rest, 368 to 473 when in easy action, 
and 525 to 735 when at hard work. 

Atwater and Rosa, average of 13 experiments, found that a man gave 
off 2200 cal. per 24 hours at rest and 3400 at work, equivalent to 364 
and 562 B. T. U. per hour, respectively. 

Standards of Ventilation. — (C-E.A. Winslow, N. Y. State Com- 
mission on Ventilation, Science, April 30, 1915.) Pettenlioffer in 1863 
showed that CO2 in itself is without effect in the highest concentrations 
which it ever attains in occupied rooms. During the last fifteen years 
the researches of Fliigge, Haldane, Hill, Benedict and others indicate 
that the effects experienced in a badly ventilated room are due to the 
heat and moisture produced by the bodies of the occupants rather than 
to CO2 or other substances from the breath. Subjects immiu-ed in 
close chambers are not at all relieved by breathing pure outdoor air 
through a tube, but are relieved completely by keeping the chamber 
artificially cool, and to a considerable extent by the mere circulating of 
the air by an electric fan. 

The experiments of the N. Y. State Commission show that the work- 
ing of the circulatory and heat regulating machinery of the body was 
markedly influenced by a slight increase in room temperature, as from 
68° to 75° with 50% relative humidity in both cases. Psychological 
tests failed to show that 86° and 80% relative humidity had any effect 
on the power to do mental work, but with physical work (lifting 
dumb bells and riding a stationary bicycle), when the subjects had 
a choice they accomplished 15% less work at 75°, and 37% less at 
86°, than they did at 68°. As to the effect of stagnant breathed air 
contaminated so as to show from 20 to 60 parts CO2 per 10,000, the re- 
sults are entirely negative so far as mental and physical tests are con- 
cerned. 

In practice, an un ventilated room is an overheated room. Ventila- 
tion is just as essential to remove the heat produced by hiunan bodies as 
it was once thought to be to remove the CO2 produced by the lungs. 
The quantitative standards of air change estabUshed on the old chemical 
basis serve very well in the new, or heat change, basis. An average 
adult producing 400 B.T.U. per hour will require 2000 cubic feet of 
air per hour at 60° to prevent the temperature rising above 70°. An 
ordinary gas burner produces 300 B.T.U. per candle-power hour, and 
requires 1500 cubic feet of air per hour per candle power. In crowded 
auditoria every bit of the 2000 cubic feet of air per hour per person is 
needed, and in many industrial processes, where the heat from hiunan 
beings is reinforced by friction and other sources, even more wiU be 
required. 

Recent research has on the whole strengthened the arguments for 
ventilation. The thermometer is the first essential; a rise above 70° 
must be recognized as a sign of discomfort, of decreased efficiency and 
lowered vitality. The standard of 30 cubic feet of air per minute per 
capita remains as the amount necessary to supply if an occupied room 
is to be kept cool and fresh. 

The question of humidity remains to be solved. A lack of humidity 
makes hot air feel cooler and cold air feel warmer. Extreme dryness, 
at high or moderate temperatures, is believed by many to be in itself 
harmful, but t here is no solid experimental evidence on this point. 

Air Washing. — (D. D. Kimball, N. Y. State Commission on Ventila- 
tion, Science, April 30. 1915.) An air washer consists of a sheet-metal 



HEATING AND VENTILATING PROBLEMS. 



687 



chamber in which the air is passed through a heavy mist and then 
through baffles or ehminator plates by whicli the entrained moisture is 
removed. The base of tiie washer is a tank into which the spray falls 
and from wliich it is drawn by a centrifugal pump. The piunp forces 
the water through spray nozzles in the spray chamber of the washer. 
Manufacturers customarily guarantee the removal of 98 % of the dust 
in the air. Practically all the larger particles are removed, but there is 
always a residue of fine dust which no washer will remove. When there 
is very little dust in the air, as after a heavy rain, the -percentage of the 
remaining dust that can be removed is quite small. M. C. Whipple's 
tests showed that the dust removed varied from 64 % to 7 %. 

The best results in artificial humidification have been obtained by 
means of the air washer. The degree of humidification is controlled by 
thermostatic devices. The air washer may also be used for air cooling. 
The evaporation in the spray chamber will lower the temperatm-e to 
the extent of 75% or more of the difference between the wet and dry 
bulb temperatures, equivalent to a temperature reduction often 
amounting to 10 to 15 degrees. Unfortunately cooling by means of an 
air washer is expensive. Roughly, the cost of cooling 10 degrees equals 
the cost of heating 70 degrees. 

Contamination of Air. — The following data are found in "The Air 
and Ventilation of Subways," by G. A. Soper (1908). 

Carbon dioxide in air in streets of European cities, 3.01 to 5.02 parts 
in 10,000. Center of Paris annual average varied from 3.06 to 3.44 
parts. Average of 309 analyses in New York, 3.67 parts. 

An average adult inhales about 396 cubic inches per minute. Analysis 
of inspired air: O, 20.81; N, 79.15; CO2, 0.04. Expired air: O, 16.00; 
N, 79.59; CO2, 4.38. Air highly charged with CO2 is not dangerous to 
breathe for a considerable time. CO2 must be present to 40 times the 
amoimt present when the room begins to smell "stuffy" before it in- 
creases the rate of breathing. Neither does a decrease of 2 or 3 per cent 
in the oxygen produce any immediate effect. Long before the air be- 
comes so vitiated as this other impurities from the lungs make the air 
extremely unpleasant. 

The CO2 in badly vitiated places seldom rises above 50 parts in 
10,000. 

The air becomes uncomfortably close and musty when CO2 exceeds 
8 parts in 10,000. 

Amount of CO2 exhaled by a man, average per hour: at rest, 16.11 
grams, or 8198 cu. cm.; at work, 30.71 grams, or 15,628 cu. cm. 

STAJVDAKD VALUES FOR USE IN CALCUXATION OF HEATING 
AND VENTILATING PROBLEMS. 

Heating Value of CoaL 



Volatile 
Matter in 
the Com- 
bustible, 
Per Cent. 



Heating Value 

per lb. 

Combustible, 

B.T.U. 



Aver- 
age. 



Moisture, 

in 
Air-dried 

Coal, 
Per Cent. 



Ash in 
Air-dried 

Coal, 
Per Cent. 



Anthracite 

Semi-anthracite . . 
Semi-bituminous . 

Bit. eastern 

Bit western 

Lignite 



3 to 7.5 
7.5 to 12.5 
12.5 to 25 
25 to 40 
35 to 50 
Over 50 



14.700 to 14,900 
14,900 to 15,500 
15.500 to 16.000 
14,800 to 15.000 
13.500 to 14,800 
11.000 to 13,500 



14.800 
15.200 
15.750 
15.150 
14,150 
12.250 



0.5 to 1.0 

0.5 to 1.0 

0.5 to 1.0 

1. to 4. 

4. to 14. 

10. to 18. 



10. to 18. 
10. to 18. 

5. to 10. 

5. to 15. 
10. to 25. 

5. to 25. 



Average Heating Value of Air- Dried Coat.— Antliracite, 12,600; semi- 
anthracite, 12,950; semi-bituminous, 14,450; bituminous eastern, 13,250; 
bituminous western, 10,400; lignite, 9,700. 

Eastern bituminous coal is that of the Appalachian coal field extending 
from Pennsylvania and Oliio to Alabama. Western bituminous coal 
is that of the great coal fields west of Oliio. 

Steam Boiler Efficiency. — The maximum efficiency obtainable \\ith 
anthracite in low-pressure steam boilers, water heaters or hot-air furnaces 
is about 80 per cent, when the thickness of the coal bed and the draft 
are such as to cause enough air to be supplied to effect complete combus- 
tion of the carbon to CO2. With coals high in volatile matter the max- 



688 



HEATING AND VENTILATION. 



imum eflaciency is probably not over 70 per cent. Very much lower 
eflflciencies than these figures are ob tamed when the air supply is either 
deficient or greatly in excess, or when the furnace is not adapted to burn 
the volatile matter in the coal. D. T. Randall, in tests made in 190S 
for the U. S. Geological Survey, with house-heating boilers, obtained 
efficiencies ranging from 0.62 with coke, 0.61 with anthracite, and 0.58 
with semi-bituminous, down to 0.39 with Ilhnois coal. 

Available Heating Value of the Coal. — Using the figures given above as 
the average heating value of coal stored in a dry cellar, the following are 
the probable maximum values in B. T.U., of the heat available for fur- 
nishing steam or heating water or air, for the several efficiencies stated : 



Anthracite. 


Semi-An. 


Semi-Bit. 


Bit. East. 


Bit. West. 


Lignite. 


Eff'y 0.80 

B.T.U... 10.080 


0.77 
9.933 


0.75 
10.837 


0.70 
9.275 


0.65 
6,760 


0.60 
5,820 



For average values in practice, about 10 per cent may be deducted from 
these figures. (It is possible that an efficiency higher than 80% mav be 
obtained with anthracite in some forms of air-heating furnaces in which 
the escaping chimney gases are cooled, by contact with the cold air inlet 
pipes, to comparatively low temperatures.) 

The value 10,000 B.T.U. is usually taken as the figure to be used in 
calculation for design of heating and ventilating apparatus. For coals 
v^ith lower available heating values proper reductions must be made. 

Heat Transmission through Walls, Windows, etc., in B.T.U. per 
Sq. Ft. per Hour per Degree of Difference of Temperature. 



Wolff. 
B.T.U. 



Hauss. I 
B.T.U.) 



Wolff. Hauss. 
B.T.U. B.T.U. 



Glass Surfaces. 

Vault light 

Single window 

Double window 

Single skylight 

Double skylight 



1.42 
1.20 
0.56 
1.03 
0.50 



Doors. 

Door 

I-in. pine 

2-in. pine 



0.40 
0.28 



Partitions. 

Solid plaster, 

13/4 to 2 1/4 in. 

21/2 to 3 1/4 in. 

Fireproof 

2-in. pine board.. . 



0.30 
0.28 



1.00 
0.46 
1.06 

0.48 



0.40 



0.60 
0.48 



Floors. 

Joists with double 
floor 

Concrete floor 

Fireproof construc- 
tion, planked over. 

Wooden beam con- 
struction, planked 
over 

Concrete floor 
brick arch 

Stone floor on arches 

Planks laid on earth 

Planks laid on as- 
phalt 

Arch with air space . . 

Stones laid on earth. 



Ceilings. 
Joists with single 

floor ^ 

Arches with air_"space 



0.10 
0.31 



124 



0.083 



0.07 



0.22 
0.20 
0.16 

0.20 
0.09 
0.08 



0.10 
CM 



Brick Walls. 



Thickness , 
In. 



Wolff. 



Hauss. 



Average . 
B.T.U 



Thickness, 
In. 



Wolff. 



Hauss. 



Average, 
B.T.U.* 



4 

43/4 

8 
10 
12 
15 
16 
20 
24 



0.66 






0.48 


0.45 






0.34 


0.33 






0.26 


0.27 




0.23 


0.22 


0.20 





0.537 
0.508 
0.397 
0.351 
0.313 
0.272 
0.260 
0.222 
0.194 



25 
28 
30 
32 
35 
36 
40 
45 





0.18 


0.18 






0.16 


0.16 






0.13 


0.145 




0.13 


0.12 




0.11 



0.188 
0.172 
0.163 
0.154 
0.143 
0.140 
0.128 
0.116 



*The average figure for brick walls was obtained by plotting the 
reciprocals of Wolff's and Hauss's figures and drawing a straight line 



RESIDENCE HEATING. 



689 



l 



Solid Sandstone Walls. (Hauss.) 

Thickness, in. . . 12 16 20 24 28 32 36 40 44 48 

B.T.U 0.45 0.39 0.35 0.32 0.29 0.26 0.24 0.22 0.20 0.19 

For limestone walls, add 10 per cent. 

Allowances for Exposures. — Wolff adds 25% for north and west ex- 
posures, 15% for east, and 5% for south exposures, also 10% additional 
for reheating, and 10% to the transmission through hoor and ceilings. 
The allowance for reheating Mr. Wolff explains as foUows in a letter to 
the author, Mar. 10, 1905. The allowance is made on the basis that the 
apparatus will not be run continuously ; in other words, that it will not be 
run at all, or only lightly, overnight. The rooms will cool off below the 
required temperature of 70°, and to be able to heat up quickly in the 
morning an allowance of 10% is made to the transmission figures to meet 
tliis condition. Hauss makes aUowances as follows: 5% for rooms with 
unusual exposure; 10% where exposures are north, east, northeast, 
northwest and west; 3V3% where the height of ceiling is more than 13 ft.; 
62/3% where it is more than 15 ft.; 10% where it is more than 18 ft. For 
rooms heated daily, but where heating is interrupted at night, add 

A = 0.0025 [(N - 1) TFi] -^ Z. 
For rooms not heated daily, add B = [0.1 TF (8 - Z)] -*- Z. 
In these formulas TFi = B.T.U. transmitted per hour by exposed sup- 
faces; W = total B.T.U. necessary, including that for ventilation or 
changes of air; A'" = time from cessation of heating to time of starting 
fire again, hours; Z = time necessary after fire is started until required 
room temperature is reached, hours. 

Allowance for Exposure and for Leakage. — In calculations of the 
quantity of heat required by ordinary residences, the formula total heat 

/W nC\ 

=s (Ti— To) {^+ G+ -^j is commonly used. Ti = temp, of room, 

To — outside temp., W = exposed wall surface less mndow surface, 
G = glass surface, C = cubic contents of room, n = number of changes 
of air per hour. The factor n is usually assumed arbitrarily or guessed 
at; some writers take its value at 1, others 1 for the rooms, 2 for the halls, 
etc.; others object to the use of C as a factor, saying that the allowance for 
exposure and leakage should be made proportional to the exposed wall 
and glass surface since it is on these surfaces that the leakage occurs, 
and omitting the term nC/56 they multiply the remainder of the ex- 
pression by a factor for exposure, c = 1.1 to 1.3, depending on the direc- 
tion of the exposure. To show what different results may be obtained 
by the use of the two methods, the following table is calculated, apply- 
ing both to six rooms of widely differing sizes. Two sides of each room» 
north and east, are exposed. T^i = 70; To = 0; G = 1/5 (If + (?). 













S 


G 












^ 


Total Wall, 


^^ 


+ 


+ 









f, 


Size, ft. 


6 



(W + G) 









10 


6 


ti5 

CO 

6 






11 



sq. ft. 





it 



g 


A 


10x10x10 


1,000 


20x10= 200 


40 


5 


5,600 


1,250 


1,120 


1,680 


B 


10x20x10 


2,000 


30x10= 300 


60 


62/3 


8,400 


2,500 


1,680 


2,525 


C 


20x20x12 


4,800 


40x12= 480 


96 


10 


13,440 


6,000 


2,688 


4,032 


D 


20x40x14 


11,200 


60x14= 840 


168 


171/3 


23,520 


14.000 


4,704 


7,036 


E 


40 X 40 X 1 3 


24.000 


80x15=1200 


240 


20 


33.600 


30.000 


6,720 


10.080 


1^' 


40x80x16 


51,200 


120x16=1920 


384 


262/3 


54.460 


64.000 


10,892 


16.33d 



The figures in the column headed H = 70 (TF/4 + G) represent the 
heat transmitted through the waUs. those in the column 70 Cy56 are the 

between them, representing the average heat resistances, and then taking 
the reciprocals of the resistances for different thicknesses. The resist- 
ance corresponds to the straight hne formula R = 0.12 -I- 0.165 t, where 
t = thickness in inches. (Hauss's figures are from a paper by Chas. 
F. Hauss, of Antwerp, Belgium, in Trans. A, S, H, V, E., 1904.) 



690 HEATING AND VENTILATION. 

heat required for one change of air per hour ; 0.2 H is the heat correspond- 
ing 10 an allowance ot 20% tor exposure and leakage, and 0.3 H corre- 
sponds to an allowance of 30%. For the small rooms A and B the 
difference between 70 C/56 and 0.2 H or 0.3 H is not of great importance, 
but it becomes very important in the largest rooms; in room F the differ- 
ence between 70 CV56 and 0.2 H is nearly equal to the total heat trans- 
mitted through the walls, indicating that the use of the cubic contents 
as a factor in calculations of large rooms is likely to lead to great errors. 
This is due to the fact that the ratio C -^ {W + G) varies greatly with 
different sizes of rooms. 

With forced ventilation, the quantity of heat needed depends chiefly 
upon the number of persons to be provided for. Assuming 2000 cu. ft. 
per hour per person, heated from 0° to 70°, and 1, 2 and 4 persons per 
100 sq. ft. of floor surface, the heat required for the air is as follows: 
Room A B C D E F 

1 person per 100 sq. ft. 2,500 5,000 10,000 20,000 40,000 80.000 

2 persons per 100 sq. ft. 
4 persons per 100 sq. ft. 
Ratio of last line to H. . 

Heating by Hot-air Furnaces. — A simple formula for calculating the 
total heat in British Thermal Units required for heating and ventilating 

by any system is 77=0^^+ -~\ + -^ ( Ti — To) . (See notation above.) 

The formula is derived as follows: The heat transmitted through 1 sq. ft. 
of single glass window is approximately 1 B.T.U. per hour per degree of 
difference of temperature, and that through 1 sq. ft. of 16-in. brick wall 
about 0.25 B.T.U. (For more accurate calculations figures taken from 
the tables (p. 688) should be used.) The specific heat of air is taken at 
0.238, and the w^eight of 1 cu. ft. air at 70° F. at 0.075 lb. per cu. ft. 
The product of these figures is 0.01785, and its reciprocal is 56. 

For a difference Ti - Tq = 70°, 0.01785 X 70 == 1.2495, we may, 
therefore, write the formula 



5,000 10,000 


20,000 40,000 


80,000 160,000 


10,000 20,000 


40,000 80,000 


160,000 320,000 


1.8 2.4 


3.0 3.4 


4.8 5.9 



Total heat = 70 [c(g + ^)] + 1.25 A 



heat conducted through walls 4- heat exhausted in 
ventilation. 

A is the cubic feet of air (measured at 70°) supplied to and exhausted 
from the building. This formula neglects the heat conducted through 
the roof, for which a proper addition should be made. 

There are two methods of heating by hot-air furnaces; one in which 
all the air for both heating and ventilation is taken from outdoors and 
exhausted from the building, and the other in wiiich only the air for 
ventilation is taken from outdoors, and additional air is recirculated 
through the furnace from the building itself. The first method is an 
exceedingly wasteful one in cold weather. By the second it is possible 
to heat a building with no greater expenditure of fuel than is required 
for steam or hot-water heating. 

Example. — Required the amount of heat and the quantity of air to be 
circulated by the two methods named for a building wliich has G = 400, 
W == 2000, C = 16,000, n = 2, Ti = 70°, To = 0°, T2, the temperature 
at which the air leaves the furnace, being taken for three cases as 100°, 
120°, and 140°. Assume c, the coefficient for exposure, including heat 
lost through roof, = 1.2. When only enough air for ventilation is taken 
into and exhausted from the building, the formula gives 
70 X 1.2 (500 + 400) +1.25 X 32,000 = 115,600 B.T.U. = 75,600 for 
heat + 40,000 for ventilation. 

Suppose all the air required for heating is taken from outdoors at 0° F., 
and all exhausted at 70°, the quantity. A, then, instead of being 32,000 
cu. ft., has to be calculated as follows: 

Total heat = c (^ + ^) (^1- Tq) + A X 0.01785 X {Ti - To) 

= 0.01785^ {T2 - To), 
Heat supplied by furnace = heat for conduction 4- heat for ventilation 



CARRYING CAPACITY OF AIR PIPES. 



691 



from which we find A= c (g+^) (^i - To) -^ 0.01785 (T2 - Ti) 
= 75,600 -H 0.01785 {T2 - 70°). 

For the value of ^2 ^2 = 100 7^2 = 120 Ts = 140 

A = cu. ft 141,117 84,706 60,504 

Heat lost by exhausting this air at 70° . . . 176,396 105,882 75,630 

Adding 75,600 loss by walls gives total . . . 251,996 181,482 152,230 
Excess above 115,600 actually required 

for heating and ventilating, % 118.0 57.0 31.7 

British Thermal Units Absorbed in Heating 1 Cu. Ft. of Air, or given 

up in cooling it. — (The air is measured at 70° F.) 

Ti - T2 ^ 
10° 20 30 40 50 56 60 70 80 90 100 110 120 126 130 140 
0.18 0.36 0.54 0.71 0.89 1. 1.07 1.25 1.43 1.61 1.78 1.96 2.14 2.25 2.32 2.5 



Area in Square Inches of Pipe required to Deliver 100 Cu. Ft. of 
Air per Minute, at Different Velocities. — The air is measured at the 
temperature of the air in the pipe. 

Velocity per second 2 

Area, sq. in 120 



3 


4 


5 


6 


7 


8 


9 10 


80 


60 


48 


40 


34.3 


30 


26.7 24 



The quantity of air required for ventilation or heating should be 
figured at a standard temperature, say 70° F., but when warmer air is 
to be delivered into the room through pipes, the area of the pipes should 
be calculated on the basis of the temperature of the warm air, and not on 
that of the room. 

Example. — A room requires to be supplied v/ith 1000 cu. ft. per min. 
at 70° F. for ventilation, but the air is also used for heating and is dehvered 
into the room at 120° F. Required, the area of the deUvery pipe, if the 
velocity of the heated ail In the pipe is 6 ft. per second. 

From the table of volumes, given on the next pasre, 1000 cu. ft. at "70** 
= 1094 cu. ft. at 120°. From the above table of areas, at 6 ft. velocity 
40 sq. in. area is required for 100 cu. ft., therefore 1094 cu. ft. will require 
10.94 X 40 = 437.6 sq. in. or about 3 sq. ft. 

Carrying Capacity of Air Pipes. 





Area in 
Sq. In. 


Area, 
Sq. Ft. 


Velocity, Feet per Second. 


Diam. 


3 


4 1 5 


6 


7 


8 






Cu. Ft. 


per Min. 






5 


19.63 


.1364 


24.6 


32.7 


40.9 


49.1 


57.3 


65.5 


6 


28.27 


.1963 


35.3 


47.1 


58.9 


70.7 


82.4 


94.2 


7 


38.48 


.2673 


48.1 


64.2 


80.2 


96.2 


112. 


128. 


8 


50.27 


.3491 


62.8 


83.8 


105. 


126. 


147. 


168. 


9 


63.62 


.4418 


80.0 


106. 


133. 


159. 


186. 


212. 


10 


78.54 


.5454 


98.2 


131. 


164. 


196. 


229. 


262. 


11 


95.03 


.6600 


119. 


158. 


198. 


238. 


277. 


317. 


12 


113.1 


.7854 


141. 


188. 


236. 


283. 


330. 


377. 


13 


132.7 


.9218 


166. 


221. 


277. 


332. 


387. 


442. 


14 


153.9 


1.069 


192. 


257. 


321. 


385. 


449. 


513. 


15 


176.7 


1.227 


221. 


294. 


368. 


442. 


515. 


589. 


11.3 


100. 


0.694 


125. 


167. 


208. 


250. 


292. 


333. 


13.6 


144. 


1. 


180. 


240. 


300. 


360. 


420. 


480. 



The figures in the table give the carrying capacity of pipes in cu. ft. 
of air at the temperature of the air flowing in the pipes. To reduce the 
figures to cu. ft. at a standard temperature (such as 70° F.) divide by 
the ratio of the volume per cu. ft. of the air in the pipe to that of the air 
of the standard temperature, as in the following table: 



692 



HEATING AND VENTILATION. 



Volume of Air at Different Temperatures. 

(Atmospheric pressure.) 



Fahr. 


Cu. Ft. 


Deg. 


in 1 lb. 





11.583 


32 


12.387 


40 


12.586 


50 


12.840 


62 


13.141 


70 


13.342 


80 


13.593 



Compar- 


Fahr. 


Cu. Ft. 


ative 
Volume. 


Deg. 


in 1 lb. 


0.867 


90 


13.845 


0.928 


100 


14.096 


0.943 


110 


14.346 


0.962 


120 


14.596 


0.985 


130 


14.848 


1.000 


140 


15.100 


1.019 


150 


15.351 



Compar- 
ative 
Volume. 



1.038 
1.056 
1.075 
1.094 
1.113 
1.132 
1.151 



Fahr. 


Cu. Ft. 


Deg. 


in 1 lb. 


160 


15.603 


170 


15.854 


180 


16.106 


190 


16.357 


200 


16.608 


210 


16.860 


212 


16.910 



Compar- 
ative 
Volume 



1.169 
1.188 
1.207 
1.226 
1.245 
1.264 
1.267 



Sizes of Air Pipes Used in Furnace Heating. (W. G. Snow, Eng. 
News, April 12, 1900.) 











Length of Room, Ft. 










W'th. 

of 
Room 

Ft. 


10 


12 


14 


16 


18 


20 


22 


24 


26 


28 


30 


Diameter of Pipe, Ins. 


8.... 


8,7 
8,7 


8,7 
9,8 
9,8 


9,8 
9,8 
10, 8 
10,8 


9,8 
10. 8 

10, 8 
10,9 

11, 9 
















10 . 


10, 8 

10, 9 

11, 9 

11, 9 

12, 10 


10, 9 

11, 9 

11, 9 

12, 10 

12, 10 

13, 11 












12.... 


11, 9 

12, 10 

12, 10 

13, 11 
\3, 11 


12, 10 

12, 10 

13, 10 
13, 11 
13, 11 








14 




13, 10 
13, 10 

13, 11 

14, 12 


13, 10 

13, 11 

14, 12 
14, 12 




16.... 






13, 11 


18.... 








14, 12 


20.... 










14, 12 

















The first figure in each column shows the size of pipe for the first floor 
and the second figure the size for the second floor. Temperature at regis- 
ter, 140°; room, 70°; outside, 0°. Rooms 8 to 16 ft. in width assumed to 
be 9 ft. high; 18 to 20 ft. width, 10 ft. high. When first-floor pipes are 
longer than 15 ft. use one size larger than that stated. For third floor, 
use one size smaller than for second floor. For rooms witli three expo- 
sures, increase the area of pipe in proportion to the exposure. 

The table was calculated on the following basis: 

The loss of heat is calculated by first reducing the total exposure to 
equivalent glass surface. This is done by adding to the actual glass 
surface one-quarter the area of exposed wood and plaster or brick walls 
and V20 the area of floor or ceiling. Ten per cent is added where the 
exposure is severe. The window area assumed is 20% of the entire ex- 
posure of the room. 

Multiply the equivalent of glass surface by 85. The product will be 
the total loss of heat by transmission per hour. 

Assuming the temperature of the entering air to be 140° and that of 
the room to be 70°, the air escaping at approximately the latter tempera- 
ture will carry away one-half the heat brought in. The other half, corre- 
sponding to the drop in temperature from 140° to 70°, is lost by trans- 
mission. With outside temperature zero, each cubic foot of air at 140° 
brings into the room 2.2 heat units. Since one-half of this, or 1.1 heat 
units, can be utilized to offset the loss by transmission, to ascertain the 
volume of air per hour at 140° required to heat a given room, divide the 
loss of heat by transmission by 1.1. This result divided by 60 gives the 
number of cubic feet per minute. In calculating the table, maximum 
velocities of 280 and 400 ft. were used for pipes leading to the first and 
aecond floors respectively. The size of the smaller pipes was based on 
lower velocities, according to their size, to allow for their greater resist- 
ance ajnd loss of temperature. 



BOILERS FOR HOUSE HEATING. 



693 



Furnace-Heating with Forced Air Supply. {The Metal Worker, 
April 8, 1905.) —Tests were made of a Kelsey furnace with the air supply 
furnished by a 48-in. Sturtevant disk fan driven by a 5 H.P. electric 
motor. A connection was made from the air intake, between the fan and 
the furnace, to the ash pit so that the rate of combustion could be regu- 
lated independently of the chimney-draft condition. The furnace had 
4.91 sq. ft. of grate surface and 238 sq. ft. of heating surface. The volume 
of air was determined by anemometer readings at 24 points in a cross- 
section of a rectangular intake of 11.88 sq. ft. area. The principal 
results obtained in two tests of 8 hours each are as follows: 

Av. temp, of the cold air 

Per cent humidity of the cold air 

Av. temp, of the warm air 

Air delivered to heater, cu. ft. per hour. . . . 

B.T.U. absorbed by the dry air per hour. . . 

B.T.U. absorbed by the vapor per hour. . . . 

Avge. no. of pounds of coal burned per hour 
p B.T.U. given by the coal per hour 529,200 

Per cent efficiency of the furnace 

Grate Surface and Rate of Burning Coal. 

In steam boilers for power plants, which are constantly attended by 
firemen, coal is generally burned at between 10 and 30 lbs. per sq. ft. 
of grate per hour. In small boilers, house heaters and furnaces, which 
even in the coldest weather are supplied with fresh coal only once in 
several hours, it is necessary to burn the coal at very much slower rates. 
Taking a cubic foot of coal as weighing 60 lbs., in a bed 12 inches deep, 
and 1 sq. ft. of grate area, it v/ould be one-half burned away in 71/2 hours 
at a rate of burning of 4 lbs. per sq. ft. of grate per hour. This figure, 
4 lbs., is commonly taken in designing grate surface for house-heating 
boilers and furnaces. Using this figure we have the following as the 
rated capacity of different areas of grate surface. 



39° 


58° 


71 


56 


135° 


152° 


250,896 


249,195 


451,872 


421,496 


2,016 


3,102 


36 


33.5 


529,200 


492,450 


85.7 


86.2 



Rated Capacity of Furnaces and Boilers for House Heating. 






Coal- 
burning 
Capacity 




Equiv. 


Equiv. 


Equiv. 


Diam. 




Capacity, 


lbs. 


lbs. 


cu.ft. 


of 
Round 


Area in — 


B.T.U. 

per 


Steam 
Evap. 


Air per 
Hour 


Air at 
70° 


Grate. 




per 
Hour. 


Hour. 


212° per 
Hour. 


Heated 
100°. 


Heated 
100°. 


ins. 


sq.in. 


sq.ft. 


lbs. 


(a) 


(b) 


(c) 


(d) 


12 


113.1 


785 


3.142 


31,420 


32.5 


1,320 


17,610 


14 


153.9 


1.069 


4.276 


42,760 


44.3 


1,797 


23,970 


16 


201.1 


1.396 


5.585 


55,850 


57.8 


2,347 


31,300 


18 


254.5 


1.767 


7.069 


70,690 


73.2 


2,970 


39,620 


20 


314.2 


2.182 


8.728 


87,280 


90.4 


3,667 


48,920 


22 


380.1 


2.640 


10.560 


105,600 


109.4 


4,437 


59,190 


24 


452.4 


3.142 


12.566 


125,660 


130.1 


5,280 


70,430 


26 


530.9 


3.687 


14.748 


147,480 


152.7 


6,197 


82,670 


28 


615.8 


4.276 


17.104 


171,040 


177.1 


7,187 


95,870 


30 


706.9 


4.909 


19.636 


196,360 


203.3 


8,260 


110,190 


32 


804.2 


5.585 


22.340 


223,400 


231.3 


9,387 


125,220 


34 


907.9 


6.305 


25.220 


252,200 


261.2 


10,597 


141,360 


36 


1017.9 


7.069 


28.276 


282,760 


292.8 


11,881 


158.490 



Figures in column (b) = (a) -^ 965.7. 

Figures in column (c) = (a) -h (100 X 0.238). 

Figures in column (d) = (c) X 13.34. 

Latent heat of steam at 212° = 965.7 B.T.U. [new steam tables give 
970.4]. 

Specific heat of air = 0.238. 

Note that the figures in the last three columns are all based on the rate 
of combustion of 4 lbs. of coal per sq. ft. of grate per hour, which is taken 
as the standard for house heating. For heating schoolhouses and other 
large buildings where the furnace is fed with coal more frequently a 



1 sq. ft. 


100 sq. ins. 


grate equals 


grate equals 


4 


2.775 


40,000 


27,750 


41.25 


28.61 


156.5 


108.7 



694 HEATING AND VENTILATION. 

much higher actual capacity may be obtained from the grate surface 
named. A committee of the Am. Soc. H. and V. Engrs. in 1909 says: 

The grate surface to be provided depends on the rate of combustion, 
and this in turn depends on the attendance and draft, and on the size of 
the boiler. Small boilers are usually adapted for intermittent attention 
and a slow rate of combustion. The larger the boiler, the more attention 
is given to it, and the more heating surface is provided per square foot 
of grate. The following rates of combustion are common for internally 
fired heating boilers: 

Sq. ft. of grate 4 to 8 10 to 18 20 to 30 

Lbs. coal per sq. ft. grate per hr. not over 4 6 10 

Capacity of 1 sq. ft. and of 100 sq. in. of Grate Surface, for Steam, 
Hot-water, or Furnace Heating. 

(Based on burning 4 lbs. of coal per sq. ft. of grate per hour and 10,000 
B.T.U. available heating value of 1 lb. of coal.) 

lbs. of coal per hour. 
B.T.U. per hour. 

lbs. of steam evap. from and at 212° per hr. 
sq. ft. of steam radiating surface == B.T.U. 
-^ 255.6*. 

261.4 181.5 sq. ft. of hot-water radiating surface = 

B.T.U. -^ 153 t. 
22,420. 15,570. cu. ft. of air (measured at 70° F.) per hour 

heated 100°. 
* Steam temperature 212°, room temperature 70°, radiator coefficient, 
that is the B.T.U, transmitted per sq. ft. of surface per hour per degree of 
difference of temperature, 1.8. 

t Water temperature 160°, room temperature 70°, radiator co- 
efficient 1.7. 

For any other rate of combustion than 4 lbs., multiply the figures In the 
table by that rate and divide by 4. 

STEAI^I-HEATING. 

The Rating of House-heating Boilers. 

(W. Kent, Trans. A. S. H. V.E.,1909.) 
The rating of a steam-boiler for house-heating may be based upon one 
or more of several data: 1, square feet of grate-surface; 2, square feet of 
heating-surface; 3, coal-burning capacity; 4, steam-making capacity; 
5, square feet of steam-radiating-surface, including mains, that it will 
supply. In establishing such a rating the following considerations should 
be taken into account: 

1. One sq. ft. of cast-iron radiator surface will give off about 250 B.T.U. 
per hour under ordinary conditions of temperature of steam 212°, and 
temperature of room 70°. 

2. One pound of good anthracite or semi-bituminous coal under the 
best conditions of air-supplv, in a boiler properly proportioned, will 
transmit about 10,000 B.T.U. to the boiler. 

3. In order to obtain this economical result from the coal the boilers 
should be driven at a rate not greatly exceeding 2 lbs. of water evaporated 
from and at 212° per sq. ft. of heating-surface per hour, corresponding 
to a heat transmission of 2 X 970 = 1940, or, say, approximately 2000 
B.T.U. per hour per sq. ft. of heating-surface. 

4. A satisfactory boiler or furnace for house-heating should not 
require coal to be fed oftener than once in 8 hours; this requires a rate 
of burning of only 3 to 5 pounds of coal per sq. ft. of grate per hour. 

5. For commercial and constructive reasons, it Is not convenient to 
establish a fixed ratio of heating- to grate-surface for all sizes of boilers. 
The grate-surface is limited by the available area in which it may be 
placed, but on a given grate more heating-surface maybe piled in one 
form of boiler than in another, and in boilers of one general form one 
boiler may be built higher than aneWier, thus obtaining a greater amount 
of heating-surface. 



STEAM- HEATING. 



695 



6. The rate of burning coal and the ratio of heating- to grate-surface 
both being variable, the coal-burning rate and the ratio may be so related 
to each other as to establish condition 3, viz., a rate of evaporation of 
2 lbs. of water from and at 212° per sq. ft. of heating-suiface per hour. 
These general considerations lead to the following calculations: 
1 lb. of coal, 10,000 B.T.U. utihzed in the boiler, will supply 10,000 -^ 
250 = 40 sq. ft. radiating-surface, and wiU require 10,000 -^ 2000 = 
5 sq. ft. boiler heating-surface. 1 sq. ft. of boiler-surface will supply 
2000 -^ 250 or 40 -^ 5 = 8 sq. ft. radiating-surface. 



Low 
Boiler. 



Medi- 
um. 



High Boiler. 



I sq. ft, of grate should burn . . . . 
I sq. ft. of grate should develop. 

1 sq. ft. of grate will require 

1 sq. f t. of grate will supply 

Type of boiler, depending on 
ratio heating- -^ grate-surface. 



3 

30,000 

15 

120 



4 

40,000 

20 

160 

B. 



5 lb. coal per hour. 
50,000 B.T.U. per hour. 
25 sq. ft. heating-surf. 
200 sq.ft. radiating-sur. 

C. 











Table of 


Ratings. 










6 


6 






. 03 




d 


6 

i 










c3 


02 






u o 

h 


i' 








-A 

O 0) 




1. . 


A 1... 


1 


15 


3 


30 


120 


B 8... 


8 


160 


32 


320 


1,280 


A 2... 


2 


30 


6 


60 


240 


C 6... 


6 


150 


30 


300 


1,200 


A 3... 




45 


9 


90 


360 


C 7... 


7 


175 


35 


350 


1,400 


A 4... 




60 


12 


120 


480 


C 8... 


8 


200 


40 


400 


1,600 


A 5... 




75 


15 


150 


600 


C 10... 


10 


250 


50 


500 


2,000 


B 4... 




80 


16 


160 


640 


C 12... 


12 


300 


60 


600 


2,400 


B 5... 




100 


20 


200 


800 


C 14... 


14 


350 


70 


700 


2,800 


B 6... 




120 


24 


240 


960 


C 16... 


16 


400 


80 


800 


3,200 


B 7... 




140 


28 


280 


1,120 















The table is based on the utilization in the boiler of 10,000 B.T.U. per 
pound of good coal. For poorer coal the same figures will hold good 
except the pounds coal burned per hour, which should be increased in 
the ratio of the B.T.U. of the good to that of the poor coal. Thus for 
coal from which 8000 B.T.U. can be utilized the coal burned per hour 
will be 25 per cent greater. 

For comparison with the above table the following figures are taken 
and calculated from the catalogue of a prominent maker of cast-iron 
boilers: 



Height. 



Low 

Medium. 
High.... 





H 


R 










Heat- 


Radiat- 


H 


R 


R 


G 


mg- 


mg-sur- 


— 


— 


— 


Grate. 


sur- 
face. 


face. 


G 


G 


H 


S 2.1 


45 


210 


21.5 


100 


AJ 


\ 4.7 


90 


600 


19.1 


128 


6.7 


\ 8.2 


103 


600 


24.5 


143 


5.8 


195 


1,500 


23.8 


183 


7.7 


( 6.7 
114.7 


210 


1,200 


31.3 


179 


5.7 


420 


3,300 


28.6 


225 


7.9 



B.T.U. 


^ ^ 


per Hour 


H ^ 


= i2x250 


« 


52,500 


1,167 


150.000 


1,667 


150,000 


1,456 


375,000 


1,923 


300,000 


1,476 


825,000 


1,964 



* Equals B.T.U. per hour -J- 10,000 G, 



696 HEATING AND VENTILATION. 



Testing Cast-iron House-heating Boilers. 

The testing of the evaporating power and the economy of small-sized 
boilers is more difficult than the testing of large steam-boilers for the 
reason that the small quantity of coal burned in a day makes it impossible 
to procure a uniform condition of the coal on the grate throughout the 
test, and large errors are apt to be made in the calculation on account of 
the difference of condition at the beginning and end of a test. The 
following is suggested as a method of test which will avoid these errors. 

(a) Measure the grate-surface and weigh out an amount of coal equal 
to 30, 40, or 50 lbs. per sq. ft. of grate, according to the type A, B, or C, 
or the ratio of heating- to grate-surface. 

(b) Disconnect the steam-pipe, so that the steam may be wasted at 
atmospheric pressure. Fill the boiler with cold water to a marked level, 
and take the weight of this water and its temperature. 

(c) Start a brisk fire with plentj^ of wood, so as to cause the coal to 
ignite rapidly; feed the coal as needed, and gradually increase the thick- 
ness of the bed of coal as it burns brightly on top, getting the fire-pot full 
as the last of the coal is fired. Then burn away all the coal until it ceases 
to make steam, when the test may be considered as at an end. 

(d) Record the temperature of the gases of combustion in the flue every 
half-hour. 

(e) Periodically, as needed, feed cold water, which has been weighed, 
to bring the water level to the original mark. Record the time and the 
weight. 

Calculations. 

Total water fed to the boiler, including original cold 
water, pounds X (212° — original cold-water tem- 
perature) = B.T.U. 

Water apparently evaporated, pounds X 970 = B.T.U. 

Add correction for increased bulk of hot water: 

Original water, pounds X ^^^'^ "/^'^^ X 970 = B.T.U. 

Total B.T.U. 

Divide by 970 to obtain equivalent water evaporation from and at 
212° F. 

Divide by the number of pounds of coal to obtain equivalent water per 
pound of coal. 

The last result may be considerably less than 10 pounds on account of 
imperfect combustion at the beginning of the test, excessive air-supply 
when the coal bed is thin in the latter half of the test, and loss by radiation, 
but the results will be fairly comparable with results from other boilers 
of the same size and run under the same conditions. The records of water 
fed and of temperature of gases should be plotted, with time as the base, 
for comparison with other tests. 

Proportions of House-heating Boilers. — A committee of the Am. 
Soc. Heating and Ventilating Engineers, reporting in 1909 on the method 
of rating small house-heating boilers, shows the following ratings, in square 
feet of radiating surface supplied by certain boilers of nearly the same 
nominal capacity, as given in makers' catalogues. 

Boiler A. B. C. D. E. F. 

Rated capacity 800 800 775 750 750 750 

Square inches of grate 616 740 648 528 630 648 

Ratio of grate to 100 sq. ft. of capacity 77 92.5 83.6 70.4 84 86.2 

Estimated rate of combustion 5.1 4.2 4.65 5.63 4.4 4.5 

The figures in the last line are lbs. of coal per sq. ft. of grate surface per 
hour, and are based on the assumptions of 10,000 B.T.U. utilized per 
lb. of coal and 270 B.T.U. transmitted by each sq. ft. of radiating sur- 
face per hour. 



STEAM- HEATING. 



697 



" The question of heating surface in a boiler seems to be an unknown 
quantity, and inquiry among the manufacturers does not produce much 
information on the subject." 

Following is the list of sizes and ratings of the "Manhattan" sectional 
steam boiler. The figures for sq. ft. of grate surface and for the ratio of 
heating to grate surface (approx.) have been computed from the sizes 
given in the catalogue (1909). 





'O:^ 




^ c 


bi 




"o k 




■tj fl 




<u c 


^ ^ c — 


Size of 


-1. 

OJ «-i (-1 


O g o 


<P o 


an 


Size of 




o 2 S 


eg 
1^ 


Grate. 






1- 


Grate. 


S; 3 Qj 

1^1 








ins. 


sq.ft. 










ins. 


sq.ft. 






4 


450 


18x19 


2.37 


68 


29 


10 


2250 


24x63 


10.5 


212 


20 


5 


600 


18x25 


3.75 


84 


23 


6 


2200 


36x36 


9 


256 


28 


6 


750 


18x31 


3.87 


100 


26 


7 


2700 


36x43 


11.74 


298 


26 


7 


900 


18x37 


4.65 


116 


25' 


8 


3200 


36x50 


13.33 


340 


26 


8 


1050 


18x43 


5.37 


132 


25 


9 


3700 


36x57 


14.25 


382 


26 


5 


1000 


24x30 


5 


111 


22 


10 


4200 


36x64 


16 


424 


26 


6 


1250 


24x36 


6 


128 


21 


11 


4700 


36x71 


17.5 


466 


27 


7 


1500 


24x43 


7.16 


149 


21 


12 


5200 


36x78 


19.5 


508 


26 


8 


1750 


24x50 


8.33 


170 


20 


13 


5700 


36x84 


21 


550 


26 


9 


2000 


24x57 


9.5 


191 


20 


14 


6200 


36x90 


22.5 


592 


26 



It appears from this list that there are three sets of proportions, corre- 
sponding to the three mdths of grate surface. The average ratio of 
heating to grate surface in the three sets is respectively 25.0, 20.7, and 
25.8; the rated sq. ft. of radiating surface per sq. ft. of grate is 185, 208, 
and 259, and the sq. ft. of radiating surface per sq. ft. of boiler heating 
surface is 7.4, 10.1, and 9.8. Taking 10,000 B.T.U. utihzed per lb. of 
coal, and 250 B.T.U. emitted per sq. ft. of radiating surface per hour, 
the rate of combustion required to supply the radiating surface is respec- 
tively 4.62, 5.22, and 6.40 lbs. per sq. ft. of grate per hour. 

Coeificient of Heat Transmission in Direct Radiation. — The value 
of K, or the B.T.U. transmitted per sq. ft. of radiating surface per hour 
per degree of difference of temperature between the steam (or hot water) 
and the air in the room, is commonly taken at 1.8 in steam heating^ 
\\ith a temperature difference of about 142°, and 1.6 in hot-water heat- 
ing, \\ith a temperature difference averaging 80°. Its value as found by 
test varies with the conditions; thus the total heat transmitted is not 
directly proportional to the temperature difference, but increases at a 
faster rate; single pipes exposed on all sides transmit more heat than 
pipes in a group; low radiators more than liigh ones; radiators exposed 
to currents of cool air more than those in relatively quiet air; radiators 
with a free circulation of steam throughout more than those that are 
partly filled with water or air, etc. The total range of the value of K, 
for ordinary conditions of practice, is probably between 1.5 and 2.0 for 
steam-heating with a temperature difference of 140°, averaging 1.8, and 
between 1.2 and 1.7, averaging 1.6, for hot-water heating, with a tem- 
perature difference of 80%. 

C. F. Hauss, Trans. A. S. H. V. E., 1904, gives as a basis for calcula- 
tion, for a room heated to 70° with steam at IV2 lbs. gauge pressure 
(temperature difference 146° F.) 1 sq. ft. of single column radiator gives 
off 300 B.T.U. per hour; 2-column, 275; 3-column, 250; 4-column, 225. 

Value of K in Cast-iron Direct Radiators. (J. R. Allen, Tran%, 
A. S. H. V. E., 1908.) Ts = temp, of steam; Tx= temp, of room. 

Ts-T^=- 110 120 130 140 150 160 

2-col. rad 1.71 1.745 1.76 1.82 1.855 1.895 

3-col. rad 1.65 1.695 1.745 1.79 1.835 1.885 

Ts-T,= 170 180 200 220 240 260 

2-col. rad 1.93 1.965 2.04 2.11 2.185 2.265 

3-col. rad 1.93 1.98 2.075 2.165 2.260 2.36 



698 HEATING AND VENTILATION. 

B.T.U. Transmitted per Hour per Sq. Ft, of Heating Surface in 
Indirect Radiators. (W. S. Munroe, Eng. Rec, Nov. 18, 1899.) 

Cu. ft. of air per hour per sq. ft. of surface. 
100 200 300 400 500 600 700 800 900 
B.T.U. per hour per sq. ft. of heating surface. 
"Gold Rn "Ha). .. 200 325 450 560 670 780 870 950 1030 

radiator [(ft) . . . 300 550 760 950 1130 1300 
"Whittier" (6)... 250 400 520 "620 710 

B.T.U. per hr. per sq. ft. per deg. diff. of temp.* 

Gold Pin (a) 1.3 2.2 3.0 3.7 4.5 5.2 5.8 6.3 6.9 

Gold Pin (6) 2.0 3.7 5.1 6.3 7.7 8.7 

Wliittier (6) 1.7 2.7 3.5 4.1 4.7 

Temperature difference between steam and entering air, (a) 150; 
(&) 215. 

* Between steam and entering air. 

Short Rules for Computing Radiating-Surfaces. — In the early days 
of steam-heating, when Uttle was known about " British Thermal Units," 
it was customary to estimate the amount of radiating-surface by dividing 
the cubic contents of the room to be heated by a certain factor supposed 
to be derived from "experience." Two of these rules are as follows: 

One square foot of surface will heat from 40 to 100 cu. ft. of space to 
75° in — 10° latitudes. This range is intended to meet conditions of 
exposed or corner rooms of buildings, and those less so, as intermediate 
ones of a block. As a general rule, 1 sq. ft. of surface will heat 70 cu. ft. 
of air in outer or front rooms and 100 cu. ft. in inner rooms. In large 
stores in cities, with buildings on each side, 1 to 100 is ample. The 
following are approximate proportions: 

One square foot radiating-surface will heat: 

In Dwellings, In Hall, Stores, In Churches, 
Schoolrooms, Lofts, Factories, Large Audito- 
Offices, etc. etc. riums, etc. 

By direct radiation. ... 60 to 80 ft. 75 to 100 ft. 150 to 200 ft. 

By indirect radiation.. 40 to 50 ft. 50 to 70 ft. 100 to 140 ft. 

Isolated buildings exposed to prevailing north or west winds should 
have a generous addition made to the heating-surface on their exposed 
sides. 

1 sq. ft. of boiler-surface will supply from 7 to 10 sq. ft. of radiating- 
surface, depending upon the size of boiler and the efficiency of its surface, 
as well as that of the radiating-surface. Small boilers for house use 
should be much larger proportionately than large plants. Each horse- 
power of boiler will supply from 240 to 360 ft. of 1-in. steam-pipe, or 
80 to 120 sq. ft. of radiating-surface. Under ordinary conditions 1 
horse-power will heat, approximately, in — 

Brick dwellings, in blocks, as in cities 15,000 to 20,000 cu. ft. 

Brick stores, in blocks 10,000 " 15,000 

Brick dwellings, exposed all round 10,000 " 15,000 '* 

Brick mills, shops, factories, etc 7,000 '* 10,000 '* 

Wooden dweUings, exposed 7,000 " 10,000 '* 

Foundries and wooden shops 6,000 " 10,000 '* 

Exhibition buildings, largely glass, etc 4,000 " 15,000 " 

Such "rules of thumb," as they are called, are generally supplanted by 
the modern "heat-unit" methods. 

Carrying Capacity of Pipes in Low -Pressure Steam Heating. (W. 

Kent, Trans. A. S. H. V. E., 1907.) — The following table is based on an 
assumed drop of 1 pound pressure per 1000 feet, not because that is 
the drop which should always be used — in fact the writer believes that 
in large installations a far greater drop is permissible — but because it 
Ifives a basis upon which the flow for any other drop may be calculated, 



FLOW OF STEAM IN PIPES. 



699 



merely by multiplying the figures in the tables by the square root of the 
assigned drop. The formula from which t he tables' are calculated is the 



well known one, W= 60Xc 



Al 



1^ (Pi — Pi) d^ ' 



in which 17= weight of steam 



in lbs. per hour; w = weight of steam in pounds per cubic foot, at 
the entering pressure, pj ; /?2 the pressure at the end of the pipe; d the 
actual diameter of standard wrought-iron pipe in inches, and L the 
length in feet. The coefficients c are derived from Babcock's formula 
(see page 618) which is beheved to be as accurate as any that has been 
derived from the very few recorded experiments on steam. 



Nominal diam. of 
pipe 

Value of c — 

Nominal diam. of 
pipe 

Value of c — 



1/2 

33.4 


3/4 
37.5 


1 
41.3 


\y.% 


11/2 

48.4 


2 
52.5 


U{1 


3 
59.0 


4 
63.2 


41/2 

64.8 


5 
66.5 


6t.7 


7 
70.7 


8 
72.2 


9 
73.4 


10 

74.5 



31/2 

61.3 

12 
76.3 



Flow of Steam in Pipes for a Drop of 1 lb. per 1000 Ft. Length. 

(Pounds per Hour.) 



2 fl 


l.s 

a'6 


pi=0.3 


Pi=1.3 


Pi=2.3 


Pi=3.3 


Pi=4.3 


Pi=5.3 


Pi = 6.3 


2)1 = 8.3 


pi-10.3 


H £ 


w= 


w = 


w = 


w = 


w= 


w = 


w = 


w= 


w = 




5-2 


.03732 


.04042 


.04277 


.04512 


.04746 


.04980 


.05213 


.05676 


.0614 


I 


1.049 


17.1 


17.8 


18.3 


18.8 


19.2 


19.7 


20.2 


21.0 


21.9 


11/4 


1.380 


37.6 


39.1 


40.2 


41.3 


42.4 


43.4 


44.4 


46.3 


48.2 


11/2 


1.610 


58.4 


60.7 


62.5 


64.1 


65.8 


67.4 


68.9 


71.9 


74.8 


2 


2.067 


118.2 


123.0 


126.6 


130.0 


133.3 


136.6 


139.7 


145.8 


151.6 


21/2 


2.469 


194.9 


202.8 


208.7 


214.3 


219.7 


225.1 


230.3 


240.3 


250.0 


3 


3.068 


356.6 


371.0 


381.8 


392.0 


402.1 


411.9 


421.4 


439.7 


457.3 


31/2 


3.548 


532.7 


554.5 


570.5 


585.8 


600.8 


615.4 


629.8 


481.5 


683.8 


4 


4.026 


753.6 


784.2 


807.0 


828.6 


849.6 


870.6 


890.4 


929. A 


966.6 


41/2 


4.506 


1025. 


1066. 


1096. 


1126. 


1154. 


1184. 


1210. 


1262. 


1315. 


5 


5.047 


1395. 


1451. 


1494. 


1534. 


1573. 


1611. 


1649. 


1720. 


1789. 


6 


6.065 


2281. 


2374. 


2443. 


2509. 


2573. 


2635. 


2696. 


2813. 


2926. 


7 


7.023 


3387. 


3525. 


3628. 


3725. 


3820. 


3913. 


4003. 


4177. 


4345. 


8 


7.981 


4776. 


4970. 


5114. 


5250. 


5385. 


5518. 


5644. 


5889. 


6123. 


9 


8.941 


6429. 


6693. 


6885. 


7070. 


7250. 


7430. 


7604. 


7934. 


8251. 


10 


10.020 


8676 


9030. 


9294. 


9545. 


9785. 


10025. 


10239. 


10702. 


11123. 


11 


11.000 


11106. 11556. 


11892. 


12210. 


12522. 


12828. 


13128. 


13698. 


14244. 


12 


12.000 


13950. 


14520. 


14940. 


15342. 


15732. 


16116. 


16488. 


17202. 


17892. 



Pi = initial pressure, by gauge, lb. per sq. in. 
per cu. ft. 



w = density, lb. 



For any other drop of pressure per 1000 feet length, multiply the fig ■ 
ures in the table by the square root of that drop, or by the factor below. 

Drop lb. per 

1000 ft.... % ^2 2 3 
Factor 0.5 0.71 1.41 1.73 



4 6 8 10 15 20 
2.0 2.45 2.83 3.16 3.87 4.47 



In all cases the judgment of the engineer must be used in the assump- 
tion of the drop to be allowed. For small distributing pipes it will gen- 
erally be desirable to assume a drop of not more than one pound per 
1000 feet to insure that each single radiator shall always have an ample 
supply for the worst conditions, and in that case the size of piping given 
In the table up to two inches may be used; but for main pipes supplying 
totals of more than 500 square feet, greater drops may be allowed. 



700 



HEATING AND VENTILATION. 



Proportioning Pipes to Radiating Surface. 

Figures Used in Calculation of Radiating Surface. 

P = Pressure by gauge, lbs. per sq. in. 
0. 0.3 1.3 2.3 3.3 4.3 5.3 6.3 8.3 10.3 

L = latent heat of evaporation, B.T.U. per lb.* 
965.7 965.0 962.6 960.4 958.3 956.3 954.4 952.6 949.1 945.8 

Temperature Fahrenheit, Ti. 
212. 213. 216.3 219.4 222.4 225.2 227.9 230.5 235.4 240.0 

2^2 = Ti— 70°, difference of temperature. 
142. 143. 146.3 149.4 152.4 155.2 157.9 160.5 165.4 170.0 

Hi = Ti X l.S = heat transmission per sq. ft. radiating surface, B.T.U. 

per hour. 
255.6 257.4 263.3 268.9 274.3 279.2 284.2 288.9 297.7 306.0 

Hi-^ L '= steam condensed per sq. ft. radiating surface, lbs. per hour. 
0.2647 0.267 0.274 0.280 0.286 0.292 0.298 0.303 0.314 0.324 

Reciprocal of above = radiating surface per lb. of steam condensed per 

hour. 
3.78 3.75 3.65 3.57 3.50 3.42 3.36 3.30 3.18 3.09 

The last three lines of figures are based on the empirical constant 1.8 
for the average British thermal units transmitted per square foot of radi- 
ating surface per hour per degree of difference of temperature. Tliis 
figure is approximately correct for several forms of both cast-iron radia- 
tors and pipe coils, not over 30 inches high and not over two pipes in 
width. 



Radiating Surface Supplied by Different Sizes of Pipe. 

On basis of steam in pipe at 0.3 and 10.3 lbs. gauge pressure, tempera- 
ture of room 70°, heat transmitted per square foot radiating surface 257.4 
and 306 British thermal units per hour, and drop of pressure in pipe at 
the rate of 1 lb. per 1000 feet length; = pounds of steam per hour in the 
table on the preceding page, 1st column, X 3.75, and last column, X 3.09. 



Size of 


Radiating 


Size of 


Radiating 


Size of 


Radiating 


Pipe. 


Surface, 
Sq. Ft. 


Pipe, 


Surface, 
Sq. Ft. 


Pipe. 


Surface, 
Sq. Ft. 


In. 


0.3 1b. 


10.3 lb. 


In, 


0.3 1b. 


10.31b. 


In. 


0.3 1b. 


10.31b. 


1/2 


16 


16 


21/2 


734 


769 


6 


7,541 


7,901 


3/4 


36 


38 


3 


1,296 


1,357 


7 


11,010 


11,535 


1 


71 


75 


31/2 


1,895 


1,986 


8 


15,307 


16,040 


11/4 


150 


157 


4 


2,630 


2,755 


9 


20,482 


21,451 


11/2 


230 


241 


41/2 


3,520 


3,686 


10 


27,427 


28.718 


2 


453 


475 


5 


4,695 


4,919 


12 


43,312 


45,423 



For Greater drops than 1 lb. per 1000 ft. length of pipe, multiply ttie 
figures by the square root of the drop. 

* The latest steam tables (1909) give somewhat higher figures, but the 
difiference is unimportant here. 



SIZES OP STEAM PIPES FOR HEATING. 



701 



Sizes of Steam Pipes in Heating Plants. — G. W. Stanton, in Heating 
and Ventilating Mag., April, 1908, gives tables for proportioning pipes to 
radiating surface, from which the following table is condensed: 



Sup- 
ply 


Radiating Surface Sq 


.Ft. 


Returns. 


Drips. 


Connections. 


Pipe. 
Ins. 


A 


B 


C 


D 


B 


CiD 


A 


BiCiD 


Ai 


A2BA 


B2C2 


1 

11'4 

11/2 

21/9 


24 

60 

125 

250 

600 

800 

1,000 

1,600 

1,900 

2,300 

4,100 

6,500 

9,600 

13,600 


60 

100 

200 

400 

700 

1,000 

1,600 

2,300 

3,200 

4,100 

6,500 

9,600 

13,600 


36 

11 

120 

280 

528 

900 

1,320 

1,920 

2,760 

3,720 

6,000 

9,000 

12,800 

17,800 

23,200 

37,000 

54,000 

76,000 


60 

120 

240 

480 

880 

1,500 

2,200 

3,200 

4,600 

6,200 

10,000 

15,000 

21,600 

30,000 

39,000 

62,000 

92,000 

130,000 


1 

11/4 
11/2 

2 

21/2 
21/2 
21/2 

3 

31/2 
4 


1 
1 
11/4 

-v. 

21/2 
21/2 

3 

31/2 
31/2 

4 
41/2 

6 
7 
8 


3/4 
,3/4 

11/4 
11/4 
11/2 

11/9 

11/2 


3/4 
3/4 
1 
1 

11/4 
11/4 
11/4 
11/4 


11/4 

21/2 
3 

41/2 


1 

11/4 

11/2 


11/4 
11/2 


3'' 






31/9 






4 






41/2 






5 
6 
7 
8 
9 
10 


Supply mains and risers 
are of the same size. 
Riser connections on 
the two-pipe system to 
be the same size as the 
riser. 


12 






14 






16 

























A. For single-pipe steam-heating system to 5 lb. pressure. ^1, 
riser connections. Ai, radiator connections. 

B. Two-pipe system to 5 lb. pressure; B\, Ci, radiator connections, 
supply; Bi, C2, radiator connections, return. 

C. D. Two-pipe system 2 and 5 lbs. respectively, mains and risers not 
over 100 ft. length. For other lengths, multiply the given radiating 
surface by factors, as below: 

Length, ft.... 200 300 400 500 600 700 800 900 1000 
Factor 0.71 0.58 0.5 0.45 0.41 0.38 0.35 0.33 0.32 

Mr. Stanton says: Theoretically both supply and return mains could 
be much smaller, but in practice it has been found that while smaller 
pipes can be used if a job is properly and carefully figured and propor- 
tioned and installed, for work as ordinarily installea it is far safer to use 
the sizes that have been tried and proven. By using the sizes given a 
job will circulate throughout with 1 lb. steam pressure at the boiler. 

Resistance of Fittings. — Where the pipe supplying the radiation con- 
tains a large number of fittings, or other conditions make such a refine- 
ment necessary, it is advisable to add to the actual distance of the radia- 
tion from the source of supply a distance equivalent to the resistance 
offered by the fittings, and by the entrance to the radiator, the value of 
which, expressed in feet of pipe of the same diameter as the fitting, will 
be found in the accompanying table. Power, Dec, 1907. 

Feet of Pipe to be Added for Each Fitting. 



Size Pipe. 


1 


IV4 


11/2 


2 


21/2 


3 


31/2 


4 


41/2 


5 


6 


7 


8 


9 


10 


Elbows... 


3 


4 


5 


7 


8 


10 


12 


13 


15 


17 


20 


23 


27 


30 


33 


Globe v.. 


7 


8 


10 


13 


17 


20 


23 


27 


30 


33 


40 


47 


53 


60 


67 


Entrance 


5 


6 


8 


10 


12 


15 


18 


20 


23 


25 


30 


35 


40 


45 


50 



702 HEATING AND VENTILATION. 

Overhead Steam-pipes. (A. R. Wolff, Stevens Indicator, 1887.) — 
When the overhead system of steam-heating is employed, in which sys- 
tem direct radiating-pipes, usually IV4 in. in diam., are placed in rows 
overhead, suspended upon horizontal racks, the pipes running horizon- 
tallv, and side by side, around the whole interior of the building, from 2 
to 3 ft. from the walls, and from 2 to 4 ft. from the ceiling, the amount 
of lV4-in. pipe required, according to Mr. C. J. H. Woodbury, for heating 
mills (for which use tliis system is deservedly much in vogue), is about 
1 ft. in length for every 90 cu. ft. of space. Of course a great range of 
difference exists, due to the special character of the operating machinery 
in the mill, both in respect to the amount of air circulated by the ma- 
chinery, and also the aid to warming the room by the friction of the 
journals. 

Removal of Air from Radiators. Vacuum Systems. — In order 
that a steam radiator may work at its highest capacity it is necessary 
that it be neither water-bound nor air-bound. Proper drainage must 
therefore be provided, and also means for continuously, or frequently, 
removing air from the system, such as automatic aif-valves on each 
radiator, an air-pump or an air-ejector on a chamber or receiver into 
which the returns are carried, or separate air-pipes connecting each 
radiator with a vacuum chamber. When a vacuum system is used, 
especially with a high vacuum, much low^er temperatures than usual may 
be used in the radiators, which is an advantage in moderate weather. 

Steam.-consumption in Car-heating. 

C, M. & St. Paul Railway Tests. (Engineering, June 27, 1890, p. 764.) 

Outside Temperature. Inside Temperature. ^^^per'c^^^^^^^ 

40 70 70 lbs. 

30 70 85 

10 70 100 

Heating a Greenhouse by Steam. — Wm. J, Baldwin answers a 
question in the American Machinist as below: With five pounds steam- 
pressure, how many square feet or inches of heating-surface is necessary 
to heat 100 square feet of glass on the roof, ends, and sides of a green- 
house in order to maintain a night heat of 55° to 65°, w^hile the thermom- 
eter outside ranges at from 15° to 20° below zero; also, what boiler- 
surface is necessary? W^hich is the best for the purpose to use — 2" pipe 
or 1 1/4'' pipe? 

Ans. — ReUable authorities agree that 1.25 to 1.50 cubic feet of air in 
an enclosed space will be cooled per minute per sq. ft. of glass as many 
degrees as the internal temperature of the house exceeds that of the air 
outside. Between + 65° and —20° there will be a difference of 85°, or, 
say, one cubic foot of air cooled 127.5° F. for each sq. ft. of glass for the 
most extreme condition mentioned. Multiply this by the number of 
square feet of glass and by 60, and we have the number of cubic feet of 
air cooled 1° per hour witliin the building or house. Divide the number 
thus found by 48, and it gives the units of heat required, approximately. 
Divide again by 953, and it will give the number of pounds of steam that 
must be condensed from a pressure and temperature of five pounds 
above atmosphere to water at the same temperature in an hour to main- 
tain the heat. Each square foot of surface of pipe will condense from 
1/4 to nearly 1/2 lb. of steam per hour, according as the coils are exposed 
or well or poorly arranged, for which an average of 1/3 lb. may be taken. 
According to tliis, it will require 3 sq. ft. of pipe surface per lb. of steam 
to be condensed. Proportion the heating-surface of the boiler to have 
about one fifth the actual radiating-surface, if you wish to keep steam 
over night, and proportion the grate to burn not more than six pounds 
of coal per sq. ft. of grate per hour. With very slow combustion, such 
as takes place in base-burning boilers, the grate might be proportioned 
for four to five pounds of coal per hour. It is cheaper to make coils of 
1 1/4" pipe than of 2", and there is nothing to be gained by using 2'' pipe 
unless the coils are very long. The pipes in a greenhouse should be 
under or in front of the benches, with every chance for a good circulation 



HOT-WATER HEATING. 703 

of air. "Header" coils are better than "return-bend" coils for this 
purpose. 

Mr. Baldwin's rule may be given the following form: Let H = heat- 
units transferred per hour, T = temperature inside the greenhouse, t — 
temperature outside, S = sq. ft. of glass surface: then H = 1.5 S (T — t) 
X 60 H- 48 = 1.875 S (T - t). Mr. Wolff's coefficient K for single sky- 
lights gives H = 1.03 S {T - t), and for single windows. 1.20 S {T - t). 

Heating a Greenhouse by Hot Water. — W. M. Mackay, of the 
Richardson & Boynton Co., in a lecture before the Master Plumbers' 
Association, N. Y., 1889, says: I find that while greenhouses were for- 
merly heated by 4-inch and 3-inch cast-iron pipe, on account of the large 
body of water which they contained, and the supposition that they gave 
better satisfaction and a more even temperature, florists of long experi- 
ence who have tried 4 -inch and 3-inch cast-iron pipe, and also 2-inch 
wrought-iron pipe for a number of years in heating their greenhouses 
by hot water, and who have also tried steam-heat, tell me that they get 
better satisfaction, greater economy, and are able to maintain a more 
even temperature with 2-inch wrought-iron pipe and hot water than by 
any other system they have used. They attribute this result principally 
to the fact that this size pipe contains less water and on this account the 
heat can be raised and lowered quicker than by any other arrangement 
of pipes, and a more uniform temperature maintained than by steam or 
any other system. 

HOT-WATER HEATING. 

The following notes are from the catalogue of the Nason Mfg. Co.: 

There are two distinct forms or modifications of hot-water apparatus, 
depending upon the temperature of the water. 

In the first or open-tank system the w^ater is never above 212° tempera- 
ture, and rarely above 200°. This method always gives satisfaction 
where the surface is sufficiently liberal, but in making it so its cost is 
considerably greater than that for a steam-heating apparatus. 

In the second method, sometimes called (erroneously) high-pressure 
hot-water heating, or the closed-system apparatus, the tank is closed. 
If it is provided with a safety-valve set at 10 lbs. it is practically as safe 
as the open-tank system. 

Law of Velocity of Flow. — The motive power of the circulation in a 
hot-water apparatus is the difference between the specific gravities of 
the water in the ascending and the descending pipes. This effective 
pressure is very small, and is equal to about one grain for each foot in 
height for each degree difference between the pipes; thus, with a height 
of 1 ft. '* up " pipe, and a difference between the temperatures of the 
up and down pipes of 8°, the difference in their specific gravities is equal 
to 8.16 grains (0.001166 lb.) on each square inch of the section of return- 
pipe, and the velocity of the circulation is proportioned to these differ- 
ences in temperature and height. 

Main flow-pipes from the heater, from which branches may be taken, 
are to be preferred to the practice of taking off nearly as many pipes from 
the heater as there are radiators to supply. 

It is not necessary that the main flow and return pipes should equal in 
capacity that of all their branches. The hottest water will seek the 
highest level, while gravity will cause an even distribution of the heated 
water if the surface is properly proportioned. 

It is good practice to reduce the size of the vertical mains as they ascend, 
say at the rate of one size for each floor. 

As with steam, so with hot water, the pipes must be unconfined to allow 
for expansion of the pipes consequent on having their temperatures in- 
creased. 

An expansion tank is required to keep the apparatus filled with water, 
which latter expands 1/24 of its bulk on being heated from 40° to 212°, 
and the cistern must have capacity to hold certainly this increased bulk. 
It is recommended that the supply cistern be placed on level with or 
above the highest pipes of the apparatus, in order to receive the air which 
collects in the mains and radiators, and capable of holding at least 1/20 of 
the water in the entire apparatus. 

Arrangement of Mains for Hot-water Heating. (W. M. Mackay, 
Lecture before Master Plumbers' Assoc, N. Y., 1889). — There are two 
different systems of mains in general use, either of whjch, if properly 



704 HEATING AND VENTILATION. 

E laced, will give good satisfaction. One is the taking of a single large- 
ow main from the heater to supply all the radiators on the several floors, 
with a corresponding return main of the same size. The other is the tak- 
ing of a number of 2-inch wrought-iron mains from the heater, with the 
same number of return mains of the same size, branching off to the several 
radiators or coils with 11/4-inch or 1-inch pipe, according to the size of 
the radiator or coil. A 2-inch main will supply three 11/4-inch or four 
1-inch branches, and these branches should be taken from the top of the 
horizontal main with a nipple and elbow, except in special cases where it 
it is found necessary to retard the flow of water to the near radiator, for 
the purpose of assisting the circulation in the far radiator: in tliis case 
the branch is taken from the side of the horizontal main. The flow and 
return mains are usually run side by side, suspended from the basement 
ceiling, and should have a gradual ascent from the heater to the radiators 
of at least 1 inch in 10 feet. It is customary, and an advantage where 
2-inch mains are used, to reduce the size of the main at every point where 
a branch is taken off. 

The single or large main system is best adapted for large buildings; but 
there is a limit as to size of main wliich it is not wise to go beyond — 
generally 6-inch, except in special cases. 

The proper area of cold-air pipe necessary for 100 square feet of indi- 
rect radiation in hot-water heating is 75 square inches, while the hot-air 
pipe should have at least 100 square inches of area. There should be a 
damper in the cold-air pipe for the purpose of controUing the amount of 
air admitted to the radiator, depending on the severity of the weather. 

Sizes of Pipe for Hot-water Heating. — A theoretical calculation of 
the required size of pipe in hot-water heating may be made in the follow- 
ing manner. Having given the amount of heat, in B.T.U. to be emitted 
by a radiator per minute, assume the temperatures of the water entering 
and leaving, say 160° and 140°. Dividing the B.T.U. by the difference 
in temperatures gives the number of pounds of water to be circulated, 
and tills divided by the weight of water per cubic foot gives the number 
of cubic feet per minute. The motive force to move tliis water, per 
square inch of the area of the riser, is the difference in weight per cu. ft. 
of water at the two temperatures, divided by 144, and multiplied by H, 
the height of the riser, or for Ti = 160 and T2 = 140, (61.37 - 60.98) 
-^ 144 = 0.00271 lb. per sq. in, for each foot of the riser. Dividing 144 
by 61.37 gives 2.34, the ft. head of water corresponding to 1 lb. per sq. 
in., and 0.00271 X 2.34 = 0.0066 ft. head, or if the riser is 20 ft. high, 
20 X 0.0066 = 0.132 ft. head, wliich is the motive force to move the water 
over the whole length of the circuit, overcoming the friction of the riser, 
the return pipe, the radiator and its connections. If the circuit has a 
resistance equal to that of a 50-ft. pipe, then 50 -^ 0.132 = 380 is the 
ratio of length of pipe to the head, which ratio is to be taken with the 
number of cubic feet to be circulated, and by means of formulae for flow 
of water, such as Darcy's, or hydraulic tables, the diameter of pipe re- 
quired to convey the given quantity of water with this ratio of length of 
pipe to head is found. This tedious calculation is made more compHcated 
by the fact that estimates have to be made of the frictional resistance of 
the radiator and its connections, elbows, valves, etc., so that in practice 
it is almost never used, and "rules of thumb" and tables derived from 
experience are used instead. 

On this subject a committee of the Am. Soc. Heating and Ventilating 
Engineers reported in 1909 as follows: 

The amount of water of a certain temperature required per hour by 
radiation may be determined by the following formula: 

20 x^eo.s^x 60 = ""• "■ °* ^'^*"' P" "''"""'• 

R = square feet of radiation; X = B.T.U. given off per hour by 1 sq. 
ft. of radiation (150 for direct and 230 for indirect) with water at 170°. 
Twenty is the drop in temperature in degrees between the water entering 
the radiation and that leaving it; 60.8 is the weight of a cubic foot of 
water at 170 degrees; 60 is to reduce the result from hours to minutes. 

The average sizes of mains, as used by seven prominent engineers in 
regular practice for 1800 square feet of radiation, are given below; 



HOT-WATER HEATING. 



705 



2-pipe open-tank system, 100 ft. mains, 5-in. pipe = 26.6 ft. per min. 

1-pipe open-tank system, 100 ft. mains, 6-in. pipe = 18.4 ft. per min. 

Overhead open-tank system, 100 ft. mains, 4-in. pipe = 41.8 ft. per min. 

Overhead open-tank system, 100 ft. mains, 3-in. pipe = 72.1 ft. per 
min. 

For 1200 sq. ft. indirect radiation with separate main, 100 ft. long, 
direct from boiler, open system, the bottom of the radiator being 1 ft. 
above the top of the boiler — 5-in. pipe = 22.4 ft. per min. 

Capacity of Mains 100 ft. Long, 
Expressed in the number of square feet of hot-water radiating sur- 
face they will supply, the radiators being placed in rooms at 70° F., and 
20° drop assumed. 



Diameter of 
Pipes, Ins. 


Two-Pipe 

up Feed 

Open Tank. 


One-Pipe 

up Feed 

Open Tank. 


Overhead 
Open 
Tank. 


Overhead 
Closed 
Tank. 


Two-Pipe 
Open 
Tank. 


11/4 


75 

107 

200 

314 

540 

780 

1,060 

1,860 

2,960 

4,280 

5,850 


45 

65 

121 

190 

328 

474 

645 

1,130 

1,800 

2,700 

3,500 


127 

181 

339 

533 

916 

1,334 

1,800 

3,150 

5,000 

7,200 

9,900 


250 

335 

667 

1,060 

1,800 

2,600 

3,350 

6,200 

9,800 

13,900 

19,500 


48 


11/2 


69 


2 


129 


21/2 


202 


3. :::::::::::: 


348 


31/2 


502 


4 


684 


5 


1 200 


6 


1,910 


7 


2,760 


8. • 


3 778 







The figures are for direct radiation except the last column which is for 
indirect, 12 in. above boiler. 

Capacity of Risers. 

Expressed in the number of sq. ft. of direct hot-water radiating sur- 
face they \^ill supply, the radiators being placed in rooms at 70° P., and 
20° drop' assumed. The figures in the last column are for the closed-tank 
overhead system the others are for the open-tank system. 



Diameter 
of Riser. 
Inches. 


1st Floor. 


2d Floor. 


3d Floor. 


4th Floor. 


Drop 

Risers, not 

exceeding 

4 floors. 


1 


33 

71 
100 

187 
292 
500 


46 
104 
140 
262 
410 
755 


57 
124 
175 
325 
492 
875 


64 
142 
200 
375 
580 
1,000 


48 


11/4 


112 


11/2 


160 


2 


300 


21/2 


471 


3. :::::::::::. 


810 







All horizontal branches from mains to risers or from risers to radiators, 
more than 10 ft. long (unless within 15 ft. of the boiler), should be in- 
creased one size over that indicated for risers in the above table. 

'For indirect radiation, the amount of surface may be computed as 
follows: 

Temperature of the air entering the room, 110° = T. 

Average temperature of the air passing through the radiator, 55°. 

Temperature of the air leaving the room, 70° = t. 

Velocity of the air passing through the radiator, 240 ft. per min. 

Cubic feet of air to be conveyed per hour, = C = (//" X 55) -^ {T — t). 

H = exposure loss in B.T.U. per hour. 

Heat necessary to raise this air to the entering temperature from 
0° F., r X C + 55 = H. 



706 



HEATING AND VENTILATION. 



The amount of radiation is found by dividing the total heat by the 
emission of heat by indirect radiators per square foot per hour per degree 
difference in temperature. This varies with the velocity, as shown below: 
Velocity, ft. per min... . 174 246 300 342 378 400 428 450 474 492 
B.T.U 1.70 2.00 2.22 2.38 2.52 2.60 2.67 2.72 2.76 2.80 

The difference between 170 degrees (average temperature of the water 
in the radiator) and 55 degrees (average temperature of the air. in the 
radiator) being 115, the emission at 240 ft. per min. is 2. per degree differ- 
ence or 230 B.T.U. 

Ordinarily the amount of indirect radiation required is computed by 
adding a percentage to the amount of direct radiation [computed by the 
usual rules], and an addition of 50% has been found sufficient in many 
cases; but in buildings where a standard of ventilation is to be maintained, 
the formula mentioned seems more likely to give satisfactory results. 
Free area betw^een the sections of radiation to allow passage of the re- 
quired volume of air at the assumed velocity must be maintained. The 
cold-air supply duct, on account of less frictional resistance, may ordi- 
narily have 80% of the area between the radiator sections. The hot-air 
flues may safely be proportioned for the following air velocities per min- 
ute: First floor, 200 feet; second floor, 300 feet; tliird floor, 400 feet. 

Pipe Sizes for Hot- water Heating. 
Based on 20° difference in temperature between flow and return water. 
(C. L. Hubbard, The Engineer July 1, 1902.) 



Diam. of ) i 
Pipe. \ ' 


11/4 


11/2 


2 


21/2 


3 


31/2 


4 


5 


6 


7 


Length of 
Run. 


Square Feet of Direct Radiating Surface. 


Feet. 
100 


30 


60 
50 


100 
75 
50 


200 
150 
125 
100 
75 


350 
250 
200 
175 
150 
125 


550 
400 
300 
275 
250 
225 
200 
175 
150 


850 
600 
450 
400 
350 
325 
300 
250 
225 


1,200 
850 
700 
600 
525 
475 
450 
400 
350 








200 


1,400 
1,150 
1.000 
900 
850 
775 
725 
650 






300 






400 






1,600 
1,400 
1,300 
1,200 
1,150 
1,000 




500 










600 










700 










1,700 


800 












1,600 


1000 












1.500 


















Square Feet of Indirect Radiation. 


100 


15 


30 
20 


50 
30 


100 
70 


200 
120 


300 
200 


400 
300 


600 
400 


1,000 
700 






200 












Square Feet of Direct Radiating Surface. 


1st story 


30 
55 
65 
75 
85 
95 


6C 
90 

no 

125 
140 
160 


100 
140 
165 
185 
210 
240 


200 
275 
375 
425 
500 


350 
275 


550 


850 










2d " 










3d 














4th " 
















5th " 
















6lh •• 



































The size of pipe required to. supply any given amount of hot-water 
radiating surface depends upon'(l) The square feet of radiation; (2) its 
elevation above the boiler: (3) the difference in temperature of the water 
in the supply and return pipes; (4) the length of the pipe connecting the 
radiator with the boiler. 

In estimating the length of a i)ipe the number of bends and valves must 
be taken into account. It is customary to consider an elbow as equivalent 
to a pipe 60 diameters in length, and a return bend to 120 diameters. A 
globe valve may be taken about the same as an elbow. 

A series of articles on The Determination of the Sizes of Pipe for Hot 
Water Heating, by F. E. Geiseeke, is printed in Domestic Engineering, 
begimiing in May, 1909. 



HOT -WATER HEATING. 



707 



Sizes of Flow and Return Pipes Approximately Proportioned to 
Surface of Direct Radiators for Gravity Hot-Water Heating. 

(G. W. Stanton, Heat. & Ventg. Mag., April, 1908.) 



Size 

of 

Mains. 



Miiins. 



In Cellar 

or 

Basement. 



On One 

or More 

Floors. 

Average. 



Branches of Mains. 



First 
Floor 
10'-15'. 



Second 
Floor 

\y-2y. 



Third 
Floor 
25'-35'. 



Fourth 

or Fifth 

Floor 

35'-45'. 



Square Feet of Radiatingr Surface. 



,3/. 

11/4 

11/2 

2 

21/2 
31/2 

41/2 

5 

6 

7 

8 

9 
10 
11 
12 



100 

135 

225 

320 

500 

650 

850 

1,050 

1,350 

2,900 

3,900 

5,000 

6,300 

7,900 

9,500 

1 1 .400 



135 

220 

350 

460 

675 

850 

1,100 

1,350 

1,700 

3,600 

4,800 

6,200 

7,700 

9,800 

11,800 

1 4.000 



50 
110 
180 
290 
400 
620 
820 
1,050 
1,325 



40 


45 


75 


80 


120 


135 


195 


210 


320 


350 


490 


525 


650 


690 


870 


920 


1,120 


1,185 


1,400 


1,485 



50 

85 

150 

230 

370 

550 

730 

970 

1,250 

1,560 



Note. — The heights of the several 
floors are taken as: 
1st. 10 to 15 ft.; 2d. 15 to 25 ft. 
3d. 25 to 35 ft.; 4th. 35 to 45 ft. 



Sizes of Pipe for Gravity Hot-Water Heating. (John Jaeger, Heating 
and Ventilating Mag., Feb., 1912.) — The assumed temperature of the 
water supplied to the radiators is 185°, and the drop 36^, giving a mean 
temperature of 170°. The temperature difference creates a water 
pressure of 0.148 in. of water per foot of height. With the assimaed 
heights, H, between the center of the boiler and the center of the 
radiator on the several floors, and the assumed lengths, L, of the 
circuit, making allowance for resistance of connections, as given in the 
table, and using the ordinary tables for flow of water in pipes, the 
figures for number of square feet of radiating surface that will be 
supplied by different sizes of pipe are obtained, assuming that each 
square foot emits 170 B. T. U. per hour. 

Floor H. L. Size of Pipe, In. 

Ft. Ft. 1/2 3/4 1 11/4 11/2 

Sq. Ft. of Radiating Surface. 

3.5 80 11 32 57 127 180 

6 100 13 39 70 156 221 

19 125 22 62 130 238 377 

150 26.5 74 160 290 450 

175 29 81 175 314 490 



Basement. . . 
First floor . . 
Second floor 

Third floor 31 

Fourth floor 42 



Healing by Hot Water, with Forced Circulation. —The principal 
defect of gravity hot-water systems, that the motive force is only the 
difference in weight of two columns of water of different temperatures, is 
overcome by giving the water a forced circulation, either by means of a 
pump or by a steam ejector. For large installations a pump gives facili- 
ties for forcing the hot water to any distance required. The design of 
such a system is chiefly a problem in hydraulics. After determining the 
quantity of heat to be given out by each radiator, a certain drop in 
temperature is assumed, and from that the volume of water required by 
each radiator is calculated. The piping system then has to be designed 
so that it will carry the proper supply of water to each radiator without 
short-circuiting, and with a minimum total cost for power to force the 
water, for loss by radiation, and for interest, etc., on cost of plant. No 
short rules or formulae have been established for designing a forced hot- 
water system, and each case has to be studied as an original problem to 



708 HEATING AND VENTILATION. 

be solved by application of the laws of heat transmission and hydraulics. 
Forced systems using steam ejectors have come into use to some extent 
in Europe in small installations, and some of them are described in the 
Transactions of the Amer. Soc'y of Heating and Ventilating Engmeers. 

A system of distributing heat and power to customers by means of hot 
water pumped from a central station was adopted by the Boston Heating 
Co in 1888. It was not commercially successful. A description of the 
plant is given by A. V, Abbott in Trans, A. I, M. E., 1888. 

Corrosion of Pipe in Hot-Water Heating Systems.— The chief agent 
of internal corrosion in hot-water pipes appears to be oxygen dissolved 
in the water. If this is removed corrosion is prevented. Buildings 
equipped with closed heating systems have suffered serious damage m 
six or eight years, while no such damage has been found m open or 
vented systems, in which the air dissolved in the water is allowed to 
escape in an open tank placed at the top of the system. (F.N. SpeUer, 
Eng. News, Feb. 13, 1913.) 

THE BLOWER SYSTEM OF HEATEVG. 

The system pro\ades for the use of a fan or blower which takes its sup- 
ply of fresh air from the outside of the building to be heated, forces it 
over steam coils, located either centrally or divided up into a number oi 
independent groups, and then into the several ducts or flues leading to the 
various rooms. The movement of the warmed air is positive, and the 
deUvery of the air to the various points of supply is certain and entirely 
independent of atmospheric conditions. 

Advantages and Disadvantages of the Plenum System. (Pro'. 
W. F. Barrett, Brit. Inst. H. <& V. Engrs., 1905.)— Advantages: (1) The 
evenness of temperature produced; (2) the ventilation of the building 
is concurrent with its warming; (3) the air can be drawn from sources 
free from contamination and can be filtered from suspended impurities, 
warmed and brought to the proper hygrometric state before its intro- 
duction to the different rooms or wards; (4) the degree of temperature 
and of ventilation can be easily controlled in any part of the building, 
and (5) the removal of ugly pipes running through the rooms has a great 
architectural and esthetic advantage. 

Disadvantages: (1) The most obvious is that no windows can be 
opened nor doors left open; double doors with an air lock between must 
also be provided if the doors are frequently opened and closed; (2) the 
mechanical arrangements are elaborate and the system requires to be 
used with inteUigent care; (3) the whole elaborate system needs to be 
set going even if only one or two rooms in a large building require to 
be warmed, as often happens in the winter vacation of a college; (4) the 
temporary failure of the system, through the breakdown of the engines 
or other cause, throws the whole system into confusion, and if, as in the 
Royal Victoria Hospital, the windows are not made to open, imminent 
danger results; (5) then, also, in the case of hospital w^ards and asylums 
it is possible that the outlet ducts may become coated with disease germs, 
and unless periodically cleansed, a back current through a high wind or 
temporary failure of the system may bring a cloud of these disease germs 
back into the wards. 

Heat Radiated from Coils in the Blower System. — The committee 
on Fan-blast Heating, of the A. S. H. V. E., in 1909, gives the foUowing 
formula for amount of heat radiated from hot-blast coils with different 
velocities of air passing through the heater: £' = B.T.U. per sq. ft. of sur- 
face per hour per degree of difference between the average temperature of 
the air and the steam temperature, = V4 V, in w^hich V= velocity of the 
air through the free area of the coil in feet per second. A plotted curve 
of 20 tests of different heaters shows that the formula represents the aver- 
age results, but individual tests show a wide variation from the average, 
thus: For velocity 1000 ft. per min., average 9 B.T.U., range 7.5 to 11; 
1600 ft. per min., average 10.4, range 9.5 to 12. 

The committee also gives the following formula for the rise in tem- 
perature of each two-row section of a coil: 

^_ (T,-Ta)XHXE 

AX V^XWXQOX 0.2377 ' 
In which R = degrees F. rise for each two-row section ; Tg = tern- 



THE BLOWER SYSTEM OF HEATING. 



709 



face in two-row section-. E = B.T.U. per degree difference between air 
and steam; E = v^4 Vg, in which Vg = air velocity in ft. per sec; 
A = area through heater in sq. ft.; Vm = velocity of air in ft. per min.; 
W = weight of 1 cii. ft. of air, lbs. 

The value of R is computed for each two-row section in a coil, and the 
results added. From a set of curves plotted from the formula the follow- 
ing figures are taken. 





Number of Rows. 




4 


8 


12 


16 


20 


24 


28 




Temperature Rise, Degrees. 


Steam, 80 lbs. Vm = 1,200 

Steam, 80 lbs. Vm = 1,800 

Steam, 5 lbs. Fm = 1,200 

Steam. 5 lbs. Vm = 1,800 


43 
36 
31 
25 


83 
68 
53 

48 


115 
96 
80 
68 


144 
122 
100 
85 


167 
145 
118 
101 


189 
165 
133 
115 


209 
182 
146 
128 



A formula for the rise in temperature of air in passing through the 
coils of a hot-blast heater is given by Perry West, Trans. A. S. H. V. E.^ 

1909, page 57, as follows: R= KDZ^N -r- ^V, in which i2=rise in 
temperature of the air; K = a constant depending on the kind of heat- 
ing surface; D = an average of the summation of temperature differ- 
ences between the air and the steam = {Ti — Tq) -^ logg [{Tg — Tq) h- 
{Tg — T\)]\ Z = number of sq. ft. of heating surface per sq. ft. of clear 
area per unit depth of heater, m = a power applicable to Z and depend- 
ing on the type of heating surface; N = number of units in depth of 
heater; V = velocity of the air at 70° F. in ft. per min. through the clear 
area: n = a root applicable to V and depending on experiment. 

For practical purposes and within the range of present knowledge on 
the subject the formula may be written 22 = 0.085 DZN ^ Kjv, and from 
this formula with T^ = 227° and Tq = 0°, with different values of Ti, the 
temperature of the air leaving the coils, a set of curves is plotted, from 
which the figures in the following table are taken. 





Sq. ft. of heating surface -r- sq. ft. free area through heater. 


Velocity, 
Ft. per Min. 


20 


30 


40 


50 


60 


70 


80 90 100 


120 




Rise in Temperature, Degrees F. 


500 


43 
38 
36 
34 
29 


63 
55 
52 
49 
42 


79 
70 
66 
63 
55 


95 
84 
79 
75 
66 


108 
97 
92 
87 
76 


120 
108 
102 
98 
86 


131 
118 
112 
108 
95 


141 
128 
121 
117 
104 


151 
138 
130 
125 
112 


170 


800 


157 


1000 


147 


1200 


140 


2000 


127 









Burt S. Harrison {Htg. and Ventg. Mag., Oct. and Nov., 1907) gives the 
followingformula,i2=— — z.(r — ^tttt — tti^^ in which r = temp. of steam 

^ y o/iv + 0.z4 

in coils, ( = temp. of air entering coils, 7 = velocity of air through coils in 
ft. per sec, N= no. of rows of 1-in. pipe in depth of heater. Charts are 
given by means of which heaters may be designed for any set of con- 
ditions. 

Tests of Cast-iron Heaters for Hot-blast Work, — An extensive 
series of tests of the Amer. Radiator Co's, "Vento" cast-iron heater is 
described by Theo. Weinshank in Trans. A. S. H. V. E., 1908. The tests 
were made under the supervision of Prof. J. H. Kinealy. The principal 
results are given in the table on page 710. 



710 



HEATING AND VENTILATION. 



Tests of a " Vento" Cast-Iron Heater. 



Velocity, 

Ft. per 

Min. 



Number of sections heater is 
deep. 



Number of sections heater is 
deep. 



I|2|3|4I5|6 112 



4 I 5 



Rise of temperature, K, per de- 
gree difference between tem- 
perature of steam and mean 
temperature of air for differ- 
ent velocities of air. 



Heat units transmitted per 
square foot of heating surface 
per hour per degree difference 
between the temperature of 
the steam and the mean tem- 
perature of the air. 



1600... 
1500... 
1400... 
1300... 
1200... 
1100... 
1000... 

900... 

800... 



0.124 
0.132 
0.139 
0.147 
0.154 
0.162 
0.170 
0.177 
0.185 



0.253 
0.261 
0.268 
0.276 
0.283 
0.291 
0.299 
0.306 
0.314 



0.649 


0.657 


0.664 


0.672 


0.679 


0.687 


0.695 


0.702 


lo 710 



0.761 
0.769 
0.776 
0.784 
0.791 
0.799 
0.807 
0.814 
822 



11.94 
11.91 
11.70 
11.50 
11.11 
10.72 
10.23 
9.39 
8.90 



12.17 
11.76 
11.28 
10.79 
10.21 
9.63 
8.99 
8.28 
7.56 



12.67 


12.67 


12.11 


12.06 


11.50 


11.41 


10 89 


10 75 


10.22 


10.05 


9.55 


9.34 


8.84 


8.61 


8.08 


7.85 


7.31 


7.08 



12.50 
11.86 
11.18 
10.51 
9.81 
9.09 
8.36 
7.60 
6.48 



12.20 
11.56 
10.89 
10.22 
9.52 
8.82 
8.10 
7.35 
6.60 



Final temperature, T, of air 
when entering heater at 0° F. 
Temperature of steam in 
heater, 227°. 



Velocity, 

Ft. per 

Min. 



Friction loss in inches of water 
due to the sections. 



1600. 
1300. 
1400. 
1300. 
1200. 
1100. 
1000. 

900. 

800. 



26.5 
28.1 
29.5 
31.1 
32.4 
34.0 
35.6 
36.9 
38 5 



51.0 
52.4 
53.8 
55.0 
56.4 
57.7 
59.1 
60.1 
61.6 



74.9 
76.3 
77.2 
77.6 
79.6 
80.5 
82.0 
83.0 
84 3 



94.7 
95.8 
96.7 
97.9 
99.0 
100.0 
100.1 
102.1 
103.1 



111.3 

112.4 
113.3 
114.3 
115.3 
116.2 
117.2 
118.0 
119.0 



125.2 
126.0 
126.8 
127.7 
128.7 
129.6 
130.5 
131.3 
132.3 



0.2360 

0.2070 

0.180 

0.156 

0.133 

0.111 

0.092 

0.074 

0.059 



288'0. 
2530. 
22O1O, 



5430 
47710 
415 



672I0.6OO 
590 0.703 
.5140.613 



443 
378 
.318 
.262 
.212 
.167 



0.528 
0.450 
0.378 
0.312 
0.253 
0.200 



Formiiiae. — s = no. of sections; V= velocity, ft. per min., air meas- 
ured afc70°; k = rise of temp, per degree difference; t = final tempera- 
ture. /= friction loss in in. of water. ^ = 454 fc -^ i2-\-k). k = 

s (0.167 - O.OOo s) - 0.061 ( ^ g^Q^^ ) • /= (0-85 + 0.2) (V/4000)2. 

Values of k and/ when 5 = 2 or more. 

Factory Heating by the Fan System, 

In factories where the space provided per operative is large, warm air 
is recirculated, sufficient air for ventilation being provided by leakage 
through the walls and windows. The air is commonly heated by steam 
coils furnished with exhaust steam from the factory engine. When the 
engine is not running, or when it does not supply enough exhaust steam 
for the purpose, steam from the boilers is admitted to the coils through 
a reducing valve. The following proportions are commonly used in de- 
signing. Coils, pipes 1-in., set 21/8 in. centers: free area through coils, 
40% of cross area. Velocity of air through free area, 1200 to 1800 ft. 
per min.; number of coils in series 8 to 20- circumferential speed of fan, 
4000 to 6000 ft. per min.; temperature of air leaving coils, 120° to 160^ 
F.; velocity of air at outlet of coil stack. 3000 to 4000 ft. per min.: veloc- 
ity in branch pipes, 2000 to 2800 ft., the lower velocities in the longest 
pipes. 

In factories in which mechanical ventilation as well as heating is re- 
quired, outlet flues at proper points must be provided, to avoid the neces- 
sity of opening windows, and the outflow of air in them may be assisted 
either by exhaust fans or by steam coils in the flues. 

Cooling Air for Ventilation. 

The chief diflflculty in the artificial cooling of air is due to the moisture 
it contains, and the great quantity of heat that has to be absorbed or 
abstracted from the air in order to condense this moisture. The cooled 



THE BLOWER SYSTEM OF HEATING. 



711 



and moisture-laden air also needs to be partially reheated in order to 
bring it to a degree of relative humidity that will make it suitable for ven- 
tilation. To cool 1 lb. of dry air from 82° to 72° requires the abstracting 
of 10 X 0.2375 B.T.U. (0.2375 being the specific heat at constant pres- 
sure). If the air at 82° is saturated, or 100% relative humidity it 
contains 0.0235 lb. of water vapor, while 1 lb. at 72° contains 0.0167 lb., 
60 that 0.0068 lb. will be condensed in cooling from vapor at 82° to 
water at 72°. The total heat (above 32°) in 1 lb. vapor at 82° is 1095.6 
B.T.U. and that in 1 lb. of water at 72° is 40 B.T.U. The difference, 
1055.6 X 0.0068 = 7.178 B.T.U., is the amount of heat abstracted in 
condensing the moisture. The B.T.U. in 1 lb. vapor at 72° is 1091.2. 
and the B.T.U. abstracted in cooling the remaining vapor from 82° to 
72° is 0.0167 X (1095.6 - 1091.2) = 0.073 B.T.U. The sum, 7.251 
B.T.U., is more than three times that required to cool the dry air from 
82° to 72°. Expressing these principles in formulae we have: 

Let Ti = original and T2 the final temperature of the air, 
a = vapor in 1 lb. saturated air at Ti; & = do. at T2, 
H = relative humidity of the air at Ti; h = desired do. at T2, 
U = total heat, in B.T.U., in 1 lb. vapor at Ti; u = do. at T2, 
w = total heat in water at T2. 
Then total heat abstracted in cooling air from Ti to T2 = (aH — bh) X 
(L^- w) + bh {U- u) + 0.2375 (Ti - T2), or aHU - bhu - (aH - bh) w 
+ 0.2375 (Ti - T2), or aH (U - w) - bh (u - w) + 0.2375 {Ti - T2). 

Example. — Required the amount of heat to be abstracted per hour 
in cooling the air for an audience chamber containing 1000 persons, 
1500 cu. ft. (measured at 70° F.), being supplied per person per hoiu-, 
the temperature of the air before cooling being 82°, with relative 
humidity 80%, and after cooling 72°, with humidity 70%. 
1000 X 1500 = 1,500.000 cu. ft., at 0.075 lb. per cu. ft. 
= 112,500 lbs. 
For 1 lb. aH (U - w) - bh {u - w) + 0.2375 (Ti - T2). 

0.0235 X 0.8 X (1095.6 - 40) - 0.0167 X 0.7 X (1091.2 - 40) 
+ 2.375 = 9.932 B.T.U. 

112,500 X 9.932 = 1,061,100 B.T.U. 
Taking 142 B.T.U. as the latent heat of melting ice, this amount is 
equivalent to the heat that would melt 7472 lbs. of ice per hour. 

See also paper by W. W. Macon, Trans. A. S. H. V. E., 1909, and 
Air-cooling of the New York Stock Exchange, Eng. Rec, April, 1905, 
and The Metal Worker, Aug. 5, 1905. 

Capacities of Fans or Blowers for Hot-Blast or Plenum Heating. 

(Computed by F. R. Still, American Blower Co., Detroit, Mich.) 



2§ 


"a; 

-a 
c 

'0 


1 
c 

(1 

K 

1 

'00 




1 

. > 


Ft. of Air DeUv- 
ed per Minute by 
m through 
eater. 


ft 

< 


. - 3 s 
fl 


•+ 


ir Minute. 

3 Area between 
pes in Sq. Ft. 


. - . 3 

c cro 

-4^ (h (^ 


it 


Sw 


.2 


£^ 


v^« 


A <ufeW 


sW 


^K< 


'^^ 
%* 


tK gS 


m 


r 


M 


Q 


0^ 


w 








w 


> 


P^ 


w 


70 


42 


360 


21/2 


6,900 


415,200 


1,021,000 


9 


30 7.7 


1760 


580 


80 


48 


320 


3 


8,500 


510,000 


1,255,000 




9.45 






714 


90 


54 


280 


4 


10,500 


630,000 


1,550,000 




' 11.66 






880 


100 


60 


250 


5 


12,503 


750.000 


1,845,000 




' 13.9 






1050 


110 


66 


230 


6 


15,833 


948,000 


2,335,000 




' 17.55 






1325 


120 


72 


210 


8 


19,833 


1,113,000 


2,900,000 




' 22. 






1650 


140 


84 


180 


10 


26,200 


1,572,000 


3,870,000 




' 29.1 






2200 


160 


96 


160 


12 


33,000 


1,980,000 


4,870,000 




' 36.7 






2770 


180 


108 


140 


15 


41,600 


2,496,000 


6,130,000 




' 46.3 






3490 


200 


120 


125 


18 


50.000 


3,000.000 


7.375,000 


• 55.5 


" 


4140 



712 



HEATING AND VENTILATION. 



Capacities of Fans or Blowers for Hot-blast or Plenum Heating — 

Continued. 





-C 


-3 








Ci 


Oi 




r^ 




C 




r^ 


<D 




hH 




<o 


t4 


M 


<L 


"13 




s 




c 


G 




rr 




O 


O 


^ 


OJ 


3 




'^i 


IS 




P^ 




|'5 




s 


% 


o 






a 
1 


5 

0) 




0).- 


Sa 


■ o 

IS) 


0) 


72 


h-1 




m 


m 


70 


1,740 


1055 


31/9 


2 


80 


2,142 


1295 


4 


2 


90 


2,640 


1600 


41/9 


21/9 


100 


3,150 


1900 


5 


21/9 


110 


3,975 


2410 


51/9 


3 


120 


4,950 


2990 


6 


3 


140 


6,600 


3990 


7 


31/? 


160 


8,310 


5025 


8 


4 


180 


10,470 


6325 


9 


41/9 


200 


12,420 


7560 


10 


5 



^ II 






35 

43 
53 
63 
80 
100 
133 
167 
211 
252 



•;372 
dm 






lO o 
CO -^ 

^§ 

01 1: 

+^ o ^ 



525 

645 

795 

945 

1200 

1500 

1995 

2505 

3165 

3780 



15 
18 
23 
27 
34 
43 
57 
72 
90 
108 



<jj o 



8,700 
10,700 
13,200 
15,800 
19,900 
25,000 
33,100 
41,700 
52,500 
63,200 









«3 ^-M 



9.67 
13.05 
14.72 
17.55 
22.20 
27.80 
36.80 
46.30 
58.40 
70.25 



g S 3 
> o g.t: 



8,200 
10,000 
12,500 
15,000 
18,900 
23,800 
31,400 
39,600 
50,000 
60,000 



Temperature of fresh air, 0°; of air from coils, 120°; of steam, 227°; 
Pressure of steam, 5 lbs. 

Pe ipheral velocity of fan-tips, 4000 ft.: number of pipes deep in coil. 
24; depth of coil. 60 inches; area of coils approximately twice free area. 

Relative Efficiency of Fans and Heated Chimneys for Ventila" 
tion. — W. P. Trowbridge, Trans'. A. S. M. E. vii. 531, gives a theoretical 
solution of the relative amounts of heat expended to remove a given 
volume of impure air by a fan and by a chimney. Assuming the total 
efficiency of a fan to be only 1/25, which is made up of an efficiency of 1/10 
for the engine, o/^q for the^ fan itself, and 8/10 for efficiency as regards 
friction, the fan requires an expenditure of heat to drive it of only 1/38 of 
the amount that would be required to produce the same ventilation by 
a chimney 100 ft. high. For a chimney 500 ft. high the fan will be 7.6 
times more efficient. 

The following figures are given by Atkinson {Coll. Engr., 1889). show- 
ing the minimum depth at which a furnace would be equal to a ventilating- 
machine, assuming that the sources of loss are the same in each case, i.e., 
that the loss of fuel in a furnace from the cooling in the upcast is equiva- 
lent to the power expended in overcoming the friction in the machine, 
and also assuming that the ventilating-machine utilizes 60 per cent of the 
engine-power. The coal consumption of the engine per I.H.P. is taken 
at 8 lbs. per hour. 

Average temperature in upcast 100° F. 150° F. 200° F. 

Minimum depth for equal economy.. 960 yards. 1040 yards. 1130 yards. 



PERFORMANCE OF HEATING GUARANTEE. 

Heating a Building to 70° F. Inside when the Outside Tempera- 
ture is Zero. — It is customary in some contracts for heating to guaran- 
tee that the apparatus will heat the interior of the building to 70° in zero 
weather. As it may not be practicable to obtain zero weather for the 
purpose of a test, it may be difficult to prove the performance of the 
guarantee unless an equivalent test may be made when the outside tem- 
perature is above zero, heating the building to a higher temperature 
than 70°. The following method was proposed by the author (Eng. Rec.t 



ELECTRICAL HEATING. 713 

Aug. 11, 1894) for determining to what temperature the rooms should 
be heated for various temperatures of the outside atmosphere and of the 
steam or hot water in the radiators. 

Let S = sq. ft. of surface of the steam or hot-water radiator; 
\{r = sq. ft. of surface of exposed walls, windows, etc.; 
Ts = temp, of the steam or hot water, Ti= temp, of inside of 
building or room, To — temp, of outside of building or room ; 
a = heat-units transmitted per sq. ft. of surface of radiator per 

hour per degree of difference of temperature; 
b = average heat-units transmitted per sq. ft. of walls per hour 
per degree of difference of temperature, including allow- 
ance for ventilation. 
It is assumed that witliin the range of temperatures considered New- 
ton's law of cooling holds good, viz., that it is proportional to the differ- 
ence of temperature between the two sides of the radiating-surface. 

Then aS {Ts - T{) = bW {Tt - To). Let ~ = C; then 

_ _ ^«+ ^^0 _Ts - Ti 
Ts -~ Ti — CiTi~ To) ; Ti 1"+"^ — ' ^ ~ T — — T ' 

Ts - 70 
If Ti = 70, and To = 0, C = -~^ — 

Let Ts = 140° 160° 180° 200° 212° 220° 250° 300° 

ThenC= 1 1.286 1.571 1.857 2.029 2.143 2.571 3.286 

and from the formula Ti= iTs+ CTo) -^ (1 + C) we find the inside 

temperatures corresponding to the given values of Ts and To which 

should be produced by an apparatus capable of heating the building to 



70° in zero weather. 
















For To = 


-20 


- 10 





10 


20 


30 


40° F. 




Inside Temperatures Tx. 








For Ts = 140° F. 


60 


65 


70 


75 


80 


85 


90 


160 


58.7 


64.3 


70 


75.6 


81.3 


86.9 


92.5 


180 


57.8 


63.9 


70 


76.1 


82.2 


88.4 


94.5 


200 


57.0 


63.5 


70 


76.5 


83.0 


89.5 


96.0 


212 


56.6 


63.3 


70 


76.7 


83.4 


90.1 


96.8 


220 


56.4 


63.2 


70 


76.8 


83.6 


90.5 


97.3 


250 


55.6 


62.8 


70 


77.2 


84.4 


91.6 


98.8 


300 


54.7 


62.4 


70 


77.7 


85.3 


93.0 


100.7 



J. R. Allen (Trans. A. S. H. V. E., 1908) develops a complex formula 
for the inside temperature which takes into consideration the fact that 
the coefficient of transmission of the radiator is not constant but in- 
creases with the temperature. With Ts = 221 and a two-column cast-iron 
radiator he finds for To = -20-10 10 20 30 40 
7^1 = 58 64 70 77.5 83 90 97 

For all values of To between — 10 and 40 these figures are within one 
degree of those computed by the author's method. 

ELECTRICAL HEATING. 

Heating by Electricity. — If the electric currents are generated by a 
dynamo driven by a steam-engine, electric heating will prove very ex- 
pensive, since the steam-engine wastes in the exhaust-steam and by 
radiation about 90% of the heat-units supplied to it. In direct steam- 
heating, with a good boiler and properiy covered supply-pipes, we can 
utihze about 60% of the total heat value of the fuel. One pound of coal, 
with a heating value of 13,000 heat-units, would supply to the radiators 
about 13,000 X 0.60 = 7800 heat-units. In electric heating, suppose we 
have a first-class condensing-engine developing 1 H.P. for every 2 lbs. of 
coal burned per hour. This would be equivalent to 1,980,000 ft.-lbs. •»• 



714 HEATING AND VENTILATION. 

778 = 2545 heat-units, or 1272 heat-units for 1 lb. of coal. The friction 
of the engine and of the dynamo and the loss by electric leakage and 
by heat radiation from the conducting wires might reduce the heat- 
units delivered as electric current to the electric radiator, and there con- 
verted into heat, to 50% of tWs, or only 636 heat-units, or less than one 
twelfth of that delivered to the steam-radiators in direct steam-heating. 
Electric heating, therefore, will prove uneconomical unless the electric 
current is derived from water or wind power wliich would otherwise be 
wasted. (See Electrical Engineering.) 

MINE-VENTILATION. 

Friction of Air in Underground Passages. — In ventilating a mine or 
other underground passage the resistance to be overcome is, according 
to most writers on the subject, proportional to the extent of the iric- 
tional surface exposed; that is, to the product lo of the length of the pan^r- 
way by its perim.eter, to the density of the air in circulation, to the 
square of its average speed, v, and lastly to a coefficient k, whose numer- 
ical value varies according to the nature of the sides of the gangway and 
the irregularities of its course. 

The formula for the loss of head, neglecting the variation in density as 

unimportant, is p = , in which p = loss of pressure in pounds per 

square foot, s = square feet of rubbing-surface exposed -to the air, v the 
velocity of the air in feet per minute, a the area of the passage in square 
feet, and k the coefficient of friction. W. Fairley, in Colliery Engineer, 
Oct. and Nov., 1893, gives the following formulae for all the quantities 
involved, using the same notation as the above, with these additions: 
h = horse-power of ventilation: I = length of air-channel; o = perimeter 
of air-channel; q = quantity of air circulating in cubic feet per minute 
u = units of work, in foot-pounds, applied to circulate the air ; ly = water- 
gauge in inches. Then, 

ksv^q _ ksv^ _ J£ _ ^ 
u pv pv ~' V ' 

qp _ 5.2 qw 
33,000 ^ 33,000* 
_ p _ 5.2 w 



lo 


a 


ksv" k, 
P 


2. 


h 


u 


33,000 


3. 


k 


_ pa _ u 


4. 


I 


s pa 
kv^o 


5. 





s pa 
I kvH 


6. 


P 


ksv^- u 



sv^ -T- a sv^ 



\y ks ] a q av 

I ^iny u 

7. pa = ksv"^ ^ 1 V/ 7~ I ^^"^ ~" • ^^^ ^ kaq^. 



^ ; / u 

^ ~ ~ p ~ p ~ \ ks ~ \ ks ' 



u ksv^ 



q — V^ — JL — 9JL — ^^^ _ 7 

kv^ ~ kv^ ~ kv^ ~ Icv^ ~ 
10. u = qp = vpa = ^^ = ksv^ = 5.2 qw = 33,000 /i. 

11 0, = ^ _ ^ _ * / - _ . V^P _ * / ^« . 



pa a y ks y ks y 



12. v^^^ 
ks 



MINE -VENTILATION. 



715 



/Co /Co /Co 

To find the quantity of air with a given horse-power and efficiency (e) 
of engine: 

h X 33,000 X e 
9= ^ 

The value of A:, the coefficient of friction, as stated, varies according to 
the nature of the sides of the gangway. Widely divergent values have 
been given by different authorities (see Colliery Engineer, Nov., 1893), the 
most generally accepted one until recently being probably that of J. J. 
Atkinson, .0000000217, which is the pressure per square foot in decimals 
of a pound for each square foot of rubbing-surface and a velocity of one 
foot per minute. Mr. Fairley, in his "Theory and Practice of Ventilating 
Coal-mines," gives a value less than half of Atkinson's or .00000001; and 
recent experiments by D. Murgue show that even this value is high under 
most conditions. Murgue's results are given in his paper on Experi- 
mental Investigations in the Loss of Head of Air-currents in Under- 
ground Workings, Trans. A. I. M. E., 1893, vol. xxiii. 63. His coefficients 
are given in the following table, as determined in twelve experiments: 

Coefficient of Loss of 
Head by Friction. 
French. British. 

{Straight, normal section 00092 .000,000,00486 
Straight, normal section 00094 .000,000,00497 
Straight, large section 00104 .000,000,00549 
Straight, normal section 00122 .000,000,00645 

(Straight, normal section 00030 .000,000,00158 
Straight, normal section 00036 .000,000,00190 
Continuous curve, normal section .00062 .000,000,00328 
Sinuous, intermediate section 00051 .000,000,00269 
Sinuous, small section 00055 .000,000,00291 

TimKor^^ ( Straight, normal section 00168 .000,000,00888 

crar^Sra.rc \ Straight, uormal section 00144 .000,000,00761 

gangways, j slightly sinuous, smaU section. . . .00238 .000,000,01257 

The French coefficients which are given by Murgue represent the height 
of water-gauge in millimeters for each square meter of rubbing-surface 
and a velocity of one meter per second. To convert them to the British 
measure of pounds per square foot for each square foot of rubbing-surface 
and a velocity of one foot per minute they have been multiplied by the 
factor of conversion, .000005283. For a velocity of 1000 feet per minute, 
since the loss of head varies as v"^, move the decimal point in the coefficients 
six places to the right. 

Equivalent Orifice. — The head absorbed by the working-chambers 
of a mine cannot be computed a priori, because the openings, cross- 
passages, irregular-shaped gob-piles, and daily changes in the size and 
shape of the chambers present much too complicated a network for accu- 
rate analysis. In order to overcome this difficulty Murgue proposed in 
1872 the method of equivalent orifice. This method consists in substitut- 
ing for the mine to be considered the equivalent thin-lipped orifice, 
requiring the same height of head for the discharge of an equal volume 
of air. The area of this orifice is obtained when the head and the dis- 
charge are known, by means of the following formulae, as given by Fairley: 

Let Q = cfuantitv of air in thousands of cubic feet per minute; 
w = inches of water-gauge; 
A = area in square feet of equivalent orifice. 

Then 

^ Vw 2.7 V ly 0.37 \^/ 

* »» . . 0.38 Q , ^T . . 0.403 Q ^ ^^« 

* Murgue gives A = — j^, and Noms A = — -^=^ • See page 672, ante. 



716 



WATER. 



Motive Column or the Head of Air Due to Differences of Tem- 
perature, etc. (Fairley.) 

Let M = motive column in feet ; 
T = temperature of upcast; 
f = weight of one cubic foot of the flowing air; 
t = temperature of downcast; 
D = depth of downcast. 
Then 

^ T-t 5.2XW v-vy Tir fXM V 

To find diameter of a round airway to pass the same amount of air as a 
square airway, the length and power remaining the same: 

Let D = diameter of round airway, A = area of square airway; = 

perimeter of square airway. Then D^ = a / ^ X 3.1416 



-i/i^ 



.78543 X 
If two fans are employed to ventilate a mine, each of which when 
worked separately produces a certain quantity, which may be indicated 
by A and B, then the quantit y of air t hat will pass when the two fans are 
worked together will be ^ A^ -{■ B^. (For mine-ventilating fans, see 
page 672.) 

WATER. 

Expansion of Water. — The following table gives the relative vol- 
umes of water at different temperatures, compared with its volume at 
4° C. according to Kopp, as corrected by Porter. 



Cent. 


Fahr. 


Volume. 


Cent. 


Fahr. 


Volume. 


Cent. 


Fahr. 


Volume. 


4° 


39.1° 


1.00000 


35° 


95° 


1.00586 


70° 


158° 


1.02241 


5 


41 


1.00001 


40 


104 


1.00767 


75 


167 


1.02548 


10 


50 


1.00025 


45 


113 


1.00967 


80 


176 


1.02872 


15 


59 


1.00083 


50 


122 


1.01186 


85 


185 


1.03213 


20 


68 


1.00171 


55 


131 


1.01423 


90 


194 


1.03570 


25 


77 


1.00286 


60 


140 


1.01678 


95 


203 


1.03943 


30 


86 


1.00425 


65 


149 


1.01951 


100 


212 


1.04332 



Weight of 1 cu. ft. at 39.1° F. = 62.4245 lb. -^- 1.04332 = 59.833. 
weight of 1 cu. ft. at 212° F. 

Weight of Water at Different Temperatures. — The weight of 
water at maximum density, 39.1°, is generally taken at the figure given 
by Rankine, 62.425 lbs. per cubic foot. Some authorities give as low as 
62.379. The figure 62.5 commonly given is approximate. The highest 
authoritative figure is 62.428. At 62° F. the figures range from 62.291 to 
62.360. The figure 62.355 is generally accepted as the most accurate. 

At 32° F. figures given by different writers range from 62.379 to 62.418. 
Hamilton Smith, Jr. (from Rosetti) gives 62.416. 



Weight of Water at Temperatures above 200° F. 

Bornstein's Tables, 1905.) 



(Landolt and 





Lbs. 




Lbs. 




Lbs. 




Lbs. 




Lbs. 




Lbs. 


Deg. 


Per 


Deg. 


Per 


Deg. 


Per 


Deg. 


Per 


Deg. 


Per 


Deg. 


Per 


F. 


Cu. 


F. 


Cu. 


F. 


Cu. 


F. 


Cu. 


F. 


Cu. 


F. 


Cu. 




Ft. 




Ft. 




Ft. 




Ft. 




Ft. 




Ft. 


200 


60.12 


270 


58.26 


340 


55.94 


410 


53.0 


480 


49 7 


550 


45.6 


210 


59.88 


280 


57.96 


350 


55.57 


420 


52.6 


490 


49.2 


560 


44.9 


220 


59.63 


290 


57.65 


360 


55.18 


430 


52.2 


500 


48 7 


570 


44.1 


230 


59.37 


300 


57.33 


370 


54.78 


440 


51.7 


510 


48 1 


580 


43.3 


240 


59.11 


310 


57.00 


380 


54.36 


450 


51.2 


520 


47 6 


590 


42.6 


250 


58.83 


320 


56.66 


390 


53.94 


460 


50.7 


530 


47 


600 


41.8 


260 


58.55 


330 


56.30 


400 


53.5 


470 


50.2 


540 


46.3 







WATER. 



717 



Weight of Water per Cubic Foot, from 32° to 212* F., and beat- 
units per pound, reckoned above 32^ F.: The figures for weight of water 
in following table, made by interpolating the table given by Clark as cal- 
culated from Rankine's formula, with corrections for apparent errors, was 
pubhshed bv the author in 1884, Trans. A. S. M. E., vi. 90. The figures 
for heat units are from Marks and Davis's Steam Tables, 1909. 





i« 


^ 




io 


w 




is 


w 




i« 


4 


abb 








III 


'S 




W)^ o 


'5 


a2fbb 


""IS 

bJO «H O 


■4J 

"5 


2^ 


:Sa^ 


^ 


S 3 0; 
0) +^T3 


i 


i5-§ 


|S^ 


^ 




'iKa 


S 


H 


^ . 


w 


rH 


^ 


w 


H 


tn 


r-i 


^ 


W 


32 


62.42 


6. 


78 


62.25 


46.04 


123 


61.68 


90.90 


168 


60.81 


135.86 


33 


62.42 


1.01 


79 


62.24 


47.04 


124 


61.67 


91.90 


169 


60.79 


136.86 


34 


62.42 


2.02 


80 


62.23 


48.03 


125 


61.65 


92.90 


170 


60.77 


137.87 


35 


62.42 


3.02 


81 


62.22 


49.03 


126 


61.63 


93.90 


171 


60.75 


138.87 


36 


62.42 


4.03 


82 


62.21 


50.03 


127 


61.61 


94.89 


172 


60.73 


139.87 


37 


62.42 


5.04 


83 


62.20 


51.02 


128 


61.60 


95.89 


173 


60.70 


140.87 


38 


62.42 


6.04 


84 


62.19 


52.02 


129 


61.58 


96.89 


174 


60.68 


141.87 


39 


62.42 


7.05 


85 


62.18 


53.02 


130 


61.56 


97.89 


175 


60.66 


142.87 


40 


62.42 


8.05 


86 


62.17 


54.01 


131 


61.54 


98.89 


176 


60.64 


143.87 


41 


62.42 


9.05 


87 


62.16 


55.01 


132 


61.52 


99.88 


177 


60.62 


144.88 


42 


62.42 


10.06 


88 


62.15 


56.01 


133 


61.51 


100.88 


178 


60.59 


145.88 


43 


62.42 


11.06 


89 


62.14 


57.00 


134 


61.49 


101.88 


179 


60.57 


146.88 


44 


62.42 


12.06 


90 


62.13 


58.00 


135 


61.47 


102.88 


180 


60.55 


147.88 


45 


62.42 


13.07 


91 


62.12 


59.00 


136 


61.45 


103.88 


181 


60.53 148.88 


46 


62.42 


14.07 


92 


62.11 


60.00 


137 


61.43 


104.87 


182 


60 50 149.89 


47 


62.42 


15.07 


93 


62.10 


60.99 


138 


61.41 


105.87 


183 


60.48 


150.89 


48 


62.41 


16.07 


94 


62.09 


61.99 


139 


61.39 


106.87 


184 


60.46 


151.89 


49 


62.41 


17.08 


95 


62.08 


62.99 


140 


61.37 


107.87 


185 


60.44 


152.89 


50 


62.41 


18.08 


96 


62.07 


63.98 


141 


61.36 


108.87 


186 


60.41 


153.89 


51 


62.41 


19.08 


97 


62.06 


64.98 


142 


61.34 


109.87 


187 


60.39 


154.90 


52 


62.40 


20.08 


98 


62.05 


65.98 


143 


61.32 


110.87 


188 


60.37 


155.90 


53 


62.40 


21.08 


99 


62.03 


66.97 


144 


61.30 


111.87 


189 


60.34 156.90 


54 


62.40 


22.03 


100 


62.02 


67.97 


145 


61.28 


112.86 


190 


60.32 157.91 


55 


62.39 


23.08 


101 


62.01 


68.97 


146 


61.26 


113.86 


191 


60.29 158.91 


56 


62.39 


24.08 


102 


62.00 


69.96 


147 


61.24 


114.86 


192 


60.27 


159.91 


57 


62.39 


25.08 


103 


61.99 


70.96 


148 


61.22 


115.86 


193 


60.25 


160.91 


58 


62.38 


26.08 


104 


61.97 


71.96 


149 


61.20 


116.86 


194 


60.22 


161.92 


59 


62.38 


27.08 


105 


61.96 


72.95 


150 


61.18 


117.86 


195 


60.20 


162.92 


60 


62.37 


28.08 


106 


61.95 


73.95 


151 


61.16 


118.86 


196 


60.17 


163.92 


61 


62.37 


29.08 


107 


61.93 


74.95 


152 


61.14 


119.86 


197 


60.15 


164.93 


62 


62.36 


30.08 


108 


61.92 


75.95 


153 


61.12 


120.86 


198 


60.12 


165.93 


63 


62.36 


31.07 


109 


61.91 


76.94 


154 


61.10 


121.86 


199 


60.10 


166.94 


64 


62.35 


32.07 


110 


61.89 


77.94 


155 


61.08 


122.86 


200 


60.07 


167.94 


65 


62.34 


33.07 


111 


61.88 


78.94 


156 


61.06 


123.86 


201 


60.05 


168.94 


66 


62.34 


34.07 


112 


61.86 


79.93 


157 


61.04 


124.86 


202 


60.02 


169.95 


67 


62.33 


35.07 


113 


61.85 


80.93 


158 


61.02 


125.86 


203 


60.00 


170.95 


68 


62.33 


36.07 


114 


61.83 


81.93 


159 


61.00 


126.86 


204 


59.97 


171.96 


69 


62.32 


37.06 


115 


61.82 


82.92 


160 


60.98 


127.86 


205 


59.95 


172.96 


70 


62.31 


38.06 


116 


61.80 


83.92 


161 


60.96 


128.86 


206 


59.92 


173.97 


71 


62.31 


39.06 


117 


61.78 


84.92 


162 


60.94 


129.86 


207 


59.89 


174.97 


72 


62.30 


40.05 


118 


61.77 


85.92 


163 


60.92 


130.86 


208 


59.87 


175.98 


73 


62.29 


41.05 


119 


61.75 


86.91 


• 164 


60.90 


131.86 


209 


59.84 


176.98 


74 


62.28 


42.05 


120 


61.74 


87.91 


165 


60.87 


132.86 


210 


59.82 


177.99 


75 


62.28 


43.05 


121 


61.72 


88.91 


166 


60.85 


133.86 


211 


59.79 


178.99 


76 


62.27 


43.04 


122 


61.70 


89.91 


167 


60.83 


134.86 


212 


59.76 


180.00 


77 


62.261 


45.04 














1 



Later authorities give figures for the weight of water which differ in the 
second decimal place only from those given above, as follows: 

Temp. F 40 

Lbs. per cu. ft 62.43 

Temp. F 100 

Lbs. per cu. ft.. . 62.00 

Temp. F 160 

Lbs. per cu. ft.. . 61.00 



50 


60 


70 


80 


90 


62.42 


62.37 


62.30 


62.22 


62.11 


110 


120 


130 


140 


150 


61.86 


61.71 


61.55 


61.38 


61.18 


170 


180 


190 


200 


210 


60.80 


• 60.50 


60.36 


60.12 


69.88 



718 



WATER. 



Comparison of Heads of Water in Feet with Pressures in Various 

Units. 

One foot of water at 39.1° Fahr. = 62 425 lbs. on the square foot; 

= 4-335 lbs. on tiie square incti; 
** " " = 0.0295 at-nosphere; 

** *' " = O.SS2j inch ot mercury at 32°; 

« .4 .. ^ y-,Q 3 I feet of air at 32° and 

■ \ at.ajspheric pressure; 
One lb. on the square foot, at 39.1° Fahr. = 0.01G02 foot of water; 
One lb. on the square inch, at 39.1° Faar .. = 2.307 feet of water: 
One atmosphere of 29 . 922 in. of mercury . . = 33 . 9 feet of water; 

One inch of mercury at 32° = 1 . 133 feet of water: 

One foot of air at 32°, and 1 atmosphere. . = 0.001293 feet of water; 

One foot of average sea-water = 1 .028 foot of pure water: 

One foot of water at 62° F = 62.355 lbs. per sq. foot; 

One foot of water at 62° F = 0.43302 lb. per sq. inch; 

One inch of water at 62° F. = .5774 ounce = . 036085 lb. per sq. inch: 
One lb. of water on the square inch at 62° F= 2.3094 feet of water. 
One ounce of water on the square inch at 

62° F = 1 . 732 inches of water. 

Pressure in Pounds per Square Inch for Different Heads of Water. 

At 62° F. 1 foot head = 0.4331b. per square inch. 0.433 X 144 = 62.352 
lbs. per cubic foot. 



Head, feet. 





1 


2 


3 


4 


5 


6 


7 


8 


9 







0.433 


0.866 1.2 9 1.732 2.165 


2.598 


3.031 


3.464 


3.897 


10 


4.330 


4.763 


5.196 5.629 6.0j2 6.495 


6.928 


7.361 


7.794 


8.227 


20 


8.660 


9.093 


9.525 9.959 10.3)2 10.8251 1 .258: 1 1 .691 


12.124 


12.557 


30 


12.9)0 


13.423 


13. 856114.289 14.722 15. 155 15.588 16.021 i 16.454 


16.887 


40 


17.320 


17.753 18.186 18.619 19.052 19.485 19.918 20.351 !20. 784 


21.217 


50 


21.650 


22.083 22.516,22.949 23.382 23.815 24.243 24.681 25. 1 14 


25.547 


60 


25.980 26.413 


26.846 27.279 27.712 28.145 28.578 29.011129.444 


29.877 


70 


30.31030.743 


31 . 176 31 .609 32.042 32.475 32.908 33.341 i33.774i34.207 


80 


34. 640 '35. 073 


35.506 35.939l36.372 36.805 37.238 37.671 138.104 38.537 


90 


38.970,39.403,39.836 40.269:40.702 41 . 135 41 .568 42.001 42. 436|42. 867 



Head in Feet of Water, Corresponding to Pressures in Pounds per 
Square Inch.* 

1 lb. per square inch = 2.30947 feet head, 1 atmosphere = 14.7 lbs. 
per sq. inch = 33.94 ft. head. 



Pressure. 




10 
20 
30 
40 
50 
60 
70 
80 
90 



23.0947 
46.1894 
69.2841 
92.3788: 
115.4735 
138.5682, 
161.66291 
184.7576 
207.8523 



2.309 
25.404 
48.499 
71.594 
94.688 
117.78' 
140.88 
163.97 
187.07 
1210.16 



4.619 6.928 
27.714 30.023 
50.808 53.118 
73.903 76.213 
96.998 99.307 
120.09' 122.40 
143.19|145.50 
166.231168.59 
189.38,191.69 
212.47214.78 



9.238 
32.333 
55.427 
78.522 
101.62 
124.71 
147.81 
170.90 
194.00 
217.09 



11.547 13.857 
34.642 36.952 
57.737 60.046 
80.831 83.141 
103.93 106.24 
127.02 129.33 
150.12 152.42 
173.21 175.52 
196.31 198.61 
219.40 221.71 



16.166 18.476 20.785 
39.261:41.570|43.880 
62.356 64.665 66.975 
85.450,87.760190.069 



108.551110.85 
131.64 133.95 



154.73 
177.83 
200.92 



157.04 
180.14 
203.23 



224.02 226.33 



113.16 
136.26 
159.35 
182.45 
205.54 
228.64 



WATER. 719 

Pressure of Water due to its "VTeight. — The pressure of still water 
in pounds per square inch against the sides of any pipe, channel, or vessel 
of any shape whatever is due solely to the "* head," or height of the 
level surface of the water above the point at which the pressure is con- 
sidered, and is equal to 0.43302 lb. per square inch for every foot of head, 
or 62.355 lbs. per square foot for every foot of head (at 62° F.). 

The pressure per square inch is equal in all directions, downwards, 
upwards, or sideways, and is independent of the shape or size of the 
containing vessel. 

The pressure against a vertical surface, as a retaining-wall, at any 
point is in direct ratio to the head above that point, increasing from at 
the level surface to a maximum at the bottom. The total pressure 
against a vertical strip of a unit's breadth increases as the area of a 
right-angled triangle whose perpendicular represents the height of tlie 
strip and whose base represents the pressure on a unit of surface at the 
bottom: that is, it increases as the square of the depth. The sum oT all 
the horizontal pressures is represented by the area of the triangle, and 
the resultant of this sum is equal to this sum exerted at a point one third 
of the height from the bottom. (The center of gravity of the area of a 
triangle is one third of its height.) 

The horizontal pressure is the same if the surface is inclined instead 
of vertical. 

(For an elaboration of these principles see Trautwine's Pocket-Book, 
or the chapter on Hydrostatics in any work on Physics. For dams, 
retaining-walls, etc., see Trautwine.) 

The amount of pressure on the interior walls of a pipe has no appreci- 
able effect upon the amount of flow. 

Buoyancy. — When a body is immersed in a liquid, whether it float or 
sink, it is buoyed up by a force equal to the weight of the bulk of the 
liquid displaced by the body. The weight of a floating body is equal to 
the weight of the bulk of the liquid that it displaces. The upward 
pressure or buoyancy of the liquid may be regarded^ as exerted at the 
center of gravity of the displaced w^ater, w^hich is called the center of 
pressure or of buoyancy. A vertical hne drawn through it is called the 
axis of buoyancy or of flotation In a floating body at rest a Une joining 
the center of gravity and the center of buoyancy is vertical, and is called 
the axis of equilibrium. When an external force causes the axis of 
equilibrium to lean, if a vertical line be drawn upward from the center 
of buoyancy to this axis, the point where it cuts the axis is called the 
metacerder. If the metacenter is above the center of gravity the distance 
between them, is called the metacentric height, and the body is then said 
to be in stable equiUbrium, tending to return to its original position 
when the external forc3 is removed. 

Boiling-point. — Water boils at 212° F. (100° C.) at mean atmos- 
pheric pressure at the sea-level, 14.696 lbs. per square inch. The tem- 
perature at which water boils at any given pressure is the same as the 
temperature of saturated steam at the same pressure. For boiling-point 
of water at other pressure than 14.696 lbs. per square inch, see table of 
the Properties of Saturated Steam. 

The Boiling-point of Water may be Raised. — When w ater is 
entirely freed of air, which may be accomplished by freezing or boiling, 
the cohe ion of its atoms is greatly increased, so that its temperature 
may be raised over 50° above the ordinary boiling-point before ebullition 
takes place. It was found by Faraday that when such air-freed water 
did boil the rupture of the Uquid was like an explosion. When water 
is surrounded by a film of oil, its boiling temperature may be raised 
considerably above its normal standard. This has been applied as a 
theoretical explanation in the instance of boiler explosions. 

The freezing-point also may be lowered, if the water is perfectly quiet, 
to — 10° C, or 18° Fahrenheit below the normal freezing-point. (Hamilton 
Smith, Jr., on HydrauUcs, p. 13.) 

Freezing-point. — Water freezes at 32° F. at the ordinary atmos- 
pheric pressure, and ice melts at the same temperature. In the melting 
of 1 pound of ice into water at 32° F. about 142 heat-units are absorbed, 
or become latent: and in freezing 1 lb. of water into ice a like quantity 
of heat is given out to the surrounding medium. 

Sea-water freezes at 27° F. The ice is fresh. (Trautwine.) 



720 



WATER. 



Ice and Snow. (From Clark.) — 1 cubic foot of ice at 32° F. weighs 
67.50 lbs.; 1 pound of ice at 32° F. has a volume of 0.0174 cu. ft. = 30 067 
cu. in. 

Relative volume of ice to water at 32° F., 1.0855, the expansion in 
passing into the solid state being 8.55%. Specific gravity of ice = 922 
water at 62° F. being 1. 

At high pressures the melting-point of ice is lower than 32° F., being at 
.the rate of 0.0133° F. for each additional atmosphere of pressure. 

The specific heat of ice s 0.504, that of water being 1. 

1 cubic foot of fresh snow, according to humidity of atmosphere: 
5 lbs. to 12 lbs. 1 cubic foot of snow moistened and compacted by 
ram: 15 lbs. to 50 lbs. (Trautwine.) ^ 

The latent heat of fusion of ice is 143.6 B.T.U. per lb. 

Specific Heat of Water. (From Davis and Marks 's Steam Tables.) 



Deg. Sp. 


Deg. 


Sp. 


Deg. 


Sp. 


Deg. 


Sp. 


Deg. 


Sp. 


Deg. 


Sp. 


F. Ht. 


F. 


Ht. 


F. 


Ht. 


F. 


Ht. 


F. 


Ht. 


F. 


Ht. 


20 1.0168 


120 


0.9974 


220 


1.007 


320 


1.035 


420 


1.072 


520 


1.123 


30 1.0098 


130 


0.9974 


230 


1.009 


330 


1.038 


430 


1.077 


530 


1.128 


40 1.0045 


140 


0.9986 


240 


1.012 


340 


1.041 


440 


1.082 


540 


1.134 


50 1.0012 


150 


0.9994 


250 


1.015 


350 


1.045 


450 


1.086 


550 


1.140 


60 0.9990 


160 


1.0002 


260 


1.018 


360 


1.048 


460 


1.091 


560 


1.146 


70 0.9977 


170 


l.OOIO 


270 


1.021 


370 


1.052 


470 


1.096 


570 


1.152 


80 0.9970 


180 


1.0019 


280 


1.023 


380 


1.056 


480 


1.101 


580 


1.158 


90 0.9967 


190 


1.0029 


290 


1.026 


390 


1.060 


490 


1.106 


590 


1.165 


100 0.9967 


200 


1.0039 


300 


1.029 


400 


1.064 


500 


1.112 


600 


1.172 


110 0.9970 


210 


1.0050 


310 


1.032 


410 


1.068 


510 


1.117 







These figures are based on the mean value of the heat unit, that is, 
Vi80 of the heat needed to raise 1 lb. of water from 32° to 212°. 

Compressibility of Water. — Water is very slightly compressible. 
Its compressibility is from 0.000040 to 0.000051 for one atmosphere, 
decreasing with increase of temperature. For each foot of pressure dis- 
tilled water will be diminished in volume 0.0000015 to 0.0000013. Water 
is so incompressible that even at a depth of a mile a cubic foot of water 
wiU weigh only about half a pound more than at the surface. 



THE I3IPURITIES OF WATER. 

(A. E. Hunt and G. H. Clapp, Trans. A,I. M. E., xvii. 338.) 

Commercial analyses are made to determine concerning a given water: 
(1) its applicability for making steam; (2) its hardness, or the facility 
with which it will "form a lather" necessary for washing; or (3) its 
adaptation to other manufacturing purposes. 

At the Buffalo meeting of the Chemical Section of the A. A. A. S. it 
was decided to report all water analyses in parts per thousand, hundred- 
thousand, and million. 

To convert grains per imperial (British) gallon into parts per 100,000, 
divide by 0.7. To convert parts per 100,000 into grains per U. S. gallon, 
multiply by 0.5835. To convert grains per U. S. gallon into parts per 
miUion multiply by 17.14. 

The most common commercial analysis of water is made to determine 
its fitness for making steam. Water ^containing more than 5 parts per 
100.000 of free sulphuric or nitric acid is liable to cause serious corrosion, 
not only of the metal of the boiler itself, but of the pipes, cylinders, pistons, 
and valves with which the steam comes in contact. 

The total residue in water used for making steam causes the interior 
linings of boilers to become coated, and often produces a dangerous hard 



THE IMPtTEITIES OF WATER. 



721 



scale, which prevents the cooling action of the water from protecting 
the metal against burning. 

Lime and magnesia bicarbonates in water losetheir excess of carbonic acid 
on boiling, and often, especially when the water contains sulphuric acid, 
produce, with the other solid residues constantly being formed by the 
evaporation, a very hard and insoluble scale. A larger amount than 100 
parts per 100,000 of total solid residue will ordinarily cause troublesome 
scale, and should condemn the water for use in steam-boilers, unless a 
better supply cannot be obtained. 

The following is a tabulated form of the causes of trouble with, water 
for steam purposes, and the proposed remedies, given by Prof. L. M. 
Norton. 

Causes of Incrustation. 

1. Deposition of suspended matter. 

2. Deposition of deposed salts from concentration. 

3. Deposition of carbonates of lime and magnesia by boiling off 
carbonic acid, which holds them in solution. 

4. Deposition of sulphates of lime, because sulphate of lime is but 
slightly soluble in cold water, less soluble in hot water, insoluble above 
270° F. 

5. Deposition of magnesia, because magnesium salts decompose at high 
temperature. 

6. Deposition of lime soap, iron soap, etc., formed by saponification of 
grease. 

Means for Preventing Incrustation. 

1. Filtration. 

2. Blowing off. 

3. Use of internal collecting apparatus or devices for directing the 
circulation. 

4. Heating feed-water. 

5. Chemical or other treatment of water in boiler. 

6. Introduction of zinc into boiler. 

7. Chemical treatment of water outside of boiler. 



Tabular View. 



Troublesome Substance. 
Sediment, mud, clay, etc. 
Readily soluble salts. 

Bicarbonates of lime, magnesia, 
iron. 

Sulphate of lime. 

Chloride and sulphate of mag- 
nesium. 

Carbonate of soda in large 
amounts. 

Acid (in mine waters). 

Dissolved carbonic acid and 
oxygen. 

Grease (from condensed w^ater). 
Organic matter (sewage). 



Trouble. Remedy or Palliation. 

Incrustation. Filtration; blowing off. 

" Blowing off. 

J f Heating feed. Addition of 

[ " < caustic soda, lime, or 

' ' magnesia, etc. 

i. (Addition of carb. soda, 

( baium hydrate, etc. 
( Addi ion cf carbonate of 
I soda, etc. 

J Addition of barium chlo- 
( ride, etc. 
Alkali. 

( Feed milk of lime to the 
<l boiler, to form a thin in- 
' ternal coating. 

lPncn?'tat"ion''lI^i^^re"t cases require dif- 
PrifrfnL i lerent remedies. Consult 
) corrosion or f speciaUst on the sub- 
( incrustation.-' ^^^' 



Corrosion. 

Priming. 
Corrosion. 

Corrosion. 



The mineral matters causing the most troublesome boiler-scales are 
bicarbonates and sulphates of lime and magnesia, oxides of iron and 
alumina, and silica. The analyses of some of the most common and 
troublesome boiler-scales are given in the following table: 



722 



WATER. 





.Inalyses of Boiler-scale. ^Chandler. 


) 






Sul- 
phate 

of 
Lime. 


Mag- 
nesia. 


Silica. 


Per- 
oxide 

of 
Iron. 


Water. 


Car- 
bonate 

of 
Lime. 


N.Y.C. 


&H.R.Ry.,No. I 

No. 2 

'; " No. 3 

No. 4 
No. 5 
No. 6 
No. 7 
No. 8 
No. 9 


74.07 

71.37 

62.86 

53.05 

46.83 

30.80 

4.95 

0.88 

4.81 

30.07 


9.19 
■■i8:95" 

"3i.i7' 
2.61 
2.84 


0.65 
1.76 
2.60 
4.79 
5.32 
7.75 
2.07 
0.65 
2.92 
8.24 


0.08 


1.14 


14.78 


;; 


0.92 


1.28 


12.62 


(1 








«« 


1.08 
1.03 
0.36 


2.44 
0.63 
0.15 


26.93 
86.25 
93.19 


INO. lU 1 










1 











Analyses in parts per 100,000 of Water giving Bad Results in 
Steam-boilers. (A. E. Hunt.) 



Coal-mine water. . 

Salt-well 

Spring 

Monongahela River. '. 



)^"o 

*^ 

O ;» 



Allegheny R., near Oil-works '. 



c.S 

C3 O 

c.t: 

O (B 

rO O 



890 590 

3601 990 

310 21 

2101 38 

2l9i 210 

28i 190 

890 I 42 



80 30 



I 



1310 
36 



harm than good^or ^50116? fone of tht wnr^.f n'.^' -'k'I'*' fhesedo more 
acted upon by acids or alkaH^s n^t h;,fHnt^'^''S ^•^^''^ ''■^^'' ^^hi^h is not 



PURIFYING WATER. 



723 



Hardness of TTater. — The hardness of water, or its opposite quality, 
indicated by the ease with which it will form a lather with soap, depends 
almost altogetiier upon t jo presence of compounds of lime and masmesia. 
Almost ail soaps coii.^i t, cliemically, of oleate, stearate, and palmitate of 
rn alicaliie base, usuah/ soda and potash. The more lime and magnesia 
in a sample of water, t>ie more soap a given volume of the wate^^r will 
decompose, so as to give insoluble oleate, palmitate, and stearate of 
lime an 1 magnesia, an I consequently the more soap must be added in 
order that the nece.-sary q-iantity of soap may remain in solution to 
f jr n the lather. The relative hardness of samples of water is generally 
expressed in terms of the number of standard soap-measures consumed 
by a gallon of water in yielding a permanent lather. 

In Great Britain the standard soap-measure is the quantity required to 
pre ipitate one g"ii:i of carbonate of lime: in the L'. S. it is the quantity 
required to precipitate one milUgramme. 

If a water charged with a bicarbonate of lime, magnesia, or iron 
is boiled, it will, on the excess of the carbonic acid being expelled, 
deposit a considerable qiantity of the lime, magnesia, or iron, and con- 
sequently the water will be softer. The hardness of the water after 
this deposit of lime, after long boiling, is called the perfnane?it hardness 
and the difference between it and the total hardness is called temporary 
ha.'driess. 

Lime salts in water react immediately on soap-solutions, precipitating 
the oleate, palmitate, or stearate of lime at once. Magnesia salts, on the 
contrary, require some considerable time for reaction. They are, how- 
ever, more powerful hardeners; one equivalent of m.agnesia salts con- 
suming as mmch soap as one and one-half equivalents of lime. 

The presence of soda and potash salts softens rather than hardens 
water. Each grain of carbonate of lime per gallon of water causes an 
increased expenditure for soap of about 2 ounces per 100 gallons of w^ater. 
{Eng'g News, Jan. 31, 1885.) 

Low degrees of hardness (down to 200 parts of calcium carbonate 
(CaCOs) per million) are usually determined by means of a standard 
solution of soap. To 50 c.c. of the water is added alcoholic soap solu- 
tion from a burette, shaking well after each addition, until a lather is 
obtained which covers the entire surface of the liquid when the bottle is 
laid on its side and which lasts five minutes. From the number of c.c. 
of soap solution used, the hardness of the water may be calculated by 
the use of Clark's table, given below, in parts of CaCOa per miUion. 



c.c. Soap 
Sol. 


Pts. 

CaCOs. 


c.c. Soap 
Sol. 


Pts. 
CaCOs. 


c.c. Soap 
Sol. 


Pts. 
CaCOs. 


c.c. Soap 
Sol. 


Pts. 
CaCOs. 


0.7 

I.O 




5 

19 

32 


4.0 

5.0 

6.0 

7.0 


46 

60 

74 

89 


8.0 

9.0 


103 

. .118 


12.0 

13.0 

14.0 

15.0 


164 

180 


2.0 

3.0 


10.0 

11.0 


133 

148 


196 

212 



For waters which are harder than 200 parts per million, a solution of 
soap ten times as strong may be used, the end or determining point being 
reached when sufficient soap has been added to deaden the harsh sound 
produced on shaking the bottle containing the water. — A. H. Gill, En- 
gine-Room Chemistry. 

Purifying: Feed-water for Steam-boilers. (See also Incrustation 
and Corrosion, p. 927 J — When the water used for steam-boilers con- 
tains a large amount of scale-forming material it is usually advisable to 
purify it before allowing it to enter the boiler rather than to attempt the 
prevention of scale by the introduction of chemicals into the boiler. 
Carbonates of lime and magnesia may be removed to a considerable 
extent by simple heating of the water in an exhaust-steam feed-water 
heater or, still better, by a live-steam heater. (See circular of the Hoppes 
Mfg. Co., Springfield, O.) When the water is very bad it is best treated 



724 WATER. 

with chemicals — lime, soda-ash, caustic soda, etc. --in tanks, the pre- 
cipitates being separated by settling or filtering. For a description ol 
several systems of water purification see a series of articles on the sub- 
ject by Albert A. Gary in Eng'g Mag., 1897. 

Mr. H. E. Smith, chemist of the Chicago, Milwaukee & St. Paul Ry. 
Co., in a letter to the author, June, 1902, writes as follows concerning 
the chemical action of soda-ash on the scale-forming substances in boiler 
waters: 

Soda-ash acts on carbonates of lime and magnesia in boiler water in the 
following manner: — The carbonates are held in solution by means of 
the carbonic acid gas also present which probably forms bicarbonates of 
lime and magnesia. Any means wiiich will expel or absorb this carbonic 
acid will cause the precipitation of the carbonates. One of these means 
is soda ash (carbonate of soda), which absorbs the gas with the forma- 
tion of bicarbonate of soda. This method would not be practicable for 
softening cold water, but it serves in a boiler. The carbonates precipi- 
tated in this manner are in flocculent condition instead of semi-crystalline 
as when thrown down by heat. In practice it is desirable and sufficient 
to precipitate only a portion of the lime and magnesia in flocculent 
condition. As to equations, the following represent what occurs; — 

Ca (HC03)2 +- Na2C03 = CaCOa 4- 2 NaHCOa. 
Mg (HCOs)a + Na2C03 = MgCOa 4- 2 NaHCOa. 
(free) CO2 + Na2C03 + H2O = 2 NaHCOa. 

Chemical equivalents: — 106 pounds of pure carbonate of soda — 
equal to about 109 pounds of commercial 58 degree soda-ash — are 
chemically equivalent to -^ i.e., react exactly with — the following 
weights of the substances named: Calcium sulphate, 136 lbs.; magnesium 
sulphate, 120 lbs.; calcium carbonate, 100 lbs.; magnesium carbonate, 
84 lbs.; calcium chloride, 111 lbs.; magnesium chloride, 95 lbs. 

Such numbers are simply the molecular w^eights of the substances 
reduced to a common basis with regard to the valence of the component 
atoms. 

Important work in this line should not be undertaken by an amateur. 
"Recipes" have a certain field of usefulness, but will not cover the whole 
subject. In water purification, as in a problem of mechanical engineer- 
ing, methods and apparatus must be adapted to the conditions presented. 
Not only must the character of the raw w^ater be considered but also the 
conditions of purification and use. 

Water-softening Apparatus. (From the Report of the Committee 
on Water Service, of the Am. Railway Eng'g and Maintenance of Way 
Assn., Eng. Rec, April 20, 1907). — Between three and four hours is nec- 
essary for reaction and precipitation. Water taken from running streams 
in winter should have at least four hours' time. At least three feet of 
the bottom of each settling tank should be reserved for the accumulation 
of the precipitates. 

The proper capacities for settling tanks, measured above the space 
reserved for sludge, can be determined as follows: a == capacity of soft- 
ener in gallons per hour; b = hours required for reaction and precipitation; 
c = number of settling tanks (never less than two); x = number of 
hours required to fill the portion of settling tank above the sludge portion; 
y = number of hours required to transfer treated w^ater from one settling 
tank to the storage tank (y should never be greater than x). 

Where one pump alternates between filling and emptying settling 
tanks, X = y. Settling capacity in each tank= 2 ax = ab -i- {c — 1). 

For plants where the quantity of water supplied to the softener and the 
capacity of the plant are equal, the settling capacity of each tank is equal 
to ax. The number of hours required to fill all the settling tanks should 
equal the number of hours required to fill, precipitate and empty one 
tank, as expressed by the following equation: ex =* x ■{• b + y. 

If y = x, ax = ab -^ (c — 2). 

If J/ =- 1/2 X, ax = ab + {c — 1.5). 



PTJBIFYING WATER. 



725 



An article on "The Present Status of Water Softening," by G. C. 
Whipple, in Cass. Mag., Mar., 1907, illustrates several different forms of 
water-purifying apparatus. A classification of degrees of hardness cor- 
responding to parts of carbonates and sulphates of lime and magnesia 
per milhon parts of water is given as follows: Very soft, to 10 parts; 
soft, 10 to 20; shghtly hard, 25 to 50; hard, 50 to 100; very hard, 100 to 
200; excessively hard, 200 to 500; mineral water, 500 or more. The 
same article gives the following figures showing the quantity of chemicals 
required for the various constituents of hard water. For each part per 
miUion of the substances mentioned it is necessary to add the stated 
number of pounds per million gallons of lime and soda. 



For Each Part per Million of 



Free CO2 

Free acid (calculated as H2SO4) 

Alkalinity 

Incrustants 

Magnesium 



Pounds per Million 


Gallons. 


Lime. 


Soda. 


10.62 





4.77 


9.03 


4.67 





0.00 


8.85 


19.48 






The above figures do not take into account any impurities in the 
chemicals. These have to be considered in actual operation. 

An illustrated description of a water-purifying plant on the Chicago 
& Northwestern Ry. by G. M. Davidson is found in Eng. News, April 2, 
1903. Two precipitation tanks are used, each 30 ft. diam., 16 ft. high, 
or 70,000 gallons each. As some water is left with the sludge in the 
bottom after each emptying, their net capacity is about 60,000 gallons 
each. The time required for filling, precipitating, settling and trans- 
ferring the clear water to supply tanks is 12 hours. Once a month the 
sludge is removed, and it is found to make a good whitewash. Lime and 
soda-ash, in predetermined quantity, as found by analysis of the water, 
are used as precipitant s. The following table shows the effect of treat- 
ment of well water at Council Bluffs, Iowa. 



Total solid matter, grains per gallon 

Carbonates of lime and magnesia 

Sulphates of lime and magnesia 

Silica and oxides of iron and aluminum . . 

Total incrusting solids 

Alkali chlorides. - 

Alkali sulphates 

Total non-incrusting solids. 

Pounds scale-forming matter in 1000 gals. 




The minimum amount of scaling matter which will justify treatment 
cannot be stated in terms of analysis alone, but should be stated in terms 
of pounds incrusting matter held in solution in a day's supply. Besides 
the scale-forming solids, nearly all water contains more or less free car- 
bonic acid. Sulphuric acid is also found, particularly in streams adjacent 
to coal mines. Serious trouble from corrosion will result from a small 
amount of this acid. In treating waters, the acids can be neutralized, 
and the incrusting matter can be reduced to at least 5 grains per gallon in 
most cases. 



726 



HYDRAULICS. 



QUANTITT OF PURE ReaGEXTS REQUIRED TO ReMO.T: OnE PoUND OF 
IXCRUSTING OR CORRQSIVE MaTTER FROM THE W ATER 

Incrusting or Corrosive ' 
Substance Held in 
Solution. 



Sulphuric acid 

Free carbonic acid . . , . 

Calcium carbonate 

Calcium sulphate 

Calcium chloride 

Calcium nitrate 

Magnesium carbonate. 
Magnesium sulphate. . , 
Magnesium chloride. . . 
Magnesium nitrate 



Amount of Reagent. (Pure.) 



Calcium carbonate 

Magnesium carbonate. . 

Magnesium sulphate 

*Calcium sulphate 



0.571b. lime plus 1.08 lbs. soda ash 

1 .2/ lbs. lime 

0.56 lb. lime 

0. 78 lb. soda ash. 

0.96 lo. soda ash 

0.65 lb. soda ash 

1 .33 los. lime 

0.47 lb. lime plus 0. 88 lb! soda ash.' 

0.38 lb. hme plus 0.72 lb. soda ash. 

1.71 lbs. barium hydrate 

4.05 lbs. barium hydrate. . . . . . 

1 .42 lbs. barium hydrate . .' ! .' . .' ' ' " 
1 .26 lbs. barium hydrate ...... 



Foaming Mat- 
ter Increased. 



1.45 lbs. 

None 

None 

1.04 lbs. 

1.05 lbs. 
1.04 lbs. 
None 
1.18 lbs. 
1.22 lbs. 
1.15 lbs. 

None 
None 
None 
None 



tated 



t^ Ff m^'nf i^f -^^^ "^^^^^^^ sulphate, there would also be 
tea U./4 lb. ot calcium carbonatP nr n qi IK ^f _„ .„„/7^^'-' '-'^ 



precipi- 



reduced. ^ treatment can be correspondingly 

m connection with the t^eatin1T.\ter^'o'^ning^'3o'ir ^ul^Lte?'^* 

HYDRAULICS -FLOW OF WATER. 

FoT"/e?;^^„llro?ifr^uYaf orfflc'^"l^fth**JK.^.«'-'««^ ''."'» "^<''-. - 
Of the orifice to the surface '^s^i^l^ infteTel^'l^lVelT.^r'' 

Q = C^2gI{Xa ",, 

fpVachf ^'"^ "° allowancejor increased head due to Veloci'ty of 

Q = C2/3V2gHXLH. . . ,„> 

f^o°r?n\fl^a'a^^on"fhetrotositTon°\'],\?et'5flT^^^ °h^ "-""^'^' ""fi^S 
water passing throu.i? r^'oS\^-£^X,?™e'^'?^'^llf ^^^^^^^^^^ 

Q =cL2/3V2gx (V///.3 _ Vjnj ,.. 

i* or rectangular vertical weirs J ^^ 

^_ Q =c2/sV2gHXLh. . . . ,. 

p?ximar?^i^cienrfo'r' fcJ^^Yafll? a'nt'?/^ ^^^ ^^^^^^ '^ = apl 
for (3) and (4). lormuias (1) and (2): c = correct coefficient 

Values Of the^c^ffidents c and C are given below 

off:. Vh 1 ^"'' ■'¥ ^^''=''^-i^^-=^1-rhor:^^ o1 

vfodtyf/a^p'rrch'rryrrssT V2°T" ' = ^'.^""^^'^^ ^- 
traction and^ + 14 v 2/ont ^a(2gtoi weirs with no end con- 

square f;et if length Kee' """ "''' ^"' contraction: a= area in 



HYDRAULICS. 



727 



Flow of Water from Orifices. — The theoretical velocity of water 
flowing from an orifice is the same as the velocity of a falling body which 
has fallen from a height equal to the head of water, = V2 gH. The 
actual velocity at the smaller section of the vena contracta is substan- 
tially the sam e as the theoretical, but the velocity at the plane of the 
orifice is C ^2 gH, in which the coefficient C has the nearly constant 
value of 0.62, The smallest diameter of the vena contracta is therefore 
about 0.79 of that of the orifice. If C be the approximate coefficient 
= 0.62, and c the correct coefficient, the ratio C /c varies with different 
ratios of the head to the diameter of the vertical orifice, or to H/D. Ham- 
ilton Smith, Jr., gives the following: 

H/D=0.5 0.875 1. 1.5 2. 2.5 5. 10. 

C/c =0.9604 0.9849 0.9918 0.9965 0.9980 0.9987 0.9997 1. 

For vertical rectangular orifices of ratio of head to width W; 

For H/W= 0.5 0.6 0.8 1 1.5 2. 3. 4. 5. 8. 

C/c = .9428 .9657 .9823 .9890 .9953 .9974 .9988 .9993 .9996 .9998 

For H -i- D OT H -T- W over S, C =-- c, practically. 

For great heads, 312 ft. to 336 ft., with converging mouthpieces, c 
has a value of about one, and for small circular orifices in thin plates, 
with full contraction, c = about 0.60. 

Mr. Smith as the result of the collation of many experimental data of 
others as well as his own, gives tables of the value of c for vertical orifices, 
with full contraction, with a free discharge into the air, with the inner 
face of the plate, in which the orifice is pierced, plane, and with sharp 
inner corners, so that the escaping vein only touches these inner edges. 
These tables are abridged below. The coefficient c is to be used in the 
formulae (3) and (4) above. For formulae (1) and (2) use the coeflficient 
C found from the values of the ratios C/c above. 



Values of Coefficient c for Vertical Orifices with Sharp !Edi?es, 
Full Contraction, and Free Discharge into Air. (Hamilton 
Smith, Jr.) 





Square Orifices 


. Length of the Side of the Square, in feet 




*> fl3 E 


.02 


.03 


.04 


.05 


.07 


.10 


.12 


.15 


.20 


.40 


.60 


.80 


1.0 


Woo 




























0.4 






.643 
.636 


.637 
.630 


.628 
.623 


.621 
.617 


.616 
.613 


.611 
.610 












0.6 


.660 


.645 


.605 


.601 


.598 


.596 




1.0 


.648 


.636 


.628 


.622 


.618 


.613 


.610 


.608 


.605 


.603 


.601 


.600 


.599 


3.0 


.632 


.622 


.616 


.612 


.609 


.607 


.606 


.606 


.605 


.605 


.604 


.603 


.603 


6.0 


.623 


.616 


.612 


.609 


.607 


.605 


.605 


.605 


.604 


.604 


.603 


.602 


.602 


10. 


.616 


.611 


.608 


.606 


.605 


.604 


.604 


.603 


.603 


.603 


.602 


.602 


.001 


20. 


.606 


.605 


.604 


.603 


.602 


.602 


.602 


.602 


.602 


.601 


.601 


.601 


.600 


100. (?) 


.599 


.598 


.598 


.598 


.598 


.598 


.598 


.598 


.598 


.598 


.598 


.598 


.598 









Circuk 


irOri 


fices. 


Dial 


neter 


s, in feet. 








H. 


.02 


.03 


.04 


.05 

.637 

.624 


.07 


.10 


.12 

.612 

.609 


.15 


.20 


.40 


.60 


.80 


1.0 


4 








.628 
.618 


.618 
.613 


.606 
.605 










0.6 


.655 


.640 


.630 


.601 


.596 


.593 


.590 




1.0 


.644 


.631 


.623 


.617 


.612 


.608 


.605 


.603 


.600 


.598 


.595 


.593 


.591 


2. 


.632 


.621 


.614 


.610 


.607 


.604 


.601 


.600 


.599 


.599 


.597 


.596 


.595 


4. 


.623 


.614 


.609 


.605 


.603 


.602 


.600 


.599 


.599 


.598 


.597 


.597 


.596 


6. 


.618 


.611 


.607 


.604 


.602 


.600 


.599 


.599 


.598 


.598 


.597 


.596 


.596 


10. 


.611 


.606 


.603 


.601 


.599 


.598 


.598 


.597 


.597 


.597 


.596 


.596 


.595 


20. 


.601 


.600 


.599 


.598 


.597 


.596 


.596 


.596 


.596 


.596 


.596 


.595 


.594 


50.(?) 


.596 


.596 


.595 


.595 


.594 


.594 


.594 


.594 


.594 


.594 


.594 


.593 


.593 


100. (?) 


.593 


.593 


.592 


.592 


.592 


.592 


.592 


.592 


.592 


.592 


.592 


.592 


.592 



I 



728 HYDRAULICS. 



HYDRAULIC FORMULA. — FLOW OF WATER IN OPEN AND 
CLOSED CHANNELS. 

Flow of Water in Pipes. — The quantity of water discharged 
through a pipe depends on the "head"; that is, the vertical distance 
between the level surface of still water in the chamber at the entrance 
end of the pipe and the level of the center of the discharge end of the 
pipe: also upon the length of the pipe, upon the character of its interior 
surface as to smoothness, and upon the number and sharpness of the 
bends: but it is independent of the position of the pipe, as horizontal, 
or inclined upwards or downwards. 

The head, instead of being an actual distance between levels, may be 
caused by pressure, as by a pump, in which case the head is calculated 
as a vertical distance corresponding to the pressure, 1 lb. per sq. in. 
= 2.309 ft. head, or 1 ft. head = 0.433 lb. per sq. in. 

The total head operating to cause flow is divided into three parts: 

1. The velocity -head, which is the height through which a body must 
fall in vacuo to acquire the velocity with which the water flows into the 
pipe = i;2 ^ 2 9', in which v is the velocity in ft. per sec. and 2 g = 64.32; 

2. the entry-head, that required to overcome the resistance to entrance 
to the pipe. With sharp-edged entrance the entry-head = about 1/2 the 
velocity-head; with smooth rounded entrance the entry-head is inap- 
preciable; 3. the friction-head, due to the frictional resistance to flow 
within the pipe. 

In ordinary cases of pipes of considerable length the sum of the entry 
and velocity heads required scarcely exceeds 1 foot. In the case of 
long pipes with low heads the sum of the velocity and entry heads is 
generally so small that it may be neglected. 

General Formula for Flow of Water in Pipes or Conduits, 



Mean velocity in ft. per sec. = c v^mean hydraulic radius X slope 



Do. for pipes running full = c V ;; X slope, 



^diameter , 



In which c is a coefficient determined by experiment. (See pages following.) 

area of wet cross-section 



The mean hydraulic radius = ■ 



wet perimeter 



In pipes running full, or exactly half full, and in semicircular open 
channels running full it is equal to 1/4 diameter. 

The slope = the head (or pressure expressed as a head, in feet) 

-^ length of pipe measured in a straight line from end to end. 

In open channels the slope is the actual slope of the surface, or its 
fall per unit of length, or the sine of the angle of the slope with the horizon. 

Chezy's Formula: v = c^r^s = c Vrs; r = mean hydraulic 
radius, s = slope = head -^ length, v = velocity in feet per second, all 
dimensions in feet. 

Quantity of Water Discharged. — If Q = discji^arge in cubic feet 
per second and a = area of channel, Q = av = ac ^rs. 

a Vr is approximately proportional to the discharge. It is a maxi- 
mum at 308^ of the circumference, corresponding to i9/20 of the diameter, 
and the flow of a conduit 19/20 full is about 5 per cent greater than that of 
one completely filled. 

Values of the Coefficient c. (Chiefly condensed from P. J. Flynn 
on Flow of Water.) — Almost all the old hydraulic formulae for finding the 



HYDRAULIC FORMULiB. 



729 



mean velocity in open and closed channels have constant coefficients, 
and are therefore correct for only a small range of channels. They 
have often been found to give incorrect results with disastrous effects. 
Ganguillet and Kutter thoroughly investigated the American, French, 
and other experiments, and they gave as the result of their labors the 
formula now generally known as Kutter's formula. There are so many 
varying conditions affecting the flow of water, that all hydrauUc for- 
mulcie are only approximations to the correct result. 

When the surface-slope measurement is good, Kutter's formula will 
give results seldom exceeding 71/ 2% error, provided the rugosity co- 
efficient of the formula is known for the site. For small open channels 
Darcy's and Bazin's formulae, and for cast-iron pipes Darcy's formulae, 
are generally accepted as being approximately correct. 



Table giving Fall in Feet per Mile, the Distance on Slope corresponding 
to 1 Ft. Fall, the Fall in 1000 Ft., the Equivalent Loss in Pressure 
in Pipes per 1000 Ft. Length; also Values of Vs for Use in the 
Formula v = c \/rs. 

s = H -^ L = sine of angle of slope = fall of water surface (H) 
in any distance (L) divided by that distance. 









Loss of 










Loss of 




Fall 




Slope, 


Pres- 




Fall 




Slope, 


Pres- 




in 


Slope, 


Feet 


sure per 




in 


Slope, 


Feet 


sure per 




Feet 


1 Ft. 


1000. 


1000 


vr 


Feet 


1 Ft. 


per 
1000. 


1000 


vr 


per 


In 


Feet. 




per 


In 


Feet. 




Mile. 






Lb. per 

sq. in. 




Mile. 






Lb. per 
sq. in. 




0.25 


21120 ft. 


0.0473 


0.02048 


0.00688 


20 


264 ft. 


3.7879 


1.640 


0.06155 


.30 


17600 


.0568 


.02459 


.00754 


21.12 


250 


4.0000 


1.732 


.06325 


.40 


13200 


.0758 


.03282 


.00870 


22 


f240 


4.1667 


1.804 


.06455 


.50 


10560 


.0947 


.04101 


.00973 


24 


220 


4.5455 


1.968 


.06742 


.60 


8800 


.1136 


.04919 


.01066 


26.4 


200 


5.0000 


2.165 


.07071 


.80 


6600 


.1515 


.06560 


.01231 


28 


188.6 


5.3030 


2.296 


.07282 




5280 


.1894 


.08201 


.01376 


31.68 


166.7 


6.0000 


2.598 


.07746 


1.056 


5000 


.2000 


.08660 


.01414 


35.20 


150 


6.6667 


2.887 


.08165 


1.25 


4224 


.2367 


.1025 


.01539 


42.24 


125 


8.0000 


3.464 


.08944 


1.5 


3520 


.2841 


.1230 


.01685 


44 


120 


8.3333 


3.608 


.09129 


1.75 


3017 


.3314 


.1435 


.01821 


48 


110 


9.0909 


3.936 


.09535 


2 


2640 


.3788 


.1640 


.01946 


52.8 


100 


10.000 


4.330 


.10000 


2.5 


2112 


.4735 


.2050 


.02176 


60 


88 


11.364 


4.913 


.10660 


2.64 


2000 


.5000 


.2165 


.02236 


63.36 


83.3 


12.000 


5.196 


.10954 


3 


1760 


.5682 


.2460 


.02384 


66 


80 


12.500 


5.413 


.11180 


3.5 


1508 


.6631 


.2871 


.02575 


70.4 


75 


13.333 


5.773 


.11547 


4 


1320 


.7576 


.3280 


.02752 


79.20 


66.7 


15.000 


6.495 


.12247 


5 


1056 


.9470 


.4101 


.03077 


88 


60 


16.667 


7.217 


.12910 


5.28 


1000 


1.0000 


.4330 


.03162 


105.6 


50 


20.000 


8.660 


.14142 


6 


880 


1.1364 


.4921 


.03371 


120 


44 


22.727 


9.841 


.15076 


7 


754.3 


1.3257 


.5740 


.03642 


132 


40 


25.000 


10.83 


.15811 


8 


660 


1.5152 


.6561 


.03893 


160 


33 


30.303 


13.12 


.17408 


9 


586.6 


1.7044 


.7380 


.04129 


220 


24 


41.667 


18.04 


.20412 


10 


528 


1.8939 


.8201 


.04352 


264 


20 


50.000 


21.65 


.22361 


10.56 


500 


2.0000 


.8660 


.04472 


330 


16 


62.500 


27.06 


.25000 


12 


440 


2.2727 


.9841 


.04767 


440 


12 


83.333 


36.08 


.28868 


13 


406.1 


2.4621 


1.066 


.04962 


528 


10 


100.00 


43.30 


.31623 


14 


377.1 


2.6515 


1.148 


.05149 


660 


8 


125.00 


54.13 


.35355 


15 


352 


2.8409 


1.230 


.05330 


880 


6 


166.67 


72.17 


.40825 


16 


330 


3.0303 


1.312 


.05505 


1056 


5 


200 


86.60 


.44721 


18 


293.3 


3.4091 


1.476 


.05839 


1320 


4 


250 


108 25 


.50000 



730 



HYDRAULICS. 



Values of Vr for Circular Pipes, Sewers, and Coualuits of Different 
Diameters. 



r = mean hydraulic depth = ^^~^^= Vi diam. for circular pipes 
running full or exactly half full. 



Kutter's Formula for measures in feet is 



1.811 



+ 41.6 + 



0.00281 



V -=j 



1 + (41.6 + 



0.00281> 



[x'^. 



Vr) 



Diam., 


vr 


Diam., 


vr 


Diam.. 


v; 


Diam. 


vC 


ft. in. 


in Feet. 


ft. 


in. 


in Feet. 


ft. 


in. 


in Feet. 


ft. in'.* 


in Feet. 


3/8 
1/2 


0.088 
.102 


2 
2 


1 


0.707 

.722 




6 

7 


1.061 
1.070 


9 
9 3 


1.500 
1.521 
1.541 
1.561 
1.581 
1.601 
1.620 
1.639 
1.658 
1.677 
1.696 
1 714 


3/4 


.125 


2 


2 


.736 




8 


1.080 


9 6 


1 
11/4 


.144 
.161 


2 
2 


3 

4 


.750 
.764 




9 
10 


1.089 
1.099 


9 9 
10 


11/9 


.177 


2 


5 


.777 




11 


1.109 


10 3 


13/; 


.191 


2 


6 


.790 






1.118 


10 6 


2 

21/2 


.204 

.228 


2 
2 


7 
8 


.804 
.817 




i 
2 


1.127 
1.137 


10 9 
11 


3 


.251 


2 


9 


.829 




3 


1.146 


11 3 


4 


.290 


2 


10 


.842 




4 


1.155 


11 6 


5 


.323 




11 


.854 




5 


1.164 


11 9 


6 


.354 






.866 




6 


1.173 


12 


1^732 

1.750 

1.768 

1.785 

1.803 

1.820 

1.837 

1.871 

1.904 

1.936 

1.968 

2. 

2 031 

2.061 

2.091 

2.121 

2.180 

2.236 


7 


.382 




1 


.878 




7 


1.181 


12 3 


8 


.408 




2 


.890 




8 


1.190 


12 6 


9 


.433 




3 


.901 




9 


1.199 


12 9 


10 


.456 




4 


.913 




10 


1.208 


13 


11 

1 
1 1 


.479 
.500 
.520 




5 
6 
7 


.924 
.935 
.946 


6 
6 


11 
3 


1.216 
1.225 
1.250 


13 3 
13 6 
14 


1 2 


.540 




8 


.957 


6 


6 


1.275 


14 6 


1 3 


.559 




9 


.968 


6 


9 


1.299 


15 


1 4 
1 5 


.577 
.595 




10 
11 


.979 
.990 


7 
7 


3 


1.323 
1.346 


15 6 
16 


1 6 
1 7 
1 8 
1 9 
1 10 
1 11 


.612 
.629 
.646 
.661 
.677 
.692 




1 

2 
3 
4 
5 


1. 

1.010 

1.021 

1.031 

1.041 

1.051 


7 
7 
8 
8 
8 
8 


6 
9 

3 

6 

9 


1.369 
1.392 
1.414 
1.436 
1.458 
1.479 


16 6 
17 

17 6 
18 

19 
20 



in which v = mean velocity in feet per second; r= - = hydraulic mean 
depth in feet = area of cross-section in square feet divided by wetted 
perimeter in hneal feet; s = fall of water-surface (fi) in any distance (i) 
divided by that distance, =p= sine of slope; n = the coefficient of 

if wl'llt ?h?Tr^}Tprm nf ^f h^^^'^'g.'^t ^^§ ^^"^"^ «^ s^^f^^^ «f the channel. 
It we let the hrst term of the nght-hand side of the equation equal c, we 

have Chezy's formula, v = c ^rs = c X ^X^*7. 

miTf nTnpn'n^ "Jj o ^"V^'''^ Formula. —The accuracy of Kutter's for- 
mula depends, in a great measure, on the proper selection of the coefficient 



HYDRAULIC FORMULA. 731 

of roughness n. Experience is required in order to give the right value to 
this coefficient, and to this end great assistance can be obtained, in making 
this selection, by consulting and comparing the results obtained from 
experiments on the how of water already made in different channels. 

In some cases it would be weU to provide for the contingency of future 
deterioration of channel, by selecting a high value of n, as, for instance, 
where a dense growth of weeds is likely to occur in small channels, and 
also where channels are likely not to be kept in a state of good repair. 

The following table, giving the value of n for different materials, is 
compiled from Kutter, Jackson, and Hering, and this value of n applies 
also in each instance to the surfaces of other materials equaUy rough. 

Value of n in Kutter's Foraiula for Different Channels. 

n = .009, well-planed timber, in perfect order and alignment; otherwise, 
perhaps .01 would be suitable. 

n = .010, plaster in pure cement; planed timber; glazed, coated, or 
enameled stoneware and iron pipes; glazed surfaces of every sort in 
perfect order. 

n = .011, plaster in cement with one-third sand, in good condition; 
also for iron, cement, and terra-cotta pipes, well joined, and in best order. 

n = .012, unplaned timber, when perfectly continuous on the inside; 
flumes. 

n = .013, ashlar and well-laid brickw^ork; ordinary metal; earthen and 
stoneware pipe in good condition, but not new; cement and terra-cotta 
pipe not well jointed nor in perfect order, plaster and planed wood in 
imperfect or inferior condition; and, generally, the materials mentioned 
with n = .010, when in imperfect or inferior condition. 

n = .015, second class or rough-faced brickwork; well-dressed stone- 
work; foul and slightly tuberculated iron; cement and terra-cotta pipes, 
with imperfect joints and in bad order; and canvas lining on wooden 
frames. 

n = .017, brickwork, ashlar, and stonew^are in an inferior condition; 
tuberculated iron pipes; rubble in cement or plaster in good order; hue 
gravel, well rammed, i/3 to 2/3 inch diameter; and, generally, the materials 
mentioned with n = .013 when in bad order and condition. 

n = .020, rubble in cement in an inferior condition; coarse rubble, 
rough set in a normal condition; coarse rubble set dry: ruined brickwork 
and masonry; coarse gravel well rammed, from 1 to IVs inch diameter; 
canals with beds and banks of very firm, regular gravel, carefully trimmed 
and rammed in defective places; rough rubble with bed partially covered 
with silt and mud; rectangular wooden troughs with battens on the 
inside two inches apart; trimmed earth in perfect order. 

n = .0225, canals in earth above the average in order and regimen. 

n = .025, canals and rivers in earth of tolerably uniform cross-section; 
slope and direction, in moderately good order and regimen, and free from 
stones and w^eeds. 

n = ,0275, canals and rivers in earth below the average in order and 
regimen. 

n = .030, canals-^nd rivers in earth in rather bad order and regimen, 
having stones and weeds occasionally, and obstructed by detritus. 

n = .035, suitable for rivers and canals with earthen beds in bad order 
and regimen, and having stones and weeds in great quantities. 

n = .05, torrents encumbered with detritus. 

Kutter's formula has the advantage of being easily adapted to a change 
in the surface of the pipe exposed to the flow of water, by a change in 
the value of n. For cast-iron pipes it is usual to use n ■■= .013 to provide 
for the future deterioration of the surface. ^ __ 

Reducing Kutter's formula to the form v = cX ^r X ^s, and taking 
n, the coefficient of roughness in the formula, = .011, .012, and .013. and 
s ■= .001, w^e have the following values of the coefficient c of different 
diameters of conduit. 



732 



HYDRAULICS. 



Values of c in Formula v = c x^rx ^s for Metal Pipes and 
Moderately Smooth Conduits Generally. 

By Kutter's Formula, (s =0.001 or greater.) 



Diameter. 


n = .011 


n=.012 


n = .013 


Diameter. 


n=.011 


n = .012 


n=.013 


ft. in. 


c = 


c = 


c = 


ft. 


c = 


c = 


c = 


6 


87.4 


77.5 


69.5 


8 


155.4 


141.9 


130.4 


1 


105.7 


94.6 


85.3 


9 


157.7 


144.1 


132.7 


1 6 


116.1 


104.3 


94.4 


10 


159.7 


146 


134.5 


2 


123.6 


111.3 


101.1 


11 


161.5 


147.8 


136.2 


3 


133.6 


120.8 


IIO.I 


12 


163 


149.3 


137.7 


4 


140.4 


127.4 


116.5 


14 


165.8 


152 


140.4 


5 


145.4 


132.3 


121.1 


16 


168 


154.2 


142.1 


6 


149.4 


136.1 


124.8 


18 


169.9 


156.1 


144.4 


7 


152.7 


139.2 


127.9 


20 


171.6 


157.7 


146 



For circular pipes the hydraulic mean depth r equals V4 of the 
diameter. 

According to Kutter's formula the value of c, the coefficient of 
discharge, is the same for all slopes greater than 1 in 1000. At a 
slope of 1 in 5000 the value of c is slightly lower, and it further 
decreases as the slope becomes flatter. 

The reliability of the values of the coefficient of Kutter's formula for 
pipes of less than 6 in. diameter is considered doubtful. 

Values of c ror Earthen Channels, by KuUer's Formula, foy Use 
in Formula i? = c ^r§. 





Coefficient of Roughness, 


Coefficient of Roughness. 






n=.0225. 


n=.035. 




v^ in feet. 


v^r in feet. 




0.4 


1.0 


1.8 


2.5 


4.0 


0.4 


1.0 


1.8 

c 


2.5 


4.0 


Slope, 1 in 


c 


c 


c 


c 


c 


c 


c 


c 


c 


1,000 


35.7 


62.5 


80.3 


89.2 


99.9 


19.7 


37.6 


51.6 


59.3 


69 2 


1,250 


35.5 


62.3 


80.3 


•89.3 


100.2 


19.6 


37.6 


51.6 


59,4 


69 4 


1,667 


35.2 


62.1 


80.3 


89.5 


100.6 


19.4 


37.4 


51.6 


59.5 


69 a 


2,500 


34.6 


61.7 


80.3 


89.8 


101.4 


19.1 


37.1 


51.6 


59.7 


70 4 


3,333 


34. 


61.2 


80.3 


90.1 


102.2 


18.8 


36.9 


51.6 


59 9 


71 


5,000 


33. 


60.5 


80.3 


90.7 


103.7 


18.3 


36.4 


51,6 


60.4 


V. 7 


7,500 


31.6 


59.4 


80.3 


91.5 


106.0 


17.6 


35.8 


51 6 


60.9 


73 q 


10,000 


30.5 


58.5 


80.3 


92.3 


107.9 


17.1 


35.3 


51.6 


60.5 


75 4 


15,840 


28.5 


56.7 


80.2 


93.9 


112.2 


16.2 


34.3 


51.6 


62.5 


78 6 


20,000 


27.4 


55.7 


80.2 


94.8 


115.0 


15.6 


33.8 


51.5 


63 1 


80.6 



Darcy's Formula for clean iron pipes under pressure is 

rs ^ 1/2 

v= \^ ^^^^^„^^ , 0.00000162 



0.00007726 + 

According to XJnwin and other authors Darcy's experiments are 
represented approximat ely by th e formula 

/64.4 h d ^ , 
V =\^—f — T -J feet per second 

in which/, called the "coefficient of friction," =0.006 I 1 +^2^ I' ^ 

being the loss of head, I the length of the pipe, h/l the slope s, and 
d/4 the mean hydraulic radius r, of the Chezy formula. All the dimen- 
sions are in feet. 

Darcy's formula, as given by J. B. Francis, for old cast-iron pipe, 
lined with deposit and under pressure is 

^, _/ 144rf2s \l/2 

'' V0.00082(12d+1)/ ' 



in which d = diameter in feet. 



HYDRAULIC rORMUIi.E. 



733 



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734 



HYDRAULICS. 



The relation of the value of c in Chezy's formula 7 = c >/r5 to the 



value of the coefficient of friction /is c — 



/= .0035 
c = 135.5 
/= .0070 
c= 95.8 



c = 



60 
.018 



70 
.013 



.0040 

127.8 

.0075 

92.6 

80 90 



.0045 

119.6 

.0080 

89.7 

100 



.010 .008 .0064 



.0050 
113.4 
.0090 
84.5 
110 
.0053 



2 g/j. 

.0055 .0060 .0065 

108.1 103.5 99.4 

.010 .011 .012 

80.2 76.5 73.2 

120 130 140 150 

.0045 .0038 .0033 .0029 



Unwin derives the following equat ions fr om the Darcy formula: 

Velocity, ft. per sec i;= 4.012 ^dh/{fl)= 1.273 Q/d^= cv/rf/Tx v^. 

Diameter, ft d= 0.0622 f vl/h = 1.12SVq/v. 

Quantity, cu. ft. per sec. Q== 3.149 '^hd=/fL 
Head, ft h = 0.1008 fQH/d^. 

Rough preliminary calculations mav be made by the following approx- 
imate forraulse. They are least accurate for small pipes. 5 = slope, =h/l. 
New and clean pipes. Old and incrusted pipes, 

v = 56 Vds, V = 40 Vrfs^ 

Q = 44 \^d^s. Q = 31.4 '^d^s. 

d = 0.22 {jQ'^/s. d = 0.252 ^Qvi. 

Weisbach gives/ =0.00644, which Unwin says is possibly too small 
for tubes of small bore, and he gives / =0.006*^ to 0.01 for 4-in. tubes 
and/ =0.0084 to 0.012 for 2-in. tubes. Another formula by Weisbach is 

;.=/0.0144+5:^Wi:! 
\ V^^ )d 2g 

William Cox (Amer. Mach., Dec. 28, 1893) gives a simpler formula 



which gives almost identical results: 
H = friction-head in feet = 



(1) 

(2) 
feet 



L 4V2+ 5V- 2 
d 1200 • • * 

Hd^ 4V2 4- 5V- 2 

L 1200 

In this formula H and L are in feet, d in inches, and V in 
per second. 

Values of the Coefficient of Friction. Un win's "Hydraulics" gives 
values of/ based on Darcv's experiments, as follows: Clean and smooth 
pipes, /= 0.005 [1 + 1/(12^)]. Incrusted pipes, /= 0.01 [1 + l/(12rf)]. 
In 1886 Unwin examined all the more carefully made experiments on 
flow in pipes, including those of Darcy, classifying them according to 
the quality and condition of their surfaces, and showing the relation 
of the value of / to both diameter and velocity. The results agree 
fairly closely with the following values, /= a (1 + /3/f/). 



Kind of Pipe. 



Drawn wought iron. 
Asphalted cast iron. 
Clean cast iron. 



Values of a for Velocities in ft. per Second. 



]-7 
.00375 
.00492 
.00405 



Incrusted cast iron at all velocities a 



2-3 
.00322 
.00455 
.00395 

= 0.00855 



3-4 
.00297 
.00432 
.00387 



4-5 
.00275 
.00415 
.00382 



Values 
of |8 



0.37 
0.20 
0.28 
0.26 



From the experiments of Clemens Herschel, 1892-6. on clean steel 
riveted pipes, Unwin derives the following values of / for different 
velocities. 

2 
. 0060 
.0058 
.0071 
Unwin attributes the anomalies in this table to errors of observation. 
In comparing the results with those on cast-iron pipes, the roughness of 
the rivet heads and joints must be considered, and the resistance can 
only be determined by direct experiment on riveted pipes. 



Ft. per sec 1 

48-in. pipe, av. of 2 0066 

42-in. pipe, av. of 2 0067 

36-in. pipe 0087 



3 


4 


5 


6 


0057 


. 0055 


.0055 


.0055 


0054 


. 0054 


.0054 


.0054 


0060 


. 0053 


.0047 


.0042 



HYDRAULIC FORMULA. 



735 



Two portions of the 48-in. main were tested after being four years in 
use, and the coefficients derived from them differ remarkably. 

Ft. per sec 1 2 3 4 5 6 

Upper part 0106 .0080 .0075 .0073 .0072 .0072 

Lower part 0068 .0060 .0058 .0060 .0060 .0060 

Marx, Wing, and Hopkins in 1897 and 1899 made gaugings on a 6-ft. 
main, part of which was of riveted steel and part of wood staves. (Trans. 
A. S. C. E., xl, 471, and xliv, 34.) From these tests Unwin derives the 
following values of/. 



Ft. per sec. 1 
Steel pipe: 
1897.../= .0053 
1899.../= .0097 

Wood staves: 
1897.../= .0064 



1.5 



.0052 
.0076 



.0053 
.0067 



2.5 



.0055 
.0063 



3 



.0055 
.0061 



.0048 0043 

.0045 0044 



.0053 
1899.../= .0048 .0046 

Freeman's experiments on fire hose pipes (Trans. 
give the following values of/. 

Velocity, ft. per sec 4 6 

Unlined canvas 0095 .0095 

Rough rubber-Uned cotton 0078 .0078 

Smooth rubber-fined cotton 0060 .0058 



.0052 
.0060 



.0041 
.0043 



5.5 



.0058 .0058 



.0043 
A. S. C. E., xxi, 



10 
.0093 
.0078 
.0055 



15 

.0088 
.0075 
.0048 



.0043 
303) 

20 
.0085 
.0073 
.0045 



The Resistance at the Inlet of a Pipe is equal to the frictional resist- 
ance of a straight pipe whose length is Zo = (l +/o) rf-5-4/. Values of /o are: 
(A) for end of pipe flush with reservoir wall, 0.5; (B) pipe entering wall, 
straight edges, 0.56; (C) pipe entering wafi, sharp edges, 1.30; (D) bell- 
mouthed inlet, 0.02 to 0.05. Values of k/d are for 

/= 0.005 A, 53 B,75 C, 78 Z), 115 

0.010 26 38 39 58 

Multiplying these figures by d gives the length of straight pipe to he 
added to the actual length to allow for the inlet resistance. In long 
lengths of pipe the relative value of this length is so small that it may be 
neglected in practical calculations. — (Unwin.) 

Loss of Head in Pipe by Friction. — Loss of head by friction in 
each 100 feet in length of riveted pipe when discharging the following 
quantities of water per minute (Pelton Water-wheel Co.). 

V = velocity in feet per second; h = loss of head in feet; Q = dis- 
charge in cubic feet per minute. 





Inside Diameter of Pipe in Inches. 




7 


8 


9 


10 


11 


12 


V 


h 


Q 


h 


Q 


h 


Q 


h 


Q 


h 1 Q 


h 


Q 


2.0 


0.338 


32.0 


0.296 


41.9 


0.264 


53 


0.237 


65.4 


0.216 


79,2 


0.198 


94.2 


3.0 


0.698 


48.1 


0.611 


62.8 


0.544 


79.5 


0.488 


98.2 


0.444 


119 


0.407 


141 


4.0 


1.175 


64.1 


1.027 


83.7 


0.913 


106 


0.822 


131 


0.747 


158 


0.685 


188 


5.0 


1.76 


80.2 


1.54 


105 


1.37 


132 


1.23 


163 


1.122 


198 


1.028 


235 


6.0 


2.46 


96.2 


2.15 


125 


1.92 


159 


1.71 


196 


1.56 


237 


1.43 


283 


7.0 


3.26 


112.0 


2.85 


146 


2.52 


185 


2.28 


229 


2.07 


277 


1.91 


330 




Bin. 


14 in. 


15 in. 


16 in. 


18 in. 


20 in. 


V 


h 


Q 


h 


Q 


h 


Q 


h 


Q 


h 


Q 


h 


Q 


2.0 


0.183 


no 


0.169 


128 


0.158 


147 


0.147 


167 


0.132 


212 


0.119 


262 


3.0 


.375' 166 


.349 


192 


.325 


221 


.306 251 


.271 


318 


.245 393 


4.0 


.632^ 221 


.587 


256 


.548 


294 


.513 335 


.456 


424 


.410 523 


5.0 


.949 276 


.881 


321 


.822 


368 


.770 419 


.685 


530 


.617 654 


6.0 


1.325, 332 


1.229 


385 


1.H8 


442 


1.076 502 


.957 


636 


.861 785 


7.0 1.75 i 387 


1.63 


449 


1.52 


515 


1.43 ! 586 


1.27 


742 


1.1431 916 



736 



HYDRAULICS. 



Loss of Head (Continued). 





Diameter of Pipe in Inches. 




22 in. 


24 in. 


26 in. 


28 in. 


30 in. 


36 in. 


V 


h 


Q 


h 


Q 


h 


Q 


h 


Q 


h 


Q 


h 


Q 


2,0 


0.108 


316 


0.098 


377 


0.091 


442 


0.084 


513 


0.079 


589 


0.066 


848 


3.0 


.222 


475 


.204 


565 


.188 


663 


.174 


770 


.163 


883 


.135 


1273 


4.0 


.373 


633 


.342 


754 


.315 


885 


.293 


1026 


.273 


1178 


.228 


1697 


5.0 


.561 


792 


.513 


942 


.474 


1106 


.440 


1283 


.411 


1472 


.342 


2121 


6,0 


.782 


950 


.717 


1131 


.662 


1327 


.615 


1539 


.574 


1767 


.479 


2545 


7.0 


1.040 


1109 


.953 


1319 


.879 


1548 


.817 


1796 


.762 


2061 


.636 


2868 



This table is based on Cox's reconstruction of Weisbach's formula, 
using the denominator 1000 instead of 1200, to be on the safe side, allow- 
ing 20% for the loss of head due to the laps and rivet-heads in the pipe. 
Example. — Given 200 ft. head and 600 ft. of 11-inch pipe, carrying 
119 cubic feet of water per minute. To find effective head: In right- 
hand column, under 11-inch pipe, find 119 cubic ft.; opposite this will 
be found the loss by friction in 100 ft. of length for this amount of water, 
which is 0.444. Multiply this by the number of hundred feet of pipe, 
which is 6, and we have 2.66 ft., which is the loss of head. Therefore 
the effective head is 200 - 2.66 = 197.34. 

Explanation. — The loss of head by friction in a pipe depends not 
only upon diameter and length, but upon the quantity of water passed 
through it. The head or pressure is what would be indicated by a 
pressure-gauge attached to the pipe near the wheel. Readings of gauge 
ehould be taken while the water is flowing from the nozzle. 

To reduce heads in feet to pressure in pounds multiply by 0.433. To 
reduce pounds pressure to feet multiply by 2.309. 

Exponential Formulae. Williams and Hazen's Tables. — From 
Chezy's formula, v = c ^rs, it would appear that the velocity varies as 
the square root of the head, or that the head varies as the square of the 
velocity; this is not true, however, for c is not a constant, but a variable, 
depending on both r and s. Hazen and WiUiams, as a result of a study 
of the best records of experiments and plotting them on logarithmic ruled 
paper, found an exponential formula v = cr^'^^ s^'^^,m which the coefficient 
c is practically independent of the diameter and the slope, and varies onlv 
with the condition of the surface. In order to equalize the numerical 
value of c to that of the c in the Chezy formula, at a slope of 0.001, they 
added the factor 0.001—0-04 to the formula, so that the working formula 
of Hazen and Williams is 

X) = cr^-^^ so.54 O.OO1-0-04 = i.3ig cr^M 50.54. 
Approximate Values of C in the Hazen «&; Williams Formula. 
(fl) 140 for the very best cast-iron pipe, laid straight and when new; 

for very smooth and clean masonry conduits; 

for straight lead, copper, brass, tin, and glass pipes. 
(6) 130 for good new cast-iron pipe, and other pipes under {a) when 

not quite smooth.* 
(c) 120 for cast-iron pipe 5 years old, for smooth new iron pipes, 

smooth wooden stave pipes and ordinary masonry conduits. 
id) 110 for new riveted steel pipe, for vitrified pipe, and for cast-iron 

pipe 10 years old. 
(e) 100 for ordinary iron pipes, 14 to 20 years old, for riveted steel 

pipe 10 years old, and for brick sewers. 
(/) 80 for old iron pipes, and for very rough cast-iron pipes over 

60 inches diameter. 
{g) 60 down to 40, for very rough pipes, the lower figure for the 

smaller diameters. 
* 130 niay also be used for straight lead, tin, and drawn copper pipes. 
Computations of the exponential formula are made by logarithms, or by 
the Hazen-Williams hydrauhc slide rule. On logarithmic ruled paper 
values of v for different values of c, r and s may be plotted in straight 
lines. (See " Hydrauhc Tables," by WiUiams and Hazen, John Wiley & 
Sons.) 



FLOW OF WATER, 



737 



Values of Coefficient K for Reducing the Hazen andWilliams 
Formula to tlie Style of Chezy's Formula v = c \/r \/V 



Diam. , 


Slope = Head -r- Length of Pipe. 


Ft.In. 


0.0005 


0.001 


0.002 


0.003 


0.005 


0.01 


0.02 


0.04 


0.06 


0.10 


0.20 


V. 


0.5374 


0.5525 


0.5680 


0.5773 


0.5892 


0.6058 


0.6228 


0.6403 


0.6508 


0.6642 


0.6829 


1 


.5880 


.6046 


.6216 


.6317 


.6448 


.6629 


.6815 


.7007 


.7122 


.7269 


.7473 


2 


.6435 


.6616 


.6802 


.6913 


.7056 


.7254 


.7458 


.7667 


.7793 


.7954 


.8177 


4 


.7042 


.7240 


.7443 


.7565 


.7721 


.7938 


.8161 


.8390 


.8528 


.8704 


.8949 


8 


.7706 


.7922 


.8145 


.8278 


.8449 


.8686 


.8931 


.9182 


.9332 


.9525 


.9792 


12 


.8123 


.8351 


.8586 


.8726 


.8906 


.9157 


.9414 


.9679 


.9837 


1.004 


1.032 


2 


.8889 


.9138 


.9395 


.9549 


.9746 


1.002 


1.030 


1.059 


1.076 


1.099 


1 130 


4 


.9727 


1.000 


1.028 


1.045 


1.067 


1.096 


1.127 


1.159 


1.178 


1.202 


1.236 


8 


1.064 


1.094 


1.125 


1.143 


1.167 


1.200 


1.234 


1.268 


1.289 


1.316 


1.353 


12 


1.122 


1.154 


1.186 


1.205 


1.230 


1.265 


1.300 


1 337 


1.359 


1 387 


1.426 


16 


1.165 


1.197 


1.231 


1.251 


1.277 


1.313 


1.350 


1.388 


1.411 


1.440 


1.480 


20 


1.199 


1.233 


1.267 


1.288 


1.315 


1.352 


1.390 


1.429 


1.452 


1.482 


1.524 



H. & W. Formula: 



V= 1.318 cro.63 50.54 = iCc 
1.318 crO-63 sO-54 



i^ = - 



1.318 



(?) 



0.13 5O.O4 



^^0,50 5O.5O 

Short Formulae. E. Sherman Gould, Eng. News, Sept. 6, 1900, 
shows that Darcy s formulae for cast-iron pipes may be reduced to the fol- 
lowing approximate forms, in which h is loss of head or drop of hydraulic- 
grade line in feet per 1000, d in ft., v in ft. per sec, Q in cu. ft. per sec. 



8 in. to 48 in. diam. 



3 to 6 in. diam. 



( Rough, Q^=hd^: v = 1.27 V5^. 
(Smooth, Q2 = 2M5; v = 1.80 v^. 

( Rough, Q2=o.785 hd^; v = 1.13 Vd^. 
I Smooth, Q2 = i 57 /i(^5; V = 1.60 v^. 
FLOW OF WATER— EXPERIMENTS AND TABLES. 

The Flow of Water through New Cast-iron Pipe was measured by 
S. Bent Russell, of the St. Louis, Mo., Water-works. The pipe was 12 
inches in diameter, 1631 feet long, and laid on a uniform grade from 
end to end. Under an average total head of 3.36 feet the flow was 
43,200 cubic feet in seven hours; under an average head of 3.37 feet the 
flow was the same; under an average total head of 3.41 feet the flow 
was 46,700 cubic feet in 8 hours and 35 minutes. Making allowance for 
loss of head due to entrancejand to curves, it was found that the value 

of c in the formula v = c ^rs was from 88 to 93. (Eng'g Record, April 
14, 1894.) 

Flow of Water in a 20-inch Pipe 75,000 Feet Long. — A com- 
parison of experimental data with calculations bv different formulae is 
given by Chas. B. Brush, Trans. A. S. C. E., 1888. The pipe experi- 
mented with was that supplying the city of Hoboken, N. J. 

Results Obtained by the Hackensack Water Co., from 1882-1887, 
IN Pumping Through a 20-in. Cast-iron Main 75,000 Feet Long. 

Pressure in lbs. per sq. in. at pumping-station: 

95 100 105 110 115 120 

Total effective head in feet: 

55 66 77 89 100 112 

Discharge in U. S. gallons in 24 hours, 1 = 1000: 

2,848 3,165 3,354 3,566 3,804 3,904 
Theoretical discharge by Darcy 's formula: 

2,743 3,004 3,244 3,488 3,699 3,915 
Actual velocity in main in feet per second: 

2.00 2.24 2.36 2.52 2.68 2.76 



125 


130 


123 


135 


4,116 


4,255 


4,102 


4,297 


2.92 


3.00 



738 



HYDRAULICS. 



Flow of Water in Circular Pipes, Sewers, etc., Flowing Full. 
Based on Kutter's Formula, with n = 0.013. 

Discharge in cubic feet per second. 



Diam- 




Slope, or Head Divided by Length of Pipe. 




eter. 


1 in 40 1 1 in 70 1 1 in lOOj 1 in 200] 1 in 306| 1 in 400 


1 in 500 


1 in 600 


5 in. 


0.456 


0.344 


0.288 


0.204 


0.166 


0.144 


0.137 


0.118 


6 " 


0.762 


0.57.- 


0.482 


0.341 


0.278 


0.241 


0.230 


0.197 


7 " 


1.17 


0.889 


0.744 


0.526 


0.430 


0.372 


0.355 


0.304 


8 " 


1.70 


1.29 


1.08 


0.765 


0.624 


0.54 


0.516 


0.441 


9 " 


2.37 


1.79 


1.50 


1.06 


0.868 


0.75 


0.717 


0.613 


s = 


1 in 60 


1 in 80 


1 in 100 


1 in 200 


1 in 300 


1 in 400 


1 in 500 


1 in 600 


10 in. 


2.59 


2.24 


2.01 


1.42 


1.16 


1.00 


0.90 


0.82 


11 •• 


3.39 


2.94 


2.63 


1.86 


1.52 


1.31 


1.17 


1.07 


12 " 


4.32 


3.74 


3.35 


2.37 


1.93 


1.67 


1.5 


1.37 


13 " 


5.38 


4.66 


4.16 


2.95 


2.40 


2.08 


1.86 


1.70 


14 " 


6.60 


5.72 


5.15 


3.62 


2.95 


2.57 


2.29 


2.09 


5 = 


1 in 100 


1 in 200 


1 in 300 


1 in 400 


1 in 500 


1 in 600 


1 in 700 


1 in 800 


15 in. 


6.18 


4.37 


3.57 


3.09 


2.77 


2.52 


2.34 


2.19 


16 " 


7.38 


5.22 


4.26 


3.69 


3.30 


3.01 


2.79 


2.61 


18 " 


10.21 


7.22 


5.89 


5.10 


4.56 


4.17 


3.86 


3.61 


20 " 


13.65 


9.65 


7.88 


6.82 


6.10 


5.57 


5.16 


4.83 


22 •* 


17.71 


12.52 


10.22 


8.85 


7.92 


7.23 


6.69 


6.26 


s = 


1 in 200 


1 in 400 


1 in 600 


1 in 800 


1 in 1000 


lin 1250 


lin 1500 


1 in 1800 


2ft. 


15.88 


11.23 


9.1; 


7.94 


7.10 


6.35 


5.80 


5.29 


2ft. 2in. 


19.73 


13.96 


11.39 


9.87 


8.82 


7.89 


7.20 


6.58 


2 " 4 " 


24.15 


17.07 


13.94 


12.07 


10.80 


9.66 


8.82 


8.05 


2 " 6 " 


29.08 


20.56 


16.79 


14.54 


13.00 


11.63 


10.62 


9 69 


2 " 8 " 


34.71 


24.54 


20.04 


17 35 


15.52 


13.88 


12.67 


11.57 


s = 


1 in 500 


I in 750 


1 in 1000 


1 in 1250 


lin 1500 


lin 1750 


1 in 2000 


1 in 2500 


2ft. lOin. 


25.84 


21.10 


18.27 


16.34 


14.92 


13.81 


12.92 


11.55 


3 " 


30.14 


24.61 


21.31 


19.06 


17.40 


16.11 


15.07 


13.48 


3 " 2in. 


34.90 


28.50 


24.68 


22.07 


20.15 


18.66 


17.45 


15.61 


3 " 4 " 


40.08 


32.72 


28.34 


25.35 


23.14 


21.42 


20.04 


17.93 


3 " 6 " 


45.66 


37.28 


32.28 


28.87 


26.36 


24.40 


22.83 


20.41 


s = 


1 in 500 


1 in 750 


1 in 1000 


1 in 1250 


lin 1500 


1 in 1750 


1 in 2000 


1 in 25G0 


3ft. 8in. 


51.74 


42.52 


36.59 


32.72 


29.87 


27.66 


25.87 


23.14 


3 " 10 " 


58.36 


47.65 


41.27 


36.91 


33.69 


31.20 


29.18 


26.10 


4 •• 


65.47 


53.46 


46.30 


41.41 


37.80 


34.50 


32 74 


29.28 


4 " 6 in. 


89.75 


73.28 


63.47 


56.76 


51.82 


47.97 


44.88 


40.14 


5 '• 


118.9 


97.09 


84.08 


75.21 


68.65 


63.56 


59.46 


53.18 


5 = 


1 in 750 


1 in 1000 


1 in 1500 


I in 2000 


1 in 2500 


1 in 3000 


1 in 3500 


1 in 4000 


5 ft. 6 in. 


125.2 


108.4 


88.54 


76.67 


68.58 


62.60 


57.96 


54.21 


6 '♦ 


157.8 


136.7 


111.6 


96.66 


86.45 


78.92 


73.07 


68.35 


6 " 6 " 


195.0 


168.8 


137.9 


119.4 


106.8 


97.49 


90.26 


84.43 


7 " 


237.7 


205.9 


168.1 


145.6 


130.2 


118.8 


110.00 


102.9 


7 " 6 " 


285.3 


247.1 


201.7 


174.7 


156.3 


142.6 


132.1 


123.5 


s= 


1 in 1500 


1 in 2000 


1 in 2500 


1 in 3000 


1 in 3500 


1 in 4000 


1 in 4500 


1 in 5000 


8 ft. 


239.4 


207.3 


195.4 


169.3 


156.7 


146.6 


138.2 


131.1 


8 " 6in. 


281.1 


243.5 


217.8 


198.8 


184.0 


172.2 


162.3 


154.0 


9 " 


327 


283.1 


253.3 


231.2 


214.0 


200.2 


188.7 


179.1 


9 " 6 " 


376.9 


326.4 


291.9 


266.5 


246.7 


230.8 


217.6 


206.4 


10 " 


431.4 


373.6 


334.1 


305.0 


282.4 


264.2 


249.1 


236.3 



For U. S. gallons multipl.v the figures in the table by 7.4805. 

For a given diameter the quantity of flow varies as the square root of 
the sine of the slope. From this principle the flow for other slopes than 
those given in the table may be found. Thus, what is the flow for a 



FLOW OF WATER IN PIPES. 



739 



pipe 8 feet diameter, slope 1 in 125? From the table take Q = 207.3 
for slope 1 in 2000. The given slope 1 in 125 is to 1 in 2000 as 16 to 
1, and the square root of this ratio is 4 to 1. Therefore the flow required 
is 207.3 X 4 = 829.2 cu. ft. 

Circular Pipes, Conduits, etc.. Flowing FuIL ^ 

Values of the factor ac \/r in the formula Q = ac \/r X \/s corre- 
sponding to different values of the coefficient of roughness, n. (Based 
on Kutter's formula.) 



Diam., 
Ft. In. 



Value of ac \/r. 



n=.OIO. I n=.011. 1 n=.012. | n=.OI3. | n =.015. | w =.017. 



2 


307.6 


274.50 


247.33 


224.63 


188.77 


164 


2 3 


421.9 


377.07 


340.10 


309.23 


260.47 


223.9 


2 6 


559.6 


500.78 


452.07 


411.27 


347.28 


299.3 


2 9 


722.4 


647.18 


584.90 


532.76 


451.23 


388.8 


3 


911.8 


817.50 


739.59 


674.09 


570.90 


493.3 


3 3 


1128.9 


I0I3.1 


917.41 


836.69 


709.56 


613.9 


3 6 


1374.7 


1234.4 


1118.6 


1021.1 


866.91 


750.8 


3 9 


1652.1 


1484.2 


1345.9 


1229.7 


1045 


906 


4 


1962.8 


1764.3 


1600.9 


1463.9 


1245.3 


1080.7 


4 6 


2682.1 


2413.3 


2193 


2007 


1711.4 


1487.3 


5 


3543 


3191.8 


2903.6 


2659 


2272.7 


1977 


5 6 


4557.8 


4111.9 


3742.7 


3429 


2934.8 


2557.2 


6 


5731.5 


5176.3 


4713.9 


4322 


3702.3 


3232.5 


6 6 


7075.2 


6394.9 


5825.9 


5339 


4588.3 


4010 


7 


8595.1 


7774.3 


7087 


6510 


5591.6 


4893.2 


7 6 


10296 


9318.3 


8501.8 


7814 


6717 


5884.3 


8 


12196 


11044 


10083 


9272 


7978.3 


6995.3 


8 6 


14298 


12954 


11832 


10889 


9377.9 


8226.7 


9 


16604 


15049 


13751 


12663 


10917 


9580 


9 6 


19118 


17338 


15847 


14597 


12594 


11061 


10 


21858 


19834 


I8I34 


16709 


14426 


12678 


10 6 


24823 


22534 


20612 


18996 


16412 


14434 


If 


28020 


25444 


23285 


21464 


18555 


16333 


II 6 


31482 


28593 


26179 


24139 


20879 


18395 


12 


35156 


31937 


29254 


26981 


23352 


20584 


12 6 


39104 


35529 


32558 


30041 


26012 


22938 


13 


43307 


39358 


36077 


33301 


28850 


25451 


13 6 


47751 


43412 


39802 


36752 


31860 


28117 


14 


52491 


47739 


43773 


40432 


35073 


30965 


14 6 


57496 


52308 


47969 


44322 


38454 


33975 


15 


62748 


57103 


52382 


48413 


42040 


37147 


16 


74191 


67557 


62008 


57343 


49823 


44073 


17 


86769 


79050 


72594 


67140 


58387 


51669 


18 


1 00617 


91711 


84247 


77932 


67839 


60067 


19 


115769 


105570 


96991 


89759 


78201 


69301 


20 


132133 


120570 


110905 


102559 


89423 


79259 



Flow of Water in Pipes from s/g Inch to 12 Inches Diameter for a 
Uniform Velocity of 100 Ft. per 3Iin. 



Diam. 
in In. 


Area 
Sq. Ft. 


Cu. Ft. 
per. Min. 


U. S. 
Gallons 
per Min. 


Diam. 
in In. 


Area 
Sq. Ft. 


Cu. Ft. 
per Min. 


U.S. 
Gallons 
per Min. 


3/8 


.00077 


0.077 


.57 


4 


.0873 


8.73 


65.28 


1/2 


.00136 


0.136 


1.02 


5 


.136 


13.6 


102.00 


3/4 


.00307 


0.307 


2.30 


6 


.196 


19.6 


146.88 


1 


.00545 


0.545 


4.08 


7 


.267 


26.7 


199.92 


11/4 


.00852 


0.852 


6.38 


8 


.349 


34.9 


261.12 


11/2 


.01227 


1.227 


9.18 


9 


.442 


44.2 


330.48 


13/4 


.01670 


1.670 


12.50 


10 


.545 


54.5 


408.00 


2 


.02182 


2.182 


16.32 


11 


.660 


66.0 


493.68 


21/2 


.0341 


3.41 


25.50 


12 


.785 


78.5 


587.52 


3 


.0491 


4.91 


36.72 











740 



HYDRAtJLICS. 



Flow of Water in Circular Pipes, Conduits, etc., Flowing undeY 

Pressure. 

Based on Darcj^'s formulae for the flow of water through cast-iron 
pipes. With comparison of results obtained by Kutter's formula, with 
n = 0.013. (Condensed from Flynn on Water rower.) _ 

Values of a, and also the value^ of the factors c ^/^ and ac ^/r for use 

in the formulae Q = av\ v = c v^r X ^s, and Q = ac v^x ^s. 

Q = discharge in cubic feet per second, a = area in square feet, v =» 
velocity in feet per second, r = mean hydraulic depth, 1/4 diam. for 
pipes running full, s^ = sine of slope. 

(For values of V's see page 729.) 



Size of Pipe. 


Clean Cast-iron 
Pipes, 


Value of 
acVr by 
Kutter's 
Formula, 


Old Cast 
Lined w 


-iron Pipes 
th Deposit. 


d—diam. 


a = area in 


For 


For Dis- 


For 


For 




in 


square 


Velocity, 


charge, 


when 


Velocity, 


Discharge, 


ft 


in. 


feet. 


acVr. 


n=.013. 


cVr. 


acVr. 


2 




3.142 


78.80 


247.57 


224.63 


52.961 


166.41 


2 


2 


3.687 


28.15 


302.90 




55.258 


203.74 


2 


4 


4.276 


85.39 


365.14 




57.436 


245.60 


2 


6 


4.909 


88.39 


433.92 


411.37 


59.455 


291.87 


2 


8 


5.585 


91.51 


511.10 




61.55 


343.8 


2 


10 


6.305 


94.40 


595.17 




63.49 


400.3 


3 




7.068 


97.17 


686.76 


674.09 


65.35 


461 .9 


3 


2 


7.875 


99.93 


786.94 




67.21 


529.3 


3 


4 


8.726 


102.6 


895.7 




69 


602 


3 


6 


9.621 


105.1 


1011.2 


1021.1 


70.70 


680.2 


3 


8 


10.559 


107.6 


1136.5 




72.40 


764.5 


3 


10 


11.541 


110.2 


1271.4 




74.10 


855.2 


4 




12.566 


112.6 


1414.7 


1463.9 


75.73 


951.6 


4 


3 


14.186 


116.1 


1647.6 




78.12 


1108.2 


4 


6 


15.904 


119.6 


1901.9 


2007 


80.43 


1279.2 


4 


9 


17.721 


122.8 


2176.1 




82.20 


1456.8 


5 




19.635 


126.1 


2476.4 


2659 


84.83 


1665.7 


5 


3 


21.648 


129.3 


2799.7 




86.99 


1883.2 


5 


6 


23.758 


132.4 


3146.3 


3429 


89.07 


2116.2 


5 


9 


25.967 


135.4 


3516 




91.08 


2365 


5 




28.274 


138.4 


3912.8 


4322 


93.08 


2631.7 


6 


6 


33.183 


144.1 


4728.1 


5339 


96.93 


3216.4 


. 7 




38.485 


149.6 


5757.5 


6510 


100.61 


3872.5 


7 


6 


44.179 


154.9 


6841.6 


7814 


104.11 


4601.9 


8 




50.266 


160 


8043 


9272 


107.61 


5409.9 


8 


6 


56.745 


165 


9463.7 


10889 


111 


6299.1 


9 




63.617 


169.8 


10804 


12663 


114.2 


7267.3 


9 


6 


70.882 


174.5 


12370 


14597 


117.4 


8329.6 


10 




78.540 


179.1 


14066 


16709 


120.4 


9460.9 


10 


6 


68.590 


183.6 


15893 


18996 


123.4 


10690 


11 




95.033 


187.9 


17855 


21464 


126.3 


12010 


11 


6 


103.869 


192.2 


19966 


24139 


129.3 


13429 


12 




113.098 


196.3 


22204 


26981 


132 


14935 


12 


6 


122.719 


200.4 


24598 


30041 


134.8 


16545 


13 




132.733 


204.4 


27134 


33301 


137.5 


18252 


13 


6 


143.139 


208.3 


29818 


36752 


140.1 


20056 


14 




153.938 


212.2 


32664 


40432 


142.7 


21971 


14 


6 


165.130 


216.0 


35660 


44322 


145.2 


23986 


15 




176.715 


219.6 


38807 


48413 


147.7 


26103 


15 


6 


188.692 


223.3 


42125 


52753 


150.1 


28335 


16 




201.062 


226.9 


45621 


57343 


152.6 


30686 


16 


6 


213.825 


230.4 


49273 


62132 


155 


33144 


17 




226.981 


233.9 


53082 


67140 


157.3 


35704 


17 


6 


240.529 


237.3 


57074 


72409 


159.6 


38389 


18 




254.170 


240.7 


61249 


77932 


161.9 


41199 


19 




283.529 


247.3 


70154 


89759 


166.4 


47186 


20 




314.159 


253.8 


79736 


102559 


170.7 


53633 



FLOW OF ■WATER IN PIPES. 



741 



Flow of Water in Circular Pipes from 3/8 Inch to 13 Inches 
Diameter. 

Based on Darcy's formula for clean cast-iron pipes. Q = ac v^r v'^. 



Value 
ofcuyr. 



.00403 
.00914 
.02855 
.06354 
.11659 
.19115 
.28936 
.41357 
.74786 
1.2089 
2.5630 
4.5610 
7.3068 
10.852 
15.270 
20.652 
26.952 
34.428 
42.918 



Dia, 
in. 



3/8 

V: 

3/4 
1 

11/4 
ll/o 
13/4 
2 
21/2 

3 

4 

5 

6 

7 

8 

9 
10 
11 
12 



Slope, or Head Divided by Length of Pipe. 



1 in 10 1 in20 I in 40 1 in 60 1 in 80 1 in 100 1 in 150 1 in 200 



.00127 
.00289 
.00903 
.02003 
.03687 
.06044 
.09140 
.13077 
.23647 
.38225 
.81042 
1.4422 
2.3104 
3.4314 
4.8284 
6.5302 
8.5222 
10.886 
13.571 



Quan 
.00090 
.00204 
.00638 
.01416 
.02607 
.04274 
.06470 
I .09247 
.16722 
.27031 
.57309 
1.0198 
1.0338 
2.4265 
;3.4143 
|4.6178 
6.0265 
7.6981 
19.5965 



tity in 
.00064 
.00145 
.00451 
.01001 
.01843 
.03022 
.04575 
.06539 
.11824 
.19113 
.40521 
.72109 
1.1552 
1.7157 
2.4141 
3.2651 
4.2611 
5.4431 
6.7853 



cubic 
.00052 
.00118 
.00369 
.00818 
.01505 
.02468 
.03736 
.05339 
.09655 
.15607 
.33088 
.58882 
.94331 
1.4110 
1.9713 
2.6662 
3.4795 
4.4447 
5.5407 



feet per 

.00045 

.00102 

.00319 

.00708 

.01303 

.02137 

.03235 

.04624 

.08361 

.13515 

.28654 

.50992 

.81690 

1.2132 

1.7072 

2.3089 

3.0132 

3.8491 

4.7982 



second. 
.00040 
.00091 
.00286 
.00633 
.01166 
.01912 
.02894 
.04136 
.07479 
.12039 
.25630 
.45610 
.73068 
1.0852 
1.5270 
2.0652 
2.6952 
3.4428 
4.2918 



.00033 
.00075 
.00233 
.00517 
.00952 
.01561 
.02363 
.03377 
.06106 
.09871 
.20927 
.37241 
.59660 
.88607 
1.2468 
1.6862 
2.2006 
2.8110 
3.5043 



Value of V s = 



0.1291 



0.1118 



0.1 



0.08165 0.07071 



Value, 
of a^Vr. 


Dia. 
in. 


1 in 250 


1 in 300 


I in 350 


1 in 400 


1 in 450 


1 in 500 


1 in 550 


1 in 600 


.00403 


3/8 


.00025 


.00023 


.00022 


.00020 


.00019 


.00018 


.00017 


.00016 


.00914 


1/0 


.00058 


.00033 


.00049 


.00046 


.00043 


.00041 


.00039 


.00037 


.02855 


3/4 


.00181 


.00165 


.00153 


.00143 


.00134 


.00128 


.00122 


.00117 


.06334 


1 


.00400 


.003661 .00339 


.00317 


.00298 


.00283 


.00270 


.00259 


.11659 


11/4 


.00737 


.00673 .00623 


.00583 


.00549 


.00321 


.00497 


.00476 


.19115 


ll/'> 


.01209 


.011041 .01022 


.00956 


.00901 


.00855 


.00815 


.00780 


.28936 


13/4 


.01830 


.016711 .01547 


.01447 


.01363 


.01294 


.01234 


.01181 


.41357 


2 


.02615 


.02388 


.02211 


.02068 


.01948 


.01849 


.01763 


.01688 


.74786 


21/9 


.04730 


.04318 


.03997 


.03739 


.03523 


.03344 


.03189 


.03053 


1.2089 


3 


.07645 


.06980 


.06462 


.06045 


.05695 


.05406 


.05155 


.04935 


2.5630 


4 


.16208 


.14799 


. 13699 


.12815 


.12074 


.11461 


.10929 


.10463 


4.5610 


5 


.28843 


.26335 


.24379 


.22805 


.21487 


.20397 


.19448 


.19620 


7.3068 


6 


.46208 


.42189 


.39055 


.36534 


.34422 


.32676 


.31156 


.29830 


10.852 


7 


.68628 


.62660 


.58005 


.54260 


.51124 


.48530 


.46273 


.44303 


15.270 


8 


.96567 


.88158 


.81617 


.76350 


.71936 


.68286 


.65111 


.62340 


20.652 


9 


1 3060 


1.1924 


1.1038 


1.0326 


.97292 


.92356 


.88060 


.84310 


26.952 


10 


1.7044 


1 .5562 


1.4405 


1.3476 


1.2697 


1.2053 


1.1492 


1.1003 


34.428 


11 


2.1772 


1.9878 


1.8402 


1.7214 


1.6219 


1.5396 


1.4680 


1.4055 


42.918 12 


2.7141 


2.4781 


2.2940 


2.1459 


2.0219 


1.9193 


1.8300 


1.7521 


Value of \/s= 


.06324 


.05774 


.05345 


.05 


.04711 


.04472 


.04264 


.04082 



For U. S. gals, per sec, multiply the figures in the table by 7.4805 

** min., •• " •' " ... 448.83 

" '• •• hour, *• •• *• "... 26929.8 

" •• 24hrs., ** •• " *• ...646315. 

For any other slope the flow is proportional to the square root of the 
slope; thus, flow in slope of 1 in .100 is double that in slope of 1 in 400. 



742 



HYDRAULICS. 



^ <N 



O 
in 

O 



O 

o 





«N 












O 




Sg 








r<^ 


(D 






lA 

\0 


o 


(N 


ft 


§ 


.B 


f^ 






moooOc^OvO'^oOiA 

r^mo^ — <Nr^c«^ — mm — iA(^ — rvi— 



DiA(Nc<^ — o^ — oOc^m 
:>O<Nc^fNTrtriiAwnOO(Nt^vAOCvc0 
-<NT}-vO<NO^'«j-OOr*.(Nr^T}-NO>rMn — r>iOOC^(S — mTj- 



oo 

OO 
OO 



— OiTiO — -^O^ — m-^ 

— <NT}-oOfOr<^'^oONO(^<NO^(^mrors)t>if<M«H.— (vjrj-sO 
OOOO — (NcO'vj-vOoO-^Oa^O^t^oOin — tT — O^OtT 



moo 

O t- 0^ — CVJ <N 
0000Oc0<NOT}-iAT}-rsjsDs0 



<N Tj- (N ON Tj- — sO 

OOv0v0mrrT}-(«O|O<N00r^<N 

— rj-r^m<^m(Ncooo<NOmOpi^\OoO'^r>.mmc^m 
OOO — fNTj-r^(N00vOvOmr^rr>00c^QOC30r<^'— oOOr<^ — <N 
OOOOOOO — — <Nr<^"<1-t>.— m — 00\0v0O<Nh>i(Na^a^ 



— — (N<Nf<^Tj-\Or^ooO — m 



r^OsO 

r^t^fNt^ — <NoOrsirr>fn — Ot^ — 

— (NinOsD — OC0C^O00<N0^0^OO'^s000t>*a^r>.TJ•ff^ 
OOO,— — r<^Tl-QO(N0O"^ — (Nt>s,ONr>.oOcnoO<^OoOc^ONiA 
OOOOOOOO -(Nr^Mnr^O-^OMn — — OONO — O^ 



— — — (Nf^^-^miTit^ooo 



<N(NCO(N 

— — Ot^r<^cOooaN-^ 

ONONsO^ — -^rsisOC>Ot>*sOf<^oOO 

O — r<^r>. — ^TrooOT}-0"<^-^mO — Tf^<NiAmoOoOm(N 

OOOO — (Nc^vOcorsjt^ — sOr<Mn — vO'^ON'^'^ — (^r<^r<^ 

OOOOOOOOO — — fNc<^mt^Of^r^ — OO-^ — oOvOm 



— — — -<Nrsjf<^T}-T}-mr^ 



r^ vn<N m t>. 

rsj — ooOmt^t^^t^ON 

vOc^-^ — vO'^mr^ — (Ntj-vOvDiaqO-^-^ 

o — (Nmt^-'tT^ — — u°Nr^t^Ooom«r>coo^oor^C>(Nt^sOO 

OOOOO — (Ntj-vocO — -^mvO — OcOiO^OtnsOc<^fsr^oO 

OOOOOOOOOO — — rsc^msOC^ — mOc(^ooc<^oo — 



— — — rs|(Nroc<Mri 



r^\0 

(^OO — vOsO — — t^Of«^ 

■<i-Ost>»mcs) — fNr>.OsDt^vAfomoOc^'^0 

OO — f<MnOsOoO<NcOO — rs|r<^'^G0u-\-^r^v£>O000N\0rA 

OOOOO — — <NTl-Lr^oOOt^mlr^r^■^rslc<^'<t•c^^■<^QO^OvO 

OOOOOOOOOOO — — (Ntx^-^sDoOOf^^sOONfNsOm 



'—'—'—-- <N (N c^ 



5 ' M 

C c oj 

>M C rj 






<N T5-osoor^ONoOoOvOvOt^m<^ — — -^rvirsj 

(NtNTj-cO — sOvOsO-^fNO-^vOfNOOTj-fNOOmmm — 0000 
NOooOc^vOO-^OmOiAOOOO^ONOOOfNfNfNrsj — — 



O — — — <N (N m cO( -"^ -^ m »0 r^ t>i OO O — rsj pr, -^ m vO r>. O^ 



"^--^ V^ >-^ ->^ . . . 

- — — <M fsi c*^ cn Tj- Tj" m ^O CN 00 0^ O — fs c<^ Tj- in *^ "^ *^ 

— — — '-'- — t^oOO 

— — (N 



FLOW OP WATEK. 



743 



Flow of Water in Cubic Feet per Second. 
Pipes 1 Ft. to 20 Ft. Diameter. 

Calculated from the Hazen and Williams formula with C -- 



100. 





Fall, Feet per 1 000 


Actual 
Internal 


1 


1 2 


3 1 4 1 6 1 8 1 10 1 15 1 20 1 40 


Diam., 
In. 


Drop in 


Pressure, Lb. per Sq. In. per 1000 Ft. Length. 


0.433 


0.866 


1.299 


1.732 


2.598 


5.464 


4.330 


6.495 


8.660 


17.32 


12 


1.037 


1.508 


1.877 


2.192 


2.729 


3.188 


3.596 


4.475 


5.228 


8.335 


13 


1.280 


1.861 


2.317 


2.706 


3.368 


3.934 


4.438 


5.524 


6.453 


10.29 


14 


1.555 


2.262 


2.815 


3.288 


4.093 


4.781 


5.393 


6.713 


7.842 


12.50 


15 


1.865 


2.712 


3.375 


3.943 


4.908 


5.732 


6.466 


8.048 


9.402 


14.99 


16 


2.210 


3.213 


4.000 


4.672 


5.815 


6.793 


7.663 


9.537 


11.14 


17.76 


18 


3.012 


4.380 


5.452 


6.368 


7.927 


9.259 


10.45 


13.00 


15.19 


24.21 


20 


3.974 


5.778 


7.193 


8.402 


10.46 


12.22 


13.78 


17.15 


20.04 


31.94 


22 


5.100 


7.415 


9.231 


10.78 


13.42 


15.68 


17.68 


22.01 


25.71 


40.99 


Diam., Ft. 






















2 


6.420 


9.334 


11.62 


13.57 


16.89 


19.73 


22.26 


27.70 


32.36 


51.60 


21/2 


n.54 


16.79 


20.89 


24.41 


30.38 


35.48 


40.03 


49.80 


58.20 


92.79 


3 


18.65 


27.11 


33.75 


39.42 


49.07 


57.32 


64.66 


80.48 


94.01 


149.9 


31/2 


27.97 


40.67 


50.62 


59.13 


73.60 


85.97 


96.98 


120.7 


141.0 


224.8 


4 


39.74 


57.78 


71.92 


84.01 


104.6 


122.1 


137.8 


171.5 


200.3 


319.4 


41/2 


54.17 


78.76 


98.04 


114.5 


142.5 


166.5 


187.8 


233.8 


273.1 


435.4 


5 


71.46 


103.9 


129.3 


151.1 


188.1 


219.7 


247.8 


308.4 


360.3 


574.4 


51/2 


91.82 


133.5 


166.2 


194.1 


241.7 


282.2 


318.4 


396.3 


462.9 


738.0 


6 


115.4 


167.8 


208.9 


244.0 


303.8 


354.8 


400.2 


498.2 


581.9 


927.8 


61/2 


142.5 


207.2 


257.9 


301.2 


374.9 


437.9 


494.0 


614.9 


718.3 


1145 


7 


173.1 


251.7 


313.4 


366.0 


455.6 


532.2 


600.3 


747.2 


872.9 


1392 


71/2 


207.6 


301.8 


375.7 


438.8 


546.3 


638.1 


719.8 


859.9 


1047 


1668 


8 


246.0 


357.7 


445.2 


520.0 


647.3 


756.1 


852.9 


1062 


1240 


1977 


81/2 


288.5 


419.5 


522.2 


609.9 


759.2 


886.8 


1000 


1245 


1455 


2319 


9 


335.3 


487.5 


606.9 


708.9 


882.4 


1031 


1163 


1447 


1690 


2695 


10 


442.4 


643.2 


800.6 


935.2 


1164 


1360. 


1534 


1909 


2230 


3556 


11 


568.4 


826.4 


1029 


1202 


1496 


1747 


1971 


2453 


2866 


4568 


12 


714.6 


1015 


1293 


1511 


1880 


2196 


2478 


3084 


3602 


5743 


13 


882.0 


1282 


1596 


1865 


2321 


2711 


3058 


3807 


4447 


7089 


14 


1072 


1558 


1940 


2266 


2820 


3294 


3716 


4625 


• 5403 


8614 


15 


1285 


1868 


2326 


2717 


3381 


3950 


4456 


5546 


6478 


10328 


16 


1223 


2214 


2756 


3219 


4007 


4681 


5280 


6572 


7677 


12239 


17 


1786 


2597 


3232 


3776 


4700 


5490 


6193 


7708 


9004 


14354 


18 


2076 


3018 


3757 


4388 


5462 


6380 


7197 


8958 


10464 


16683 


19 


2393 


3479 


4331 


5059 


6297 


7355 


8297 


10327 


12063 


19232 


20 


2738 


3982 


4956 


5789 


7206 


8417 


9495 


11818 


13806 


22010 



Long Pipe Lines. — (1) Vyrnwy to Liverpool, 68 miles: 40 million gals. 
(British) per day. Three hnes of cast-iron pipe, 42 to 39 in. diam. One 
of the 42-in. Hnes after being laid 12 years, with a hydrauhc gradient of 
4.5 ft. per mile, discliarged 15 miiiion gallons per day; velocity, 2.892 ft. 
per sec, / = 0.00574. 

(2) East Jersey riveted steel pipe hne, Newark, N. J., 21 miles long, 48 
in. diam., 50 million U. S. gals, per day; velocity about 6 ft. per sec. 

(3) Perth to Coolgarlie, Western Australia, 351 miles, 30 in. steel pipe 
with lock-bar joints. Eight pumping stations in the Hne. Two tests 
showed deUvery of 5 and 5.6 milUon gals, per day; hydrauhc gradient 
2.25 and 2.8 ft. per mile; velocity, 1.889 and 2.115 ft. per sec.;/= o 00480 
and 0.00486. 

Flow of Water in Riveted Steel Pipes. — The laps and rivets tend 
to decrease the carrying capacity of the pipe. See paper on *'New 
Formulas for Calculating the Flow of Water in Pipes and Channels," by 
W. E. Foss, Jour. Assoc. Eng. Soc, xiii, 295. Also Clemens Herschel's 
book on "115 Experiments on the Carrying Capacity of Large Riveted 
Metal Conduits," John Wiley & Sons, 1897. 



744 



HYDRAULICS. 



Flow of Water in House-service Pipes. 

Mr. E. Kuichling, C. E., furnished the following table to the Thomson 
Meter Co.: 





. 


Discharge, 


or Quantity 


capable of being delivered, in 




•S 


Cubic Feet per 


Minute, from the Pipe, under the 




Pressure in Mi 
pounds per 
square inch. 




conditions 


specified in 


the first column. 


Condition of 
Discharge. 


Nominal Diameters of Iron or Lead Service-pipe in 
Inches. 




1/2 


5/8 


3/4 


1 


11/2 


2 


3 


4 


6 




30 


1.10 


1.92 


3.01 


6.13 


16.58 


33.34 


88.16 


173.85 


444.63 


Through 35 


40 


1.27 


2.22 


3.48 


7.08 


19.14 


38.50 


101.80 


200.75 


513.42 


feet of ser- 


50 


1.42 


2.48 


3.89 


7.92 


21.40 


43.04 


113.82 


224.44 


574.02 


vice-pipe, 


60 


1.56 


2.71 


4.26 


8.67 


23.44 


47.15 


124.68 


245.87 


628.81 


no back 


75 


1.74 


3.03 


4.77 


9.70 


26.21 


52.71 


139.39 


274.89 


703.03 


pressure. 


100 


2.01 


3.50 


5.50 


11.20 


30.27 


60.87 


160.96 


317.41 


811.79 




130 


2.29 


3.99 


6.28 


12.77 


34.51 


69.40 


183.52 


361.91 


925.58 




30 


0.66 


1.16 


1.84 


3.78 


10.40 


21.30 


58.19 


118.13 


317.23 


Through 100 


40 


0.77 


1.34 


2.12 


4.36 


12.01 


24.59 


67.19 


136.41 


366.30 


feet of ser- 


50 


0.86 


1.50 


2.37 


4.88 


13.43 


27.50 


75.13 


152.51 


409.54 


vice-pipe, 


60 


0.94 


1.65 


2.60 


5.34 


14.71 


30.12 


82.30 


167.06 


448.63 


no back 


75 


1.05 


1.84 


2.91 


5.97 


16.45 


33.68 


92.01 


186.78 


501.58 


pressure. 


too 


1.22 


2.13 


3.36 


6.90 


18.99 


38.89 


106.24 


215.68 


579.18 




130 


1.39 


2.42 


3.83 


7.86 


21.66 


44.34 


121.14 


245.91 


660.36 


Through 100 
feet of ser- 


30 


0.55 


0.96 


1.52 


3.11 


8.57 


17.55 


47.90 


97.17 


260.56 


40 


0.66 


1.15 


1.81 


3.72 


10.24 


20.95 


57.20 


116.01 


311.09 


50 


0.75 


1.31 


2.06 


4.24 


11.67 


23.87 


65.18 


132.20 


354.49 


vice-pipe, 
and 15 feet 
vertical 


60 


0.83 


1.45 


2.29 


4.70 


12.94 


26.48 


72.28 


146.61 


393.13 


75 


0.94 


1.64 


2.59 


5.32 


14.64 


29.96 


81.79 


165.90 


444.85 


100 


1.10 


1.92 


3.02 


6.21 


17.10 


35.00 


95.55 


193.82 


519.72 


rise. 


130 


1.26 


2.20 


3.48 


7.14 


19.66 


40.23 


109.82 


222.75 


597.31 




30 


0.44 


0.77 


1.22 


2.50 


6.80 


14.11 


38.63 


78.54 


211.54 


Through 100 


40 


0.55 


0.97 


1.53 


3.15 


8.68 


17.79 


48.68 


98.98 


266.59 


feet of ser- 


50 


0.65 


1.14 


1.79 


3.69 


10.16 


20.82 


56.98 


115.87 


312.08 


vice-pipe, 


60 


0.73 


1.28 


2.02 


4.15 


11.45 


23.47 


64.22 


130.59 


351.73 


and 30 feet 


75 


0.84 


1.47 


2.32 


4.77 


13.15 


26.95 


73.76 


149.99 


403.98 


vertical 


100 


1.00 


1.74 


2.75 


5.65 


15.58 


31.93 


87.38 


177.67 


478.55 


rise. 


130 


1.15 


2.02 


3.19 


6.55 


18.07 


37.02 


101.33 


206.04 


554.96 



In this table it is assumed that the pipe is straight and smooth inside; 
that the friction of the main and meter are disregarded; that the inlet 
from the main is of ordinary character, sharp, not flaring or rounded, and 
that the outlet is the full diameter of pipe. The deliveries given will be 
increased if, first, the pipe between the meter and the main is of larger 
diameter than the outlet; second, if the main is tapped, say for 1-inch 
pipe, but is enlarged from the tap to 1 1/4 or 1 1/2 inch; or, third, if pipe on 
the outlet is larger than that on the inlet side of the meter. The exact 
details of the conditions given are rarely met in practice; consequently 
the quantities of the table may be expected to be decreased, because the 
pipe is Uable to be throttled at the joints, additional bends may inter- 
pose, or stop-cocks may be used, or the back-pressure may be increased. 



LOSS OF HEAD. 



745 



Friction Loss in Clean Cast-iron Pipe. 

Compiled from Weston's "Friction of Water in Pipes" as computed from 
formulas of Henry Darcy. 
Pounds loss per 1000 feet in pipe of pven diameter. (Small lower 
figures give Velocity in Feet per Second.) 



U. S.Gals per 


Diameter of Pipe in Inches. 


Min. and (Cu. 
Ft. per Sec.) 


3 


4 

20 

6.4 

82 

13.0 

184 

19.0 

328 

26.0 


5 


6 


8 


10 


12 


14 


16 


20 


24 


30 


250 

(0.56) 
500 
(1.11) 
750 
(1.67) 
1,000 
(2.23) 


60 

11 
220 

23 
477 

34 


6.4 

4.0 
25.8 

8.2 
58.0 
12.2 
103.0 
16.3 


2.5 

2.8 
10.0 

6.0 
23.0 

8.0 
40.0 
11.0 


0.6 

1.6 
2.3 
3.2 
5.0 
4.8 
9.0 
6.4 


0.2 
1.2 
0.7 
2.4 
1.6 
3.1 
2.9 
4.1 


0.07 

0.7 

0.29 

1.4 

0.66 

2.1 

1.20 

2.8 


0.03 
0.52 
0.13 
1.04 
0.30 
1.56 
0.53 
2.08 


0.02 

0.4 

0.07 

0.8 

0.15 

1.2 

0.27 

1.6 


0.01 

0.20 
0.02 
0.51 
0.05 
0.77 
0.09 
1.0 


0.00 
0.18 
0.01 
0.35 
0.02 
0.53 
0.03 
0.71 


0.00 
0.23 

o;6i 

0.45 


1,250 

(2.79) 






161.0 
20.4 

231.9 
24.5 


63.0 
14.0 
91.0 
17.0 

123.0 
20.0 

160.0 
23.0 


14.0 
8.0 
21.0 
10.0 
28.0 
11.0 
37.0 
13.0 


4.6 
5.1 
6.6 
6.1 
9.0 
7.1 
12.0 
8.2 


1.80 

3.6 

2.00 

4.3 

3.60 

5.0 

4.70 

5.7 


0.83 
2.60 
1. 10 
3.13 
1.64 
3.65 
2.14 
4.17 


0.42 

2.0 

0.61 

2.4 

0.83 

2.8 

1.10 

3.2 


0.14 

1.3 

0.20 

1.5 

0.27 

1.8 

0.35 

2.0 


0.06 
89 
0.08 
1.06 
0.11 
1.24 
0.14 
1.42 










1,500 






o^ 


(3.34) 






0,68 


1,750 








(3.90) 










2,000 








O'i 


(4.46) 








91 










2,500 


Dian 
Pipe 


1. of 
inln. 






58.0 
16.0 


18.0 
10.2 
26.0 
12.0 


7.30 
7.1 
10.00 

8.5 


3.34 
5.21 
4.81 
6.25 
8.55 
8.34 


1.70 

4.0 

2.40 

4.8 

4.30 

6.4 

6.80 

8.0 


0.55 

2.6 

0.79 

3.1 

1.40 

4.1 

2.20 

5.1 


0.22 
1.80 
0.32 
2.10 
0.56 
2.80 
1.00 
3.60 


07 


(5.57) 






1.13 


3,000 

(6.68) 








10 


36 


48 








1 40 


4,000 








18 


(8.91) 
















1 SO 


5,000 


0.11 
1.6 


0.03 

0.89 












79 


(11.14) 














2 30 


















6,000 


0.16 

1.9 

0.23 

2.2 

0.29 

2.5 

0.37 

2.8 

0.45 

3.1 


0.04 

1.06 

0.05 

1.2 

0.07 

1.4 

0.09 

1.6 

o.n 

1.8 
















3.20 
6.1 
4.30 
7.1 


1.30 
4.30 
1.70 
5.00 
2.20 
5.70 
2.80 
6.40 


41 


(13.37) 
















2 70 


7,000 
















16 


(15.60) 

















3 20 


8,000 
















73 


(17.82) 


















3 60 


9,000 


















9? 


(20.05) 


















4 10 


10,000 


















1 n 


(22.28) 




















4.50 



Vel.ft.per sec. 
Hd.duevel.ft 



Vel.ft.per sec. 
Hd.duevel.ft. 



I 
0.016 



2 
0.062 



13 
2.6 



14 
3.1 



3 

0.14 



15 
3.5 



4 
0.25 



5 

0.39 



16 
4.0 



6 
0.56 



18 
5.0 



7 
0.76 



19 
5.6 



20 
6.2 



25 
9.3 



30 
14.0 



40 
24.8 



12 
2.2 

"^ 
38.8 



These losses are for new, clean, straight, tar-coated, cast-iron pipes. For 
pipes that have been in service a number of years the losses 
will be larger on account of corrosion and incrustation, and 10 years 1.3 
the losses in the tables should be multiplied under average 20 " 1.6 
conditions by the factors opposite; but they must be used 30 '* 2.0 
with much discretion, for some waters corrode pipes much 50 *' 2.6 
more rapidly than others. . 75 '* 3.4 

The same figures may be used for wrought-iron pipes which are not 
subject to a frequent change of water. 



746 HYDRAULIC FORMULA. 

Approximate Hydraulic Formulae. (The Lombard Governor Co., 

Boston, Mass.) 

Head (//) in feet. Pressure (P) in lbs. per sq. in. Diameter (D) in 
feet. Area (A) in sq. ft. Quantity (Q) in cubic ft. per second. Time 
{T) in seconds. 

Spouting velocity = 8.02 \/ll. 

Time (Ti) to acquire spouting velocity in a vertical pipe, or (Tj) in a 
pipe on an angle (0) from horizontal: 

Ti= 8.02 V^ H- 32.17, T2= 8.02 ^H h- 32.17 sin ^. 

Head (H) or pressure (P) which will vent any quantity (Q) through a 
round orifice of any diameter (D) or area (A): 
H = Q'-^ 14.1 Z>4 = ^2 ^ 23.75 A^] P = Q^ ^ 34.1 D^ = (?2 _=_ 55.3 ^2. 

Quantity (Q) discharged through a round orifice of any diameter (D) or 
area (A) under any pressure (P) or under any head {H): 



Q = Vp X 55.3 X A^ = VPX 34.1 X D^; 
= ^H X 23.75 X A2 =Vhx 14.71 X £>*. 

Diameter (D) or area (^) of a round orifice to vent any quantity (Q) 
under any head (H) or under any pressure (P) : 



D = \^Q-t-3.84:VH =\/q-4-5.8 Vp; ^=Q-h4.89V^ =Q-^7.35 Vp. 

Time (T) of emptying a vessel of any area (A) through an orifice of any 
area (a) anywhere in its side: T = 0.416 A ^H -^ a. 

Time {T) of lowering a water level from (Z/") to {h) in a tank of area A 
through an orifice of any area (a) in its side. r = 0.416A(V^ — v^) -^a. 

Ivinetic energy {K) or foot-pounds in water in a round pipe of any 
diameter (D) when moving at velocity (7): K = 0.76 XD^ XL XV^. 

Area (a) of an orifice to empty a tank of any area (A) in any time {T) 
from any head {H): a = T ^ 0.409 A ^H. 

Area (a) of an orifice to lower water in a tank of area {A) from head {H) 
to {h) in time (7^): a = T ^ 0.409 X A X {'^H - V/i). 

Compound Pipes and Pipes with Branches. (Unwin.) — Loss of 
head in a main consisting of different diameters. (1) Constant discharge. 
Total loss of head i/ = /ii 4- /12 + /13 = 0.1008 /Q2 {ljdt^+ hJd2^-{- U/dz^). 

(2) Constant velocity in the main, the discharge diminishing^ from sec- 
tion to section. H = 0.0551 fv ^^2 (li/^Qi-^ UJ^^ + hf^Qz). Equiv- 
alent main of uniform diameter. Length of equivalent main 

I = cf5 (Zi/(fi5 + i^/d.^ + h/dz^). 

Loss of head in a main of uniform diameter in which the discharge de- 
creetses uniformly along its length, such as a main with numerous branch 
pipes uniformly spaced and deUvering equal quantities: h = 0.0336 
fQH/d^, Q being the quantity entering the pipe. The loss of head is just 
one-third of the loss in a pipe carrying the uniform quantity Q through- 
out its length. 

Loss of head in a pipe that receives Q cu. ft. per sec. at the inlet, and 
delivers Q^ cu. ft. at x ft. from the inlet, having distributed qx cu. ft. 
uniformly in that distance, h^= 0.1008 /a: (Q^+ 0.55 qx)/d^. 

Delivery by two or more mains, in parallel. Total discharge = Qi + Q 
■+-Q3 = 3.149 ^^^hTf W dx^ /lx+^ d2^ /h-\-^ dz^ /h) . Diameter of an equivalent 
main to discharge the same total quantity, d=(v^+v^cf25+v^d30^/^. 

Rifled Pipes for Conveying Heavy Oils. {Eng. Rec, May 23, 1908.)— 
The oil from the California fields is a heavy, viscous fluid. Attempts 
to handle it in long pipe lines of the ordinary type have not been practi- 
cally successful. High pumping pressures are required, resulting in large 
expense for pipe and for pumping equipment. 



p 



LOSS OF HEAD. 



747 



The method of pumping in the rifled-pipe line is to inject about 10 per 
cent of water with the oil and to give the cil and water a centrifugal 
motion, by means of the rifled pipe, sufficient to throw the water to the 
outside, where it forms a tliin film of lubrication between the oil and the 
sides of the pipe that greatly reduces the friction. The rifled pipe de- 
livers at ordinary temperatures eight to ten times as much oil, through a 
long line, as does a line of ordinary pipe under similar conditions. An 
8-in. rifled pipe line 282 miles in length has been built from the Kern oil 
fields to Porta Costa, on tidewater near San Francisco. The pipe is 
rifled with six helical grooves to the circumference, these grooves making 
a complete turn through 360 deg. in 10 ft. of length. 

Loss of Pressure Caused by Valves and Fittings — The data given 
below are condensed from the results of experiments by John R. Freeman 
xor the Inspection Department of the Assoc. Facty. Mut. Ins. Cos. The 
friction losses in ells and tees are approximate. Fittings of the same nom- 
inal size with the different curvatures and different smoothness as made 
by different manufacturers wiU cause materially different friction losses. 
The figures are the number of feet of clean, straight pipe of same size 
which would cause the same loss as the fitting. Grinnell dry-pipe valve, 
6-in., 80 ft.; 4-in., 47 ft. Grinnell alarm check, 6-in., 100 ft.; 4-in., 47 ft. 
Pratt & Cady check valve, 6-in., 50 ft.; 4-in., 25 ft. 4-in. Walworth globe 
check valve, 6-in., 200 ft.; 4-in., 130 ft. 21/2 in. to 8-in. ells, long-turn, 
4 ft.; short-turn 9 ft. 3-ia. to 8-in. tees, long-turn, 9 ft.; short-turn, 17 ft. 
One-eighth bend, 5 ft. 

Effect of Bends and Curves in Pipes. — Weisbach's rule for bends: 

Loss of head in feet = ["0.131 + 1.847 (^^^^J X g|^ X ^, in which r 

= internal radius of pipe in feet, R = radius of curvature of axis of pipe, 
V = velocity in feet per second, and a = the central angle, or angle sub- 
tended by the bend. 

Hamilton Smith, Jr., in his work on Hydrauhcs, says: The experimental 
data at hand are entirely insufficient to permit a satisfactorj^ analysis of 
this quite complicated subject; in fact, about the only experiments of 
value are those made by Bossut and Dubuat with small pipes. 

Curves. — If the pipe has easy curves, say with radius not less than 5 
diameters of the pipe, the flow will not be materially diminished, provided 
the tops of all curves are kept below the hydraulic grade-line and provision 
be made for escape of air from the tops of all curves. (Trautwine.) 

WilUams, Hubbefi and Fenkel (Trans. A. S. C. E., 1901) conclude from 
an extensive series of experiments that curves of short radius, down to 
about 21/2 diameters, offer less resistance to the flow of water than do 
those of longer radius, and that earUer theories and practices regarding 
curve resistance are incorrect. For a 90° curve in 30 in. cast-iron pipe, 
6 ft. radius, they found the loss of head 15.7% greater than that of a 
straight pipe of equal length; with 10 ft. radius. 17.3% erreater: with 25 ft. 
radius, 52 7% greater; and with 60 ft. radius, 90.2% greater. 

Friction Heads for Elbows. Heads Required to Overcome the 
Resistance of Circular 90° Bends. 

(U. S. Cast Iron Pipe & Foundry Co.) 



Velocity 




Radius of Bend in 


Diameters of Pipe. 




in Feet 
Per 


0.5 1 


0.75 1 


1.00 


1.25 


1.5 


2.0 


3.0 


5.0 


Second. 


Head, in Feet. 


1 


0.016 


0.005 


0.002 


0.002 


0.001 


0.001 


0.001 


0.001 


2 


.062 


.018 


.009 


.007 


.005 


.005 


.004 


.004 


3 


.140 


.041 


.020 


.015 


.012 


.011 


.010 


.009 


4 


.245 


.072 


.036 


.026 


.021 


.019 


.017 


.016 


5 


.388 


.113 


.056 


.041 


.033 


.029 


.027 


.025 


6 


.559 


.162 


.081 


.059 


.048 


.042 


.038 


.036 


7 


.761 


.221 


.110 


.080 


.066 


.057 


.052 


.050 


8 


.994 


.288 


.144 


.104 


.086 


.074 


.069 


.065 


9 


1.260 


.365 


.182 


.132 


.108 


.094 


.086 


.082 


10 


1.550 


.450 


.225 


.163 


.134 


.116 


.106 


.101 


12 


2.340 


.649 


.324 


.236 


.192 


.167 


.153 


.145 



748 



HYDRAULICS. 



Loss of Head in Pipes, Tees and Elbows. — Results of tests made 
on locomotive water colmmis by Arthm* N. Talbot and Melvin L. 
Enger (Bulletin No. 48, Univ. of 111. Engineering Experiment Station) 
may be expressed by the following formula: Loss of head in 100 ft. of 
new cast-iron pipe for sizes above 6 in. diam. = 0.044 v^-^ -r- c?i-25, in 
which V = velocity of flow in feet per sec. , and d = internal diameter of 
pipe, in ft. The results for pipes from 8 to 24 in. in diameter agree 
closely with those obtained by WiUiams and Hazen for pipes after 
about three years of service, with the diagram given in Tm*neaure and 
Russell's "Public Water Supplies," and with the formula of Unwin; 
they are, however, generally smaller than those given by the ElUs and 
Howland tables and by Darcy's formula. 

The following tables are taken from diagrams included in the Bulle- 
tin; they give the values selected by the Committee on Water Service, 
Am. Ry. Eng'g and Maintenance of Way Association, as representing 
the maximum results of numerous tests. 

LOSS OF HEAD IN TEES, IN FEET. 



Discharge, 

Gal. per 

Min. 


Cu. Ft. 


Sizes of Tees. 


Sin. 


10 In. 


12 In. 


14 In. 


16 In. 


18 In. 


1000 


20.5 

41 

61.5 

82 

102.5 
123 
143.5 
164 


1.1 

4 
8.7 


0.4 
1.7 
3.9 
6.7 
10.3 


0.25 
0.95 
1.95 
3.35 
5.20 
7.30 








2000 


0.40 
1.00 
1.75 
2.70 
3.90 
5.30 
6.80 


0.25 
0.60 
I.IO 
1.60 
2.30 
3.10 
3.90 


0.13 


3000 


0.35 


4000 


0.65 


5000 


1.00 


6000 


1.45 


7000 






2.00 


8000 








2.60 









LOSS OF HEAD IN ELBOWS, IN FEET. 

(Radius of curvature of elbow axis = 1.5 X diameter of elbow.) 



Discharge, 

Gal. per 

Min. 


Cu. Ft. 

per 
Sec. 


Sizes of Elbows. 


8 In. 


10 In. 


12 In. 


14 In. 


16 In. 


18 In. 


1000 


20.5 

41 

61.5 

82 

102.5 
123 
143.5 
164 


0.2 
1.2 
2.8 












2000 


0.5 
1.1 
1.9 
3.2 


0.20 
0.50 
0.95 
1.50 
2.20 
3.00 


0.10 
0.25 
0.50 
0.75 
1.15 
1.65 
2.10 






3000 


0.15 
0.25 
0.40 
0.60 
0.87 
1.15 




4000 


0.10 


5000 


0.15 


6000 


0.25 


7000 






0.50 


8000 






0.70 



(Radius of curvature = 3 X diameter.) 



1000 


20.5 

41 

61.5 

82 

102.5 
123 
143.5 
164 


0.25 
0.75 
2.00 
4.00 












2000 


0.35 
0.80 
1.45 
2.25 


0.10 
0.40 
0.70 
1.10 
1.60 
2.20 
3.00 








3000 


0.15 
0.33 
0.50 
0.70 
1.00 
1.45 






4000 


0.12 
0.20 
0.40 
0.58 
0.85 




5000 


07 


6000 


0.10 


7000 






0.25 


8000 






0.45 



Hydraulic Grade-line. — In a straight tube of uniform diameter 
throughout, running full and discharging freely into the air, the hydraulic 
grade-line is a straight line drawn from the discharge end to a point imme- 
diately over the entry end of the pipe and at a depth below the surface 
equal to the entry and velocity heads. (Trautwine.) 

In a pipe leading from a reservoir, no part of its length should be above 
the hydraulic prade-line. 

Air-bound Pipes. — A pipe is said to be air-bound when, in conse- 
quence of air being entrapped at the liigh points of vertical curves in the 
line, water will not flow out of the pipe, although the supply is higher than 
the outlet. The remedy is to provide cocks or valves at the high points. 



FIRE-STREAMS. 749 

through which the air may be discharged. The valve may be made 
automatic by means of a float. 

Water-Hammer. — When selecting valves and fittings, the possibility 
of shock or strain due to water-hammer, in excess of the average work- 
ing pressure of the line or system, should be considered. Many valves 
and fittings, installed where the working pressure under nomal con- 
ditions would be low, have failed because of pressure due to water- 
hammer. This danger can be avoided by proper cushioning of the 
line by air chambers, or by reUef valves. 

When a valve in a pipe is closed while the w ater is flowing, the velocity 
of the water behind the valve is retarded and a dynamic pressure is 
produced. When the valve is closed quickly tliis dynamic pressure 
may be very great. It is then called "water-hammer" or "water- 
ram," and it causes in many cases fracture of the pipe. It is provided 
against by arrangements which prevent the rapid closing of the valve. 
Formulse for the pressure produced by this shock are (see Merriman's 
Hydraulics) 

p = 0.027 j^- Po + Pi. . . (1) p = 6Sv-po+Pi (2) 

where po = the static pressure, lb. per sq. in., when there is no flow, 
Pi = the static pressure when the flow is in progress, p = the maximum 
dynamic pressure due to the water-hammer in excess over the pressure 
Po, V = the velocity in feet per second, L = length of pipe back from 
the valve in feet, and t = time of closing the valve in seconds. Formula 
(1) is to be used when t is greater than 0.000428L and (2) when t is 
equal to or less than this. 

From the first of these formulae the value of t when p = is found 
to be ^ = 0.027 Lv -r- (po — Pi), which is the time required for the 
valve closing in order that there may be no water-hammer. 

Vertical Jets. (Molesworth.) — H = head of water, h = height of 
jet, d = diameter of jet, K = coefficient, varying with ratio of diameter 
of jet to head ; then h = KH. 

ItH = dXSOO 600 1000 1500 1800 2800 3500 4500 
K= 0.96 0.9 0.85 0.8 0.7 0.6 0.5 0.25 

Water Delivered through 3Ieters. (Thomson Meter Co.) — The 
best modern practice limits the velocity in water-pipes to 10 lineal feet 
per second. Assume this as a basis of delivery, and we find, for the sev- 
eral sizes of pipes usually metered, the following approximate results: 
Nominal diameter of pipe in inches: 

3/8 5/8 3/4 1 11/2 2 3 4 6 

Quantity delivered, in cubic feet per minute, due to said velocity: 
0.46 1.28 1.85 3.28 7.36 13.1 29.5 52.4 117.9 

Prices Charged for Water in Different Cities. (National Meter Co.) 

Average minimum price for 1000 gallons in 163 places 9.4 cents. 

Average maximum price for 1000 gallons in 163 places 28 

Extremes, 2V2 cents to 100 ** 

FIRE-STREAMS. 

Fire-Stream Tables. — The tables on pages 750 and 751 are con- 
densed from one contained in the pamphlet of "Fire-Stream Tables" 
of the Associated Factory Mutual Fire Ins. Cos., based on the experi- 
ments of John R. Freeman, Trans. A. S. C. E., vol. xxi, 1889. 

The pressure in the first column is that indicated by a gauge attached 
at the base of the play pipe and set level with the end of the nozzle. The 
vertical and horizontal distances, in 2d and 3d cols., are those of effective 
fire-streams with moderate wind. The maximum limit of a " fair stream " 
is about 10% greater for a vertical stream; 12% for a horizontal stream. 
In still air much greater distances are reached by the extreme drops. 
The pressures given are for the best quality of rubber-lined hose, smooth 
inside. The hose friction varies greatly in different kinds of hose, accord- 
ing to smoothness of inside surface, and pressures as much as 50% 
greater are required for the same delivery in long lengths of inferior 
rubber-lined or linen hose. The pressures at the hydrant are those while 
the stream is flowing, and are those required with smooth nozzles. Ring 



750 



HYDRAULICS. 



nozzles require greater pressures. With the same pressures at the base 

or ine piay pipe, the discharge of a3/4-in. smooth nozzle is the same as that 
of a 7/8-in. ring nozzle; of a T/g-in. smooth nozzle, the same as that of a 
1-in. ring nozzle. 

The figures for hydrant pressure in the body of the table are derived 
by adding to the nozzle or play-pipe pressure the friction loss in the 
hose, and also the friction loss of a Chapman 4-way independent gate 
hydrant ranging from 0.86 lb. for 200 gals, per min. flowing to 2.31 lbs. 
for 600 gals. 

The following notes are taken from the pamphlet referred to. The 
discharge as stated in Ellis's tables and in their numerous copies in trade 
catalogues is from 15 to 20% in error. 

In the best rubber-Uned hose, 21/2-in. diam., the loss of head due to 
friction, for a discharge of 240 gallons per minute, is 14.1 lbs. per 100 ft. 
length; in inferior rubber-Uned mill hose, 25.5 lbs., and in unhned linen 
hose, 33.2 lbs. 

Less than a li/g-in. smooth-nozzle stream with 40 lbs. pressure at the 
base of the play pipe, discharging about 240 gals, per min., cannot be 
called a first-class stream for a factory fire. 80 lbs. per sq. in. is con- 
sidered the best hydrant pressure for general use; 100 lbs. should not be 
exceeded, except for very high buildings, or lengths of hose over 300 ft. 

Hydrant Pressures Required with DifiPerent Sizes and Lengths of 

Hose. (J. R. Freeman, Trans. A. S. C. E., 1889.) 

3/4-inch smooth nozzle. 





Fire- 
steam 
Distance. 


s 

I 




Hydrant Pressure with Different Lengths of 


1-^ 


Hose to Maintain Pressure at Base of Play Pipe. 


2^ 


Vert. 


Hor. 


50 ft. 100 ft. 


200 ft. 


300 ft. 


400 ft. 


500 ft. 


600 ft. 


800 ft. 


1000 

ft. 


10 


17 


19 


52 


10 


11 


11 


12 


13 


13 


14 


15 


16 


?,0 


33 


29 


73 


21 


22 


23 


24 


25 


26 


28 


30 


32 


30 


48 


37 


90 


31 


32 


34 


36 


38 


40 


41 


45 


49 


40 


60 


44 


104 


42 


43 


46 


48 


50 


53 


55 


60 


6!) 


•50 


67 


50 


116 


52 


54 


57 


60 


63 


66 


69 


73 


81 


60 


72 


54 


17.7 


63 


65 


68 


72 


76 


79 


83 


90 


97 


70 


76 


58 


137 


73 


75 


80 


84 


88 


92 


97 


105 


114 


80 


79 


62 


147 


84 


86 


91 


96 


101 


106 


111 


120 


130 


90 


81 


63 


156 


94 


97 


102 


108 


113 


119 


124 


135 


146 


100 


83 


68 


164 


105 


108 


114 


120 


126 


132 


138 


150 


163 











7/8-inch smooth nozzle. 










10 


18 


21 


71 


11 


11 


13 


14 


15 


16 


17 


19 


?? 


20 


34 


33 


100 


22 


23 


25 


27 


30 


32 


34 


39 


43 


30 


49 


42 


123 


33 


34 


38 


41 


45 


48 


51 


58 


65 


40 


62 


49 


142 


43 


46 


50 


55 


59 


64 


68 


78 


87 


50 


71 


55 


159 


54 


57 


63 


69 


74 


80 


86 


97 


108 


60 


77 


61 


174 


65 


69 


75 


82 


89 


96 


103 


116 


130 


70 


81 


66 


188 


76 


80 


88 


96 


104 


112 


120 


136 


157 


80 


85 


70 


201 


87 


91 


101 


110 


119 


128 


137 


155 


173 


90 


88 


74 


213 


98 


103 


113 


123 


134 


144 


154 


174 


195 


100 


90 


76 


224 


109 


114 


126 


137 


148 


160 


171 


194 


216 













1-inch smooth no2 


5zle. 










10 


18 


21 


93 


12 


12 


14 


16 


18 


20 


22 


26 


30 


20 


35 


37 


132 


23 


25 


29 


33 


37 


41 


45 


52 


60 


30 


51 


47 


161 


34 


37 


43 


49 


55 


61 


67 


79 


90 


40 


64 


55 


186 


46 


50 


58 


66 


73 


81 


89 


105 


120 


50 


73 


61 


208 


57 


62 


72 


82 


92 


102 


111 


131 


151 


60 


79 


67 


228 


69 


75 


87 


98 


110 


122 


134 


157 


181 


70 


85 


72 


246 


80 


87 


101 


113 


128 


142 


156 


183 


211 


80 


89 


76 


263 


92 


100 


113 


131 


147 


162 


178 


209 


241 


90 


92 


80 


279 


103 


112 


130 


147 


165 


183 


200 


236 


.... 


100 


96 


83 


295 


115 


123 


144 


164 


183 


203 


223 








FIRE-STREAMS. 



751 



Hydrant Pressures Required with Different Sizes and Lengths of 

Hose. — Continued. 
1 1/8-inch smooth nozzle. 



i 


Fire- 
Steam 
Distance. 


a 

a 
I 

O 


Hydrant Pressure with Different Lengths of 


Hi 


Hose to Maintain Pressure at Base of Play Pipe. 




Vert. 


Hor. 


50 ft. 


100 ft. 


200 ft. 


300 ft. 


400ft. 


500 ft. 


600 ft. 


800 ft. 


1000 

ft. 


10 


18 


22 


119 


12 


14 


17 


20 


24 


27 


30 


36 


43 


20 


36 


38 


168 


25 


28 


34 


41 


47 


54 


60 


73 


85 


30 


52 


50 


206 


37 


42 


52 


61 


71 


80 


90 


109 


128 


40 


65 


59 


238 


50 


56 


69 


81 


94 


107 


120 


145 


171 


50 


75 


66 


266 


62 


70 


86 


102 


118 


134 


150 


181 


213 


60 


83 


72 


291 


74 


84 


103 


122 


141 


160 


180 


218 


256 


70 


88 


77 


314 


87 


98 


120 


143 


165 


187 


209 


254 




80 


92 
96 
99 


81 
85 
89 


336 
356 
376 


99 
112 
124 


112 
126 
140 


138 
155 
172 


163 
183 
204 


188 
212 
236 


214 
241 


239 






90 






100 




























1 1/4-inch smooth nozzle. 










10 


19 


22 


148 


14 


16 


21 


26 


31 


36 


41 


51 


61 


20 


37 


40 


209 


27 


32 


42 


52 


62 


72 


82 


101 


121 


30 


53 


54 


256 


41 


49 


63 


78 


93 


108 


123 


152 


182 


40 


67 


63 


296 


55 


65 


84 


104 


124 


144 


164 


203 


243 


50 


77 


70 


331 


68 


81 


106 


130 


155 


180 


204 


254 




60 


85 
91 
95 
99 
101 


76 
81 
83 
90 
93 


363 
392 
419 
444 
468 


82 
96 
110 
123 
137 


97 
113 
129 
145 
162 


127 
148 
169 
190 
211 


156 

182 
208 
234 
261 


186 
217 
248 


216 
252 


245 






70 






80 








90 










100 

































1 3/8-inch smooth nozzle. 










10 

20 
30 
40 


20 
38 
55 
69 
79 
87 
92 
97 
100 
103 


23 
42 
56 
66 
73 
79 
84 
88 
92 
96 


182 
257 
315 
363 
406 
445 
480 
514 
545 
574 


16 
31 
47 
62 
78 
93 
109 
124 
140 
156 


19 
39 
58 
77 
96 
116 
135 
154 
173 
193 


27 
53 
80 
107 
134 
160 
187 
214 
240 


34 
68 
103 
137 
171 
205 
239 


42 
83 
125 
166 
208 
250 


49 
98 
147 
196 

245 


56 
113 

169 
226 


71 
143 
214 


86 
173 
259 


50 






60 








70 










80 












90 














100 































Pump Inspection Table. 

Discharge of nozzles attached to 50 ft. of 2 i, 2-in. best quality rubber- 
lined hose, inside smooth. (J. R. Freeman.) 



a 3 

t~, Oi 


Size of Smooth Nozzle. 


Ring Nozzle. 




1 3/4 


1 1/2 


1 3/8 


1 1/4 


1 1/8 


1 


7/8 


3/4 


1 V8 


1 1/4 


1 1/8 


10 


193 


163 


146 


127 


107 


87 


68 


51 


118 


101 


84 


20 


274 


232 


206 


179 


151 


123 


96 


72 


167 


143 


119 


30 


335 


283 


251 


219 


184 


150 


118 


88 


205 


175 


145 


40 


387 


327 


291 


253 


213 


173 


136 


101 


237 


202 


168 


50 


432 


366 


325 


283 


238 


194 


152 


113 


264 


226 


188 


60 


473 


400 


357 


309 


261 


213 


167 


124 


289 


247 


205 


70 


510 


432 


385 


334 


281 


230 


180 


134 


313 


267 


222 


80 


546 


461 


412 


357 


301 


246 


192 


144 


334 


285 


237 


90 


579 


490 


437 


379 


319 


261 


204 


152 


355 


303 


252 


100 


610 


515 


461 


400 


337 


275 


215 


161 


374 


319 


266 



762 



HYDRAULICS. 



Pipe Sizes for Ordinary Fire-Streams. 

(U. S. Cast Iron Pipe & Foundry Co., 1914.) 



No. 


40 Lb. 


50 


Lb. 


60 


Lb. 


70 


Lb. 


80 Lb. 


90 Lb. 


of 

1 1/8 

In 


Pressure. 


Pressure. 


Pressure. 


Pressure. 


Pressure. 


Pressure. 


c 




d 




d 




d 




d 




d 










1— 1 




















Hose 
Noz- 


aS 


^ 


£s 


g 


as 


^ 


as 


i 


^^: 


o 


^f^ 


1 


zles. 


Sw 


fe 


f^w 


fe 


'p^m 


fe 


Sc^ 


E 


s'^ 


fe 


Sc^ 


f^ 


I 


4 


20 


6 


23 


6 


25 


6 


27 


6 


29 


6 


30 


2 


6 


40 


8 


45 


8 


50 


8 


53 


8 


57 


8 


61 


3 


8 


61 


8 


68 


10 


74 


10 


80 


10 


86 


10 


91 


4 


10 


81 


10 


90 


10 


99 


10 


107 


12 


114 


12 


121 


5 


10 


101 


12 


113 


12 


124 


12 


134 


12 


143 


12 


152 


6 


12 


121 


12 


135 


12 


149 


14 


160 


14 


172 


14 


182 


7 


12 


141 


14 


158 


14 


174 


14 


187 


14 


200 


16 


212 


8 


12 


162 


14 


181 


14 


199 


16 


214 


16 


229 


16 


242 


9 


14 


182 


14 


203 


16 


223 


16 


241 


16 


257 


18 


273 


10 


14 


202 


16 


226 


16 


248 


16 


267 


18 


286 


18 


303 


11 


16 


222 


16 


248 


18 


273 


18 


294 


18 


314 


18 


333 


12 


16 


243 


18 


271 


18 


298 


18 


321 


20 


343 


20 


364 


13 


16 


263 


18 


293 


18 


323 


20 


348 


20 


372 


20 


'394 


14 


18 


283 


18 


316 


20 


348 


20 


374 


20 


400 


20 


424 


15 


18 


303 


20 


339 


20 


372 


20 


401 


20 


429 


24 


455 



Flow given in cubic feet per minute. Figures are based on 1 H-in. 
smooth-bore nozzles, playing simultaneously and attached to 200 ft. 
of best quality rubber-lined hose; pressures measured at hose connec- 
tions. Velocity of water in pipe, approximately 3 ft. per second. 

Friction Loss in Rubber-Lined Cotton Hose witli Smoothest Lining. 



i 


Gallons per Minute Flowing. 


.. o 


Velocity 






II 

5 • 


Head 
y2 - 2g. 


*-• 

o 


100 


200 


300 


400 


500 


600 


700 


800 


1000 


S 




^e 






S 


Friction Loss, Pounds per 100 ft. Length. 


Ft. 


Lbs. 


2 


6.836 
5.170 
3.790 
2.895 


27.3 
20.7 
15.2 
11.6 


61.5 
46.5 
34.1 
26.1 


109 
82.7 
60.6 
46.3 


171 
129 
94.7 

72.4 










5 
10 
15 
20 


0.39 
1.6 
3.5 
6.2 


0.17 


21/8 
21/4 
23/8 


189 
136 
104 








0.69 


186 
138 






1.5 


185 




2.7 


21/. 


2.240 


9.0 


20.2 


35.8 


56.0 


80.6 


no 


143 


224 


25 


9.7 


4.2 


25/8 


1.748 


7.0 


15.7 


28.0 


43.7 


62.9 


85.7 


112 


175 


30 


14.0 


6.1 


23/4 


1.391 


5.6 


12.5 


22.3 


34.8 


50.1 


68.2 


89.0 


139 


35 


19.0 


8.2 


27/a 


1.097 


4.4 


9.9 


17.6 


27.4 


39.5 


53.8 


70.2 


110 


40 


24.8 


10.7 


3 


0.900 


3.6 


8.1 


14.4 


22.5 


32.4 


44.1 


57.6 


90 


45 


31.4 


13.6 


3V? 


0.416 


1.7 


3.7 


6.7 


10.4 


15.0 


20.4 


26.6 


41.6 


50 


38.8 


16.7 


4 


0.214 


0.9 


1.9 


3.4 


5.4 


7.7 


10.5 


13.7 


21.4 









The above table is computed on the basis of 14 lbs. per 100 ft. length 
of 21/2-in. hose with 250 gals, per min. flowing, as found in Freeman's 
tests, assuming that the loss varies as the square of tlie quantity, and 
for different diameters and the same quantity inversely as the 5th power 
of the diameter. 

Rated Capacities of Steam Fire-engines, which Is perhaps one third 
greater than their ordinary rate of work at fires, are substantially as 
follows: 

3d size, 550 gals, per min., or 792,000 gals, per 24 hours. 

2d •" 700 " •• 1,008,000 

1st •• 900 " " 1,296,000 

1 ext.. 1.100 " •• 1.584.000 " " 



FLOW OF WATER THROUGH NOZZLES. 



753 



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754 HYDRAULICS. 



THE SIPHON. 

The Siphon is a bent tube of unequal branches, open at both ends, and 
is used to convey a liquid from a higher to a lower level, over an interme- 
diate point higher than either. Its parallel branches being in a vertical 
plane and plunged into two bodies of liquid whose upper surfaces are at 
different levels, the fluid will stand at the same level both within and 
without each branch of the tube when a vent or small opening is made 
at the bend. If the air be withdrawn from the siphon through this vent, 
the water will rise in the branches by the atmospheric pressure without, 
and when the two columns unite and the vent is closed, the liquid will 
flow from the upper reservoir as long as the end of the shorter branch 
of the siphon is below the surface of the liquid in the reservoir. 

If the water was free from air the height of the bend above the supply- 
level might be as great as 33 feet. 

If A = area of cross-section of the tube in square feet, // = the differ- 
ence in level between the two reservoirs in feet, D the density of the 
liquid in pounds per cubic foot, then ADH measures the inte nsity of the 
force which causes the movement of the fluid, and V = ^2gH= 8.02 
^H is the theoretical velocity, in feet per second, which is reduced by 
the loss of head for entry and friction, as in other cases of flow of liquids 
through pipes. In the case of the difference of level being greater than 
33 feet, however, the velocity of the water in the shorter leg is limited 
to that due to a height of 33 feet, or that due to the difference between 
the atmospheric pressure at the entrance and the vacuum at the bend. 

Long Siphons. — Prof. Joseph Torrey, in the Amer. Machinist, de- 
scribes a long siphon which was a partial failure. 

The length of the pipe w^as 1792 feet. The pipe v/as 3 inches diameter, 
and rose at one point 9 feet above the initial level. The final level was 
20 feet below the initial level. No automatic air valve was provided. 
The highest point in the siphon was about one third the total distance 
from the pond and nearest the pond. At this point a pump was placed, 
whose mission was to fill the pipe when necessary. This siphon would 
flow for about two hours and then cease, owing to accumulation of air in 
the pipe. When in full operation it discharged 431/2 gallons per minute. 
The theoretical discharge from such a sized pipe with the specified head 
is 551/2 gallons per minute. 

Siphon on the Water-supply of 3Iount Vernon, N. Y. (Eng'g 
News, May 4, 1893.) — A 12-inch siphon, 925 feet long, with a maximum 
lift of 22.12 feet and a 45° change in alignment, was put in use in 1892 
by the New York City Suburban Water Co. At its summit the siphon 
crosses a supply main, which is tapped to charge the siphon. The air- 
chamber at the siphon is 12 inches by 16 feet long. A 1/2-inch tap and 
cock at the top of the chamber provide an outlet for the collected air. 

It was found that the siphon with air-chamber as described would run 
until 125 cubic feet of air had gathered, and that this took place only 
half as soon with a 14-foot Uft as with the full lift of 22.12 feet. The 
siphon will operate about 12 hours without being recharged, but more 
water can be gotten over by charging every six hours. It can be kept 
running 23 hours out of 24 with only one man in attendance. With the 
siphon as described above it is necessary to close the valves at each end 
of the siphon to recharge it. It has been found by weir measurements 
that the discharge of the siphon before air accumulates at the summit is 
practically the same as through a straight pipe. 

A successful siphon is described by H. S. Hale in Jour. Assoc. Eng. 
Soc, 1900. A 2-in. galvanized pipe had been used, and it had been nec- 
essary to open a waste-pipe and thus secure a continuous flow in order 
to keep the siphon in operation. The trouble seemed to be due to very 
small air leaks in the joints. When the 2-in. iron pipe was replaced by a 
1-in. lead pipe, the siphon was entirely successful. The maximum rise 
of the pipe above the level of the pond was 12 ft., the discharge about 
350 ft. below the level, and the length 500 ft. 



VELOCITY OF WATER IN OPEN CHANNELS. 



755 



VELOCITY OF WATER IN OPEN CHANNELS- 

Irrigation Canals. — The minimum mean velocity required to pre- 
vent the deposit of silt or the growth of aquatic plants is in Northern 
India taken at 1 1/2 feet per second. It is stated that in America a higher 
velocity is required for this purpose, and it varies from 2 to 31/2 feet per 
second. The maximum allowable velocity will vary with the nature of 
the soil of the bed. A sandy bed will be disturbed if the velocity exceeds 
3 feet per second. Good loam with not too much sand will bear a velocity 
of 4 feet per second. The Cavour Canal in Italy, over a gravel bed, has a 
velocity of about 5 per second. (Flynn's "Irrigation Canals.") 

Mean Surface and Bottom Velocities. — According to the formula 

of Bazin. 

v== Tmax " 25.4 Vrs] v = Vb+ 10.87 \/rs. 

.*. V5 =« V — 10.87 ^rs, in which v = mean velocity in feet per second, 
Vax= maximum surface velocity in feet per second, vi,= bottom velocity 
in feet per second, r = hydraulic mean depth in feet = area of cross-section 
in square feet divided by wetted perimeter in feet, s = sine of slope. 

The least velocity, or that of the particles in contact with the bed, is 
almost as much less than the mean velocity as the greatest velocity is 
greater than the mean. 

Rankine states that in ordinary cases the velocities may be taken as 
bearing to each other nearly the proportions of 3, 4, and 5. In very slow 
currents they are nearly as 2, 3, and 4. 

Safe Bottom and Mean Velocities. — Ganguillet & Kutter give the 
following table of safe bottom and mean velocities in channels, calculated 
from the formula v = Vb + 10.87\/ri: 



Material of Channel. 


Safe Bottom Velocity 
Vfj, in Feet per Second. 


Mean Velocity v, in 
Feet per Second. 


Soft brown earth 


0.249 
0.499 
1.000 
1.998 
2.999 
4.003 
4.988 
6.006 
10.009 


0.328 


Soft loam 


656 


Sand 


1.312 


G ravel 


2.625 


Pebbles 


3.938 


Broken stone, jflint . . , 


5.579 


Conglomerate, soft slate 

Stratified rock 


6.564 
8.204 


Hard rock 


13.127 



Ganguillet & Kutter state that they are unable for want of observations 
to judge how far these figures are trustworthy. They consider them to be 
rather disproportionately small than too large, and therefore recommend 
them more confidently. 

Water flowing at a high velocity and carrying large quantities of silt is 

very destructive to channels, even when constructed of the best masonry. 

Resistance of Soils to Erosion by Water. — W. A. Burr, Eng-g 

News, Feb. 8, 1894, gives a diagram showing the resistance of various soils 

to erosion by flowing water. 

Experiments show that a velocity greater than 1.1 feet per second will 
erode sand, while pure clay will stand a velocity of 7.35 feet per second. 
The greater the proportion of clay carried by any soil, the higher the per- 
missible velocity. Mr. Burr states that experiments have shown that the 
line describing the power of soils to resist erosion is parabolic. From his 
diagram the following figures are selected as representing different classes 
of soils : 

Pure sand resists erosion by flow of 1.1 feet per second. 

Sandy soil, 15% clay 1.2 

Sandy loam, 40% clay 1.8 

Loamy soil, 65% clay 3.0 

Clay loam, 85% clay 4.8 

Agricultural clay, 95% clay 6.2 

Clav 7.35 

Abrading and Transporting Power of Water. — Prof. J. LeConte, 
in his "Elements of Geology," states: 

The erosive power of water, or its power of overcoming cohesion, 
varies as the square of the velocity of the current. 



756 



HYDRAULICS. 



The transporting power of a current varies as 'the sixth power of the 
velocity. * * * If the velocity therefore be increased ten times, the 
transporting power is increased 1,000,000 times. A current running 
three feet per second, or about two miles per hour, will bear fragments 
of stone of the size of a hen's egg, or about three ounces weight. A 
current of ten miles an hour will bear fragments of one and a half tons, 
and a torrent of twenty miles an hour will carry fragments of 100 tons. 

The transporting power of water must not be confounded with its 
erosive power. The resistance to be overcome in the one case is weight, 
in the other, cohesion; the latter varies as the square: the former as the 
sixth power of the velocity. 

In many cases of removal of slightly cohering material, the resistance 
is a mixture of these two resistances, and the power of removing mate- 
rial will vary at some rate between v^ and v^. 

Baldwin Latham has found that in order to prevent deposits of sewage 
silt in small sewers or drains, such as those from 6 inches to 9 inches 
diameter, a mean velocity of not less than 3 feet per second should be 
produced. Sewers from 12 to 24 inches diameter should have a velocity 
of not less than 21/2 feet per second, and in sewers of larger dimensions 
in no case should the velocity be less than 2 feet per second. 

The specific gravity of the materials has a marked effect upon the 
mean velocities necessary to move them. T. E. Blackwell found that 
coal of a sp. gr. of 1.26 was moved by a current of from 1.25 to 1.50 ft. 
per second, while stones of a sp. gr. of 2.32 to 3.00 required a velocity of 
2.5 to 2.75 ft. per second. 

Chailly gives the following formula for finding the velocity required to 
move rounded stones or shingle: _ 

V = 5.67 ^ag, 
in which v = velocity of water in feet per second, a = average diameter 
in feet of the body to be moved, g = its specific gravity. 

Geo. Y. Wisner, Eng'g News, Jan. 10, 1895, doubts the general accuracy 
of statements made by many authorities concerning the rate of flow of 
a current and the size of particles which different velocities will move. 
He says: 

The scouring action of any river, for any given rate of current, must 
be an inverse function of the depth. The fact that some engineer has 
found that a given velocity of current on some stream of unknown depth 
will move sand or gravel has no bearing whatever on what may be ex- 
pected of currents of the same velocity in streams of greater depths. In 
channels 3 to 5 ft. deep a mean velocity of 3 to 5 ft. per second maj^ 
produce rapid scouring, while in depths of 18 ft. and upwards current 
velocities of 6 to 8 ft. per second often have no effect whatever on the 
channel bed. 

Frietional Resistance of Surfaces Moved in Water. (Ency. Brit., 
11th ed. Vol. xiv, p. 58.) — Froude's experiments were made by pulling 
boards 19 in. wide, 3/8 in. thick, finely sharpened at both ends, set edge- 
wise in water. The following table gives: A, the power of the speed 
to which the resistance is proportional; B, the mean resistance in 
pounds per sq. ft. of the whole surface of a board of the lengths stated 
in the table, at the standard speed of 10 ft. per second. 



Surface. 




Length of Surface, in Feet. 




2 ft. 


8 ft. 


20 ft. 


50 ft. 


Varnish 

Paraffin 


A 
2.00 


B 
0.41 
0.38 
0.30 
0.87 
0.81 
0.90 
1.10 


A 
1.85 
1 .94 
1.99 
1.92 
2.00 
2.00 
2.00 


B 
0.325 
0.314 
0.278 
0.626 
0.583 
0.625 
0.714 


A 
1.85 
1.93 
1.90 
1.89 
2.00 
2.00 
2.00 


B 
0.278 
0.271 
0.262 
0.531 
0.480 
0.534 
0.588 


A 
1.83 


B 
0.226 


Tinfoil 

Calico 

Fine Sand 

Medium Sand. . 
Coarse Sand . . . 


2.16 
1.93 
2.00 
2.00 
2.00 


1.83 
1.87 
2.06 
2.00 


0.232 
0.423 
0.337 
0.456 



Unwin's experiments (Proc. Inst. Civ. Engrs., Ixxx) were made with 
disks 10, 15, and 20 in. diam. rotated in water by a vertical shaft, in 
Cliambers 22 in. diam., and 3, 6, and 12 in. deep. In all cases the fric^ 



MEASUREMENT OF FLOWING WATER. 757 

tional resistances increased a little as the chamber was made larger. 
The friction depends not only on the surface of the disk, but to some 
extent on the surface of the chamber in which it rotates. For the 
smoother surface the friction varied as the 1.85 power of the velocity. 
For rougher surfaces it varied as the 1.9 to the 2.1 power. The friction 
decreased 18 per cent with increase of temperature from 41° to 130° F. 
The resistances in pounds per sq. ft. at 10 ft. per second were as 
follows for diflerent surfaces: Bright brass, 0.202 to 0.229; Varnish, 
0.220 to 0.233; Fine sand, 0.339; Very coarse sand, 0.587 to 0.715. 
The results agree fairly well with those obtained by Froude with planks 
60 ft. long. 

Grade of Sewers. — The following empirical formula is given in Bau- 

meister's "Cleaning and Sewerage of Cities," for the minimum grade 

for a sewer of clear diameter equal to d inches, and either circular or 
oval in section; 

Minimum grade, in per cent = ■ , , -^ ' 

5 a + 50 

As the lowest limit of grades which can be flushed, 0.1 to 0.2 per cent 
may be assumed for sewers which are sometimes dry, while 0.3 per cent 
is allowable for the trunk sewers in large cities. The sewers should run 
dry as rarely as possible. 

MEASUREMENT OF FLOWING WATER. 

Piezometer. — If a vertical or oblique tube be inserted into a pipe 
containing water under pressure, the water will rise in the former, and the 
vertical height to which it rises will be the head producing the pressure 
at the point where the tube is attached. Such a tube is called a piezom- 
eter or pressure measure. If the water in the piezometer falls below 
its proper level it shows that the pressure in the main pipe has been 
reduced by an obstruction between the piezometer and the reservoir. If 
the water rises above its proper level, it indicates that the pressure there 
has been increased by an obstruction beyond the piezometer. 

If we imagine a pipe full of water to be provided with a number of pie- 
zometers, then a line joining the tops of the columns of water in them 13 
the hydrauUc grade-hne. 

Pitot Tube Gauge. — The Pitot tube is used for measuring the veloc- 
ity of fluids in motion. It has been used with great success in measuring 
the flow of natural gas. (S. W. Robinson, Report Ohio Geol. Survey, 1890.) 
(See also Van Nos^rand's Mag., vol. xxxv.) It is simply a tube so bent 
that a short leg extends into the current of fluid flowing from a tube, with 
the plane of the entering orifice opposed at right angles to the direction of 
the current. The pressure caused by the impact of the current is trans- 
mitted through the tube to a pressure-gauge of any kind, such as a column 
of water or of mercury, or a Bourdon spring-gauge. From the pressure 
thus indicated and the known density and temperature of the flowing gas 
is obtained the head corresponding to the pressure, and from this the 
velocity. In a modification of the Pitot tube described by Prof Robinson, 
there are two tubes inserted into the pipe conveying the gas, one of which 
has the plane of the orifice at right angles to the current, to receive the 
static pressure plus the pressure due to impact; the other has the plane of 
its orifice parallel to the current, so as to receive the static pressure only. 
These tubes are connected to the legs of a Utube partly filled with mercury, 
which then registers the difference in pressure in the two tubes, from which 
the velocity may be calculated. Comparative tests of Pitot tubes with 
gas-meters, for measurement of the flow of natural gas, have shown an 
agreement within 3%. 

It appears from experiments made by W. M. White, described in a 
paper before the Louisiana Eng'g Socy., 1901, by Williams, Hubbell and 
Fenkel {Trans. A. S. C. E., 1901), and by W. B. Gregory {Tran s. A. S. 
M. E., 1903), that in the formula for the Pitot tube. V= c\^2gH,in 
which V is the velocity of the current in feet per second, H the head In 
feet of the fluid corresponding to the pressure measured by the tube, 
and c an experimental coefficient, c = 1 when the plane at the point of 



758 . HYDRAULICS. 

the tube is "Exactly at right angles with the direction of the current 
and when the static pressure is correctly measured. The total pressure 
produced by a jet striking an extended plane surface at right angles to 
It, and escaping parallel to the plate, equals twice the product of the 
area of the jet into the pressure calculated from the "head due the veloc- 
\&..^,^^ ^°^ ^^^^ ^^^^ i/ = 2 X F2/2 g instead of FV2 g; but as found in 
Whites expenments the maximum pressure at a point on the plate 
exactly opposite the jet corresponds Xo h = Vy2 g. Experiments made 
with four different shapes of nozzles placed under the center of a falling 
stream of water showed that the pressure produced was capable of sus- 
taimng a column of water almost exactly equal to the height of the 
source of the falling water. 

Tests by J. A. Knesche (Indust. Eng'g, Nov., 1909), in which a Pitot 
tube was inserted ma 4-in. water pipe, gave C = about 0.77 for velocities 
of 2.5 to 8 ft. per sec, and smaller values for lower velocities. He holds 
that the coefficient of a tube should be determined by experiment before 
Its readings can be considered accurate. 

For a brief discussion of various theories of the Pitot tube see Eng'g 
News, April 17, June 5, and July 31, 1913. 

Maximum and Mean Velocities in Pipes. — Williams, Hubbell and 
Fenkel {Trans. A. S. C. E., 1901) found a ratio of 0.84 between the mean 
and the maximum velocities of water flowing in closed circular conduits, 
imder normal conditions, at ordinary velocities; whereby observations of 
velocity taken at the center under such conditions, with a properly rated 
Pitot tube, may be relied on to give results within 3 % of correctness. 

The Venturi 3Ieter, invented by Clemens Herschel, and described In 
a pamphlet issued by the Builders' Iron Foundry of Providence, R.I., is 
named from Venturi, wiio first called attention, in 1796, to the relation be- 
tween the velocities and pressures of fluids when flowing through converg- 
ing and diverging tubes. It consists of two parts — the tube, through 
which the water flows, and the recorder, which registers the quantity of 
water that passes through the tube. The tube takes the shape of two trun- 
cated cones joined in their smallest diameters by a short throat-piece. At 
the up-stream end and at the throat there are pressure-chambers, at 
which points the pressures are taken. 

The action of the tube is based on that property which causes the small 
section of a gently expanding frustum of a cone to receive, without material 
resultant loss of head, as much Water at the smallest diameter as is dis- 
charged at the large end, and on that further property which causes the 
pressure of the water flowing through the throat to be less, by virtue of its 
greater velocity, than the pressure at the up-stream end of the tube, each 
pressure being at the same time a function of the velocity at that point and 
of the hydrostatic pressure which would obtain were the water motionless 
within the pipe. 

Tne recorder is connected with the tube by pressure-pipes which lead to 
it from the chambers surrounding the up-stream end and the throat of the 
tube. It may be placed in any convenient position within 1000 feet of the 
meter. It is operated by a weight and clockwork. The difference of pres- 
sure or head at the entrance and at the throat of the meter is balanced in 
the recorder by the difference of level in two columns of mercury in 
cylindrical receivers, one within the other. The inner carries a float, the 
position of which is indicative of the quantity of water flowing through 
the tube. By its rise and fall the float varies the time of contact between 
an integrating drum and the counters by which the successive readings 
are registered. 

There is no limit to the sizes of the meters nor the quantity of water 
that may be measured. Meters with 24-inch, 36-inch, 48-lnch, and even 
20-foot tubes can be readily made. 

Measurement by Venturi Tubes. (Trans, A. S. C. E., Nov., 1887, 
and Jan., 1888.) — Mr. Herschel recommends the use of a Venturi tube, in- 
serted in the force-main of the pumping engine, for determining the 
quantity of water discharged. Such a tube applied to a 24-inch main has 
a total length of about 20 fe«t. At a distance of 4 feet from the end 
nearest the engine the inside diameter of the tube is contracted to a throat 
having a diameter of about 8 inches. A pressure-gauge is attaclied to each 
of twochambers, the onesurroundingand communicating with the entrance 
or main pipe, the other with the throat. According to experiments made 



MEASUREMENT OF FLOWING WATER. 759 

upon two tubes of this kind, one 4 in. in diameter at the throat and 12 In. 
at the entrance, and the other about 36 in. in diameter at the throat and 
9 feet at its entrance, the quantity of water whicli passes through the tube 
is very nearly the theoretical discharge through an opening having an area 
equal to that of the throat, and a velocity which is that due to the difference 
in head shown by the two gauges. Mr. Herschel states that the coefficient 
for these two widely-varjing sizes of tubes and for a wide range of velocity 
through the pipe, was found to be within two per cent, either way, of 98%. 
In other words, the quantity of water flowing through the tube per se cond 
is expressed within two per cent by the formula W= 0.98 X ^ X ^2 gh, 
in which A is the area of the throat of the tube, h the head, in feet, corre- 
sponding to the difference in the pressure of the water entering the tube and 
that found at the throat, and g = 32.16. 

Coefficient of Flow in Venturi Meters. — (Allen Hazen, Eng. News, 
July 31. 1913.) The formula for flow in a Venturi meter is 

Q =Kxc ^' yr 



V('-l)' 



d and D respectively are diameters of the throat and entrance, in inches, 
h is the head on the meter, C a coefficient which depends on the frictional 
resistance and has an average value of very close to 0.99 for ordinary 
waterworks conditions. K = 28,276 if Q is the quantity in U. S. gal- 
lons per 24 hours and h is measured in feet of water. If C = 0.99 then 
KC = 27,993 for h in feet of water, 8081 if h is in inches of water and 
28,684 if h is in inches of mercury. For Q in cubic feet per second, di- 
vide these figures by 646,315 giving respectively KC = 0.04331, 0.01250 
and 0.04438. 

Measurement of Discharge of Pumping-engines by means of 
Nozzles. {Trans, A, S. M. E., xii, 575.) — The measurement of water 
by computation from its discharge through orifices, or through the nozzles 
of fire-hose, furnishes a means of determining the quantity of water de- 
livered by a pumping-engine which can be applied without much difficulty. 
John R. Freeman, Trans. A, S. C. E., Nov., 1889, describes a series of ex- 
periments covering a wide range of pressures and sizes, and the results 
showed that the coefficient of discharge for a smooth nozzle of ordinary 
good form was within one-half of one per cent, either way, of 0,977; the 
diameter of the nozzle being accurately calipered, and the pressures being 
determined by means of an accurate gauge attached to a suitable piezom- 
eter at the base of the play-pipe. 

In order to use this method for determining the quantity of water dis- 
charged by a pumping-engine, it would be necessary to provide a pressure- 
box, to which the water vrould be conducted, and attach to the box as 
many nozzles as would be required to carry off the water. According to 
Mr. Freeman's estimate, four 1 1/4-inch nozzles, thus connected, with a 
pressure of 80 lbs. per square inch, would discharge the full capacity of a 
two-and-a-half-million engine. He also suggests the use of a portable 
apparatus with a single opening for discharge, consisting essentially of a 
Siamese nozzle, so-called, the water being carried to it by three or more 
lines of fire-hose. 

To insure reliability for these measurements, it is necessary that the 
shut-off valve in the force-main, or the several shut-off valves, should be 
tight, so that all the water discharged by the engine may pass through the 
nozzles. 

The Lea V-Notch Recording Water Meter is described by D. Robert 
Yarnall in Trans. A. S. M. E., 1912. It is extensively used in large 
power plants for recording the flow of boiler feed water. It consists 
of a metering tank or flume from which the water passes over a 90° 
V-notch into a catch basin below, the height of the water above the 
notch being recorded on a clock-driven paper chart which revolves 
once in 24 hours. The formula for the 90° V-notch is cu. ft. per min. = 
0.305i? \/H, in which H is the height in inches of the still water behind 
the notch measured above the level of the bottom of the notch. Tests 
by Mr. YarnaU of a recording meter made on this principle showed an 



760 



HYDRAULICS. 



average error of 0.5%. The Yarnall- Waring Co., Philadelphia, makers 
of the meter give the following figures for the flow of water in pounds 
per hour corresponding to different heights of water in inches above 
the notch: 

Height, in.: 

12 3 4 5 6 7 8 

Flow, lb. per hour: 
1,140 6,480 17,830 36,610 63,940 100,860 148,290 207,060 

Height, in.: 

9 10 11 12 13 14 15 

Flow, lb. per hour: 
277,960 361,740 459,030 568,720 694,710 836,110 993,510 

Flow through Rectangular Orifices. (Approximate. See p. 727.) 

Cubic Feet of Water Discharged per Minute through an Orifice 
One Inch Square, under any Head of Water from 3 to 72 Inches. 

For any other orifice multiply by its area in square inches. 
Formula, Q' = 0.624 '^ h" X a. Q'= cu. ft. per min.; a = area in sq. in. 



'd 




-d 




13 




n 




r3 




TS 




73 


(U 




<u 




o 




0) 




o 




<v 




V 


o.m 


« tn 


m 


fl ^ 


III 


fl t«' 


m 


fl TO 




^ m 




^ TO 


m 


— S ^-d P. 


'Z s 


'^rC g 


■;;! ^ 


^^ g 


'Z ^ 


•^rC g 


"T^ ^ 


^-^ £ 


"Z ^ 


■^ja B 


":^ ^ 


'^M a 


•d'o 


•2-^ 




•2-fe 




•2-fe 


3^ 


■^-l 


J^^ 

o o 


•^"fe 




•H^fe 


-S-g 


•H-fe 


J-2 


^5S 


S ^ 


-35 a 


i£ 


^5 a 


ia 


^5S 


BS 


^5£ 


is 


-gss 


is 


-§5^ 


HH 


o 


M*" 


d 




5 


a 


o 


W 


o 


53 


" 


63 


o 




1.12 




2.20 


23 


2.90 


33 


3.47 


43 


3.95 


4.39 


4.78 




1.27 




2.28 


24 


2.97 


34 


3.52 


44 


4.00 


54 


4.42 


64 


4.81 




1.40 




2.36 


25 


3.03 


35 


3.57 


45 


4.05 


55 


4.46 


65 


4.85 




1.52 




2.43 


26 


3.08 


36 


3.62 


46 


4.09 


56 


4.52 


66 


4.89 




1.64 




2.51 


27 


3.14 


'37 


3.67 


47 


4.12 


57 


4.55 


67 


4.92 


8 


1.75 


18 


2.58 


28 


3.20 


38 


3.72 


48 


4.18 


58 


4.58 


68 


4.97 


9 


1.84 


19 


2.64 


29 


3.25 


39 


3.77 


49 


4.21 


59 


4.63 


69 


5.00 


10 


1.94 


20 


2.71 


30 


3.31 


40 


3.81 


50 


4.27 


60 


4.65 


70 


5.03 


n 


2.03 


21 


2.78 


31 


3.36 


41 


3.86 


51 


4.30 


61 


4.72 


71 


5.07 


12 


2.12 


22 


2.84 


32 


3.41 


42 


3.91 


52 


4.34 


62 


4.74 


72 


5.09 



Measurement of an Open Stream by Velocity and Cross-section. — 

Measure the depth of the water at from 6 to 12 points across the stream at 
equal distances between. Add all the depths in feet together and divide 
by the number of measurements made: this "^ill be the average depth of 
the stream, which multiplied by its width will give its area or cross-section. 
Multiply this by the velocity of the stream in feet per minute, and the 
result will be the discharge in cubic feet per minute of the stream. 

The velocity of the stream can be found by laying off 100 feet of the bank 
and throwing a float into the middle, noting the time taken in passing over 
the 100 ft. Do this a number of times and take the average; then, divid- • 
ing this distance by the time gives the velocity at the surface. As the top 
of the stream flows faster than the bottom or sides — the average velocity 
being about 83% of the surface velocity at the middle — it is convenient to 
measure a distance of 120 feet for the float and reckon it as 100 



MEASUREMENT OF FLOWING WATER. 



761 



Miner's Inch Measurements. (Pelton Water Wheel Co.) 

The cut, Fig. 149, shows the form of measuring-box ordinarily used, and 
the following table gives the discharge in cubic feet per minute of a miner's 
inch of water, as measured under the various heads and different lengths 
and heights of apertures used in California. 




Fig. 149. 



Length 


Openings 2 Inches High. 


Openings 4 Inches High. 














Opening 
in 


Head to 


Head to 


Head to 


Head to 


Head to 


Head to 


inches. 


Center, 


Center, 


Center, 


Center, 


Center, 


Center, 




5 inches. 


6 inches. 


7 inches. 


5 inches. 


6 inches. 


7 inches. 




Cu. ft. 


Cu.ft. 


Cu. ft. 


Cu. ft. 


Cu.ft. 


Cu. ft. 


4 


1.348 


1.473 


1.589 


1.320 


1.450 


1.570 


6 


1.355 


1.480 


1.596 


1.336 


1.470 


1.595 


8 


1.359 


1.484 


1.600 


1.344 


1.481 


1.608 


10 


1.361 


1.485 


1.602 


1.349 


1.487 


1.615 


12 


1.363 


1.487 


1.604 


1.352 


1.491 


1.620 


14 


1.364 


1.488 


1.604 


1.354 


1.494 


1.623 


16 


1.365 


1.489 


1.605 


1.356 


1.496 


1.626 


18 


1.365 


1.489 


1.606 


1.357 


1.498 


1.628 


20 


1.365 


1.490 


1.606 


1.359 


1.499 


1.630 


22 


1.366 


1.490 


1.607 


1.359 


1.500 


1.631 


24 


1.366 


1.490 


1.607 


1.360 


1.501 


1.632 


26 


1.366 


1.490 


1.607 


1.361 


1.502 


1.633 


28 


1.367 


1.491 


1.607 


1.361 


1.503 


1.634 


30 


1.367 


1.491 


1.608 


1.362 


1.503 


1.635 


40 


1.367 


1.492 


1.608 


1.363 


1.505 


1.637 


50 


1.368 


1.493 


1.609 


1.364 


1.507 


1.639 


60 


1.368 


1.493 


1.609 


i.365 


1.508 


1.640 


70 


1.368 


1.493 


1.609 


1.365 


1.508 


1.641 


80 


1.368 


1.493 


1.609 


1.366 


1.509 


1.641 


90 


1.369 


1.493 


1.610 


1.366 


1.509 


1.641 


100 


1.369 


1.494 


1.610 


1.366 


1.509 


1.642 



Note. — The apertures from which the above measurements were ob- 
tained were through material 1 1/4 inches thick, and the lower edge 2 inches 
above the bottom of the measuring-box, thus giving full contraction. 



762 



HYDRAULICS. 



Flow of Water Over Weirs. Weir Dam Measurement. (Pelton 
Water Wheel Co.) — Place a board or plank in the stream, as shown in 
the sketch, at some point where a pond will form above. The length of 
the notch in the dam should be from two to four times its depth for small 
quantities and longer for large quantities. The edges of the notch should 
be beveled -toward the intake side, as shown. The overfall below the notch 
should not be less than twice its depth. Francis says a fall below the 
crest equal to one-half the head is sufficient, but there must be a free access 
of air under the sheet. 



H\M ^ H . ,^« 




Fig. 150. 

In the pond, about 6 ft. above the dam, drive a stake, and then obstruct 
the water until it rises precisely to the bottom of the notch and mark the 
stake at this level. Then complete the dam so as to cause all the water to 
flow through the notch, and, after time for the water to settle, mark the 
stake again for this new level. If preferred the stake can be driven with 
its top precisely level with the bottom of the notch and the depth of the 
water be measured with a rule after the water is flowing free, but the marks 
are preferable in most cases. The stake can then be withdrawn; and the 
distance between the marks is the theoretical depth of flow corresponding 
to the Quantities in the weir table on the foUowing page. 

Francis's Formulae for Weirs. 

Q = discharge in cubic feet per second, L = length of the weir, 
H = depth of water on the weir, h = head due the velocity of ap- 
proach = y2 -^ 64.3; dimensions in feet, velocity in feet per second. 

Francis's formula, Q = 3.33 (L - 0.2H) X H^h. 

This formula applies to weirs having perfect contraction at each end 
and the velocity of approach negligible. When the velocity of approach 
is considered the formula is Q = 3.33 (L - 0.2 H) X[{H-\- h) ^h - h^'h-]. 
The Francis formula is not applicable when the depth on the weir 
exceeds one-third of the length nor to very small depths. The distance 
from the side of the canal to the end of the weir should not be less than 
three times the depth on the weir. 



MEASUREMENT OF FLOWING WATER. 



763 



With both end contractions suppressed the term 0.2 // is omitted from 
the formula, and with one end contraction suppressed it becomes 
0.1 H, 

If Q' == discharge in cubic feet per minute, and U and h' are taken in. 
inches, the first of theabove formulae reduces to Q' = 0.4 Uh' ^2- From this 
formula the following table is calculated. The values are sufficiently 
accurate for ordinary computations of water-power for weirs without end 
contraction, that is, for a weir the full width of the channel of approach. 
For weirs with full end contraction multiply the values taken from the 
table by the length of the weir crest in inches less 0.2 times the head in 
inches, to obtain the discharge. 

Weir Table. 

Giving Cubic Feet of Water per Minute that will Flow over a Weir 
One Inch Wide and from Vs to 207/8 Inches Deep. 





For other widths multiply by the width in inches. 




Depth. 




1/8 in. 


1/4 in. 


3/8 in. 


1/2 in. 


5/8 in. 


3/4 In. 


7/8 in. 


in. 


cu. ft. 


CU. ft. 


cu. ft. 


cu. ft. 


cu.ft. 


cu.ft. 


cu.ft. 


cu.ft. 





.00 


.01 


.05 


.09 


.14 


.19 


.26 


.32 


1 


.40 


.47 


.55 


.64 


.73 


.82 


.92 


1.02 


2 


1.13 


1.23 


1.35 


1.46 


1.58 


1.70 


1.82 


1.95 


3 


2.07 


2.21 


2.34 


2.48 


2.61 


2.76 


2.90 


3.05 


4 


3.20 


3.35 


3.50 


3.66 


3.81 


3.97 


4.14 


4.30 


5 


4.47 


4.64 


4.81 


4.98 


5.15 


5.33 


5.51 


5.69 


6 


5.87 


6.06 


6.25 


6.44 


6.62 


6.82 


7.01 


7.21 


7 


7.40 


7.60 


7.80 


8.01 


8.21 


8.42 


8.63 


8.83 


8 


9.05 


9.26 


9.47 


9.69 


9.91 


10.13 


10.35 


10.57 


9 


10.80 


11.02 


11.25 


11.48 


11.71 


11.94 


12.17 


12.41 


10 


12.64 


12.88 


13.12 


13.36 


13.60 


13.85 


14.09 


14.34 


11 


14.59 


14.84 


15.09 


15.34 


15.59 


15.85 


16.11 


16.36 


12 


16.62 


16.88 


17.15 


17.41 


17.67 


17.94 


18.21 


18.47 


13 


18.74 


19.01 


19.29 


19.56 


19.84 


20.11 


20.39 


20.67 


14 


20.95 


21.23 


21.51 


21.80 


22.08 


22.37 


22.65 


22.94 


15 


23.23 


23.52 


23.82 


24.11 


24.40 


24.70 


25.00 


25.30 


16 


25.60 


25.90 


26.20 


26.50 


26.80 


27.11 


27.42 


27.72 


17 


28.03 


28.34 


28.65 


28.97 


29.28 


29.59 


29.91 


30.22 


18 


30.54 


30.86 


31.18 


31.50 


31.82 


32.15 


32.47 


32.80 


19 


33.12 


33.45 


33.78 


34.11 


34.44 


34.77 


35.10 


35.44 


20 


35.77 


36.11 


36.45 


36.78 


37.12 


37.46 


37.80 


38.15 



When the velocity of the approaching water is less than 1/2 foot per 
second, the result obtained by the table is fairly accurate. When the vel- 
ocity of approach is greater than 1/2 foot per second, a correction should be 
applied, see page 727. 

For more accurate computations, the coefficients of flow of Hamilton 
Smith, Jr., or of Bazin should be used. In Smith's Hydraulics will be found 
a collection of results of experiments on orifices and weirs of various shapes 
made by many different authorities, together with a discussion of their 
several formulfe. (See also Trautwine's Pocket Book, Unwin's Hydrau- 
lics, Church's Mechanics of Engineering, Merriman's Hydraulics, 
Williams and Hazen's Hydraulic Tables, Hughes and Safford's Hydrau- 
lics, and Weir Experiments, Coefficients and Formulas, by R. E. 
Horton, Water Supply and Irrigation paper No. 200 of the U. S. 
Geological Survey.) 

Bazin's Experiments. — M. Bazin (Annates des Fonts et Chaussees, 
Oct., 1888, translated by Marichal and Trautwine, Proc. Engrs. Club of 
Phila., Jan., 1890) made an extensive series of experiments wdth a sharp- 
crested weir without lateral contraction, the air being admitted freely be- 
hind the falling sheet, and found values of m varying from 0.42 to 0.50, 
with variations of the length of the weir from 19 3/4 to 78 3/4 in., of the 
height of the crest above the bottom of the channel from 0.79 to 2.46 ft., 



764 



HYDRAULICS. 



and of the head from 1 .97 to 23.62 In. From these experiments he deduces 
the following formula: 

Q = [0.425 + 0.21 (p^-^yJLF Vj^, 

!n which P is the height in feet of the crest of the weir above the bottom of 
the channel of approach, L the length' of the weir, // the head, both in feet, 
and Q the discharge in cu. ft. per sec. This formula, says M. Bazin, is 
entirely practical where errors of 2% to 3% are admissible. The following 
table is condensed from M. Bazin's paper: 



"Values of the Coefficient m in the Formula Q — mLH ^2 gH, for a 
Sharp-crested Weir without Lateral" Contraction ; the Air 
being Admitted Freely Behind the Falling Sheet. 





Height of Crest of Weir Above Bed of Channel. 


Head. H. 














Feet... 0.66 


0.98 


1.31 


1.64 


1.97 


2.62 


3.28 


4.92 


6.56 


CO 




Inches 7.87 


11.81 


15.75 


19.69 


23.62 


31.50 


39.38 


59.07 


78.76 


00 


Ft. 


Tn. 


m 


m 


m 


m 


m 


m 


m 


m 


m 


m 


164 


1.97 


0.458 


0.453 


0.451 


0.450 


0.449 


0.449 


0.449 


0.448 


0.448 


0.4481 


230 


2 76 


0.455 


0,448 


0.445 


0.443 


0.442 


0.441 


0.440 


0.440 


0.439 


0.4391 


0,295 


3 54 


0.457 


0,447 


0.442 


0.440 


0.438 


0.436 


0.436 


0.435 


0.434 


0.4340 


0.394 


4.72 


0.462 


0.448 


0.442 


0.438 


0.436 


0.433 


0.432 


0.430 


0.430 


0.4291 


0.523 


6,30 


0.471 


0.453 


0.444 


0.438 


0.435 


0.431 


0.429 


0.427 


0.426 


0.4246 


0.656 


7.87 


0.480 


0.459 


0.447 


0.440 


0.436 


0.431 


0.428 


0.425 


0.423 


0.4215 


0,787 


9,45 


0.488 


0.465 


0.452 


0.444 


0.438 


0.432 


0.428 


0.424 


0.422 


0.4194 


0,919 


11 02 


0.496 


0.472 


0.457 


0.448 


0.441 


0.433 


0.429 


0.424 


0.422 


0.4181 


1.050 


12.60 
14.17 
15.75 
17.32 
18.90 
20.47 
22.05 
23.62 




0.478 
0.483 
0.489 
0.494 


0.462 
0.467 
0.472 
0.476 
0.480 
0.483 
0.487 
0.490 


0.452 
0.456 
0.459 
0.463 
0.467 


0.444 
0.448 
0.451 
0.454 
457 


0.436 
0.438 
0.440 
0.442 
0.444 
0.446 
0.448 
0.451 


0.430 
0.432 
0.433 
0.435 
0.436 
0.438 
0.439 
0.441 


0.424 
0.424 
0.424 
0.425 
0.425 
0.426 
0.427 
0.427 


0.421 
0.421 
0.421 
0.421 


0.4168 


1.181 


' 


0.4156 


1.312 




0.4144 


1.444 




0.4134 


1.575 




0.421 0.4122 


1 706 






0.470 0.460 
0.473 0.463 
0.476 0.466 


0.421 0.4112 


1.837 






0.421 0.4101 


1.969 






0.421 0.4092 

















A comparison of the results of this formula with those of experiments, 
says M. Bazin, justifies us in believing that, except in the unusual case of a 
very low weir (which should always be avoided), the preceding table will 
give the coefficient m in all cases within 1% ; provided, however, that the 
arrangements of the standard weir are exactly reproduced. It is especially 
important that the admission of the air behind the falling sheet be perfectly 
assured. If this condition is not complied with, m may vary within much 
wider Umits. The type adopted gives the least possible variation in the 
coeflScient. 

Triangular Weir. — For the formula of the triangular or V-notch 
weir, see the Lea Recorder, page 759. 

The Cippoleti, or Trapezoidal Weir. — Cippoleti found that by using 
a trapezoidal weir with the sides inclined 1 horizontal to 4 vertical, with 
end contraction, the discharge is equal to that of a rectangular weir 
without end contraction (that is with the width of the weir equal to the 
width of the channel) and is represented by the simple formula Q = 3.367 
LH^/2. A. D. Flinn and C. W. D. Dyer {Trans. A. S. C. E., 1894), in 
experiments with a trapezoidal weir, with values of L from 3 to 9 ft. 
and of H from 0.24 to 1.40 ft., found the value of the coefficient to aver- 
age 3.334, the water being measured by a rectangular weir and the results 
being computed by Francis's formula, and 3.354 when Smith's formula 
was used. They concliAle that Cippoleti's formula when applied to a 
properly constructed trapezoidal weir will give the discharge with an 
error due to combined inaccuracies, not greater than 1%. 



WATER-POWER. 765 



WATER-POWER, 

Power of a Fall of Water — Efficiency. — The gross power of a fall 

of water is the product of the weight of water discharged in a unit of time 
Into the total head, i.e., the diffeience of vertical elevation of the upper 
surface of the water at the points where the faU in question begins and 
ends. The term "head" used in connection with water-wheels is the 
difference in height from the surface of the water in the wheel-pit to the 
surface in the pen-stock when the wheel is running. 

If Q = cubic feet of water discharged per second, D = weight of a cubic 
foot of water = 62.36 lbs. at 60° F., H = total head in feet; then 

DQH = gross power in foot-pounds per second, 
and DQH -5- 550 = 0.1134 QH = gross horse-power. 

If Q' is taken in cubic feet per minute, H.P. = 33000' .00189Q'i7. 

A water-wheel or motor of any kind cannot utilize the whole of the head 
H, since there are losses of head at both the entrance to and the exit from 
the wheel. There are also losses of energy due to friction of the water in 
Its passage through the wheel. The ratio of the power developed by the 
wheel to the gross power of the fall is the efficiency of the wheel. For 75% 

efficiency, net horse-power = 0.00142 Q'H = ^t^* 

A head of water can be made use of in one or other of the following ways, 
viz.: 

1st. By its weight, as in the water-balance and in the overshot-wheel. 

2d. By its pressure, as in turbines and in the hydraulic engine, hydraulic 
press, crane, etc. 

3d. By its impulse, as in the undershot-wheel, and in the Pelton wheel. 

4th. By a combination of the above. 

Horse-power of a Running Stream. — The gross horse-power is 
H.P. = QH X 62.36 -^ 550 = 0.1134 QH, in which Q is the discharge in 
cubic feet per second actually impinging on the float or bucket, and H = 

theoretical head due to the velocity of the stream = r— = ^z—- . in which 

2 g 64.4 
V is the velocity in feet per second. If Q' be taken in cubic feet per minute, 
H.P. = 0.00189 Q'H. 

Thus, if the floats of an undershot-wheel driven by a current alone be 5 
feet X 1 foot, and the velocity of stream = 210 ft. per minute, or 31/2 ft. 
per sec, of which the theoretical head is 0.19 ft.. Q = 5 sq. ft. X 210 = 1050 
cu. ft. per minute; H.P. = 1050 X 0.19 X 0.00189 = 0.377 H.P. 

The wheels would realize only about 0.4 of this power, on account of 
friction and slip, or 0.151 H.P., or about 0.03 H.P. per square foot of 
float, which is equivalent to 33 sq. ft, of float per H.P. 

Current Motors. — A current motor could only utilize the whole 
power of a running stream if it could take all the velocity out of the water, 
so that it would leave the floats or buckets with no velocity at all; or in 
other words, it would require the backing up of the whole volume of the 
stream until the actual head was equivalent to the theoretical head due to 
the velocity of the stream. As but a small fraction of the velocity of the 
stream can be taken up by a current motor, its efficiency is very small. 
Current motors may be used to obtain small amounts of power from large 
streams, but for large powers they are not practicable. 

Bernouilli's Theorem. — Energy of Water Flowing in a Tube. — 

The head due to the velocity is -^ ; the head due to the pressure is — ; the 

2 g ^ w 

head due to actual height above the datum plane is h feet. The total head 

Is the sum of these = ;r— +h+ — , in feet, in which v — velocity in feet per 
2 g w J t^ 

second,/ = pressure in lbs. per sq. ft., w = weight of 1 cu. ft. of water = 



766 WATER-POWER. 

62.36 lbs. If p = pressure in lbs. per sq. in., ^ = 2.309 p. If a constant 

quantity of water is flowing through a tube in a given time, the velocity 
varying at different points on account of changes in the diameter, the 
energy remains constant (loss by friction excepted) and the sum of the 
three heads is constant, the pressure head increasing as the velocity de- 
creases, and vice-versa. This principle is known as " Bernouilli's Theo- 
rem." 

In hydraulic transmission the velocity and the height above datum are 
usually small compared with the pressure-head. The work or energy of a 
given quantity of water under pressure = its volume in cubic feet X its 
pressure in lbs. per sq. ft.; or if Q = quantity in cubic feet per second, 
and p = pressure in lbs. per square inch, W = 144 pQ, and the H.P. 

= iff = 0.2618 ,«. 

3Iaxiinum Efficiency of a Long Conduit. — A. L. Adams and R. C. 
Gemmell (Eng'g News, May 4, 1893) show by mathematical analysis that 
the conditions for securing the maximum amount of power through a long 
conduit of fixed diameter, without regard to the economy of water, is that 
the draught from the pipe should be such that the frictional loss in the pipe 
will be equal to one-third of the entire static head. 

Mill-Power. — A "mill-power" is a unit used to rate a water-power 
for the purpose of renting it. The value of the unit is different in different 
localities. The following are examples (from Emerson): 

Holyoke, Mass. — Each mill-power at the respective falls is declared to 
be the right during 16 hours in a day to draw 38 cu. ft. of water per second 
at the upper fall when the head there is 20 feet, or a quantity proportionate 
to the height at the falls. This is equal to 86.2 horse-power as a maximum. 

Lowell, Mass. — The right to draw during 15 hours in the day so much 
water as shall give a power equal to 25 cu. ft. a second at the great fall, 
when the fall there is 30 feet. Equal to 85 H.P. maximum. 

Lawrence, Mass. — The right to draw during 16 hours in a day so much 
water as shall give a power equal to 30 cu. ft. per second when the head is 
25 feet. Equal to 85 H.P. maximum. 

Minneapolis, Minn. — 30 cu. ft. of water per second with head of 22 feet. 
Equal to 74.8 H.P. 

Manchester, N.H. — Divide 725 by the number of feet of fall minus 1, 
and the quotient will be the number of cubic feet per second in that fall. 
For 20 feet fall this equals 38.1 cu. ft., equal to 86.4 H.P. maximum. 

Cohoes, N.Y. — " Mill-power" equivalent to the power given by 6 cu. ft. 
per second, when the fall is 20 feet. Equal to 13.6 H.P., maximum. 

Passaic, N.J. — Mill-power: The right to draw 8 1/2 cu. ft. of water per 
sec, fall of 22 feet, equal to 21.2 horse-power. Maximum rental $700 per 
year for each mill-power = S33.00 per H.P.' 

The horse-power maximum above given is that due theoretically to the 
weight of water and the height of the fall, assuming the water-wheel to 
have perfect efficiency. It should be multiplied by the efficiency of the 
wheel, say 75% for good turbines, to obtain the H.P. delivered by the 
wheel. 

Value of a Water-power. — In estimating the value of a water- 
power, especially where such value is used as testimony for a plaintiff 
whose water-power has been diminished or confiscated, it is a common 
custom for the person making such estimate to say that the value is repre- 
sented by a sum of money which, when put at interest, would maintain a 
steam-plant of the same power in the same place. 

Mr. Charles T. Main {Trans. A. S. M. E., xiii. 140) points out that this 
system of estimating is erroneous; that the value of a power depends upon 
a great number of conditions, such as location, quantity of water, fall or 
head, uniformity of flow, conditions which fix the expense of dams, canals, 
foundations of buildings, freight charges for fuel, raw materials and finished 
product, etc. He gives an estimate of relative cost of steam and water- 
power for a 500 H.P. plant from which the following is condensed: 

The amount of heat required per H.P. varies with different kinds of 
business, but in an average plain cotton-mill, the steam required for heat- 
ing and slashing is equivalent to about 25% of steam exhausted from the 
high-pressure cylinder of a compound engrine of the power required to run 
that mill, the steam to be taken from the receiver. 



WATER-POWER. 767 

The coal consumption per H.P. per hour for a compound ensrine is taken 
at 13/4 lbs. per hour, when no steam is taken fiom the receiver for heating 
purposes. The gross consumption when 25% is taken from the receiver is 
about 2.06 lbs. 

75% of the steam is used as in a compound engine at 1.75 lbs.= 1.31 lbs. 
25% of the steam is used as in a high-pressure engine at 3.00 lbs. = .75 lb. 

2.06 lbs. 
The running expenses per H. P. per year are as follows: 
2.06 lbs. coal per hour = 21.115 lbs. for 10 V4 hours or one day = 

6503.42 lbs. for 308 days, which, at $3.00 per long ton = $8.71 

Atendance of boilers, one man @ $2.00, and one man @ $1.25 = 2.00 
Attendance of engine, one man @ $3.50. 2.16 

Oil, waste, and supplies. .80 

The cost of such a steam-plant in New England and vicinity of 500 
H. P. is about $65 per H. P. Taking the fixed expenses as 4% 
on engine, 5% on boilers, and 2% on other portions, repairs at 
2%, interest at 5%, taxes at 1V2% on 8/4 cost, and insurance at 
1/2% on exposed portion, the total average per cent is about 
121/2%, or $65 X 0.121/2 = 8.13 



Gross cost of power and low-pressure steam per H. P. $21.80 

Comparing this with water-power, Mr. Main says: "At Lawrence the 
cost of dam and canals was about $650,000, or $65 per H. P The cost 
per H. P. of wheel-plant from canal to river is about $45 per H. P. of 
plant, or about $65 per H. P. used, the additional $20 being caused by 
making the plant large enough to compensate for fluctuation of power 
due to rise and fall of river. The total cost per H. P. of developed plant 
is then about $130 per H. P. Placing the depreciation on the whole 
plant at 2%, repairs at 1%, interest at 5%, taxes and insurance at 1%, 
or a total of 9%, gives: 

Fixed expenses per H. P. $1.30 X .09 = $11.70 
Running expenses per H. P. (Estimated) 2.00 

$13.70 

"To this has to be added the amount of steam required for heating 
purposes, said to be about 25% of the total amount used, but in winter 
months the consumption is at least 371/2%. It is therefore necessary to 
have a boiler plant of about 37 1/2% of the size of the one considered with 
the steam-plant, costing about $20 X 0.375 = $7.50 per H. P of total 
power used. The expense of running this boiler-plant is, per H. P. of 
the total plant per year: 

Fixed expenses 121/2% on $7.50 $0.94 

Coal 3 . 25 

Labor 1 . 23 

Total $5.43 

Making a total cost per year for water-power with the auxiliary boiler 
plant $13.70 + $5.43 = $19.13 which deducted from $21.80 makes a 
difference in favor of water-power of $2.67, or for 10,000 H. P. a saving 
of $26,700 per year. 

"It is fair to say," says Mr. Main, "that the value of this constant 
power is a sum of money which when put at interest will produce the 
saving; or if 6% is a fair interest to receive on money thus invested the 
value would be $26,700 h- 0.06 = $445,000." 

Mr. Main makes the following general statements as to the value of a 
water-power: "The value of an undeveloped variable power is usually 
nothmg if its variation is great, unless it is to be supplemented by a 
steam-plant. It is of value then only when the cost per horse-power'for 
the double-plant is less than the cost of steam-power under the same 
conditions as mentioned for a permanent power, and its value can be 
represented in the same manner as the value of a permanent power has 
been represented. r 



768 WATER-POWER. 

"The value of a developed power is as follows: If the power can be 
run cheaper than steam, the value is that of the power, plus the cost of 
plant, less depreciation. If it cannot be run as cheaply as steam, con- 
sidering its cost, etc., the value of the power itself is nothing, but the 
value of the plant is such as could be paid for it new, which would bring 
the total cost of running down to the cost of steam-power, less deprecia- 
tion." 

Mr. Samuel Webber, Iron Age, Feb. and March, 1893, writes a series of 
articles showing the development of American turbine wheels, and inci- 
dentaUy criticises the statements of Mr. Main and others who have 
made comparisons of costs of steam and of water-power unfavorable to 
the latter. He says: "They have based their calculations on the cost 
of steam, on large compound engines of 1000 or more H. P. and 120 
pounds pressure of steam in their boilers, and by careful 10-hour trials 
succeeded in figuring down steam to a cost of about S20 per H. P., ignor- 
ing the well-known fact that its average cost in practical use, except 
near the coal mines, is from $40 to S50. In many instances dams, 
canals, and modern turbines can be all completed for a cost of SlOO per 
H. P.; and the interest on that, and the cost of attendance and oil, will 
bring water-power up to about $10 or $12 per annum; and with a man 
competent to attend the dynamo in attendance, it can probably be 
safely estimated at not over $15 per H. P." 

WATER- WHEELS. 

Water-wheels are classified as vertical wheels (including current motors, 
undershot, breast, and overshot wheels), turbine wheels, and impulse 
wheels. TJndershot and breast wheels give very low efficiency, and are 
now no longer built. The overshot wheel when made of large diameter 
(wheels as high as 72 ft. diameter have been made) and properly designed 
have given efficiencies of over 80%, but they have been almost entirely 
supplanted by turbines, on account of their cumbersomeness, high cost, 
leakage, and inability to work in back water. 

Turbines are generally classifi.ed according to the direction in which the 
water flows through them, as follows: 

Tangential flow: Barker's miU. Parallel flow: Jonval. Radial out- 
ward flow: Fourneyron. Radial inward flow: Thompson vortex: Francis. 
Inward and downward flow: Central discharge scroll wheels and earlier 
American type of wheels; Swain turbine. Inward, downward, and out- 
ward flow: The American type of turbine. 

TURBINE WHEELS. 

Proportions of Turbines. — Prof. De Volson Wood discusses at 
length the theory of turbines in his paper on Hydraulic Reaction Motors, 
Trans. A. S. M. E. xiv. 266. His principal deductions which have an 
immediate bearing upon practice are condensed in the following: 
Notation. 

Q = volume of water passing through the wheel per second, 

hi = head in the supply chamber above the entrance to the buckets, 

hi = head in the tail-race above the exit from the buckets, 

zi = fall in passing through the buckets, 

H = hi -^ zi — h2, the effective head, 

Ml = coefficient of resistance along the guides, 

/i2 = coefficient of resistance along the buckets, 

n = radius of the initial rim, 

ri = radius of the terminal rim, 

V = velocity of the water issuing from supply chamber, 

vi = initial velocity of the water in the bucket in reference to the bucket, 

Vi = terminal velocity in the bucket, 

to = angular velocity of the wheel, 

a = terminal angle between the guide and initial rim = CAB, Fig. 151, 

Yi = angle between the initial element of bucket and initial rim = EAD, 

72 = GFI, the angle between the terminal rim and terminal element of 
the bucket, 

a = eb, Fig. 152 = the arc subtending one gate opening. 



TURBINE WHEELS. 



769 



ai = the arc subtending one bucket at entrance. (In practice ai is 
larger than a,) 

a2 = gh, the arc subtending one bucket at exit, 

K = bf, normal section of passage, it being assumed that the passages 
and buckets are very narrow. 

fci = bd, initial normal section of bucket, 

k2 = gi, terminal normal section, 
(ori = velocity of initial rim, 
<or2 = velocity of terminal rim, 

= HFI, angle between the terminal rim and actual direction ol 
the water at exit, 

Y = depth of K, y, of ai, and 2/2 of K2, then 

K = Ya sin a; Ki = yiai sin 71; K2 = 2/202 sin 72. 



wr2 




Fig. 151. 



Fig. 152. 



Three simple systems are recognized, n < 7*2, called outward flow; 
n > r2, cal'ed inward flow: ri = r2, called parallel flow. The first and 
second may be combined with the third, making a mixed system. 

Value of 72 (the quitting angle). — The efficiency is increased as 71 
decreases, and is greatest for 72 = 0. Hence, theoretically, the terminal 
element of the bucket should be tangent to the quitting rim for best 
efficiency. This, however, for the discharge of a finite quantity of 
water, would require an infinite depth of bucket. In practice, there- 
fore, this angle must have a finite value. The larger the diameter of 
the terminal rim the smaller may be this angle for a given depth of wheel 
and given quantity of water discharged. In practice 72 is from 10° to 20°. 

In a wheel in which all the elements except 72 are fixed, the velocity of 
the wheel for best effect must increase as the quitting angle of the bucket 
decreases. 

Values 0/ a+ 71 must be less than 180°, but the best relation cannot 
be determined by analysis. However, since the water should be de- 
flected from its course as much as possible from its entering to its leaving 
the wheel, the angle a for this reason should be as small as practicable. 

In practice, a cannot be zero, and is made from 20° to 30°. 

The value n = 1.4 r2 makes t_he width of the crown for internal flow 
about the same as for n = ra >/V2 for outward flow, being approximately 
0.3 of the external radius. 



770 WATER-POWER. 

Values of m and fii. — The frictional resistances depend upon the con- 
struction of the wheel as to smoothness of the surfaces, sharpness of the 
angles, regularity of the curved parts, and also upon the speed it is run. 
These values cannot be definitely assigned beforehand, but Weisbach 
gives for good conditions m = }i2 = 0.05 to 0.10. 

They are not necessarily equal, and ^^i may be from 0.05 to 0.075, and /ij 
from 0.06 to 0.10 or even larger. 

Values of vi must be less than 180° — a. 

To be on the safe side, yi may be 20 or 30 degrees less than 180° — 2 a, 
giving 

yi = 180° - 2 a - 25 (say) = 155° - 2 a. 

Then if a = 30°, 71 = 95°. Some designers make 71 90°; others more, 
and still others less, than that amount. Weisbach suggests that it be less, 
so that the bucket will be shorter and friction less. This reasoning appears 
to be correct for the inflow wheel, but not for the outhow w-heel. In the 
Tremont turbines, described in the Lowell Hydraulic Experiments, this 
angle is 90°, the angle a 20°, and 72 10°, which proportions insured a posi- 
tive pressure in the wheel. Fourneyron made 71 = 90°, and a from 30° to 
33° which values made the initial pressure in the wheel near zero. 

Form of Bucket. — The form of the bucket cannot be determined analyti- 
cally. From the initial and terminal directions and the volume of the 
water flowing through the wheel, the area of the normal sections may be 
found. 

The normal section of the buckets will be: K = -y' ki= — ; k2= — 

V Vl V2 

The depths of those sections will be: 

,^ K ki k2 

Y = : ; yi = : ; 7/2= : 

a sm a' " ai sm 71 02 sin 72 

The changes of curvature and section must be gradual, and the general 
form regular, so that eddies and whirls shall not be formed. For the same 
reason the wheel must be run with the correct velocity to secure the best 
effect. In practice the buckets are made of two or three arcs of circles, 
mutually tangential. 

The Value of co. — So far as analysis indicates, the w'heel may run at any 
speed; but in order that the stream shall flow smoothly from the supply 
chamber into the bucket, the velocity V should be properly regulated. 

If ,«i = j«2 = 0.10, 7*2 -^ ri = 1.40, a = 25°, 71 = 90°, 72 = 12°, the 
velocity of the initial rim for outward flow will be for maximum efficiency 
0.614 of the velocity due to the head, or 6jr i = .614 V'2 gH. 

The velocity due to the head would be V2 gH = 1.414 '^gH. 

For an inflow wheel for the case in w^hich ri^ = 2 rj^, and the other 
dimensions as given above, wri = 0.682 ^2 gH. 

The highest efficiency of the Tremont turbine, found experimentally, 
was 0.79375, and the corresponding velocity, 0.62645 of that due to the 
head, and for all velocities above and below this value the efficiency was 
less. 

In the Tremont wheel a = 20° instead of 25°. and 72 = 10° instead of 12°. 
These would make the theoretical efficiency and velocity of the wheel some- 
what greater. Experiment showed that the velocity might be consider- 
ably larger or smaller than this amount without much diminution of the 
efficiency. 

It was found that if the velocity of the initial (or interior) rim was not 
less than 44% nor more than 75 % of that due to the fall, the efficiency was 
75% or more. This wheel was allowed to run freely without any brake 
except its own f riction, and the velocity of the initial rim was observed to 
be 1.335 ^2 gH, half of which is 0.6675 ^2 gH, which is not far from the 
velocity giving maximum effect; that is to say, when the gate is fully 
raised the coefficient of effect is a maximum when the wheel is moving with 
about half its maximum velocity. 

Number of Buckets. — Successful wheels have been made in which the 
distance between the buckets was as small as 0.75 of an inch, and others as 
much as 2.75 inches. Turbines at the Centennial Exposition had buckets 
from 41/2 inches to 9 inches from center to center. If too large they will 
not work properly. Neither should they be too deeu. Horizontal parti- 



TURBINE WHEELS. 771 

tions are sometimes introduced. These secure more efficient working in 
case the gates are only partly opened. The form and number of buckets 
for commercial purposes are chiefly the result of experience. 

Ratio of Radii. — Theory does not limit the dimensions of the wheel. In 
practice, 

for outward flow, r2 -*- ri is from 1.25 to 1.50; 

for inward flow, rz -^ ri is from 0.66 to 0.80. 

It appears that the infiow-wheel has a higher efficiency than the outward- 
flow wheel. The inflow-wheel also runs somewhat slower for best effect. 
The centrifugal force in the outward-flow wheel tends to force the water 
outward faster than it would otherwise flow; while in the inward-flow 
wheel it has the contrary effect, acting as it does in opposition to the 
velocity in the buckets. 

It also appears that the efficiency of the outward-flow wheel increases 
slightly as the width of the crown is less and the velocity for maximum 
efficiency is slower; while for the inflow-wheel the efficiency slightly in- 
creases for increased width of crown, and the velocity of the outer rim at 
the same time also increases. 

Efficiency. — The exact value or the efficiency for a particular wheel 
must be found by experiment. 

It seems hardly possible for the effective efficiency to equal, much less 
exceed, 86%, and all claims of 90 or more per cent for these motors should 
be discarded as improbable. A turbine yielding from 75% to 80% is 
extremely good. Experiments with higher efficiencies have been reported. 

The celebrated Tremont turbine gave 79 1/4% without the "diffuser," 
which might have added some 2%. A Jonval turbine (parallel flow) was 
reported as yielding 0.75 to 0.90, but Morin suggested corrections reducing 
it to 0.63 to 0.71. Weisbach gives the results of many experiments, in 
which the efficiency ranged from 50% to 84%. Numerous experiments 
give E = 0.60 to 0.65. The efficiency, considering only the energy im- 
parted to the wheel, will exceed by several per cent the efficiency of the 
wheel, for the latter will include the friction of the support and leakage at 
the joint between the sluice and wheel, which are not included in the 
former; also as a plant the resistances and losses in the supply-chamber 
are to be still further deducted. 

The Crowns. — The crowns may be plane annular disks, or conical, or 
curved. If the partitions forming the buckets be so thin that they may be 
discarded, the law of radial flow will be determined by the form of the 
crowns. If the crowns be plane, the radial flow (or radial component) 
will diminish, for the outward-flow wheel, as the distance from the axis 
increases — the buckets being full — for the angular space will be greater. 

Prof. Wood deduces from the formulse in his paper the tables on the 
next page. 

It appears from these tables: 1. That the terminal angle, a, has 
frequently been made too large in practice for the best efficiency. 

2. That the terminal angle, a, of the guide should be for the inflow less 
than 10° fcr the wheels here considered, but when the initial angle of the 
bucket is 90°, and the terminal angle of the guide is 5° 28', the gain of 
efficiency is not 2% greater than when the latter is 25°. 

3. That the initial angle of the bucket should exceed 90° for best effect 
for out flow-wheels. 

4. That with the initial angle between 60° and 120° for best effect on 
inflow wheels the efficiency varies scarcely 1%. 

5. In the outflow-wheel, column (9) shows that for the outflow for best 
effect the direction of the quitting water in reference to the earth should be 
nearly radial (from 76° to 97°), but for the inflow wheel the water is thrown 
forward in quitting. This shows that the velocity of the rim should some- 
what exceed the relative final velocity backward in the bucket, as shown 
in columns (4) and (5). , 

6. In these tables the velocities given are in terms of v 2 gh, and the 
coefficients of this exi)ression will be the part of the head which would 
produce that velocity if the water issued freely. There is only one case, 
column (5), where the coefficient exceeds unity, and the excess is so small 
it may be discarded; and it may be said that in a properly proportioned 
turbine with the conditions here given none of the velocities will equal 
that due to the head in the supply-chamber when running at best efifect. 



772 



WATER-POWEK. 



c 
II 





Z 


0.67 
0.7d 
0.84 
1.00 


Head 

Equivalent 

of Energy 

in quitting 

Water. 

2g 


o 


0.051 H 
0.039 H 
0.031 H 
0.022 H 


Direc- 
tion of 
quitting 
Water. 


ON 


t^ ^ 00 ^ 


Termi- 
nal 
Angle of 
Guide, 
a 


00 


?. :b ^^ :^ 

o o o o 


Velocity of 
Exit from 
Supply- 
Chamber. 
V 


h> 


5:3 a: ::: 13: 

cs c» ex ?a 
m NO o^ NO 

On ?s ^ 00 

»n NO i>N CO 
o" o o o 


Relative 

Velocity of 

Entrance. 

v\ 


>o 


NO '^ vO NO 

in r^ QO — 

r<^ fS <N -^ 

o o" O O 


Relative 

Velocity of 

Exit. 

V2 


•r» 


52 Ji: ::: It! 

<5j C6 c» !:» 
rsi fN^ (Ni rs 
>>>> 
(BO — fo r^ 

3 sc> 3; <=> 

o ON oo r>. 
— ' o o o" 




"V 


13: ;i:i;i: a: 

ca C55 Od ?:» 

>>>> 

r-> o^ in — 
NO NO in in 
O* o o o" 


Velocity 
Outer Rim. 


<^ 


ti3 :i: t:: ^ 

CID C» Cs Cb 

<s cni rs <s 
>>>> 

ON oo r^ f^ 

d d d d 




<S 


-r oo ON — 

O r^ *^ fNj 

oo oo oo On 

d d d d 


Initial 
Angle. 


- 


O o o 



II 


1^' 


oo o m in 
T in m o 


^1^ 


0.010 H 
0.010 // 
0.010 H 
0.009 H 




Q> 


o o o o 
O NO in r>» 
— o o o 




ti 


o o o o 
r>» ir> -"T n^ 


m 

C 

1 

o 


l:^ 


d c» c» ca 
eg (S cvi rN| 

>>>> 

fS — ON r«^ 
r^ o^ o '«r 
NO S_ hN r>. 

d d d d 



^ 


<:» d ^ !a> 

On ON rs o 

00 -o r^ r^ 
d d d d 




ii: :i: ::: ti: 

C» C» C» Cs 

rN4 ?N «N r^ 

>>>> 

$ 1 s a 

d d d d 


IF 

t— 1 


^ ;i: 15: ^ 

CS C6 C* O 
CnJ (S M fv| 

>>>> 

— r». ro OO 

S * !?. ? 

d d d d 




C35 Cft "^ <2s 

>>>> 

ON 00 00 -r 

00 NO «^ 

rx NO NO so 
d d d d 


fej 


S ^ 2: 2 

On On ON ON 

d d d d 


?- 


© 



TURBINE WHEELS. 



773 



7. The inflow turbine presents the best conditions for construction for 
producing a given effect, the only apparent disadvantage being an increased 
first cost due to an increased depth, or an increased diameter for producing 
a given amount of work. The larger efficiency should, however, more than 
neutralize the increased first cost. 

Tests of Turbines. — Emerson says that in testing turbines it is a 
rare thing to find two of the same size which can be made to do their best 
at the same speed. The best speed of one of the leading wheels is in- 
variably wide from the tabled rate. It was found that a 54-in. Leffel 
wheel under 12 ft. head gave much better results at 78 revolutions per 
minute than at 90. 

Overshot wheels have been known to give 75% efficiency, but the 
average performance is not over 60%. 

A fair average for a good turbine wheel may be taken at 75%. In tests 
of 18 wheels made at the Philadelphia Water-works in 1859 and 1860, one 
wheel gave less than 50% efficiency, two between 50% and 60%, six 
oetween 60% and 70%, seven between 71% and 77%, two 82%, and one 
87.77%. (Emerson.) 

Tests of Turbine \^Tieels at the Centennial Exhibition, 1876. 
(From a paper bv R. H. Thurston on The Systematic Testing of Turbine 
Wheels in the United States, Trans. A. S. M. E., viii. 359.) — In 1876 the 
judges at the International Exhibition conducted a series of trials of 
turbines. Many of the wheels offered for tests were found to be more or 
less defective in fitting and workmanship. The following is a statement 
of the results of all turbines entered wiiich gave an efficiency of over 75%. 
Seven other wheels were tested, giving results between 65% and 75%. 







^ 


■^^ 1 


+^ 1 


^ 


^ 


^ 




— tn 


3 m 


3 en 


:3 tn 


D in 


3 m 


3 <n 




feQ 


2a 


iS 


Za 


£q 


io 


S'a 




^ 


c3 — 


ri — 


Cj-, 


ee_ 


c3 — 


a— 


Maker's Name, or Name the 


?.o . 


^^ . 


«fe . 


^.= . 


'"fa • 


^rrl . 


«>2 . 


Wheel i3 Known by. 




c^S 






=.:» 


c-v?i 
















^"^ ^ 


O oc3 


O I,c3iO :3 


O I,c3 


O C3 


O o c3 




feo^ 


'--^'f. 


l--55^ 


tnC!:^ 


t,-5?-c 


T-~S?-^ 


I.^-^ 










djin o 


(U^O 


OJ^O 




pLi 


Ph 


PlH 


p^ 


PLh 


fll 


&. 


Risdon 


87.68 
83.79 
83.30 




86.20 


82.41 
70.79 




75.35 




National . 




Geyelin (single) 












Thos Tait 


82.13 
81.21 
78.70 
79.59 
77.57 








70.40 
55.90 


66.35 




55 00 


Goldie & McCullough 


71:66 


71.01 
'8i!24 




Rodney Hunt Mach. Co 


68.60 


51.03 


69^59 




Tyler Wheel 


79.92 67.23 




Geyelin (duplex) 








Know^lton & Dolan 


77.43 
76 94 


74.25 






62.75 






E. T. Cope & Sons 


69.92 








Barber & Harris 


76.16 
75.70 


73.33 






70.87 
62.06 


71.74 




York Manufacturing Co 


67.08 


67.57 




W. F. Mosser & Co 


75.15 


74.89 


71.90 


70.52 




66.04 









The limits of error of the tests, says Prof. Thurston, were very uncertain; 
they are undoubtedly considerable as comoared vvith the later work done 
in the permanent flume at Holyoke — possibly as much as 4% or 5%. 

Experiments with "draught-tubes," or "suction-tubes," which were 
actually "diffusers" in their effect, so far as Prof. Thurston has analyzed 
them, indicate the loss by friction which should be anticipated in such 
cases, this loss decreasing as the tube increased in size, and increasing as 
its diameter approached that of the wheel — the minimum diameter tried. 
It was sometimes found very difficult to free the tube from air completely, 
and next to im.possible, during the interval, to control the speed v.ith the 
brake. Several trials were often necessary before the power due to the full 
head could be obtained. The loss of power by gearing and by belting was 
variable with the proportions and arrangement of the gears and pulleys, 
length of belt, etc., but averaged not far from 30% for a single pair of bevel- 



774 WATER-iPOWER. 

gears, uncut and dry, but smooth for such gearing, and but 10% for the 
same gears, well lubricated, after they had been a short time in operation. 
The amount of power transmitted was. however, small, and these figures 
are probably much higher than those representing ordinary practice. 
Introducing a second pair — spur-gears — the best figures were but Uttle 
changed, although the difference between the case in which the larger gear 
was the driver, and the case in which the small wheel w^as the driver, was 
perceivable, and was in favor of the former arrangement. A single straight 
belt gave a loss of but 2% or 3%, a crossed belt 6% to 8%, when transmit- 
ting 14 horse-power with maximum tightness and transmitting power. A 
"quarter turn" wasted about 10% as a maximum, and a "quarter twist" 
about 5%. 

Dimensions of Turbines. — For dimensions, power, etc., of standard 
makes of turbines consult the catalogues of different manufacturers. 
The wheels of different makers vary greatly in their proportions for any 
given capacity. 

Rating and Efficiency of Turbines. — The following notes and tables 
are condensed from a pamphlet entitled "Turbine Water-w^heel Tests 
and Power Tables," by R. E. Horton. Water-supply and Irrigation 
Paper No. 180, U. S. Geol. Survey, 1906. 

Theory does not indicate the numbers of guides or buckets most desir- 
able. If, however, they are too few, the stream will not properly follow 
the flow lines indicated by theory. If the buckets are too small and too 
numerous, the surface-friction factor will be large. 

It is customary to make the number of guide chutes greater than the 
number of buckets, so that any object passing through the chutes will be 
likely to pass through the buckets also. 

With most forms of gates the size of the jet is decreased as the gate is 
closed, the bucket area remaining unchanged, so that the wheel operates 
mostly by reaction at full gate and by impulse to an increasing extent as 
the gate is closed. Hence, the spee^d of maximum efficiency varies as 
the gate is closed. The ratio peripheral velocity h- velocity due head for 
maximum efficiency for a 36-inch Hercules turbine is given below: 

Proportional gate opening . . . Full 

Maximum efficiency 85 . 6 

Periph. vel. -i- vel. due head. . 0.677 

American turbine practice differs from European practice in that water 
wheels are placed on the market in standard or stock sizes, whereas in 
Europe, notably on the Continent, each turbine is designed for the special 
conditions under which it is to operate, the designs being based on mathe- 
matical theory and following chiefly^ the Jonval and Fourneyron types. 

Having been developed by experiment after successive Holyoke tests, 
American stock pattern turbines probably give their best efficiencies at 
about the head under which those tests are made — i.e., 14 to 17 ft. 
The shafts, runners, and cases are so constructed as to enable stock sizes 
of wheels to be used under heads ranging from 6 to 60 ft. For very low 
heads they are perhaps unnecessarily cumbersome. For heads exceed- 
ing 60 ft. American builders commonly resort to the use of bronze buckets 
and "special wheels," not designed along theoretical lines, as in Europe, 
but representing modifications of the standard patterns. 

The double Fourneyron turbine used in the first installation of the 
Niagara Falls Power Co. is operated under a head of about 135 ft. Two 
wheels are used, one being placed at the top and the other at the bottom 
of the globe penstock. The runner and buckets are attached to the verti- 
cal shaft. Holes are provided in the upper penstock drum to allow 
water under full pressure of the head to pass through and act vertically 
against the upper runner. In this way the vertical pressure of the great 
column of water is neutralized and a means is provided to counterbalance 
the weight of the long vertical shaft and the armature of the dynamo at 
its upper end. These turbines discharge 430 cu. ft. per second, make 
250 rev. per min., and are rated at 5000 H.P. 

A Fourneyron turbine at Trenton Falls, N. Y., operates under 265 ft. 
gross head and has 37 buckets, each 5^ in. deep and \l inch wide at the 
least section. The total area of outflow at the minimum section is 165 
sq. in. The wheel develops 950 H.P. 

The theoretical horse-power of a given quantity of water Q, in cu. ft. 
per min., falling through a height H, in it., is H.P. = 0.00189 QH, 



0.806 


0.647 


0.489 


379 


87.1 


86.3 


80 


73.1 


0.648 


0.641 


0.603 


0.585 



TTJEBINE WHEELS. 775 



In practice the theoretical power is multiplied by an efficiencjr factor E 
to obtain the net power available on the turbine shaft as determinable by 
dynamometrical test. 

Manufacturers' rating tables are usually based on efficiencies of about 
80%. In selecting turbines from a maker's list the rated efficiency may 
be obtained .by the following formula: 

E = tabled efficiency. H.P. = tabled horse-power, and Q = tabled 

discharge (C.F.M.) for any head H, E = f^^^^^ ^ ^^j^ = 528.8 J^ • 

Relations of Power, Speed and Discharge. — Nearly all American turbine 
builders publish rating tables showing the discharge in cu. ft. per min., 
rev. per min., and H.P. for each size pattern under heads varying from 
3 or 4 ft. to 40 ft. or more. 

Examples of each size of a number of the leading types of turbines 
have been tested in the Holyoke flume. For such turbines the rating 
tables have usually been prepared directly from the tests. 

Let M, R, and Q denote, respectively, the H.P., r.p.m., and discharge 
In cu. ft. per min. of a turbine, as expressed in the tables, for any head 
H in feet. The subscripts 1 and 16 added signify the power, speed, and 
discharge for the particular heads 1 and 16 ft., respectively. 

Let P, N, and F denote coefficients of power, speed, and discharge, 
which represent, respectively, the H.P., r.p.m., and discharge in cu. ft. 
per sec. under a head of 1 ft. 

The speed of a turbine or the number of rev. per min. and the discharge 
are proportional to the square root of the head. The H.P. varies with 
the product of the head and discharge, and is consequently proportional 
to the three-halves power of the head. 

Given the values of M, R, and Q from the tables for any head H, these 
quantities for any other head h are: 

Mff :Mf,:: H^l^ : h^f2 ; Rj^iRf^: : H^'i : /iV2 ; QjjiQj,:: ^V2 : /1V2. 

If H and h are taken at 16 ft. and 1 ft., respectively, the values of the 
coefficients P, N, and F are: 

P = Mxc/H^l^ = Mi6/64 = 0.01562 Mis 

N = i?i6/HV2= j?i6/4 = 0.25 7^16 

F = Q16/6O i/V2= Qi6/240 = 0.00417 Q^. 

P, N, and F, when derived for a given wheel, enable the power, speed, 
and discharge to be calculated without the aid of the tables, and for any 
head H, by means of the following formulas: 

M = MxH^IVJh ^ PH^fL 

R^Rx ^ H/Hr = N \^H _ 

Q = Qi ^H/Hi = 60 F Vh, 
Since at a head of 1 ft^ and Mi, Ru and Qi equal P, AT, and 60 P, 
respectively, Fi^/2 and ^Hi each equals 1. Calculations involving H^/2 
may be facilitated by the use of the appended table of three-halves 
powers. Rating tables for sizes other than those tested are computed 
usually on the following basis: 

1. The efficiency and coefficients of gate and bucket discharge for the 
sizes tested are assumed to apply to the other sizes also. 

2. The discharge for additional sizes is computed in proportion to the 
measured area of the vent or discharge orifices. 

Having these data, together with the efficiency, the tables of discharge 
and horse-power can be prepared. The peripheral speed corresponding 
to maximum efficiency determined from tests of one size of turbine may 
be assumed to apply to the other sizes also. From this datum the revo- 
lutions per minute can be computed, the number of revolutions required 
to give a constant peripheral speed being inversely proportional to the 
diameter of the turbine. 

In point of discharge, the writer's observation has been that the rating 
tables are usually fairly accurate. In the matter of efficiency there ar^ 
undoubtedly much larger discrepancies. 



776 WATER-POWER. 

Table op H^/2for Calculating Horse-Power of Turbines. 



0.0 



0.2 



0.4 



0.6 



0.8 



T3 






0.0 


51 


364.21 


52 


374.98 


53 


385.85 


54 


396.81 


55 


407.89 


56 


419.07 


57 


430.34 


58 


441.71 


59 


453.09 


60 


464.75 


61 


476.42 


62 


488.19 


63 


500.04 


64 


512.00 


65 


524.04 


66 


536.18 


67 


548.42 


68 


560.74 


69 


573.16 


70 


585.66 


71 


598.25 


72 


610.93 


73 


623.71 


74 


636.57 


75 


649.52 


76 


662.55 


77 


675.67 


78 


688.87 


79 


702.16 


80 


715.54 


81 


729.00 


82 


742.54 


83 


756.16 


84 


769.87 


85 


783.66 


86 


797.53 


87 


811.48 


88 


825.51 


89 


839.62 


90 


853.81 


91 


868.08 


92 


882.43 


93 


896.86 


94 


911.36 


95 


925.94 


96 


940.60 


97 


955.33 


98 


970.14 


99 


985.03 


100 


1000.00 



0.2 



0.4 



0.6 0.8 



0.00 
1.00 
2.83 
5.20 
8.00 
11.18 

14.70 
18.52 
22.63 
27.00 
31.62 

36.48 
41.57 

46.87 
52.38 
58.09 

64.00 
70.09 
76.37 
82.82 
89.44 

96.23 
103.19 
110.30 



0.09 
1.32 
3.26 
5.72 
8.61 
11.86 

15.44 
19.32 
23.48 
27.91 
32.58 

37.48 
42.61 
47.96 
53.51 
59.26 

65.20 
71.33 
77.64 
84.13 
90.79 

97.61 
104.60 
111.74 



0.25 
1.66 
3.72 
6.27 
9.23 
12.55 

16.19 
20.13 
24.35 
28.82 
33.54 

38.49 
43.66 
49.05 
54.64 
60.43 

66.41 

75.58 
78.93 
85.45 
92.14 

99.00 
106.02 
113.19 



0.46 
2.02 
4.19 
6.83 
9.87 
13.25 

16.96 
20.95 
25.22 
29.75 
34.51 

39.51 
44.73 
50.15 
55.79 
61.61 

67.63 
73.84 
80.22 
86.77 
93.50 

100.39 
107.44 
114.65 



117.58 119.05 120.53 122.01 
125.00 126.50 128.01 129.53 



57134. 
30 141. 
161149, 



172.60 



32 181 

33 1 189. 

34 198. 

35 ,207. 



174 



02 182 
571191 
25 200 
061208 



llil35. 
86 143. 
75,151. 
79 159. 
961167. 

27|175. 
72 184, 
30 193, 
00 201 , 
84 210, 



0.72 

2.42 
4.69 
7.41 
10.52 
13.97 

17.73 
21.78 
26.11 
30.68 
35.49 

40.53 
45.79 
51.26 
56.94 
62.80 

68.85 
75.10 
81.52 
88.10 
94.86 

101.79 
108.87 
116.11 
123.50 
131.05 



65 137.19 138.74 
43 145.00!l46.58 
35 152.95)154.56 



216.00 217.80 219.61 
225. 06|226. 89 228.72 
234.25 236.10 237.96 



243.56 245. 43247. 31 249.20 



161.04 162.68 
169.27 170.93 

177.64 179.33 
186.13 187.85 
194.76 196.51 
203.52 205.29 
212.41 214.20 



221.42 
230.56 
239.82 



252.981254. 



223.24 
232.40 
241.68 
251.09 



256.79,258.70 260.61 



262.53 264.45 266.381268.311270.25 
272. 19 274. 14 276.09 278.05 280.01 
281 .97,283.94 285.91 287.89 289.88 
291 .861293. 861295. 851297. 85 299.86 
301 .87|303. 88,305. 90l307. 93 309.95 

311.99,314.02!316.07l318.1ll320.16 
322.22 324.27 326.34 328.41 330.48 
332.55 334.63 336.72 338.81 340.90 
343.00 345.10 347.21 349.32,351.43 
353.55,355.671357.80 359.93 362.07 



366.36 368.50 370.66 372.82 
377.14:379.31 381.48 383.66 



388.03 
399.02 
410.11 

421.31 
432.60 
444.00 
455.49 
467.08 



390.22 
401.23 
412.35 

423.56 
434.87 
446.29 
457.80 
469.41 



392.42 
403.45 
414.58 



478.77 481.12 
490.55 492.92 
502.43 504.82 
514.40 516.80 
526.46 528.89 



538.62 
550.87 
563.22 
575.65 
588.17 

600.79 
613.48 
626.2/ 
639.15 
652.11 

665.17 
678.20 
691.52 
704.83 
718.22 

731.70 
745.26 
758.90 
772.62 
786.42 

800.31 
814.27 
828.32 
842.45 
856.66 



541.07 
553.33 
565.70 
578.14 
590.68 

603.32 
616.04 
628.84 
641.74 
654.72 

667.79 

680.94 

694.1 

707.50 

720.92 

734.40 
747.98 
761.63 
775.37 
789.20 

803.10 
817.08 
831.15 
845.29 
859.51 



870.94 873.81 
885.30 888.19 
899.75 902.65 
914.27 917.18 
928.87 931.79 

943.54 946.48 
958.29 961.25 
973.11 976.09 
988.02 991.01 



394.61 
405.67 
416.82 



425.81 428.07 
437.15 439.43 
448.58'450.88 

460.12 462.43 
471. 751474.08 

483. 47; 485. 82 
495.29 497.67 
507.20 509.60 
519.22 521.63 
531.31i533.75 

543.511545.96 
555.80 558.27 
568.18 570.66 
580.65 583.15 
593.20j595.73 

605. 85 '608. 39 
618.59 621.15 
631.41 633.99 
644.33 646.92 
657.33 659.94 

670.41 673.04 
683.58 686.23 
696.84 699.50 
710.18712.85 
723.60|726.30 

737.11739.82 
750.70753.43 
764.38 767.12 

778.13 780.89 
791.97|794.75 

805.89 808.68 
819.88 822.70 



833.97 
848.13 
848.37 



836.79 
850.96 
865.22 



876.68 879.55 
891.07 893.96 
905.55 908.45 
920.10 923.02 
934.73 937.66 

949.43 952.38 
964.21 967.17 
979.07,982.05 
994. 00 1996. 99 



Rating Table for Turbines. 

Leffel Standard (New Type). Pivot Gate. [1900 list.] 



Diameter of 


Manufacturer's Rating for 
a Head of 16 Ft. 


Coefficients. 


Runner in 
Inches. 


II. P. 


Cu. Ft. 
per min. 

(=Q). 


Revs, 
per min. 


Power 
( = P). 


Dis- 
charge. 


Speed 


10 


3.70 
4.9 
6.5 
8.4 
11.00 
14.9 
19.4 
25.25 
33.61 
44.3 
58.2 
67.75 
84.1 
142 
168 
2C2 
247 


53 

201 

267 

348 

455 

602 

802 

1,043 

1,390 

1,831 

2,406 

2,800 

3,475 

5,858 

6,950 

8,340 

10.222 


535 
463 
404 
351 
306 
268 
233 
202 
176 
153 
134 
122 
110 
96 
87 
80 
72 


0.058 

.076 

.101 

.131 

.172 

.232 

.303 

.393 

.524 

.691 

.908 

1.058 

1.312 

2.215 

2.621 

3.151 

3.853 


0.220 

.838 

1.113 

1.451 

1.897 

2.510 

3.344 

4.339 

5.796 

7.635 

10.033 

11.676 

14.490 

24.428 

28.982 

34.778 

42.623 


133 8 


111/-. 


115.8 


131/4 . . 


101 


I5I4 


87 8 


171/1......:::: 


76.5 


20 ... 


67 


23 


58 2 


26 1/9 


50.5 


301/9 


44 


35 ::::::::::::: 


38 2 


40 


- 33 5 


44 


30 5 


48 


27 5 


56 


24 


61 


21 8 


66 

74 


20 
18 



Leffel Improved Samson. Pivot Gate. [1897 and 1900 lists.] 



20 


51.7 
68.3 
87.3 
116 

158 
207 
262 
324 
405 
497 
597 
708 


2,111 

2,792 

3,569 

4,751 

6,440 

8,446 

10,689 

13,196 

16,554 

20,292 

24,409 

28,906 


325 

283 
250 
217 
186 
163 
145 
130 
116 
105 
96 
88 


0.806 
1.065 
1 362 
1.810 
2.465 
3.229 
4.087 
5.054 
6.318 
7.753 
9.313 
11.045 


8.803 
11.643 
14.883 
19.812 
26.855 
35.220 
44.573 
55.027 
69.030 
84.618 
101.786 
120.538 


81 3 


23 


70.8 


26 


62.5 


30 


54 3 


35 

40 


46.5 
40.8 


45 ... 


36 3 


50 


32 5 


55 


29.0 


62 

68 


26.3 
24 


74 


22.0 



Victor High Pressure Turbine. Cylinder Gate. [1903 list.] 
Ratings for 100 Ft. Head. 



14 

16 

18 

20 


37 
50 
66 
82 
106 
128 
151 
173 
191 
228 
272 
303 
343 
387 
426 
462 
504 
544 
590 
619 
680 
742 
799 


247 

332 

442 

542 

707 

850 

1,001 

1,147 

1,265 

1,512 

1,805 

2,005 

2,277 

2,563 

2,820 

3,063 

3,340 

3,605 

3,907 

4,100 

4,505 

4,910 

5.290 


656 
574 
510 
459 
417 
383 
353 
328 
306 
278 
255 
235 
219 
204 
191 
180 
170 
161 
153 
146 
139 
133 
127 


0.037 
.050 
.066 
.082 
.106 
.128 
.151 
.173 
.191 
.228 
.272 
.303 
.343 
.387 
.426 
.462 
.504 
.544 
.590 
.619 
.680 
.742 
.799 


0.412 
.553 
.733 
.903 
1.178 
1.417 
1.668 
1.912 
2.108 
2.520 
3.008 
3.342 
3.795 
4.272 
4.700 
5.105 
5.567 
6.008 
6.512 
6.833 
7.508 
8.183 
8.817 


65.6 
57.4 
51.0 
45.9 


22 

24 

26 

28 


41.7 
38.3 
35.3 

32 8 


30 


30 6 


33 


27.8 


36 . 


25 5 


39 

42 


23.5 
21.9 


45 


20.4 


48 


19 1 


51 


18 


54 


17.0 


57 


16 


60 


15 3 


63 


14 6 


66 


13 9 


69 


13 3 


72 


12.7 



(777) 



778 WATER-POWER. 

The discharge of turbines is nearly always expressed in cubic feet pel 
minute. The "vent" in square inches is also used by millwrights and 
manufacturers, although to a decreasing extent. The vent of a turbine 
is the area of an orihce which would, under any given head, theoretically 
discharge the same quantity of water that is vented or passed through a 
turbine under that same head when the wheel is so loaded as to be run- 
ning at maximum efficiency. 

If F = vent in sq. in., Q = discharge in cu. ft. per min. under a head H, 
F = disc harge in cu. ft. per sec. under a head of 1 foot, then Q = 60 F/144 
^2gH = 3.344 V^H, and V = O.SQ/\^H; also V= 17.94 F and F = 
0.0557 V. 

The vent of a turbine should not be confused with the area of the out- 
let orifice of the buckets. The actual discharge through a turbine is 
commonly from 40 to 60% of the theoretical discharge of an orifice whose 
area equals the combined cross-sectional areas of the outlet ports meas- 
ured in the narrowest section. 

The liigh-pressure turbine is a recent design (1903), and is tabled for 
heads of 70 to 675 feet. 

A 10,000 H.P. Turbine at Snoqualmie, Wash. (Arthur Giesler, 
Eng. News, Mar. 20, 1906.)— The fall is about 270 ft. high. The machin- 
ery is placed in an underground chamber excavated in the rock about 
250 ft. below the surface, and 300 ft. up-stream from the crest of the falls. 
A tail-race tunnel runs to the lower reach of the river. The \vheel w^as 
designed by the Piatt Iron Works Co., Dayton, O., for an effective head 
of 260 ft. and 300 r.p.m., the latter being fixed by the limitations of 
dynamo design. There was no precedent for a generator approximating 
10,000 H.P. running at such a speed. The turbine is a horizontal shaft 
machine, of the Francis type, radial inward flow with central axial dis- 
charge. The turbine proper has only one bearing, 8^8 X 26 in., the gen- 
erator having three bearings. The draft tube is on the generator (front) 
side. The shaft-bearing, thrust-bearing and thrust-balancing devices are 
at the back side. The wheel is 66 in. outside diam. by 9 in. wide through 
the vanes. It has 34 vanes which extend a short distance beyond the 
end plate of the wheel on the discharge side. There are 32 guide vanes, 
of the swivel type, connected to a rotatable ring w^hich is actuated by a 
Lombard governor. The turbine wheel or runner is an annular steel 
casting. It is bolted to a disk 46' in. diam., which is an enlargement of 
the 131/2 in. hollow nickel-steel shaft. A test for efficiency was made, in 
which the output was measured on the electrical side, and the input by 
the drop of head across the head gate. At 10,000 H.P. the efficiency 
show^n w^s 84%, the figure being subject to the inaccuracy of the water 
measurement. The maximum capacity registered was 8250 K.W. or 
11.000 H.P. With the generator and the governor disconnected, with 
full gates and no load, the wheel ran at 505 r.p.m. 

Turbines of 13,500 H.P. — Four Francis turbines, with vertical shafts, 
rated at 13,500 H.P. each, have been built by Allis-Chalmers Co., for the 
Great Northern Powder Co., Duluth. Minn. The available head is 365 ft., 
and the wheels run at 375 r.p.m.; discharging, at full load, about 400 cu. 
ft. per second, each. The runners are 62 in. diam. The penstock for 
each wheel is 84 in. diam., reduced gradually to 66 in. at the wheel. 
(BulleUn No. 1613, A.-C. Co.) 

The *' Fall-increaser " for Turbines. — A circular issued Nov., 1908, 
by Clemens Herschel, the inventor of the Venturi Meter, illustrates a 
device, based on the principle of the meter, for diminishing the back- 
water head which acts against the turbine. The surplus water, which 
would otherwise run to waste, is caused to flow- into a tube of the Venturi 
shape, and the pressure in the narrow section, or throat of this tube, is 
less than that due to the head of the back-water into which the tube dis- 
charges. The throat is perforated with a great number of 6-in. holes, 
through which the discharge-water of the turbine is caused to flow, the 
velocity through the holes being never over 4 ft. per second. The circular 
j^ays : 

The fall-increaser is a form of power-house foundation construction so 
made that by running through it water, which would otherwise waste 
over the dam, the fall acting on the turbines is increased, and the output 
of power is kept at its maximum quantity, in spite of the back-water 



TANGENTIAL OR IMPULSE WATER-WHEELS. 779 

which always accompanies an abundance of river flow passing down the 
river. 

The results show that fall-increasers add about 10% to the annual 
output of power with no appreciable increase in operating expenses. 

For half the days of the year the fall-increasers are shut down because 
there is not enough, or only enough, water to supply the plain turbines: 
but for the other half of the year the fall-increasers keep the output of 
power practically constant, and at the full output, where this power 
output would fall to half the full output or less if the fall-increasers had 
not been built. 

An illustrated description of the fall-increaser, with results of tests, is 
given in the Harvard Eng'g Journal, June, 1908. See also U. S. Pat. 
No. 873,435 and Eng. News, June 11, 1908. 

TANGENTIAL OR IMPULSE WATER-WHEELS. 

The Pelton Water-wheeL — Mr. Ross E. Browne (Eng'g News, Feb. 
20, 1892) thus outlines the principles upon which this water-wheel is 
constructed: 

The function of a water-wheel, operated by a jet of water escaping 
from a nozzle, is to convert the energy of the jet, due to its velocity, into 
useful work. In order to utilize this energy fully the wheel-bucket, 
after catching the jet, must bring it to rest before discharging it, without 
inducing turbulence or agitation of the particles. 

This cannot be fully effected, and unavoidable difficulties necessitate 
the loss of a portion of the energy. The principal losses occur as follows: 
First, in sharp or angular diversion of the jet in entering, or in its course 
through the bucket, causing impact, or the conversion of a portion of the 
energy into heat instead of useful work. Second, in the so-called fric- 
tional resistance offered to the motion of the water by the wetted surfaces 
of the buckets, causing also the conversion of a portion of the energy into 
heat instead of useful work. Third, in the velocity of the water, as it 
leaves the bucket, representing energy which has not been converted into 
work. 

Hence, in seeking a high efficiency: 1. The bucket-surface at the en- 
trance will be approximately parallel to the relative course of the jet, and 
the bucket should be curved in such a manner as to avoid sharp angular 
deflection of the stream. If, for example, a jet strikes a surface at an 
angle and is sharply deflected, a portion of the water is backed, the 
smoothness of the stream is disturbed, and there results considerable 
loss by impact and otherwise. 

2. The path of the jet in the bucket should be short; in other words, 
the total wetted surface of the bucket should be small, as the loss by fric- 
tion will be proportional to this. 

3. The discharge end of the bucket should be as nearly tangential to 
the wheel periphery as com^patible with the clearance of the bucket which 
follows; and great differences of velocity in the parts of the escaping 
water should be avoided. In order to bring the water to rest at the dis- 
charge end of the bucket, it is shown, mathematically, that the velocity 
of the bucket should be one half the velocity of the jet. 

A bucket, such as shown in Fig. 153, will cause the heaping of more or 
less dead or turbulent water at the point indicated by dark shading. 
This dead water is subsequently thrown from the wheel with considerable 
velocity, and represents a large loss of energy. The introduction of the 
wedge in the Pelton bucket (see Fig. 154) is an efficient means of avoiding 
this loss. 






Fig. 153. Fig. 154. Fig. 155. 

A wheel of the form of the Pelton (Fig. 155) conforms closely in con- 
struction to each of these requirements. [In wheels as now made (1909) 



780 WATER-POWER. 

the sharp corners shown in this bucket are eliminated. See catalogues 
of the Pelton Water Wheel Co., Joshua Hendy Iron Works, and Abner 
Doble Co., all of San Francisco.] 

Considerations in the Choice of a Tangential Wheel (Joshua 
Hendy Iron Works.) — The horse-power that can be developed by a tan- 
gential wheel does not depend upon the size of the wheel but solely upon 
the head and volume of water available. The number of revolutions per 
minute that a wheel makes (running under normal conditions) depends 
solely upon two factors, viz., its diameter and the head of water. 

The choice of the diameter of a wheel is not therefore controlled by the 
power required but by the speed required when working under a. given 
head. If a wheel has no load, and is not governed, it will speed up until 
the periphery is revolving at approximately the same velocity as the 
spouting velocity of the jet, but as soon as the wheel commences to de- 
velop power by driving machinerj% etc., its velocity will drop. In a 
properly designed wheel the velocity of the rim in lineal feet per minute, 
at full load, will be from 48 to 50% of the spouting velocity of the jet. 

The diameter of pulley wheels on wheel shaft and countershafts of 
machinery should be so proportioned that the water wheel shall run at 
the speed given in the table. 

The width, area and curvature of buckets are designed to meet condi- 
tions of volume of flow under given heads. The higher the peripheral 
velocity of the wheel, the greater the volume of w^ater that the buckets 
can handle, and consequently the same standard wheel can handle more 
water, the higher the head. 

Standard wheels can generally be adapted one size larger or one size 
smaller to meet conditions of a variation of speed or volume of flow 
under a given head. Wheels designed for a given horse-power can be 
used for smaller powers (within reasonable limits) \Nith very little loss of 
efficiency, but an increase in the volume to be used requires a larger 
bucket. If, for the purpose of maintaining the same speed conditions, 
the same diameter of wheel is to be adhered to, then a special wheel 
must be built with either very large buckets or with two or more nozzles, 
or else a double or multiple unit must be adopted. 

It is advised to subdivide large streams between two, three or more 
runners, as this insures a greater freedom from breakdown and is often 
cheapest in the end. Single-nozzle, multiple runner units are easier to 
govern than multiple-nozzle, single runner units. When two or more 
nozzles are used in combination on one nmner, the increased volume to 
be dealt with is divided between the different nozzles, wiiich are so 
arranged that their respective jets impinge on different buckets at differ- 
ent parts of the periphery. Three-nozzle and five-nozzle wheels have 
many disadvantages, when governing is required, and should only be 
adopted for handling a very large volume of water when other designs 
cannot be used. 

Combined Heads. — When two or more water powers are available at 
the same site, but under different heads, it is possible to utilize them by 
mounting wheels of different diameters in paraUel, or, w hen the difference 
of head and volume is very great, it would even be possible to arrange 
for a turbine for the low head and a tangential wheel for the high head, 
although, in the latter case, it would probably be best to mount them 
independently and connect to the machinery through the medium of 
belts and countershafts. In either case, separate pipe lines must be 
employed. 

Reversible Wheels. — In the case of reversible wheels desired for use 
with hoists, cableways, etc., two wheels of proper dimensions and the 
same type may be mounted parallel on the same shaft, one of the wheels 
having the buckets and nozzles arranged to run in the opposite direction 
to the other. Suitable valves, levers and pipe connections can be arranged 
to cut the water off one wheel and turn it on to the other. 

Horizontal Wheels. — For electric generating stations, when it is de- 
sired to place the wheels below the floor of the generators, where vertical 
direct-connected equipments are used, tangential wheels may be mounted 
horizontally with vertical shafts and step bearings. 

Notes on Hydraulic Power Installations. (Joshua Hendy Iron 
Works.)— Apertures of screens must be slightly smaller than the diameter 
of the smallest nozzle used. 



i 



TANGENTIAL OR IMPULSE WATER-WHEELS. 781 

When not in use, keep the pipe full by closing the valve at the lower 
end. There is less liabilit^^ for trouble from expansion and contraction 
with a full pipe line. 

Equip the pipe line with air valves, approximately one for every 20 ft. 
of head. 

When operating under high heads, when no other precaution has been 
taken to avoid water ram during the process of governing, it is advisable 
to install relief valves between the lower end of the pipe line and the 
gates or controllers. 

When operating under even moderately high heads, if no safety device 
or by-pass has been installed, and a plain valve is to be used, sliding 
gates and butterfly valves should not be employed, but only screw gates, 
as the former would be too rapid in their action and might set up a 
dangerous water ram. 

The size of the nozzle that must be used on a wheel for maximum 
efficiency must be such as will just keep the pipe line full. If water 
overflows, put on a larger nozzle. If the pipe remains partly empty, put 
on a smaller nozzle, as otherwise the effective head is reduced, with con- 
siderable loss of efficiency. 

The nozzles may be placed either above or below the wheel, depending 
on the direction of rotation required. 

Control of Tangential Water-Wheels. — The methods of regulating 

tangential water-wheels may be classified under five heads: 

1. Permanently or semi-permanently altering the area of efflux of the 
nozzles, with water economy and without loss of efficiency. 

2. Reducing the volume of flow without altering the area of efflux, 
with water economy but with loss of efficiency. 

3. Variable alteration of the area of efflux without loss of efficiency 
and with water economy. 

4. Deflection of the jet, so that only a portion of its energy is trans- 
mitted to the wheel, without water economy. 

5. Combined regulation of 3 and 4, producing an effect whereby the 
energy of the jet is reduced rapidly without water ram and the area of 
efflux reduced slowly to effect water economy, or by a combination of 3 
with some form of by-pass. 

Governors. — Of the five methods of control enumerated above, the 
first cannot be done automatically: the other four, however, are suscep- 
tible to either hand regulation or automatic regulation by means of gov- 
ernors, the function of the governor being merely to automatically bring 
into action the particular controlling device with which the wheel has 
been equipped. There are two leading types of governors, the hydraulic 
and the mechanical. In the first, the mechanism of the water-wheel 
regulator is actuated by a hydraulically operated piston, the motive 
power being taken from a small branch pipe from the main water supply, 
or from an independent high-pressure oil-pumping system, the position 
of the piston in the cylinder and consequent relative position of the 
controlling mechanism being dependent upon the amount of fluid under 
pressure admitted to the cylinder at either end. This is controlled by a 
main valve, operated by a very sensitive relay valve which, in turn, is 
directly controlled by the centrifugal balls of the governor. 

The second type, or mechanically operated governor, consists of a 
device for automatically controlling and directing the transmission of 
the requisite amount of energy taken from the wheel shaft, to operate 
the water-regulating mechanism. The Lombard governor is a represen- 
tative of the first type, and the Lombard-Replogle governor of the 
second. 

The close regulation that can be obtained with the latter is remarkable. 
Any size will go into operation and make connection at so slight a devia- 
tion as one-tenth of one per cent from normal, and in installations which 
have been made they will not permit of a departure of more than five to 
eight per cent temporarily where there is an instantaneous drop from 
full load to practically no load. When there is sufficient fly-wheel effect, 
the deviation will not be over two per cent. The adoption of fly wheels 
greatly facilitates many problems of governing. 



782 



WATER-POWER. 



Tangential Water-Wheel Table. (Joshua Hendy Iron Works.) 

P = horse-power, Q = cubic feet per minute, R = revs, per min. The 
smaller figures in the first column give the spouting velocity of the jet 
in feet per minute. (The table is greatly condensed from the original; 
6-in., 15-in., and 30-in. wheels are also listed. F and Q are the same, 
with any given head, for a 30 as for a 36-in. wheel, but i? is 20% greater.) 



tEi.a 



12 

Inch. 



.12 

3.91 

342 

.23 

4.79 

418 

.35 

5.53 

484 

.49 

6.18 

541 

.65 

6.77 

592 

.82 

7.31 

640 

1.00 

7.82 

684 

1.20 

8.29 

726 

1.40 

8.74 

765 

1.84 
9.57 

838 

2.33 

10.34 

906 

2.84 

11.05 

969 

3.39 
11.72 

1024 

3.97 
12.36 

1080 



5.56 

13.82 

1209 



18 

Inch. 



.37 
11.72 

228 

.69 

14.36 

279 

1.06 

16.59 

323 

1.49 

18.54 

361 

1.96 

20.31 

395 

2.47 

21.94 

427 

3.01 

23.46 

456 

3.60 

24.88 

484 

4.21 

26.22 

510 

5; 54 

28.72 

559 

6.99 

31.03 

604 

8.54 

33.17 

646 
10.19 
35.18 

683 
11.93 
37.08 

720 



16.68 

41.46 

806 



24 

Inch. 



.66 

20.83 

171 

1.22 

25.51 

209 

1.89 

29.46 

242 

2.65 

32.93 

270 

3.48 

36.08 

296 

4.39 

38.97 

320 

5.36 

41.66 

342 

6.39 

44.19 

363 

7.49 

46.58 

332 

9 

51.02 
419 

12.41 
55.11 

453 
15.17 
58.92 

484 
18.10 
62.49 

513 
21.20 
65.87 

540 



29.63 

73.64 

605 



36 

Inch. 



1.50 

46.93 

114 

2.76 

57.44 

139 

4.24 

66.36 

161 

5.98 

74.17 

180 

7 

81.25 
197 
9. 

87.76 

2.13 

12.04 

93.84 

228 

14.40 

99.52 

242 

16.84 

104.83 

255 

22.18 

114.91 

279 

27.96 

124.12 

302 

34.16 

132.68 

323 

40.77 

140.74 

342 

47.75 

148.35 

360 

56.99 

157.33 

382 

66.74 

165.86 

403 



48 

Inch, 



2.64 

83.32 

85 

4. 

102.04 

104 

7.58 

107.84 

121 

10.60 

131.72 

135 

13.94 

144.32 

148 

17.58 

155.88 

160 

21.44 

166.64 

, 171 

25.59 

176.75 

181 

29.93 

186.32 

191 

39.41 

204.10 

209 

49.64 

220.44 

226 

60.68 

235.68 

242 

72.41 

249.97 

256 

84.81 

263.49 

270 

101.20 

279.44 

287 

118.54 

294.59 

302 



60 

Inch. 



4.18 

130.36 

70 

7.69 

159.66 

83 

11.85 

184.36 

96 

16.63 

206.13 

108 

21.77 

225.80 

118 

27.51 

243.89 

130 

33.54 

260.73 

137 

40.04 

276.55 

145 

46.85 

291.51 

152 

61.65 

319.33 

167 

77.71 

344.92 

181 

94.94 

368.73 

193 

113.30 

391.10 

206 

132.70 

412.25 

216 

158.38 

437.23 

229 

185.47 

460.91 

241 



72 

Inch. 



6.00 

187.72 

57 

11.04 

229.76 

69 

16.96 

265.44 

80 

23.93 

296.70 

90 

31.36 

325.00 

98 

39.52 

351.04 

106 

48.16 

375.36 

114 

57.60 

398.08 

121 

67.36 

419.52 

127 

88.75 

459.64 

139 

111.85 

496.48 

151 

136.65 

530.75 

161 

163.08 

562.96 

171 

191.00 

593.40 

180 

227.96 

629.32 

191 

266.96 

663.45 

202 



8 

Feet. 



10.64 

332.70 

43 

19.53 

407.03 

52 

30.08 

470.27 

62 

42.05 

525.90 

69 

55.20 

576.00 

75 

70.00 

624.00 

81 

85.76 

666.56 

87 

102.36 

707.00 

93 

119.72 

745.28 

96 

157.64 
816.40 

105 
198.56 
881.76 

114 
242.72 
942.72 

121 
289.64 
999.83 

128 

339.24 
1053.96 
135 
404.80 
1117.76 
144 
474.16 
1178.36 
151 



10 

Feet. 



16.48 

515.04 

34 

30.00 

630.00 

41 

46.60 

728.16 

49 

65.00 

814.32 

55 

85.62 

892.00 

60 

107.80 

966.24 

64 

134.16 

1042.92 

69 

160.16 

1106.20 

73 

187.40 

1166.04 

77 

246.64 

1277.32 

83 

310.84 

1379.68 

90 

377.76 

1474.92 

97 

453.20 

1564.40 

103 

530.80 

1649.00 

108 

633.52 

1748.92 

115 

741.88 

1843.64 

121 



12 

Feet. 



23.80 

748.95 

29 

43.80 

916.47 

35 

67.60 

1058.86 

40 

94.50 

1184.15 

46 

124.50 

1297.00 

50 

157.50 

1405.17 

54 

192.64 

1501.44 

58 

230.40 

1592.32 

62 

269.44 

1678.08 

64 

355.00 

1838.56 

70 

447.40 

1985.92 

75 

546.60 

2123.00 

81 

652.32 

2251.84 

86 

764.00 

2373.60 

90 

911.84 

2517.28 

96 

1067.84 

2653.80 

101 



TANGENTIAL OR IMPULSE WATER-WHEELS. 



783 



Tangential Water- Wheel Tsihle*— Continued, 



i2 


P 

p 

Q 
R 


12 
Inch. 


18 

Inch. 


24 

Inch. 


36 

Inch. 


48 

Inch. 


60 

Inch. 


72 

Inch. 


8 

Feet. 


10 

Feet. 


12 

Feet. 


275 1 

7975 j 








77.00 
173.94 
423 
87.73 
181.59 
442 


136.76 
308.92 

317 
155.83 
322.71 

331 


214.00 
483.39 

253 
243.82 
504.91 

265 


308.00 
695.76 

211 
350.94 
726.76 

221 


547.04 
1235.68 
159 
623.32 
1290.84 
166 


856.00 

1933.56 

127 

975.28 

2019.64 

133 


1232 00 








2783 04 








106 


300 ( 

8335 1 


7.31 

15.13 

1326 


21.93 

45.42 

884 


38.95 

80.67 

663 


1403.76 

2907.04 

111 


325 ( 

8672) 


P 

P 
Q 
R 








98.93 
189.10 

460 
110.56 
196.25 

477 


175.68 
335.84 

344 
196.38 
348.57 

358 


274.94 
525.50 

276 
307.25 
545.36 

275 


395.72 
756.40 

230 
442.27 
785.00 

238 


702.72 
1343.36 
172 
785.52 
1394.28 
179 


1099.76 
2102.00 

138 
1229.00 
2181.44 

143 


1582 88 








3025 60 








113 


350 ( 

9002) 


9.21 

16.35 

1432 


27.64 

49.06 

955 


49.09 

87.14 

716 


1769.08 

3140.00 

119 


400 ( 

9624) 


P 


11.25 

17.48 

1531 


33.77 

52.45 

1021 


59.98 

93.16 

765 


135.08 

209.80 

510 


239.94 

372.64 

382 


375.40 

583.02 

306 


540.35 

839.20 

255 


959.76 

1490.56 

101 


1501.60 

2332.08 

153 


2161.40 

3356.80 

128 


450 ( 

10208 I 


P 


13.43 

18.54 

1624 


40.79 

55.63 

1083 


71.57 

98.81 

812 


161.19 

222.52 

541 


286.31 

395.24 

406 


447.95 

618.38 

324 


644.78 

890.11 

270 


1145.24 

1580.96 

203 


1791.80 

2473.52 

162 


2579.12 

3560.44 

135 


500 ( 

0760 ( 


P 


15.73 

19.54 

1713 


47.20 

58.64 

1142 


83.83 

104.15 

856 


188.80 

234.56 

571 


335.34 
416.62 

428 


524.66 
651.83 

342 


755.20 

938.25 

285 


1341.36 

1666.48 

214 


2098.64 

2607.02 

171 


3020.80 

3753.00 

143 


550 ( 

1279) 


P 
P 








217.82 
246.00 

599 
248.16 
256.95 

625 


386.84 

436.92 

449 

440.77 

456.38 

469 


605.31 
683.62 

359 
689.63 
714.05 

375 


871.28 
984.00 

299 
992.65 
1027.80 

312 


1547.36 
1747.68 

225 
1763.08 
1825.52 

235 


2421.24 

2734.48 

179 

2758.52 

2856.20 

188 


3485 12 








3936 00 








150 


600 ( 

1787) 


24.26 

25.12 

1876 


62.04 

64.24 

1251 


110.19 

114.09 

938 


3970.60 

4111.20 

156 


640 ( 


P 
P 








270.97 
264.63 

644 
312.73 
277.54 

675 


484.16 
466.12 

483 
555.46 
492.95 

506 


748.80 
731.59 

387 
869.06 
771.26 

405 


1083.88 
1058.52 

322 
1250.92 
1110.16 

337 


1936.64 
1864.48 

242 
2221.84 
1971.80 

253 


2995.20 
2926.36 

194 
3476.24 
3085.04 

203 


4335 52 








4234.08 


2169 ) 








161 


700 ( 

2731 ) 


30.57 

27.13 

2026 


78.18 

69.38 

1351 


138.86 

123.23 

1013 


5003.68 

4440.64 

169 


750 ( 

3178) 


P 


33.91 

28.08 
2098 


86.70 

71.82 

1309 


154.00 

127.56 

1049 


346.83 

287.28 

699 


616.03 

510.25 

524 


963.82 

798.33 

419 


1387.34 

1149.13 

349 


2464.12 

2041.00 

262 


3855.28 

3193.32 

210 


5549.36 

4596.52 

175 


800 ( 

3610) 


P 


37.35 

29.00 

2166 


95.52 

74.17 

1444 


169.66 

131.74 

1083 


382.09 

296.70 

722 


678.66 

526.99 

542 


1061.81 

824.51 

433 


1528.36 

1186.81 

361 


2714.64 

2107.96 

271 


4247.24 

3298.04 

217 


6113.44 

4747.24 

181 


900 ( 

4436) 


P 
Q 
R 


44.57 

30.76 

2298 


113.98 

78.67 

1532 


202.45 

139.74 

1149 


455.94 

314.70 

766 


809.82 
558.96 

574 


1267.02 

874.53 

459 


1823.76 

1258.81 

383 


3239.28 

2235.84 

287 


5068.08 

3498.12 

229 


7295.04 

5035.24 

192 


L000( 

5217) 


P 


52.20 

32.42 

2420 


133.50 

82.93 

1615 


237.12 

147.30 

1210 


534.01 

331.72 

807 


948.48 

589.19 

605 


1483.97 
921.83 

484 


2136.04 

1326.91 

403 


3793.92 

2356.76 

303 


5935.88 

3687.32 

242 


8544.16 

5287.64 

202 



The above tables are compiled on. the following basis: 

The head (h) is the net effective head at the nozzle. Proper allowanco 

must be made for all losses in the pipe line. 
The velocity of efflux (V) is the approximate spout ing velocity of the 

jet in feet per minute as it issues from the nozzle = ^2 g^/i X 60 == 481.2 

'Vh. 

The discharge in cubic feet per minute = Q = V X a, where a equals 
the cross-section area of nozzle opening in sq. ft., no allowance being 
made for friction in the nozzle. 



784 



WATER-POWER. 



The weight of a cubic foot of water is taken at 39.2° Fahr. = 62.425 Ibs. 

The theoretical horse-power = Q X 62.425 Xh -i- 33.000 = O.0O189 Qh. 

The horse-power in the tables is based on 85% mechanical efficiency for 
the wheels. 

The diameter is the effective diameter at the line of the nozzle center, 
where the jet impinges on the center of the bucket. 

The number of revolutions is based on a peripheral speed for the effec- 
tive diameter, of half the velocity of efflux of the jet, and equals V -^ 2 C, 
where C = the circumference (in feet) of the effective diameter. 

Small wheels, up to 24-in. diam., are commonly called motors. 



Amount of Water Required to Develop a Given Horse-Power, with 
a Given Available Eflfective Head. 





Horse-Power Based on 


85% Efficiency of the Water Wheel. 


Effective 
Head in 


10 


20 


30 


40 


50 


60 


70 


80 


90 


100 


Feet. 


I 


""low in 


Cubic Feet of Water per Minute Required to 
Develop Power. 




50 


125 
104 
88 
77 
70 
63 
59 
52 
48 
45 
42 
39 
37 
35 
33 
31 
30 
28 
27 
26 
25 
24 
23 
22 
21 
20 
19 
19 
19 
18 
18 
18 
17 
17 
16 
16 


250 
208 
177 
155 
140 
125 
118 
104 
96 
89 
83 
78 
73 
69 
65 
62 
59 
57 
54 
52 
50 
48 
46 
45 
43 
42 
41 
40 
38 
37 
36 
35 
34 
33 
32 
31 


375 

312 

266 

232 

210 

186 

176 

156 

143 

133 

125 

117 

110 

104 

98 

93 

89 

85 

81 

78 

75 

72 

69 

67 

65 

62 

60 

59 

57 

55 

53 

52 

50 

49 

48 

47 


500 

416 

355 

311 

280 

248 

234 

208 

192 

178 

166 

155 

146 

138 

132 

124 

118 

113 

108 

104 

100 

96 

92 

89 

86 

83 

80 

78 

76 

74 

71 

69 

67 

66 

64 

63 


625 

520 

444 

388 

350 

312 

293 

260 

240 

222 

208 

195 

183 

172 

164 

155 

148 

141 

135 

130 

125 

120 

115 

111 

107 

104 

100 

97 

94 

92 

89 

86 

84 

82 

80 

77 


750 
624 
532 
466 
420 
372 
350 
312 
287 
266 
250 
233 
220 
207 
198 
186 
177 
169 
162 
155 
149 
144 
138 
133 
129 
124 
120 
117 
113 
110 
106 
102 
100 
98 
96 
94 


875 
726 
621 
544 
490 
435 
410 
364 
335 
310 
292 
272 
256 
242 
230 
218 
206 
198 
190 
181 
174 
167 
161 
156 
150 
14S 
140 
136 
132 
128 
124 
121 
117 
114 
111 
105 


1000 
830 
709 
622 
560 
498 
467 
415 
385 
355 
332 
312 
293 
276 
262 
248 
236 
225 
216 
207 
199 
191 
184 
178 
172 
166 
160 
136 
151 
146 
142 
138 
134 
130 
127 
124 


1125 
934 
798 
699 
630 
558 
525 
467 
430 
400 
375 
350 
330 
310 
295 
280 
266 
255 
243 
233 
224 
215 
207 
200 
193 
187 
180 
175 
170 
165 
160 
155 
151 
147 
144 
140 


1250 


60 


1038 


70 

80 


886 
876 


90 


700 


100 

no 


622 
585 


!20 


520 


130 


478 


140 

150 

160 

170 

180 


443 
416 
388 
365 
345 


190. . 


326 


200 


310 


210 


295 


220 


283 


230 


270 


240 


258 


250 


248 


260 


238 


270 


230 


280 


222 


290 


215 


300 


208 


310 


200 


320 


194 


330 


188 


340 . 


183 


350 

360 


178 
172 


370 


168 


380 


164 


390 


160 


400 


156 







Efficiency of the Doble Nozzle. — The nozzle tip is of brass, highly 
pohshed in the interior, with concave curves near the end. It contains ' 
a conical regulating needle, which is set at any desired distance from the 
opening to regulate the size of the opening and the diameter of the jet. 
A jet flowing from the nozzle has a clear, glassy appearance. Tests 



TANGENTIAL OR IMPULSE WATER-WHEELS. 785 

by H. C. Crowell and G. C. D. Lenth, at Mass. Inst, of Tech., 1903, gave 
eflaciencies under constant head from 96.4 to 99.3% for different settings 
of the needle, the coefficient of velocity being from 0.982 to 0.997. The 
efficiency of a jet is equal to the ratio of the velocity head in the jet to 
the total head at the entrance to the nozzle, and equal to the square of 
the coefficient of velocity. — Bulletin of the Ahner Doble Co., No. 6, 1904. 
Tests of a 12-in. Doble Laboratory Motor (Bulletin No. 12, 1908. 
Abner Doble Co.). — The tests were made by students at the University 
of Missouri. The available head was 46 ft. The needle valve was 
opened two, four, six and eight turns in the four series of tests, and with 
each opening different loads were applied by a Prony brake. The results 
were recorded and plotted in curves showing the relation of speed, load 
and efficiency, and from these curves the following approximate figures 
are taken: 

Speed, Revolutions per Minute. 

Valve open 200 300 400 500 600 700 800 

T-^.^+,irr.e IB.H.P 0.20 0.26 0.27 0.26 0.22 0.14 0.03 

iwo turns | gffy. % 62 75 80 77 64 41 13 

Fnnr f,irn« i B.H.P 0.36 0.45 0.51 0.50 0.42 0.30 0.12 

l^our turns {g^y (^^ ^j ^^ g^ 33 ^^ ^q ^g 

Qj^+^T-ric. JB.H.P 0.41 0.55 0.63 0.66 0.60 0.41 0.20 

bix turns j p.f=fy c/^ 4g g4 73 ^g ^^ gg ^^ 

T?,Vhf tnrn« JB.H.P 0.48 0.62 0.70 0.71 0.64 0.43 0.19 

ii^ight turns | ^^^^ ^^ ^3 ^q ^9 g^ ^2 50 23 

Water-power Plants Operating under High Pressures. — The fol- 
lowing notes are contributed by the Pelton Water Wheel Co.: 

The Consolidated Virginia & Col. Mining Co., Virginia, Nev., has a 3-ft. 
steel-disk Pelton wheel operating under 2100 ft. fall, equal to 911 lbs. 
per sq. in. It runs at a peripheral velocity of 10,804 ft. per minute and 
has a capacity of over 100 H.P. The rigidity with which water under 
such a high pressure as this leaves the nozzle is shown in the fact that it 
is impossible to cut the stream with an axe, however heavy the blow, 
as it will rebound just as it would from a steel rod travelling at a high 
rate of speed. 

The London Hydraulic Power Co. has a large number of Pelton wheels 
from 12 to 18 in. diameter running under pressure of about 1000 lbs. per 
sq. in. from a system of pressure-mains. The 18-in. wheels weighing 
30 lbs. have a capacity of over 20 H.P. (See Blaine's "Hydraulic Ma- 
cliinery.") 

HydrauUc Power-hoist of Milwaukee Mining Co., Idaho. — One cage 
travels up as the other descends; the maximum load of 5500 lbs. at a 
speed of 400 ft. per min. is carried by one'of a pair of Pelton wheels (one 
for each cage). Wheels are started and stopped by opening and closing 
a small hydraulic valve at the engineer's stand which operates the larger 
valves by hydraulic pressure. An air-chamber takes up the shock that 
would otherwise occur on the pipe line under the pressure due to 850 ft. 
fall. 

The Mannesmann Cycle Tube Works, North Adams, Mass., are using 
four Pelton wheels, having a fly-wheel rim, under a pump pressure of 
600 lbs. per sq. in. These wheels are direct-connected to the rolls 
through which the ingots are passed for drawing out seamless tubing. 

The Alaska Gold Mining Co., Douglass Island, Alaska, has a 22-ft. 
Pelton wheel on the shaft of a Riedler duplex compressor. It is used as 
a fly-wheel as well, weighing 25,000 lbs., and develops 500 H.P. at 75 
revolutions. A valve connected to the pressure-chamber starts and 
stops the wheel automatically, thus maintaining the pressure in the 
air-receiver. 

At Pachuca in Mexico five Pelton wheels having a capacity of 600 
H.P. each under 800 ft. head are driving an electric transmission plant. 
These w^heels weigh less than 500 lbs. each, showing over a horse-power 
per pound of metal. 

Formulae for Calculating the Power of Jet W^ater-wheels, such as 
the Pelton (F. K. Blue). —i7P = horse-power deUvered; 5 = 62.36 lbs. 
per cu. ft.; E = efficiency of turbine: q = quantity of water, cubic feet 
per minute; h = feet effective head; d = inches diameter of jet; p = 
pounds per square inch effective head; c = coefficient of discharge from 
nozzle, which may be ordinarily taken at 0.9. 



786 WATER-POWER. 

HP= 3^^ =.00189^g/i = .00436£;gp = .00496Ecrf2\/^=.0174£;cd2Vp3". 

q = 529.2 ^ = 229 ^^ =2.62 C(P ^h= 3.99 cd^ \^p. 
Eh Ep 



<^=2«i-«if5?3= ''■' 



-JLP ^0.381-^ = 0.25-^. 



THE POWER OF OCEAN WAVES. 

Albert W. Stahl, U. S. N. (Trans. A. S. M. E., xiii. 438), gives the fol- 
lowing formulae and table, based upon a theoretical discussion of wave 
motion: 

The total energy of one whole wave-length of a wave H feet high, L feet 
long, and one foot in breadth, the length being the distance between suc- 
cessive crests, and the height the vertical distance between the crest and 

the trough, is £; = 8 LH^ f 1 - 4.935 jj) foot-pounds. 

The time required for each wave to travel through a distance equal to 

its own length is P = -\/ - -i 90 seconds, and the number of waves passing 

any given point in one minute is N = -p = 60 -v ' ' • Hence the total 

energy of an indefinite series of such waves, expressed in horse-power per 
foot of breadth, is 



EXN 
33,000 



0.0329 ,51(1- 4.935 f:). 



By substituting various values for H -^ L, within the limits of such 
values actually occurring in nature, we obtain the following table of 



Total Energy of Deep-sea Waves in Terms of Horse-power per 
Foot of Breadth. 



Ratio of 
Length to 






Length of Waves in 


Feet. 






Height of 


















Waves. 


25 


50 


75 


100 


150 


200 


300 


400 


50 


0.04 


0.23 


0.64 


1.31 


3.62 


7.43 


20.46 


42.01 


40 


0.06 


0.36 


1.00 


2.05 


5.65 


11.59 


31.95 


65.58 


30 


0.12 


0.64 


1.77 


3.64 


10.02 


20.57 


56.70 


116.38 


20 


0.25 


1.44 


3.96 


8.13 


21.79 


45.98 


120.70 


260.08 


15 


0.42 


2.83 


6.97 


14.31 


39.43 


80.94 


223.06 


457.89 


10 


0.98 


5.53 


15.24 


31.29 


86.22 


177.00 


487.75 


1001.25 


5 


3.30 


18.68 


51.48 


105.68 


291.20 


597.78 


1647.31 


3381.60 



The figures are correct for trochoidal deep-sea waves only, but they 
give a close approximation for any nearly regular series of waves in deep 
water and a fair approximation for waves in shallow water. 

The question 01 the practical utilization of the energy which exists in 
ocean waves divides itself into several parts: 

1. The various motions of the water which may be utilized for power 
purposes. 



I 



POWER OF OCEAN WAVES. 787 

2. The wave-motor proper. That is, the portion of the apparatus in 
direct contact with the water, and receiving and transmitting tlie energy 
thereof; together with the mechanism for transmitting this energy to the 
machinery for utilizing the same. 

3. Regulating devices, for obtaining a uniform motion from the irregu- 
lar and more or less spasmodic action of the waves, as well as for adjusting 
the apparatus to the state of the tide and comUtion of the sea. 

4. Storage arrangements for insuring a continuous and uniform output 
of power during a calm, or when the waves are comparatively small. 

The motions that may be utilized for power purposes are the following: 
1. Vertical rise and fall of particles at and near the surface. 2. Hori- 
zontal to-and-fro motion of particles at and near the surface. 3. Vary- 
ing slope of surface of wave. 4. Impetus of waves rolling up the beach 
in the form of breakers. 5. Motion of distorted verticals. All of these 
motions, except the last one mentioned, have at various times been 
proposed to be utilized for power purposes; and the last is proposed to 
be used in apparatus described by Mr. Stahl. 

The motion of distorted verticals is thus defined: A set of particles, 
originally in the same vertical straight line when the water is at rest, 
does not remain in a vertical line during the passage of the wave; so that 
the line connecting a set of such particles, while vertical and straight in 
still water, becomes distorted, as well as displaced, during the passage 
of the wave, its upper portion moving farther and more rapidly than its 
lower portion. 

Mr. Stahl's paper contains illustrations of several wave-motors designed 
upon various principles. His conclusion as to their practicability is as 
follows: "Possibly none of the methods described in this paper may ever 
prove commercially successful: indeed the problem may not be susceptible 
of a financially successful solution. My own investigations, however, so 
far as I have yet been able to carry them, incline m.e to the belief that 
wave-power can and will be utilized on a paying basis." 

Continuous Utilization of Tidal Power. (P. Decoeur, Proc. Inst, 
C. E. 1890.) — In connection with the training- walls to be constructed in 
the estuary of the Seine, it is proposed to construct large basins, by means 
of which the power available from the rise and fall of the tide could be 
utilized. The method proposed is to have two basins separated by a 
bank rising above high water, within which turbines would be placed. 
The upper basin would be in communication with the sea during the hi< her 
one-third of the tidal range, rising, and the lower basin during the lower 
one-third of the tidal range, falhng. If H be the range in feet, the 
level in the upper basin would never fall below 2/3 H micasured from low 
water, and the level in the lower basin would never rise above 1/3 -H". 
The available head varies between 0.53 H and 0.80 H, the mean value 
being 2/3 H. If S square feet be the area of the lower basin, and the 
above conditions are fulfilled, a quantity VsSH cu. ft. of water is deliv- 
ered through the turbines in the space of 91/4 hours. The miCan flow is, 
therefore, SH -r- 99,900 cu. ft. per sec, and, the mean fall being VsH, 
the available gross horse-power is about Vso S'H"^, where >S' is measured 
in acres. This might be increased by about one-third if a variation of 
level in the basins amounting to 1/2 H were permitted. But to reach this 
end the number of turbines would have to be doubled, the mean head 
being reduced to 1/2 H, and it would be more difficult to transmit a con- 
stant power from the turbines. The turbine proposed is of an improved 
model designed to utilize a large flow with a moderate diameter. One 
has been designed to produce 300 horse-power, v/ith a minimum head of 
5 ft. 3 in. at a speed of 15 revolutions per minute, the vanes having 13 ft. 
internal diameter. The speed would be maintained constant by regulat- 
ing sluices. 



788 



PUMPS AND PUMPING ENGINES. 



PUMPS AND PUMPINa ENGINES. 

Theoretical Capacity of a Pump. — Let Q'=cu. ft. per min.; 
G' = U. S. gals, per min. = 7.4805 Q' \ d = diam. of pump in inches; 
I = stroke in inches; A' = number of single strokes per min. 

■n (P IN 
Capacity in cu. ft. per min. "" ^' "" 4 ' 144 ' 12 ^ 0.0004545 NaH; 

NdU 
4 ' 231 * ■ • 
Capacity in gals, per hour = 0.204 NdH. 



Capacity in U. S. gals, per min. G' = ■ 



= 0.0034 ATd^/; 



\v ^ V 



Diameter required for a ) rf = 46 

given capacity per min'. j tt ^u. 

If v = piston speed in feet per min., d = 13.54 - 

If the piston speed is 100 feet per min.: 

Nl = 1200, and d = 1.354 Vq' = 0.495 V^'; G' = 4.08 d"^ per min. 

The actual capacity will be from 60% to 95% of the theoretical, accord- 
ing to the tightness of the piston, valves, suction-pipe, etc. 

Theoretical Horse-power Required to Raise Water to a Given 
Height. — Horse-power = 

Volume in cu. ft. per min. X pressure per sq. ft. _ Weight X height of Uft 
33,000 ~ 33,000 

Q' = cu. ft. per min.; G' = gals, per min.; W = wt. in lbs.; P = 
pressure in lbs. per sq. ft.; j) = pressure in lbs. per sq. in.; i7 == height of 
lift in ft.; W = 62.355 Q', P = 144 p, p = 0.433 /f, i7 = 2.3094 p, G' = 
7.4805 Q'. 

XTT. Q'P Q'/f X 144 X 0.433 Q'H G'H 1.0104: G'H 



HP. = 



33,000 33,000 529.23 3958.9 

WH ^ Q'X 62.355 X 2.3094 p _ Q'p _ G'p 
33,000 



4000 



33,000 33,000 229.17 1714.3 

For the actual horse-power required an allowance must be made for 
the friction, slips, etc., of engine, pump, valves, and passages. 

Depth of Suction. — Theoretically a perfect pump wiU draw water 
from a height of nearly 34 feet, or the height corresponding to a perfect 
vacuum (14.7 lbs. X 2.309 = 33.95 feet); but since a perfect vacuum 
cannot be obtained on account of valve-leakage, air contained in the 
water, and the vapor of the water itself, the actual height is generally 
iess than 30 feet. When the water is warm the height to wliich it can be 
lifted by suction decreases, on account of the increased pressure of the 
vapor. In pumping hot water, therefore, the water must flow into the 
pump by gravity. The following table shows the theoretical maximum 
depth of suction for different temperatures, leakage not considered: 



Temp. 
Fahr. 


Absolute 

Pressure 

of Vapor, 

lbs. per 

sq. in. 


Vacuum 

in 
Inches of 
Mercury. 


Max. 

Depth 
of 
Suc- 
tion, 
feet. 


Temp. 
Fahr. 


Absolute 
Pressure 
of Vapor, 
lbs. per 
sq. m. 


Vacuum 

in 
Inches of 
Mercury. 


Max. 
Depth 
of 
Suc- 
tion, 
feet. 


102.1 
126.3 
141.6 
153.1 
162.3 
170.1 
176.9 


2 
3 

4 
5 
6 

7 


27.88 
25.85 
23.83 
21.78 
19.74 
17.70 
15.67 


31.6 
29.3 
27.0 
24.7 
22.3 
20.0 
17.7 


182.9 
188.3 
193.2 
197.8 
202.0 
.205.9 
209.6 


8 
9 
10 
11 
12 
13 
14 


13.63 
11.60 
9.56 
7.52 
5.49 
3.45 
1.41 


15.4 
13.1 
10.8 
8.5 
6.2 
3.9 
1.6 



PUMPS AND PUMPING ENGINES. 



789 



The Deane Single 


Boiler-feed 


or Pressure Pump. — 


Suitable for 


pumping clear liquids 


at a pressure not exceeding 150 lbs. 






Sizes. 




Capacity 
per min. 


m 




Sizes of Pipes. 










at Oiven 


(D 


¥. 


















Speed. 




•§ 










fc 


1 


"^ , 


<i5 



^6 






.s 


fl 




^ 




i 


^ 


^1 
|.l 

«2 


i- 


^^ 


G 


CO 

9, 




■5 


^ 


1 


05 





^ 


;z; 









2 







T3 







(5 





3 


2 




.07 


150 


10 


291/2 


7 


1/2 


3/4 


11/4 


1 


I 


31/2 


21/4 




.09 


150 


13 


331/2 


71/2 


1/2 


3/4 


11/4 


1 


1V2 


4 


2 3/8 




.10 


150 


15 


331/2 


71/2 


1/2 


3/4 


n/4 


1 


2 


4 


21/2 




.11 


150 


16 


331/2 


71/2 


1/2 


3/4 


11/4 


1 


21/2 


43/4 


3 




.15 


150 


22 


34 


81/2 


1/2 


3/4 


11/2 


11/4 


3 


5 


31/4 




.25 


125 


31 


431/2 


91/4 


3/4 


1 


2 


1V2 


4 


51/2 


33/4 




.33 


125 


42 


43 1/2 


91/4 


3/4 


1 




1V2 


41/?, 


7 


41/4 


8 


.49 


120 


58 


511/0 


12 




11/2 




2 


5 


7 


41/2 


10 


.69 


100 


69 


55 


12 




11/2 




2 


6 


71/?, 


5 


10 


.85 


100 


85 


55 


12 




1V2 




2 


6 1/2 


8 


5 


12 


1.02 


100 


102 


63 


14 




IV? 




21/2 


7 


10 


6 


12 


1.47 


100 


147 


69 


19 


1 1/2 


2 




4 


8 


12 


7 


12 


2.00 


100 


•200 


69 


19 


2 


21/2 




4 


9 


14 


8 


12 


2.61 


100 


261 


69 


21 


2 


21/2 




5 



The Deane Single Tank 


or Light-service 


Pum 


p. — These 1 


Dumps 


will all stand a constant working pressure of 75 lbs. on t 


le water-cylinders. 




Sizes. 






Capacity 
per min. 


CO 






Sizes of Pipes. 










at Criven 


0) 


^ 


















Speed. 














% . 


t . 


"oa 




^6 






3 




.tJ 




6 
to 


V «; 


1 ^ 


X-^ 


<n^ 


TO 


r> 


JH 






en 


d 


f-i 


b 


^^ 0^ 


t: 


c 


<D 


fl 


t3 


JH 




3 


^0 


c6 














bd 

g 


^ 

? 


J 

X 


'■+3 


02 


s 


4 


4 


5 


.27 


130 


35 


33 


91/2 


1/2 


3/4 


2 


1 1/2 


5 


4 


7 


.38 


125 


48 


451/2 


15 


3/4 


1 




21/2 


51/2 


51/2 


7 


.72 


125 


90 


451/2 


15 


3/4 


1 




21/2 


71/2 


71/2 


10 


1.91 


110 


210 


58 


17 


1 


1 V2 






8 


6 


12 


1.46 


100 


146 


67 


201/2 


1 


1 1/2 






6 


7 


12 


2.00 


100 


200 


66 


17 


3/4 


1 






8 


7 


12 


2.00 


100 


200 


67 


201/2 


1 


IV2 






8 


8 


12 


2.61 


100 


261 


68 


30 


I 


11/2 






10 


8 


12 


2.61 


100 


261 


68 1/2 


30 


1V2 


2 






8 


10 


12 


4.08 


100 


408 


68 


201/2 




11/2 


8 


8 


10 


10 


12 


4.08 


100 


408 


68 1/2 


30 


11/2 


2 


8 


8 


12 


10 


12 


4.08 


100 


408 


64 


24 


2 


21/2 


8 


8 


10 


12 


12 


5.87 


100 


587 


68 1/2 


30 


11/2 


2 


8 


8 


12 


12 


12 


5.87 


100 


587 


64 


281/2 


2 


21/2 


8 


8 


10 


12 


18 


8.79 


70 


616 


95 


25 


11/2 


2 


8 


8 


12 


12 


18 


8.79 


70 


616 


95 


281/2 


2 


21/2 


8 


8 


12 


14 


18 


12.00 


70 


840 


95 


281/2 


2 


21/2 


8 


8 


14 


16 


18 


15.66 


70 


1096 


95 


34 


2 


21/2 


12 


10 


16 


16 


18 


15.66 


70 


1096 


95 


34 


2 


21/2 


12 


10 


18 


16 


18 


15.66 


70 


1096 


97 


34 


3 


31/2 


12 


10 


16 


18 


24 


26.42 


50 


1321 


115 


40 


2 


21/2 


14 


12 


18 


18 


24 


26.42 


50 


1321 


135 


40 


3 


31/2 


14 


12 



790 PUMPS AND PUMPING ENGINES. 

Amount of Water raised by a Single-acting Lift-pump. — It ia 

common to estimate that the quantity of water raised by a single-acting 
bucket-valve pump per minute is equal to the number of strokes in one 
direction per minute, multiplied by the volume traversed by the piston 
in a single stroke, on the theory that the water rises in the pump only 
when the piston or bucket ascends; but the fact is that the column of 
water does not cease flowing when the bucket descends, but flows on 
continuously through the valve in the bucket, so that the' discharge of 
the pump, if it is operated at a high speed, may amount to considerably 
more than that calculated from the displacement multiplied by the num- 
ber of single strokes in one direction. 

Proportioning the Steam-cylinder of a Direct-acting Pump. — 

Let 

A = area of steam-cylinder; a = area of pump-cylinder; 

D = diameter of steam-cylinder; d = diameter of pump-cylinder; 

P = steam-pressure, lbs. per sq. in.; p = resistance per sq. in. on pumps; 

H = head = 2.309 p; p = 0.433 H\ 

r, zK . . ^, work done in pump-cylinder 

E = eflaciency of the pump = r— 5 t^ — -77- — r^—^ — ,. , » 

^ ^ work done by the steam-cylmder 

. ap EAP ^ - l~p , ^I'EP^ ap EAP 

EP p \ EP \ p EA' ^ a 



I = ;^ = ^^1^; i^ = 2.309^P^. If £;= 75%, i? = 1.732P^. 

E is commonly taken at 0.7 to 0.8 for ordinary direct-acting pumps. 
For the highest class of pumping-engines it may amount to 0.9. The 
steam-pressure P is the mean effective pressure, according to the indi- 
cator-diagram; the water-pressure p is the mean total pressure acting 
on the pump plunger or piston, including the suction, as could be shown 
by an indicator-diagram of the water-cylinder. The pressure on the 
pump-piston is frequently much greater than that due to the height of 
the lift, on account of the friction of the valves and passages, which 
increases rapidly with velocity of flow. 

Speed of Water through Pipes and Pump-passages. — The speed 

of the water is commonly from 100 to 200 feet per minute. If 200 feet 
per minute is exceeded, the loss from friction may be considerable. 



mu ^- . - . • J • ^ r^c / gallons per minute 
The diameter of pipe required is 4.95a/ 



I velocity in feet per minute 



For a velocity of 200 feet per minute, diam. = 0.35 X v^gallons per min. 

Sizes of Direct-acting Pumps. — The tables on pages 789 and 791 
are selected from catalogues of manufacturers, as representing the two 
common types of direct-acting pump, viz., the single-cylinder and the 
duplex. Both types are made by most of the leading manufacturers. 

Efficiency of Small Direct-acting Pumps. — Chas. E. Emery, in 
Reports of Judges of Philadelphia Exhibition, 1876, Group xx., says: 
*' Experiments made with steam-pumps at the American Institute Exhibi- 
tion of 1867 showed that average-sized steam-pumps do not, on the aver- 
age, utiUze more than 50 per cent of the indicated power in the steam- 
cyUnders,the remainder being absorbed in the friction of the engine, but 
more particularly in the passage of the water through the pump. It 
may be safely stated that ordinary steam-pumps rarely require less than 
120 pounds of steam per hour for each horse-power utilized in raising 
water, equivalent to a duty of only 15,000,000 foot-pounds per 100 
pounds of coal. With larger steam-pumps, particularly when they are 
proportioned for the work to be done, the duty will be materially in- 
creased." 



PUMPS AND PUMPING ENGINES. 



791 



The Worthington Duplex Pump, 

Standard Sizes for Ordinary Service. 











".'§ 


^B 

0) 3 






Sizes of Pipes for 








ft 


a^'i . 




Short Lengths. 


ft) 


£ 




03 


a ^ 


^^ 


t^a 


To be increased as 








c 


HI 


fl 


2 s s 
'-art 




length 


increases. 


">» 










« 


"a 




^ S 


^ d a 




u, ;- K 










i 


(I 


d 




i>-. 


-0 ^ 












o; 


c3 


r^ 


"^ o 


DQ tJ" ej 


(D CO oc 


3;:='^ 










0) 


0) 


2 

•4-5 

m 


B ^ 


<i) fli i^ 

2 S o 


III 


5&0 


1 


6 

*a 


6 
a 




a 
a 

i 


•fd 


^ 


CH 


C^ 


»2 *« 






M 


c 




« 


a> 


•5 


a 


O Oi'O 


c^ 


'^ Z'^' 


s 
1 


73 


.2 






e3 




.2^ 


20:5 




=2 cj^ 


1^ 




3 


00 


3 


5 


t-^ 


Q 


Ph 





Q 


^ 


W 


fg 


'q 


3 


2 


3 


.04 


100 to 250 


8 to 20 


27/8 


3/8 


1/2 


11/4 


, 


41/2 


23/4 


4 


.10 


100 to 200 


20 to 40 


4 


1/2 


3,4 


2 


11/2 


51/4 


31/2 


5 


.20 


100 to 200 


40 to 80 


5 


34 


II4 


21/2 


IV2 


6 




6 


.33 


100 to 150 


70 to 100 


55/8 


1 


11.2 


3 


2 


71/2 


41/2 


6 


.42 


100 to 150 


85 to 125 


638 


11/2 


2 


4 




71/2 




6 


.51 


100 to 150 


100 to 150 


7 


11/2 


2 


4 




71/2 


41/2 


10 


.69 


75 to 125 


100 to 170 


6 3/8 


11/2 


2 


4 




9 


51/4 


10 


.93 


75 to 125 


135 to 230 


71/2 


2 


21/2 


4 




10 




10 


1.22 


75 to 125 


180 to 300 


81/2 


2 


21/2 


5 




10 




10 


1.66 


75 to 125 


245 to 410 


9 7/8 


2 


21/2 


6 




12 




10 


1.66 


75 to 125 


245 to 410 


9 7/8 


21/2 


3 


6 




14 




10 


1.66 


75 to 125 


245 to 410 


9 7/8 


21/2 


3 


6 




12 


81/2 


10 


2.45 


75 to 125 


365 to 610 


12 


21/2 


3 


6 




14 


81/2 


10 


2.45 


75 to 125 


365 CO 610 


12 


2I2 


3 


6 




16 


81/2 


10 


2.45 


75 to 125 


365 to 610 


12 


21,2 


3 


6 




1812 


81/2 


10 


2.45 


75 to 125 


365 to 610 


12 


3 


31/2 


6 




20 


81/2 


10 


2.45 


75 to 125 


365 to 610 


12 


4 


5 


6 




12 


101'4 


10 


3.57 


75 to 125 


530 to 890 


141/4 


21 '2 


3 


8 




14 


101/4 


10 


3.57 


75 to 125 


530 to 890 


141/4 


21/2 


3 


8 




16 


101/4 


10 


3.57 


75 to 125 


530 to 890 


141/4 


21 2 


3 


8 




181/2 


101/4 


10 


3.57 


75 to 125 


530 to 890 


141/4 


3 


31/2 


8 




20 


101/4 


10 


3.57 


75 to 125 


530 to 890 


141/4 


4 


5 


8 




14 


12 


10 


4.89 


75 to 125 


730 to 1220 


17 


21/2 


3 


10 


8 


16 


12 


10 


4.89 


75 to 125 


730 to 1220 


17 


21/2 


3 


10 


8 


181/2 


12 


10 


4.89 


75 to 125 


730 to 1220 


17 


3 


31/2 


10 


8 


20 


12 


10 


4.89 


75 to 125 


730 to 1220 


17 


4 


5 


10 


8 


181/2 


14 


10 


6.66 


75 to 125 


990 to 1660 


19 3/4 


3 


31/2 


12 


10 


20 


14 


10 


6.66 


75 to 125 


990 to 1660 


193,4 


4 


5 


12 


10 


17 


10 


15 


5.10 


50 to 100 


510 to 1020 


14 


3 


31/2 


8 


7 


20 


12 


15 


7.34 


50 to 100 


730 to 1460 


17 


4 


5 


12 


10 


20 


15 
15 


15 
15 


11.47 
11.47 


50 to 100 
50 to 100 


1145 to 2290 
1145 to 2290 


21 
21 










25 





















Speed of Piston. — A piston speed of 100 feet per minute is commonly 
assumed as correct in practice, but for short-stroke pumps this gives too 
high a speed of rotation, requiring too frequent a reversal of the valves. 
For long-stroke pumps, 2 feet and upward, this speed may be consider- 
ably exceeded, if valves and passages are of ample area. 



792 



PUMPS AND PUMPING ENGINES. 



Number of Strokes Required to Attain a Piston Speed from 50 to 

125 Feet per Minute for Pumps Having Strolces 

from 3 to 18 Inclies in Length. 



Speed of 

Piston, in 

Feet per 

Min. 


Length of Stroke in Inches. 


3 


1 4 


1-5 1 6 1 7 


( 8 


I 10 


1 12 


1 15 


1 18 






Number of Strokes per 


Minute. 






50 


200 


150 


120 


100 


86 


75 


60 


50 


40 


33 


55 


220 


165 


132 


110 


94 


82.5 


66 


55 


44 


37 


60 


240 


180 


144 


120 


103 


90 


72 


60 


48 


40 


65 


260 


195 


156 


130 


111 


97.5 


78 


65 


52 


43 


70 


280 


210 


168 


140 


120 


105 


84 


70 


56 


Al 


75 


300 


225 


180 


150 


128 


112.5 


90 


75 


60 


50 


80 


320 


240 


192 


160 


137 


120 


96 


80 


64 


53 


85 


340 


255 


204 


170 


146 


127.5 


102 


85 


68 


57 


90 


360 


270 


216 


180 


154 


135 


108 


90 


72 


60 


95 


380 


285 


228 


190 


163 


142.5 


114 


95 


76 


63 


100 


400 


300 


240 


200 


171 


150 


120 


100 


80 


67 


105 


420 


315 


252 


210 


180 


157.5 


126 


105 


84 


70 


no 


440 


330 


264 


220 


188 


165 


132 


110 


88 


73 


115 


460 


345 


276 


230 


197 


172.5 


138 


115 


92 


77 


120 


480 


360 


288 


240 


206 


180 


144 


120 


96 


80 


125 


500 


375 


300 


250 


214 


187.5 


150 


125 


100 


83 



Underwriters' Pumps — Standard Sizes. 

(National Board of Fire Underwriters, 1908.) 



Pump Sizes, In. 


Capacity at 100 Lb. 
at Pump. 


Boiler Power 
Required. 


Full Speed. 


Steam. 

Water. 
Stroke 


No. of 
1 V2-In. 
Streams. 


Nomi- 
nal 
Gals, 
per 
Min. 


Actual 
Gals, 
per 
Min. 


Horse- 
Power. 


Steam 
Pres- 
sure 
at 
Pump, 
Lb. 


Revs, 
per 
Min. 


Piston 
Speed, 

Ft. 

per 
Min. 


14 X 7 X12 
14 X 71/4X12 
16 X 9 X12 
18 X20 X12 
18 1/2X10 1/4X12 
20 X12 X16 


;-Two] 

Three 

[ Four -j 

Six 


500 
750 
1000 
1500 


\ 483 1 
1 520 f 

806 

S 999) 

1 1050 ( 

1655 


100 
115 
150 
200 


40 
45 
45 
50 


70 
70 
70 
60 


140 
140 
140 
160 



The standard allowance for a good 1 i/s-in. (smooth nozzle) fire- 
stream is 250 gal. per minute. 

riston Speed of Pumping-engines. — (John Birkinbine, Trans. A, /. 
M. E., V. 459.) — In dealing with such a ponderous and unyielding sub- 
stance as water there are many difficulties to overcome in making a pump 
work with a high piston speed. The attainment of moderately high speed 
is, however, easily accomplished. Well-proportioned pumping-engines of 
large capacity, provided with ample water-ways and properly constructed 
valves, are operated successfully against heavy pressures at a speed of- 
250 ft. per minute, without "thug," concussion, or injury to the appara- 
tus, and there is no doubt that the speed can be still further increased. 

Speed of Water through Valves. — If areas through valves and 
water passages are sufficient to give a velocity of 250 ft. per min. or less, 
they are ample. The water should be carefully guided and not too 
abruptly deflected. (F. W. Dean, Eng. News, Aug. 10, 1893 ) 

Boiler-feed Pumps. — Practice has shown that 100 ft. of piston speed 
per mmute is the limit, if excessive wear and tear is to be avoided. 

The velocity of water through the ^suction-pine must not exceed 200 ft. 
per mmute, else the resistance of the suction is too great. 



PUMPS AND PUMPING ENGINES. 793 

Tne approximate size of suction-pipe, where the lene:th does not exceed 
25 ft. and there are not more than two elbows, may be found as follows- 

7/10 of the diameter of the cylinder multiplied by 1/100 of the pistoii 
speed in feet. For duplex pumps of small size, a pipe one size larger is 
usually employed. The velocity of flow in the discharge-pipe should not 
exceed 500 ft. per minute. The volume of discharge anci length of pipe 
vary so greatly in different installations that where the water is to be 
forced more than 50 ft. the size of discharge-pipe should be calculated 
for the particular conditions, allowing no greater velocity than 500 ft 
per minute. The size of discharge-pipe is calculated in single-cvlinder 
pumps from 250 to 400 ft. per minute. Greater velocity is permitted in 
the larger pipes. 

In determining the proper size of pump for a steam-boiler, allowance 
must be made for a supply of water sufficient for the maximum capacity 
of the boiler when over driven, with an additional allowance for feeding 
water beyond this maximum capacity when the water level in the boiler 
becomes low. The average run of horizontal tubular boilers will evapor- 
ate from 2 to 3 lbs. of water per sq. ft. of heating-surface per hour but 
may be driven up to 6 lbs. if the grate-sui^face is too large or the draught 
too great for economical working. 

Pump- Valves. — A. F. Nagle (Trans. A. S. M. E., x. 521) gives a 
number of designs with dimensions of double-beat or Cornish valves 
used in large pumping-engines, with a discussion of the theory of their 
proportions. Mr. Nagle says: There is one feature in which the Cornish 
valves are necessarily defective, namely, the lift must always be quite 
large, unless great power is sacrificed to reduce it. A small valve pre- 
sents proportionately a larger surface of discharge with the same lift than 
a larger valve, so that whatever the total area of valve-seat opening, its 
full contents can be discharged 'pithless lift through numerous small valves 
than with one large one. See also Mr. Nagle's paper on Pump Valves and 
Valve Areas, Trans. A. S. M. E., 1909. 

Henry II. Worthington was the first to use numerous small rubber 
valves in preference to the larger metal valves. These valves work well 
under all the conditions of a city pumping-engine. A volute spring is 
generally used to limit the rise of the valve. 

In the Leavitt high-duty sewerage-engine at Boston (Am. Machinist^ 
May 31, 1884), the valves are of rubber, 3/4 inch tliick, the opening in 
valve-seat being 131/2X41/2 inches. The valves have iron face and 
back-plates, and form their own hinges. 

The large pumping engines at the St. Louis water works have rub- 
ber valves 31/2 in. outside diam. There are seven valve cages in each 
of the suction and discharge diaphragms, each cage having 28 valves. 
The aggregate free area of 196 valves is 7.76 sq. ft., the area of one 
plunger being 6.26 sq. ft. The suction and discharge pipes are each 
36 in. diam., = 7.07 sq. ft. area. (Bull. No. 1609, Allis-Chalmers Co. 
Such liberal proportions of valves are found usually only in the highest 
grade of large high-duty engines. In small and medium sized pumps 
a valve area equal to one-tliird the plunger area is commonly used.) 

The Worthington "High-Duty" Pumping Engine dispenses with a 
fly-wheel, and substitutes for it a pair of oscillating hydrauhc cylinders, 
which receive part of the energy exerted by the steam during the first 
half of the stroke, and give it out in the latter half. For description see 
catalogue of H. R. Wortliington, New York. A test of a triple expan- 
sion condensing engine of tliis type is reported in Eng. News, Nov. 29, 

1904. Steam cylinders 13, 21, 34 ins.: plungers 30 in., stroke 25 in. 
Steam pressure, 124 lbs. Total head, 79 ft.: capacity, 14,267,000 gal. 
in 24 hrs. Duty per million B.T.U., 102,224,000 ft.-lbs. 

The d'Auria Pumping Engine substitutes for a fly-wheel a compen- 
sating cylinder in line with the plunger, with a piston which pushes water 
to and fro through a pipe connecting the ends of the cylinder. It is built 
by the Builders' Iron Foundry, Providence, R. I. 

A 72,000,000-gallon Pumping Engine at the Calf Pasture Station of 
the Boston Main Drainage Works is described in Eng. News, July 6, 

1905. It has three cylinders, I8I/2, 33 and 523/4 ins., and two plungers, 
60-in. diam.; stroke of all, 10 ft. The piston-rods of the two smaller 
cylinders connect to one end of a walldng beam and the rod of the third 
cylinder to the other. Steam pressure 185 lbs. gauge; revolutions per 
min. 17: static head 37 to 43 ft. Suction valves 128; ports, 4 X I6V4 in.: 



794 



PUMPS AND PUMPING ENGINES. 



total port area 8576 sq. in. Delivery valves, 96; ports, 4 X 163/4 to 203/4 
in.; total port area 7215 sq. in. The valves are rectangular, rubber flaps, 
backed and faced with bronze and weighted with lead. They are set with 
their longest dimension horizontal, on ports which incline about 45° to the 
horizontal. At 17 r.p.m. the displacement is 72,000,000 gallons in 24 hours. 
The Screw PumiMng Engine of the Kinnickinick Flushing Tunnel, 
Milwaukee, has a capacity of 30,000 cubic feet per minute (= 323,000,000 
gal. in 24 hrs.) at 55 r.p.m. The head is 31/2 ft. The wheel 12.5 ft. 
diam., made of six blades, revolves in a casing set in the tunnel lining. 
A cone, 6 ft. diam. at the base, placed concentric with the wheel on 
the approach side diverts the water to the blades. A casing beyond 
the wheel contains stationary deflector blades wliich reduce the swirling 
motion of the water (Allis-Chalmers Co., Bulletin No. 1610). The two 
screw pumping engines of the Chicago sewerage system have wheels 
143/4 ft. diam., consisting of a hexagonal hub surmounted by six blades, 
and revolving in cylindrical casings 16 ft. long, allowing 1/4 in. clearance 
at the sides. The pumps are driven by vertical triple-expansion engines 
with cylinders 22, 38 and 62 in. diam., and 42 in. stroke. 

Finance of Pumping Engine Economy. — A critical discussion of 
the results obtained by the Nordberg and other high-duty engines is 
printed in Eng. News, Sept. 27, 1900. It is shown that the practical 
question in most cases is not how great fuel economy can be reached, 
but how economical an engine it will pay to install, taking into consid- 
eration interest, depreciation, repairs, cost of labor and of fuel, etc. 
The following table is given, showing that with low cost of fuel and 
labor it does not pay to put in a very high duty engine. Accuracy is 
not claimed for the figures; they are given only to show the method 
of computation that should be used, and to show the influence of different 
factors on the final result. 

Tabular Statement of Total, Annual Cost of Pumping with an 

800-H .P. Engine, as Influenced by Varying Duty of Engine, 

Varying Price of Fuel, and Varying Time of Operation. 



First cost: 

Engine 

Engine, per H.P 

Boilers, economizers 

Engine and boilers . . 

Int. and depreciation: 

On engine, at 6% 

Boilers, 8% 

Total 

Labor per annum 

Fuel cost: 
4,000 hrs. peryr.: 

$3.00 per ton 

4.00 per ton 

5.00 per ton 

6,000 hrs. per yr.: 

$3.00 per ton 

4.00 per ton 

5.00 per ton 

Total annual cost: 
4,000 hrs. per yr.: 
Coal, $3 per ton 

4 per ton 

5 per ton 

6,000 hrs. per yr. 
Coal, $3 per ton 

4 per ton 

5 per ton 



Duty per million B.T.U. 



50. 

$24,000 

30.00 

27,000 

51,000 


100. 

$48,000 

60.00 

13,500 

61,500 


120. 

$68,000 

85.00 

11,250 

79,250 


150. 

$118,000 

147.50 

9,000 

127,000 


180. 

$148,000 

185.00 

7,500 

155,500 


1,440 
2,160 
3,600 
6,022 


2,880 
1,080 
3,960 
6,022 


4,080 

900 

4,980 

7,655 


7,080 

720 

7,800 

9,307 


8,880 

600 

9,480 

10,220 


17,280 
23,040 
28,800 


8,640 
11,520 
14,400 


7,200 
9,600 
12,400 


5,760 
7,680 
9,600 


4,800 
6,400 
8,000 


25,920 
34,560 
43,200 


12,960 
17,280 
21,600 


10,800 
14,400 
18,600 


8,640 
11,520 
14,400 


7,200 
9,600 
12,000 


26,902 
32,662 
38,422 


18,622 
21,502 
24,382 


19,835 
22,235 
25,035 


22,867 
24,787 
26,707 


24,500 
25,100 
27,700 


35,522 
44,182 
52,822 


22,942 
27,262 
31,582 


23,435 
27,035 
31,235 


25,747 
28,627 
31,507 


26,900 
29,300 
31,700 



PUMPS AND PUMPING ENGINES. 



795 



Cost of Electric Current for .Pumping 1000 Gallons per Minute 

100 ft. High. (Theoretical H.P. with 100% efficiency = 

100,000 -5- 3958.9 = 25.259 H.P.) 

Assume cost of current = 1 cent per K.W. hour delivered to the motor- 
efficiency of motor = 90%; mechanical efficiency of triplex pumps =' 
80%: of centnfugal pumps = 72%; combined efficiency, triplex pumps. 
72%: centnfugal, 64.8%. 1 K.W. = 1.-34 electrical H.P. on wire 

Triplex, 1.34.x 0.72 = 0.9648 pump H.P.; X 33,000= 31,838 ft -lbs 
per mm. 

Centrifugal, 1.34 X 0.648 = 0.86382 pump H.P.; X 33,000 = 28,654 
ft .-lbs. per mm. 

1000 gallons 100 ft. high = 833,400 ft.-lbs. per min. 

Triplex^ 833,400 -^ 31,838 = 26.1763 K.W. X 8760 hours per year 
X wO.Ol — ^ZZ\)3.{j'±. 

Centrifugal, 833,400 
X $0.01 = $2547.76. 

For 100% efficiency, $2293.04 X 0.72 = $1650.00. For any other effi- 
ciency, divide $1650.00 by the efficiency. For any other cost per K W 
hour, in cents, multiply by that cost. 



28,655 = 29.0840 K.W. X 8760 hours per year 



Cost of Fuel per Year for Pumping 1,000 Gallons per Minute 
100 Ft. High by Steam Pumps. 



(1) 


100%Effy 


2) 

. 90% 


(3) 


(4) 


(5) 


(6) 


(7) 


10. 


198. 


178.2 


142.56 


0.5846 


0.42090 


153.63 


460.89 


11.88 


166.667 


150. 


120. 


0.6945 


0.50004 


182.51 


547.53 


14. 


141.433 


127.87 


101.83 


0.8184 


0.58926 


215.08 


645.24 


14.256 


138.889 


125. 


100. 


0.8334 


0.60005 


219.02 


657.06 


15. 


132. 


118.8 


95.04 


0.8769 


0.63125 


230.44 


691.32 


16. 


123.75 


111.375 


89.10 


0.9354 


0.67344 


245.80 


737.40 


17.82 


111.111 


100. 


80. 


1.0417 


0.75006 


273.77 


821.31 


20. 


99. 


89.1 


71.28 


1.1692 


0.84180 


307.26 


921.78 


23.76 


83.333 


75. 


60. 


1.3890 


1.00008 


365.03 


1095.09 


30. 


66. 


59.4 


47.52 


1.7538 


1.26270 


460.89 


1382.67 


35.64 


55.556 


50. 


40. 


2.0835 


1.50012 


547.54 


1642.62 


40. 


49.5 


44.5 


35.64 


2.3384 


1.68360 


614.52 


1843.56 


47.52 


41.667 


37.5 


30. 


2.7780 


2.00015 


730.06 


2190.18 


50. 


39.6 


35.64 


28.51 


2.9230 


2.10450 


768.15 


2304.45 


a 


b 


c 


d 


e 


f 


ff 


h 



(1) Lbs. steam per I. H.P. per hour. 



(2) 
(3) 



Duty milUon ft.-lbs. per 1000 lbs. steam, b, 100% effy., c, 90%. 
Duty per 100 lbs. coal, 90%, effy., 8 lbs. steam per lb. coal. 

(4) Lbs. coal per min. for 1000 gals., 100 ft. high. 

(5) Tons, 2000 lbs. in 24 hours. 

(6) Tons per year, 365 days. 

(7) Cost of fuel per year at $3.00 per ton. 

Factors for calculation: b = 1980 -^ a: c = b X 0.9; d = c X 0.8; 
e = 8334 -r- 100 d:f=eX 0.72; g = f X 365: h = g X 3. 

For any other cost of coal per ton, multiply the figures in the last 
column by the ratio of that cost to $3.00. 

Cost of Pumping 1000 Gallons per Minute 100 ft. High by 
Gas Engines. 

Assume a gas engine supplied by an anthracite gas producer using 1.5 
lbs. of coal per brake H.P. hour, coal costing $3.00 per ton of 2000 lbs. 

Efficiency of triplex pump 80%, of centrifugal pump, 72%. 

1000 gals, per min. 100 ft. high = 833,400 ft.-lbs. per min. -5- 33,000 
= 25.2545 H.P. 

Fuel cost per brake H.P. hour 1.5 lbs. X 300 cents -^ 2000 = 0.225 
cent X 8760 hours per year= $19.71 per H.P. X 25.2545= $497,766 for 
100% efficiency. 

For 80% effy., $622.21 : for 72% effy., $691.34; or the same as the cost 
with a steam pumping engine of 95,000,000 foot-pounds duty per 100 
lbs. of coal. 



796 PUMPS AND PUMPING ENGINES. 

Cost of Fuel for Electric Current. 

Based on 10 lbs. steam per I.H.P. hour, 8 lbs. steam per lb. coal, or 
1.25 lbs. coal per I.H.P. per hour. (Electric line loss not included.) 

Efficiency of en^ne 0.90, of generator 0.90, combined effy. 0.81. 

I.H.P. = 0./46 K.W., 0.746 X 0.81 = 0.6426 K.W. on wire for 10 lbs. 
steam. Reciprocal = 16.5492 lbs. steam per K.W. hour. 8 lbs. steam 
per lb. coal = 2.06865 lbs. coal, at $3.00 per ton of 2,000 lbs. = 0.3103 
cents per K.W. hour. 

Lbs. steam per I.H.P. hr. — 

12 14 16 18 20 30 40 

Fuel cost, cents per K.W. hr. — 

0.3724 0.4344 0.4965 0.5585 0.6206 0.9309 1.2412 

CENTRIFUGAI. PUMPS. 

Theory of Centrifugal Pumps. — Bulletin No. 173 of the Univ. of 
Wisconsin, 1907, contains an investigation by C. B. Stewart of a 6-in. 
centrifugal pump which gave a maximum efficiency, under the best 
conditions of load, of only 32%, together with a discussion of the general 
theory of M. Combe, 1840, which has been followed by W^eisbarh, Ran- 
kine, and Unwin. Mr. Stewart says that the theory of the centrifugal 
pump, at the times of these writers, seemed practically settled, but it 
was found later that the pump did not follow the theoretical laws de- 
rived, and the subject is still open for investigation. The theoretical 
head developed by the impeller can be stated for the condition of impend- 
ing delivery, but as soon as flow begins the ordinary theory does not 
seem to apply/ Experiment shows that the main difficulty to be over- 
come in order to secure high efficiency with the centrifugal pump is in 
providing some means of transforming the portion of the energy which 
exists in the kinetic form, at the outlet of the impeller, to the pressure 
form, or of reducing the loss of head in the pump casing to a minimum. 
The theoretical head for impending delivery is V^-r-g, while experiment 
shows that the maximum actual head approaches V^-t- 2g as a limit. 
As the flow commences each pound of water discharged will possess the 
kinetic energy V^-^2g in addition to its pressure energy. To secure 
high efficiency some means must be found of utilizing this kinetic energy. 
The use of a free vortex or wliirlpooi, surrounding the impeller, and this 
surrounded by a suitable spiral discharge chamber, is practically accepted 
as one means of utilizing the energy of the velocity head. Guide vanes 
surrounding the impeller also provide a means of changing velocity head 
to pressure head, but the comparative advantage of these two means 
cannot be stated until more experimental data are obtained. 

The catalogue of the Alberger Pump Co., 1908, contains the following: 

It was not until the year 1901 that the centrifugal pump was shown to 
be nothing more or less than a water turbine reversed, and when designed 
on similar lines was capable of dealing with heads as great, and with 
efficiencies as good, as could be obtained with the turbines themselves. 
Since this date great progress has been made in both the theory and 
design, until now it is quite possible to build a pump for any reasonable 
conditions and to accurately estimate the efficiency and other charac- 
teristics to be expected during actual operation. 

The mechanical power delivered to the shaft of a centrifugal pump by 
the prime mover is transmitted to the water by means of a series of 
radial vanes mounted together to form a single member called the im- 
peller, and revolved by the shaft. The water is led to the inner ends of 
the impeller vanes, which gently pick it up and with a rapidly .accelerat- 
ing motion cause it to flow radially between them so that upon reaching 
the outer circumference of the impeller the water, owing to the velocity 
and pressure acquired, has absorbed all the power transmitted to the 
pump shaft. The problem to be solved in impeller design is to obtain 
the required velocity and pressure with the minimum loss in shock and 
friction. Since the energy of the water on leaving the pump is required to 
be mostly in the form of pressure, the next problem is to transform into 
pressure the kinetic energy of the water due to its velocity on leaving the 
impeller and furthermore to accomplish this with the least possible loss. 

The next consideration in impeller design is the proportions of the 
vanes and the water passages, and to properly solve this problem an 



CENTRIFUGAL PUMPS. 797 

extensive use of intricate mathematical formulse is necessary in addition 
to a wide knowledge of the practical side of the question. It is possible 
to obtain the same results as to capacity and head with practically an 
infinite number of different shapes, each of which gives a different effi- 
ciency as well as other varied characteristics. The change from velocity 
to pressure is accomplished by slowing down the speed of the water in an 
annular diffusion space extending from the impeller to the volute casing 
itself and so designed that there is the least loss from eddies or shock. 
It is necessary that this change shall take place gradually and uniformly, 
as otherwise most of the velocity would be consumed in producing eddies. 
With a proper design of the diffusion space and volute it is possible to 
transform practically the whole of the velocity into pressure so that the 
loss from this source may be very small. 

It is necessary also to furnish a uniform supply of water to all parts of 
the inlet or suction opening of the impeller, for unless all the impeller 
vanes receive the same quantity of water at their inner edges, they 
cannot deliver an equal quantity at their outer edges, and this would 
seriously interfere with the continuity of the flow of water and the suc- 
cessful operation of the pump. 

Relation of the Peripheral Speed to the Head. — For constant speed 
the discharge of a centrifugal pump for any lift varies with the square 
root of the difference between the actual lift and the hydrostatic head 
created by the pump without discharge. If any centrifugal pump con- 
nected to a source of supply and to a discharge pipe of considerable 
height is put in revolution, it will be found that it is necessary to main- 
tain a certain peripheral runner speed to hold the water 1 ft. high without 
discharge, and that for any other height the requisite speed will be very 
nearly proportional to the square root of the height. 

Experiments prove that the peripheral speed in ft. per min. neces- 
sary to lift water to a given height with_vanes of di_fferent forrns is approx^^ 
Imately as follows: a, 481 ^h-, b, 554 V/i; c, 610 ^h: d, 780 ^h:e, 394 ^h. 
o is a straight radial vane, 6 is a straight vane bent backward, c is a curved 
vane, its extremity making an angle of 27° with a tange it to the impeller, 
d is a curved vane with an angle of 18°, e is a vane curved in the reverse 
direction so that outer end is radial. _ 

Applying the above formula, speed ft. per min. =^coeff. X ^h, to the 
design of Mr. Clifford, gives 60 X 75.05 = C X ^85, whence C = 488. 
The vane angle was 12°. It is evident that the value of C depends on 
other things than the shape or angle of the vanes, such as smoothness of 
the vanes and other surfaces, shape and area of the diffusion vanes, and 
resistance due to eddies in the pump passages. 

The coefficient varies with the shape of the vanes: this means that 
different speeds are necessary to hold water to the same heights with 
these different forms of vanes, and for any constant speed or lift there 
must be a form of vane more suitable than any other. It would seem at 
first glance that the runner which creates a given hydrostatic head with 
the least peripheral velocity must be the most efficient, but practically 
It is apparent from tests that the curvature of the vanes can be designed 
to suit the speed and lift without materially lowering the efficiency. 
(L. A. Hicks, Eng. News, Aug. 9, 1900.) 

The quotient of the radial velocity of flow in a centrifugal pump 
divided by the peripheral velocity is a constant C. By plotting eflS- 
ciency curves for various speeds in the discharge-elfflciency diagram, 
it is found that the points of maximum efficiency of the various curves 
lie nearly in a straight line, hence the constant C varies but little with 
the speed. Examination of the data from a large number of pumps 
of various designs shows that high speeds are consistent with good 
efficiency, and that the best values for C lie between the limits of 0.12 
and 0.15. There is no advantage in the use of excessively wide im- 
pellers. — (N. W. Akimoff, Jour. Franklin Institute, May, 1911.) 

Design of a Four-stage Turbine Pump. — C. W. Clifford, in Am. 
Mach., Oct. 17, 1907, describes the design of a four-stage pump of a 
capacity of 2300 gallons per minute = 5.124 cu. ft. per sec. Following 
is an abstract of the method adopted. The total head was 1000 ft. 
Three sets of four-stage pumps were used at elevations of 16. 332, and 
666 ft., the discharge of the first being the suction of the second, and so on. 



798 PUMPS AND PUMPING ENGINES. 

The speed of the motor shaft is 850 r.p.m. This gives, for the diameter 
of the impeller, d = 12 X 60 X 75.05 ->- 850 tt = 20.24 in. arcumfer- 
ence C = 63.6 in; h — head for eac h im peller, in ft. 

V = peripheral speed = 1.015 V2 gh = 75.05 ft. per sec, 1.015 being 
an assumed coefficient. The velocity V is divided into two parts by the 
formula Fi= F - T2; V2 = 2 gh -*■ 2 V; whence Vi = 38.65 ft. per sec. 
This is the tangential component of the actual velocity of the water as it 
leaves the vane of the impeller. The radial component, or the radial 
velocity, was taken approximately at 8 ft. per sec; 8 -^ 38.65 = tang, of 
11° 42^, the calculated angle between the vane and a tangent at the 
periphery. Taking this at 12° gives tang. 12° X 38.65 = 8.215 ft. per sec. 
= radial velocity V. The outflow area at the impeller then is 5.124 X 
144 -*• (8.215 X 0.85) = 105 sq. in.: the 0.85 is an allowance for contrac- 
tion of area in the impeller. The thickness of the vane measured on the 
periphery is approximately 13/4 in.; taking this into account the width 
of the impeller was made 17/8 in. [105 ■*■ (63.6 - 6 X 13/4) = 1.98 in.]. 
The vanes were then plotted as shown in Fig. 156, keeping the distance 
between them neariy constant and of uniform section. Care was taken 
to increase the velocity as gradually as possible. 

The suction velocity was 9.37 ft. per sec, the diam. of the opening being 
10 in. This was increased to 11 ft. per sec at the opening of the im- 
peller, from which, after deducting the area of the shaft, the diameter, d, 
of the impeller inlet was found. Three long and three short vanes were 
used to reduce the shock. 

The diffusive vanes, Fig. 157, were then designed, the object being to 
change the direction of the water to a radial one, and to reduce the 
velocity gradually to 2 ft. per sec at the discharge through the ports. 

Fig. 158 shows a cross-section of the pump. The pumps were thor- 
oughly tested, and the following figures are derived from a mean curve 
of the results: 

Gals, per min.. 500 1000 1500 2000 2200 2400 2500 3000 3500 

Efficiency, % 30 51 68 78 79 78 76 61 31 

A Combination Single-stage and Two-stage Pump, for low and 

high heads, designed by Rateau, is described by J. B. Sperry in Power, 
July 13, 1909. It has two runners, one carried on the main driving- 
shaft, and the other on a hollow shaft, driven from the main shaft by a 
clutch. It has two discharge pipes, either one of which may be closed. 
When the hollow shaft is uncoupled, one runner only is used, and the 
pump is then a single-stage pump for low heads. When the shafts are 
coupled, the water passes through both runners, and may then be deliv- 
ered against a high head. 

Tests of De Laval Centrifugal Pumps. — The tables on pp. 800, 801 con- 
tain a condensed record of tests of three De Laval pumps made by Prof. 
J. E. Benton and the author in April, 1904. Two of the pumps were 
driven by De Laval steam turbines, and the other one by an elect: ic 
motor. In the two-stage pump the small wheel was coupled direct to 
the high-speed shaft of the turbine, running at about 20,500 r.p.m., ajid 
the large wheel was coupled to the low-speed shaft, which is driven by the 
first through gears of a ratio of 1 to 10. The water deUvery and the 
duty were computed from weir measurements, Francis's formula being 
used, and this was checked by calibration of the weir at different heads 
by a tank, the error of the formula for the weir used being less than 1%. 
Pltot tube measurements of the water delivered through a nozzle were 
also made. 

One inch below the center of the nozzle was located one end of a thin 
half-inch brass tube, tapered so as to make an orifice of 3/32 inch diameter. 
The other end of this tube was connected to a vertical glass tube, fastened 
to the wall of the testing room, graduated in inches over a height of about 
30 ft. The stream of water issuing from the nozzle impinged upon the 
orifice of the brass tube, and thereby maintained a height of water in 
the glass tube. This height afforded a "Pitot Tube Basis" of measure- 
ment of the quantity of water flowing, the rehability of which was tested 
by the flow as determined from the weir. The Pitot tube gave the 
same result as the weir from the formula Qi = C X Area of Nozzle X 
y/2gh with a value of C varying only between 0.953 and 0.977 for the 
large nozzle, and between 0.942 and 0.960 for the small nozzle. 



CENTRIFUGAL PUMPS. 



799 




Fig. 157. 



Fig. 156. 




Fig. 158. 



800 



PUMPS AND PUMPING ENGINES. 



Test op Steam Turbine Centrifugal Pump, Rated at 1700 Gals. 
PER MiN., 100 Ft. Head. 





Steam 










•^o 


C 


a 


13 


d 




Press, at 


a 

> 




g 


^ . 


S2S 

i3l 


s 


'^S 


o 


S 


No. of 
Test. 


the Gover- 
nor Valve. 
Lbs. per 
Sq. In. 


M 

|i 

> M 


^-3 




o 


4-. 

ti 


II 

Si 


3 




i 


i 




r^ 


S6 


c3 O 


^8^ 


c4 




r 


1 






< 








« 
* 


* 


Qf=H 


^ 


^ 


^ 


w 


6 


190 


126 


251/4 


1,547 


47.7 


25.45 


37.43 


22.95 


45.97 


1,978 


0.481 


10 


190 


148 


251/9 


1,536 


56.65 


24.42 


50.44 


34.95 


70.75 


1,958 


U 617 


1 


188 


155.2 


25 


1,553 


59.6 


24.06 


61.50 


44.54 


94.9 


1,860 


0.747 


2 


188 


153.5 


251/4 


1,547 


58.9 


24.21 


61.86 


44.55 


100.37 


1,759 


0.756 


3 


188 


150.7 


251/4 


1,540 


57.7 


24.33 


61.47 


43.59 


106.94 


1.615 


0.755 


4 


188 


143.5 


251/0 


1,549 


54.8 


24.53 


60.00 


40.72 


115.46 


1,398 


0.743 


5 


188 


161 


253/8 


1,540 


47.5 


24.5 


54.47 


31.80 


125.85 


1,001 


0.676 


6A 
t9 


189.5 
189 
189 
189 


170 
169.5 
169 
169.7 


251/2 


1 565 


24 9 




Shut-'^ff T 


142 15 






r,537 
1,535 
1,538 






45.15 
45.12 
44.62 


43.85 
43.82 


95.14 
99.05 


1,826 
1,753 
1,629 














42.93|104.42 





* The brake H.P. and the steam per B.H.P. hour were calculated by a 
formula derived from Prony brake tests of the turbine, 
t Non-condensing. 



Test of Electric Motor Centrifugal Pump. Diam. of Pump Wheel 
89/32 In. Rated at 1200 Gals. Per Min. — 45 Ft. Head. 
2000 Revs. Per Min. 



1 

d 




< 




* 




Cubic Feet of 

Water per Sec. 

by Weir. 


1 

6 

CO 

1 
1 


-J 

1 


i-i 

^0 


d 


1 


242.5 


55.2 


17.94 


15.07 


2,006 


3.158 


10.25 


28.52 


1,417 


0.680 


2 


242.3 


54.8 


17.80 


14.94 


1,996 


3.126 


10.67 


30.12 


1,403 


0.714 


3 


242 


59 


19.14 


16.22 


1,996 


2.885 


11.80 


36.1 


1,295 


0.728 


4 


242 


62.4 


20.24 


17.27 


2,005 


2.826 


12.18 


38.05 


1,268 


0.706t 


5 


241.8 


62.9 


20.39 


17.41 


2,000 


2.525 


13.06 


45.66 


1,133 


0.750 


6 


240.8 


66 


21.30 


18.28 


2,005 


2.504 


13.40 


47.25 


1,124 


0.733t 


7 


241.4 


64 


20.71 


17.71 


2,003 


2.197 


13.12 


52.7 


986 


0.742 


8 


239.7 


66.3 


21.30 


18.28 


1,997 


2.179 


13.15 


53.28 


978 


0.720t 


9 


240.9 


63.2 


20.41 


17.43 


2,007 


1.735 


11.42 


58.10 


779 


0.665t 


10 


242 


62 


20.11 


17.14 


2,003 


1.760 


11.71 


58.76 


790 


0.683 


11 


248 


34 


11.30 


8.74 


2.040 


Shut-Off 




68.39 







* Brake H.P. calculated from a formula derived from a brake test of 
the motor. 

t Tests marked f were made with the pump suction throttled so as to 
make the suction equal to about 22 ft. of water column. In the other 
tests the suction was from 5.6 to 10.9 ft. 



CENTRIFUGAL PUMPS. 



801 



Test of Steam Turbine Two-Stage Centrifugal Pump. Rated at 

250 Gals, per Min. 700 Ft. Head. Large Pump Wheel, 

2050 R.P.M.; Small Wheel, 20,500 R.P.M. 



Steam 


Pressure between 

Pumps. 

Lbs. Sq. In. 




c 
c 








o 




£ 


u C 


Press, at 
the Gover- 
nor Valve. 

Lbs. per 
Sq. In. 


a 


U 

s 


m . 

C CD 

■$ = 

3.S 

-OS 








Si 


III 

i.ii 


o 3 


> 

o 


1 


a1 


< 


0) 




m 








{^ 


^ 


Q 




186 


120.7 


28.1 


25.25 


341 


2,104 


0.830 


135.76 


12.83 


373 


18.63 


106.2 


175 


138.3 
162.3 


27.5 
27.05 


24.4 
25.5 


385 


2,092 
2,074 


0.799 
0.790 


193.85 

288 


17.54 
25.78 


359 
354 






181 


28.73 


68.9 


178 


173.7 


26.2 


25.5 


316 


2,056 


0.775 


358.78 


31.50 


347 


32.9 


60.2 


180 


180.3 


26 


25.3 


326 


2,027 


0.750 


420.5 


35.60 


336 


36.00 


54.9 


181 


182 


25.3 


25.25 


325 


2,001 


0.731 


494.35 


40.92 


328 


41.55 


47.7 


180 


182 
188.3 


24.9 
25.5 


25.35 
26.3 


iii 


1,962 
2,014 


0.697 
0.664 


585.06 
632.6 


46.19 

47.58 


312 
299 






186 


47.43 


41.77 


185 


185 


30 


25.3 


331 


2,012 


0.558 


756.38 


47.81 


251 


47.67 


41.5 


185 


184 


29 


26.5 


325 


2,029 


0.544 


781.4 


48.15 


244 


48.88 


40.50 



A Test of a Lea-Deagan Two-Stage Pump, by Prof. J. E. Denton, 
IS reported in Eng. Rec, Sept. 29, 1908. The pump had a 10-in. suction 
and discharge line, and impellers 24 in. diam., each with 8 blades. The 
following table shows the principal results, as taken from plotted curves 
of the tests. The pump was designed to give equal efficiency at different 
speeds. 

GaL per min. 

400 800 1200 1600 2000 2400 2800 3000 3200 3400 3600 3800 
Efficiency. 

400 r.p.m. 42 61 69 ' 75 77 77 70 

500 " 39 56 65 71 75 77 77.6 77 74 70'.'. 

600 •• 35 50 62 68 71 74 76 77 78 78 76 54 
Head. 

400 r.p.m. 55 55 53 51 47 42 34 

500 " 63 86 84 82 78 73 67 63 58 51'.".'. 

600 " 126 127 125 122 118 115 107 104 101 97 87 ' 55 

The following results were obtained under conditions of maximum 
efficiency: 

400 r.p.m. 77.7% effy. 2296 gals, per min. 43.6 ft. lift 
500 " 77.6 " 2794 " " 67.4 

600 " 77.97 " 3235 " " 100.7 

A High-Duty Centrifugal Pump. — A 45,000,000 gal. centrifugal pump 
at the Deer Island sewage pumping station, Boston, Mass., was tested 
in 1896 and showed a duty of 95,867,476 ft.-lbs., based on coal fired to 
the boilers. — (AUis-Chalmers Co., BuUetin No. 1062.) 

Rotary Pumps. — Pumps with two parallel geared shafts carrying 
vanes or impellers wiiich mesh with each other, and other forms of posi- 
tive driven apparatus, in wliich the water is pushed at a moderate veloc- 
ity, instead of being rotated at a high velocity as in centrifugal pumps, 
are known as rotary pumps. They have an advantage over recipro- 
cating pumps in being valveless, and over centrifugal pumps in working 
under variable heads. They are usually not economical, but when care- 
fully designed with the impellers of the correct cycloidal shape, like 
those used in positive rotary blowers, they give a high efficiency. 
They are especially useful in handling large volumes of water at 
heads from 10 to 50 feet and also as vacuum pumps for condensers. 



802 



PUMPS AND PUMPING ENGINES. 



They are not well adapted for lifting small quantities of water at 
high pressure. 

By calibrating the discharge per revolution and attaching a revolu- 
tion counter a rotary pump may be used as a water meter. 

An improvement in rotary pumps is to drive the two impellers 
by a cross-compound engine, the two cylinders of which are so set that 
the high-pressure piston drives one impeller and the low-pressure pis- 
ton the other. In this arrangement the transmission of power from 
one impeller shaft to the other through gearing is avoided. (Conners- 
viUe Blower Co., 1915.) 

Tests of Centrifugal and Rotary Pumps. (W. B. Gregory, Bull. 
183 U. S. Dept. of Agriculture, 1907.)— These pumps are used for irri- 
gation and drainage in Louisiana. A few records of small pumps, giving 
very low efficiencies, are omitted. Oil was used as fuel in the boilers, 
except in the pump of the New Orleans drainage station No. 7 (figures in 
the last column), which was driven by a gas-engine. 



Actual lift 

Disch. cu. ft. per sec. . 
Water horse-power. . . . 

I.H.P 

Effy., engine, gearing 

and pumps 

Duty, per 1000 lbs. stea. 
Duty, per rGillion 

B.T.U. infuel 

Therm, effy. from stea. 
Kind of engine, and 

pump 



15.5 
72.6 
127.5 
155.6 

81.7 
72.1 

37.8 
8.16 

a.f 



16.2 
157.0 

287.4 
671.2 

42.9 
34.3 

18.3 
4.23 

b.g 



11.2 
116.0 
147.1 
229.8 

64.2 
40.7 

20.7 
4.68 

b.g 



30.2 

93.2' 

318.0 

648.0 

49.0 

33.8 

24.2 
4.16 

b,g 



9.5 
71.4 
76.5 
137.7 

55.6 



22.1 



c, g 



23.7 

68.7 

222.8 

503.9 

44.3 
33.9 

17.3 
4.09 

b,g 



31.7 

85.6 

306.8 

452.3 

67.9 
78.2 

51.1 
9.70 

a, g 



6 
130.5 
98.8 
193.6 

51.0 
31.4 

16.7 
3.93 

d, g 



31.6 
152.9 
547.9 
657.7 

83.3 
75.4 

50.1 
9.61 

a, g 



13.4 
30.5 
46.2 
90.6 

51.0 



82.4 



e, g 



a, Tandem compound condensing Corliss: b, Simple condensing Cor- 
liss; c, Simple non-condensing Corliss; d, Triple-expansion condensing, 
vertical; e, Three-cylinder vertical gas-engine, with gas-producer, 0.85 lb. 
coal per I.H.P. per hour; /, Rotary pump; g, Cycloidal rotary. 

The relatively low duty per miUion B.T.U. is due to the low efficiency 
of the boilers. The test whose figures are given in the next to the last 
column is reported by Prof. Gregory in Trans. A. S. M, E., to vol. xxviii. 

DUTY TRIALS OF PUMPING-ENGINES. 

A committee of the A. S. M. E. {Trans., xii. 530) reported in 1891 on a 
standard method of conducting duty trials. Instead of the old unit of 
duty of foot-pounds of work per 1 00 lbs. of coal used, the commJttee recom- 
mend a new unit, foot-pounds of work per million heat-units furnished by 
the boiler. The variations.in quantity of coal make the old standard unfit 
as a basis of duty ratings. The new unit is the precise equivalent of 100 
lbs. of coal in cases where each pound of coal imparts 10,000 heat-units to 
the water in the boiler, or where the evaporation is 10,000 -r- 970.4 = 10.305 
lbs. of water from and at 212° per pound of fuel. This evaporative result 
is readily obtained from all grades of Cumberland or other semi-bitumi- 
nous coal used in horizontal return tubular boilers, and, in many cases, 
from the best grades of anthracite coal. 

The committee on Power Tests (1915) reaffirmed the new unit, de- 
fining it as follows: 

The duty per miUion heat-units is found by dividing the number of 
foot-pounds of work done during the trial by the total number of heat- 
units consumed, and multiplying the quotient by 1,000,000. The 
amount of work is found in the case of reciprocating pumps by mul- 
tiplying the net area of the plunger in sq. in., the total head expressed 
In pounds per square inch * b.y the length of the stroke in feet, and 
the total number of single strokes during the trial; finally correcting 

^ The total head is determined by adding together the pressure 
shown by the gage on the force main, the vacuum shown by the gage 
on the suction main, and the vertical distance between the center of 
the force-main gage and the point where ithe suction-gage pipe con- 
nects to the suction main, all expressed in the same units (pounds per 
tjc^uare inch or foot). A pet-cock should be attached to the gage p> yj 



DUTY TRIALS OF PUMPING ENGINES. 803 

for the percentage of leakage of the pump. In cases where the water 
dehvered is determined by weir or other measurement, the work done is 
found by multiplying the weight of water discharged during the trial by 
the total head in feet. 

The water horse-powder of a pump is found by dividing the num- 
ber of foot-pounds of work done per minute by 33,000. 

Capacity. — The capacity in gallons per 24 hours for reciprocating 

Eumps in cases where the water delivered is not measured, is found 
y multiplying the net area of the plunger in square inches by the 
length of the stroke in feet (in direct-connected engines the average 
length of stroke); then by the number of single strokes per minute; 
and the product of these three by the constant 74.8; finally correcting 
for the percentage of leakage of the pump. 

Leakage of Pump. — The percentage of leakage is the percentage 
borne by the quantity of leakage, found on the leakage trial, to the 
quantity of water discharged on the duty run determined from plunger 
displacement. 

Leakage Test of Pump. — The leakage of an inside plunger (the only 
type which requires testing) is most satisfactorilv determined by making 
the test with the cylinder-head removed. A wide board or plank may be 
temporarily bolted to the lower part of the end of the cylinder, so as to 
hold back the water in the manner of a dam, and an opening made in the 
temporary head thus pro\ided for the reception of an overflow-pipe. 
The plunger is blocked at some intermediate point in the stroke (or, if 
this position is not practicable, at the end of the stroke), and the water 
from the force main is admitted at full pressure behind it. The leakage 
escapes through the overflow-pipe, and it is collected in barrels and 
measured. The test should be made, if possible, with the plunger in 
various positions. . ,.^ , 

In the case of a pump so planned that it is difficult to remove the 
cyUnder-head, it may be desirable to take the leakage from one of the 
openings which are provided for the inspection of the suction-valves, 
the head being allowed to remain in place. 

It is assumed that there is a practical absence of valve leakage. Exami- 
nation for such leakage should be made, and if it occurs, and it is found to 
be due to disordered valves, it should be remedied before making the 
plunger test. Leakage of the discharge valves will be shown by water 
passing down into the empty cylinder at either end when they are under 
pressure. Leakage of the suction-valves will be shown by the disappear- 
ance of water which covers them. 

If valve leakage is found which cannot be remedied the quantity oi 
water thus lost should also be tested. One method is to measure the 
amount of water required to maintain a certain pressure in the pump 
cylinder when this is introduced through a pipe temporarily erected, no 
water being allowed to enter through the discharge valves of the pump. 

Triction. — The percentage of total friction in a reciprocating 
pump is the percentage of the friction horse-power to the indicated 
norse-power of the steam cylinders. 

Data and Results. — The. data and results should be reported in 
accordance with the form given herewith, adding lines for data not 

below each gage cock, and opened occasionaUy so as to free the pipe 
of air in the case of the force-main gage and of water in the case of 
the suction gage. If the suction main is under a pressure instead of 
a vacuum the suction gage should be attached at such a level that the 
connecting pipe may be filled with v/ater when the pet-cock is opened, 
in which case the correction for difference in elevation of gages is 
the vertical distance between the centers of the gages, and the reading 
of the suction gage is to be subtracted from that of the force-main 
gage. 

If the water is drawn from an open well beneath the pump, the 
total head is that shown by the force-main gage corrected for the 
elevation of the center of the gage above the level of water in the 
pump well. 

If there is a material difference in velocity of the water at *.he 
points where the two gages are attached, a correction should be made 
for the corresponding difference in "velocity-head." 



804 PUMPS AND PUMPING ENGINES. 

• 

provided for, or omitting tnose not required, as may conform to the 
object in view. 

In the case of a pumping engine of the reciprocating class for which 
a record of the complete performance is desired, the additional engine 
data and results given in the Steam Engine Code may supplement 
those here given. 

DATA AND RESULTS OF STEAM PUMPING MACHINERY 

TEST. 

Code of 1915. 



1. Test of pump located at. 

To determine 

Test conducted by 



DIMENSIONS, ETC. 

2. Type of machinery 

3. Rated capacity in gallons per 24 hrs gals. 

4. Size of engine or turbine 

5. Size of pump 

6. Auxiliaries (steam or electric driven) 

7. Date 

8. Duration hrs. 

AVERAGE PRESSURES AND TEMPERATURES. 

9. Pressure in steam pipe near throttle by gage lbs. 

10. Vacuum in condenser ins. 

11. Temperature of steam, if superheated, at throttle degs. 

12. Temperature corresponding to pressure in exhaust pipe 

near engine or turbine degs. 

13. Pressure in force main by gage lbs. 

14. Vacuum or pressure in suction main by gage ins. or lbs. 

(a) Correction for difference in elevation of the two 

gages lbs. 

15. Total head expressed in lbs. perssure per sq. in lbs. 

(a) Total head expressed in feet ft. 

QUALITY OF STEAM. 

16. Percentage of moisture in steam, degrees superheating, % or degs. 

TOTAL QUANTITIES. 

17. Total water fed to boilers lbs. 

18. Total condensed steam from surface condenser (corrected 

5 for condenser leakage) lbs. 

19. Total dry steam consumed (Item 19 or 20 less moisture 

in steam) lbs. 

20. Total gals, of water discharged, by measurement gals. 

(o) Total gals, of water discharged, by plunger dis- 
placement, uncorrected gals. 

,^^ ^ ^ ^ ,. /Item 20a - Item 20\ _ ,^^ , 

(6) Percentage of slip { ^^^ ^^ 1 X 100. percent. 

(c) Leakage of pump gals. 

\d) Total gals, of water discharged, by calculation 
from plunger displacement, corrected for 
leakage gals. 

(e) Total weight of water discharged, as measured . . Fbs. 

(/) Total weight of water discharged, by calculation 
from plunger displacement, corrected for 
leakage Iba. 

HOURLY QUANTITIES. 

21. Total water fed to boilers or drawn from surface con- 

denser per hr lbs. 

22. Total dry steam consumed for all purposes per hour, 

(Item 19 -r Item 8) lbs. 



DUTY TRIALS OF PUMPING ENGINES. 805 

23. Steam consumed per hour for all purposes foreign to 

main engine lbs. 

24. Dry steam consumed by engine or turbine per hour 

(Item 23 - Item 24) lbs. 

25. Weight of water discharged per hour, by measurement . . lbs. 

(a) Weight of water discharged per liour, calculated 
from plimger displacement, corrected lbs. 

HOURLY HEAT DATA. 

26. Heat-units consumed by engine or turbine per hour 

(Item 24 X total heat of one lb. of steam above exhaust 
temperature of Item 12) B.T.U. 

INDICATOR DIAGRAMS. 

27. Mean effective pressure, each steam cylinder lbs. per sq. in. 

(a) Mean effective pressure, each water cyUnder. lbs. persq. in 

SPEED AND STROKE. 

28. Revolutions per minute R.P.M . 

(a) Number of single strokes per minute strokes 

(b) Average length of stroke feet. 

POWER. 

29. Indicated horse-power developed I.H.P. 

30. Water horse-power H.P. 

31. Friction horse-power (Item 29 - Item 30) H.P. 

32. Percentage of I.H.P. lost in friction per cent* 

CAPACITY. 

33. Gallons of water pumped in 24 hrs., as measured gals. 

(a) Gals, of water pumped in 24 hrs., calculated from 
plunger displacement, corrected. . gals. 

(b) Gals, of water pumped per minute, as measiu*ed. . gals. 

(c) Gals, of water pumped per minute, calculated from 
plunger displacement, corrected gals. 

ECONOMY RESULTS. 

34. Heat-units consumed per I.H.P.-hr B.T.U. 

EFFICIENCY RESULTS. 

35. Thermal efficiency referred to I.H.P. (2546.5 -^ Item 34) 

X 100 per cent . 

DUTY. 

36. Duty per 1,000,000 heat-units ft.-lbs. 

WORK DONE PER HEAT-UNIT. 

37. Ft.-lbs. of work per B.T.U. (1,980,000 -^ Item 34) ft.-lbs. 

The Nordberg Pumping Engine at Wildwood, Pa. — Eng. News 
May 4, 1899, Aug. 23, 1900, Trans. A. S. M. E., 1899. The pecuUar 
feature of this engine is the method used in heating the feed-water. The 
ens:ine is quadruple expansion, with four cyUnders and three receivers. 
There are five feed-water heaters in series, a, b, c, d, e. The water is 
taken from the hot-well and passed in succession through a which is 
heated by the exhaust steam on its passage to the condenser; 6 receives 
its heat from the fourth cylinder, and c, d and e respectively from the 
third, second and first receivers. An approach is made to the requirement 
of the Carnot thermodynamic cycle, i.e., that heat entering the system 
should be entered at the highest temperature; in tliis case the water 
receives the heat from the receivers at gradually increasing temperatures. 
The temperatures of the water leaving the several heaters were, on the 
test, 105°, 136°, 193°, 260°, and 311° F. The economy obtained with this 
engine was the highest on record at the date (1900) viz., 162,948,824 ft. 
lbs. per milUon B.T.U., and it has not yet been exceeded (1909), 



806 



PUMPS AND PUMPING ENGINES. 



Notable High-duty Pumping Engine Eecords. 



Date of test . 
Locality 



Capacity, mil. gal., 24 hrs. 
Diam. of steam cylinders, in. 

Stroke, in 

No. and diam. of plungers. 
Piston speed, ft. per min.. 

Total head, ft 

Steam pressure 

Indicated Horse-power — 

Friction, % 

Mechanical efficiency, %.. . 
Dry steam per I.H.P. hr.. 
B.T.U. per I.H.P. per min.. . 

Duty, B.T.U. basis.. 

Duty per 1000 lbs. steam 

Thermal efficiency, % 



(1) 

1899 

Wildwood, 

Pa. 



(2) 
1900 
St. 
Louis 
(10). 



(3) 
1900 
Boston 
Chest- 
nut Hill 



19.5,29,49.5 

57.5x42 

(2) 143/4 

256 

504 

200 

712 

6.95 

93.05 

12.26, 11.4 

186* 

162.9* 147.5t 

150.2* 

22.81 



15 

34, 62,92 

X42 

292 

126 

801 

3.16 

96.84 

10.68 

202 

158.07 

179.45 

21.00 



30 



(4) 

1901 

Boston, 

Spot 

Pond. 



(5) 

1906 

St. 
Louis 

(3) 

Bissell's 

Point. 



30 

, 56,87 

X66 

(3)42 

195 

140 

185 

801 

6.71 

93.29 

10.34 

196 

156.8 

178.49 

21.63 



22, 



30 

41.5,62 

x60 

(3) 30.5 

244 

125 

151 

464 

3.47 

96.53 

11.09 

203 

156.59 

172.40 

20.841 



20 
34, 62,94 

72 

(3)337/8 

198 

238 

146 

859 

2.27 

97.73 



202.8 
158.85 
181.30 
20.92 



* With reheaters. 



t Without reheaters. 



^^^o.^^-^-- 



(3) Do. Aug. 23, 1900. 
Bulletin No. 1609. The 



From Eng. News, Sept. 27, 1900. 
(4) Do. Nov. 4, 1901. (5) AlUs-Chalmers Co., 
Wildwood engine has double-acting plungers. 

The coal consumption of the Chestnut Hill engine was 1.062 lbs. per 
I.H.P. per hour, the lowest figure on record at that date, 1901. 

VACUU3I PUMPS. 

The Pulsometer. — In the pulsometer the water is raised by suction 
into the pump-chamber by the condensation of steam within it, and is 
then forced into the delivery-pipe by the pressure of a new quantity of 
steam on the surface of the water. Two chambers are used which work 
alternately, one raising while the other is discharging. 

Test of a Pulsometer. — A test of a pulsometer is described by De Volson 
Wood in Trans. A. S. M. E., xiii. It had a 3V2-inch suction-pipe, stood 
40 in. high, and weighed 695 lbs. 

The steam-pipe was 1 inch in diameter. A throttle was placed about 
2 feet from the pump, and pressure gauges placed on both sides of the 
throttle, and a mercury well and thermometer placed beyond the throttle. 
The wire drawing due to throttling caused superheating. 

The pounds of steam used were computed from the increase of the 
temperature of the water in passing through the pump. 

Pounds of steam X loss of heat = lbs. of water sucked in X increase of 
temp. 

The loss of heat in a pound of steam is the total heat in a pound of 
saturated steam as found from "steam tables" for the given pressure, 
plus the heat of superheating, minus the temperature of the discharged 
water; or 

T^ , . ^ lbs. water X increase of temp. 
Pounds of steam = H-OASt-T 

The results for the four tests are given in the table on p. 807. 

Of the two tests having the highest hft (54.05 ft.), that was more 
efficient which had the smaller suction (12.26 ft.), and this was also the 
most efficient of the four tests. But, on the other hand, the other two 
tests having the same Uft (29.9 ft.), that was the more efficient which had 
the greater suction (19.67), so that no law in this regard was established. 
The pressures used, 19, 30, 43.8, 26.1. follow the order of magnitude of 
the total heads, but are not proportional thereto. No attempt was made 
to determine what pressure would give the best efficiency for any par- 



THE JET PUMP. 



807 



Test of , 


I Pulsometer. 






Data and Results. 


1 


2 


3 


4 


Strokes per minute 


71 


60 


57 


64 


Steam pressure in pipe before 
throttling 




114 
19 


no 

30 


127 
43.8 


104.3 


Steam pressure after throttling. . 


26.1 


Steam temp, after throttling, °F. . 


270.4 


277 


309.0 


270.1 


Steam superheating, °F 


3.1 


3.4 


17.4 


1.4 


Steam used, lbs 


1617 
404,786 


931 
186,362 


1518 
228,425 


1019.9 


Water pumped, lbs 


248,053 


Water temp, before entering pump 


75.15 


80.6 


76.3 


70.25 


Water temperature, rise of 


4.47 


5.5 


7.49 


4.55 


Water head by gauge on lift, ft.. . . 


29.90 


54.05 


54.05 


29.90 


Water head by gauge on suction. . 


12.26 


12.26 


19.67 


19.67 


Water head by gauge, total (H) .. 


42.16 


66.31 


73.72 


49.57 


Water head by measure, total (h) 


32.8 


57.80 


66.6 


41.60 


Coeffi. of friction of plant, h/H 


0.777 


0.877 


0.911 


0.839 


Efficiency of pulsometer 


0.012 


0.0155 


0.0126 


0.0138 


Eff'y of plant exclusive of boiler 


0.0093 


0.0136 


0.0115 


0.0116 


Eff'y of plant if that of boiler be 0.7 


0.0065 


0.0095 


0.0080 


0.0081 


Duty, if 1 lb. evaporates 10 lbs. 










water 


10.511,400 


13,391,000 


11,059,000 


12,036,300 



ticular head. The pressure used was intrusted to a practical runner, 
and he judged that when the pump was running regularly and well, the 
pressure then existing was the proper one. It is pecuUar that, in the first 
test, a pressure of 19 lbs. of steam should produce a greater number of 
strokes and pump over 50% more water than 26.1 lbs., the lift being the 
same as in the fourth experiment. 

Chas. E. Emery in discussion of Prof. Wood's paper says, referring to 
tests made by himself and others at the Centennial Exhibition in 1876 
(see Report of the Judges, Group xx.), that a vacuum-pump tested by 
him in 1871 gave a duty of 4.7 millions; one tested by J. F. Flagg, at the 
Cincinnati Exposition in 1875, gave a maximum duty of 3.25 millions. 
Several vacuum and small steam-pumps, compared later on the same 
basis, were reported to have given duties of 10 to 11 milUons, the steam- 
pumps doing no better than the vacuum-pumps. Injectors, when used 
for lifting water not required to be heated, have an efficiency of 2 to 5 
millions; vacuum-pumps vary generally between 3 and 10; small steam- 
pumps between 8 and 15; larger steam-pumps, between 15 and 30, and 
puraping-engines between 30 and 140 millions. 

A very high record of test of a pulsometer is given in Eng'g, Nov. 24, 
1893, p. 639, viz.: Height of suction 11.27 ft.; total height of lift, 102.6 
ft.; horizontal length of delivery-pipe, 118 ft.; quantity delivered per 
hour, 26,188 British gallons. Weight of steam used per H. P. per hour, 
92.76 lbs.; work done per pound of steam 21,345 foot-pounds, equal to a 
duty of 21,345,000 foot-pounds per 100 lbs. of coal, if 10 lbs. of steam 
were generated per pound of coal. 

The Jet-pump. — This machine works by means of the tendency of a 
stream or jet of fluid to drive or carry contiguous particles of fluid along 
with it. The water-jet pump, in its present form, was invented by Prof, 
James Thomson, and first described in 1852. In some experiments on a 
small scale as to the efficiency of the jet-pump, the greatest efficiency was 
found to take place when the depth from which the water was drawn by 
the suction-pipe was about nine tenths of the height from which the 
water fell to form the jet; the fiow up the suction-pipe being in that case 
about one fifth of that of the jet, and the efficiency, consequently, 9/io X 
1/5 = 0.18. This is but a low efficiency; but it is probable that it maj^ be 
increased by improvements in proportions of the machine. (Rankine, 
S. E.) 

The Injector when used as a pump has a very low efficiency. (See 
Injectors, under Steam-boilers.) 



808 PUMPS AND PUMPING ENGINES. 

GAS-ENGINE PUMPS. 

The Humphrey Gas Pump is a single-acting reciprocating pumping 
engine, the motive power of which is furnished by the explosion of a 
mixture of gas and air, as in a gas engine, the force of the explosion 
acting directly on the surface of a column of water in the vertical 
cylindrical part of a J or V-shaped pipe instead of on a reciprocating 
piston. The upper part of the cy Under contains tlie combustion 
chamber and valves similar to those of an Otto cycle gas engine. The 
lower part contains a suction valve box through which water enters 
into the "play pipe" and through which it passes to a surge tank and 
thence to the delivery pipe or reservoir. The charge of gas and air 
for starting is forced into the combustion chamber by a 2-cylinder 
air-compressor. When the explosion takes place the water is forced 
into the surge tank while the products of combustion expand to a 
low pressure, the inertia of the moving column of water in the play 
pipe causing it to continue in motion after the pressure upon it has 
decreased to atmospheric pressure. The scavenging valves of the gas 
cylinder and the suction valves of the water pump then open, admitting 
air and water. INIost of the water follows the moving column in the 
play pipe while the rest rises in the explosion cylinder. After the 
kinetic energy in the moving column is expended in forcing water into 
the surge tank the column comes to rest and starts to flow back into 
the cylinder, the suction valves closing. When the surface reaches 
the level of the exhaust valves of the gas cylinder these are closed 
and the kinetic energy of the backward moving column is expended in 
compressing the imprisoned mixture of gases and scavenging air to a 
pressure higher than that of the surge tank, which starts the water 
moving downward again until the pressure is again reduced below 
that of the atmosphere. A fresh charge of gas and air is then drawn 
into the explosion chamber, compressed by the next return of the 
to-and-fro moving water column and then ignited. The motion of 
the water is similar to the swing of the pendulum of a clock, the time 
of vibration being nearly proportional to the square root of the length 
of the moving column. The pump was invented in 1906 by Mr. H. A. 
Humphrey. For illustrated descriptions see Eng'g, Nov. 26 and Dec. 
3, 1909, and circulars of the Humphrey Gas Pump Co., Syracuse, 
N. Y., makers imder the Humphrey and Smyth patents. 

Tests of five pumps at Chingford, England, gave the following 
figures: Four pumps, capacity each 47,000 to 48,000 U. S. gal. per 
min.; lift 30 to 32 ft.; water H.P. developed, 301 to 323; gas used per 
min., 390 to 400 cu. ft. (at 60° F. and 30 in. bar.) ; heating value of 
gas (lower value) B.T.U. per cu. ft., 142 to 146; thermal efficiency, 
22.19 to 24.07%; anthracite per water H.P.-hour, 0.881 to 0.957 lb. 
A smaller pump, capacity 26,000 U. S. gal. per min., gave a thermal 
efiiciency of 26.63% and a coal consumption of 0.796 lb. per water 
H.P.-hour. The cylinders of the larger engine are 7 ft. diam., the play 
pipe, 6 ft. (Eng'g, Feb. 14, 1913). 

A Humphrey gas pump of 26,000 gal. capacity per min. at 37 ft. head 
has been installed for irrigation purposes at Del Rio, Texas. It is guar- 
anteed to deliver not less than 26,000 gal. per min. with a thermal 
efficiency of 20% when using producer gas of a heating value of not 
less than 100 B.T.U. per cu. ft. The principal dimensions are: Ex- 
plosion cylinder, 66 in. diam. X 41 in.; water cylinder, 66 in. X 89 in. 
long; valve boxes, 66 in. X 73 in. long; number of 5-in. valves, 400; 
lift, 1 in.; total discharge area of valves, 4160 sq. in.; play pipe diam., 
66 in., length, including 135° bend, 106 ft. Number of explosions, 12 
to 20 per min. 

Humphrey pumps without discharge valves are limited to heads of 
about 15 to 40 ft., but a pump with an intensifier and discharge valves 
is made for heads up to 150 ft. 

PUMPING BY COMPRESSED AHl— THE AIR-LIFT PUMP. 

Air-lift Pump. — The air-lift pump consists of a vertical water-pipe 
with its lower end submerged in a well, and a smaller pipe delivering air 
into it at the bottom. The rising column in the pipe consists of air 
mingled with water, the air being in bubbles of various sizes, and is there- 
fore lighter than a column of water of the same height; consequently the 



PUMPING BY COMPRESSED AIR. 809 

water in the pipe is raised above the level of the surrounding water. 
This method of raising water was proposed as early as 1797, bjr Loescher, 
of Freiberg, and was mentioned by Collon in lectures in Paris in 1876, 
but its first practical application probably was by Werner Siemens in 
Berlin in 1885. Dr. J. G. Pohle experimented on the principle in Cali- 
fornia in 1886, and U. S. patents on apparatus involving it were granted 
to Pohle and Hill in the same year. A paper describing tests of the air- 
lift pump made by Randall, Browne and Behr was read before the Tech- 
nical Society of the Pacific Coast in Feb., 1890. 

The diameter of the pump-column was 3 in., of the air-pipe 0.9 in., and 
of the air-discharge nozzle s/g in. The air-pipe had four sharp bends and a 
length of 35 ft. plus the depth of submersion. 

The water was pumped from a closed pipe-well (55 ft. deep and 10 in. 
in diameter). The efficiency of the pump was based on the least work 
theoretically required to compress the air and deliver it to the receiver. 
If the efficiency of the compressor be taken at 70%, the efficiency of the 
pump and compressor together would be 70% of the efficiency found for 
the pump alone. 

For a given submersion (h) and lift (//), the ratio of the two being kept 
within reasonable limits, (H) being not much greater than (h), the effi- 
ciency was greatest when the pressure in the receiver did not greatly 
exceed the head due to the submersion. The smaller the ratio H -^ h, 
the higher was the efficiency. 

The pump, as erected, showed the following efficiencies: 

FoTH^h=^ 0.5 1.0 1.5 2.0 

Efficiency =50% 40% 30% 25% 

The fact that there are absolutely no moving parts makes the pump 
especially fitted for handling dirty or gritty water, sewage, mine water, 
and acid or alkali solutions in chemical or metallurgical works. 

In Newark, N. J., pumps of this type are at work having a total capacity 
of 1,000,000 gallons daily, lifting water from three 8-in. artesian wells. 
The Newark Chemical Works use an air-lift pump to raise sulphuric acid 
of 1.72° gravity. The Colorado Central Consolidated Mining Co., in one 
of its mines at Georgetown, Colo., lifts water in one case 250 ft., using a 
series of Ufts. 

For a full account of the theory of the pump, and details of the tests 
above referred to, see Eng'g News, June 8, 1893. 

Numerous tests of air-lift pumps are described in Greene's "Pumping 
Machinery." Greene says that the air pipe should be introduced near 
the bottom of the discharge pipe and should be immersed so that the 
ratio hi/h is 3 to 1 at the start and 2.2 to 1 in operation, hi is the 
depth of immersion below the water level and h the height of the dis- 
charge at the top of the well measured above the water level. Different 
tests give the following efficiencies for various ratios hi/h. 
h/hi = 

3.1 to 2.2 0.6 1 1.4 2.4 3.9 1.5 1 0.66 0.5 0.43 

Efficiency, % : 

36 16 to 43 19 to 42 34 to 41 15 to 24 2 50 40 30 25 20 

The efficiency is the ratio of the work done in raising the water to 
the work of compressing the air. 

The amount of free air required varies according to different manu- 
facturers. One gives cu. ft. air per min. = LW -^ 19; another LW ^\b\ 
L = lift of water above the water level, in ft., W = cu. ft. of water per 
min. 

Air-Lifts for Deep Oil-Wells are described by E. M. Ivens, in Trans. 
A. S. M. E. 1909, p. 341. The following are some results obtained in wells 
in Evangeline, La.: 

Cu. ft. free air per minute, displacement of 

compressor 650 442 702 536 

Cu. ft. oil pumped per minute 4.35 4.87 13.7 5.54 

Air pressure at well, lbs. per sq. in 155 200 202 252 

Pumping head, from oil level while pumping, ft. 1155 1081 1076 917 

Submergence, from oil level to air entrance, ft. 358 412 419 583 

Submergence -^ total ft. of vertical pipe, %. . . 23.6 27.6 28 39 

Pumping efficiency, % 9.3 13.4 19.5 10.3 



810 PUMPS AND PUMPING ENGINES. 

Artesian Well Pumping by Compressed Air. — H. Tipper, Eng. News, 
Jan. 16, 1908, mentions cases where 1-in. air lines supplied air for 6-in. 
wells, with the inside air-pipe system; the length of the pipe was 300 ft. 
from the well top, and another 350 ft. to the compressor. The wells 
pumped 75 gals, per min., using 200 cu. ft. of air, the efficiency being 61/2%. 
Changing the pipes to 2 1/2 in. above the well, and 2 in. in the well, and 
putting an air receiver near the compressor, raised the delivery to 180 
gals, per min., with a little less air, and the efficiency to 23%. A large 
receiver capacity, a large pipe above ground, a submergence of 55%, 
well piping proportioned for a friction loss of not over 5%, with lifts not 
over 200 ft., gave the best results, 1 gal. of water being raised per cu. ft. 
of air. The utmost net efficiency of the air-lift is not over 25 to 30%. 

Eng. News, June 18, 1908, contains an account of tests of eleven wells 
at Atlantic City. The Atlantic City wells were 10 in. diam., water pipes, 
4 to 51/4 in., air pipes, 3/4 to II/4 in. The maximum hft of the several 
wells ranged from 26 to 40 ft., the submergence, 37 to 49 ft., ratio of sub- 
mergence to lift, 0.9 to 1.8, submergence % of length of pipe, 53 to 64. 
Capacity test, 3,544,900 gals, in 24 hrs., mean lift, 26.88 ft., air pressure, 
31 lbs., duty of whole plant, 19,900,000 ft. lbs. per 1000 lbs. of steam used 
by the compressors. Two-thirds capacity test, deli verv, 2,642,900 gals., 
mean lift, 25.43 ft., air pressure, 26 lbs., duty, 24,207,000. 

An article in The Engineer (Chicago), Aug. 15, 1904, gives the following 
formulae and rules for the design of air-lifts of maximum efficiency. The 
authority is not given. 

Ratio of area of air pipe to area of water pipe, 0.16. 

Submerged portion = 65% of total length of pipe. 

Economical range of submersion ratio, 55 to 80%. 

Velocity of air in air pipe, not over 4000 ft. per min. 

Volume of air to raise 1 cu. ft. of water, 3.9 to 4.5 cu. ft. 

C = cu. ft. of water raised per min., A = cu. ft. of air used, L =» lift 
above water level, D = submergence, in feet. 

A = LC ^ 16.824; C = 8.24 AD h- L\ 

Where L exceeds 180 ft. it will be more economical to use two or more 
air-lifts in series. 

THE HYDRAULIC RAM. 

Efficiency. —The hydraulic ram is used where a considerable flow of 
water with a moderate fall is available, to raise a small portion of that flow 
to a height exceeding that of the fall. The following are rules given bv 
Eytelwein as the results of his experiments (from Rankine)- 
• rS-^ 9 }^^}u^ ^^^l^. supply of water in cubic feet per second, of which a 
]f l^i^S }^^ height /i above the pond, and Q - ^ runs to waste at the 
?^?h^£o^f^°r[ ^^^ P^^^/ ^'.^^^ length of the supply-pipe, from the pond 
to the waste-clack; D, its diameter in feet; then 

I> = V(i.63Q); L = H+h-{-~X2feet; 

Efficiency, (qJ^^^^ =1.12-0.2 ^J~ , when ^does not exceed 20; 
or 

1 -f- (1 + 7i/10 H) nearly, when h/H does not exceed 12. 

D'Aubuisson gives ^^ ^ jt ^ =1.42-0.28 -a/—- 

^ Clark, using five sixths of the values given by D'Aubuisson's formula. 

Ratio of lift to fall. 4 6 8 10 12 14 16 18 20 22 24 26 
Efficiency per cent. 72 61 52 44 37 31 25 19 14 9 4 
The efficiency as calculated by the two formulae given above is neariv 
the same for high ratios of lift, but for low ratios there is considerable 
difference. For example: 

L^ Q = 100 i/ = 10, II +h= 20 40 100 200 

Efficiency, D'Aubuisson's formula, % 80 72 44 14 
g = effy. XQ^-^ (// +/.)= '^"40 18 4.4 0.7 

Efficiency by Rankine's formula, % 662/3 65.9 41.4 13.4 
D'Aubuisson's formula is that of the machine itself, on the basis that 



THE HYDRAtTLIC RAM. 



811 



the energy put into the machine is that of the whole column of water, 
Q, falling through the height h and that the energy delivered is that of q 
raised through the whole height above the ram, H -\- h; while Rankine's 
efficiency is that of the whole plant, assuming that the energy put in is 
only that of the water that runs to waste, and that the work done is 
lifting the quantity q not from the level of the ram but only from that of 
the supply pond. D'Aubuisson's formula is the one in harmony with 
the usual definition of efficiency. It also is applicable (as Rankine's is 
not) to the case of a ram which uses the quantity Q from one source of 
supply to pump water of different quality from a source at the level of 
the ram. 

An extensive mathematical investigation of the hydraulic ram, by 
L. F. Harza, is contained in Bulletin No. 205 of the University of Wiscon- 
sin, 1908, together with results of tests of a Rife "hydraulic engine," 
which appear to verify the theory. It was found both by theory and by 
experiment that the efficiency bears a relation to the velocity in the 
drive pipe. From plotted diagrams of the results the following figures 
(roughly approximate) are taken: Length of 2-in. drive pipe, 85.4 ft.; 
supply head, 8.2 ft. 

Max. vel. in drive pipe, ft. per sec. . . 1.5 2 3 4 5 6 

Efficiency of machine, %. 
Pumping head, ft 2.6 

12.3 

23.2 

43.5 

63.1 

The author of the paper concludes that the comparison of experiment 
and theory has demonstrated the practicability of the logical design of 
a hydrauUc ram for any given working conditions. 

An interesting historical account, with illustrations, of the develop- 
ment of the hydraulic ram, with a description of Pearsall's hydraulic 
engine, is given by J. Richards in Jour. Assn. Eng'g Societies, Jan., 1898. 
For a description of the Rife hydraulic engine see Eng. News, Dec. 31, 
1896. 

The Columbia Steel Co., Portland, Ore., furnished the author in July, 
1908, records of tests of four hydraulic rams, from which the following 
is condensed, the efficiency, by D'Aubuisson's formula, being calculated 
from the data given. L = length in ft. and D = diam. in ins. of the 
drive pipe, I and d, length and diameter of the discharge pipe. 





80 


20 


15 


7 





60 


60 


45 


33 


18 





60 


65 


53 


40 


20 





55 


60 


53 


42 


30 







60 


55 


50 


28 






Size of Ram. 


H 


H 


Q* 


g* 


L 


D 


I 


d 


Effy. 
% 


Ins. 
3 


Ft. 

4 

5 

12 
37.6 


Ft. 

28 

43 

36.4 
144.1 


35 
100 
200 
6.26 


3.5 

8 
50.5 
1.15 


Ft. 

28 

40 

60 
192.5 


Ins. 
3 

41/2 
41/2 
6 


Ft. 

1008 
325 
945 

1785 


Ins. 

IV2 

"21/2 

lot 


58.9 


41/9 


72.0 


6 '^ .; 


76.6 


6 


70.4 









* Q and q are in gallons per min., except the last line, which is In cu. 
ft. per sec. 

t Eleven rams discharge into one 10-in. jointed wood pipe. The loss 
of head in the drive pipe was 0.7 ft., and in the discharge pipe, 2.7 ft. On 
another test 1 cu. ft. per sec. was deUvered with less than 5 cu. ft. enter- 
ing the drive pipe. Taking 5 cu. ft. gives 76.6% efficiency. 

A description and record of test of the Foster "impact engine" is given 
in Eng'g News, Aug. 3, 1905. Two engines are connected into one 8-in. 
delivery pipe. Using the same notation as before, the data of the tests 
of thetwo engines are as follows: Q, gal. per min., 582, 578; q, 232, 228; 
H, 36.75, 37.25: H -\- h, 84, 84; strokes per min., 130, 130; Effy. (D'Aubu- 
isson), 91.23, 89.06%. 

Prof. R. C. Carpenter (Eng'g Mechanics, 1894) reports the results of 
four tests of a ram constructed by Rumsey & Co., Seneca Falls. The 
supply-pipe used was II/2 inches in diameter, about 50 feet long, with 3 
elbows. Each run was made with a different stroke for the waste-valve, 
the supply and .delivery head being constant;. the object of the experi- 



812 HYDRAULIC-PRESSUKE TRANSMISSION. 

ment was to find that stroke of clack-valve which would give the highest 
efficiency. 



Length of stroke percent 


100 


80 


60 


46 


Number of strokes per minute 


52 


56 


61 


66 


Supply head, feet of water 

DeHvery head, feet of water 


5.67 


5.77 


5.58 


5.65 


19.75 


19.75 


19.75 


19.75 


Total water pumped, pounds 


297 


296 


301 


297.5 


Total water suppHed, pounds 


1615 


1567 


1518 


1455.5 


Efficiency, per cent 


64.1 


64.7 


70.2 


71.4 



The highest efficiency reahzed was obtained when the clack-valve trav- 
eled 60% of its full stroke, the full travel being i5/i6 in. 

HYDEAULIC-PRESSURE TRANSMISSION. 

Water under high pressure (700 to 2000 lbs. per sq, in. and upwardsy 
affords a satisfactory method of transmitting power to a distance, espe- 
ciaUy for the movement of heavy loads at small velocities, as by cranes 
and elevators. The system consists usually of one or more pumps ca- 
pable of developing the required pressure; accumulators, which are vertical 
cylinders with heavily-weighted plungers passing through stuffing-boxes 
in the upper end, by which a quantity of water may be accumulated at the 
pressure to which the plunger is v/eiglited; the distributing-pipes; and the 
presses, cranes, or other machinery to be operated. 

The earUest important use of hydraulic pressure probably was in the 
Bramah hydraulic press, patented in 1796. Sir. W. G. Armstrong in 
1846 was one of the pioneers in the adaptation of the hydraulic system 
to cranes. The use of the accumulator by Armstrong led to the extended 
use of hydraulic machinery. Recent developments and appUcations of 
the system are largely due to Ralph Tweddell, of London, and Sir Joseph 
Whitworth. Sir Henry Bessemer, in his patent of May 13, 1856, No, 
1292, first suggested the use of hydraulic pressure for compressing steel 
ingots while in the fluid state. 

The Gross Amount of Energy of the water under pressure stored in 
the accumulator, measured in foot-pounds, is its volume in cubic feet X 
its pressure in pounds per square foot. The horse-power of a given 
quantity steadily flowing is H.P. = 144 pQ/o50 =0.2618 pQ, in which Q is 
the quantity flowing in cubic feet per second and p the pressure in pounds 
per square inch. 

The loss of energy due to velocity of flow in the pipe is calculated as 
follows (R. G. Blaine, Eng'g, May 22 and June 5, 1891): 

According to Darcy, every pound of water loses A4L/Z) times its kinetic 
energy, or energy due to its velocity, in passing along a straight pipe L 
feet in length and D feet diameter, where A is a variable coefficient. For 

clean cast-iron pipes it may be taken as A =0.005 (l +7^77)) » or for di- 
ameter in inches = d, 

d = 1/2 1 2 3 4 5 6 7 8 9 10 12 

A = .015 .01 .0075 .00667 .00625 .006 .00583 .00571 .00563 .00556 .0055 .00542 

, The loss of energy per minute is 60 X 62.36 Q X ~J^ ^ * and the 

,_ . ^ . .u • . Trr 0.6363AL(H.F )3 . u- u V 

norse-power wasted in the pipe is W = t^. , in which A 

varies with the diameter as above, p = pressure at entrance in pounds 
per square inch. Values of 0.6363 A for different diameters of pipe in 
inches are: 

d = 1/2 12 3 4 5 6 7 8 

.00954 .00636 .00477 .00424 .00398 .00382 .00371 .00363 .00358 

9 10 12 

.00353 .00350 .00345 

Efficiency of Hydraulic Apparatus. — The useful effect of a direct 
hydraulic plunger or ram is usually taken at 93%. The following is 
given as the efficiency of a ram with chain-and-pulley multiplying gear 
properly proportioned and well lubricated: 

Gear 2 to 1 4 to 1 6 to 1 8 to 1 10 to 1 12 to 1 14 to 1 16 to 1 
Eff'y 0.80 0.76 0.72 0.67 0.63 0.59 0.54 0.50 



HYDRAULIC-PRESSURE TRANSMISSION. 813 

With large sheaves, small steel pins, and wire rope for multiplying 
gear the efficiency has been found as high as 66% for a multiplicafioh of 
20 to 1. 

Henry Adams gives the following formula for effective pressure in 
cranes and hoists: P = accumulator pressure in pounds per square inch; 
m = ratio of multiplying power; E = effective pressure in pounds per 
square inch, including all allowances for friction; 
E= P (0.84- 0.02 m). 

J. E. Tuit (Eng'g, June 15, 1888) describes some experiments on the 
friction of hydraulic jacks from 3V4 to IS^/s-inch diameter, fitted with 
cupped leather packings. The friction loss varied from 5.6% to 18.8% 
according to the condition of the leather, the distribution of the load on 
the ram, etc. The friction increased considerably with eccentric loads. 
With hemp packing a plunger, 14-inch diameter, showed a friction loss 
of from 11.4% to 3.4%, the load being central, and from 15.0% to 7.6% 
with eccentric load, the percentage of loss decreasing in both cases with 
increase of load. 

Thickness of Hydraulic Cylinders. — Sir W. G. Armstrong gives the 
following, for cast-iron cylinders, for a pressure of 1000 lbs. per sq. in.: 
Diam. of cylinder, inches — 

2 4 6 8 10 12 16 20 24 

'T*Vii r>irrjgeQ inches 

0.832 1.146 1.552 1.875 2.222 2.578 3.19 3.69 4.11 

For any other pressure multiply by the ratio of that pressure to 1000. 
These figures correspond nearly to the formula t = 0.175 d + 0.48, in 
which t = thickness and d = diameter in inches, up to 16 inches diam- 
eter, but for 20Jnches diameter the addition 0.48 is reduced to 0.19 and 
at 24 inches it disappears. For formulae for thick cylinders see page 339. 

Cast iron should not be used for pressures exceeding 2000 lbs. per 
square inch. For higher pressures steel castings or forged steel should 
be used. For working pressures of 750 lbs. per square inch the test 
pressure should be 2500 lbs. per square inch, and for 1500 lbs. the test 
pressure should not be less than 3500 lbs. 

Speed of Hoisting by Hydraulic Pressure. — The maximum allow- 
able speed for warehouse cranes is 6 feet per second; for platform cranes 
4 feet per second; for passenger and wagon hoists, heavy loads, 2 feet per 
second. The maximum speed under any circumstances should never 
exceed 10 feet per second. 

The Speed of Water Through Valves should never be greater than 
100 feet per second. 

Speed of Water Through Pipes. — Experiments on water at 1600 
lbs. pressure per square inch flowing into a flanging-machine ram, 20- 
inch diameter, through a 1/2-inch pipe contracted at one point to V4-inch, 
gave a velocity of 114 feet per second in the pipe, and 456 feet at the 
reduced section. Through a 1/2-inch pipe reduced to s/g-inch at one 
point the velocity was 213 feet per second in the pipe and 381 feet at the 
reduced section. In a 1/2-inch pipe without contraction the velocity 
was 355 feet per second. 

For many of the above notes the author is indebted to Mr. John Piatt, 
consulting engineer, of New York. 

High-pressure Hydraulic Presses in Iron-works are described by 
R. M. Daelen, of Germany, in Trans. A. I M. E., 1892. The following 
distinct arrangements used in different systems of tdgh-pressure hydrau- 
lic work are discussed and illustrated: 

1. Steam-pump, with fly-wheel and accumulator. 

2. Steam-pump, without fly-wheel and with accumulator. 

3. Steam-pump, without fly-wheel and without accumulator. 

In these three systems the valve-motion of the working press is oper- 
ated in the high-pressure column. This is avoided in the following: 

4. Single-acting steam-intensifier without accumulator. 

5. Steam-pump with fly-wheel, without accumulator and with pipe- 
circuit. 

6. Steam-pump with fly-wheel, without accumulator and without 
pipe-circuit. 

The disadvantages of accumulators are thus stated: The weighted 



814 HYDRAULIC-PRESSURE TRANSMISSION. 

plungers which formerly served in most cases as accumulators, cause 
violent shocks in the pipe-line when changes take place in the move- 
ment of the water, so that in many places, in order to avoid bursting 
from this cause, the pipes are made exclusively of forged and bored steel. 
The seats and cones of the metallic valves are cut by the water (at high 
speed), and in such cases only the most careful maintenance can prevent 
great losses of power. 

Hydraulic Power in London. — The general principle involved is 
pumping water into mains laid in the streets, from which service-pipes 
are carried into the houses to work lifts or three-cylinder motors when 
rotary power is required. In some cases a small Pelton wheel has been 
tried, working under a pressure of over 700 lbs. on the square inch. 
Over 55 miles of hydrauUc mains are at present laid (1892). 

The reservoir of power consists of capacious accumulators, loaded to 
800 lbs. per sq. in. 

The engine-house contains six sets of triple-expansion pumping en- 
gines. Each pump will deliver 300 gallons of water per minute. 

The water deUvered from the main pumps passes into the accumu- 
lators. The rams are 20 inches in diameter, and have a stroke of 23 
feet. They are each loaded with 110 tons of slag, contained in a wrought- 
iron cylindrical box suspended from a cross-head on the top of the ram. 
One of the accumulators is loaded a little more heavily than the other, 
so that they rise and fall successively; the more heavily loaded actuates a 
stop-valve on the main steam-pipe. 

The mains in the public streets are so constructed and laid as to be per- 
fectly trustworthy and free from leakage. Every pipe and valve used 
throughout the svstem is tested to 2500 lbs. per sq. in. before being placed 
on the ground and again tested to a reduced pressure in the trenches to 
insure the perfect tightness of the joints. The jointing material used is 
gutta-percha. 

The average rate obtained by the company is about 3 sliillings per 
thousand gallons. The principal use of the power is for intermittent 
work in cases where direct pressure can be employed, as, for instance, 
passenger elevators, cranes, presses, warehouse hoists, etc. 

An important use of the hydraulic power is its application to the 
extinguishing of fire by means of Greathead's injector hydrant. By the 
use of these hydrants a continuous fire-engine is available. 

Hydraulic Riveting-machines. — Hydraulic riveting was introduced 
in England by Mr. R. H. Tweddell. Fixed riveters were first used about 
1868. Portable riveting-macliines were introduced in 1872. 

The riveting of the large steel plates in the Forth Bridge was done by 
small portable machines working with a pressure of 1000 lbs. per square 
inch. In exceptional cases 3 tons per inch were used. {Proc. Inst. M. E., 
May, 1889.) 

An application of hydraulic pressure invented by Andrew Higglnson, 
of Liverpool, dispenses with the necessity of accumulators. It consists 
of a three-throw pump driven by shafting or worked by steam and 
depends partially upon the work accumulated in a heavy fly-wheel. 
The water in its passage from the pumps and back to them is in con- 
stant circulation at a very feeble pressure, requiring a minimum of 
power to preserve the tube of water ready for action at the desired 
moment, when by the use of a tap the current is stopped from going 
back to the pumps, and is thrown upon the piston of the tool to be set 
in motion. The water is now confined, and the driving-belt or steam- 
engine, supplemented by the momentum of the heavy fly-wheel, is 
employed in closing up the rivet, or bending or forging the object sub- 
jected to its operation. 

Hydraulic Forging-press. 

For a very complete illustrated account of the development of the 
hydraulic forging-press, see a paper by R. H. Tweddell in Proc. Inst. 
C. E., vol. cxvii. 1893-4. 

In the Allen forging-press the force-pump and the larga or main cylinder 
of the press are in direct and constant communication. There are no 
intermediate valves of any kind, nor has the pump any clack-valves, 
but it simply forces its cylinder full of water direct into the cvlinder of 
the press, and receives the same water, as it were, back again on the return 



HYDRAULIC-PRESSURE TRANSMISSION. 815 

stroke. Thus, when both cyUnders and the pipe connecting them are 
full, the large ram of the press rises and falls simultaneously with each 
stroke of the pump, keeping up a continuous oscillating motion, the ram. 
of course, traveling the shorter distance, owing to the larger capacity oi 
the press cylinder. {Journal Iron and Steel Institute, 1891. See also 
illustrated article in "Modern Mechanism," page 668.) 

A 2000-ton forging-press erected at the Couillet forges in Belgium is 
described in Eng. and M. Jour., Nov. 25, 1893. The press is composed 
essentially of two parts — the press itself and the compressor. The com- 
pressor is" formed of a vertical steam-cylinder and a hydraulic cylinder. 
The piston-rod of the former forms the piston of the latter. The hy- 
draulic piston discharges the water into the press proper. The distribu- 
tion is made by a cylindrical balanced valve; as soon as the pressure is 
released the steam-piston falls automatically under the action of gravity. 
During its descent the steam passes to the other face of the piston to 
reheat the cylinder, and finally escapes from the upper end. 

When steam enters under the piston of the compressor-cylinder the 
piston rises, and its rod forces the water into the press proper. The 
pressure thus exerted on the piston of the latter is transmitted through a 
cross-head to the forging which is upon the anvil. To raise the cross- 
head two small single-acting steam-cylinders are used, their piston-rods 
being connected to the cross-head: steam acts only on the pistons of these 
cylinders from below. The admission of steam to the cylinders, which 
stand on top of the press frame, is regulated by the same lever which 
directs the m.otions of the compressor. The movement given to the dies 
is sufficient for all the ordinary purposes of forging. 

A speed of 30 blows per minute has been attained. A double press on 
the same system, having two compressors and giving a maximum pressure 
of 6000 tons, has been erected in the Krupp works, at Essen. 

Hydraulic Engine driving an Air-compressor and a Forging- 
hammer. ( Iron Age, May 12, 1892.) — The great hammer in Terni, 
near Rome, is one of the largest in existence. Its faUing weight amounts 
to 100 tons, and the foundation belonging to it consists of a block of cast 
iron of 1000 tons. The stroke is 16 feet 43/4 inches; the diameter of the 
cylinder 6 feet 3V2 inches; diameter of piston-rod 133/4 inches; total 
height of the hammer, 62 feet 4 inches. The power to work the hammer, 
as well as the two cranes of 100 and 150 tons respectively, and other 
auxiliary appUances belonging to it, is furnished by four air-compressors 
coupled together and driven directly by water-pressure engines, by 
means of which the air is compressed to 73.5 pounds per square inch. 
The cylinders of the water-pressure engines, which are provided with a 
bronze lining, have a 133/4-inch bore. The stroke is 473/4 inches, with a 
pressure of water on the piston amounting to 264.6 pounds per square 
inch. The compressors are bored out to 311/2 inches diameter, and have 
473/4-inch stroke. Each of the four cylinders requires a power equal to 
280 horse-power. The compressed air is delivered into huge reservoirs, 
where a uniform pressure is kept up by means of a suitable water-column. 

The Hydraulic Forging Plant at Bethlehem, Pa., is described in a 
paper by R. W. Davenport, read before the Society of Naval Engineers 
and Marine Architects, 1893. It includes two hydraulic forging-presses 
complete, with engines and pumps, one of 1500 and one of 4500 tons 
capacity, together with two Whitworth hydraulic traveling forging- 
cranes and other necessary appliances for each press; and a complete 
fluid-compression plant, including a press of 7000 tons capacity and a 
125-ton, hydraulic traveling crane for. serving it (the. upper and lower 
heads of this press weighing respectively about 135 and 120 tons). 

A later forging-press designed by John Fritz, for the Bethlehem 
Works, of 14,000 'tons capacity, is run by engines and pumps of 15,000 
horse-power. The plant is served by four open-hearth steel furnaces of 
a united capacity of 120 tons of steel per heat. 

The Davy High-speed Steam-hydraulic Forging Press is described 
in the Iron Age, April 15, 1909. It is built in sizes ranging from 150 to 
12,000 tons capacity. In the four-column type, in wliich all but the 
smaller sizes are built, there is a central press operated by hydraulic 
pressure from a steam intensifier, and two steam balance cylinders 
carried on top of the entablature. A single lever controls the press. 
The operator admits steam to the balance cylinders, lifting the cross- 



816 FUEL. 

liead and the main plunger, and forcing the water from the press cylinder 
into the water cyUnder of the intensifier. Exhausting the steam from 
the balance cylinders, allows the plunger to descend and rest on the 
forging. To and fro motions of the lever, slow or fast as the operator 
desires, up to 120 a minute, then are made to reduce the forging. The 
smaller, or single frame, type has only one balance cylinder, immediately 
above the press cylinder. The Dav5^ press is made in the United States 
by the United Engineering & Foundry Co., Pittsburgh. 

Some References on Hydraulic Transmission. — Reuleaux's " Con- 
structor;" "Hydraulic Motors, Turbines, and Pressure-engines," G. 
Bodmer, London, 1889: Robinson's "Hydraulic Power and Hydraulic 
Machinery," London, 1888: Colyer's "HydrauUc Steam, and Hand-power 
Lifting and Pressing Machinerv " London, 1881, See also Engineering 
(London), Aug. 1, 1884. p. 99; March 13, 1885, p. 262: May 22 and June 
5, 1891, pp. 612, 665; Feb. 19, 1892, p. 25; Feb. 10, 1893, p. 170. 



FUEL, 

Theory of Combustion of Solid FueL (From Rankine, somewhat 
altered.) — The ingredients of every kind of fuel commonly used may be 
thus classed: (1) Fixed or free carbon, which is left in the form of char- 
coal or coke after the volatile ingredients of the fuel have been distilled 
away. These ingredients burn either wholly in the solid state (C to CO2), 
or part in the solid state and part in the gaseous state (CO + O = CO2), 
the latter part being first dissolved by previously formed carbon dioxide 
by the reaction CO2 + C = 2 CO. Carbon monoxide, CO, is produced 
when the supply of air to the fire is insufficient. 

(2) Hydrocarbons, such as olefiant gas, pitch, tar, naphtha, etc., ail of 
which must pass into the gaseous state before being burned. 

If mixed on their first issuing from amongst the burning carbon with a 
large quantity of hot air, these inflammable gases are completely burned 
with a transparent blue flame, producing carbon dioxide and steam. 
When mixed with cold air they are apt to be chilled and pass off unburned. 
When raised to a red heat, or thereabouts, before being mixed with a 
sufficient quantity of air for perfect combustion, they disengage carbon 
in fine powder, and pass to the condition partly of marsh gas, CH4 and 
partly of free hydrogen; and the higher the temperature, the greater is 
the proportion of carbon thus disengaged. 

If the disengaged carbon is cooled below the temperature of ignition 
before coming in contact with oxygen, it constitutes, while floating in the 
gas, smoke, and when deposited on solid bodies, soot. 

But if the disengaged carbon is maintained at the temperature of igni- 
tion and supplied with oxygen sufficient for its combustion, it burns 
wlile floating in the inflammable gas, and forms red, yellow, or white 
flame. The flame from fuel is the larger the more slov/ly its combustion 
is effected. The flame itself is apt to be cliilled by radiation, as into the 
heating surface of a steam-boiler, so that the combustion is not completed, 
and part of the gas and smoke pass off unburned. 

(3) Oxygen or hydrogen either actually forniing water, or existing in 
combination with the other constituents in the proportions which form 
water. Such quantities of oxygen and hydrogen are to be left out of 
account in determining the heat generated by the combustion. If the 
quantity of water actually or virtually present in each pound of fuel is so 
great as to make its latent heat of evaporation worth considering, that 
heat is deducted from the total available heat of combustion of the fuel. 

(4) Nitrogen, either free or in combination with other constituents. 
This substance is simply inert. 

(5) Sulpliide of iron, which exists in coal and is detrimental, as 
tending to cause spontaneous combustion. 

(6) Other inert mineral compoimds of various kinds form the ash 
left after complete combustion of the fuel, and also the clinker or glassy 
material ])roduced by fusion of the ash. which tends to choke the grate. 

The imperfect combustion of carbon, making carbon mo?ioxide, 
produces less than one-third of the heat which is yielded by tiie com- 
plete combustion, making carbon dioxide. 



FUEL. 



817 



The total heat of combustion of any compound of hydrogen and carbon 
is nearly the sum of the quantities of heat wiiich the constituents would 
produce separately by their combustion. (Marsh-gas is an exception.) 

In computing the total heat of combustion of compounds containing 
oxygen as well as hydrogen and carbon, the following principle is to be 
observed: When hydrogen and oxygen exist in a compound in the proper 
proportion to form water (that is, bj?^ weight one part of hydrogen to 
eight of oxygen), these constituents have no effect on the total heat of 
combustion. If hydrogen exists in a greater proportion, only the surplus 
of hydrogen above that which is required by the oxygen is to be taken 
into account. 

The following is a general formula (Dulong's) for the total heat of com- 
bustion of any compound of carbon, hydrogen, and oxygen: 

Let C, H, and O be the fractions of one pound of the compound, which 
consists respectively of carbon, hydrogen, and oxygen, the remainder 
being nitrogen, ash, and other impurities. Let h be the total heat of 
combustion of one pound of the compound in British thermal units. 

Then h == 14,600 C + 62,000 {H - Vs 0). 

Oxygen and Air Be quired for the Combustion of Carbon, Hydro- 
gen, etc. 











Gase- 


Heat of 




Lbs. 


Lbs.N, 
= 3.32 


Air per 


ous 


Combus- 


Chemical Reaction. 


per lb. 


lb.= 


Prod- 


tion, 




Fuel. 


4.32 0. 


ucts 


B.T.U. 










per lb. 


per lb. 


CtoC02 C+20=C02 


2% 


8.85 


n.52 


12.52 


14,600 


C to CO C + O = CO 


11/3 


4.43 


5.76 


6.76 


4.450 


CO to CO2 CO + = CO2 


4/7 


1.90 


2.47 


3.47 


4,350 


HtoHsO 2H + = H20 


8 


26.56 


34.56 


35.56 


62,000 


CH4toC02) CH4 + 4O 
andllsO ] =C02 + 2H20 












4 


13.28 


17.28 


18.28 


23,600 


StoS02 S + 20 = S02 


\ 


3.32 


4.32 


5.32 


4,050 


CO to CO2, per lb. of C or pe 


r 2 1/3 It 


3. of CO, 14,600 


- 4^50 


= 10,150. 



For heat of combustion of various fuels see Heat, page 560. 

Analyses of Gases of Combustion. — The following are selected 
from a large number of analyses of gases from locomotive boilers, to 
show the range of composition under different circumstances (P. H. 
.Dudley, Trans. A. I. M. E., iv, 250): 



Test. 


CO2 


CO 





N 


1 
2 


13.8 
11.5 


2.5 


2.5 
6 


81.6 
82.5 


3 


8.5 




8 


83 


4 
5 
6 

7 
8 
9 


2.3 
5.7 
6.4 
12 
3.4 
6 


"\'.2 
1 


17.2 
14.7 
8.4 
4.4 
16.8 
13.5 


80.5 
79.6 

82 
82.6 
76.8 
81.5 



No smoke visible. 

Old fire, escaping gas white, engine working 

hard. 
Fresh fire, much black gas, engine working 

hard. 
Old fire,damper closed, engine standing still. 
" " smoke white, engine working hard. 
New fire, engine not working hard. 
Smoke black, engine not working hard. 
*' dark, blower on, engine standingstill. 
** white, engine working hard. 



In analyses on the Cleveland and Pittsburgh road, in every instance 
when the smoke was the blackest, there was found the greatest percent- 
age of unconsumed oxygen in the product, showing that something 
besides the mere presence of oxygen is required to effect the combustion 
of the volatile carbon of fuels. (What is needed is thorough mixture of 
the oxygen with the volatile gases in a hot combustion chamber.) 

Temperature of the Fire. (Rankine, S. E., p. 283.) — By temper- 
ature of the fire is meant the temperature of the products of combustion 
at the instant that the combustion is complete. Tlie elevation of that 
temperature above the temperature at which the air and the fuel are 
supplied to the furnace may be computed by dividing the total heat of 



818 



FUEL. 



combustion of one lb. of fuel by the weight and by the mean specific 
heat ot the whole products of combustion, and of the air employed for 
their dilution under constant pressure. 

Temperature of the Fire, the Fuel Containing Hydrogen and 
Water. — The foUowing formula is developed in the author's "Steam- 
boiler Economy" on the assumptions that all the hydrogen and the 
water exist in the combustion chamber as superheated steam at the tem- 
perature of the fire, and that the specific heat of the gases is a constant, 
= 0.237. The last assumption is probably largely in error, since it is 
now known that the specific heat of gases increases with the tempera- 
ture. (See page 564. ) The formula will give approximate results, how- 
ever, and is sufficiently accurate when relative figures only are desired. 

Let C, H, O, and W represent respectively the percentages of carbon, 

hydrogen, oxygen, and water in a fuel, and / the pounds of dry gas per 

pound of fuel, = CO2+ JSI + excess air, then the theoretical elevation of 

the temperature of the fire above the temperature of the atmosphere, 

616 C+ 2200 g- 327 0~ 44 W 

/+0.02 PF + 0.18 H 

Example. — Required the maximum temperature obtainable by burn- 
ing moist wood of the composition C, 38; //, 5; O, 32; ash, 1 ; moisture 24; 
the dry gas being 15 lbs. per pound of wood, and the temperature of the 
atmosphere 62° 



r = 



616 X 38 + 2220 X 5 - 327 X 32 - 44 X 24 



= 1403, add 62** = 1465°. 



15+0.02 X 24 +0.18X5 
Rise of Temperature in Combustion of Gases. {Eng'g, March 
12 and April 2, 1886.) — It is found that the temperatures obtained by 
experiment fall short of those obtained by calculation. Three theories 
have been given to account for this: 1. The cooling effect of the sides of 
the containing vessel; 2. The retardation of the evolution of heat caused 
by dissociation; 3. The increase of the specific heat of the gases at very 
high temperatures. The calculated temperatures are obtainable only on 
the condition that the gases shall combine instantaneously and simulta- 
neously throughout their whole mass. This condition is practically im- 
possible in experiments. The gases formed at the beginning of an explo- 
sion dilute the remaining combustible gases and tend to retard or check 
the combustion of the remainder. 

CLASSIFICATION OF SOLID FUELS. 

Gnmer classifies sohd fuels as follows {Eng'g and M'g Jour., July, 1874). 



Name of Fuel. 



Pure cellulose 

Wood (cellulose and encasing matter) . . 

Peat and fossil fuel 

Lignite, or brown coal 

Bituminous coals 

Anthracite 



Ratio 7-, 

O+N* 



8- 
7 

^ 1 
^0.75 



Proportion of Coke of 
Charcoal yielded by 
the Dry Pure Fuel. 



0.28 @ 0.30 
.30 @ .35 

.35® 
.40 @ 
.50® 
.90® 



.40 
.50 
.90 
92 



* The nitrogen rarely exceeds 1 per cent of the weight of the fuel. 





Progressive Change from Wood to Graphite. 

(J. S. Newberry in Johnson's Cyclopedia.) 








i 
1 


I 


i 


1 


1 

i2 3 rt 


J 


2 . 


I 


is 

0^ 


Carbon 


49.1 
6.3 
44.6 


18.65 

3.25 

24.40 


30.45 

3.05 

20.20 


12.35 

1.85 

18.13 


18.10 
1.20 
2.07 


3.57 
0.93 
1.32 


14.53 
0.27 
0.65 


1.42 
0.14 
0.65 


13.11 


Hydrogen 


0.13 


Oxygen 


0.00 










100.0 


46.30 


53.70 


32.33 


21.37 


5.82 


15.45 


2.21 


13 J4 



CLASSIFICATION OF SOLID FUELS. 



819 



Classification of Coals. 

It is convenient to classify the several varieties of coal according to 
the relative percentages of carbon and volatile matter contained in their 
combustible portion as determined by proximate analysis. The follow- 
ing is the classification given in the author's "Steam-boiler Economy": 









Heating 


Relative 




Fixed 


Volatile 


Value 


Value of 




Carbon. 


Matter. 


per lb. of Combus- 
Combustible tible. Semi- 
B.T.U. bit. = 100 


Anthracite 


97 to 90 
90 to 85 


3 to 10 
10 to 15 


14800 to 15400| 93 


Semi-anthracite 


15400 to 15500, 97 


Semi-bituminous 


85 to 70 


15 to 30 


15400 to 16000 100 


Bituminous, Eastern. . 


70 to 55 


30 to 45 


14800 to 15600 96 


Bituminous, Western . 


65 to 50 


35 to 50 


12500 to 14800! 90 


Lignite 


under 50 


over 50 


11000 to 135001 77 



The anthracites, with some unimportant exceptions, are confined to 
three small fields in eastern Pennsylvania. The semi-anthracites are 
found in a few small areas in the western part of the anthracite field. 
The semi-bituminous coals are found on the eastern border of the great 
Appalachian coal field, extending from north central Pennsylvania across 
the southern boundary of Virginia into Tennessee, a distance of over 300 
miles. They include the coals of Clearfield, Cambria, and Somerset 
counties, Pennsylvania, and the Cumberland, Md., the Pocahontas, Va., 
and the New River, W. Va., coals. 

It is a pecuharity of the semi-bituminous coals that their combustible 
portion is of remarkably uniform composition, the volatile matter usually 
ranging between 18 and 22% of the combustible, and approaching in its 
analysis marsh gas, CH4, with very Uttle oxygen. They are usually low 
also in moisture, ash, and sulphur, and rank among the best steaming 
coals in the world. 

The eastern bituminous coals occupy the remainder of the Appala- 
chian coal field, from Pennsylvania and eastern Ohio to Alabama. They 
are liigher in volatile matter, ranging from 30 to over 40%, the higher 
figures in the western portion of the field. The volatile matter is of 
lower heating value, being higher in oxygen. The western bituminous 
coals are found in most of the states west of Ohio. They are higher in 
volatile matter and in oxygen and moisture than the bituminous coals 
of the Appalacliian field, and usually give off a denser smoke when 
burned in ordinary furnaces. 

A later classification by the author (Trans. A. S. M. E., 1914; 
" Steam-boiler Economy," 2d edition, 1915) is given in the table below. 
It divides the bituminous coals into three grades, high, medium and 
low, the chief distinction between them being the percentage of 
moisture found in the coal after it is air-dried. The coals highest 
in inherent moisture are also highest in oxygen. 

Classes: I. Anthracite. II. Semi-anthracite. III. Semi-bitumi- 
nous. IV. Cannel. V. Bituminous, high grade. VI. Bituminous, me- 
dium grade. VII. Bituminous, low grade. VIII. Sub-bituminous and 
lignite. 



Class. 



I 

II 

III 

IV* 

V 

VI 

VII 

VIII 



Volatile 
Matter, % 
of Com- 
bustible. 



less than 10 
10 to 15 
15 to 30 
45 to 60 
30 to 45 
32 to 50 
32 to 50 
27 to 60 



Oxygen 
in Com- 
bustible 
Per Cent. 



1 to 4 
I to 5 
I to 6 
5 to 8 

5 to 14 

6 to 14 

7 to 14 
10 to 33 



Moisture 

in Air-dry, 

Asli-free 

Coal, % 



less than 1.8 

less than 1.8 

less than 1.8 

less than 1.8 

1 to 4 

2.5 to 6.5 

5 to 12 

7 to 26 



B.T.U. 

per lb. 
Combustible. 



14,800 to 
15,400 to 
15,400 to 
15,700 to 
14,800 to 
13,800 to 
12,400 to 
9,600 to' 



15,400 
15,500 
16,050 
16,200 
15,600 
15,100 
14,600 
13,250 



B.T.U. per 

lb. Air-dry, 

Ash-free 

Coal 



14,600 to 
15,200 to 
15,300 to 
15,500 to 
14,350 to 
11,300 to 
11,300 to 
7,400 to 



15,400 
15,500 
16,000 
16,050 
14,400 
14,400 
13,400 
11,650 



* Eastern cannel. The Utah cannel is much lower in heating value. 



820 FUEL. 

The U. S. Geological Survey classifies coals into six groups, as follows: 
(1) anthracite; (2) semi-anthracite; (3) semi-bituminous; (4) bitu- 
minous; (5) sub-bituminous, or black lignite; and (6) hgnite. 

Classes 5 and 6 are described as follows: 

Sub-bituminous coal is commonly known as "lignite," "lignitic coal," 
"black lignite," "brown coal," etc. It is generally black and shining, 
closely resembling bituminous coal, but it weathers more rapidly on 
exposure and lacks the prismatic structure of bituminous coal. Its 
calorific value is generally less than that of bituminous coal. The local- 
ities in wliich this sub-bituminous coal is found include Montana, Idaho, 
Washington, Oregon, California, Wyoming, Utah, Colorado, New Mexico, 
and Texas. 

Lignite is commonly known as "lignite," "brown lignite," or "brown 
coal." It usually has a woody structure and is distinctly brown in color, 
even on a fresh fracture. It carries a higher percentage of moisture than 
any other class of coals, its mine samples showing from 30 to 40% of 
moisture. The localities in which lignite is found are chiefly North 
Dakota, South Dakota, Texas, Arkansas, Louisiana, Mississippi, and 
Alabama. 

The following: analyses of representative coals of the six classes are 
given by Prof. N. W. Lord: 

Class 1 — Anthracite Culm. Penna. 

Class 2 — Semi-anthracite. Arkansas. 

Class 3 — Semi-bituminous. W. Va. 

Class 4(a) — Bituminous coking. Councils ville, Pa. 

Class Mb) — Bituminous non-coking. Hocking Valley, Ohio. 

Class 5 — Sub-bituminous. Wyoming, black lignite. 

Class 6 — Lignite. Texas. 

Composition of Illustratwe Coals — Car-Load Samples. 
Proximate Analysis of "Air-dried" Sample. 

Class 1 2 3 4a 4& 5 6 

Moisture 2.08 1.28 0.65 0.97 7.55 8.68 9.88 

Vol. comb 7.27 12.82 18.80 29.09 34.03 41.31 36.17 

Fixed carbon 74.32 78.69 75.92 60.85 52.57 46.49 43.65 

Ash 16.33 12.21 4.63 9.09 5.85 3.52 10.30 

Loss on air-drying . 3.40 1.10 1.10 4.20 Undet. 11.30 23.50 

Ultimate Analysis of Coal Dried at 105° C. 

Hydrogen 2.63 3.63 4.54 4.57 5.06 5.31 4.47 

Carbon 76.86 78.32 86.47 77.10 75.82 73.31 64.84 

Oxygen 2.27 2.25 2.68 6.67 10.47 15.72 16.52 

Nitrogen 0.82 1.41 1.08 1.58 1.50 1.21 1.30 

Sulphur 0.78 2.03 0.57 0.90 0.82 0.60 1.44 

Ash 16.64 12.36 4.66 9.18 6.33 3.85 11.43 

Results Calculated to an Ash and Moisture-Free Basis. 

Volatile comb 8.91 14.82 19.85 32.34 39.30 47.05 45.31 

Fixed carbon 91.09 85.18 80.15 67.66 60.70 52.95 54.69 

Ultimate Analysis. 

Hydrogen 3.16 4.14 4.76 5.03 5.41 5.50 5.05 

Carbon 92.20 89.36 90.70 84.89 80.93 76.35 73.21 

Oxygen 2.72 2.57 2.81 7.34 11.18 16.28 18.65 

Nitrogen 0.98 1.61 1.13 1.74 1.61 1.25 1.47 

Sulphur 0.94 2.32 0.60 1.00 0.87 0.62 1.62 

Calorific Value in B.T.U. per lb., by Dulong's formula. 
Air-dried coal. 12, 472 13,406 15,190 13,951 12,510 11,620 10,288 
Combustible .. 15,286 15,496 16,037 15,511 14,446 13,235 12,889' 

Caking and Non-caking Coals. — Bituminous coals are sometimes 
classified as caking and non-caking coals, according to their behavior 
when subjected to the process of coking. The former undergo an incipi- 
ent fusion or softening when heated, so that the fragments coalesce and 
yield a compact coke, while the latter (also called free-burning) preserve 
their form, producing a coke wliich is only serviceable when made from 



CLASSIFICATION OF SOLID FUELS. 



821 



large pieces of coal, the smaller pieces being incoherent. The reason of 
this difference is not clearly understood, as non-caking coals are often of 
similar ultimate chemical composition to caking coals. Some coals 
which cannot be made into coke in a bee-hive oven are easily coked in 
gas-heated ovens. 

Cannel Coals are coals that are higher in hydrogen than ordinary 
coals. They are valuable as enrichers in gas-making. The following are 
some ultimate analvses: 





C. 


H. 


0+N. 


S. 


Ash. 


Combustible. 




C. 


H. 


O+N. 


Boghead, Scotland . . 

Albertite, Nova Scotia . . 


63.10 
82.67 
79.34 


8.91 
9.14 
10.41 


7.25 
8.19 
4.93 


0.96 


19.78 


79.61 
82.67 
83.80 


11.24 
9.14 
10.99 


9.15 
8 19 


Tasmanite, Tasmania. . . 


5.32 




5.21 



Rhode Island Graphitic Anthracite. — A peculiar variety of coal is 
found in the central part of Rhode Island and in Eastern Massachusetts. 
It resembles both graphite and anthracite coal, and has about the follow- 
ing composition (A. E. Hunt, Trans. A. I. M. E., xvii. 678: Graphitic 
carbon, 78%; volatile matter, 2.60%; silica, 15.06%; phosphorus, .045%. 
It burns with extreme difficulty. 

ANALYSIS AND HEATING VALUE OF COALS. 

Coal is composed of four different things, which may be separated by 
proximate analysis, viz.: fixed carbon, volatile hydrocarbon, ash and 
moisture. In making a proximate analysis of a weighed quantity, such 
as a gram of coal, the moisture is first driven off by heating it to about 
250° F. then the volatile matter is driven off by heating it in a closed 
crucible to a red heat, then the carbon is burned out of the rem.aining 
coke at a white heat, with sufficient air suppUed, until nothing is left 
but the ash. 

The fixed carbon has a constant heating value of about 14,600 B.T.U. 
per lb. The value of the volatile hydrocarbon depends on its composi- 
tion, and that depends chiefly on the district in which the coal is mined. 
It may be as high as 21,000 B.T.U. per lb., or about the heating value of 
marsh gas, in the best semi-bituminous coals, which contain very small 
percentages of oxygen, or as low as 12,000 B.T.U. per lb., as in those 
from some of the western states, which are high in oxygen. The ash has 
no heating value, and the moisture has in effect less than none, for its 
evaporation and the superheating of the steam made from it to the tem- 
perature of the chimney gases, absorb some of the heat generated by the 
combustion of the fixed carbon and volatile matter. 

The analysis of a coal may be reported in three different forms, as per- 
centages of the moist coal, of the dry coal or of the combustible, as in the 
following table. By "combustible" is always meant the sum of the 
fixed carbon and volatile matter, the moisture and ash being excluded, 
By some- writers it is called "coal dry and free from ash" and by others 
"pure coal." 





Moist Coal. 


Dry Coal. 


Combus- 
tible. 




10 
30 
50 
10 






Volatile matter 


33.33 
55.56 
11.11 


37.50 


Fixed carbon 


62.50 


Ash 










100 


100.00 


100.00 



The sulphur, commonly reported with a proximate analysis, is deter- 
mined separately. In the proximate analysis part of it escapes with the 
volatile matter and the rest of it is found in the ash as sulphide of iron. 
The sulphur should be given separately in the report of the analysis. 

The relation of the volatile matter and of the fixed carbon in the com- 
bustible portion of the coal enables us to judge the class to which the 
coal belongs, as anthracite, semi-anthracite, semi-bituminous, bituminous, 



822 



FUEL. 



or lignite. Coals containing less than 10 per cent volatile matter in the 
combustible would be classed as anthracite, between 10 and 15 per 
cent as semi-anthracite,' between 15 and 30 per cent as semi-bituminous, 
between 30 and 50 per cent as bituminous, and over 50 per cent as lig- 
nitic coals or hgnites. In the classification of the U. S. Geological Sur- 
vey the sub-bituminous coals and hgnites are distinguished by their 
structure and color rather than by analysis. 

The figures in the second column, representing the percentages in the 
dry coal, are useful in comparing different lots of coal of one class, and 
they are better for this purpose than the figures in the first column, for 
the moisture is a variable constituent, depending to a large extent on the 
weather to which the coal has been subjected since it was mined, on the 
amount of moisture in the atmosphere at the time when it is analyzed, 
and on the extent to which it may have accidentally been dried during 
the process of sampling. 

The heating value of a coal depends on its percentage of total combus- 
tible matter, and on the heating value per pound of that combustible. 
The latter differs in different districts and bears a relation to the per- 
centage of volatile matter. It is highest in the semi-bituminous coals, 
being nearly constant at about 15,750 B.T.U. per pound. It is between 
14,800 and 15,500 B.T.U. in anthracite, and ranges from 15,500 down to 
13,000 in the bituminous coals, decreasing usually as we go westward, 
and as the volatile matter contains an increasing percentage of oxygen. 
In some lignites it is as low as 10,000, 

In reporting the heating value of a coal, the B.T.U. per pound of com- 
bustible should always be stated, for convenient comparison with other 
reports. 

In 1892 the author deduced from Mahler's tests on European coals 
the following table of the approximate heating value of coals of differ- 
ent composition. 

Approximate Heating Values of Coals. 



Per Cent 
Volatile 
Matter in 
Coal Dry 
and Free 
from Ash. 




3 
6 

10 
13 
20 
28 



Heating 
Value, B.T.U. 
per lb. 
Combus- 
tible. 



14.580 
14,940 
15.210 
15.480 
15.660 
15.840 
15.660 



Equivalent 

Water 
Evapora- 
tion from 
and at 212° 
per lb. 
Combus- 
tible. 



15.09 
15.47 
15.75 
16.03 
16.21 
16.40 
16.21 



Per Cent 
Volatile 
Matter in 
Coal Dry 
and Free 
from Ash. 



32 
37 
40 
43 
45 
47 
49 



Heating 
Value, B.T.U. 
per lb. 
Combus- 
tible. 



15.480 
15.120 
14.760 
14.220 
13.860 
13.320 
12.420 



Equivalent 

Water 
Evapora- 
tion from 
and at 212° 
per lb. 
Combus- 
tible. 



16.03 
15.65 
15.28 
14.72 
14.35 
13.79 
12.86 



The experiments of Lord and Haas on American coals (Trans. 
A.I.M.E., 1897) practically confirm these figures for all coals in which 
the percentage of fixed carbon is 60% and over of the combustible, but 
for coals containing less than 60 % fixed carbon or more than 40 % volatile 
matter in the combustible, they are liable to an error in either direction 
of about 4%. It appears from these experiments that the coal of one 
seam in a given district has the same heating value per pound of com- 
bustible within one or two per cent [true only of some districts], but coals 
of the same proximate analysis, and containing over 40 % volatile matter, 
but mined m different districts, may vary 6 or 8% in heating value. 

The coals containing from 72 to 87 per cent of fixed carbon in the com- 
bustible have practically the same heating value. This is confirmed by 
Lord and Haas's tests of Pocahontas coal. A study of these tests and of 
Mahler 's indicates that the heating value of all the semi-bituminous coals, 
75 to 87.5% fixed carbon, is within 1 ^% of 15,750 B.T.U. per pound. 

The heating value of any coal may also be calculated from its ultimate 
analysis, with a probable error not exceeding 2%, by Dulong's formula: 



ANALYSES AND HEATING VALUE OF COALS. 



823 



Heating value per lb. = 146 C + 620 |H 



("-?) 



4-40S 



in which C, H, S, and O are respectively the percentages of carbon, 
hydrogen, sulphur and oxygen. Its approximate accuracy is proved by 
both Mahler's and Lord and Haas's experiments, and any deviation of 
the calorimetric determination of any coals (cannel coals and hgnites 
excepted) more than 2 % from that calculated by the formula, is more 
likely to proceed from an error in either the calorimetric test or the 
analysis, than from an error in the formula. 

Average Results of Lord and Haas's Tests. — (" Steam Boiler 
Economy," p. 156.) 



















-M 




-M 




Name of Coal. 


C. 


H. 


0. 


N. 


S. 


1 


'o 


> 


1 


3^3 




Pocahontas, Va. 


84.87 


4.20 


2.84 


0.85 


0.59 


5.89 


0.76 


18.51 


74.84 


19.82 


15766 


Thacker, W. Va. 


78.65 


5.00 


6.01 


1.41 


1.28 


6.27 


1.38 35.68 


56.67 


38.62115237 


Pittsburg, Pa... 


75.24 


5.01 


7.04 


1.51 


1.79 


8.02 


1.37 36.80 


53.81 


40.61 


14963 


Middle Kittan- 
























ing. Pa 


75.19 


4.91 


7.47 


1.46 


1.98 


7.18 


1.81 


36.32 


54.69 


39.91 


14800 


Upper Freeport, 
























Pa. and O.... 


72.65 


4.82 


7.26 


1.34 


2.89 


9.10 


1.93 


37.35 


51.63 


41.98 


14755 


Mahoning, O . . . 


71.13 


4.56 


7.17 


1.23 


1.86 


10.90 


3.15 


35.00 


50.95 


40.72 


14728 


Jackson Co., O. . 


70.72 


4.45 


10.82 


1.47 


1.13 


3.25 


8.17 


35.79 


52.78 


40.41 


14141 


Hocking Val- 
























ley, O 


68.03 


4.97 


9.87 


1.44 


1.59 


8.00 


6.5935.77 


49.64 


41.84 


14040 



* Per lb. of combustible, by the Mahler calorimeter. The average 
figures calculated from the ultimate analyses agreed within 0.5 %, except 
in the case of the Jackson Co. coal, in which the calorimetric result was 
1.6% higher than that computed from the analysis. 

Sizes of Anthracite Coal. — When anthracite is mined it is crushed 
in a " breaker," and passed over screens separating it iuto different sizes, 
which are named as follows: 

Lump, passes over bars set 3 1/2 to 5 in. apart; steamboat, over 3 1/2 
in. and out of screen; broken, through 4 1/2 in., over 3 1/4 in. ; egg, 3 1/4 
to 2 5/16 in. ; stove, 2 s/ig to 1 s/s in. ; chestnut, 1 5/8 to 7/8 in. ; pea, 7/8 to 
9/16 in.; buckwheat. No. 1, Q/ig to 5/iq in.; No. 2, 5/iq to s/iq; No. 3, ^/m 
to 3/32 in. ; culm, through 3/32 in. 

The terms "buckwheat," "rice" and "barley" are used in some 
locaUties instead of No. 1, No. 2 and No. 3 buckwheat. 

When coal is screened into sizes for shipment the purity of the dif- 
ferent sizes as regards ash varies greatly. Samples from one mine gave 
results as follows : 





Screened. 


Analyses. 


Name of Coal. 


Through 
Inches. 


Over 

Inches. 


Fixed 
Carbon. 


Ash. 


Egg 


2.5 

1.75 

1.25 

0.75 

0.50 


1.75 
1.25 
0.75 
0.50 
0.25 


88.49 
83.67 
80.72 
79.05 
76.92 


5 66 


Stove 


10.17 


Chestnut 


12.67 


Pea 


14 66 


Buckwheat 


16.62 







Space Occupied by Anthracite Coal. (J. C. I. W., vol. iii.) — The 
cubic contents of 2240 lb. of hard Lehigh coal is a httle over 36 feet; an 
average Schuylkill white-ash, 37 to 38 feet; Shamokin, 38 to 39 feet; 
Lorberry, nearly 41. 

According to measurements made with Wilkes-Bar re anthracite coal 
from the Wyoming Valley, it requires 32.2 cu. ft. of lump, 33.9 cu. ft. 



824 



FtTEL. 



broken, 34.5 cu. ft. egg, 34.8 cu. ft. of stove, 35.7 cu. ft. of chestnut, and 

36.7 cu. ft. of pea, to make one ton of coal of 2240 lb. ; while it requires 

28.8 cu. ft. of lump, 30.3 cu. ft. of broken, 30.8 cu. ft. of egg, 31.1 cu. ft. 
of stove, 31.9 cu. ft. of chestnut, or 32.8 cu. ft. of pea, for one ton (2000 lb.) 

Bernice Basin, Pa., Coals. 

Water Vol. H.C. Fixed C. Ash. Sulphur. 
Bemice Basin, Sullivan^ 0.96 3.56 82.52 3.27 0.24 

and Lycoming Cos.; > to to to to to 

range of 8 j 1.97 8.56 89.39 9.34 1.04 

This coal is on the dividing-line between the anthracites and semi- 
anthracites, and is similar to the coal of the Lykens Valley district. 

More recent analyses {Trans. A. I. M. E., xiv. 721) give: 

Water Vol. H.C. Fixed C. Ash. Sulphur 

Working seam . 65 9 . 40 83 . 69 5 . 34 0.91 

60 ft. below seam 3.67 15.42 71.34 8.97 0.59 

The first is a semi-anthracite, the second a semi-bituminous. 

ConnellsviUe Coal and Coke. (Trans. A. I. M. E., xiii. 332.)— The 
Connellsville coal-field, in the southwestern part of Pennsylvania, is a 
strip about 3 miles wide and 60 miles in length. The mine workings are 
confined to the Pittsburgh seam, which here has its best development as 
to size, and its quality best adapted to coke-making. It generally af- 
fords from 7 to 8 feet of coal. 

The following analyses by T. T. Morrell show about its range of com- 
position: 

Moisture. Vol. Mat. Fixed C Ash. Sulphur. Phosph's. 
HeroldMine 1.26 28.83 60.79 8.44 0.67 0.013 
KintzMine. 0.79 31,91 56.46 9. .52 1.32 0.02 

In comparing the composition of coals across the Appalachian field, 
in the western section of Pennsylvania, it will be noted that the Con- 
nellsville variety occupies a peculiar position between the rather dry 
semi-bituminous coals eastw^ard of it and the fat bituminous coals flank- 
ing it on the west. 

Indiana Coals. (J. S. Alexander, Trans. A. I. M. E., iv. 100.) — The 
typical block coal of the Brazil (Indiana) district differs in chemical 
composition but little from the coking coals of Western Pennyslvania. 
The physical difference, however, is quite marked; the latter has a 
cuboid structure made up of bituminous particles lying against each 
other, so that under the action of heat fusion throughout the mass 
readily takes place, while block coal is formed of alteniate layers of rich 
bituminous matter and a charcoal-hke substance, w^hich is not only very 
slow of combustion, but so retards the transmission of heat that agglu- 
tination is prevented, and the coal burns away layer by layer, retaining 
its form until consumed. 

Illinois Coals, The IlUnois coals are generally high in moisture, 
volatile matter, ash and sulphur, and the volatile matter is high in 
oxygen; consequently the coals are low in heating value. The range of 
quality is a wide one. The Big Muddy coal of Jackson Co., which has a 
high reputation as a steam coal in the St. Louis market, has about 36% 
of volatile matter in the combustible, while a coal from Staunton, 
Macoupin Co., tested by the author in 1883 (Trans. A. S. M. E., v. 266) 
had 68%. A boiler test with this coal gave only 6,19 lbs. of water 
evaporated from and at 212° per lb. of combustible, in the same boiler 
that had given 9.88 lbs. with Jackson, O., nut. 

Prof. S. W. Parr, in Bulletin No. 3 of the 111. State Geol. Survey, 1906, 
reports the analyses and calorimetric tests of 150 Illinois coals. The 
two having the lowest and the highest value per pound of combustible 
have the following analysis: 





Air-dried Coal. 


Pure Coal. 




Moist. 


Ash. 


Vol. 


Fixed 
C. 


S. 


Vol. 


Fixed 
C. 


B.T.U. 
per lb. 


Lowest. . 
Highest . 


9.90 
5.68 


5.02 
8,90 


40.75 
33.32 


44.33 
52.10 


2.00 
1.18 


47.90 
39.02 


52.10 
60.98 


12.162 
14.830 



''ANALYSES AND HEATING VALUE OF COALS. 



825 



per lb., air dry; it contained 9.70 moisture and 31.18 ash, and the B.T.U. 
per lb. combustible was 14,623. The best coal had a heating value of 
13,303 per lb.; moisture 4.20, ash 5.50, B.T.U. per lb. combustible, 
14,734. 

Of the 150 coals, 28 gave between 14,500 and 14,830 B.T.U. per lb. 
combustible; 82 between 14,000 and 14,500; 32 between 13,500 and 
14,000; 6 between 13,000 and 13,500; one 12,535 and one 12,162. The 
average is about 14,200. The volatile matter ranged from 36.24% to 
53.80% of the combustible; the sulphur from 0.62 to 4.96%; the ash 
from 2.32 to 31.18%, and the moisture from 3.28 to 12.74%, all calcu- 
lated from the air-dried samples. The moisture in the coal as mined is 
not stated, but was no doubt considerably higher. The author has 
found over 14 % moisture in a lump of Illinois coal that was apparently 
dry, having been exposed to air, imder cover, for more than a month. 

Colorado Coals. — The Colorado coals are of extremely variable com- 
position, ranging all the way from hgnite to anthracite. G. C. Hewitt 
(Trans. A. I. M. E., xvii. 377) says: The coal seams, where unchanged 
by heat and flexure, carry a lignite containing from 5 % to 20 % of water. 
In the southeastern corner of the field the seams have been metamor- 
phosed so that in four miles the same seams are an anthracite, coking, 
and dry coal. The dry seams also present wide chemical and physical 
changes in short distances. A soft and loosely bedded coal has in a 
hundred feet become compact and hard without the intervention of a 
fault. A couple of hundred feet has reduced the water of combination 
from 12%, to 5%. 

Western Arkansas and Oklahoma (formerly Indian Territory). 
(H. M. Chance, Trans. A. I. M. E., 1890.) — ^The western Arkansas coals 
are dry semi-bituminous or semi-anthracitic coals, mostly non-coking, 
or with quite feeble coking properties, ranging from 14% to 16% in 
volatile matter, the highest percentage yet found, according to Mr. 
Winslow's Arkansas report, being 17.65. 

In the Mitchell basin, about 10 miles west from the Arkansas line, the 
coal shows 19 % volatile matter; the Mayberry coal, about 8 miles farther 
west, contains 23 % ; and the Bryan Mine coal, about the same distance 
west, shows 26%. About 30 miles farther west, the coal shows from 
38% to 41.5 % volatile matter, which is also about the percentage in 
coals of the McAlester and Lehigh districts. 

Analyses of Foreign Coals. (Selected from D. L. Barnes's paper on 
American Locomotive Practice, Trans. A. S. C. E., 1893.) 



Great Britain: 

South- Wales 

South-Wales 

Lancashire, Eng. 
Derbyshire, " 
Durham, " * 

StafiFordshire, ** 

Scotland! 

Scotlandt 

South America: 
Chili 






21.93 






88.3 
92.3 
80.1 
79.9 
86.8 
78.6 
63.1 
80.1 

70.55 



19.8 

2.4 



7.52B 



South America: 

Chili, Chiroqui. 

Patagonia 

Brazil 

Canada: 

Nova Scotia . . . 

Cape Breton. . . 
Australia: 

Lignite 

Sydney, N.S.W. 

orneo 

Tasmania 



11 


n 


H 


■^6 


24.11 


38.98 


24.35 


62.25 


40.5 


57.9 


26.8 


60.7 


26.9 


67.6 


15.8 


64.3 


14.98 


82.39 


26.5 


70.3 


6.16 


63.4 



36.91 

13.4 

1.6 

12.5 
5.5 

10.0 
2.04 
14.2 
30.45 



* Semi-bit, coking coal. f Boghead cannel gas coal. 

t Semi-bit, steam-coal. 
An analysis of Pictou, N. S., coal, in Trans. A. I. M. E., xiv. 560, is: 
vol., 29.63; carbon, 56.98; ash, 13.39; and one of Sydney, Cape Breton, 
coal is: vol., 34.07; carbon, 61.43; ash, 4.50. 

Sampling Coal for Analysis. — J. P. Kimball, Trans. A. I. M. E., 
xii. 317, says: The unsuitable sampling of a coal-seam, or the improper 
preparation of the sample in the laboratory, often gives rise to errors in 



826 FUEL. 

determinations of the ash so wide in range as to vitiate the analysis for 
all practical purposes; every other single determination, excepting mois- 
ture, showing its relative part of the error. The determinations of sul- 
phur and ash are especially Uable to error, as they are intimately asso- 
ciated in the slates. 

Wm. Forsyth, in his paper on The Heating Value of Western Coals 
(Eng'g News, Jan. 17, 1895) , says: This trouble in getting a fairly average 
sample of anthracite coal has compelled the Reading R. R. Co., in get- 
ting its samples, to take as much as 300 lb. for one sample, drawn direct 
from the chutes, as it stands ready for shipment. 

The directions for collecting samples of coal for analysis at the C, B. 
& Q. laboratory are as follows: 

Two samples should be taken, one marked "average," the other 
"select." Each sample should contain about 10 lb., made up of lumps 
about the size of an orange taken from different parts of the dump or 
car, and so selected that they shall represent as nearly as possible, first, 
the average lot; second, the best coal. 

An example ol the difference between an "average" and a "select" 
sample, taken from Mr. Forsyth's paper, is the following of an Illinois 
coal: 

Moisture. Vol. Mat. Fixed Carbon. Ash. 

Average 1.36 27.69 35.41 35.54 

Select 1.90 34.70 48.23 15.17 

The theoretical evaporative power of the former was 9.13 lbs. of water 
from and at 212° per lb. of coal, and that of the latter 11.44 lbs. 

For methods of sampling see Kent's "Steam Boiler Economy," 2d 
edition (1915), also Report of the Power Test Committee, A. S.M.E., 
1915, and Technical Paper No. 8 of the U. S. Bureau of Mines, 1913. 

RELATIVE VALUE OF STEAM COALS. 

The heating value of a coal may be determined, with more or less 
approximation to accuracy, by three different methods. 

1st, by chemical analysis; 2d, by combustion in a coal calorimeter; 
3d, by actual trial in a steam-boiler. 

The accuracy of the first two methods depends on the precision of the 
method of analysis or calorimetry adopted, and upon the care and skill 
of the operator. The results of the third method are subject to numer- 
ous sources of variation and error, and may be taken as approximately 
true only for the particular conditions under which the test is made. 
Analysis and calorimetry give with considerable accuracy the heating 
value which may be obtained under the conditions of perfect combus- 
tion and complete absorption of the heat produced. A boiler test gives 
the actual result under conditions of more or less imperfect combustion, 
and of numerous and variable wastes. It may give the highest practical 
heating value, if the conditions of grate-bars, draft, extent of heating 
surface, method of firing, etc., are the best possible for the particular 
coal tested, and it may give results far beneath the highest if these con- 
ditions are adverse or unsuitable to the coal. 

In a paper entitled Proposed Apparatus for Determining the Heating 
Power of Different Coals {Trans. A. I. M. E., xiv. 727) the author de- 
scribed and illustrated an apparatus designed to test fuel on a large 
scale, avoiding the errors of a steam-boiler test. It consists of a fire- 
brick furnace enclosed in a water casing, and two cylindrical shells con- 
taining a great number of tubes, which are surrounded by cooling water 
and through which the gases of combustion pass while being cooled. 
No steam is generated in the apparatus, but water is passed through it 
and allowed to escape at a temperature below 200° F. The product of 
the weight of the water passed through the apparatus by its increase in 
temperature is the measure of the heating value of the fuel. 

A study of M. Mahler's calorimetric tests shows that the maximimi 
difference between the results of these tests and the calculated heating 
power by Dulong's law in any single case is only a httle over 3%, 
and the results of 31 tests show that Dulong's formula gives an aver- 
age of only 47 thermal units less than the calorimetric tests, the 



RELATIVE VALUE OF STEAM COALS. 827 

average total heating value being over 14,000 B.T.U., a difference of 
less than 0.4%.* 

The close agreement of the results of calorimetric tests when properly- 
conducted, and of the heating power calculated from the ultimate chemi- 
cal analysis indicates that either the chemical or the calorimetric method 
may be accepted as correct enough for all practical purposes for deter- 
mining the total heating power of coal. The results obtained by either 
method may be taken as a standard by which the results of a boiler test 
are to be compared, and the difference between the total heating power 
and the result of the boiler test is a measure of the inefficiency of the 
boiler under the conditions of any particular test. 

The heating value that can be obtained in boiler practice from any 
given coal depends upon the efficiency of the boiler, and this largely 
upon the difficulty of thoroughly burning the volatile combustible 
matter in the l)oiler furnace. 

With the best anthracite coal, in which the combustible portion is, 
say, 97% fixed carbon and 3% volatile matter, the highest result that 
can be expected in a boiler-test with all conditions favorable is 12.2 lb. 
of water evaporated from and at 212° per lb. of combustible, which is 
79% of 15.47 lb., the theoretical heating-power. With the best semi- 
bituminous coals, such as Cumberland and Pocahontas, in which the 
fixed carbon is 80% of the total combustible, 12.5 lb., or 76% of the 
theoretical 16.4 lb., may be obtained. For Pittsburgh coal, with a 
fixed carbon ratio of 68%, 11 lb., or 69% of the theoretical 16.03 lb., is 
about the best practically obtainable with the best boilers when hand- 
fired, with ordinary furnaces. (The author has obtained 78% with an 
automatic stoker set in a "Dutch oven" furnace.) With some good 
Ohio coals, with a fixed carbon ratio of 60%, 10 lb., or 66% of the the- 
oretical 15.28 lb., has been obtained, under favorable conditions, with a 
fire-brick arch over the furnace. With coals mined west of Ohio, with 
lower carbon ratios, the boiler efficiency is not apt to be as high as 60% 
unless a special furnace, adapted to the coal, is used. 

From these figures a table of probable maximum boiler-test results 
with ordinary furnaces from coals of different fixed carbon ratios may 
be constructed as follows: 

Fixed carbon ratio 97 80 68 60 54 50 

Evap. from and at 212° per lb. combustible, maximum in boiler-tests: 

12.2 12.5 11 10 8.3 7.0 

Boiler efficiency, per cent 80 76 69 66 60 55 

Loss, chimney, radiation, imperfect combustion, etc.: 

20 24 31 34 40 45 

The difference between the loss of 20% with anthracite and the great- 
er losses with the other coals is chiefiy due to imperfect combustion of 
the bituminous coals, the more highly volatile coals sending up the 
chimney the greater quantity of smoke and unburned hydrocarbon 
gases. It is a measure of the inefficiency of the boiler furnace and of the 
inefficiency of heating-surface caused by the deposition of soot, the 
latter being primarily caused bj^ the imperfection of the ordinary 
furnace and its unsuitability to the proper burning of bituminous coaL 
If in a boiler-test with an ordinary furnace lower results are obtained 
than those in the above table, it is an indication of unfavorable condi- 
tions, such as bad firing, wrong proportions of boiler, defective draft, a 
rate of driving beyond the capacity of the furnace, or beyond the 
capacity of the boiler to absorb the heat produced in the furnace. It is 
quite possible, however, with automatic stokers and fire-brick com- 
bustion chambers to obtain an efficiency of 70% with the highly 
volatile western coals. 

Under exceptionally good conditions, with mechanical stokers, very 
large combustion chambers, and the air supply controlled according to 
the indications of gas analyses, as high as 81 % efficiency has been 
obtained. See under Steam -Boilers, page 898. 

* The formula commonly used m the United States is 14,600 C -{• 
62,000 (H - i/sO) + 4050 S. For a description of the Mahler calori- 
meter and its method of operation see the author's "Steam Boiler 
Economy." Prof. S. W. Parr, of the University of Illinois, has put a 
calorimeter on the market which gives results practically equal to those 
obtained with Mahler's instrument. 



828 


Classified List of Coals. 






As Received. 


Combustible. 


Air-dry ,Ash-free 




Moist. 1 Ash. |b.T.U. 


Vol. 1 S. 1 O. 1 B.T.U. 


Moist. 1 B.T.U. 







I. 


Anthracite 








7.43 


14.36 


11,891 


8.8 


0.73 


4.04 


15.203 


1.55 


2.70 


5.83 


14,099 


3.6 


0.87 


1.32 


15,413 


1.08 


2.80 


7.83 


13,298 


1.3 


1.00 


2.13 


14,882 


1.43 


3.30 


9.12 


13,351 


3.7 


0.68 


2.41 


15,248 


0.83 








8.5 


0.72 


2.67 


15.410 


0.80 



Ark.... 

Pa 

Va 



II. Semi-anthracite. 



2.36 


12.08 


13.259 


14.8 


2.33 2.57 


15,496 


1.45 


3.38 


11.50 


13,156 


1 0.0 


0.74 2.17 


15,457 


0.91 


4.80 


18.03 


11,961 


13.1 


0.82 4.18 


15,500 


0.90 



III. Semi-bituminous. 



3.08 


3.75 


14,681 


28.8 


0.59 


4.45 


15.757 


1.15 


2.38 


4.88 


14,487 


27.9 


1.58 


3.42 


15.620 


0.94 


5.14 


5.00 


14.065 


15.5 


1.29 


3.02 


15.651 


0.60 


2.77 


9.07 


13.774 


16.7 


3.16 


1.69 


15.624 


0.86 


3.21 


9.29 


13.588 


17.0 


3.57 


1.25 


15.530 


0.92 


0.96 


8.62 


14,330 


23.8 


0.58 


4.34 


15.849 


0.83 


3.07 


9.16 


13,990 


25.8 


0.72 


2.29 


15,939 


1.43 


3.80 


14.49 


12,791 


19.4 


1.55 


5.96 


15.653 


0.74 


3.20 


6.70 


14,100 


16.0 


1.02 


2.54 


15.640 


1.10 


2.60 


6.80 


14.360 


17.5 


0.98 


2.47 


15.856 


0.66 


2.05 


8.31 


14.092 


18.3 


0.96 


2.93 


15.721 


0.61 


2.37 


8.83 


13,840 


21.7 


1.15 


2.87 


15.586 


0.53 


5.11 


8.03 


13.662 


15.7 


1.36 


1.87 


15.728 


0.70 


4.25 


7.87 


13,513 


24.8 


1.81 


5.50 


15,376 


0.40 


1.10 


7.41 


14,499 


17.3 


1.63 


2.82 


15.847 


0.65 


4.00 


4.31 


14,520 


19.0 


0.68 


3.42 


15.840 


0.54 


4.10 


3.18 


14,740 


17.5 


0.68 


2.23 


15.910 


0.64 


5.81 


17.04 


11.776 


16.3 


0.48 


3.97 


15.264 


1.67 


3.71 


3.39 


14.306 


25.3 


0.86 


4.13 


15,399 


1.18 


1.75 


4.58 


15.023 


19.9 


0.60 


2.80 


16.038 


0.69 



IV. Cannel.* 



2.36 


10.49 


13,770 


55.5 


1.38 


7.57 


15,800 


0.92 


1.70 


9.31 


14,251 


57.0 


1.15 


7.61 


16,013 


1.44 


1.80 


3.44 


15,330 


47.4 


0.92 


5.34 


16.176 


0.84 


7.35 


23.24 


10,355 


67.6 


2.32 


13.68 


14.918 


8.26 







V. Bituminous, 


High 


-GRADE 


, 






Ala.... 


2.18 


2.79 


14.816 


33.4 


1.13 


6.99 


15.590 


1.23 


15.400 


Ala.... 


3.83 


5.48 


13,799 


35.3 


1.07 


7.00 


15.214 


1.77 


14.947 


Colo. . . 


2.64 


5.21 


13,529 


31.3 


0.72 


9.38 


14.681 


1.01 


14.533 


Colo. . . 


2.28 


9.16 


13,781 


33.7 


0.56 


8.77 


15.559 


0.87 


15,423 


Ill 


7.81 


8.38 


12,418 


40.0 


2.82 


9.74 


14.818 


2.34 


14,470 


Kan... 


2.50 


12.45 


12,900 


39.8 


6.68 


5.26 


15.167 


2.86 


14,734 


Kan... 


9.04 


15.72 


11,142 


39.5 


4.93 


7.27 


14.809 


2.49 


14,436 


Ky.... 


3.41 


5.73 


13.928 


35.3 


0.58 


8.05 


15.328 


1.64 


15,095 


N.Mex. 


2.78 


14.57 


12.294 


41.5 


0.74 


8.79 


14.875 


1.64 


14,630 


N.Mex. 


2.45 


17.40 


12.200 


34.4 


0.96 


6.93 


15.221 


0.80 


15.099 


Ohio... 


3.53 


9.12 


13.072 


42.9 


3.97 


7.04 


14.965 


2.38 


14,642 


Ohio... 


5.59 


8.29 


12.773 


42.8 


3.66 


9.01 


14.832 


3.83 


14.431 


Okla... 


2.09 


20.07 


11.695 


35.5 


7.36 


3.71 


15.025 


1.38 


14.814 


Okla... 


2.81 


8.75 


13.320 


40.8 


2.06 


7.35 


15,061 


1.57 


14.825 


Pa 


2.61 


6.17 


13.997 


38.3 


1.38 


6.94 


15,345 


1.42 


15.127 


Pa 


5.13 


8.71 


13,365 


32.4 


1.00 


7.35 


15.511 


1.07 


15.346 


Tenn. . . 


6.39 


9.53 


12,578 


38.4 


1.17 


7.94 


14.960 


1.97 


14.665 


Tenn. . . 


3.89 


14.43 


12,514 


33.8 


0.95 


6.70 


15.320 


1.08 


15,137 


Va 


4.44 


5.98 


13.363 


40.2 


0.85 


12.18 


14,918 


2.52 


14,381 


Va 


3.31 


3.76 


14,209 


35.3 


0.97 


5.65 


15,291 


1.49 


15.069 


Wash.. 


2.32 


13.58 


12.443 


44.0 


5.23 


13.93 


14,796 


1.55 


14.569 


W.Va.. 


4.21 


7.22 


13,379 


40.0 


0.72 


10.10 


15.107 


2.11 


14,787 


W.Va. . 


2.86 


5.83 


14,105 


36.4 


0.73 


5.14 


15.448 


1.36 


15.237 


Wyo... 


5.49 


3.12 


13.570 


39.3 


0.99 


11.40 


14.848 


2.13 


14.552 



* H in combustible 
The highest H in the 



: Ky., 7.13. and 7.46; W. Va., 7.13; Utah, 7.73. 
other coals is 5.78, a Missouri bituminous. 



ANALYSIS AND HEATING VALUE OF COALS. 829 



Classified List of Coals. — ConHnued. 



As Received. 



Moist. Ash. B.T.U. 



Combustible. 



Air-dry , Ash-free 



Vol. 



B.T.U. Moist. B.T.U. 





VI. Bituminous Medium Grade 




3.95 


14.59 


11.785 


37.7 


1.37 


10.45 


14,467 


2.69 


7.06 


21.78 


9.846 


44.2 


1.83 


14.11 


13.838 


2.55 


6.95 


6.23 


12.447 


53.8 


4.80 


11.47 


14.336 


5.19 


8.12 


8.63 


12.064 


41.4 


1.36 


12.02 


14,492 


5.15 


8.86 


11.66 


11.702 


39.3 


3.10 


9.03 


14,724 


3.71 


16.91 


17.37 


9.524 


40.9 


2.88 


9.50 


14,492 


5.48 


7.88 


14.20 


11.146 


47.3 


6.60 


9.96 


14,305 


5.01 


13.88 


14.01 


10.244 


51.2 


8.53 


8.96 


14.206 


5.35 


8.24 


16.00 


1 1 ,027 


40.6 


6.64 


8.03 


14.555 


6.24 


6.95 


12.19 


11,905 


44.2 


9.94 


5.64 


14.724 


4.09 


2.50 


12.45 


12.900 


39.8 


5.22 


5.98 


14.922 


4.30 


7.92 


10.06 


12.022 


44.0 


4.29 


8.90 


14.657 


6.52 


5.27 


14.18 


11.950 


43.5 


5.64 


7.46 


14.836 


2.98 


11.91 


6.84 


11.781 


38.8 


1.53 


9.54 


14.499 


4.70 


11.55 


3.25 


12.442 


37.1 


1.11 


10.51 


14.603 


5.59 


17.30 


23.38 


8.240 


44.6 


4.% 


11.83 


13,892 


3.42 


12.67 


4.83 


12.487 


50.2 


6.21 


6.12 


15,134 


5.68 


3.51 


19.50 


10,881 


34.3 


4.86 


9.50 


14,134 


2.42 


5.77 


10.57 


12,281 


39.6 


0.60 


9.77 


14,681 


2.30 


5.02 


12.00 


12.064 


44.3 


0.68 


12.70 


14,539 


3.06 


4.14 


9.38 


12,874 


37.8 


0.63 


11.58 


14,269 


4.69 


7.71 


11.95 


11.515 


47.7 


5.74 


9.44 


14,332 


3.30 


7.04 


10.01 


12,202 


41.7 


2.31 


9.26 


14,711 


4.31 


5.58 


8.99 


12,170 


45.6 


0.60 


13.30 


14.245 


4.98 


6.05 


4.87 


13.151 


47.2 


0.62 


10.93 


14.764 


2.47 


6.02 


19.35 


10.708 


41.8 


0.57 


12.38 


14.348 


3.26 


3.96 


4.77 


13.502 


39.6 


0.84 


9.25 


14.793 


2.73 



VII. Bituminous Low Grade. 



sk£ 


I. 


10.77 


14.87 


9.641 




11.35 


13.40 


10.733 






14.43 


13.28 


10.064 






12.11 


6.83 


11.952 






13.18 


15.63 


10.030 


^a. 




14.08 


10.96 


10.723 






15.36 


10.99 


10,460 


nt 




9.76 


16.42 


10,235 


nt 




10.88 


26.88 


7.742 


^lex. 


12.29 


6.99 


11.252 


^ex. 


15. /9 


9.37 


9,970 


a.. . 


8.29 


25.05 


9.110 


ih... 


16.35 


9.62 


10.874 


h... 


14.19 


9.92 


9.927 


sh 




12.05 


10.41 


10.414 



[ 40.8 


0.94 


18.83 


12,964 


5.42 


46.0 


6.33 


10.53 


14,263 


6.75 


40.8 


5.55 


12.02 


13,921 


6.02 


42.2 


1.78 


10.55 


14.746 


9.60 


44.8 


6.73 


9.69 


14.089 


6.17 


47.5 


5.69 


9.73 


14,305 


11.33 


47.3 


4.85 


10.68 


14,202 


7.37 


37.5 


0.86 


16.21 


13,865 


7.58 


32.6 


2.88 


16.14 


12,438 


8.09 


42.8 


0.78 


14.00 


13.939 


11.70 


46.8 


2.38 


15.69 


13.322 


7.87 


45.9 


5.93 


10.62 


13.667 


7.74 


48.1 


1.65 




14.618 


11.88 


45.4 


7.27 


10.05 


13.586 


9.65 


44.0 


7.10 


14.18 


13.081 


11,47 


47.5 


0.44 


17.11 


13.423 


6.56 







VIII 


Sub-bituminous and Lignite. 






Ark.... 


39.43 


9.71 


6.356 


52.1 


0.96 


21.17 


12,497 


22.00 


9.750 


Cal.... 


18.51 


15.49 


8.507 


53.5 


4.62 


16.79 


12,890 


10.95 


11.478 


Colo... 


19.65 


6.00 


8.638 


41.4 


0.44 


16.97 


11,619 


8.21 


10.664 


Colo. . . 


19.28 


4.70 


9.064 


45.5 


0.51 


16.52 


13,239 


15.35 


10.094 


Mont. . 


30.00 


11.90 


6.914 


69.0 


1.86 


23.47 


1 1 .900 


15.55 


10.143 


Mont . . 


24.59 


14.01 


6,208 


54.1 


0.67 


26.64 


10.211 


25.02 


7,656 


N.Dak. 


35.96 


7.75 


7,069 


56.7 


2.04 


17.69 


12.557 


26.20 


8,886 


N.Dak. 


38.92 


5.39 


6.739 


45.9 


0.86 


22.67 


12.101 


11.66 


10,885 


Ore 


16.10 


13.17 


9.031 


44.0 


1.15 


19.68 


12.769 


10.16 


11,471 


Ore.... 


13.77 


7.46 


9,054 


47.0 


5.52 




11.493 


7.05 


10,684 


S. Dak. 


30.45 


12.15 


6,944 


40.0 


0.68 




12.098 


15.77 


10.189 


Tex. . . . 


34.70 


• 11.20 


7,056 


59.6 


1.46 


18.99 


13.043 


15.73 


11.077 


Tex. . . . 


33.71 


7.28 


7,348 


49.6 


0.90 


20.54 


12,452 


11.82 


11.036 



{Table continued on p. 830.) 



830 



FUEL. 



Classified List of Coals. — Continued. 



As Received. 



Moist. Ash. B.T.U. 



Combustible. 



Vol. S. 



B.T.U. 



Air-dry, Ash-free 



Moist. B.T.U. 



VIII. Sub-bituminous and Lignite. — Continued, 



Utah... 
Wash . . 
Wyo... 
Wyo... 



16.59 
27.17 
10.26 
31.37 



13.44 
10.92 
9.83 
10.12 



7,882 

7.569 

10,354 

5.634 



46.6 
54.6 
27.8 
50.6 



4.88 
0.53 
1.09 
2.17 



22.14 
22.06 
10.94 
29.86 



11.264 
12.226 
12.956 
9.630 



15.35 

17.21 

9.56 

22.69 



9.535 
10.122 
11.573 

7.458t 



Not Classified.! 



R.I... 


23.68 


30.77 


5.976 


6.6 


0.05 


5.59 


13.120 


1.26 


12.955 


R. I. .. 


2.41 


19.06 


10.996 


6.3 


0.09 


3.27 


14.002 


0.52 


13.930 


Alaska . 


5.71 


34.15 


8,386 


21.7 


10.76 


5.28 


13.945 


4.77 


13.279 


Ark. . . . 


5.26 


24.81 


10,451 


21.0 


1.43 


6.44 


14,945 


1.77 


14,722 


Idaho.. 


34.28 


13.38 


8,613 


50.9 


4.77 




16,457 


16.42 


13.757 



* These two samples are classed as sub-bituminous by the Bureau of 
Mines. 

t Sample from surface exposure; coal badly weathered. 

t The Rhode Island coals are graphitic and are not used as fuel. The 
two samples from Alaska and Arkansas may be classed as semi-bitumi- 
nous by their percentage of volatile matter, but they are higher in 
oxygen and in moisture, and lower in heating value than other semi- 
bituminous coals. The Idaho coal is apparently a cannel coal very 
high in moisture, but the ultimate analysis is lacking. 

Purchase of Coal under Specifications. — It is customary for large 
users of coal to purchase it under specifications of its analysis or heating 
value with a penalty attached for failure to meet the specifications. Tlie 
following standards for a specification were given by the author in his 
"Steam Boiler Economy," 1901. (Revised in 2d edition, 1915): 

Anthracite and Semi-anthracite . — The standard is a coal containing 
5% volatile matter, not over 2% moisture, and not over 10% ash. A 
premium of 0.5% on the price will be given for each per cent of volatile 
matter above 5 % up to and including 15 % , and a reduction of 2 % on 
the price will be made for each 1% of moistm-e and ash above the 
standard. 

Semi-bituminous and Bituminous. — The standard is a semi-bitumi- 
nous coal containing not over 20% volatile matter, 2 % moisture, 6 % ash. 
A reduction of 1 % in the price will be made for each 1 % of volatile mat- 
ter in excess of 25 % , and of 2 % for each 1 % of ash and moisture in excess 
of the standard. 

For western coals in which the volatile matter differs greatly in its 
percentage of oxygen, the above specification based on proximate analy- 
sis may not be sufficiently accurate, and it is well to introduce either the 
heating value asdetermined by a calorimeter or the percentage of oxygen. 
The author has proposed the following for IlUnois coal: 

The standard is a coal containing not over 6% moisture and 10% ash 
in an air-dried sample, and whose heating value is 14,500 B.T.U. per 
pound of combustible. For lower heating value per lb. of the com- 
bustible, the price shall be reduced proportionately, and for each 1% 
increase in ash or moisture above the specified figures, 2% of the price 
shall be deducted. 

Several departments of the U.S. government now purchase coal under 
specifications. See paper on the subject by D. T. Randall, Bulletin No. 
339, U. S. Geological Survey, 1908, also "Steam Boiler Economy," 
2d edition. 

Weathering of Coal. (I. P. Kimball, Trans. A.I.M.E., viii, 204.)— 
The effect of the weathering of coal, while sometimes increasing its 
weight, is to diminish the carbon ana disposable hydrogen and to increase 
the oxygen and indisposable hydrogen. Hence a reduction in the cal- 
orific value. An excess of pyrites in coal tends to produce rapid oxida- 
tion and mechanical disintegration of the mass, with 'development of 
heat, loss of coking power, and spontaneous ignition. 

The only appreciable results of the weathering of anthracite are con- 



PRESSED FUEL. 831 

fined to the oxidation of its accessory pyrites. In coking coals, however, 
weathering reduces and finally destroys the coking power. 

Richters found that at a temperature of 158° to 1 80° Fahr., three coals 
lost in fourteen days an average of 3.6% of calorific power. It appears 
from the experiments of Richters and Reder that wlien there is no rise 
of temperature of coal piled in heaps and exposed to the air for nine to 
twelve months, it undergoes no sensible change, but wh^i the coal 
becomes heated it suffers loss of C and H by oxidation and increases in 
weight by the fixation of oxygen. (See also paper by R. P. Rothwell, 
Trans. A. I. M. E., iv. 55.) 

Experiments by S. W. Parr and N. D. Hamilton (Bull. No. 17 of 
Univ'y of 111. Eng'g Experiment Station, 1907) on samples of about 
100 lb. each, show that no appreciable change takes place in coal sub- 
merged in water. Their conclusions are: 

(a) Submerged coal does not lose appreciably in heat value. 

(&) Outdoor exposure results in a loss of heat value varying from 2 
to 10 per cent. 

(c) Dry storage has no advantage over storage in the open except 
with high sulphur coals, where the disintegrating effect of sulphur in the 
process of oxidation facilitates the escape or oxidation of the hydrocar- 
bons. 

^■' (d) In most cases the losses in storage appear to be practically com- 
plete at the end of five months. From the seventh to the ninth month 
the loss is inappreciable. 

This paper contains also a historical review of the literature on weath- 
ering and on spontaneous combustion, with a summary of the opinions 
of various authorities. 

Later experiments on storing carload lots of Illinois coals (W. F. 
Wheeler, Trans. A. I. M. E., 1908) confirms the above conclusions, ex- 
cept that 4 per cent seems to be amply sufficient to cover the losses sus- 
tained by Illinois coals under regular storage-conditions, the larger 
losses indicated in the former series being probably due to the small size 
of the samples exposed. 

Investigations by the U. S. Bureau of IMines in 1910 (Technical 
Paper No. 2) showed that New River (Va.) coal lost less than 1% in 
heating value in one year by weathering in the open, and Pocahontas 
coal less than 4 ^d 

Pressed Fuel. (E. F. Loiseau, Trans. A. I. M. E., viii. 314.) — 
Pressed fuel has been made from anthracite dust by mixing the dust with 
ten per cent of its bulk of dry pitch, which is prepared by separating 
from tar at a temperature of 572° F. the volatile matter it contains. The 
mixture is kept heated by steam to 212°, at which temperature the pitch 
acquires its cementing properties, and is passed between two rollers, on 
the periphery of which are milled out a series of semi-oval cavities. The 
lumps of the mixture, about the size of an egg, drop out under the 
rollers on an endless belt, which carries them to a screen in eight minutes, 
which time is sufficient to cool the lumps, and they are then ready for 
delivery. 

The enterprise of making the pressed fuel above described was not 
commercially successful, on account of the low price of other coal. In 
France, however, ''briquettes'" are regularly made of coal-dust (bitu- 
minous and semi-bituminous). 

Experiments with briquets for use in locomotives have been made 
by the Penna. R. R. Co., with favorable results, which were reported at 
the convention on the Am. Ry. Mast. Mechs. Assn. (Eng. N'ews, July 2, 
1908). A rate of evaporation as high as 19 lb. per sq. ft. of heating 
surface per hour was reached. The comparative economy of raw coal 
and of briquets was as follows : 

Evap.persq. ft. heat. surf. per hr., lbs. 8 10 12 14 16 
Evap. from and at / Lloy dell coal. . . 9.5 8.8 8.0 7.3 6.6 
212° per lb. of fuel \ Briquetted coal. 10.7 10.2 9.7 9.2 8.7 

The fuel consumed per draw-bar horse-power with the locomotive 
running at 37.8 miles per hour and a cut-off of 25% was: with raw coal, 
4.48 lbs.; with round briquets, 3.65 lbs. 

Experiments on different binders for briquets are discussed by J. E. 
Mills in Bulletin No. 343 of the U. S. Geological Survey, 1908. 

Briquetting tests made at the St. Louis exhibition, 1904, with 



832 FUEL. 

descriptions of the machines used are reported in Bulletin No. 261 of 
the U.S. Geological Survey, 1905. See also paper on Coal Briquetting 
in the U. S.. by E. W. Parker, Trans. A. I. M. E., 1907. 

Spontaneous Combustion of Coal. (Technical Paper 10, U. S. 
Bureau of Mines, 1912.) — Spontaneous combustion is brought about 
by slow oxidation in an air supply sufficient to support the oxidation, 
but insufficient to carry away all the heat formed. Mixed lump and 
fine, i. e., run-of-mine, with a large percentage of dust, and piled so as 
to admit to the interior a limited supply of air, make ideal conditions 
for spontaneous heating. High volatile matter does not of itself in- 
crease the liabiUty to spontaneous heating. 

Pocahontas coal gives a great deal of trouble with spontaneous 
fires in the large storage piles at Panama. The liigh- volatile coals of the 
west are usually very liable to spontaneous heating. 

The influence of moisture and that of sulphur upon spontaneous 
heating of coal are questions not yet settled. Observation by the 
Bureau of ^Vlines in many actual cases has not developed any instances 
where moisture could be proven to promote heating. Sulphur has been 
shown to have, in most cases, only a minor influence. ^On the other 
hand, a Boston company, using Nova Scotia coal of 3 to 4 per cent 
sulphur, has much trouble with spontaneous fires in storage. 

Freshly mined coal and even fresh surfaces exposed by crushing 
lump coal exhibit a remarkable avidity for oxygen, but after a time be- 
come coated with oxidized material, "seasoned," as it were, so that the 
action of the air becomes much less vigorous. It is found that if coal 
which has been stored for six wrecks or two months and has even be- 
come already somewhat heated, be rehandled and thoroughly cooled 
by the air, spontaneous heating rarely begins again. 

Wliile the following recommendations may under certain conditions 
be found impracticable, they are offered as being advisable precautions 
for safety in storing coal whenever their use does not involve an un- 
reasonable expense. 

1. Do not pile over 12 feet deep nor so that any point in the interior 
will be over 10 feet from an air-cooled surface. 

2. If possible, store only in lump. 

3. Keep dust out as much as possible; therefore reduce handling 
to a minimum. 

4. Pile so that lump and fine are distributed as evenly as possible; 
not, as is often done, allowing lumps to roU down from a peak and form 
air passages at the bottom. 

5. Rehandle and screen after two months. 

6. Keep away external sources of heat even though moderate in 
degree. 

7. Allow six weeks' "seasoning" after mining before storing. 

8. Avoid alternate wetting and drying. 

9. Avoid admission of air to interior of pile through interstices 
around foreign objects such as timbers or irregidar brick work; also 
through porous bottoms such as coarse cinders. 

10. Do not try to ventilate by pipes, as more harm is often done 
than good. 

COKE. 

Coke is the solid material left after evaporating the volatile ingredi- 
ents of coal, either by means of partial combustion in furnaces called 
coke ovens, or by distillation in the retorts of gas-works. 

Coke made in ovens is preferred to gas coke as fuel. It is of a dark 
gray color, with slightly metallic luster, porous, brittle, and hard. 

The proportion of coke yielded by a given w^eight of coal is very differ- 
ent for different kinds of coal, ranging from 0.9 to 0.35. 

Being of a porous texture, it readily attracts and retains water from 
the atmosphere, and sometimes, if it is kept without proper shelter, 
from 0.15 to 0.20 of its gross weight consists of moisture. 



COKE. 



833 



Analyses of Coke. 

(From report of John R. Proctor, Kentucky Geological Survey.) 



Where Made. 


Fixed 
Carb'n. 


Ash. 


Sul- 
phur. 


Connellsville, Pa. (Average of 3 samples) 

Chattanooga, Tenn. " "4 " 

Birmingham, Ala " "4 " 

Pocahontas, Va. " "3 " 

New River, W. Va. " "8 " 

Big Stone Gap, Ky. ** "7 " 


88.96 
80.51 
87.29 
92.53 
92.38 
93.23 


9.74 
16.34 
10.54 
5.74 
7.21 
5.69 


0.810 
1.595 
1.195 
0.597 
0.562 
0.749 



Experiments in Coking. Connellsville Region. 
(Jolin Fulton, _A7ner. Mfr., Feb. 10, 1893.) 

















Per cent of Yield. 




M 


SO 




1 

s 

< 


O qJ 


O 

1^ 


0) 

o ^ 






d 


4 
< 


i 


1^* 


1" 






h. m. 


lb. 


lb. 


lb. 


lb. 


lb. 












1 


67 00 


12.420 


99 


385 


7.518 


7.903 


0.80 


3.10 


60.53 


63.63 


35.57 


2 


68 00 


11.090 


90 


359 


6.580 


6.939 


0.81 


3.24 


59.33 


62.57 


36.62 


3 


45 00 


9.120 


77 


272 


5.418 


5.690 


0.84 


2.98 


59.41 


62.39 


36.77 


4 


45 00 


9,020 


74 


349 


5,334 


5,683 


0.82 


3.87 


59.13 


63.00 


36.18 



These results show, in a general average, that Connellsville coal care- 
fully coked in a modern beehive oven will yield 66.17% of marketable 
coke, 2.30% of small coke or breeze, and 0.82% of ash. 

The total average loss in volatile matter expelled from the coal in 
coking amounts to 30.71 %. 

The beehive coke oven is 12 feet in diameter and 7 feet high at crown 
of dome. It is used in making 48 and 72 hour coke. [The Belgian type 
of beehive oven is rectangular in shape.] 

In making these tests the coal was weighed as it was charged into the 
oven; the resultant marketable coke, small coke or breeze and ashes 
weighed dry as they were drawn from the oven. 

Coal Washing. — In making coke from coals that are high in ash and 
sulphur, it is advisable to crush and wash the coal before coking it. A 
coal-washing plant at Brookwood, Ala., has a capacity of 50 tons per 
hour. The average percentage of ash in the coal during ten days' rim 
varied frorq 14 % to 21 % , in the washed coal from 4.8 % to 8.1 % , and in 
the coke from 6.1% to 10.5%. During three months the average re- 
duction of ash was 60.9%. {Eng. and Mining Jour., March 25, 1893.) 

An experiment on washing Missouri No. 3 slack coal is described in 
Bulletin No. 3 of the Engineering Experiment Station of Iowa State Col- 
lege, 1905. The raw coal analyzed: moisture, 14.37; ash, 28.39; sul- 
phur, 4.30; and the washed coal, moisture, 23.90; ash, 7.59; sulphur, 
2.89. Nearly 25 % of the coal was lost in the operation. 

Recovery of By-products in Coke Manufacture. — In Germany 
considerable progress has been made in the recovery of by-products. 
The Hoffman-Otto oven has been most largely used, its principal feature 
being that it is connected with regenerators. In 1884 40 ovens on this 
system were running, and in 1892 the number had increased to 1209. 

A Hoffman-Otto oven in Westphalia takes a charge of 6 1/4 tons of dry 
coal and converts it into coke in 48 hours. The product of an oven 
annually is 1025 tons in the Ruhr district, 1170 tons in Silesia, and 960 
tons in the Saar district. The yield from dry coal is 75% to 77% of 
coke, 2.5% to 3% of tar, and 1.1% to 1.2% of sulphate of ammonia in 
the Ruhr district; 65% to 70% of coke, 4% to 4.5% of tar, and 1% to 
1.25% of sulphate of ammonia in the Upper Silesia region, and 68% to 
72%, of coke, 4%, to 4.3% of tar and 1.8% to 1.9% of sulphate of 



834 



FUEL. 



ammonia in the Saar district. A group of 60 Hoffman ovens, therefore, 
yields annually the following: 



District. 



Ruhr 

Upper Silesia 
Saar 



Coke, 
tons. 



51.300 
48,000 
40.500 



Tar, 
tons. 



1.860 
3.000 
2.400 



Sulphate 
Ammo- 
nia, tons. 



780 
840 
492 



An oven which has been introduced lately into Germany in connection 
with the recovery of by-products is the Semet-Solvay, which works hot- 
ter than the Hoffman-Otto, and for this reason 73% to 77% of gas coal 
can be mixed with 23 % to 27 % of coal low in volatile matter, and yet 
yield a good coke. Mixtures of this kind yield a larger percentage of 
coke, but, on the other hand, the amount of gas is lessened, and there- 
fore the yield of tar and ammonia is not so great. 

The yield of coke by the beehive and the retort ovens respectively is 
given as follows in a pamphlet of the Solvay Process Co. : Connellsville 
coal: beehive, 66%, retort, 73%; Pocahontas: beehive, 62%, retort, 83%; 
Alabama: beehive, 60%, retort, 74%. (See article in Mineral Industry, 
vol. viii. 1900.) 

References: F. W. Luerman, Verein Deutscher Eisenhuettenleute 
1891, Iron Age, March 31, 1892; Amer. Mfr., April 28, 1893. An ex- 
cellent series of articles on the manufacture of coke, by John Fulton, of 
Johnstown, Pa., is pubUshed in the Colliery Engineer, beginning in 
January, 1893. 

Since the above was written, great progress in the introduction of coke 
ovens with by-product attachments has been made in the United States, 
especially by the Semet-Solvay Co., Syracuse, N. Y. See paper on The 
Development of the Modern By-product Coke-oven, by C. G. Atwater, 
Trans. A. /. M. E., 1902. 

Generation of Steam from Waste Heat and Gases of Coke-ovens. 
(Erskine Ramsey, Amer. Mfr., Feb. 16. 1894.) — The gases from a num- 
ber of adjoining ovens of the beeliive type are led into a long horizontal 
flue, and thence to a combustion-chamber under a battery of boilers. 
Two plants are in satisfactory operation at Tracy City, Tenn., and two 
at Pratt Mines, Ala. 

A Bushel of Coal. — The weight of a bushel of coal in Indiana is 70 
lbs.; in Penna., 76 lbs.; in Ala., Colo., Ga., lU., Ohio, Tenn., and W. 
Va., it is 80 lbs. 

A Bushel of Coke is almost uniformly 40 lbs., but in exceptional 
cases, when the coal is very hght, 38, 36. and 33 lbs. are regarded as a 
bushel, in others from 42 to 50 lbs. are given as the weight of a bushel; 
in this case the coke would be quite heavy. 

Products of the Distillation of Coal. — S. P. Sadler's Handbook of 
Industrial Organic Chemistry gives a diagram showing over 50 chemical 
products that are derived from distillation of coal. The first derivatives 
are coal-gas, gas-liquor, coal-tar, and coke. From the gas-liquor are 
derived ammonia and sulphate, chloride and carbonate of ammonia. 
The coal-tar is split up into oils lighter than water or crude naphtha, 
oils heavier than water — otherwise dead oil or tar, commonly called 
creosote, — and pitch. From the two former are derived a variety of 
chemical products. 

From the coal-tar there comes an almost endless chain of known com- 
binations. The greatest industry based upon their use is the manufac- 
ture of dyes, and the enormous extent to which this has grown can be 
judged from the fact that there are over 600 different coal-tar colors in 
use, and many more which as yet are too expensive for this purpose. 
Many medicinal preparations come from the series, pitch for paving 
purposes, and chemicals for the photographer, the rubber manufacturers 
and tanners, as well as for preserving timber and cloths. 

The composition of the hydrocarbons in a soft coal is uncertain and 
quite complex; but the ultimate analysis of the average coal shows that 
it approaches quite nearly to the composition of CH4 (marsh-gas). (W, 
H. Blauvelt. Trans, A, I. M. E., xx. 625.) 



WOOD AS FUEL. 



835 



WOOD AS FUEL. 

Wood, when newly felled, contains a proportion of moisture which 
varies very much in different kinds and in different specimens, ranging 
between 30% and 50%, and being on an average about 40%. After 8 
or 12 months ordinary drying in the air the proportion of moisture is 
from 20 to 25%. This degree of dryness, or almost perfect dryness if 
required, can be produced by a few days' drying in an oven supplied with 
air at about 240° F. When coal or coke is used as the fuel for that oven, 
1 lb. of fuel suffices to expel about 3 lb. of moisture from the wood. 
This is the result of experiments on a large scale by Mr. J. R. Napier. 
If air-dried wood were used as fuel for the oven, from 2 to 2 K lb. of 
wood would probably be required to produce the same effect. 

The specific gravity of different kinds of wood ranges from 0.3 to 1.2. 

Perfectly dry wood contains about 50 % of carbon, the remainder con- 
sisting almost entirely of oxygen and hydrogen in the proportions which 
form water. The coniferous family contains a small quantity of turpen- 
tine, which is a hydrocarbon. The proportion of ash in wood is from 
1 % to 5 % . The total heat of combustion of all kinds of wood, when dry, 
is almost exactly the same, and is that due to the 50% of carbon. 

The above is from Rankine: but according to the table by S. P. Sharp- 
less in Jour. C. I. W., iv. 36, the ash varies from 0.03% to 1.20% in 
American woods, and the fuel value, instead of being the same for all 
woods, ranges from 3667 (for white oak) to 5546 calories (for long-leaf 
pine) = 6600 to 9883 British thermal units for dry wood, the fuel value 
of 0.50 lb. carbon bemg 7300 B.T.U. 

Heating Value of Wood. — The following table is given in several 
books of reference, authority and quaUty of coal referred to not stated. 

The weight of one cord of different woods (thoroughly air-dried) in 

gounds is about as follows: - 

[ickory or hard maple . . 4500 equal to 1800 coal. 

White oak 3850 " 1540 " 

Beech, red and black oak 3250 " 1300 " 
Poplar, chestnut, & elm. . 2350 " 940 " 

The average pine 2000 " 800 " 

Referring to the figures in the last column, it is said: 
From the above it is safe to assume that 2 1/4 lb. of dry wood are equal 
to 1 lb. average quality of soft coal and that the full value of the same 
weight of different woods is very nearly the same — that is, a pound of 
hickory is worth no more for fuel than a pound of pine, assuming both to 
be dry. It is important that the wood be dry, as each 10% of water or 
moisture in wood will detract about 12% from its value as fuel. 

Taking an average wood of the analysis C51%,H6.5%,O42.0%, ash 
0.5%, perfectly dry, its fuel value per pound, according to Dulong's 

formula, V = 1^14,600 C + 62,OOo/h -^jl, is 8221 British thermal 

units. If the wood, as ordinarily dried in air, contains 25 % of moisture, 
then the heating value of a pound of such wood is three quarters of 
8221 =6165 heat-units, less the heat required to heat and evaporate the 
1/4 lb. of water from the atmospheric temperature, and to heat the steam 
made from this water to the temperature of the chimney gases, say 
150 heat-units per pound to heat the water to 212°, 970 units to evap- 
orate it at that temperature, and 100 heat-units to raise the temperature 
of the steam to 420° F., or 1220 in all = 305 for 1/4 lb., which, subtracted 
from the 6165, leaves 5860 heat-units as the net fuel value of the wood 
per poimd, or about 0.4 that of a pound of carbon. 

Composition of Wood. 
(Analysis of Woods, by M. Eugene Chevandier.) 



(Others give 2000.) 
( - 1715.) 

( " 1450.) 

( " 1050.) 

( " 925.) 



Woods. 


Carbon. 


Hydro- 
gen. 


Oxygen. 


Nitrogen. 


Ash. 


Beech 

Oak 

Birch 


49.36% 

49.64 

50.20 

49.37 

49.96 


6.01% 

5.92 

6.20 

6.21 

5.96 


42.69% 

41.16 

41.62 

41.60 

39.56 


0.91% 

1.29 

1.15 

0.96 

0.96 


1.06% 
1.97 
81 


Poplar 


1 86 


Willow 


3.37 


Average 


49.70% 


6.06% 


41.30% 


1.05% 


K80% 



836 



FUEL. 



The following table, prepared by M. Violette, shows the proportion of 
water expelled from wood at gradually increasing temperatures: 



Temperature. 


Water Expelled from 1 GO Parts of Wood. 


Oak. 


Ash. 


Elm. 


Walnut. 


257° Fahr 


15.26 
17.93 
32.13 
35.80 
44.31 


14.78 
16.19 
21.22 
27.51 
33.38 


15.32 

17.02 

36.94? 

33.38 

40.56 


15.55 


302° Fahr 


17.43 


347° Fahr 


21.00 


392° Fahr 


41.77? 


437° Fahr 


36.56 



The wood operated upon had been kept in store during two years. 
When wood which has been strongly dried by means of artificial heat is 
left exposed to the atmosphere, it reabsorbs about as much water as it 
contains in its air-dried state. 

A cord of wood =4 X 4 X 8 = 128 cu. ft. About 56% sohd wood and 
44% interstitial spaces. (Marcus Bull, Phila., 1829. J, C. I. W., vol. 
i. p. 293.) 

B. E. Fernow gives the percentage of solid wood in a cord as deter- 
mined oflacially in Prussia (J". C. I. W., vol. iii. p. 20): 
Timber cords, 74.07% = 80 cu. ft. per cord; 
Firewood cords (over 6'' diam.), 69.44% = 75 cu. ft. per cord; 
"Billet" cords (over S" diam.), 55.55% = 60 cu. ft. per cord; 
"Brush" woods less than 3'' diam., 18.52%; Roots, 37.00%. 

CHARCOAL. 

Charcoal is made by evaporating the volatile constituents of wood and 
peat, either by a partial combustion of a conical heap of the material to 
be charred, covered with a layer of earth, or by the combustion of a 
separate portion of fuel in a furnace, in which are placed retorts con- 
taining the material to be charged. 

According to Peclet, 100 parts by weight of wood when charred in a 
heap yield from 17 to 22 parts by weight of charcoal, and when charred 
in a retort from 28 to 30 parts. 

This has reference to the ordinary condition of the wood used in char- 
coal-making, in which 25 parts in 100 consist of moisture. Of the re- 
maining 75 parts the carbon amoimts to one half, or 37 3^ % of the gross 
weight of the wood. Hence it appears that on an average nearly half of 
the carbon in the wood is lost during the partial combustion in a heap, 
and about one quarter during the distillation in a retort. 

To char 100 parts by weight of wood in a retort, 12 H parts of wood 
must be burned in the furnace. Hence in this process the whole expen- 
diture of wood to produce from 28 to 30 parts of charcoal is 112 ^ parts; 
so that if the weight of charcoal obtained is compared with the whole 
weight of wood expended, its amount is from 25% to 27% and the pro- 
portion lost is on an average 11 H -i- 37 H =0.3, nearly. 

According to Peclet, good wood charcoal contains about 0.07 of its 
weight of ash. The proportion of ash in peat charcoal is very variable 
and is estimated on an average at about 0.18. (Rankine.) 

Much information concerning charcoal may be found in the Journal of 
the Charcoal-iron Workers' Assn., vols. i. to vi. From this source the 
following notes have been taken: 

Yield of Charcoal from a Cord of Wood. — From 45 to 50 bushels 
to the cord in the kiln, and from 30 to 35 in the meiler. Prof. Egleston 
in Trans. A. I. M. E., viii, 395, says the yield from kilns in the Lake 
Champlain region is often from 50 to 60 bushels for hard wood and 50 
for soft wood; the average is about 50 bushels. 

The apparent yield per cord depends largely upon whether the cord is 
a full cord of 128 cu. ft. or not. 

In a four months' test of a kiln at Goodrich, Tenn., Dr. H. M. Pierce 
found results as follows: Dimensions of kiln — inside diameter of base, 
28 ft. 8 in. ; diam. at spring of arch, 26 ft. 8 in. ; height of walls, 8 ft. ; rise 
of arch, 5 ft. ; capacity, 30 cords. Highest yield of charcoal per cord of 
wood (measured) 59.27 bushels, lowest 50.14 bushels, average 53.65 
bushels. No. of charges 12, length of each turn or period from one 
charging to another 11 days. (J. C. I. W.y vol. vi. p. 26.) 



MISCELLANEOUS SOLID FUELS. 



837 



Results from Different Methods of Charcoal 


-making. 






Character of Wood Used. 


Yield. 


it 

p w o 




Coaling Methods. 


a, J 

O fc. 


li 

1— I 




Odelstjerna's experiments 


Birch dried at 230 F 




35.9 
28.3 

24.2 

27.7 

25.8 
24.7 

18.3 
22.0 

17.1 






Mathieu's retorts, fuel ex- 
cluded 


TAir dry, a v. good yel- ) 

< low pine weighing > 
( abt. 28 lbs. per cu. ft. ) 

1 Good dry fir and pine, ) 
\ mixed. ^ J 
1 Poor wood, mixed fir ) 
( and pine. ) 
( Fir and white-pine ) 
] wood, mixed. Av. 25 J 
( lbs. per cu. ft. ) 
(Av. good yellow pine) 

< weighing abt. 25 lbs. > 
( percu.ft. ) 


77.0 
65.8 
81.0 

70.0 

72.2 

52.5 
54.7 

42.9 


63.4 

54.2 

66.7 

62.0 
59.5 

43.9 
45.0 

35.0 


15.7 


Mathieu's retorts, fuel in- 
cluded 


15.7 


Swedish ovens, av. results 

Swedish ovens, av. results 

Swedish meilers excep- 
tional 


13.3 

13.3 
13.3 


Swedish meilers, av. results 
American kilns, a v. results 
American meilers, av. re- 
sults 


13.3 
17.5 
17.5 







Consumption of Charcoal in Blast-furnaces per Ton of Pig Iron: 

average consumption according to census of 1880, 1.14 tons charcoal per 
ton of pig. The consumption at the best furnaces is much below this 
average. As low as 0.853 ton is recorded of the Morgan furnace; Bay 
furnace, 0.858; Elk Rapids, 0.884. (1892.) 

Absorption of Water and of Gases by Charcoal. — Svedlius, in his 
hand-book for charcoal-burners, prepared for the Swedish Government, 
says: Fresh charcoal, also reheated charcoal, contains scarcely any water, 
but when cool it absorbs it very rapidly, so that, after twenty-four hours, 
it may contain 4 % to 8 % of water. After the lapse of a few weeks the 
moisture of charcoal may not increase perceptibly, and may Ufe esti- 
mated at 10% to 15%, or an average of 12%. A thoroughly charred 
piece of charcoal ought, then, to contain about 84 parts carbon, 12 parts 
water, 3 parts ash, and 1 part hydrogen. 

M. Saussure, operating with blocks of fine boxwood charcoal, freshly 
burnt, found that by simply placing such blocks in contact with certain 
gases they absorbed them in the following proportion: 

Volumes. Volumes. 
Ammonia 90 . 00 Carbonic oxide 9 . 42 



Hydrochloric-acid gas 85 . 00 

Sulphurous acid 65 . 00 

Sulphuretted hydrogen .... 55 . 00 
Nitrous oxide (laughing-gas) 40 . 00 
Carbonic acid 35 . 00 



Oxygen 9 . 25 

Nitrogen 6 . 50 

Carburetted hydrogen 5 .00 

Hydrogen 1 . 75 



It is this enormous absorptive power that renders of so much value a 
comparatively slight sprinkling of charcoal over dead animal matter, as a 
preventive of the escape of odors arising from decomposition. 

In a box or case containing one cubic foot of charcoal may be stored 
without mechanical compression a httle over nine cubic feet of oxygen, 
representing a mechanical pressure of one hundred and twenty-six pounds 
to the square inch. From the store thus preserved the oxgyen can be 
drawn by a small hand-pump. 

MISCELLANEOUS SOLID FUELS. 

Dust Fuel — Dust Explosions. — Dust when mixed in air burns with 
such extreme rapidity as in some cases to cause explosions. Explosions 
of flour-mills have been attributed to ignition of the dust in confined 
passages. Experiments in England in 1876 on the effect of coal-dust in 
carrying flame in mines showed that in a dusty passage the flame from a 



838 FUEL* 

blown-out shot may travel 50 yards. Prof. F. A. Abel (Trans. A. I. M. E., 
xiii. 260) says that coal-dust in mines much promotes and extends 
explosions, and that it may readily be brought into operation as a 
fiercely burning agent which will carry flame rapidly as far as its mixture 
with air extends, and will operate as an explosive agent through the me- 
dium of a very small proportion of fire-damp in the air of the mine. 
The explosive violence of the combustion of dust is largely due to the 
instantaneous heating and consequent expansion of the air. (See also 
paper on "Coal Dust as an Explosive Agent." by Dr. R. W. Raymond, 
Trans. A. I. M. E., 1894.) Experiments made in Germany in 1893 
show that pulverized fuel may be burned without smoke, and with high 
economy. The fuel, instead of being introduced into the fire-box in the 
ordinary manner, is first reduced to a powder by pulverizers of any con- 
struction. In the place of the ordinary boiler fire-box there is a com- 
bustion chamber in the form of a closed furnace fined with fire-brick and 
provided with an air-injector. The nozzle throws a constant stream of 
fuel into the chamber, scattering it throughout the whole space of the 
fire-box. When this powder is once ignited, and it is very readily done 
by first raising the fining to a high temperature by an open fire, the 
combustion continues in an intense and regular manner under the action 
of the current of air which carries it in. (Mfrs. Record, April, 1893.) 

Records of tests with the Wegener powdered-coal apparatus, which is 
now (1900) in use in Germany, are given in Eng. News, Sept. 16, 1897. 
Illustrated descriptions of different forms of apparatus are given in the 
author's " Steam Boiler Economy." Coal-dust fuel is now extensively 
used in the United States in rotary kilns for burning Portland cement. 

Powdered fuel was used in the Crompton rotary puddhng-furnace at 
Woolwich Arsenal, England, in 1873. (Jour. I. & S. I., i. 1873, p. 91.) 
Numerous experiments on the use of powdered fuel for steam boilers 
were made in the U. S. between 1895 and 1905, but they were not com- 
merciaUy successful. 

Peat or Turf, as usually dried in the air, contains from 25 % to 30 % of 
water, which must be allowed for in estimating its heat of combustion. 
This water having been evaporated, the analysis of M. Regnault gives, 
in 100 parts of perfectly dry peat of the best quaUty: C, 58%; H, 6%; 
O, 31%; Ash, 5%. In some examples of peat the quantity of ash is 
greater, amounting to 7% and sometimes to 11%. 

The specific gravity of peat in its ordinry state is about 0.4 or 0.5. 
It can t)e compressed by machinery to a much greater density. (Rankine.) 

Clark (Steam-engine, i. 61) eives as the average composition of dried 
Irish peat: C, 59%; H, 6%; O^ 30%; N, 1.25%; Ash, 4%. 

Applying Dulong's formula to this analysis, we obtain for the heating 
value of perfectly dry peat 10,260 heat-units per pound, and for air- 
dried peat containing 25% of moisture, after making allowance for 
evaporating the water, 7,391 heat-units per poimd. 

A paper on Peat in the U. S., bv M. R. Campbell, will be found in 
Mineral Resources of the U. S. (U. S. Geol. Survey) for 1905, p. 1319. 

Sawdust as Fuel. — The heating power of sawdust is naturally the 
same per pound as that of the wood from which it is derived, but if 
allowed to get wet it is more fike spent tan (which see below). The 
conditions necessary for burning sawdust are that plenty of room should 
be given it in the furnace, and sufficient air supplied on the surface of 
the mass, preferably by means of a fan-blast. The same applies to shav- 
ings, refuse lumber, etc. Sawdust is frequently burned in saw-mills, etc., 
by being blown into the furnace by a fan-blast. 

Wet Tan Bark as Fuel. — Tan, or oak bark, after having been used 
in the processes of tanning, is burned as fuel. The spent tan consists of 
the fibrous portion of the bark. The principal cause of poor economy 
in the burning of tan bark besides the difficulty of securing good com- 
bustion in the furnace, is the amount of heat that is carried away in the 
shape of superheated steam in the chimney gases. If the bark, after 
partial drying by compression, were further dried in a rotary drier by 
waste heat from the chimney gases, there woiild be an important gain 
in economy. For calculations showing the advantages of drying, and 
for illustrations of tan-bark furnaces, see "Steam Boiler Economy." 

D. M. Myers (Trans. A. S. M. E., 1909) describes some experiments 
on tan as a boiler fuel. One hundred lb. of air-dried bark fed to the 
mill will produce 213 lb. of spent tan containing 65% moisture. Tak- 



MISCELLANEOUS SOLID FUELS. 



839 



ing 9500 B.T.U. as the heating value per lb. of dry tan and 500** F. as the 
temperature of the chimney gases, the available heat in 1 lb. of wet tan 
is 2665 B.T.U. Based on this value as much as 71% efiBciency has 
been obtained in a boiler test with a special furnace, or 1.93 lb. of 
water evaporated from and at 212° per lb. of wet tan. The average 
heating value of dry hemlock tan, as found by a bomb calorimeter in six 
tests by Dr. Sherman, is 9504 B.T.U. The composition of dry tan is 
Ash, 1.42; C, 51.80; H,6.04; O, 40.74. By Dulong's formula the heating 
value would be 8152 B.T.U. 

Straw as Fuel. (Eng'g Mechanics, Feb. 1893, p. 55.) — Experiments 
in Russia showed that winter-wheat straw, dried at 230° F., had the 
following composition, C, 46.1; H, 5.6; N, 0.42: O, 43.7; Ash, 4.1. Heat- 
ing value in British thermal imits: dry straw, 6290; with 6% water. 
5770; with 10% water, 5448. With straws of other grains the heating 
value of dry straw ranged from 5590 for buckwheat to 6750 for flax. 

Clark (S. E., vol. 1, p. 62) gives the mean composition of wheat and 
barley straw as C, 36; H, 5; O, 38; N, 0.50; Ash, 4.75; Water, 15.75, the 
two straws varying less than 1%. The heating value of straw of this 
composition, according to Dulong's formula, and deducting the heat 
lost in evaporating the water, is 5155 heat-units. Clark erroneously 
gives it as 8144 heat-units. 

Bagasse as Fuel in Sugar Manufacture. — Bagasse is the name given 
to refuse sugar-cane, after the juice has been extracted. Prof. L. A. 
Becuel, in a paper read before the Louisiana Sugar Chemists' Associa- 
tion, in 1892, says: " With tropical cane containing 12.5% woody fibre, a 
juice containing 16.13% soUds, and 83.87% water, bagasse of. say, 66% 
and 72% mill extraction has the following percentage composition: 

66% bagasse: Woody Fibre, 37; Combustible Salts, 10; Water, 53. 

72% bagasse: Woody Fibre, 45; Combustible Salts, 9; Water, 46. 

"Assuming that the woody fibre contains 51% carbon, the sugar and 
other combustible matters an average of 42.1%, and that 12,906 units 
of heat are generated for every pound of carbon consumed, the 66% 
bagasse is capable of generating 297,834 heat-units per 100 lb. as against 
345,200, or a difference of 47,366 units in favor of the 72% bagasse. 

''Assuming the temperature of the waste gases to be 450° F., that of 
the surrounding atmosphere and water in the bagasse at 86° F., and the 
quantity of air necessary for the combustion of one pound of carbon at 
24 lb., the lost heat will be as follows: In the waste gases, heating air 
from 86° to 450°F., and in vaporizing the moisture, etc., the 66 % bagasse 
will require 112,546 heat-units, and 116,150 for the 72% bagasse. 

"Subtracting these quantities from the above, we find that the 66% 
bagasse will produce 185,288 available heat-units per 100 lb., or nearly 
24 % less than the 72 % bagasse, which gives 229,050 units. Accordingly 
one ton of cane of 2000 lb. at 66 % mill extraction will produce 680 lb. 
bagasse, equal to 1.259,958 available heat-units, while the same cane at 
72% extraction will produce 560 lb. bagasse, equal to 1,282,680 units. 

"A similar calculation for the case of Louisiana cane containing 10% 
woody fiore, and 16% total soUds in the juice, assuming 75% mill ex- 
traction, shows that bagasse from one ton of cane contains 1,573,956 
heat-units, from which 561,465 have to be deducted, which makes such 
bagasse worth on an average nearly 92 lb. coal per ton of cane ground. 

"It appears that with the best boiler plants, those taking up all the 
available heat generated, by using this heat economically the bagasse 
can be made to supply all the fuel required by our sugar-houses." 

The figures below are from an article by Samuel Vickess {The Engineer, 
Chicago, April 1, 1903). 

When canes with 12% fibre are ground, the juice extractions and 
liquid left in the residual bagasse are generally as follows : 



With 


Per Cent of Normal 

Juice Extracted on 

Weight of Cane. 


Per Cent of Liquid 
I^eft in Bagasse on 
Weight of Bagasse. 


Double crushing 


70 
62 
72 
76 

82 


60 


Single crushing 


68 


Crusher and double crushing 

Triple Crushing 


57 
50 


Crusher and triple crushing with 
saturation 


50 



840 



FUEL. 



The value of bagasse as a fuel depends upon the amount of woody 
fibre it contains, and the amount of combustible matter (sucrose, 
glucose, and gums), held in the liquid it retains. 100 lb. cane with 
triple crushing gives 76 lb. juice, and 24 lb. bagasse, which consists of 12 
lb. fibre and 12 lb. juice. The 12 lb. of juice contains 16% or 1.92 lb. 
sucrose, 0.5% or 0.06 lb. glucose, 2,5% other organic matter and 1% or 
0.12 lb. ash, making a total of 20%, or 2.4 lb. of solid matter, and 80% 
or 9.6 lb. of water. Reducing these figures to quantities corresponding 
to 1 lb. of bagasse, and multii)lying by the heating values of the several 
substances as given by Stohlmann, viz.: fibre, 7461; sucrose, 6957; 
glucose, 6646; organic matter, 7461, w^e find the heating value of the com- 
bustible in 1 lb. of bagasse to be 4397 B.T.U. This is the gross heating 
value which would be obtained in a calorimeter in which the products 
of combustion were cooled to the temperature of the atmosphere. To 
find approximately the heat available for generating steam in a boiler 
we may assume that 10 lb. of air is used in burning each pound of ba- 
gasse, that the atmospheric temperature is 82° and the flue gas tempera- 
ture 462°, and that in addition to the 0.4 lb. w^ater per lb. bagasse half 
of the remaining 0.6 lb. is oxygen and hydrogen in proportions which 
form water, making 0.7 lb. water w^hich escapes in the flue gas as super- 
heated steam. The heat lost in the flue gases per pound of bagasse is 
10 X 0.24 X (462 - 82) + 0.7 [(212 - 82) + 970 + 0.5 (462 - 212)] = 1770 
B.T.U. , which subtracted from 4397 leaves 2627 B.T.U. as the net or 
available heating value, wliich is equivalent to a,n evaporation of 2.7 lb. 
of water from and at 212°. Mr. Vickess states that in practice 1 lb. of 
such green bagasse evaporates 2 to 21/4 lb. from feed water at 100° 
Into steam at 90 lb. pressure. This is equivalent to from 2.31 to 2.59 
lb. from and at 212°. 

E. W. Kerr, in Bulletin No. 117 of the Louisiana Agricultural Experi- 
ment Station, Baton R^uge, La., gives the results of a study of many 
different forms of bagasse furnaces. An equivalent evaporation of 2 1/4 
lb. of steam from and at 212° was obtained from 1 lb. of wet bagasse of 
a net calorific value of 3256 B.T.U. This net value is that calculated 
from the analysis by Dulong's formula, minus the heat required to 
evaporate the moisture and to heat the vapor to the temperature of the 
escaping chimney gases, 594° F. The approximate composition of 
bagasse of 75% extraction is given as 51% free moisture, and 28% of 
water combined with 21 % of carbon in the fibre and sugar. For the 
best results the bagasse should be burned at a high rate of combustion, 
at least 100 lb. per sq. ft. of grate per hour. Not more than 1.5 lb. of 
bagasse per sq. ft. of heating surface per hour should be burned under 
ordinary conditions, and not less than 1.5 boiler horse-power should be 
provided per ton of cane per 24 hours. 

For illustrations of bagasse furnaces see ** Steam Boiler Economy." 

LIQUID FUEL. 

Products of the Distillation of Crude Petroleum. 

Crude American petroleum of sp. gr. 0.800 may be split up by fractional 
distillation as follows (" Robinson's Gas and Petroleum Engines "): 



Temp, of 

Distillation 

Fahr. 


Distillate. 


Per- 
cent- 
ages. 


Specific 
Gravity. 


Flashing 

Point. 
Deg. F. 


113° 
113 to 140° 
140 to 158° 


Rhigolene. \ 


traces. 

1.5 

10. 
2.5 
2. 


.590 to .625 

.636 to .657 
.680 to .700 
.714 to .718 
.725 to .737 




Chymogene . ) 

Gasoline (petroleum spirit) . . 
Benzine, naphtha C,benzolene 

( Benzine, naphtha B 

\ Benzine, naphtha A 

( Polishing oils 




158 to 248° 
248° 


14 


to 

347° 


32 


338° and ) 

upwards. ) 

482° 


Kerosene (lamp-oil) 

Lubricating oil 


50. 

15. 
2. 
16. 


.802 to .820 
.850 to .915 


100 to 122 
230 




Paraffine wax 






Residue and Loss 







LIQUID FDEL. 



841 



Lima Petroleum, produced at Lima, Ohio, is of a dark green color, 
very fluid, and marks 48° Baume at 15° C. (sp. gr., 0.792). 

The distillation in fifty parts, each part representing 2% by volume, 
gave the following results: 



Per 


Sp. 


Per 


Sp. 


Per 


Sp. 


Per 


Sp. 


Per 


Sp. 


Per 


Sp. 


cent. 


Gr. 


cent. 


Gr. 


cent. 


Gr. 


cent. 


Gr. 


cent. 


Gr. 


cent. 


Gr. 


2 


.680 


18 


0.720 


34 0.764 


50 


.802 


68 


.820 


88 


0.815 


4 


.683 


20 


.728 


36 


.768 


52 ] 




70 


.825 


90 


.815 





.685 


22 


.730 


38 


.772 


to } 


.806 


72 


.830 






8 


.690 


24 


.735 


40 


.778 


58 J 




73 


.830 


92 ] 


10 


.694 


26 


.740 


42 


.782 


60 


.800 


76 


.810 


to } 




12 


.698 


28 


.742 


44 


.788 


62 


.804 


78 


.820 


100 


T5 


14 


.700 


30 


.746 


46 


.792 


64 


.808 


82 


.818 




S 


16 


.706 


32 


.760 


48 


.800 


66 


.812 


86 


.816 




« 












RETURNS. 













16 per cent naphtha, 70° Baume. 
68 per cent burning oil. 



6 per cent parafilne oil. 
10 per cent residuum. 



' The distillation started at 23° C, this being due to the large amount of 
naphtha present, and when 60 % was reached, at a temperature of 310° C. 
the hydrocarbons remaining in the retort were dissociated, when gases 
escaped, lighter distillates were obtained, and, as usual in such cases, the 
temperature decreased from 310° C. down gradually to 200° C, until 
75% of oil was obtained, and from this point the temperature remained 
constant until the end of the distillation. Therefore these hydrocarbons 
in statu moriendi absorbed much heat. (Jour. Am. Chem. Soc.) 

There is not a good agreement between the character of the materials 
designated gasoline, kerosene, etc., and the temperature of distillation 
and densities employed in different places. The following table shows 
one set of values that is probably as good as any. 



Name. 



Petroleum ether . 

Gasoline 

Naphtha C 

Naphtha B 

Naphtha A 

Kerosene 



Boiling 


Specific 


Density at 


Point. 


Gravity. 


59° F. 


°F. 




°Baume. 


104-158 


0.650-0.660 


85-80 


158-176 


.660- .670 


80-78 


176-212 


.670- 707 


78-68 


212-248 


.707- .722 


68-64 


248-302 


.722- .737 


64-60 


302-572 


.753- .864 


56-32 



Gasoline is different from a simple substance with a fixed boiling 
point, and therefore theoretical calculations on the heat of combustion, 
air necesi:ary, and conditions for vaporizing or carbureting air are of 
little value. (C. E. Lucke.) 

Value of Petroleum as Fuel. — Thos. Urquhart, of Russia iProc. 
Inst. M. E., Jan., 1889), gives the following table of the theoretical 
evaporative power of petroleum in comparison with that of coal, as 
determined by ^Messrs. Favre and Silbermann : 



Fuel. 



Penna. heavy crude oil ... , 
Caucasian light crude oil . . 
Caucasian heavy crude oil 

Petroleum refuse 

Good English coal. 



Specific 
Gravity 

at 
32° F., 
Water 
= 1.000 



0.886 
0.884 
0.938 
0.928 
1.380 



Chem. Comp. 



C. 


H. 


84.9 


13.7 


86.3 


13.6 


86.6 


12.3 


87.1 


11.7 


80.0 


5.0 



1.4 
0.1 
1.1 
1.2 
8.0 



Heating 
power, 
British 

Thermal 
Units. 



20.736 
22.027 
20,138 
19.832 
14.112 



Theoret. 

Evap., 

Lb. of 

Water per 

lb. Fuel, 

from and 

at 212° F. 



21.48 
22.79 
20.85 
20.53 
14.61 



In experiments on Russian railways with petroleum as fuel Mr. 
Urquhart obtained an actual efificiency equal to 82 % of the theoretical 



842 



FUEL. 



heating-value. The petroleum is fed to the furnace by means of a 
spray-injector driven by steam. An induced current of air is carried in 
around the injector-nozzle, and additional air is supplied at the bottom 
of the furnace. 

Beaumont, Texas, oil analyzed as follows (Eng. News, Jan. 30, 1902): 
C, 84.60; H, 10.90; S, 1.63; O, 2.87. Sp. gr.,0.92; flash point, 142° F.; 
burning point, 181° F. ; heating value per lb., by oxygen calorimeter, 
19,060 B.T.U. A test of a horizontal tubular boiler with this oil, by 
J. E. Denton gave an efficiency of 78.5 %. As high as 82 % has been re- 
ported for California oil. 

Bakersfleld, Cal., oil: Sp. gr. 16° Baume; Moisture, 1%; Sulphur, 
0.5%. B.T.U. per lb., 18,500. 

Redondo, Cal., oil, six lots: Moisture, 1.82 to 2.70%; Sulphur, 2.17 to 
2.60%; B.T.U. per lb., 17,717 to 17,966. Kilowatt-hours generated per 
barrel (334 lb.) of oil in a 5000 K.W. plant, using water-tube boilers^ 
and reciprocating engines and generators having a combined efficiency of 
90.2 to 94.75% (boiler economy and steam-rate of engine not stated). 
2000 K.W. load, 237.3; 3000 K.W., 256.7; 5000 K.W., 253.4; variable 
load, 24 hours, 243.8. (C. R. Weymouth, Trans. A. S. M. E., 1908.) 

The following table shows the relative values of petroleum and coal. 
It is based on the following assumed data: B.T.U. per lb. of oil, 19,000; 
sp. gr., 0.90 =7.57 lb. per gal ; 1 barrel = 42 gal. =315 lb. 



Coal, B.T.U. 


1 lb. oil 


1 barrel oil 


1 ton coal 


per lb. 


= lb. coal. 


= lb. coal. 


= barrels oil. 


10,000 


1.9 


598 


3.34 


11.000 


1.727 


544 


3.68 


12.000 


1.583 


499 


4.01 


13.000 


1.462 


460 


4.34 


14.000 


1.357 


427 


4.68 


15,000 


1.267 


399 


5.01 



From this table we see that if coal of a heating value of only 10,000 
B.T.U. per lb. costs $3.34 per ton, and coal of 14,000 B.T.U. per lb. costs 
$4.68 per ton, then the price of oil will have to be as low as SI a barrel 
to compete with coal; or, if the poorer coal is $3.34 and the better coal 
$4.68 per ton, then oil will be th6 cheaper fuel if it is below $1 per barrel. 

Heating Values of California Fuel Oils. 

(R. W. Fenn, Eng. News, May 13, 1909.) 



(3« 


Is 


-^5 




Thousands 
B.T.U. 
per bbl. 


OJQQ 






it 


Thousands 
B.T.U. 
per bbl. 


10 


1.000 


350 


18.380 


6442 


28 


0.887 


311 


19.460 


6051 


12 


0.986 


346 


18.500 


6394 


30 


0.875 


307 


19.580 


6008 


14 


0.972 


341 


18.620 


6345 


32 


0.865 


303 


19.700 


5973 


16 


0.959 


336 


18.740 


6302 


34 


0.854 


299 


19.820 


5935 


18 


0.947 


332 


18.860 


6257 


36 


0.844 


296 


19.940 


5901 


20 


0.934 


327 


18.980 


6212 


38 


0.835 


293 


20.050 


5865 


22 


0.922 


323 


19.100 


6173 


40 


0.825 


289 


20.150 


5827 


24 


0.910 


319 


19.220 


6133 


42 


0.816 


286 


20.250 


5789 


26 


0.899 


315 


19.340 


6093 


44 


0.806 


283 


20.350 


5751 



Fuel Oil Burners. — A great variety of burners are on the market, 
most of them based on the principle of using a small jet of steam at the 
boiler pressure to inject the oil into the furnace, in the shape of finely 
divided spray, and at the same time to draw in the air supply and mix it 
intimately with the oil. So far as economy of oil is concerned these 
burners are all of about equal value, but their successful operation de- 
pends on the construction of the furnace. This should have a large 
combustion chamber, entirely surrounded with fire brick, and the 
jet should be so directed that it will strike a fire-brick surface and re- 
bound before touching the heating surface of the boiler. Burners 



ALCOHOL AS FUEL. 843 

using air at high pressure, 40 lb. per sq. in., without steam, have been 
used with advantage. Lower pressures have been found not suflQcient 
to atomize the oil. Mechanical atomizers have now (1915) largely 
replaced steam jet oil burners. See "Steam Boiler Economy." 

When boilers are forced, with a combustion chamber too small to 
allow the oil spray to be completely burned in it before passing to the 
boiler surface, dense clouds of smoke result, with a deposit of lampblack 
or soot. 

Crude Petroleum vs. Indiana Block Coal for Steam-raising at 
the South Chicago Steel Works.— (E. C. Potter, Trans. A. I. M. E., 
xvii. 807.) — With coal, 14 tubular boilers 16 ft. X 5 ft. required 25 men 
to operate them; with fuel oil, 6 men were required, a saving of 19 men 
at $2 per day, or $38 per day. 

For one week's work 2731 barrels of oil were used, against 848 tons of 
coal required for the same work, showing 3.22 barrels of oil to be equiva- 
lent to 1 ton of coal With oil at 60 cents per barrel and coal at $2.15 
per ton, the relative cost of oil to coal is as $1.93 to $2.15. No evapora- 
tion tests were made 

Petroleum as a Metallurgical Fuel.— C. E. Felton (Trans. A. I. 
M. E., xvii. 809) reports a series of trials with oil as fuel in steel-heating 
and open-hearth steel-furnaces, and in raising steam, with results as 
follows: 1. In a run of six weeks the consumption of oil, partly refined 
(the paraffine and some of the naphtha being removed), in heating 14- 
inch ingots in Siemens furnaces was about 6 1/2 gallons per ton of blooms. 
2. In melting in a 30-ton open-hearth furnace 48 gallons of oil were used 
per ton of ingots. 3. In a six weeks' trial with Lima oil from 47 to 54 
gallons of oil were required per ton of ingots. 4. In a six months' trial 
with Siemens heating-furnaces the consumption of Lima oil was 6 gal- 
lons per ton of ingots. Under the most favorable circumstances, 
charging hot ingots and running full capacity, 41/2 to 5 gallons per ton 
were required. 5. In raising steam in two 100-H.P. tubular boilers, the 
feed-water being supplied at 160° F., the average evaporation was about 
12 pounds of water per pound of oil, the best 12 hours' work being 16 
pounds. 

Specifications for the Purchase of Fuel Oil.— The U. S. government 
specifications for the purchase of fuel oil (1914) contain the following 
requirements : 

The oil should not have been distilled at a temperature high enough 
to burn it, nor at a temperature so high that flecks of carbonaceous mat- 
ter begin to separate. 

It should not flash below 140° F., in a closed Abel-Pensky or Pensky- 
Martins tester. 

The specific gravity should range from 0.85 to 0.96 at 59° F. 

It should flow readily, at ordinary atmospheric temperatures and 
under a head of 1 ft. of oil, through a 4-in. pipe 10 ft. in length. 

It should not congeal nor become too sluggish to flow at 32° F. 

It should have a calorific value of not less than 18,000 B.T.U. per lb. 
A bonus is to be paid or a penalty deducted as the fuel oil delivered 
is above or below the standard. 

It should be rejected if it contains more than 2% water, more than 
1% sulphm", or more than a trace of sand, clay or dirt. 

ALCOHOL AS FUEL. 

Denatured alcohol is a grain or ethyl alcohol mixed with a denaturant 
in order to make it unfit for beverage or medicinal purposes. Under acts 
of Congress of June 7, 1906, and March 2, 1907, denatured alcohol 
became exempt from internal revenue taxation, when used in the 
industries. 

The Government formulae for completely denatured alcohol are: 

1. To every 100 gal. of ethyl or grain alcohol (of not less than 180% 
proof) there shall be added 10 gal. of approved methyl or wood alcohol 
and H gal. of approved benzine. (180% proof = 90% alcohol, 10% 
water, by volume.) 

2. To every 100 gal. of ethyl alcohol (of not less than 180% proof) 
there shall be added 2 gal. of approved methyl alcohol and H gal. of 
approved pyridin (a petroleum product) bases. 



844 



FUEL. 



Methyl alcohol, benzine and pyridin used as denatiirants must con- 
form to specifications of the Internal Revenue Department. 

The alcohol which it is proposed to manufacture under the present 
law is ethyl alcohol, C2H0OH. This material is seldom, if ever, obtained 
pure, it being generally diluted with water and containing other alco- 
hols when used for engines. 

Specific Gravity of Ethyl Alcohol at 60° F. Compared with 
Water at 60°. (Smithsonian Tables.) 



Sp. Gr. 


Per cent Al- 
cohol. 


Sp. Gr. 


Per cent Al- 
cohol. 


Sp. Gr. 


Per cent Al- 
cohol. 




Weight. 


Vol. 


Weight. 


Vol. 


Weight. 


Vol. 


0.834 
.832 
.830 
.828 


85.8 
86.6 
87.4 
88.1 


90.0 
90.6 
91.2 
91.8 


0.826 
.824 
.822 
.820 


88.9 
89.6 
90.4 
91.1 


92.3 
92.9 
93.4 
94.0 


0.818 
.816 
.814 
.812 


91.9 
92.6 
93.3 
94.0 


94.5 
95.0 
95.5 
96.0 



The heat of combustion of ethyl alcohol, 94% by volume, as deter- 
mined by the calorimeter, is 11,900 B.T.U. per lb. — a little more than 
half that of gasoline (Lucke). Favre and Silbermann obtained 12,913 
B.T.U for absolute alcohol. Dulong's formula for C2H5OH gives 
13,010 B.T.U. 

The products of complete combustion of alcohol are H2O and CO2. 
Under certain conditions, with an insufficient supply of air, acetic acid is 
formed, which causes rusting of the parts of an alcohol engine. This 
may be prevented b3" addition to the alcohol of benzol or acetylene. 

With any good small stationary engine as small a consumption as 0.70 
lb. of gasoline, or 1.16 lb. of alcohol per brake H.P. hour may reasonably 
be expected under favorable conditions (Lucke) . 

References. — H. Diederichs, Intl. Marine Eng'g, July, 1906; Machy., 
Aug., 1906. C. E. Lucke and S. M. Woodward, Farmer's Bulletin, No, 
277. U. S. Dept. of Agriculture, 1907. Eng. Rec, Nov. 2, 1907. T. L. 
White, Eng. Mag., Sept., 1908. 

Vapor Pressure of Saturation for Various Liquids, in 

IMlLLIMETERS OF :MERCURY. 

(To convert into pounds per sq. in., multiply by 0.01934; to convert 
into inches of mercury, multiply by 0.03937.) 



Tem- 
pera- 


Pure 


Pure 






Tem- 
pera- 


Pure 


Pure 






Ethyl 
Alco- 


Methyl 
Alco- 


Water. 


Gaso- 
line. 


Ethyl 
Alco- 


Methyl 
Alco- 


Water. 


Gaso- 
line. 


ture. 


hol. 


hol. 






ture. 


hol. 


hol. 






oc. 


p 










° C. 


p^ 













32 


12 


30 


5 


99 


35 


95 


103 


204 


42 


301 


5 


41 


17 


40 


7 


115 


40 


104 


134 


259 


55 


360 


10 


50 


24 


54 


9 


133 


45 


113 


172 


327 


71 


422 


15 


59 


32 


71 


13 


154 


50 


122 


220 


409 


92 


493 


20 


68 


44 


94 


17 


179 


55 


131 


279 


508 


117 


561 


25 


77 


59 


123 


24 


210 


60 


140 


350 


624 


149 


648 


30 


86 


78 


159 


32 


251 


65 


149 


437 


761 


187 


739 



Vapor Tension of Alcohol and Water, and Degree of Saturation 
OF Air with these Vapors. 





Vapor Tension, Inches 
Mercury. 


1 Pound of Air Contains in Saturated 
Condition, in Pounds. 


Temp^ 
Degs. F. 


At 28.95 Inches. 


At 26.05 Inches. 


Alcohol 
Vapor. 


Water 
Vapor. 


Alcohol. 
Vapor. 


Water. 
Vapor. 


Alcohol 
Vapor. 


Water. 
Vapor. 


50 
59 
68 
77 
86 
104 
122 


0.950 
1.283 
1.723 
2.325 
3.090 
5.270 
8.660 


0.359 
0.500 
0.687 
0.925 
1.240 
2.162 
3.620 


0.055 
0.075 
0.104 
0.144 
0.200 
0.390 
0.827 


0.008 
0.011 
0.016 
0.022 
0.031 
0.063 
0.135 


0.061 
0.084 
0.117 
0.162 
0.227 
0.450 
1.002 


0.009 
0.013 
0.018 
0.025 
0.036 
0.072 
0.164 



FUEL GAS. 843 

FUEL GAS. 

The following notes are extracted from a paper by W. J. Taylor on 
"The Energy of Fuel" (Trans. A. I. M. E., xviii. 205): 

Carbon Gas. — In the old Siemens producer, practically all the heat 
of primary combustion — that is, the burning of sohd carbon to carbon 
monoxide, or about 30% of the total carbon energy — was lost, as httle 
or no steam was used in the producer, and nearly all the sensible heat of 
the gas was dissipated in its passage from the producer to the furnace, 
which was usually placed at a considerable distance. 

Modern practice has improved on this plan, by introducing steam 
with the air blown into the producer, and by utilizing the sensible heat of 
the gas in the combustion-furnace. It ought to be possible to oxidize 
one out of every four lbs. of carbon with oxygen derived from water- 
vapor. The thermic reactions in this operation are as follows: 

^ , Heat-units. 

4 lbs. C burned to CO (3 lbs. gasified with air and 1 lb. with 

water) develop 17,600 

1.5 lbs. of water (which furnish 1.33 lbs. of oxygen to combine 

with 1 lb. of carbon) absorb by dissociation 10,333 

The gas, consisting of 9.333 lbs. CO, 0.167 lb. H, and 13.39 lbs. N, 

heated 600°, absorbs 3,748 

Leaving for radiation and loss 3,519 

17,600 
The steam which is blown into a producer with the air is almost all con- 
densed into finely-divided water before entering the fuel, and conse- 
quently is considered as water in these calculations. 

The 1.5 lbs. of water liberates 0,167 lb. of hydrogen, which is delivered 
to the gas, and yields in combustion the same heat that it absorbs in the 
producer by dissociation. According to this calculation, therefore, 60% 
of the heat of primary combustion is theoretically recovered by the dis- 
sociation of steam, and, even if all the sensible heat of the gas be counted, 
with radiation and other minor items, as loss, yet the gas must carry 
4 X 14,500 - (3748 + 3519) = 50,733 heat-units, or 87% of the calo- 
rific energy of the carbon. This estimate shows a loss in conversion of 
13%, without crediting the gas with its sensible heat, or charging it with 
the heat required for generating the necessary steam, or taking into 
account the loss due to oxidizing some of the carbon to CO2. In good 
producer-practice the proportion of CO2 in the gas represents from 4% 
to 7% of the C burned to CO2, but the extra heat of this combustion should 
be largely recovered in the dissociation of more water-vapor, and there- 
fore does not represent as much loss as it would indicate. As a con- 
veyer of energy, this gas has the advantage of carrying 4.46 lbs. less 
nitrogen than would be present if the fourth pound of coal had been 
gasified with air; and in practical working the use of steam reduces the 
amount of clinkering in the producer. 

Anthracite Gas. — In anthracite coal there is a volatile combustible 
varying in quantity from 1.5% to over 7%. The amount of energy 
derived from the coal is shown in the following theoretical gasification 
made with coal of assumed composition: Carbon, 85% ; vol. HC, 5%; ash, 
10%: 80 lbs. carbon assumed to be burned to CO; 5 lbs. carbon burned 
to CO2; three fourths of the necessary oxygen derived from air, and one 
fourth from water. 



-Products.- 



Process. Pounds. Cubic Feet. Anal, by Vol. 

80 lbs. C burned to CO 186.66 2529.24 33.4 

5 lbs. C burned to CO2 18.33 157.64 2.0 

5 lbs. vol. HC (distilled) 5.00 116.60 1.6 

120 lbs. oxygen are required, of 
which 30 lbs. from H2O Uber- 

ateH 3.75 712.50 9.4 

90 lbs. from air are associated 

withN.., 301.05 4064.17 53.6 

514.79 7580.15 100.0 



846 FUEL. 

Energy In the above gas obtained from 100 lbs. anthracite: 

186.66 lbs CO 807,304 heat-units. 

6.00 *• CH4 117,500 

3.75 •• H 232,500 

1,157,304 

Total energy in gas per lb 2,248 " 

Total energy in 100 lbs. of coal 1,349,500 " 

Efficiency of the conversion 86%. 

The sum of CO and H exceeds the results obtained in practice. The 
sensible heat of the gas will probably account for this discrepancy and, 
therefore, it is safe to assume the possibility of delivering at least 82% 
of the energy of the anthracite. 

Bituminous Gas. — A theoretical gasification of 100 lbs of coal, con- 
taining 55% of carbon and 32% of volatile combustible (which is above 
the average of Pittsburgh coal), is made in the following table. It is 
assumed that 50 lbs. of C are burned to CO and 5 lbs. to CO2; one fourth 
of the O is derived from steam and three fourths from air; the heat value 
of the volatile combustible is taken at 20,000 heat-units to the pound. 
In computing volumetric proportions all the volatile hydrocarbons, 
fixed as well as condensing, are classed as marsh-gas, since it is only by 
some such tentative assumption that even an approximate idea of the 
volumetric composition can be formed. The energy, however, is calcu- 
lated from weight: 



-Products.- 



Process. Pounds. Cubic Feet. Anal, by Vol. 

50 lbs. C burned to CO 116.66 1580.7 27.8 

5 lbs. C burned to CO2 18.33 157.6 2.7 

32 lbs. vol. HC (aistilled) .... 32 . 00 746 . 2 13.2 

80 lbs. O are required, of which 20 
lbs., derived from H2O, liber- 
ate H 2.5 475.0 8.3 

60 lbs. O, derived from air, are as- 
sociated with N 200.70 2709.4 47.8 



• 370.19 5668.9 99.8 

Energy in 116.66 lbs. CO 504,554 heat-units. 

•• 32.00 lbs. vol. HC 640,000 

2.50 lbs. H 155,000 



1,299,554 
Energy in coal 1,437,500 

Ser cent of energy delivered in gas 90,0 
eat-units in 1 lb. of gas 3,484 

Water-gas. — Water-gas is made in an intermittent process, by blow- 
ing up the fuel-bed of the producer to a high state of incandescence (and 
in some cases, utilizing the resulting gas, which is a lean producer-gas), 
then shutting off the air and forcing steam through the fuel, which dis- 
sociates the water into its elements of oxygen and hydrogen, the former 
combining with the carbon of the coal, and the latter being liberated. 

This gas can never play a very important part in the industrial field, 
owing to the large loss of energy entailed in its production, yet there are 
places and special purposes where it is desirable, even at a great excess 
in cost per unit of heat over producer-gas; for instance, in small high- 
temperature furnaces, where much regeneration is impracticable, or 
where the "blow-up" gas can be used for other purposes instead of being 
wasted. 

The reactions and energy required in the production of 1000 feet of 
water-gas, composed, theoretically, of equal volumes of CO and H, are aa 
follows: 

500 cubic feet of H weigh 2 . 635 lbs. 

500 cubic feet of CO weigh 36.89 " 

Total weight of 1000 cubic feet 39 . 525 lbs. 

Now, as CO is composed of 12 parts C to 16 of O, the weight of C in 
36.89 lbs. is 15.81 lbs. and of O 21.08 lbs. When this oxygen is derived 



FUEL GAS. 



847 



from water it liberates, as above, 2.635 lbs. of hydrogen. The heat de- 
veloped and absorbed in these reactions (roughiy, as we will not take 
into account tlie energy required to elevate the coal from the tempera- 
ture of the atmosphere to, say, 1800°) is as follows: Hoat iin't 
2.635 lbs. H. absorb in dissociation from water 2.635 X 62,000 = 163,370* 

15.81 lbs. C burned to CO develops 15.81 X 4400 = 69,564 

Excess of heat-absorption over heat-development = 93,806 

If this excess could be made up from C burnt to CO2 without loss by 
radiation, we would only have to burn an additional 4.83 lbs. C to supply 
this heat, and we could then make 1000 feet of water-gas from 20.64 lbs. 
of carbon (equal 24 lbs. of 85 % coal) . This would be the perfection of 

gas-making, as the gas would contain really the same energy as the coal; 
but instead, we require in practice more than double this amount of coal 
and do not deliver more than 50% of the energy of the fuel in the gas, 
because the supporting heat is obtained in an indirect way and with 
imperfect combustion. Besides this, it is not often that the sum of CO 
and H exceed 90%, the balance being CO2 and N. But water-gas should 
be made with much less loss of energy by burning the "blow-up" (pro- 
ducer) gas in brick regenerators, the stored-up heat of which can be 
returned to the producer by the air used in blowing-up. 

The following table shows what may be considered average volumetric 
analyses, and the weight and energy of 1000 cubic feet, of the four types 
of gases used for heating and illuminating purposes: 





Natural 
Gas. 


Coal- 
gas. 


Water- 
gas. 


Producer-gas. 
Anthra-I Bitu. 


CO 


0.50 
2.18 
92.6 
0.31 
0.26 
3.61 
0.34 


6.0 

46.0 

40.0 

4.0 

0.5 

1.5 

0.5 

1.5 

32.0 

735,000 


45.0 

45.0 

2.0 


27.0 

12.0 

1.2 


27.0 


H 


12.0 


CHt 


2.5 


C2H4 


0.4 


CO2 


4.0 
2.0 
0.5 
1.5 
45.6 
322,000 


2.5 

57.0 

0.3 


2.5 


N 


56.2 





0.3 


Vapor . 




Pounds in 1000 cubic feet 

Heat-units in 1000 cubic feet 


45.6 
1,100,000 


65.6 
137,455 


65.9 
156,917 



Natural Gas in Ohio and Indiana. 

(Eng. and M. J., April 21. 1894.) 



Fos- 


Find- 


St. 


Muncie, 
Ind. 


Ander- 


Koko- 


toria, 


lay, 


Mary's, 


son, 


mo, 


0. 


0. 


0. 


Ind. 


Ind. 


1.89 


1.64 


1.94 


2.35 


1.86 


1.42 


92.84 


93.35 


93.85 


92.67 


93.07 


94.16 


.20 


.35 


.20 


.25 


.47 


.30 


.55 


.41 


.44 


.45 


.73 


.55 


.20 


.25 


.23 


.25 


.26 


.29 


.35 


.39 


.35 


.35 


.42 


.30 


3.82 


3.41 


2.98 


3.53 


3.02 


2.80 


.15 


.20 


.21 


.15 


15 


.18 



Mar- 
ion, 
Ind. 



Hydrogen 

Marsh-gas 

defiant gas.... 

Carbon monoxide . 
Carbon dioxide... . 

Oxygen 

Nitrogen 

Hydrogen sulphide 



1.20 
93.57 
.15 
.60 
.30 
.55 
3.42 
.20 



Natural Gas as a Fuel for Boilers. — J. M. Whitham (Trans. A. S. 
M. E., 1905) reports the results of several tests of water-tube boilers with 
natural gas. The following is a condensed statement of the results : 



Kind of Boiler. 



iCook Vertical, 



Heine. 



Cahall Vert. 



Rated H.P. of boilers 

H.P. developed 

Temperature at chimney 
Gas pressure at burners, oz. 
Cu. ft. of gas per boiler. . 

H.P.-hour 

Boiler efficiency. % 



1500 

1642 

521 

6.9 

44.9* 
72.7 



1500 
1507 
494 
6.4 

41.0* 



200 200 200 
155 218 258 
386 450 465 



46. Of 40. 7t 38.3+ 
65.8 ... 74.9 



300 300 

340 260 

406 374 

4.8 7to30 



42.3 



34 



*Reduced to 4 oz. press, and 62° F. fReduced to atmos. press, and 32° F. 



848 



FUEL. 



Six tests by Daniel Ashworth on 2-flue horizontal boilers gave cu. ft. ot 
gas per boiler H.P. hour, 58.0; 59.7; 67.0; 63.0; 74.0; 47.0. 

On the first Cook boiler test, the chimney gas, analyzed by the Orsat 
apparatus, showed 7.8 CO2; 8.05 O; 0.0 CO; 84.15 N. Tliis shows an 
excessive air supply. 

White versus Blue Flame. — Tests were made with the air supply throt- 
tled at the burners, so as to produce a white flame, and also unthrottled, 
producing a blue flame with the following results: 



Pressure of gas at burners, oz 


4 




6 




8 




Kind of flame 

Boiler H.P. made per 250-H.P. boiler 
Cu. ft. of gas (at 4 oz. and 60° F.) per 

H.P. hour 

Chimney temperature 


White 
247 

41 

436 


Blue 
213 

41 
503 


White 
297 

41.6 
478 


Blue 
271 

37.9 
511 


White 
255 

43 
502 


Blue 
227 

43.1 
508 



Average of 6 tests — White, 266 H.P., 43.6 cu. ft.: Blue, 237 H.P., 
43.8 cu. ft., showing that the economy is the same with each flame, but 
the capacity is greatest with the white flame. Mr. Whitham's principal 
conclusions from these tests are as follows: 

(1) There is but little advantage possessed by one burner over another. 

(2) As good economy is made with a blue as with a white or straw flame, 
and no better. 

(3) Greater capacity may be made with a straw'-white than with a blue 
flame. 

(4) An efficiency as high as from 72 to 75 per cent in the use of gas is 
seldom obtained under the most expert conditions. 

(5) Fuel costs are the same under the best conditions with natural gas 
at 10 cents per 1000 cu. ft. and semi-bituminous coal at $2.87 per ton of 
2240 lbs. 

(6) Considering the saving of labor with natural gas, as compared with 
hand-firing of coal, in a plant of 1500 H.P., and coal at $2 per ton of 2240 
lbs., gas should sell for about 10 cents per 1000 cu. ft< 

Analyses of Natural Gas. 

lUuminants •.. 0.45 0.15 0.50 1.6 

Carbonic oxide . 00 . 00 0.15 1.8 

Hydrogen 0.20 0.30 0.25 0.3 

Marsh gas 81.05 83.20 83.40 81.9 

Ethane 17.60 15.55 15.40 13.2 

Carbonic acid *. . 00 . 20 . 00 0.0 

Oxvgen 0.15 0.10 0.00 0.4 

Nitrogen 0.55 . 50 . 30 0.8 

B.T.U. per cu. ft. at 60° F. and 

14.7 lbs. barometer 1030 1020 1026 1098 

The first three anal.yses are of the gas from nine wells in Lewis Co., 
W. Va. : the last is from a mixture from fields in three state* supplying 
Pittsburg, Pa., used in the tests of the Cook boilero 

Producer-gas from One Ton of CoaK 

(W. H. Blauvelt, Trans. A. I. M. E., xviii, 614.) 



Analysis by Vol. 



Per 
Cent. 



CO 

H 

CH4 

C2H4 

CO2 

N (by difference) 



25.3 
9.2 
3.1 
0.8 
3.4 

58.2 

100.0 



Cubic Feet. 


Lbs. 


33,213.84 

12,077.76 

4,069.68 

1,050.24 

4,463.52 

76,404.% 


2451.20 

63.56 

174.66 

77.78 

519.02 

5659.63 


131,280.00 


8945.85 





Equal to — 


1050.51 Ibs.C+ 1400.7 lbs. 0. 
63.56 '• H. 
174.66 " CH4. 
77.78 ♦' C2H4. 
141.54 •• C + 377. 44 lbs. 0. 
7350.17 " Air. 



FUEL GAS. 



849 



Calculated upon this basis, the 131,280 ft. of gas from the ton of coal 
contained 20,311,162 B.T.U., or 155 B.T.U. per cubic ft., or 2270 B. T.U. 
per lb. 

The composition of the coal from which this gas was made was as 
follows: Water, 1.26%; volatile matter, 36.22%; fixed carbon, 57.98%; 
sulphur, 0.70%; ash, 3.78%. One ton contains 1159.6 lbs. carbon and 
724.4 lbs. volatile combustible, the energy of which is 31,302,200 B.T.U. 
Hence, in the processes of gasification and purification there was a loss of 
35.2% of the energy of the coal. 

The composition of the hydrocarbons in a soft coal is uncertain and 
quite complex; but the ultimate analysis of the average coal shows that 
it approaches quite nearly to the composition of CH4 (marsh-gas). 

Mr. Blauvelt emphasizes the following points as highly important in 
soft-coal producer-practice: 

First. That a large percentage of the energy of the coal is lost when the 
gas is made in the ordinary low producer and cooled to the temperature of 
the air before being used. To prevent these sources of loss, the producer 
should be placed so as to lose as little as possible of the sensible heat of 
the gas, and prevent condensation of the hydrocarbon vapors. A high 
fuel-bed should be carried, keeping the producer cool on top, thereby 
preventing the breaking-down of the hydrocarbons and the deposit of 
soot, as well as keeping the carbonic acid low. 

Second. That a producer should be blown with as much steam mixed 
with the air as will maintain incandescence. This reduces the percentage 
of nitrogen and increases the hydrogen, thereby greatly enriching the gas. 
The temperature of the producer is kept down, diminishing the loss of heat 
by radiation through the walls, and in a large measure preventing clinkers. 

The Combustion of Producer-gas. (H. H. Campbell, Trans. A. I. 
M. E., xix, 128.) — The combustion of the components of ordinary pro- 
ducer-gas may be represented by the following formulae: 

C2H4 +60 = 2CO2 +2H2O; 2H +0 = H2O; 

GH4 + 4 O = CO2 + 2 H2O; CO + O = CO2. 

Average Composition by Volume of Producer-gas: A, made with 
Open Grates, no Steam in Blast; B, Open Grates, Steam- jet in 
Blast. 10 Samples of Each. 

: CO2. O. C2H4, CO. H. CH4. N. 

A min 3.6 0.4 0.2 20.0 5.3 3.0 58.7 

A max 5.6 0.4 0.4 24.8 8.5 5.2 64.4 

A average 4.84 0.4 0.34 22.1 6.8 3.74 61.78 

B min 4.6 0.4 0.2 20.8 6.9 2.2 57.2 

B max 6.0 0.8 0.4 24.0 9.8 3.4 62.0 

B average 5.3 0.54 0.36 22.74 8.37 2.56 60.13 

The coal used contained carbon 82%, hydrogen 4.7%. 

The following are analyses of products of combustion: 

CO2. O. CO. CH4. H. N. 

Minimum 15.2 0.2 trace. trace. trace. 80 . 1 

Maximum 17.2 1.6 2.0 0.6 2.0 83.6 

Average 16.3 0.8 0.4 0.1 0.2 82.2 

Proportions of Gas Producers and Scrubbers. (F. C. Tryon, Power, 
Dec. 1, 1908.) — Small inside diameter means excessive draft through the 
fire. If a fire is forced, as will be necessary with too small an inside diam- 
eter, the results will be clinkers and blow-holes or chimneys through the 
fire bed, with excess CO2 and weak gas; clinkers fused to the lining, and 
burning out of grates. If sufficient steam is used to keep down the ex- 
cessive heat, the result is likely to be too much hydrogen in the gas, with 
the attendant engine troubles. 

The lining should never be less than 9 in. thick even in the smaller sizes, 
and a 100-H.P., or larger, producer should have at least 12 in. of generator 
lining. The lining next to the fire bed should be of the best quality of 
refractory material. A good lining consists of a course of soft common 
bricks put in edgewise next to the steel shell of the generator, laid in 
Portland cement; then a good firebrick 6 in. thick laid inside to fit the 
circle, the bricks being dipped as laid in a fine grouting of ground firebrick. 

If we take IV4 lbs. of coal per H.P.-hour as a fair average and 10 lbs. of 



850 



FUEL. 



coal per hour per squaie foot of internal fuel-bed cross-section, with 9 in. 
of refractory lining up to 100 H.P. and at least 12 in. of lining on larger 
sizes, the generator will give good gas without forcing and without excess- 
ive heat in the zone of complete combustion. A 200-H.P. producer on 
this basis consumes 250 lbs. of coal at full load, and at 10 lbs. per sq. ft. 
internal area 25 sq. ft. will be necessary. With a 12-in. lining the outside 
diameter will be 92 in. 

Practice has shown that the depth of the fuel bed should never be less 
than the inside diameter up to 6 ft.; above this size the depth can be 
adjusted as experience indicates the best working results. Assuming for 
a 200-H.P. producer 18 in. for the ashpit below the grate, 12 in. for the 
thickness of the grate and the ashes to protect it, 68 in. depth of fuel bed, 
24 in. above the fuel to the gas outlet, the height will be 10 ft. 4 in, to the 
top of the generator; above this the coal-feeding hopper, say 32 in. high, 
is mounted; this makes the height over all 13 ft. 

The wet scrubber of a gas producer should be of ample size to cool the 
gas to atmospheric temperature and wash out most of the impurities. 
A good rule is to make its diameter three-fourths that of the inside diam- 
eter of the generator and the height one and one-half times the height of 
the generator shell. For a 100-H.P. producer, 4 ft. inside diam.,thewet 
scrubber should be 3 ft. inside diam., and if the generator shell is 8 ft. 
6 in. high, the scrubber should be 12 ft. 9 in. high. When filled with the 
proper amount of baffling and scrubbing material (coke is commonly 
used), the scrubber will have space for about 30 cu. ft. of gas. A 100-H.P. 
gas engine using 12,000 B.T.U. per H.P.-hour will use 160 cu. ft. of 125- 
B.T.U. gas per minute. The wet scrubber will therefore be emptied 51/3 
times every minute, and would require about 8 1/3 gallons of water per 
minute; if the diameter of the scrubber were reduced one-tliird the vol- 
ume of water necessary to cool and scrub the gas would have to be doubled. 
Gas must be cooled below 90° F. to enable it to give up the impurities it 
carries in suspension, and even lower than this te condense its moisture. 

A separate dry scrubber with two compartments should always be pro- 
vided and the piping between the two scrubbers so arranged that the gas 
can be turned into either part of the dry scrubber at will. The dry 
scrubber should be equal in area to the inside of the generator, and the 
depth of each part should be sufficient to accommodate at least 2 cu. ft. 
of scrubbing material and give 1 cu. ft. of space next to the outlet. Oil- 
soaked excelsior is a good scrubbing material and should be packed as 
closely as possible. 

Taking as the standard the dimensions above stated for the different 
parts of a producer-gas plant, a list of dimensions for different horse-power 
capacities would be about as in the following table. 





Dimensions 


OF Gas Producers and Scrubbers. 






Producers. 


Wet Scrub- 
bers. 


Dry 


Scrubbers. 


H.P. 


Inside 
Diam. 


Out- 

sid3 

Diam. 


Height. 


Diam. 


Height. 




Diam. 


Height. 




in. 


in. 


ft. in. 


in. 


ft. in. 




in. 


ft. in. 


25 


24 


42 


6 6 


18 


9 9 


Single.. . 


24 


3 


35 


28 


46 


6 10 


21 


10 3 


...do.... 


28 


3 


50 


34 


52 


7 4 


26 


11 


Double. 


34 


6 


60' 


37 


55 


7 7 


28 


11 5 


...do.... 


37 


6 


75 


42 


60 


8 


32 


12 


...do.... 


42 


6 


100 


48 


72 


8 6 


36 


12 9 


...do.... 


48 


7 


125 


54 


78 


9 6 


41 


14 3 


...do.... 


52 


7 


150 


58 


82 


9 10 


44 


14 9 


...do.... 


58 


7 6 


175 


63 


87 


10 3 


48 


15 5 


...do.... 


63 


7 6 


200 


68 


92 


10 8 


51 


16 


...do.... 


68 


7 6 



The inside diameter of the producers corresponds to the formula 
H.P. = Q.25dK 



GAS PRODUCERS. 851 

Gas Producer Practice. — The following notes on gas producers are 
condensed from the catalogue of the Morgan Construction Co. 

The Morgan Continuous Gas Producer is made in the following sizes: 

Diam. inside of Uiiing, ft 6 8 10 12 

Area of gas-making surface, sq. ft 28 50 78.5 113 

24-hour capacity uith good coal, tons 4 7 10 15 

Diam. of outlet, in 20 27 33 40 

The best coal to buy for a producer in any locality is that which by 
analysis or calorimeter test shows the most heat units for a dollar. It 
rarely pays to J)uy gas coal unless it can be had at a moderate cost over the 
ordinary steam bituminous grade. For very high temperature melting 
operations a fairly high percentage of volatile matter is necessary to give a 
luminous flame and intensify the radiation from the roof of the furnace. 
Freely burning gas coals are the most easily gasified, and the capacity of 
the producer to handle these coals is twice as great as when a slaty, dirty 
coal, high in ash and sulphur, is used. It is usually best to use "run-of- 
mine" coal, crushed at the mine to pass a 4-in. ring. It never pays to use 
slack coal, for it cuts down the capacity by choking the blast, which has 
to be run at high pressure to get through the fire, overheating the gas and 
lowering the efficiency of the producer. 

There is always a certain amount of CO2 formed, even in the best practice: 
in fact, it is inevitable, and if kept within proper limits does not constitute 
a net loss of efficiency, especially with very short gas flues, because the 
energj^ of the fuel so burned is represented in the sensible heat or tem- 
perature of the gas, and results in delivering a hot gas to the furnace. 
The best result is at about 4% CO2, a gas temperature between 1100° and 
1200° F., and flues less than 100 ft. long. 

The amount of steam required to blow a gas producer is from 33% to 
40% of the weight of the fuel gasified. If 30 lbs, of steam is called a 
standard horse-pow^er, we have therefore to provide about 1 H.P. of steam 
for every 80 lbs. of coal gasified per hour or for every ton of coal gasified in 
24 hours. 

In the ori^nal Siemens air-blown producer about 70% of the whole gas 
was inert and 30% combustible. Then with the advent of steam-blown 
producers the dilution was reduced to about 60%, with 40% combustible. 
Now, under the system of automatic feed, uniform conditions, perfect 
distribution and adjustment of the steam blast here presented, we are able 
to reduce the nitrogen to 50% and sometimes less. 

In the best practice the volume of gas from the producer is now reduced 
to about 60 cu. ft. per pound of coal, of which 30 cu. ft. are nitrogen. 
These volumes are measured at 60° F. 

The temperature of the gas leaving the producer under best modem 
conditions is about 1200° F. It cah be run cooler than this, but not much, 
except at a sacrifice of both quantity and quality. At this temperature, 
the sensible heat carried by the gas is 1200 X 0.35 (average specific heat) = 
420 B.T.U. per pound. As one pound of good gas is about 16 cu. ft. and 
carries about 16 X 180 = 2880 heat units at normal temperature, we see 
that the sensible heat carried away represents about one-seventh, or over 
14% of the combustive energy, which is much too large a percentage to lose 
whenever it can be utiUzed by using the gas at the temperature at which 
it is made. 

Capacity of Producers. — The capacity of a gas producer is a varying 
quantity, dependent upon the construction of the producer and upon the 
quahty of the coal suppUed to it. The point is, not to push the producer so 
hard as to burn up the gas within it; also to avoid blowing dust through 
into the flues. These two limitations in a well-constructed automatically 
fed gas producer occur at about the same rate of gasification, namely, 
at about 10 lbs. per sq. ft. of surface per hour with bituminous coal carry- 
ing 10% of ash and 1 1/2 % of sulphur. With gas coal, having high volatile 
percentage and low ash, this rate can be safely increased to 12 lbs. and in 
some cases to 15 lbs. per sq. ft. At 10 lbs. per sq. ft., the capacity of a 
gas producer 8 ft. internal diameter is 500 lbs. per hour, which with gas 
coals may be increased to a maximum of about 700 lbs. It frequently 
happens that the cheapest coal available is of such quahty that neither 
of these figures can be reached, and the gasification per sq. ft. has to be cut 
down to 6 or 7 lbs. per hour to get the best results. 



852 FUEL 

^ Flues, — It is necessary to provide large flue capacity and to carry the 
mil area right up to the furnace ports, which latter may be shghtly reduced 
to give the gas a forward impetus. Generally speaking, the net area of a 
flue should not be less than i/i6 of the area of the gas-making surface in the 
producers supplying it. Or it may be stated thus: — The carrying capa- 
city of a hot gas flue is equivalent to 200 lbs. of coal per hour per sq. ft. of 
section. 

Loss of Energy in a Gas Producer. — The total loss from all sources in the 
gasification of fuel in a gas producer under fairly good conditions, when 
the gas is used cold or when its sensible heat is not utilized, ranges between 
20% and 25%, which under very bad conditions may be increased to 50%. 
The loss under favorable conditions, using the gas hot, is reduced to as 
low as 10%, which also includes the heat of the steam used' in blowing. 

Test of a Morgan Producer. — The following is the record of a test made 
in Chicago by Robert W. Hunt & Co. The coal used was Ilhnois " New 
Kentucky" run-of-mine of the follo\^-ing analysis: — 

Fixed carbon, 50.87; volatile matter, 37.32; moisture, 5.08; ash (1.12 
sulphur), 6.73. The average of all the gas analyses by volume is as follows: 

CO, 24.5; H, 17.8; CH4 and C2H4, 6.8; total combustibles, 49.1%; CO2, 
3.7; O, 0.4; N, 46.8: total non-combustibles, 50.9%. 

Average depth of fuel bed, 3 ft. 4 in. Average pressure of steam on 
blower, 4.7 lbs. per sq. in. Analysis of ash: combustible, 4.66%; non- 
combustible, 95.34%. Percentage of fuel lost in the ash, 4.66 X 6.73 -7- 
100 = 0.3%. 

High Temperature Required for Production of CO. — In an ordinary 
coal fire, with an excess of air CO2 is produced, with a high temperature. 
When the thickness of the coal bed is increased so as to choke the air sup- 
ply CO is produced, with a decreased temperature. It appears, however, 
that if the temperature is greatly lowered, CO2 instead of CO will be pro- 
duced notwithstanding the diminished air supply. Herr Ernst {Eng'g, 
April 4, 1893) holds that the oxidation of C begins at 752° F., and that CO2 
is then formed as the main product, with only a small amount of CO, 
whether the air be admitted in large or in small quantities. When the 
rate of combustion is increased and the temperature rises to 1292° F. the 
chief product is CO2 even when the exhaust gases contain 20% by volume 
of CO2, which is practically the maximum limit, proving that all the 
oxygen has been consumed. Above 1292° F. the proportion of CO rapidly 
increases until 1823° F. is reached, when CO is exclusively produced. 

Experiments reported by J. K. Clement and H. A. Grine in Bulletin No. 
393 of the U. S. Geological Survey, 1909, show that with the rate of flow 
of gas and the depth of fuel bed which obtain in a gas producer a temper- 
ature of 1100° C. (2012° F.) or more is required for the formation of 90% 
CO gas from CO2 and charcoal, and 1300° (2372° F.) for the same percen- 
tage from CO2 and coke, and from CO2 and anthracite coal. With a tem- 
perature 100° C. (180° F.) lower than these the resultant gas will contain 
about 50% CO. It follows that the temperature of the fuel bed of the gas 
producer must be at least 1300° C, in order to yield the highest possible 
percentage of CO. 

The Mond Gas Producer is described by H. A. Humphrey in Proc. Inst. 
C. E., vol. cxxix, 1897. The producer, which is combined with a by-prod- 
uct recovery plant, uses cheap bituminous fuel and recovers from it 90 
lbs. of sulphate of ammonia per ton, and yields a gas suitable for gas 
engines and ah classes of furnace work. The producer is worked at a much 
lower temperature than usual, due to the large quantity of superheated 
steam introduced with the air, amounting to more than twice the weight 
of the fuel. The gas containing the ammonia is passed through an absorb- 
ing apparatus, and treated so that 70% of the original nitrogen of the fuel 
is recovered. The result of a test showed that for every ton of fuel about 
2.5 tons of steam and 3 tons of air are blown through the grate, the mixture 
being at a temperature of about 480° F. The greater part of this steam 
passes through the producer undecomposed, its heat being used in a 
regenerator to furnish fresh steam for the producer. More than 0.5 ton 
of steam is decomposed in passing through the hot fuel, and nearly 4.5 tons 
of gas are produced from a ton of coal, equal to about 160,000 cu. ft. at 
ordinary atmospheric temperature. The gas has a calorific power of 81% 
of that of the original fuel. Mr. Humphrey gives the following table 
showing the relative value of different gases. 



FUEL GAS. 



853 



Volume per cent. 



Hydrogen (H) 

Marsh gas (CH4) 

^n^'^n gases 

Carbonic oxide (CO) 

Nitrogen (N) 

Carbonic acid (CO2) 

Total volume 

Total combustible gases 

Theoretical. 

Air required for combustion . . . . 
Calorific value per cu. ft., ) 

in lb. °C. units j 

Do., B.T.U. per cu. f t 

Do., per litre, gram ° C. units . . . 



i-, 1 
3 




U 1 

9. fl 


6S 




.i 


T3 ^ C 


A . 


= < 


£2 . 


i . 


3 






N CO -f.3 


^ CO 


9-S 


g^'s 


<yT5 


^c3^ 


i^^ 


-S5 


^ 


^ 


m 


Q 


Hq 


m 





24.8 


8.6 


18.73 


20.0 


56.9 


48.0 


2.3 


2.4 


0.31 




22.6 


39.5 


nil 


nil 


0.31 


4.0(?) 


3.0 


3.8 


13.2 


24.4 


25.07 


21.0 


8.7 


7.5 


46.8 


59.4 


48.98 


49.5 


5.8 


0.5 


12.9 


5.2 


6.57 


5.0 


3.0 


nil 


100. 


100.0 


100.0 


100.0 


100.0 


100.0 


40.3 


35.4 


44.42 


45.0 


91.2 


98.8 


112.4 


101.4 


113.2 


154.0 


410.0 


581.0 


85.9 


74.7 


88.9 


115.3 


284.0 


381.0 


154.6 


134.5 


160.0 


207.5 


511.2 


658.8 


1,374 


1,195 


1,432 


1,845 


4,544 


6,096 



50 






22.0 

67.0 

6.0 

0.6 

3.0 

0.6 

100.0 

95.6 



806.0 

495.8 

892.4 
7,932 



Note. — Where the volume per cent does not add up to 100 the sUght 
difference is due to the presence of oxygen. 

The foilov^ing is the analysis of gas made in a Mond producer at the 
works of the Solvay Process Co. in Detroit, Mich. (Mineral Industry, vol. 
viii, 1900): CO2, 14.1; O, 0.3; N, 42.9; H, 25.9; CH4, 4.1; CO, 12.7. Com- 
bustible, 42.7%. Calories per litre, 1540, = 173 B.T.U. per cu. ft. 

Relative Efficiencies of Different Coals in Gas Producer and 
Engine Tests. — The following is a condensed statement of the principal 
results obtained in the gas-producer tests of the U. S. Geological Survey 
at St. Louis in 1904. (R. H. Fernald. Trans. A. S. M. E., 1905.) 



Sample. 


B.t.u. 
per 
lb. 
com- 
bus- 
tible. 


Pounds per elec- 
trical H.P. hour 
at switchboard. 


Sample. 


B.t.u. 

com- 
bus- 
tible. 


Pounds per elec- 
trical H.P. hour 
at switchboard. 


Coal 

as 
fired. 


Dry 
coal. 


Com- 
bus- 
tible. 


Coal 

as 
fired. 


Dry 
coal. 


Com- 
bus- 
tible. 


Ala. No. 2.... 
Colo. No. 3... 

111. No. 3 

111. No. 4 

Ind.No. 1.... 
Ind.No. 2.... 
Okla.No.l... 
Okla.No.4... 
Iowa No. 2. . . 
Kan. No. 5... 


14820 
13210 
14560 
14344 
14720 
14500 
14800 
13890 
13950 
15200 


1.71 
2.14 
1.93 
2.01 
2.17 
1.68 
1.92 
1.57 
2.07 
1.69 


1.64 
1.71 
1.79 
1.76 
1.93 
1.55 
1.83 
1.43 
1.73 
1.62 


1.53 
1.58 
1.60 
1.57 
1.71 
1 39 
1.66 
1.17 
1.30 
1.43 


Ky.No.3.. 
Mo. No. 2.. 
Mont. No. 1 
N.Dak.No.2 
Texas No. 1 
Texas No. 2 
W.Va.No.l 
W.Va.No.4 
W.Va.No.7 
Wyo.No.2 


14650 
14280 
13580 
12600 
12945 
12450 
15350 
15600 
15800 
13820 


2.05 
1.94 
2.54 
3.80 
3.34 
2.58 
1.60 
1.32 
1.53 
2.28 


1.91 
1.71 
2.25 
2.29 
2.22 
1.71 
1.57 
1.29 
1.50 
2.07 


1.72 
1.43 
1.98 
2.05 
1.88 
1.52 
1.48 
1.17 
1.40 
1.60 



The gas was made in a Taylor pressure producer rated at 250 H.P. Its 
inside diam. was 7 ft., area of fuel bed 38.5 sq. ft., height of casing 15 ft.; 
rotative ash table; centrifugal tar extractor. The engine was a 3-cylinder 



854 



FUEL. 



vertical Westinghouse, 19 in. diam., 22 in. stroke, 200 r.p.m., rated at 
235 B.H.P. Comparing the results of the W. Va. No. 7 coal, the best 
on the list, with the North Dakota coal, the one which gave the poorest 
results, the heat values per lb. combustible of the coals are as 1 to 0.808; 
reciprocal, 1 to 1.24; the lbs. combustible per E. H. P. hour as 1 to 1.75, 
and lbs. coal as fired per E. H. P. hour as 1 to 2.88. The relative thermal 
efficiencies of the engine with the two coals are as 2.05 to 1.17, or as 1 to 
0.578. The analyses by volume of the dry gas obtained from the two 
coals was: 

CO2 






CO 


H 


CH4 


N Total 
combustible. 


0.24 


15.82 


11.16 


3.74 


58.88 30.72 


0.23 


20.90 


14.33 


4.85 


51 .00 40 . 06 



W. Va 10.16 

N. Dak 8.69 

The dry-gas analysis shows the North Dakota gas to be by far the best; 
its much lower result in the engine test is due to the smaller quantity of 
gas produced per lb. of coal, which was 22.7 cu. ft. per lb. of coal as fired, 
as compared with 70.6 cu. ft. for the W. Va. coal, measured at 62° F. and 
14.7 lb. absolute pressure. 

Use of Steam in Producers and in Boiler-furnaces. (R. W. Ray- 
mond, Trans. A. I. M. E., xx, 635.) — No possible use of steam can cause 
a gain of heat. If steam be introduced into a bed of incandescent carbon 
it is decomposed into hydrogen and oxygen. 

The heat absorbed by the reduction of one pound of steam to hydrogen 
is much greater in amount than the heat generated by the union of the 
oxygen thus set free with carbon, forming either carbonic oxide or car- 
bonic acid. Consequently, the effect of steam alone upon a bed of incan- 
descent fuel is to chill it. In every water-gas apparatus, designed to 
produce by means of the decomposition of steam a fuel-gas relatively 
free from nitrogen, the loss of heat in the producer must be compensated 
by some reheating device. 

This loss may be recovered if the hydrogen of the steam is subsequently 
burned, to form steam again. Such a combustion of the hydrogen is 
contemplated, in the case of fuel-gas, as secured in the subsequent use of 
that gas. Assuming the oxidation of H to be complete, the use of steam 
will cause neither gain nor loss of heat, but a simple transference, the 
heat absorbed by steam decomposition being restored by hydrogen com- 
bustion. In practice, it may be doubted whether this restoration is ever 
complete. But it is certain that an excess of steam would defeat the 
reaction altogether, and that there must be a certain proportion of steam, 
which permits the realization of important advantages, without too great 
a net loss in heat. 

The advantage to be secured (in boiler furnaces using small sizes of 
anthracite) consists principally in the transfer of heat from the lower 
side of the fire, where it is not wanted, to the upper side, where it is 
wanted. The decomposition of the steam below cools the fuel and the 
grate-bars, whereas a blast of air alone would produce, at that point, 
intense combustion (forming at first CO2), to the injury of the grate, the 
fusion of part of the fuel, etc. 

Gas Analyses by Volume and by Vl^eight. — To convert an analysis 
of a mixed gas by volume into analysis by weight: Multiply the percentage 
of each constituent gas by its relative density, viz: CO2 by 11, O by 8, 
CO and N each by 7, and divide each product by the sum of the products. 
Conversely, to convert analysis by weight into analysis by volume, divide 
the percentage by weight of each gas by its relative density, and divide 
each Quotient by the sum of the quotients. 

Gas-fuel for Small Furnaces. — E. P. Reichhelm (Am. Mach., Jan. 
10, 1895) discusses the use of gaseous fuel for forge fires, for drop-forging, 
in annealing-ovens and furnaces for melting brass and copper, for case- 
hardening, muffle-furnaces, and kilns. Under ordinary conditions, in 
such furnaces he estimates that the loss by draught, radiation, and the 
heating of space not occupied bv work is, with coal. 80%, with petro- 
leum 70%. and with eras above the grade of producer-gas 25%. He 
gives the following table of comparative cost of fuels, as used in these 
furnaces; 



ACETYLENE AND CALCIUM CARBIDE. 



855 



Kind of Gas. 



Natural gas 

Coal-gas, 20 candle-power 

Carburetted water-gas 

Gasolene gas, 20 candle-power , 

Water-gas from coke 

Water-gas from bituminous coal 

Water-gas and producer-gas mixed 

Producer-gas , 

Naphtha-gas, fuel 21/2 gals, per 1000 ft. , 



C3X 

KB' 

0-^ 



Ifl -So 



1,000,000 
675,000 
646,000 
690,000 
313,000 
377,000 
185,000 
150,000 
306,365 



750,000 
506,250 
484,500 
517,500 
234,750 
282,750 
138,750 
112,500 
229,774 



> a 

< 



°tn tn <y c 



SI. 25 
1.00 
.90 
.40 
.45 
.20 
.15 
.15 



Coal, $4 per ton, per 1,000,000 heat-units utiMzed 

Crude petroleum, 3 cts. per gal., per 1,000,000 heat-units.. 



$2.46 

2.06 

1.73 

1.70 

1.59 

1.44 

1.33 

.65 

.73 

.73 



Mr. Reichhelm gives the following figures from practice in melting 
brass with coal and with naphtha converted into gas: 1800 lbs. of metal 
require 1080 lbs. of coal, at $4.65 pei ton, equal to $2.51, or, say, 15 cents 
per 100 lbs. Mr. T.'s report: 2500 lbs. of metal require 47 gals, of naphtha, 
at 6 cents per gal., equal to $2.82, or, say, 11V4 cents per 100 lbs. 

Blast-Furnace Gas. — The waste-gases from iron blast furnaces 
were formerly utilized only for heating the blast in the hot-blast ovens and 
for raising steam for the blowing-engine pumps, hoists and other auxiliary 
apparatus. Since the introduction of gas engines for blowing and other 
purposes it has been found that there is a great amount of surplus gas 
available for other uses, so that a large power plant for furnishing electric 
current to outside consumers may easily be run by it. H. Freyn, in a 
paper presented before the Western Society of Engineers (Eng. Rec, 
Jan. 13, 1906), makes an elaborate calculation tor the design of such a 
plant in connection with two blast furnaces of a capacity of 400 tons of 
pig iron each per day. Some of his figures are as follows: The two fur- 
naces would supply 4,350,000 cu. ft. of gas per hour, of 90 B.T.U. average 
heat value per cu. ft. The hot-blast stoves would require 30% of this, or 
1,305,000 cu. ft.; the gas-blowing engines 720,000 cu. ft.; pumps, hoists 
and lighting machinery, 120,000 cu. ft.; gas-cleaning machinery, 120,000 
cu. ft.; losses in piping, 48,000 cu. ft.; leaving available for outside uses, in 
round numbers, 2,000,000 cu. ft. per hour. At the rate of 100 cu. ft. of gas 
per brake H.P. hour this would supply engines of 20,000 H.P., but assum- 
ing that on account of irregular working of the furnaces only half this 
amount would be available for part of the time, a 10,000-H.P. plant could 
be run with the surplus gas of the two furnaces. Taking into account the 
cost of the plant, figured at $61.60 per B.H.P., interest, depreciation, 
labor, etc., the annual cost of producing one B.H.P., 24 hours a day, is 
$17.88, no value being placed on the blast-furnace gas, and 1 K.W. hour 
would cost 0.295 cent, which is far below the lowest figure ever reached 
with a steam-engine power plant. 

Blast-furnace gas is composed of nitrogen, carbon dioxide and carbon 
monoxide, the latter being the combustible constituent. An analysis 
reported in Trans. AJ.M.E., xvii, 50, is, by volume, CO2, 7.08; CO, 27.80; 
O, 0.10; N, 65.02. The relative proportions of CO2 and CO vary con- 
siderably with the conditions of the furnace. 

ACETYLENE AND CALCIUM CARBIDE. 

Acetylene, C2H2, contains 12 parts C and 1 part H, or 92.3% C,7.7% H. 
It is described as follows in a paper on Calcium Carbide and Acetylene 
by J. M. Morehead {Am. Gas Light Jour., July 10, 1905. Revised, 
Jan., 1915). 

Acetylene is a colorlass and tasteless gas. When pure it has a sweet 
etheral odor, but in the commercial form it carries small percentages of 
phosphoreted and sulphureted hydrogen which give it a pungent odor. 



856 FUEL. 

Pure acetylene is without toxic or physiolog-ical effect. It may be in- 
haled or swallowed with impunity. One cu. ft. requires 11.91 cu. ft. of 
air for its complete combustion. Its specific gravity is 0,92, air being 1. 
It is the nearest approach to gaseous carbon, and it possesses a higher 
candle power and flame temperature than any other known substance, 
240 candles for 5 cu. ft., 4078° F. w hen burned in air, 7878° F. in oxygen. 
Its ignition temperature with air is 804° F., with oxygen 782° F. It is 
soluble in its own volume of water, and in varying proportions in ether, 
alcohol, turpentine, and acetone. The solubility increases with pressure. 
It liquefies under a pressure of 700 lbs. per sq. in. at 70° F. The pres- 
sure necessary for liquefaction varies directly with the temperature up 
to 98°, which is its critical temperature, beyond which it is impossible 
to liquefy the gas at any pressure. 

When calcium carbide is brought into contact with water, the calcium 
robs the water of its oxygen and forms hme and thus frees the hydrogen, 
which combines with the carbon of the carbide to form acetylene. 
Sixty-four lbs. of calcium carbide combine with thirty-six lbs. of water 
and produce twenty-six lbs. of acetylene and 74 lbs. of pure slacked 
lime. [The chemical reaction is CaC2 + 2H2O = C2H2 + Ca(OH)2.] 

Chemically pure calcium carbide will yield at 70° F. and 30 in. mer- 
cury 5.83 cu. ft. acetylene per pound of carbide. Commercially pure 
carbide is guaranteed to yield 5 cu. ft. of acetylene per pound, and 
usually exceeds the guarantee by a few per cent. The reaction between 
calcium carbide and water, and the subsequent slacking of the calcium 
oxide produced, give rise to considerable heat. This heat from one pound 
of chemically pure calcium carbide amoimts to sufficient to raise the 
temperature of 4.1 lbs. of water from the freezing to the boihng point. 

There are two types of generators; one in which a varying quantity of 
water is dropped on to the carbide, the other in which the carbide is 
dropped into a large excess of w^ater. Ow ing to the large amount of heat 
generated by the reaction, and the susceptibility of the acetylene to 
heat, the first, or dry type, is confined to lamps and to small machines. 

Acetylene produces 1475 B.T.U. per cubic foot (at 70° F. and 30 in.), 
as compared with 1000 for natural gas and 600 for coal or water gas. 
At the present state of development of the acetylene industry and the 
calcium carbide manufacture, this gas will not compete with coal gas or 
water gas, or with electricity as supplied in our cities. 

The explosive hmits of acetylene and air are from 3 % acetylene and 
97 % air to 24 % acetylene and 76 % air, the point of maximiun explo- 
sibility being 7.7% acetylene and 92.3% air. 

The combustion of acetylene requires theoreticaUy^ 2 J^ volumes of 
oxygen for 1 volume of acetylene. In autogenous welding and other 
oxy-acetylene processes, however, a considerable part of the necessary 
oxygen is taken from the air, and hence only from 1.25 to 1.75 cubic feet 
of oxygen per cubic foot of acetylene need be supplied. 

Of the 1475 heat units contained in a cubic foot of acetylene, 227 are 
endothermic energy, which it is believed is higher than that for any 
other substance. The balance of the energy is derived from the com- 
bination of the carbon and hydrogen of the acetylene with oxygen, as 
is the case with other combustible gases. 

Due to the extraordinary endothermic energy of acetylene the gas 
will explode of itself if it is ignited w hile at a pressure slightly in excess 
of 15 lbs. to the sqtiare inch. The compression, storage, use and trans- 
portation of unabsorbed acetylene at pressures in excess of this figure 
are forbidden by the fire, police, insurance and transportation authorities 
in practically all cities. Danger of explosion from compressed acetylene 
is removed and the use of compressed acetylene is rendered safe and 
feasible for motor car, yacht, railroad train and all other portable uses 
by absorbing the acetylene in acetone, which is itself absorbed in turn 
in asbestos, Keisselgour or other non-inflammable substances. 

Calcium carbide was discovered on May 4, 1892, at the plant of the 
Willson Aluminum Co., in North Carolina. It is a crystalline body, 
hard, brittle and varying in color from almost black to brick red. Its 
specific gravity is 2.26. A cubic foot of crushed carbide w^eighs 138 lbs., 
and in weight, color and most of its physical characteristics is about 
like granite. If broken hot, the fracture shows a handsome, bluish 
purple iridescenc(3 and the crystals are apt to be quite large. 



ACETYLENE AND CALCIUM CARBIDE. 857 

Calcium carbide, CaC2. contains 62.5% Ca and 37.5% C. It is in- 
soluble in most acids and in all alkalies; it is non-inflammable, infusible, 
non-explosive, unaffected by jars, concussions or time, and, except for 
the property of giving off acetylene when brought in contact with water, 
it is an inert and stable body. It is made by the reduction in an electric 
arc furnace of a mixture of finely pulverized and intimately mixed cal- 
cium oxide or quicklime and carbon in the shape of coke (CaO -h 3C = 
CaC2 + CO). The furnaces employ from 12,000 to 15,000 electric H.P. 
each and produce from 50 to 75 tons per day. The output is crushed to 
different sizes and it is sold in steel drums for $70 per ton at the works. 

The entire use for calcium carbide is for the production of acetylene. 
[Wohler, in 1862, obtained calcium carbide by heating an alloy of cal- 
cium and zinc together with carbon to a very high temperature.] 

Acetylene Generators and Burners. — Lewes classifies acetylene 
generators under four types: (1) Those in which water drips or flows 
slowly on a mass of carbide; (2) those in which water rises, coming in 
contact with a mass of carbide; (3) those in which water rises, coming in 
contact with successive layers of carbide; (4) those in which the carbide 
is dropped or plunged into an excess of water. He shows that the first 
two classes are dangerous; that some generators of the third_class are 
good, but that those of the fourth are the best. 

Of the various burners used for acetylene, those of the Naphey type 
are among the most satisfactory. Two tubes leading from the base of 
the burner are so adjusted as to cause two jets of flame to impinge upon 
each other at some little distance from the nozzles, and mutually to 
splay each other out into a flat flame. The tips of the nozzles, usually 
of steatite, are formed on the principle of the Bunsen burner, insuring a 
thorough mixture of the acetylene with enough air to give the best 
illumination. (H. C. Biddle, Cal. Jour, of Tech., 1907.) 

Acetylene gas is an endothermic compound. In its formation heat is 
absorbed, and there resides in the acetylene molecule the power of spon- 
taneously decomposing and liberating this heat if it is subjected to a 
temperature or pressure beyond the capacity of its unstable nature to 
withstand. (Thos. L. White, Eng. Mag., Sept., 1908.) Mr. White 
recommends the use of acetylene for carbureting the alcohol used in 
alcohol motors for automobiles. 

The Acetylene Blowpipe. — (Machy., July, 1907.) — The acetylene 
is produced in a generator and stored in a tank at a pressure of 2.2 to 3 
lbs. per sq. in. The oxygen is compressed in a tank at about 150 lbs. 
pressure. The acetylene is conveyed to the burner through a 1-in. pipe 
with one ^-in branch leading to each blow^pipe connection. The oxygen 
is conveyed through ^-in. pipe with 3^-in. branches. The blowpipe is 
of brass, made on the injector principle. As acetylene is so rich in car- 
bon — containing 92.3 % — it is possible, when mixed with air in a Bunsen 
burner, to obtain 3100° F., and when combined with oxygen, 6300° F., 
which is the hottest flame known as a product of combustion, and nearly 
equals the electric arc. This is about 1200° higher than the oyx- 
hydrogen blowpipe flame. 

In lighting the blowpipe, the acetylene is first turned on full; then the 
oxygen is added until the flame is only a single cone. At the apex of this 
cone is a temperature of 6300° F. In welding, this point is held from ^ 
to }4: in. distant from the metal to be welded. Too much acetylene pro- 
duces two cones and a white color ; an excess of oxygen is indicated by a 
violet tint. 

Theoretically, 2 }4 volumes of oxygen are required for complete com- 
bustion of 1 volume of acetylene. Practically, however, with the blow- 
pipe, the best welding results are obtained with 1.7 volumes of oxygen to 
1 volume of acetylene. The acetylene is, therefore, not completely 
burned with the blowpipe, according to the reaction: 

2C2H2 (4 vol.) -f- 5O2. (10 vol.) = 4C02 + 2H2O, 
but it is incompletely burned according to the reaction: 
C2H2 (2 vol.) + O2 (2 vol.) = 2C0 + H2. 

The Theory and Practice of Oxy-Acetylene Welding is described in an 
illustrated article by J. F. Springer in Indust. Eng'g., Oct., 1909. 
The Levoisite process of making oxygen (99.9% pure), used in acety- 



858 



ILLUMINATING - GAS. 



lene welding, is described by Max Mauran in Met. and Chem. Eng'g., 
June, 1914. 

IGNITION TEMPERATURE OF GASES. 

Mayer and IMunch {Bericht der deutscher Gesellschaft, xxvi, 2241) give 
the following : 

Marsh-gas, C2H1, 667° C. 1233° F. 

Ethane, C2H6, 616 1141 

Propane, C3H8, 547 1017 

Acetylene, C2H2, 580 1076 

Propylene, CsHe, 504 939 

Very different figures are given by other authorities. A French 
Commission obtained for hydrogen 1071° F.; CH4, 1436°; C2H4, 1022°; 
CO, 1202; CO in presence of a large quantity of CO2, 1292° F. Vivian 
Lewes gives for the ignition temperature of cannel coal 668° F.; bi- 
tuminous, 766°, semi-bituminous 870° F. W. S. Hutton gives for 
anthracite, 925° F. 

ILLUMINATING-GAS. 

Coal-gas is made by distilling bituminous coal in retorts. The retort 
is usually a long horizontal semi-cylindrical or q shaped chamber, holding 
from 160 to 300 lbs. of coal. The retorts are set in "benches" off from 
3 to 9, heated by one fire, which is generally of coke. The vapors distilled 
from the coal are converted into a fixed gas by passing through the retort, 
which is heated almost to whiteness. 

The gas passes out of the retort through an "ascension-pipe" into a 
long horizontal pipe called the hydraulic main, where it deposits a por- 
tion of the tar it contains; thence it goes into a condenser, a series of iron 
tubes surrounded by cold water, where it is freed from condensable vapors, 
as ammonia-water, then into a washer, where it is exposed to jets of 
water, and into a scrubber, a large chamber partially filled with trays 
made of wood or iron, containing coke, fragments of brick or paving- 
stones, which are wet with a spray of water. By the washer and scrubber 
the gas is freed from the last portion of tar and ammonia and from some 
of the sulphur compounds. The gas is then finally purified from sulphur 
compounds by passing it through lime or oxide of iron. The gas is drawn 
from ihe hydrauUc main and forced through the washer, scrubber, etc., 
by an exhauster or gas pump. 

The kind of coal used is generally caking bituminous, but as usually 
this coal is deficient in gases of high illuminating power, there is added to 
it a portion of cannel coal or other enricher. 

The follo\\1ng table, abridged from one in Johnson's Cyclopedia, shows 
the analysis, candle-power, etc., of some gas-coals and enrichers: 



Gas-ooals, etc. 


a 
> 


4 
6 

1 


4 
< 


ii 

CJJD 


6^ 


Coke per 

ton of 2240 

lbs. 


■ii.s 

» 




lbs. 


bush. 




Pittsburgh, Pa 


36.76 
36.00 
37.50 
40.00 
43.00 
46.00 
53.50 


51.93 
58.00 
56.90 
53.30 
40.00 
41.00 
44.50 


7.07 
6.00 
5.60 
6.70 
17.00 
13.00 
2.00 












Westmoreland, Pa 

Sterling, O 


10,642 
10,528 
10,765 
9,800 
13,200 
15,000 


16.62 
18.81 
20.41 
34.98 
42.79 
28.70 


1544 
1480 
1540 
1320 
1380 
1056 


40 
36 
36 
32 
32 
44 


6420 
3993 


Despard, W. Va 

Darlington, O 


2494 
2806 


Petonia, W. Va 


4510 


Grahamite, W. Va 





The products of the distillation of 100 lbs. of average gas-coal are about 
as follows. They vary according to the quality of coal and the tempera- 
ture of distillation. 

Coke, 64 to 65 lbs.; tar, 6.5 to 7.5 lbs.; ammonia liquor, 10 to 12 lbs.; 
purified gas. 15 to 12 lbs.; impurities and loss, 4.5% to 3.5%. 

The composition of the gas by volume ranges about as follows : Hydro- 



ILLUMINATING GAS. 859 

gen, 38 % to 48 % ; carbonic oxide, 2 % to 14 % ; marsh-gas (Methane, 
CH4), 43% to 31%; heavy hydrocarbons (CnH2n, ethylene, propylene, 
benzole vapor, etc.), 7.5% to 4.5%; nitrogen, 1% to 3%. 

In the burning of the gas the nitrogen is inert: the hvdrogen and car- 
bonic oxide give heat but no he:ht. The luminosity of the flame is due to 
the decomposition by heat of the heavy hydrocarbons into lighter hydro- 
carbons and carbon, the latter being separated in a state of extreme 
subdivision. By the heat of the flame this separated carbon is heated to 
intense whiteness, and the illuminating effect of the flame is due to the 
light of incandescence of the particles of carbon. 

The attainment of the hierhest degree of luminosity of the flame de- 
pends upon the proper adjustment of the proportion of the heavy hydro- 
carbons (with due regard to their individual character) to the nature of 
the diluent mixed therewith. 

Investigations of Percy F. Frankland show that mixtures of ethylene 
and hydrogen cease to have any luminous effect when the proportion of 
ethylene does not exceed 10% of the whole. Mixtures of ethylene and 
carbonic oxide cease to have any luminous effect when the proportion of 
the former does not exceed 20%, while all mixtures of ethylene and 
marsh-gas have more or less luminous effect. The luminosity of a mix- 
ture of 10% ethylene and 90% marsh-gas being equal to about 18 candles, 
and that of one of 20% ethylene and 80% marsh-gas about 25 candles. 
The illuminating effect of marsh-gas alone, when burned in an argand 
burner, is by no means inconsiderable. 

For further description, see the treatises on gas by King, Richards, 
and Hughes; also Appleton's Cyc. Mech., vol. i. p. 900. 

Water-gas. — Water-gas is obtained by passing steam through a bed 
of coal, coke, or charcoal heated to redness or beyond. The steam is 
decomposed, its hydrogen being liberated and its oxygen burning the 
carbon of the fuel, producing carbonic-oxide gas. The chemical reaction 
is, C + H2O = CO + 2 H, or 2 C + 2 H2O = C + CO2 4- 4 H, followed 
by a splitting up of the CO2, making 2 CO + 4 H. By weight the normal 
gas CO + 2 H is composed of C + O + H = 28 parts CO and 2 parts H, 

12 + 16 + 2 
or 93.33% CO and 6.67% H; by volume it is composed of equal parts of 
carbonic oxide and hydrogen. Water-gas produced as above described 
has great heating-power, but no illuminating-power. It may, however, 
be used for lighting by causing it to heat to whiteness some solid sub- 
stance, as is done in the Welsbach incandescent light. 

An illuminating-gas is made from water-gas by adding to it hydro- 
carbon gases or vapors, which are usually obtained from petroleum or 
some of its products. A history of the development of modern illumi- 
nating water-gas processes, together with a description of the most recent 
forms of apparatus, is given by Alex. C. Humphreys, in a paper on " Water- 
gas in the United States," read before the Mechanical Section of the 
British Association for Advancement of Science, in 1889. After describ- 
ing many earUer patents, he states that success in the manufacture of 
water-gas may be said to date from 1874, when the process of T. S. C. 
Lowe was introduced. All the later most successful processes are the 
modifications of Lowe's, the essential features of which were *' an apparatus 
consisting of a generator and superheater internally fired; the super- 
heater being heated by the secondary combustion from the generator, 
the heat so stored up in the loose brick of the superheater being used, in 
the second part of the process, in the fixing or rendering permanent of the 
hydrocarbon gases; the second part of the process consistirg in the 
passing of steam through the generator fire, and the admission of oil or 
hydrocarbon at some point between the fire of the generator and the 
loose filling of the superheater." 

The water-gas process thus has two periods: first the "blow," during 
which air is blown through the bed coal in the generator, and the par- 
tially burned gaseous products are completely burned in the superheater, 
giving up a great portion of their heat to the fire-brick work contained 
in it, and then pass out to a chimney; second, the "run" during which the 
air blast is stopped, the opening to the chimney closed, and steam is 
blown through the incandescent bed of fuel. The resulting water-gas 
passing into the carburetting chamber in the base of the superheater is 
there charged with hydrocarbon vapors, or spray (such as naphtha and 
other distillates or crude oil) , and passes through the superheater, where 



860 



ILLUMINATING- GAS. 



the hydrocarbon vapors become converted into fixed illuminating gases. 
From the superheater the combined gases are passed, as in the coal-gas 
process, through washers, scrubbers, etc., to the gas-holder. In this 
case, however, there is no ammonia to be removed. 

The specific gravity of water-gas increases with the increase of the 
heavy hydrocarbons which give illuminating power. The following 
figures, taken from different authorities, are given by F. H. Shelton in a 
paper on " Water-gas," read before the Ohio Gas Light Association, in 
1894: 



Candle-power 

Sp.gr. (Air = l).. 



19.5 20.22.5 24. 25.4 26.3 28.3 29.6 .30 to 31.9 
.571 .630 .589 .60 to .67 .64 .602 .70 .65 .65 to .71 



Analyses of Water-gas and Coal-gas Compared. 

The following analyses are taken from a report of Dr. Gideon 
Moore on the Granger Water-gas, 1885: 





Composition by Vol. 


Composition by Weight. 




Water-gas. 


Coal- 
gas. 
Heidel- 
berg. 


Water-gas. 


Coal- 
gas. 




Wor- 
cester. 


Lake. 


Wor- 
cester. 


Lake. 


Nitrogen 


2.64 

0.14 

0.06 

11.29 

0.00 

1.53 

28.26 

18.88 

37.20 


3.85 

0.30 

0.01 

12.80 

0.00 

2.63 

23.58 

20.95 

35.88 


2.15 
3.01 
0.65 
2.55 
1.21 
1.33 
8.88 
34.02 
46.20 


0.04402 
0.00365 
0.00114 
0.18759 


0.06175 
0.00753 
0.00018 
0.20454 


04559 


Carbonic acid 


09992 


Oxygen 


01569 


Ethylene 


05389 


Propylene 


03834 


Benzole vapor 


0.07077 
0.46934 
0.17928 
0.04421 


0.11700 
0.37664 
0.19133 
0.04103 


07825 


Carbonic oxide 


18758 


Marsh-gas 


41087 


Hydrogen 


06987 








100.00 


100.00 


100.00 


1 .00000 


1.00000 


1.00000 


Density: Theory 


0.5825 
0.5915 


0.6057 
0.6018 


0.4580 








Practice 


















B.T.U.fromlcu.ffc.: 
Water liquid 


650.1 
597.0 


688.7 
646.6 


642.0 
577.0 








" vapor 
















Flame-temperature, °F . . . 


5311.2 


5281.1 


5202.9 
















Average candle-power 


22.06 


26.31 















The heating- values (B.T.U.) of the gases are calculated from the 
analysis by weight, by using the multipliers given below (computed 
from results of J. Thomsen), and multiplying th3 result by the weight 
of 1 cu. ft. of the gas at 62° P., and atmospheric pressure. 

The flame-temperatures (theoretical) are calculated on the assumption 
of complete combustion of the gases in air, without excess of air. 

The candle-power was determined by photometric tests, using a pres- 
sure of 1/2-in. water-column, a candle consumption of 120 grains of sper- 
maceti per hour, and a meter rate of 5 cu. ft. per hour, the result being 
corrected for a temperature at 62° F. and a barometric pressure of 30 in. 
It appears that the candle-power may be regulated at the pleasure of the 
person m charge of the apparatus, the range of candle-power being from 
20 to 29 candies, according to the manipulation employed. 

Calorific Equivalents of Constituents of Illuminating-gas. 



Keat-units from 1 lb. 



Ethylene . . 
Propylene . 



Water 

Liquid. 

.21,524.4 

.21,222.0 



Benzole vapor .18,954.0 



Water 

Vapor. 

20.134.8 

19,834.2 

17.847.0 



Heat-units from 1 lb. 
Water Water 
Liquid. Vapor. 
Carbonic oxide . 4,395.6 4,395.6 

Marsh-gas 24,021.0 21,592.8 

Hydrogen 61 .524.0 51 .804,0 



ILLUMINATING - GAS. 



861 



Efficiency of a Water-gas Plant. — The practical efficiency of an 
illiuninating water-gas sotting is discussed in a paper by A. G. Glasgow 
{Proc. Am. Gaslight Assn., 1890) from wliicli the following is abridged: 

The results refer to 1000 cu. ft. of unpurifled{carburetted gas, reduced to 
60° F. The total anthracite charged per 1000 cu. ft. 6f gas was 33.4 lbs., 
ash and unconsumed coal removed, 9.9 lbs., leaving total combustible 
consumed, 23.5 lbs., which is taken to have a fuel-value of 14,500 B.T.U. 
per poimd, or a total of 340,750 heat-units. 





Com- 
posi- 
tion by 
Vol. 


Weight 

100 Cu. 

Ft. 


Com- 
posi- 
tion by 
W'ht. 


Specific 
Heat. 


I. Carburetted Water-gas. . ^ 


CO2 +H2S 
CnH2n • • • • 

CO 

CH4 

H 


3.8 
14.6 
28.0 
17.0 
35.6 

1.0 


.465842 
1.139968 
2.1868 
.75854 
.1991464 
.078596 


0.09647 
.23607 
.45285 
.15710 
.04124 
.01627 


0.02088 
.08720 
.11226 
.09314 
.14041 




N 


.00397 






100.0 


4.8288924 


1.00000 


.45786 


II. Uncarburetted gas < 


fC02 

CO 

H 


3.5 

43.4 

51.8 

1.3 


.429065 

3.389540 

.289821 

.102175 


.1019 
.8051 
.0688 
.0242 


.02205 
.19958 
.23424 


N 


.00591 




I 






100.0 


4.210601 


1.0000 


.46178 


III. Blast products escap- 


CO2 




17.4 

3.2 

79.4 


2 J 33066 
.2856096 
6.2405224 


.2464 
.0329 
.7207 


.05342 
.00718 


ing from superheater . . 


N 


.17585 






100.0 


8.6591980 


1 .0000 


.23645 


IV. Generator blast-gases. . 


CO2 

CO 

N 


9.7 
17.8 
72.5 


1.189123 
1.390180 
5.698210 


.1436 
.1680 
.6884 


.031075 
.041647 
.167970 






100.0 


8.277513 


1.0000 


.240692 



The heat-energy absorbed by the apparatus is 23.5 X 14,500 = 340,750 
heat-units = A. Its disposition is as follows: 

B, the energy of the CO produced; 

C, the energy absorbed in the decomposition of the steam; 

Z), the difference between the sensible heat of the escaping illuminating- 
gases and that of the entermg oii; 

E, the heat carried off by the escaping blast proaucts; 

F, the heat lost by radiation from the shells; 

G, the heat carried away from the shells by convection (air-currents) ; 
H, the heat rendered latent in the gasification of the oil; 

I, the sensible heat in the ash and unconsumed coal recovered from 
the generator. 

The heat equation is A=B+C-\-D+E-rF-^G-{-H+ I: A 

280 
being known. A comparison of the CO in Tables I and II show that t^t^ t 

434 
or 64.5% of the volume of carburetted gas, is pure water-gas, distnbuted 
thus: CO2, 2.3%; CO, 28.0%,; H, 33.4%; N, 0.8%; = 64.5%. 1 lb. of CO 
at 60° F. = 13,531 cu. ft. CO per 1000 cu. ft. of gas = 280 -^ 13.531 
= 20.694 lbs. Energy of the CO = 20.694 X 4395.6 = 91,043 heat- 
units = B. 1 lb. of H at 60° F. = 189.2 cu. ft. H per M of eras = 334 
-^ 189.2 = 1.7653 lbs. Eifergy of the H per lb. (according to Thomsen, 
considering the steam generated by its combustion to be condensed to 
water at 75° F.) = 61,524 B.T.U. In Mr. Glasgow's experiments the 
steam entered the generator at 331° F.; the heat required to raise the 
product of combustion of 1 lb. of H, viz., 8.98 lbs. H2O, from water at 75" 
to steam at 331° must therefore be deducted from Thomsen's figure, or 
61,524 - (8.98 X 1140.2) = 51,285 B.T.U. per lb. of H. Energy of 
the H, then, is 1.7653 X 51,285 = 90,533 heat-units = C. The best 



862 



ILLUMINATING-GAS. 



lost due to the sensible heat in the illuminating-gases, their temperature 
being 1450° F., and that of the entering oil 235° F., is 48.29 (weight) 
X. 45786 (sp. heat) X 1215 (rise of temperature) = 26,864 heat-units = D. 

(The specific heat of the entering oil is approximately that of the 
issuing gas.) 

The heat carried off in 1000 cu. ft. of the escaping blast products is 
86.592 (weight) X .23645 (sp. heat) X 1474° (rise of temp.) = 30,180 
heat-units: the temperature of the escaping blast gases being 1550° F., 
and that of the entering air 76° F. But the amount of the blast gases, 
by registration of an anemometer, checked by a calculation from the 
analyses of the blast gases, was 2457 cubic feet for every 1000 cubic feet 
of carburetted gas made. Hence the heat carried off per M. of carburetted 
gas is 30,180 X 2.457 = 74,152 heat-units = E. - 

Experiments made by a radiometer covering four square feet of the 
shell of the apparatus gave figures for the amount of heat lost by radia- 
tion = 12,454 heat-units = F, and by convection = 15,696 heat-units 
= G. 

The heat rendered latent by the gasification of the oil was found by 
taking the difference between all the heat fed into the carburetter and 
superheater and the total heat dissipated therefrom to be 12,841 heat- 
umts = H. The sensible heat in the ash and unconsumed coal is 9.9 lbs. 
X 1500° X .25 (sp. ht.) = 3712 heat-units = /. 

The sum of all the items B-^C+D+E+F-^G+H+I = 
327,295 heat-unitS; w^hich subtracted from the heat-energy of the com- 
bustible consumed, 340,750 heat-units, leaves 13,455 heat-units, or 4 per 
cent unaccounted for. 

Of the total heat-energy of the coal consumed, or 340,750 heat-units, 
the energy wasted is the sum of items D, E, F, G, and /, amounting to 
132,878 heat-units, or 39 per cent; the remainder, or 207,872 heat-units, 
or 61 per cent, being utilized. The efficiency of the apparatus as a heat 
machine is therefore 61 per cent. 

Five gallons, or 35 lbs. of crude petroleum, were fed into the carburetter 
per 1000 cu. ft. of gas made; deducting 5 lbs. of tar recovered, leaves 
30 lbs. X 20,000 = 600,000 heat-units as the net heating-value of the 
petroleum used. Adding this to the heating-value of the coal, 340,750 
B.T.U., gives 940,750 heat-units, of which there is found as heat-energy 
in the carburetted gas, as in the table belov/, 764,050 heat-units, or 81 
per cent, which is the commercial efficiency of the apparatus, i.e., the 
ratio of the energy contained in the finished product to the total energy 
of the coal and oil consumed. 



The heating-powder per M. cu. ft. of 
the carburetted gas is 
CO2 38.0 

C3H6*146.0 X .11 7220 x 21222.0=363200 
CO 280.0 X. 078100 X 4395.6= 96120 
CH4 170.0 X. 044620x24021. 0-1822 10 
H 356.0 X. 005594x61524.0= 122520 
N 10.0 



1000.0 



764050 



The heating-power per M. of the 
uncarburetted gas is 
CO2 35.0 

CO 434.0X.078100X 4395.6=148991 
H 518.0X. 005594x61524.0= 178277 
N 13.0 



1000.0 



327268 



The candle-power of the gas is 31, or 6.2 candle-power per gallon of oil 
used. The calculated specific gravity is .6355, air being 1. 

For description of the operation of a modern carburetted water-gas 
plant, see paper by J. Stelfox, Eng'g, July 20, 1894, p. 89. 

Space Required for a Water-gas Plant. — Mr. Shelton, taking 15 
modern plants of the form requiring the most floor-space, figures the 
average floor-space required per 1000 cubic feet of daily capacity asr 
follows: « 

Water-gas Plants of Capacity Require an Area of Floor-space for each^ 

in 24 hours of 1000 cu. ft. of about 

100,000 cubic feet 4 square feet. 

200,000 •' " 3.5 

400,000 •' " 2.75 *• 

600,000 •• " 2 to 2.5 sq. ft. 

7 to 10 million cubic feet 1.25 to 1.5 sq. ft. 

* The heating-value of the illuminants C^jH-^is assumed to equal that I 
of CsHe. 



ILLUMINATING-GAS. 



863 



These figures include scrubbing and condensing rooms, but not boiler 
and engine rooms. In coal-gas plants of the most modern and compact 
forms one with 16 benches of 9 retorts each, with a capacity of 1,500,000 
cubic feet per 24 hours, will require 4.8 sq. ft. of space per 1000 cu. ft. 
of gas, and one of 6 benches of 6 retorts each, with 300,000 cu. ft. capacity 
per 24 hours, will require 6 sq. ft. of space per 1000 cu. ft. The storage- 
room required for the gas-making materials is: for coal-gas, 1 cubic foot 
of room for every 232 cubic feet of gas made; for water-gas made from 
coke, 1 cubic foot of room for every 373 cu. ft. of gas made; and for 
water-gas made from anthracite, 1 cu. ft. of room for every 645 cu. ft. of 
gas made. 

The comparison is still more in favor of water-gas if the case is con- 
sidered of a water-gas plant added as an auxiliary to an existing coal- 
gas plant; for, instead of requiring further space for storage of coke, part 
of that already required for storage of coke produced and not at once 
sold can be cut off, by reason of the water-gas plant creating a constant 
demand for more or less of the coke so produced. 

Mr. Shelton gives a calculation showing that a water-gas of 0.625 sp. gr. 
would require gas-mains eight per cent greater in diameter than the same 
quantity coal-gas of 0.425 sp. gr. if the same pressure is maintained at the 
holder. The same quantity may be carried in pipes of the same diam- 
eter if the pressure is increased in proportion to the specific gravity. 
With the same pressure the increase of candle-power about balances the 
decrease of flow. With five feet of coal-gas, giving, say, eighteen candle- 
power, 1 cubic foot equals 3.6 candle-power; with water-gas of 23 candle- 
power, 1 cubic foot equals 4.6 candle-power, and 4 cubic feet gives 18.4 
candle-power, or more than is given by 5 cubic feet of coal-gas. Water- 
gas may be made from oven-coke or gas-house coke as well as from an- 
thracite coal. A water-gas plant may be conveniently run in connection 
with a coal-gas plant, the surplus retort coke of the latter being used as 
the fuel of the former. 

In coal-gas making it is impracticable to enrich tlie gas to over twenty 
candle-power without causing too great a tenaency lo smoke, but water- 
gas of as high as thirty candle-power is quite common. A mixture of 
coal-gas and water-gas of a higher C.P. than 20 can be advantageously 
distributed. 

Fuel- value of Illuminating-gas. — E. G. Love {School of Mines 
Qtly, January, 1892) describes F. W. Hartley's calorimeter for determin- 
ing the calorific power of gases, and gives results obtained in tests of the 
carbureted water-gas made by the municipal branch of the Consoli- 
dated Co. of New York. The tests were made from time to time during 
the past two years, and the figures give the heat-units per cubic foot at 
60° F. and 30 inches pressure: 715, 692, 725, 732, 691, 738, 735, 703, 734, 
730, 731, 727. Average, 721 heat-units. Similar tests of mixtures of 
coal- and water-gases made by other branches of the same company give 
694, 715, 684, 692, 727, 665, 695, and 686 heat-units per foot, or an 
average of 694.7. The average of all these tests was 710.5 heat-units, 
and this we may fairly take as representing the calorific power of the 
illuminating gas of New York. One thousand feet of this gas, costing 
$1.25, would therefore vield 710,500 heat-units, which would be equiva- 
lent to 568,400 heat-units for SI. 00. 

The common coal-gas of London, with an illuminating power of 16 to 
17 candles, has a calorific power of about 668 units per foot, and costs 
from 60 to 70 cents per thousand. 

The product obtained by decomposing steam by incandescent carbon, 
as effected in the Motay process, consists of about 40% of CO, and a 
little over 50% of H. 

This mixture would have a heating-power of about 300 units per cubic 
foot, and if sold at 50 cents per 1000 cubic feet would furnish 600,000 units 
for $1.00, as compared with 568,400 units for $1.00 from illuminating gas 
at $1.25 per 1000 cubic feet. This illuminating-gas if sold at $1.15 per 
thousand would therefore be a more economical heating agent than the 
fuel-gas mentioned, at 50 cents per thousand, and be much more advan- 
tageous than the latter, in that one main, service, and meter could be used 
to furnish gas for both lighting and heating. 

A large number of fuel-gases tested by Mr. Love gave from 184 to 470 
heat-units per foot, with an average of 309 units. 

Taking the cost of heat from illuminating-gas at the lowest figure given 



864 



ILLUMINATING-GAS . 



by Mr. Love, viz., $1.00 for 600,000 heat-units, it is a very expensive fuel, 
equal to coal at S40 per ton of 2000 lbs., the coal having a calorific power 
of only 12,000 heat-units per pound, or about 83% of that of pure carbon. 
600,000: (12,000 X 2000) ;: $1 : S40. 

FLOW OF GAS IN PIPES. 

The rate oi flow of gases of different densities, the diameter of pipes 
required, etc., are given in King's Treatise on Coal Gas, vol. ii, 374, as 
follows; 

If d = diameter of pipe in inches, 
Q = quantity of gas in cu. ft. per 

iiour, 
I = length of pipe in yards, 
h = pressure in inches of w^ater, 
5 = specific gravity of gas, air 
being 1, 



Molesw^orth gives Q ■■ 



1000 Vf. 



d- 



^- 



h = 



Q = 1350rf2 



(1350)2/1* 

(1350)2^5^ 

Jdh 



si 



1350 



▼ si 



_•; - 

This formula is said to be based on expenmental data, and to make 
allowance for obstructions by tar, water, and other bodies tending to check 
the flow of gas through the pipe. 

Iving's formula translated into the form of the com mon formula for the 
flow of compressed air or steam in pipes, Q == c ^{Pi — V2) d^/wL, in 
wiiich Q — cu. ft. per min., Pi — V2 = difference in pressure in lbs. per 
sq. in; ?/; = density in lbs. per cu. ft., L = length in ft., d = diam. in ins., 
gives 56.6 for the value of the coefficient c, which is nearly the same as that 
commonly used (60) in calculations of the flow of air in pipes. For values 
of c based on Darcy's experiments on flow of water in pipes see Flow of 
Steam. 

An experiment made by Mr. Clegg, in London, with a 4-in. pipe, 6 miles 
long, pressure 3 in. of w^ater, specific gravity of gas 0.398, gave a discharge 
into the atmosphere of 852 cu. ft. per hour, after a correction of 33 cu. ft. 
was made for leakage. ' 

Substituting this value, 852 cu. ft., for Q in the formula Q =C ^d^h h- si, 
we find C, the coefficient, = 997, which corresponds nearly with the formula 
given by Molesworth. 

Wm. Cox {Am. Mach., Mar. 20, 1902) gives the following formula for 
flow of gas in long pi pes. 



Q =3000 V/^^^^^P^ =41.3 V' 



d^X(Pi^-P2^) 



I ^^-^ t L 

Q= discharge in cu. ft. per hour at atmospheric pressure; d = diam. 
of pipe in ins.; p, = initial and P2 = terminal absolute pressure, lbs. per 
sq. in.; I = length of pipe in feet, L = length in miles. For pi^ — p<^ 
may be substituted (pi + P2) (Pi — Pi)- The specific gravity of the 
gas is assumed to be 0.65, air being 1. For fluids of any other sp. gr., 

s, multiply the coefficients 3000 or 41.3 by Vo.65/s. For air, s = 1, the 
coefficients become 2419 and 33.3. J. E. Johnson Jr.'s formula for air, 
page 619, translated into the same notation as Mr. Cox's, makes the coeffi- 
cients 2449 and 33.5. 

Services for Lamps. (Molesworth.) 



Lamps. 


Ft. from 
Main. 


Require 
Pipe-bore. 


Lamps. 


Ft. from 
Main. 


Require 
Pipe-bore. 


2 


40 
40 
50 
100 


3/8 in. 
V2in. 
5/8 in. 
3/4 in. 


15 


130 
150 
180 
200 


1 in. 


4 . 


20 


1 1/4 in. 


6 


25 


1 1/2 in. 


10 


30 


1 3/4 in. 









(In cold climates no service less than 3/4 in. should be used.) 



FLOW OF GAS IN PIPES. 



865 



Factors for Reducing Volumes of Gas to Equivalent Volumes at 
60° F. and 30-inches Barometer. 

(Multiply the observed volume by the factor to obtain the 
equivalent volume.) 






Barometer. 



30.0 29.8 29.6 29.4 29.2 29.0 28.8 28.6 28.4 28.2 28.0 



-30 

-25 

-20 

-15 

-10 

-- 5 



5 

10 

15 

20 

25 

30 

35 

40 

45 

50 

55 

60 

65 

70 

75 

80 

85 

90 

95 

100 

105 

110 

115 

120 



.2095 
.1956 
.1820 
.1687 
.1557 

1430 
.1306 

1184 

1065 

0948 

0834 

0722 

0613 

0506 

0400 

02971 1 

0196 I 

0097 1 1 

0000 

9905 
.9811 
.9719 
.9629 
.9541 
.9454 
.9369 
.9285 
.9203 
.9122 
.9043 
.8965 



2014 
1876 
1741 
1609 
1480 
135411 
1230 1 
1109 1 
0991 1 
.0875,1 
1 



.0762 
.0651 
.0542 
.0435 
.0331 
.022^ 
.0128 
.0030 
.9933 
.9838 
.9746 
.9655 
.9565 
.9477 
.9391 
.9306 
.9223 
.9141 
9061 
.8982 
.8905 



.1934 
.1796 
.1662 
.1531 
.1403 
.1277 
.1155 
.1035 
.0917 
.0802 
.0689 
.0579 
.0471 
.0365 
.0261 
.0160 
.0060 
.9962 
.9867 
.9772 
.9680 
.9590 
.9501 
.9414 
.9328 
.9244 
.9161 
.9080 
.9000 
.8922 
.8845 



.1853 
.1716 
.1583 
.1453 
.1326 
.1201 
.1079 
.0960 
.0843 
.0729 
.0617 
.0508 
.0401 
.0295 
0192 
0091 
9992 
.9895 
.9800 
.9706 
.9615 
.9525 
.9437 
.9350 
.9265 
.9181 
.9099 
.9019 
.8940 
.8862 
.8785 



1772 
1637 
1505 
1375 
1249 
1125 
1004 
.0885 
0770 
0656 
0545 
0436 
0330 
0225 
0123 
.0023 
.9924 
.9828 
.9733 
.9640 
.9550 
.9460 
.9373 
.9286 
.9202 
.9119 
.9037 
.8957 
.8879 
.8801 
.8726 



1692 
1557 
1426 
1297 
1172 
1049 



1.0929 1 



0811 
0696 
0585 
0473 
0365 
0259 
0155 
0053 
9954 
9856 
.9761 
.9667 
.9574 
.9484 
.9395 
.9308 
.9223 
.9139 
.9056 
.8976 
.8896 
.8818 
.8741 
.8666 



.1611 
.1476 
.1347 
.1219 
,1095 
.0973 
.0853 
.0736 
.0622 
.0510 
.0401 
.0293 
.0188 
.0085 
.9984 
.9885 
.9788 
.9693 
.9600 
.9508 
.9419 
.9331 
.9244 
.9159 
.9076 
.8994 
.8914 
.8835 
.8757 
.8681 
.8606 



1530 
1398 
1268 
1141 
1018 
0896 
0778 
0662 
0548 
0437 
.0328 
0222 
0118 
0015 
9915 
9817 
.9720 
.9626 
.9533 
.9442 
.9353 
.9266 
.9180 
.9096 
.9013 
.8931 
.8852 
.8773 
.8696 
.8621 
.8546 



1450 
1318 
1189 
1064 
0941 
0820 
0703 
0587 
0474 
0364 
0256 
0150 
0047 
9945 
9845 
9748 
9652 
9559 
9467 
9376 
9288 
9201 
9116 
9032 
8950 
8869 
8790 
8712 
8636 
8560 
8486 



1369 
1238 

nil 

0986 
0863 
0744 



1.1288 
1.1159 
1.1032 
1.0908 
1.0786 
1.0668 
0627 1.0552 
.0513 1.0438 
0401 1 1.0327 
0291 1.021 8 
0184 1.0112 
0079 1.0007 
9976 0.9905 
.9875! .9805 
.9776! .9707 
.9679 .9611 
.9584 .9516 
9491 .9424 
9400 .9333 



.9310 
.9223 
.9136 
.9052 
.8%8 
.8887 
.8807 
.8728 
.8651 
.8575 
.8500 
.8427 



.9244 
.9157 
.9071 
.8987 
.8905 
.8824 
.8744 
.8666 
.8589 
.8514 
.8440 
.8367 



Formula: Equivalent volume = observed volume X .-; — ^/r. .^ X 7777- 

t-j- 4oy .0 so 



Maximum Supply of Gas through Pipes iu cu. ft. per Hour, 
Specific Gravity being talcen at 0.45, calculated from the 
Formula = 1000 \/c«5/i :^f.^ (Molesworth . ) 

Length of Pipe = 10 Yards. 



Diameter of 






Pressure by the Water-gage in Inches. 






Pipe in 


























Inches. 


0.1 


0.2 


0.3 


0.4 1 0.5 0.6 1 0.7 


0.8 


0.9 


1.0 


V2 


26 


37 


46 


53 ! 59 ! 64 I 70 


74 


79 


83 


3/4 


73 


103 


126 


145 162 1 187 


192 


205 


218 


230 


1 


149 


211 


258 


298 


333 : 365 


394 


422 


447 


471 


IV4 


260 


368 


451 


521 


582 


638 


. 689 


737 


781 


823 


IV2 


411 


581 


711 


821 


918 


1006 


1082 


1162 


1232 


1299 


2 


843 


1192 


1460 


1686 


1886 


2066 


2231 


2385 


2530 


2667 



(Continued on p. 866) 



866 



ILLUMINATING- GAS. 



Maximum Supply of Gas through Pipes in cu. ft. per Hour, 
Specific Gravity b eing ta lcen at 0.45, calculated from the 
Formula Q = 1000 Vd^h ^ si, (Molesworth.) — (Continued) 

Length of Pipe = 100 Yards. 



Diam. 
of Pipe, 
Inches. 






Pressure by the Water-gage 


in Inches. 




0.1 


0.2 


0.3 


0.4 


0.5 1 0.75 


1.0 


1.25 


1.5 


2 


2.5 


3/4 


23 


32 


42 


46 


51 


63 


73 


81 


89 


103 


115 


1 


47 


67 


82 


94 


105 


129 ' 149 


167 


183 


211 


236 


IV4 


82 


116 


143 


165 


184 


225 260 


291 i 319 


368 


412 


IV2 


130 


184 


225 


260 


290 


356 411 


459 i 503 ! 581 


649 


2 


267 


377 


462 


533 


596 


730 843 


943 1033 1 1193 


1333 


2V2 


466 


659 


807 


932 


1042 


1276 1473 


1647 1804 1 2083 


2329 


3 


735 


1039 


1270 


1470 


1643 


2012 2323 


2593 2846 3286 


3674 


31/2 


1080 


1528 


1871 


2161 


2416 2958 3416 


3820 4184 4831 


5402 


4 


1508 


2133 


2613 


3017 


3373 ! 4131 4770 


5333 5842 | 6746 


7542 



Length of Pipe = 1000 Yards. 



Diam. 




Pressure by the Water 


-gage in Inches. 




of Pipe, 






















Inches. 


0.5 


0.75 1.0 j 1.5 


2.0 


2.5 


3.0 


1 


33 


41 


47 


58 


67 


75 


82 


IV2 


92 


113 


130 


159 


184 


205 


226 


2 


189 


231 


267 


327 


377 


422 


462 


21/2 


329 


403 


466 


571 


659 


737 


807 


3 


520 


636 


735 


900 


1039 


1162 


1273 


4 


1067 


1306 


1508 


1847 


2133 


2385 


2613 


5 


1863 


2282 


2635 


3227 


3727 


4167 


4564 


6 


2939 


3600 


4157 


5091 


5879 


6573 


7200 



Length of Pipe = 5000 Yards. 



Diameter of 
Pipe in 
Inches. 


Pressure by the Water-gage in Inches. 


1.0 


1.5 


2.0 


2.5 


3.0 


8 
9 
10 
12 


119 

329 

675 

1179 

1859 

2733 

3816 

5123 

6667 

10516 


146 

402 

826 

1443 

2277 

3347 

4674 

6274 

8165 

12880 


169 

465 

955 

1667 

2629 

3865 

5397 

7245 

9428 

14872 


189 

520 

1067 

1863 

2939 

4321 

6034 

8100 

10541 

16628 


207 

569 

1168 

2041 

3220 

4734 

6610 

8873 

11547 

18215 



Mr. A. C. Humphreys says his experience goes to show that the^e 
tables give too small a flow, but it is difficult to accurately check the 
tables, on account of the extra friction introduced by rough pipes, 
bends, etc. For bends, one rule is to allow 1/42 of an inch pressure for 
each right-angle bend. 

Where there is apt to be trouble from frost it is well to use no service 
of less diameter than 3/4 in., no matter how short it may be. In ex- 
tremely cold climates this is now often increased to 1 in., even for a 
single lamp. The best practice in the XJ. S. now condemns any service 
less than 3/4 in, 



STEAM. 867 

STEAM. 

The Temperature of Steam in contact with water depends upon 
the pressure under which it is generated. At the ordinary atmospiieric 
pressure (14.7 lb. per sq. in.) its temperature is 212° F. As the pressure 
is increased, as by the steam being generated in a closed vessel, its tem- 
perature, and that of the water in its presence, increases. 

Saturated Steam is steam of tlie temperature due to its pressure — 
not superheated. 

Superheated Steam is steam heated to a temperature above that due 
to its pressure. 

Dry Steam is steam which contains no moisture. It may be either 
saturated or superheated. 

Wet Steam is steam containing intermingled moisture, mist, or 
spray. It has the same temperature as dry saturated steam of the same 
pressure. 

Water introduced into the presence of superheated steam will flash 
into steam imtil the temperatm-e of the steam is reduced to that due its 
pressure. Water in the presence of saturated steam has the same 
temperature as the steam. Should cold water be introduced, lowering 
the temperature of the whole mass, some of the steam will be con- 
densed, reducing the pressure and temperature of the remainder, until 
equilibrium is established. 

Total Heat of Saturated Steam (above 32° F.). — According'to Marks 
and Davis, the formula for total heat of steam, based on researches 
by Henning, Knoblauch, Linde and Klebe, is H = 1150.3 + 0.3745 {t - 
212°) - 0.000550 {t - 212)2, in which H is the total heat in B.T.U. above 
water at 32° F. and t is the temperature Fahrenheit. 

Latent Heat of Steam. — The latent heat, or heat of vaporization, is 
obtained by subtracting from the total heat at any given temperature 
the heat of the liquid, or total heat above 32° in water of the same tem- 
perature. 

The total heat in steam (above 32°) includes three elements: 

1st. The heat required to raise the temperature of the water to the 
temperature of the steam. 

2d. The heat required to evaporate the water at that temperature, 
called internal latent heat. 

3d. The latent heat of volume, or the external work done by the steam 
in making room for itself against the pressure of the superincumbent at- 
mosphere (or surrounding steam if inclosed in a vessel) . 

The sum of the last two elements is called the latent heat of steam. 

Heat required to Generate 1 lb. of Steam from water at 32° F. 

Heat-units. 

Sensible heat, to raise the water from 32° to 212° = 180 . 

Latent heat, 1, of the formation of steam at 212° = 897.6 

2, of expansion against the atmospheric 
pressure, 2116.4 lb. per sq. ft. X 
26.79 cu. ft. = 55,786 foot-pounds -v- 

778= 72.8 

970.4 

Total heat above 32° F 1150 . 4 

The Heat-Unit, or British Thermal Unit.— The old definition of 
the heat-unit (Rankine), viz., the quantity of heat required to raise the 
temperature of 1 lb. of water 1° F., at or near its temperature of maxi- 
mum density (39.1° F.), is now (1909) no longer used. Peabody defines 
it as the heat required to raise a pound of water from 62° to 63° F., and 
Marks and Davis as i/iso of the heat required to raise 1 lb. of water from 
32° to 212° F. By Peabody's definition the heat required to raise 1 lb. of 
water from 32° to 212° is 180.3 instead of 180 units, and the heat of va- 
porization at 212° is 969.7 instead of 970.4 units. 

Specific Heat of Saturated Steam. — When a unit weight of saturated 
steam is increased in temperature and in pressure, the volume decreasing 
so as to just keep it saturated, the specific heat is negative, and decreases 
as temperature increases. (See Wood, Thermodynamics, p. 147; Pea- 
body, Thermodynamics, p. 93.) 



868 



STEAM. 



Absolute Zero. — The value of the absolute zero has been variously 
given as from 459.2 to 460.66 degrees below the Fahrenheit zero. Marks 
and Davis, comparing the results of Berthelot (1903) , Buckingham, 1907, 
and Ross-Innes, 1908, give as the most probable value — 459.64° F. 
The value— 460° is close enough for all engineering calculations. 

The Mechanical Equivalent of Heat. — The value generally accepted, 
based on Rowland's experiments, is 778 ft.-lb. Marks and Davis give 
the value 777.52 standard ft.-lb., based on later experiments, and on the 
value of rj = 980.665 cm. per sec. 2, = 32.174 ft. per sec. 2, fixed by inter- 
national "agreement (1901). [With this value of g and the mean gram- 
calorie being taken as equivalent to 4.1834 X 10^ dyne-centimeters, the 
equivalent of 1 B.T.U. is 777.54 ft.-lb.] These values of the absolute 
zero and of the mechanical equivalent of heat have been used by Marks 
and Davis in the computation of their steam tables. In refined in- 
vestigations involving the value of the mechanical equivalent of heat 
the value of g for the latitude in which the experiments are made must 
be considered. 

Marks and Davis give the value of the mean gram-calorie as 4.1834 
joules, which is equivalent to 777.54 ft.-lb. = 1 B.T.U. Goodenough, 
taking 1 mean calorie = 4.184 joules, gives 1 mean B.T.U. = 777.64 
ft.-lb. 

Pressure of Saturated Steam. — Holborn and Henning, Zeit. des 
Ver. deutscher Ingenieure, Feb. 20, 1909, report results of measurements 
of the pressures of saturated steam at temperatures ranging from 50° to 
200° C. (112° to 392° F.). Their values agree closely with those ob- 
tained in 1905 by Knoblauch, Linde and Klebe. From a table in the 
article giving pressures for each degree from 0° to 200° C, the following 
values have been transformed into^English measurements {Eng. Digest^ 
April, 1909). 



Deg. F. 


Lb. per sq. 
in. 


Deg. F. 


Lb. per sq. 

in. 


Deg. F. 


Lb. per sq. 

in. 


32 
68 
100 


0.0885 
0.3386 
0.9462 


150 
200 
250 


3.715 
11.527 
29.819 


300 
350 
400 


66.972 
134.508 
'248.856 



Volume of Saturated Steam.' — The values of specific volumes of satu- 
rated steam are computed by Clapeyron's equation (Marks and Davis's 
Tables), which gives results remarkably close to those found in the ex- 
periments of Knoblauch, Linde and Klebe. 

Goodenough's Steam Tables. (Properties of Steam and Ammonia, 
John Wiley & Sons, 1915.) — These tables are based on the same original 
data as those of Marks and Davis, and on some later ones. They adopt 
the same definition of the thermal unit, the mean B.T.U. or i/iso of 
the heat required to raise the temperature of 1 lb. of water from 32° 
to 212° F. The differences between the figures given in the two sets 
of tables are in general small ; the most important being that the latent 
heat of steam at 212° F. is given as 971.7 B.T.U. instead of 970.4, the 
figure given by Marks and Davis. A comparison of some figures from 
the two tables is given on p. 869, Goodenough's values being given in 
the upper lines (G), and Marks and Davis's in the lower lines (M), 
only the digits which differ from those in the upper lines being given. 

Properties of Saturated Steam at High Temperatures. — (From G. A. 
Goodenough's Properties of Steam and Ammonia, 1915.) 



Temp. 

°F. 


Pressure 


Volume of 


Weight of 


Heat of 


Heat of 


Latent 


Lb. per 


1 Lb., 


1 Cu. ft.. 


Liquid 


Vapor, 


Heat, 


Sq. in. 


Cu. ft. 


Lb. 


B.T.U. 


B.T.U. 


B.T.U. 


600 


1540 


0.272 


3.68 


604.5 


1164.2 


488.9 


620 


1784 


0.226 


4.43 


633 


1151 


452 


640 


2057 


0.186 


5.38 


664 


1134 


409 


660 


2361 


0.151 


6.60 


700 


1112 


358 


680 


2699 


0.118 


8.5 


745 


1080 


290 


700 


3075 


0.080 


12.5 


820 


1018 


171 


706.3 


3200 


0.048 


20.90 


921 


921 






STEAM. 



869 



Properties of Saturated Steam. 

Comparison of Goodenough and Marks and Davis (see p. 868.) 





Abso- 
lute 
Pres- 
sure. 


Tem- 
pera- 
ture 

°F. 


Total Heat 
Above 32°. 


Latent 
Heat. 


Vol- 
ume, 
Cu.Ft. 

in 
1 Lb. 


Weight 

of 
lCu.Ft. 


Entropy. 




In 
Water. 


In 

Steam. 


Water. 


Vapor- 
ization. 


G. 


0.0887 


32 





1073.0 


1073.0 


3296 


0.000304 





2.1826 


M. 


** 


" 


*• 


.4 


.4 


4 


** 


" 


32 


G. 


0.949 


100 


68.00 


1104.6 


1036.6 


350.3 


0.002855 


0.1296 


1.8523 


M. 


" 


•* 


7.97 


3.6 


5.6 


.8 




5 


05 


G. 


• 14.7 


212 


180 


1151.7 


971.7 


26.81 


0.03730 


0.3120 


1.4469 


M. 


•* 


" 


" 


0.4 


0.4 


.79 


2 


18 


47 


G. 


50 


281 


249.8 


1175.6 


925.9 


8.53 


0.1173 


0.4108 


1.2501 


M. 


*' 


" 


50.1 


3.6 


3.5 


1 


5 


13 


468 


G. 


100 


327.8 


297.9 


1188.4 


890.5 


4.442 10.2251 


0.4736 


1.1309 


M. 


•* 


« 


8.3 


6.3 


88.0 


29 


8 


43 


277 


G. 


150 


358.5 


329.8 


1194.7 


864.9 


3.020 


0.3311 


0.5131 


1.0573 


M. 


" 


** 


30.2 


3.4 


3.2 


12 


20 


42 


50 


G. 


200 


381.9 


354.5 


1198.5 


844.0 


2.292 


0.4364 


0.5426 


1.0030 


M. 


** 


** 


.9 


.1 


3.2 





70 


37 


19 


G. 


250 


401.1 


374.9 


1200.6 


825.8 


1.846 


0.542 


0.5663 


0.9595 


M. 


" 


'* 


5.2 


1.5 


6.3 


50 


1 


76 


600 


G. 


300 


417.5 


392.4 


1201.9 


809.4 


1.545 


0.647 


0.5863 


0.9229 


M. 


•* 




.7 


4.1 


11.3 


51 


5 


78 


51 


G. 


400 


444.8 


422.0 


1202.5 


780.6 


1.162 


0.860 


0.6190 


0.8631 


M. 


" 




'* 


8. 


6. 


70 


" 


210 


80 


G. 


500 


467.2 


446.6 


1201.7 


755.0 


0.928 


1.077 


0.6455 


0.8146 


M. 


" 


.3 


8. 


10. 


62. 


30 


80 


80 


220 


G. 


600 


486.5 


468.0 


1199.8 


731.8 


0.770 


1.30 


0.6679 


0.7735 


M. 


'* 


.6 


9. 


210. 


41. 


60 


2 


700 


830 



Volume of Superheated Steam,- 



pv = 0.5962 T- p a + 0.0014 p) 



Linda's equation (1905), 
150,300,000 



2^3 



- 0.08331 



in which p is in lb. per sq. in., v is in cu. ft. and T is the absolute 
temperature on the Fahrenheit scale, has been used in the computation 
of Marks and Davis's tables. 

Specific Heat of Superheated Steam. — Mean specific heats from the 
temperature of saturation to various temperatures at several pressures 
English and metric units. — Knoblauch and Jakob (from Peabody's 
Tables). 



Kg. per 

sq. cm. 
Lb. per 

sq. in. . 
Temp., 

sat.°C. 
Temp., 

sat. °F. 


1 

14.2 
99 
210 


2 

28.4 
120 
248 


4 

56.9 
143 
289 


85.3 
158 
316 


8 
113.3 
169 
336 


10 

142.2 
179 
350 


12 

170.6 
187 
368 


,4 

199.1 

194 

381 


16 
227.5 
200 
392 


18 
256.0 
206 
403 


20 

284.4 
211 
412 


°F. 
71? 


°C. 
100 463 






















30? 


150; .462 


478 515 


















39? 


200 462 .475 .502 


0.530 
.514 
.505 
.503 
.504 


6.560 
.532 
.517 
.512 
.512 


0.597 
.552 
.530 
.522 
.520 


0.635 
.570 
.541 
.529 
.526 


0.677 
.588 
.550 
.536 
.531 








482 
572 
662 
752 


250 
300 
350 
400 


.463 
.464 
.468 
.473 


.474 
.475 
.477 
.481 


.495 
.492 
.492 
.494 


6.609 6.635 
.561 .572 
.543 .550 
.537 .542 


0.664 
.585 
.557 
.547 



870 



STEAM. 



Properties of Superheated Steam. — See the table on page 871, con- 
densed from Marks and Davis's tables. 

The Specific Density of Gaseous Steam, that is, steam considerably 
superheated, is 0.622, that of air being 1. That is to say, the weight of a 
cubic foot of gaseous steam is about five-eighths of that of a cubic foot of 
air, of the same pressure and temperature. 

The density or weight of a cubic foot of gaseous steam is expressible by 
the same formula as that of air, except that the multipUer or coeflacient 
is less in proportion to the less specific density. Thus, 



D 



2.7074 pX 0.622 _ 1.684 p 



^+460 i+460' 

in which D is the weight of a cubic foot, p the total pressure per square 
inch and t the temperature Fahrenheit. (Clark's Steam-engine.) 

H. M. Prevost Murphy (Eng. News, June 18, 1908) shows that the 
specific density is not a constant, but varies with the temperature, and 

O 0Q2^ 

that the correct value is 0.6113 + oVq _/ 

The Rationalization of Regnault's Experiments on Steam. — 

(J. McFarlane Gray. Proc. Inst. M. E., July, 1889.) — The formulae con- 
structed by Regnault are strictly empirical, and were based entirely on 
his experiments. They are therefore not valid beyond the range of tem- 
peratures and pressures observed. 

Mr. Gray has made a most elaborate calculation, based not on experi- 
ments but on fundamental principles of thermodynamics, from which he 
deduces formulae for the pressure and total heat of steam, and presents 
tables calculated therefrom which show substantial agreement vvlth 
Regnault 's figures. He gives the follo^^ing examples of steam-pressures 
calculated for temperatures beyond the range of Regnault 's experiments. 



Temperature. 


Pounds per 
Sq. Irx. 


Temperature. 


Pounds per 


C. 


Fahr. 


C. 


Fahr. 


Sq. In. 


230 


446 


406.9 


340 


644 


2156.2 


240 


464 


488.9 


360 


680 


2742.5 


250 


482 


579.9 


380 


716 


3448.1 


260 


500 


691.6 


400 


752 


4300.2 


280 


536 


940.0 


415 


779 


5017.1 


300 


572 


1261.8 


427 


800.6 


5659.9 


320 


608 


1661.9 









These pressures are higher than those obtained by Regnault's 
formula, which gives for 415° C. only 4067.1 lbs. per square inch. 

Available Energy in Expanding Steam. — Rankine Cycle. (J. B. 
Stanwood, Power, June 9, 1908.) — A simple formula for finding, with the 
aid of the steam and entropy tables, the available energy per pound ol 
steam in B.T.U. when it is expanded adiabatically from a higher to a 
lower pressure is: 

U = H - Hi+ T(Ni - N), 

U = available B.T.U. in 1 lb. of expanding steam; H and Hi total heat 
in 1 lb. steam at the two pressures; T = absolute temperature at the 
lower pressure; N — Ni, difference of entropy of 1 lb. of steam at the two 
pressures. 

Example. — Required the available B.T.U. in 1 lb. steam expanded 
from 100 lbs. to 14.7 lbs. absolute. H = 1186.3; Hi = 1150.4; T = 672; 
N = 1.602; A^i = 1.756. 35.9 4- 103.5 = 138.4. 

Efficiency of the Cycle. — Let the steam be made from feed-water at 
212°. Heat required = 1186.3 - 180 = 1006.3; efficiency = 138.4 -J- 
1006.3 = 0.1375. 

Rankine Cycle. — This efficiency is that of the Rankine cycle, which 
assumes that the steam is expanded adiabatically to the exhaust pres- 
sure and temperature, and that the feed-water from which the steam is 
made is introduced into the system at the temperature of the exhaust. 

Carnot Cycle. — The Carnot ideal cycle, which assumes that all the 
heat entering the system enters at the highest temperature, and in which 
the efficiency is (Ti - T2) ^ Tx, gives (327.8 - 212) -h (327.8 + 460) = 
0.1470 and the available energy in B.T.U. = 0.1470 X 1006.3 = 147.9 B.T.U. 



871 



Properties of Saturated Steam. 

(Condensed from Marks and Davis's Steam Tables and Diagrams, 1909, 
by permission of the publishers, Longmans, Green & Co.) 



Sd 




Total Heat 


•^J. 


*;*« 


d (2 


03 


m . 

^ 


II 
II 


above 32° F. 


e3 

«^ d 




"3 

i 


1 i 

1 i 


the Steam 

H 
eat-Units. 


< 


H 


5 w 


^ K 


►-1 


> 


w 



f 0.0886 


32 


0.00 


1073.4 


1073.4 


0.1217 


40 


8.05 


1076.9 


1068.9 


0.1780 


50 


18.08 


1081.4 


1063.3 


0.2562 


60 


28.08 


1085.9 


1057.8 


0.3626 


70 


38.06 


1090.3 


1052.3 


0.505 


80 


48.03 


1094.8 


1046.7 


0.696 


90 


58.00 


1099.2 


1041.2 


0.946 


100 


67.97 


1103.6 


1035.6 


1 


101.83 


69.8 


1104.4 


1034.6 


2 


126.15 


94.0 


1115.0 


1021.0 


3 


141.52 


109.4 


1121.6 


1012.3 


4 


153.01 


120.9 


1126.5 


1005.7 


3 


162.28 


130.1 


1130.5 


1000.3 


6 


170.06 


137.9 


1133.7 


995.8 


7 


176.85 


144.7 


1136.5 


991.8 


8 


182.86 


150.8 


1139.0 


988.2 


9 


188.27 


156.2 


1141.1 


985.0 


10 


193.22 


161.1 


1143.1 


982.0 


11 


197.75 


165. Z 


1144.9 


979.2 


12 


201.96 


169.9 


1146.5 


976.6 


13 


205.87 


173.8 


1148.0 


974.2 


14 


209.55 


177.5 


1149.4 


971.9 


14.70 


212 


180.0 


1150.4 


970.4 


15 


213.0 


181.0 


1150.7 


969.7 


16 


216.3 


184.4 


1152.0 


%7.6 


17 


219.4 


187.5 


1153.1 


965.6 


18 


222.4 


190.5 


1154.2 


963.7 


19 


225,2 


193.4 


1155.2 


961.8 


20 


228.0 


196.1 


1156.2 


960.0 


21 


230.6 


198.8 


1157.1 


958.3 


22 


233.1 


201.3 


1158.0 


956.7 


23 


235.3 


203.8 


1158.8 


955.1 


24 


237.8 


206.1 


1159.6 


953.5 


25 


240.1 


208.4 


1160.4 


952.0 


26 


242.2 


210.6 


1161.2 


950,6 


27 


244.4 


212.7 


1161.9 


949.2 


28 


246.4 


214.8 


1162.6 


947.8 


29 


248.4 


216.8 


1163.2 


946.4 


30 


250.3 


218.8 


1163.9 


945.1 


31 


252.2 


220.7 


1164.5 


943.8 


32 


254.1 


222.6 


1165.1 


942.5 


33 


255.8 


224.4 


1165.7 


941.3 


34 


257.6 


226.2 


1166.3 


940.1 


35 


259.3 


227.9 


1166.8 


938.9 


36 


26L0 


229.6 


1167.3 


937.7 


37 


262.6 


231.3 


1167.8 


936.6 


38 


264.2 


232.9 


1168.4 


935.5 


39 


265.8 


234.5 


1168.9 


934.4 


40 


267.3 


236.1 


1169.4 


933.3 


41 


268.7 


237.6 


1169.8 


932.2 


42 


270.2 


239.1 


1170.3 


931.2 


43 


271.7 


240.5 


1170.7 


930.2 


44 


273.1 


242.0 


1171.2 


929.2 


45 


274.5 


243.4 


1171.6 


928.2 



3294 
2438 
1702 
1208 
871 
636.8 
469.3 
350.8 
333.0 
173.5 
118.5 
90.5 
73.33 
61.89 
53.56 
47.27 
42.36 
38.38 
35.10 
32.36 
30.03 
28.02 

26.79 
26.27 
24.79 
23.38 
22.16 
21.07 
20.08 
19.18 
18.37 
17.62 
16.93 
16.30 
15.72 
15.18 
14.67 
14.19 
13.74 
13.32 
12.93 
12.57 
12.22 
11.89 
11.58 
11.29 
11.01 
10.74 
10.49 
10.25 
10.02 
9.80 
9.59 
9.39 



0.000304 


0.0000 


0.000410 


0.0162 


0.000587 


0.0361 


0.000828 


0.0555 


0.001148 


0.0745 


0.001570 


0.0932 


0.002131 


0.1114 


0.002851 


0.1295 


0.00300 


0.1327 


0.00576 


0.1749 


0.00845 


0.2008 


0.01107 


0.2198 


0.01364 


0.2348 


0.01616 


0.2471 


0.01867 


0.2579 


0.02115 


0.2673 


0.02361 


0.2756 


0.02606 


0.2832 


0.02849 


0.2902 


0.03090 


0.2967 


0.03330 


0.3025 


0.03569 


0.3081 


0.03732 


0.3118 


0.03806 


0.3133 


0.04042 


0.3183 


0.04277 


0.3229 


0.04512 


0.3273 


0.04746 


0.3315 


0.04980 


0.3355 


0.05213 


0.3393 


0.05445 


0.3430 


0.05676 


0.3465 


0.05907 


0.3499 


0.0614 


0.3532 


0.0636 


0.3564 


0.0659 


0.3594 


0.0682 


0.3623 


0.0705 


0.3652 


0.0728 


0.3680 


0.0751 


0.3707 


0.0773 


0.3733 


0.0795 


0.3759 


0.0818 


0.3784 


0.0841 


0.3808 


0.0863 


0.3832 


0.0886 


0.3855 


0.0908 


0.3877 


0.0931 


0.3899 


0.0953 


0.3920 


0.0976 


0.3941 


0.0998 


0.3962 


0.1020 


0.3982 


0.1043 


0.4002 


0.1065 


0.4021 



872 







Properties of Saturated Steam. (Continued.) 




£"« 


2^ 




Total Heat 


•^^ 


^ 


d-Q 


0) 


§ 


S^ 


:^ , 




above 32° F. 


^c3 


^^ 


o3 


-c 


> 














"3 . 


2B 

"o ^ 


^ 








0. 


13 


2 <D 
















o 


< 


H 


a w 


a M 


^ 


> 


^ 


W 


W 


31.3 


46 


275.8 


244.8 


1172.0 


927.2 


9.20 


0.1087 


0.4040 


1.2607 


32.3 


47 


277.2 


246.1 


1172.4 


926.3 


9.02 


0.1109 


0.4059 


1.2571 


33.3 


48 


278.5 


247.5 


1172.8 


925.3 


8.84 


0.1131 


0.4077 


1.2536 


34.3 


49 


279.8 


248.8 


1173.2 


924.4 


8.67 


0.1153 


0.4095 


1.2502 


35.3 


50 


281.0 


250.1 


1173.6 


923.5 


8.51 


0.1175 


0.4113 


1.2468 


36.3 


51 


282.3 


251.4 


1174.0 


922.6 


8.35 


0.1197 


0.4130 


1.2432 


37.3 


52 


283.5 


252.6 


1174.3 


921.7 


8.20 


0.1219 


0.4147 


1.2405 


38.3 


53 


284.7 


253.9 


1174.7 


920.8 


8.05 


0.1241 


0.4164 


1.2370 


39.3 


54 


285.9 


255.1 


1175.0 


919.9 


7.91 


0.1263 


0.4180 


1.2339 


40.3 


55 


287.1 


256.3 


1175.4 


919.0 


7.78 


0.1285 


0.4196 


1.2309 


41.3 


56 


288.2 


257.5 


1175.7 


918.2 


7.65 


0.1307 


0.4212 


1.2278 


42.3 


57 


289.4 


258.7 


1176.0 


917.4 


7.52 


0.1329 


0.4227 


1.2248 


43.3 


58 


290.5 


259.8 


1176.4 


916.5 


7.40 


0.1350 


0.4242 


1.2218 


44.3 


59 


291.6 


261.0 


1176.7 


915.7 


7.28 


0.1372 


0.4257 


1.2189 


45.3 


60 


292.7 


262.1 


1177.0 


914.9 


7.17 


0.1394 


0.4272 


1.2160 


46.3 


61 


293.8 


263.2 


1177.3 


914.1 


7.06 


0.1416 


0.4287 


1.2132 


47.3 


62 


294.9 


264.3 


1177.6 


913.3 


6.95 


0.1438 


0.4302 


1.2104 


48.3 


63 


295.9 


265.4 


1177.9 


912.5 


6.85 


0.1460 


0.4316 


1.2077 


49.3 


64 


297.0 


266.4 


1178.2 


911.8 


6.75 


0.1482 


0.4330 


1.2050 


50.3 


65 


298.0 


267.5 


1178.5 


911.0 


6.65 


0.1503 


0.4344 


1.2024 


51.3 


66 


299.0 


268.5 


1178.8 


910.2 


6.56 


0.1525 


0.4358 


1.1998 


52.3 


67 


300.0 


269.6 


1179.0 


909.5 


6.47 


0.1547 


0.4371 


1.1972 


53.3 


68 


301.0 


270.6 


1179.3 


908.7 


6.38 


0.1569 


0.4385 


1.1946 


54.3 


69 


302.0 


271.6 


1179.6 


908.0 


6.29 


0.1590 


0.4398 


1.1921 


55.3 


70 


302.9 


272.6 


1179.8 


907.2 


6.20 


0.1612 


0.4411 


1.1896 


56.3 


71 


303.9 


273.6 


1180.1 


906.5 


6.12 


0.1634 


0.4424 


1.1872 


57.3 


72 


304.8 


274.5 


1180..4 


905.8 


6.04 


0.1656 


0.4437 


1.1848 


58.3 


73 


305.8 


275.5 


1180.6 


905.1 


5.96 


0.1678 


0.4449 


1.1825 


59.3 


74 


306.7 


276.5 


1180.9 


904.4 


5.89 


0.1699 


0.4462 


1.1801 


60.3 


75 


307.6 


277.4 


1181.1 


903.7 


5.81 


0.1721 


0.4474 


1.1778 


61.3 


76 


308.5 


278.3 


1181.4 


903.0 


5.74 


0.1743 


0.4487 


1.1755 


62.3 


77 


309.4 


279.3 


1181.6 


902.3 


5.67 


0.1764 


0.4499 


1.1730 


63.3 


78 


310.3 


280.2 


1181.8 


901.7 


5.60 


0.1786 


0.4511 


1.1712 


64.3 


79 


311.2 


281.1 


1182.1 


901.0 


5.54 


0.1808 


0.4523 


1.1687 


65.3 


80 


312.0 


282.0 


1182.3 


900.3 


5.47 


0.1829 


0.4535 


1.1665 


66.3 


81 


312.9 


282.9 


1182.5 


899.7 


5.41 


0.1851 


0.4546 


1.1644 


67.3 


-82 


313.8 


283.8 


1182.8 


899.0 


5.34 


0.1873 


0.4557 


1.1623 


68.3 


83 


314.6 


284.6 


1183.0 


898.4 


5.28 


0.1894 


0.4568 


1.1602 


69.3 


84 


315.4 


285.5 


1183.2 


897.7 


5.22 


0.1915 


0.4579 


1.1581 


70.3 


85 


316.3 


286.3 


1183.4 


897.1 


5.16 


0.1937 


0.4590 


1.1561 


71.3 


86 


317.1 


287.2 


1183.6 


896.4 


5.10 


0.1959 


0.4601 


1.1540 


72.3 


%7 


317.9 


288.0 


1183.8 


895.8 


5.05 


0.1980 


0.4612 


1.1520 


73.3 


88 


318.7 


288.9 


1184.0 


895.2 


5.00 


0.2001 


0.4623 


1.1500 


74.3 


89 


319.5 


289.7 


1184.2 


894.6 


4.94 


0.2023 


0.4633 


1.1481 


75.3 


90 


320.3 


290.5 


1184.4 


893.9 


4.89 


0.2044 


0.4644 


1.1461 


76.3 


91 


321.1 


291.3 


1184.6 


893.3 


4.84 


0.2065 


0.4654 


1.1442 


77.3 


92 


321.8 


292.1 


1184.8 


892.7 


4.79 


0.2087 


0.4664 


1.1423 


78.3 


93 


322.6 


292.9 


1185.0 


892.1 


4.74 


0.2109 


0.4674 


1.1404 


79.3 


94 


323.4 


293.7 


1185.2 


891.5 


4.69 


0.2130 


0.4684 


1.1385 


80.3 


95 


324.1 


294.5 


1185.4 


890.9 


4.65 


0.2151 


0.4694 


1.1367 


81.3 1 


96 


324.9 


295.3 


1185.6 


890.3 


4.60 


0.2172 


0.4704 


1.1348 


82.3 


97 


325.6 


296.1 


1185.8 


889.7 


4.56 


0.2193 


0.4714 


1.1330 


83.3 


98 


326.4 


296.8 


1186.0 


889.2 


4.51 


0.2215 


0.4724 


1.1312 


84.3 


99 


327.1 


297.6 


1186.2 


888.6 


4.47 


0.2237 


0.4733 


1.1295 


85.3 


100 


327.8 


298.3 


1186.3 


888.0 


4.429 


0.2258 


0.4743 


1.1277 


87.3 


102 


329.3 


299.8 


1186.7 


886.9 


4.347 


0.2300 


0.4762 


1.1242 


89.3 


104 


330.7 


301.3 


1187.0 


885.8 


4.268 


0.2343 


0.4780 


1.1208 



873 







Properties of Saturated Steam. (Continued.) 




oT . 


2d 




Total Heat 


K)-^ 


. 


3 A 


(U 


^ 








above 32° F. 


i 

1"^ 


£"3 


^^ 


^ 


? 


1^ 


id 


^ 1 




53 

i-i 


^1 

1^ 




la 

fl 


< 


H 


a W 


a W 


kA 


> 


^ 


H 


m 


91.3 


106 


332.0 


302.7 


1187.4 


884.7 


4.192 


0.2336 


0.4798 


1.117^ 


93.3 


108 


333.4 


304.1 


1187.7 


883.6 


4.118 


0.2429 


0.4816 


1.1141 


95.3 


no 


334.8 


305.5 


1188.0 


882.5 


4.047 


0.2472 


0.4834 


1.1106 


97.3 


112 


336.1 


306.9 


1188.4 


881.4 


3.978 


0.2514 


0.4852 


1.1076 


99.3 


114 


337.4 


308.3 


1188.7 


880.4 


3.912 


0.2556 


0.4869 


1.1045 


101.3 


116 


338.7 


309.6 


1189.0 


879.3 


3.848 


0.2599 


0.4886 


I.IOH 


103.3 


118 


340.0 


311.0 


1189.3 


878.3 


3.786 


0.2641 


0.4903 


1.098^ 


105.3 


120 


341.3 


312.3 


1189.6 


877.2 


3.726 


0.2683 


0.4919 


1.095^ 


107.3 


122 


342.5 


313.6 


1189.8 


876.2 


3.668 


0.2726 


0.4935 


1.092^ 


109.3 


124 


343.8 


314.9 


1190.1 


875.2 


3. 611 


0.2769 


0.4951 


1.0895 


111.3 


126 


345.0 


316.2 


1190.4 


874.2 


3.556 


0.2812 


0.4967 


1.0865 


113.3 


128 


346.2 


317.4 


II90.7 


873.3 


3.504 


0.2854 


0.4982 


1.0837 


115.3 


130 


347.4 


318.6 


1191.0 


872.3 


3.452 


0.2897 


0.4998 


1.0809 


117.3 


132 


348.5 


319.9 


1191.2 


871.3 


3.402 


0.2939 


0.5013 


1.0782 


119.3 


134 


349.7 


321.1 


1191.5 


870.4 


3.354 


0.2981 


0.5028 


1.0755 


121.3 


136 


350.8 


322.3 


1191.7 


869.4 


3.308 


0.3023 


0.5043 


1.0725 


123.3 


138 


352.0 


323.4 


1192.0 


868.5 


3.263 


0.3065 


0.5057 


1.0702 


125.3 


140 


353.1 


324.6 


1192.2 


867.6 


3.219 


0.3107 


0.5072 


1.0675 


127.3 


142 


354.2 


325.8 


1192.5 


866.7 


3.175 


0.3150 


0.5086 


1.0649 


129.3 


144 


355.3 


326.9 


1192.7 


865.8 


3.133 


0.3192 


0.5100 


1.062^ 


131.3 


146 


356.3 


328.0 


1192.9 


864.9 


3.092 


0.3234 


0.5114 


1.0599 


133.3 


148 


357.4 


329.1 


1193.2 


864.0 


3.052 


0.3276 


0.5128 


1.057^ 


135.3 


150 


358.5 


330.2 


1193.4 


863.2 


3.012 


0.3320 


0.5142 


1 .055C 


137.3 


152 


359.5 


331.4 


1193.6 


862.3 


2.974 


0.3362 


0.5155 


1.0525 


139.3 


154 


360.5 


332.4 


1193.8 


861.4 


2.938 


0.3404 


0.5169 


1.0501 


141.3 


156 


361.6 


333.5 


1194.1 


860.6 


2.902 


0.3446 


0.5182 


1.0473 


143.3 


158 


362.6 


334.6 


1194.3 


859.7 


2.868 


0.3488 


0.5195 


1.045^ 


145.3 


160 


363.6 


335.6 


1194.5 


858.8 


2.834 


0.3529 


0.5208 


1.0431 


147.3 


162 


364.6 


336.7 


1194.7 


858.0 


2.801 


0.3570 


0.5220 


1.0409 


149.3 


164 


365.6 


337.7 


1194.9 


857.2 


2.769 


0.3612 


0.5233 


1.038> 


151.3 


166 


366.5 


338.7 


1195.1 


856.4 


2.737 


0.3654 


0.5245 


1.0365 


153.3 


168 


367.5 


339.7 


1195.3 


855.5 


2.706 


0.3696 


0.5257 


1.0343 


155.3 


170 


368.5 


340.7 


1195.4 


854.7 


2.675 


0.3738 


0.5269 


1.0321 


157.3 


172 


369.4 


341.7 


1195.6 


853.9 


2.645 


0.3780 


0.5281 


1.O3O0 


159.3 


174 


370.4 


342.7 


1195.8 


853.1 


2.616 


0.3822 


0.5293 


1.027fi 


161.3 


176 


371.3 


343.7 


1196.0 


852.3 


2.588 


0.3864 


0.5305 


1.0257 


163.3 


178 


372.2 


344.7 


1196.2 


851.5 


2.560 


0.3906 


0.5317 


1.0235 


165.3 


180 


373.1 


345.6 


1196.4 


850.8 


2.533 


0.3948 


0.5328 


1.0215 


167.3 


182 


374.0 


346.6 


1196.6 


850.0 


2.507 


0.3989 


0.5339 


1.0195 


169.3 


184 


374.9 


347.6 


1196.8 


849.2 


2.481 


0.4031 


0.5351 


1.017^ 


171.3 


186 


375.8 


348.5 


1196.9 


848.4 


2.455 


0.4073 


0.5362 


1.015^ 


173.3 


188 


376.7 


349.4 


1197.1 


847.7 


2.430 


0.4115 


0.5373 


1.013^ 


175.3 


190 


377.6 


350.4 


1197.3 


846.9 


2.406 


0.4157 


0.5384 


I.OIH 


177.3 


192 


378.5 


351.3 


1197.4 


846.1 


2.381 


0.4199 


0.5395 


1.0095 


179.3 


194 


379.3 


352.2 


1197.6 


845.4 


2.358 


0.4241 


0.5405 


1.0076 


181.3 


196 


380.2 


353.1 


1197.8 


844.7 


2.335 


0.4283 


0.5416 


1.0056 


183.3 


198 


381.0 


354.0 


1197.9 


843.9 


2.312 


0.4325 


0.5426 


1.0038 


185.3 


200 


381.9 


354.9 


1198.1 


843.2 


2.290 


0.437 


0.5437 


1.001^ 


190.3 


205 


384.0 


357.1 


1198.5 


841.4 


2.237 


0.447 


0.5463 


0.997: 


195.3 


210 


386.0 


359.2 


1198.8 


839.6 


2.187 


0.457 


0.5488 


0.992^ 


200.3 


215 


388.0 


361.4 


1199.2 


837.9 


2.138 


0.468 


0.5513 


0.988f 


205.3 


220 


389.9 


363.4 


1199.6 


836.2 


2.091 


0.478 


0.5538 


0.984 


210.3 


225 


391.9 


365.5 


1199.9 


834.4 


2.046 


0.489 


0.5562 


0.979c 


215.3 


230 


393.8 


367.5 


1200.2 


832.8 


2.004 


0.499 


0.5586 


0.975i 


220.3 


235 


395.6 


369.4 


1200.6 


831.1 


1.964 


0.509 


0.5610 


0.971; 


225.3 


240 


397.4 


371.4 


1200.9 


829.5 


1.924 


0.520 


0.5633 


0.967e 


230.3 


245 


399.3 


373.3 


1201.2 


827.9 


1.887 


0.530 


0.5655 


0.9631 



874 







Properties of Saturated Steam. (Continued.) 




P C3 


« d 




Total Heat 


^^ 


_^ 


3-Q 


<u 


6. 


^^ 


^'.' 




above 32° F. 


"i 


(inO 


Oh^ 


rC 


i 


02 • 


o ft 

13 


as 

ft-C 




is 


53 






G 




1 i 


II 


o 


J2 


H 


fi w 


£ « 


>^ 


;> 


H 


w 


235.3 


250 


401.1 


375.2 


1201.5 


826.3 


1.850 


0.541 


0.5676 


0.9600 


245.3 


260 


404.5 


378.9 


1202.1 


823.1 


1.782 


0.561 


0.5719 


0.9525 


255.3 


270 


407.9 


382.5 


1202.6 


820.1 


1.718 


0.582 


0.5760 


0.9454 


265.3 


280 


411.2 


386.0 


1203.1 


817.1 


1.658 


0.603 


0.5800 


0.9385 


275.3 


290 


414.4 


389.4 


1203.6 


814.2 


1.602 


0.624 


0.5840 


0.9316 


285.3 


300 


417.5 


392.7 


1204.1 


811.3 


1.551 


0.645 


0.5878 


0.9251 


295.3 


310 


420.5 


395.9 


1204.5 


808.5 


1.502 


0.666 


0.5915 


0.9187 


305.3 


320 


423.4 


399.1 


1204.9 


805.8 


1.456 


0.687 


0.5951 


0.9125 


315.3 


330 


426.3 


402.2 


1205.3 


803.1 


1.413 


0.708 


0.5986 


0.9065 


325.3 


340 


429.1 


405.3 


1205.7 


800.4 


1.372 


0.729 


0.6020 


0.9006 


335.3 


350 


431.9 


408.2 


1206.1 


797.8 


1.334 


0.750 


0.6053 


0.8949 


345.3 


360 


434.6 


411.2 


1206.4 


795.3 


1.298 


0.770 


0.6085 


0.8894 


355.3 


370 


437.2 


414.0 


1206.8 


792.8 


1.264 


0.791 


0.6116 


0.8840 


365.3 


380 


439.8 


416.8 


m7j 


790.3 


1.231 


0.812 


0.6147 


Q.^l^B. 


375.3 


390 


442.3 


419.5 


1207.4 


787.9 


1.200 


0.833 


0.6178 


0.8737 


385.3 


400 


444.8 


422 


1208 


786 


1.17 


0.86 


0.621 


0.868 


435.3 


450 


456.5 


435 


1209 


774 


1.04 


0.96 


0.635 


0.844 


485.3 


500 


467.3 


448 


1210 


762 


0.93 


1.08 


0.648 


0.822 


535.3 


550 


477.3 


459 


1210 


751 


0.83 


1.20 


0.659 


0.801 


585.3 


600 


486.6 


469 


1210 


741 


0.76 


1.32 


0.670 


0.783 



Properties of Superheated Steam, Marlis & Davis and Goodenough 
Compared. 

V = volume, cu. ft. per lb.; h = total heat above 32° F.; n = entropy. 

The figures in the upper lines are from Marks and Davis's tables, 
those in the lower lines (the differing digits only being given) are inter- 
polated from Goodenough 's tables, in which the figures are for steam 
of given temperatures, not even degrees of superheat. 



Abso- 
lute 


Temp. 






Superheat, Degrees Fahrenheit. 






Pres- 


Sat. 




















sure. 


Steam. 


50 


100 


150 


200 


250 


300 


400 


500 


20 


228.0 


V 


21.69 
8 


23.25 

3 


24.80 
.77 


26.33 
.29 


27,35 
1 


29.37 


32.39 

1 


35.40 
30 






h 


1179.9 


1203.5 


1227.1 


1250.6 


1274.1 


1297.6 


1344.8 


1392.2 








7.3 


6.0 


9.8 


3.5 


7.0 


300.7 


8.5 


7.0 






n 


1.7652 


1.7961 


1.8251 


1.8524 


1.8781 


1.9026 


1.9479 


1.9893 








86 


8000 


92 


64 


823 


69 


530 


956 


100 


327.8 


V 


4.79 


5.14 


5.47 


5.80 


6.12 


6.44 


7.07 


7.69 








** 


3 


6 


.79 





1 


3 


4 






h 


1213.8 


1239.7 


1264.7 


1289.4 


1313.6 


1337.8 


1385.9 


1434.1 








5.9 


42.5 


8.3 


93.6 


8.7 


43.7 


93.6 


43.9 






n 


1.6358 


1.6658 


1.6933 


1.7188 


1.7428 


1.7656 


1.8079 


1.8468 








84 


91 


74 


235 


84 


720 


159 


566 


200 


381.9 


V 


2.49 


2.68 


2.86 


3.04 


3.21 


3.38 


3.71 










.50 


9 


5 


2 


.18 


4 


.66 








h 


1229.8 


1257.1 


1282.6 


1307.7 


1332.4 


1357.0 


1405.9 










1 


8.0 


5.7 


12.7 


9.0 


65.1 


16.8 








n 


1.5823 


1.6120 


1.6385 


1.6632 


1.6862 


1.7082 


1.7493 










09 


5 


411 


76 


922 


156 


596 




300 


417.5 


V 


1.69 


1.83 


1.96 


2.09 


2.21 


2.33 


2.55 












2 


4 


6 


.18 


.29 











h 


1240.3 


1268.2 


1294.0 


1319.3 


1344.3 


1369.2 


1418.6 










35.0 


5.9 


5.2 


23.3 


51.0 


78.1 


31.5 








n 


1.5530 


1.5824 


1.6082 


1.6323 


1.6550 


1.6765 


1.7168 










458 


784 


76 


44 


94 


829 


265 





STEAM. 



875 



Properties of Superheated Steam. 

(Condensed from Marks and Davis's Steam Tables and Diagrams.) 
= specific volume in cu. ft. per lb., h = total heat, from water at 
32° F. in B.T.U. per lb., n = entropy, from water at 32°. 



-^ a . 
< c 

03 J5 . 






Degrees of Superheat. 



228.0 



267.3 



292.7 



312.0 



327.8 



341.3 



353.1 



363.6 



373.1 



381.9 



389.9 



397.4 



404.5 



411.2 



417.5 



431.9 



444.8 



456.5 



467.3 



20 50 100 150 200 250 300 400 500 



V 20.08 
h 1156.2 
n 1 . 7320 

V 10.49 
h 1169.4 
n 1.6761 
v7.!7 
h 1177.0 
n 1.6432 
v5.47 
h 1182.3 
n 1.6200 
v4.43 
h 1186.3 
n 1.6020 
v3.73 
h 1189.6 
n 1.5873 
v3.22 
h 1192.2 
n 1.5747 
v2.83 
h 1194.5 
n 1.5639 
v2.53 
h 1196.4 
n 1.5543 
v2.29 
h 1198.1 
n 1.5456 
v2.09 
h 1199.6 
71 1.5379 

V 1.92 
h 1200.9 
n 1.5309 

V 1.78 
h 1202.1 
n 1.5244 

V 1.66 
h 1203.1 
n 1.5185 

V 1.55 
h 1204.1 
n 1.5129 

V 1.33 
h 1206.1 
n 1.5002 

1.17 
h 1207.7 
n 1.4894 

1.04 
h 1209 
n 1.479 
vO.93 
h 1210 
n 1.470 



20.73 

1165.7 

I . 7456 

10.83 

1179.3 

i.6895 

7.40 

1187.3 

1.6568 

5.65 

1193.0 

1.6338 

4.58 

1197.5 

1.6160 

3.85 

1201 

1.6016 

3.32 

1204.3 

1.5894 

2.93 

1207.0 

1.5789 

2.62 

1209.4 

1.5697 

2.37 

1211.6 

1.5614 

2.16 

1213.6 

1.5541 

1.99 

1215.4 

1.5476 

1.84 

1217.1 

1.5416 

1.72 

1218.7 

1.5362 

1.60 

1220.2 

1.5310 

1.38 

1223.9 

1.5199 

1.21 

1227.2 

1.5107 

1.08 

1231 

1.502 

0.97 

1233 

1.496 



21.69 

1179.9 

1.7652 

11.33 

1194.0 

1.7089 

7.75 

1202 

1.6761 

5.92 

1208.8 

1.6532 

4.79 

1213.8 

1.6358 

4.04 

1217 

1.62/6 

3.49 

1221.4 

1.6096 

3.07 

1224.5 

1.5993 

2.75 

1227.2 

1.5904 

2.49 

1229.8 

1.5823 

2.28 

1232.2 

1.5753 

2.09 

1234.3 

1.5690 

1.94 

1236.4 

1.5631 

1.81 

1238.4 

1.5580 

1.69 

1240.3 

1.5530 

1.46 

1244.6 

1.5423 

1.28 

1248.6 

1.5336 

1.14 

1252 

1.526 

1.03 

1256 

1.519 



23.25 

1203.5 

1.7961 

12.13 

1218.4 

1.7392 

8.30 

1227.6 

1.7062 

6.34 

1234.3 

1.6833 

5.14 

1239.7 

1.6658 

4.33 

1244.1 

1.6517 

3.75 

1248.0 

1.6395 

3.30 

1251 

1.6292 

2.96 

1254.3 

1.6201 

2.68 

1257.1 

1.6120 

2.45 

1259.6 

6049 
2.26 
1261.9 
1.5985 
2.10 
1264.1 
1.5926 
1.95 
1266.2 
1.5873 
1.83 
1268.2 
1.5824 

58 
1272.7 
1.5715 

40 
1276.9 
1.5625 
1.25 
1281 
1.554 

13 
1285 

548 



24.80 

1227.1 

1.8251 

12.93 

1242.4 

1.7674 

8.84 

1252.1 

1.7342 

6.75 

1259.0 

1.7110 

5.47 

1264.7 

1.6933 

4.62 

1269.3 

1.6789 

4.00 

1273.3 

1.6666 

3.53 

1276. 

i.6561 

3.16 

1279.9 

1.6468 

2.86 

1282.6 

1.6385 

2.62 

1285.2 

1.6312 

2.42 

1287.6 

1.6246 

2.24 

1289.9 

1.6186 

2.09 

1291.9 

1.6133 

1.96 

1294.0 

1.6082 

1.70 

1298.7 

1.5971 

1.50 

1303.0 

1.5880 

1.35 

1307 

1.580 

1.22 

1311 

1.573 



26.33 
1250.6 
1.8524 
13.70 
1266.4 
1.7940 
9.36 
1276.4 
1.7603 
7.17 
1283.6 
1.7368 
5.80 
1289.4 
1.7188 
4.89 
1294.1 
7041 
4.24 
1298.2 
1.6916 
3.74 
1301.7 
1.6810 
3.35 
1304.8 
1.6716 
3.04 
1307.7 
1.6632 
2.78 
1310.3 
1.6558 
2.57 
1312.8 
1.6492 
2.39 
1315.1 
1.6430 
2.22 
1317.2 
1.6375 
2.09 
1319.3 
1.6323 
1.81 
1324.1 
1.6210 
1.60 
1328.6 
1.6117 
1.44 
1333 
1.603 
1.31 
1337 
1.597 



27.85 

1274.1 

1.8781 

14.48 

1290.3 

1.8189 

9.89 

1300.4 

7849 
7.56 
1307.8 

7612 
6.12 
1313.6 
1.7428 
5.17 
1318.4 
1.7280 
4.48 
1322.6 
1.7152 
3. 
1326.2 

7043 
3.54 
1329.5 
1.6948 
3.21 
1332.4 
1.6862 
2.94 
1335.1 
1.6787 

71 
1337.6 
1.6720 
2.52 
1340.0 
1.6658 
2.35 
1342.2 
1.6603 
2 21 
1344.3 
1.6550 
1.92 
1349.3 

6436 

70 
1353.9 
1.6342 
1.53 
1358 
1.626 
1.39 
1362 
1.619 



29.37 

1297.6 

1.9026 

15.25 

1314.1 

1.8427 

10.41 

1324.3 

1.6081 

7.95 

1331.9 

1 . 7840 

6.44 

1337.8 

1.7656 

5.44 

1342.7 

1.7505 

4.71 

1346.9 

1.7376 

4.15 

1350.6 

1.7266 

3.72 

1353.9 

1.7169 

3.38 

1357.0 

1.7082 

3.10 

1359.8 

7005 
2.85 
1362.3 
1.6937 
2.65 
1364.7 
1.6874 
2.48 
1367.0 

6818 
2.33 
1369.2 
1.6765 
2.02 
1374.3 
1.6650 
1.79 
1379.1 
1.6554 
1.61 
1383 
1.647 
1.47 
1388 
1.640 



32.39 
1344.8 
1.9479 
16.78 
1361.6 
1.8867 
11.43 
1372.2 
1.8511 
8.72 
1379.8 
1.8265 
7.07 
1385.9 
1.8079 
5.96 
1391.0 
1.7924 
5.16 
1395.4 
.7792 
4.56 
1399.3 
1 . 7680 
4.09 
1402.7 
1.7581 
3.71 
1405.9 
1.7493 
3.40 
1408.8 
1.7415 
3.13 
1411.5 
1.7344 
2.91 
1414.0 
1 . 7280 
2.72 
1416.4 
1.7223 
2.55 
1418.6 
1.7168 
2.22 



1424 

1.7052 

1.97 

1429.0 

1.6955 

1.77 

1434 

1.687 

1.62 

1438 

1.679 



35.40 

1392.2 

1.9893 

18.30 

1409.3 

1.9271 

12.45 

1420.0 

1.8908 

9.49 

1427.9 

1.8658 

7.69 

1434.1 

1.8468 

6.48 

1439.4 

1.8311 

5.61 

1443.8 

1.8177 

4.95 

1447.9 

1.8063 

4.44 

1451.4 

1.7962 

4.03 

1454.7 

1.7872 

3.69 

1457.7 

1.7792 

3.40 

1460.5 

1.7721 

3.16 

1463.2 

1.7655 

2.95 

1465.7 

1.7597 

2.77 

1468.0 

1.7541 

2.41 

1473.7 

1.7422 

2.14 

1478.9 

1.7323 

1.93 

1484 

1.723 

1.76 

14aP 

1.715 



876 



STEAM. 



FLOW OF STEAM. 

Flow of Steam through a Nozzle. (From Clark on the Steam- 
engine.) — The flow of steam of a greater pressure into an atmosphere of a 
less pressure increases as the difference of pressure is increased, until the 
external pressure becomes only 58% of the absolute pressure in the boiler. 
The flow of steam is neither increased nor diminished by the fall of the ex- 
ternal pressure below 58%, or about 4/7 of the inside pressure, even to 
the extent of a perfect vacuum. In flowing through a nozzle of the best 
form, the steam expands to the external pressure, and to the volume Que to 
this pressure, so long as it is not less than 58% of the internal pressure. 
For an external pressure of 58%, and for lower percentages, the ratio of 
expansion is 1 to 1 .624. 

When steam of varying initial pressures is discharged into the atmos- 
phere — the atmospheric pressure being not more than 58% of the initial 
pressure — the velocity of outflow at constant density, that is, supposing tlie 
initial density to be maintained, is given by the formula V =.3.5953 ^h' 
V = velocity in feet per second, as for steam of the initial density; 
h = the height in feet of a column of steam of the given initial pressure, 
the weight of which is equal to the pressure on the unit of base. 

The lowest Initial pressure to which the formula applies, when the steam 
is discharged into the atmosphere at 14.7 lbs. per sq. in., is (14.7 X 100/58) 
= 25.37 lbs. per sq. in. 

From the contents of the table below it appears that the velocity of out- 
flow into the atmosphere, of steam above 25 lbs. per sq, in. absolute pres- 
sure, increases very slowly with the pressure, because the density, and the 
weight to be moved, increase with the pressure. An average of 900 ft. per 
sec. may, for approximate calculations, be taken for the velocity of out- 
flow as for constant density, that is, taking the volume of the steam at the 
Initial volume. For a fuller discussion of tWs subject see "Steam Tur- 
bines, page 1085- 

Outflow of Steam into the Atmosphere. — External pressure per 
square inch, 14.7 lbs. absolute. Ratio of expansion in nozzle, 1.624. 





. 


^ 


^ ^ 


o .; 




1 










fl . 


o 


ischarge per 
square inch o 
Orifice per min 


fH o'5G 




c . 


o 


a 


fc^ 5 ^ 


bsolute Initial 
Pressure per 
square inch. 


elocity of Out- 
flow as at Co 
stant Density 


ctual Velocity 
Outflow Ex- 
panded. 


orse-power pe 
sq. in. of Orifi 
if H.P. = 30 Ih 
per hour. 




elocity of Out- 
flow as at Co 
stant Density 


ctual Velocity 
Outflow Ex- 
panded. 


ischarge per 
square inch of 
Orifice per mi 
ute. 


orse-power pe 
sq. in. of Orifi 
if H.P. = 30 lb 
per hour. 


< 


> 


< 


Q 


m 


< 


> 


< 


Q 


X 


lbs. 


feet 
p. sec. 


feet 
pjersec. 


lbs. 


H.P. 


lbs. 


feet 
p. sec. 


feet 
per sec. 


lbs. 


H.P. 


25.37 


863 


1401 


22.81 


45.6 


90 


895 


1454 


77.94 


155.9 


30 


867 


1408 


26.84 


53.7 


100 


898 


1459 


86.34 


Mil 


40 


874 


1419 


35.18 


70.4 


115 


902 


1466 


98.76 


197.5 


50 


880 


1429 


44.06 


88.1 


135 


906 


1472 


115.61 


231.2 


60 


885 


1437 


52.59 


105.2 


155 


910 


1478 


132.21 


264.4 


70 


889 


1444 


61.07 


122.1 


165 


912 


1481 


140.46 


280.9 


75 


891 


1447 


65.30 


130.6 


215 


919 


1493 


181.58 


363.2 



Rateau's Formula. — A. Rateau, in 1895-6, made experiments \Alth 
converging nozzles 0.41, 0.59 and 0.95 in. diam., on steam of pressures from 
1.4 to 170 lbs. per sq. in. In his paper read at the Intl. Eng'g. Congress at 
Glasgow {Eng. Rec., Oct. 16, 1901) he gives the following formula, appli- 
cable when the final pressure, absolute, is less than 58% of the initial. 
Pounds per hour per sq. in. area of orifice = 3.6 F (16.3 - 0.96 log P). 
P = absolute pressure, lbs. per sq. in. 

Napier's Approximate Rule. — Flow in pounds per second = ab- 
solute pressure X area in square inches -^ 70. This rule gives results 



FLOW OF STEAM. 



877 



which closely correspond with those in the above table, and with results 
computed by Rateau's formula, as sliown below. 

Abs. press., lbs. 
per sq. in 25.37 40 60 75 100 135 165 215 

Discharge per min. . 
by table, lbs... 22.81 35.18 52.59 65.30 86.34 115.61 140.46 181.58 

By Rateau's for- 
mula 22.76 35.43 52.49 65.25 86.28 115.47 140.28 181.39 

By Napier's rule. 21.74 34.29 51.43 64.29 85.71 115.71 141.43 184.29 

Flow of Steam in Pipes. — The commonly accepted formula for 

flow of air, steam or gas in pipes is IF = c \/ ^ ^^^ ~ ^-^ , in which 

W = the weight in pounds per minute, pi and /?> = initial and final 
pressures in pounds per square inch, w = density in pounds per cubic 
foot, d = internal diameter of the pipe in inches, and L = length in 
feet, and c an experimental coefficient, which varies with the diameter 
of the pipe. It varies also with the velocity and with the smoothness 
of the pipe, but there are no authentic data for the amount of the 
variations due to these causes. For the derivation of the formula, see 
Ency. Brit., 11th ed., vol. xiv, p. 67, also "Steam," 1913 edition, 
published by the Babcock & Wilcox Co. 

The value of the coefficient c, as deduced by G. H. Babcock from 



a study of published experiments, is 87 'I/ It is probably as 

nearly correct as can be derived from the few experimental records that 
are available. For the different standard sizes of lap welded pipe the 
value of c computed from Babcock's formula are as below: 

Values of c for Standard Sizes of Lap-welded Pipe. 





Inter. 






Inter. 






Inter. 




Size, 


Diam., 


c 


Size, 


Diam., 


c 


Size, 


Diam., 


c 


In. 


In. 




In. 


In. 




In. 


In. 




1/2 


0.622 


33.4 


4 


4.026 


63.2 


12 


12.00 


76.3 


3/4 


0.824 


37.5 


41/2 


4.506 


64.8 


13 


13.25 


77.! 


1 


1.049 


41.3 


5 


5.047 


66.5 


14 


14.25 


77.7 


11/4 


1.380 


45.8 


6 


6.065 


68.7 


15 


15.25 


78.2 


1 1/2 


1.610 


48.4 


7 


7.023 


70.7 


17 0.D. 


16.214 


78.7 


2 


2.067 


52.5 


^ 8 


7.981 


72.2 


18 0.D. 


17.182 


79.1 


21/2 


2.469 


55.5 


9 


8.941 


73.4 


20 O.D. 


19.182 


79.8 


3 


3.068 


59.0 


10 


10.02 


74.5 


22 0.D. 


21.25 


80.4 


31/2 


3.548 


61.3 


11 


11 .00 


75.5 


24 O.D. 


23.25 


81.0 



The table, page 878, calculated from the formula with the above 
values of c gives the flow of steam in pounds per minute for a drop of 
1 lb. pressure per 1000 ft. of length. For any other ratio of drop to 
length multiply the figures in the table by the factors given below. 

Factors for Correction of Table of Flow^ of Steam. 
Drop lb. per 

1000 ft. ^ K 2 3 4 6 8 10 15 20 25 

Factor 0.5 0.707 1.414 1.732 2 2.45 2.83 3.16 3.87 4.47 5 

For Flow of Steam at low pressures, see Heating and Ventilation, 
page 699. 

Flow of Steam in Long: Pipes. Lodoux's Formula. — In the flow 
of steam or other gases in long pipes, the volume and the velocity are 
increased as the drop in pressure increases. Taking this into account a 
correct form ula for flow w ould be an exponential one. Ledoux gives 



meas- 



d = 0.699 \/ — TTT, Toi . his notation being reduced to EngUsh 

ures. (^Annales des Mines, 1892; Trans. A. S. M. E., xx., 365; Power, June, 
1907.) See Johnson's formula for flow of air, page 619. 



878 



STEAM. 



" II 

5:§ 




— (N r<^ r^ <N f«^ "^ o^ nO 00 — CO iTi p(^ OS r>i f<^ t^ cA -"i- Oma 

— — — — (N f<^ f«^ m 


II II 




— r^^p^^^O — — — TfO<Nrj-as— aN<Nir^c<^sO00cO«N"^<N — r^- 

— <N r«^ Tj- vO 00 p<^ 0^ 00 t>. — iri fN vO 00 r<^ 0^ 00 <N sO I 
— — r^^POvr^^OoOO^s^^r^ooor>.>o^r^ 


1 II 


vn <N t>i fO '■a- r>i 


— f«^ >0 00 r^ O^ r«>i rs) 00 'O 00 ■^ — r^ lA 0^ vA Tj- 00 m — •^ 

— »— <NcA«At>. — r>irj-fAiAr^rsjfArAiA0O"^mC^<N 

•— — rsjrOTrvrir^O^ — <rMnoO'«l- — 


Om 

7 II 
5:^ 


<^ 1^ lA vO r^ "^ 

sOaO'«>-'^iAt^P<^<N<NOOOO^ — 

— PAt^vOtA^iAvO<^OoOOO^fA<NvO — "^OO — 


^(NiAOOtAfArATf — O^oOO^ — 0>^ — — vOOr^'*iAt^C> 

— <Nf«^'^sOO^'^OoOOOOO — O^iA-^cAiAvOoOOO 

— (N<NcA'^vOt^O^ — fAlAOvOf«^ 


[Lu- 
ff's 


f<^ (T^ — sO fN Tf rN. 

«N0Ot^iAiAvA — fA — OoOiAO 

— .<NlAr^^O^O^«AO^00<N<NvOcAPAr^'-fAU-^sO — <Nr^ 


— — cAsO — r^tATj-vOvfifAOMAO — vC^OO — r^r^<Noo 
— — rsifA-^r lA — a^t^vOOrAt>.<Noot^u^oo 

— — (NtNCA'^vOt^OOO — iAO»A 
— <N(N 


'ill 


— «AfAt^t^^<N 

OOoOvOO'*<SvO<NO — — <NI 

— fA0O<NiA — vO-^ — O^OOt^-^OiAiA-^^ — t^tAh^iA 


— (N*^ t^ — vO — ^00<N(Nt^iAr>i00vOvOvO<NC000 — "^ 

— — <N<N'^t^OrAOOfAO^OONOiAiAiAO — »A 

— — — fN<NcA-^«AN0t>»OcA\0 


II • 


(VJ f<^ 00 CA CA sO — lA 

r^. vO <N (N fS r^ lA sO vO — <A vA <N — r^ 

— cA r^ — <N 1^00 (NvAt^ooa>'<Na^coooovot>.fA<N^ — 


— (NfANOO-^O^vOfAiA — cAt^fAOOr^O — l^PAhH — 

— — — (N'^sOC^fNvO — sO-^fNOoOOOOoOO^ 

.— »— CSrvlfA-^iAiAvOa^ — Tj- 




r^ — iaO — OoO'l-oo 

vOiAOr^^ — r^vOOiAt^O<NsOfA 

— canOO — '^cAiAT}-(Navt^'«rrsjr^avfNOfAvO\OO^t^'^ 


— <N PA NO O^ CA 00 -"4- CA rr Tf 00 O^ <N Tf T^ r}- — u-» — 

— — (Nttsoco — tAaNTrtNcosciTA^ONoo 

— — — CNcACA-^iAsOOOOfA 


<N 


<N — •«1-vOfAOQ0fA00 

sC^OOAjr^l^Tj-Tft^vOOOtAtNiAO 

— <NsOOnOn<NOnoO»aO<NO'^nO — sO — lAOONa^O^rAr^ 


— CA iA 00 <N t>. PA 00 vO OM^ ''T lA <N — rA fA 00 — lA <N 

— — ^^^^AlAr^OT^cOcAO^OfAOO^QO<NO^ 

— — — (NcACA-^iAiAt^OPvl 


i 


t^O^O^fAaMAOO<NO — <NiA 

— fAt^ir^vO-^ON-^tAr^ — fN — oOfAOO^OvOO 

000 — (NiAOOvO'^'^r^TriAvOOvOO^ — tNCSsOO^vCi- — vO»n 


— rNcATj-NOOvnr^avON — ^fAOOOfAi^rsjNO 

— — (NfNrriinvOoOO — tTvO — OOiA 

CsjfNfA 


Actual 
Inter- 
nal 
Diam. 
d 


<NTrO^OOr^O^OOOO\O^Or^u-^cA OOOOOO-^AjfNOO 

(NAJ-^OO — \OvOvD'«1■PsJOT^sO<NOO"^<NOOlAlAlA — OOOOlAiA 

s000OrAv0OTrOiAOiAOOOava>OOO<N(N(Nrs| CMfN 


00 — <N<NPAfA'^TrinsOr^r>HOOO — fSrA'^iAvOr^O' — CA 


— r^(N 


Nomi- 
nal 
Diam. 
of Pipe, 
In. 


QQQQQ 
>5^ >> > > > 66666 

— '-'-(S<NfAfA'«J-'«riAvOr>sOOONO — rSfA'«fiAt>iOOO«N"^ 
« ^ ,- ^ ^ « ,- ^ rs* fs <N 



FLOW OF STEAM. 



879 



Carrying Capacity of Extra Heavy Steam Pipes. 

(Power Specialty Co.) 



c o 

ego 






200 
lbs. 



150 

lbs. 



100 
lbs. 



50 

lbs. 



Pounds of steam per 
hour. 



o-S.S- « § ^ 
;z; "ft^^-S.S 



200 
lbs. 



150 
lbs. 



100 
lbs. 



50 
lbs. 



Pounds of steam per 
hour. 



1 
1 1/4 

1 1/2 

2 

2 1/2 

3 

31/2 

4 

4 1/2 

5 



0.71' 
1.27 
1.75 
2.93 
4.20 
6.56 
.85 



1210 
2000 
2750 
4610 
6610 
10300 
13900 



11.44 18000 

14.18 22300 

18.19 28610 



872 


618 


1555 


1105 


2140 


1525 


3590 


2550 


5150 


3660 


8050 


5720 


10820 


7720 


14000 


10000 


17350 


12320 


22250 


15800 



362 
646 
894 
1525 
2140 
3450 
4520 
5850 
7230 
9300 



6 
7 
8 
9 
10 
11 
12 
14 
16 
18 



25.93 
34.47 
44.18 
58.42 
74.66 
90.76 
108.43 
153.94 
176.71 
226.98 



40800 

546T)0 

69500 

92000 

117300 

142800 

170500 

242000 

277500 

357000 



31600 
42250 
54000 
71500 
91500 
111500 
133000 
188200 
216200 
278000 



22600 
30000 
38400 
50800 
65000 
79200 
94750 
133900 
153800 
197500 



13210 
17600 
22450 
29800 
38100 
463C0 
55400 
78600 
90500 
115700 



The quantities in the above table are based on the following velocities: 

Steam superheated degrees F. 50 100 150 200 250 

Velocity, ft. per min 8000 8500 8950 9450 9900 10450 

Resistance to Flow by Bends, Valves, etc. (From Briggs on 
Warming Buildings by Steam.) — The resistance at the entrance to a 
tube when no special bell-mouth is given consists of two parts. The 
head v- -^ 2g is expended in giving the velocity of flow; and the head 
0.505 v^ -^2 in overcoming the resistance of the mouth of the tube. 
Hence the whole loss of head at the entrance is 1.505 v^ h- 2 g. This resist- 
ance is equal to the resistance of a straight tube of a length equal to about 
60 times its diameter. The loss at each sharp right-angled elbow is the 
same as in flowing through a length of straight tube equal to about 40 
times its diameter. For a globe steam stop-valve the resistance is 
taken to be IV2 times that of the right-angled elbow. 

Sizes of Steam-pipes for Stationary Engines. — An old common 
rule is that steam-pipes supplying engines should be of such size that the 
mean velocity of steam in them does not exceed 6000 feet per minute, in 
order that the loss of pressure due to friction may not be excessive. The 
velocity is calculated on the assumption that the cyhnder is filled at each 
stroke. In modern practice with large engines and high pressures, this 
rule gives unnecessarily large and costly pipes. For such engines the 
allowable drop in steam pressure should be assumed and the diameter 
calculated by means of the formulae given above. 

An article in Power, May, 1893, on proper area of supply-pipes for 
engines gives a table sho^^lng the practice of leading builders. To facili- 
tate comparison, aU the engines have been rated in horse-power at 40 
pounds mean effective pressure. The table contains all the varieties of 
simple engines, from the sUde-valve to the Corhss, and it appears that 
there is no general difference in the sizes of pipe used in the different types. 
The averages selected from this table are as follows: 

Diameters of Cylinders corresponding to Variolas Sizes of 
Steam-pipes based on Piston-speed of Engine of 600 ft. per 
MiNtJTE, AND Allowable Mean Velocity of Steam in Pipe of 
4000, 6000, AND 8000 FT. PER Minute. (Steam assumed to be 
Admitted during Full Stroke.) 

Diam. of pipe, inches . . 2 

Vel. 4000 5.2 

Vel. 6000 6.3 

Vel. 8000 7.3 

Horse-power, approx. . . 20 

Diam. of pipes, inches . 7 

Vel. 4000 18.1 

Vel. 6000 22.1 

Vel. 8000 25.6 29.2 

Horse-power, approx. . . 245 

Formula. Area of pipe = , — ^ ^—r ~ — ^ — 

mean velocity of steam m pipe 
For piston-speed of 600 ft. per min. and velocity in pipe of 4000, 6000, 



2V2 


3 


31/2 


4 


41/2 


5 


6 


6.5 


7.7 


9.0 


10.3 


11.6 


12.9 


15.5 


7.9 


9.5 


11.1 


12.6 


14.2 


15.8 


19.0 


9.1 


10.9 


12.8 


14.6 


16.4 


18.3 


21.9 


31 


45 


62 


80 


100 


125 


180 


8 


9 


10 


11 


12 


13 


14 


20.7 


23.2 


25.8 


28.4 


31.0 


33.6 


36.1 


25.3 


28.5 


31.6 


34.8 


37.9 


41.1 


44.3 


29.2 


32.9 


36.5 


40.2 


43.8 


47.5 


51.1 


320 


406 


500 


606 


718 


845 


981 


Area of cylinder X piston-speed . 





880 



STEAM. 



and 8000 ft. per min., area of pipe = respectively 0.15, 0.10, and 0.075X 
area of cylinder. Diam. of pipe = respectively 0.3873,0.3162, and 0.2739X 
diam. of cylinder. The reciprocals of these are 2. 582, 3. 162 and 3. 651. 

The first line in the above table may be used for proportioning exhaust 
pipes, in which a velocitv not exceeding 4000 ft. per minute is advisable. 
The last Une, approx. H.P. of engine, is based on the velocity of 6000 ft. 
per min. in the pi pe, using the correspond ing diameter of piston, and 
taking H.P. = 1/2 (diam. of piston in inches) . 

Sizes of Steam-pipes for Marine Engines. — In marine-engine 
practice the steam-pipes are generally not as large as in stationary practice 
for the same sizes of cyUnder. Seaton gives the following rules: 

Main Steam-pives should be of such size that the mean velocity of flow 
does not exceed 8000 ft. per min. , , , ,^ . , 

In large engines, 1000 to 2000 H.P., cutting off at less than half stroke 
the steam-pipe may be designed for a mean velocity of 9000 ft., and 
10,000 ft. for still larger engines. 

In small engines and engines cutting off later than half stroke, a velocity 
of less than 8000 ft. per minute is desirable. 

Taking 8100 ft. per min. as the mean velocity, S speed of piston in feet 
per min., and D the diameter of the cylinder, 

Diam. of main steam-pipe =-= ^D^S -^ 8100 = D VS -f- 90. 

Stop and Throttle Valves should have a greater area of passages than the 
area of the main steam-pipe, on account of the friction through the cir- 
cuitous passages. The shape of the passages should be designed so as to 
avoid abrupt changes of direction and of velocity of flow as far as possible. 

Area of Steam Ports and Passages = 

Area of piston X speed of piston in ft. per min. (Diam.)^ X speed 
6000 ' ~ 7639 

Opening of Port to Steam. — To avoid wire-drawing during admission 
the area of opening to steam should be such that the mean velocity of 
flow does not exceed 10,000 ft. per min. To avoid excessive clearance 
the width of port should be as short as possible, the necessary area being 
obtained by length (measured at right angles to the line of travel of the 
valve). In practice this length is usually 0.6 to 0.8 of the diameter of 
the cylinder, but in long-stroke engines it may equal or even exceed the 
diameter. 

Exhaust Passages and Pipes. — The area should be such that the mean 
velocity of the steam should not exceed 6000 ft. per min., and the area 
should be greater if the length of the exhaust-pipe is comparatively long. 
The area of passages from cylinders to receivers should be such that the 
velocity will not exceed 5000 ft. per min. 

The following table is computed on the basis of a mean velocity of flow 
of 8000 ft. per min. for the main steam-pipe, 10,000 for opening to steam, 
and 6000 for exhaust. A = area of piston, D its diameter. 
Steam and Exhaust Openings. 



Piston- 
speed, 
ft. per min. 


Diam. of 


Area of 


Diam. of 


Area of 


Opening 


Steam-pipe 
^ D. 


Steam-pipe 

■r- A. 


Exhaust 
+ D. 


Exhaust 
■i- A. 


to Steam 
^ ^ A. 


300 


0.194 


0.0375 


0.223 


0.0500 


0.03 


400 


0.224 


0.0500 


0.258 


0.0667 


0.04 


500 


0.250 


0.0625 


0.288 


0.0833 


0.05 


600 


0.274 


0.0750 


0.316 


O.IOOO 


0.06 


700 


0.296 


0.0875 


0.341 


0.1167 


0.07 


800 


0.316 


0.1000 


0.365 


0.1333 


0.08 


900 


0.335 


0.1125 


0.387 


0.1500 


0.09 


1000 


0.353 


0.1250 


0.400 


0.1667 


0.10 



^Proportioning Steam-Pipes for Minimum Total Loss by Radiation 
and Friction. — For a given size of pipe and quantity of steam to be 
carried the loss of pressure due to friction is calculated by fornuilae given 
above, or taken from the tables. The work of friction, being converted 
into heat, tends to dry or superheat the steam, but its influence is usually 
so small that it may be neglected. The loss of heat by radiation tends to 
destroy the superheat and condense some of the steam into water. For 



FLOW OF STEAM. 



881 



well-covered steam-pipos this loss may be estimated at about 0.3 
B.T.U. per sq. it. of external surface of the pipe per houi* per degree of 
difference of temperature between that of the steam and that of the 
svuTounding atmosphere (see Steam-pipe Coverings, p. 584). 

A practical problem in power-plant design is to find the diameter of 
pipe to carry a griven quantity of steam with a minimum total loss of 
available energy due to both rhdiation and friction, considering also the 
money loss due to interest and depreciation on the value of the pipe 
and covering as erected. Each case requires a separate arithmetical 
computation, no formula yet being constructed to fit the general case. 
An approximate method of solution, neglecting the slight gain of heat by 
the steam from the work of friction, and assuming that the water con- 
densed by radiation of heat is removed by a separator and lost, is as fol- 
lows: Calculate the amount of steam required by the engine, in pounds 
per minute. From a steam pipe formula or table find the several drops 
of pressure, in lbs. per sq. in., in pipes of different assumed diameters, for 
the given quantity of steam and the given length of pipe. Compute from 
a theoretical indicator diagram of steam expanding in the engine the loss 
of available v/ork done by 1 lb. of steam, due to the several drops already 
found, and the corresponding fraction of 1 lb. of steam that will have to 
be supplied to make up for this loss of work. State this loss as equiva- 
lent to so many pounds of steam per 1000 lbs. of steam carried. Calcu- 
late the loss in lbs. of steam condensed by radiation in the pipes of the 
different diameters, per 1000 lbs. carried. Add the two losses together 
for each assumed size of pipe, and by inspection find which pipe gives the 
lowest total loss. The money loss due to cost and depreciation may also 
be figured approximately in the same unit of lbs. of steam lost per 1000 
lbs. carried, by taking the cost of the covered pipe, assuming a rate of 
interest and depreciation, finding the annual loss in cents, then from the 
calculated value of steam, wliich depends on the cost of fuel, find the 
equivalent quantity of steam wliich represents this money loss, and 
the equivalent lbs. of steam per 1000 lbs. carried. This is to be added to 
the sum of the losses due to friction and radiation, and it will be found to 
m6dify somewhat the conclusion as to the diameter of pipe and the drop 
which corresponds to a minimum total loss. 

Instead of determining the loss of available work per pound of steam 
from theoretical indicator diagrams, it may be computed approximately 
on the assumption, based on the known characteristics of the engine, 
that its efficiency is a certain fraction of that of an engine working between 
the same limits of temperature on the ideal Carnot cycle, as shown in 
the table below, and from the efficiency thus found, compared with the 
eflaciency at the given initial pressure less the drop, the loss of work may 
be calculated. 

Available Maximum >s Thermal Efficiency of Steam Expanded 
betw^een the given pressures and 1 lb. absolute, based on 
THE Carnot Cycle. (E = Ti - T2) -^ Ti. 





Maximum Initial Absolute Pressures. 


less than Maxi- 


100 


125 1 150 1 175 I 200 1 225 | 250 | 275 


300 


mum, Lbs. 


Maximum Thermal Efficiency. 




2 


0.287 
.286 
.284 
.280 
.272 


0.302 
.301 
.299 
.296 
.290 


0.314 
.313 
.312 
.309 
.304 


0.324 
.323 
.322 
.320 
.316 


0.333 
.332 
.331 
.329 
.326 


0.341 
.340 
.339 
.337 
.335 


0.348 
.347 
.346 
.345 
.342 


0.354 
.354 
.353 
.352 
.349 


0.360 
.359 


5 

10 

20 


.359 
.358 
.356 



This table shows that if the initial steam pressure is lowered from 
100 lbs. to 80 lbs., the efficiency of the Carnot cvcle is reduced from 
0.2B7 to 0.272, or over 5%, but if steam of 300 lbs. is lowered to 280 lbs. 
the efficiency is reduced only from 0.360 to 0.356 or 1.1%. With high- 
pressure steam, therefore, much greater loss of pressure by friction of 
steam pipes, valves and ports is allowable than with steam of low pressure. 

Theoretically the loss of efficiency due to drop in pressure on account 
of friction of pipes should be less than that indicated in the above table, 
since the work of friction tends to superheat the steam, but practically 
most, if not all, of the superheating is lost by radiation. 



882 



STEAM. 



By a method of calculation somewhat similar to that above outlined , 
the following figures were found, in a certain case, of the cost per day 
of the transmission of 50,000 lbs. of steam per hour a distance of 1000 
feet, with 100 lbs. initial pressure. 



Diameter of Pipe. 


6 in. 


7 in. 


8 in. 


10 in. 


12 in. 


1. Interest, etc., 12% per annum. . 

2. Condensation 


$0.39 
1.51 
0.86 


$0.46 
1.76 
0.38 


$0.53 
2.01 
0.19 


$0.66 
2.51 
0.06 


$0.84 
3.02 


3. Friction 


0.02 






Total per day 


$2.76 


$2.60 


$2.73 


$3.23 


$3.88 



STEAM-PIPES. 



Bursting-tests of Copper Steam-pipes. 

Engineer Melville, U. S. N., for 1892.) • ^ 



(From Report of Chief 
, ■ Some tests were made at the 
New York Navy Yard which show the unreliability of brazed seams in 
copper pipes. Each pipe was 8 in. diameter inside and 3 ft. 1 5/8 in. long. 
Both ends were closed by ribbed heads and the pipe was subjected to a 
hot-water pressure, the temperature being maintained constant at 371° F. 
Three of the pipes were made of No. 4 sheet copper (Stubs gauge) and the 
fourth was made of No. 3 sheet. 

The following were the results, in lbs. per sq. in., of bursting-pressure: 

Pipe number 1 2 3 4 4' 

Actual bursting-strength . . 835 785 950 1225 1275 

Calculated " " 1336 1336 1569 1568 1568 

Difference 501 551 619 343 293 

The tests of specimens cut from the ruptured pipes show the injurious 
action of heat upon copper sheets; and that, while a wliite heat does not 
change the character of the metal, a heat of only shghtly gi eater degree 
causes it to lose the fibrous nature that it has acquired in rolling, and a 
serious reduction in its tensile strength and ductiUty results. 

A Failure of a Brazed Copper Steanoi-pipe on the British steamer 
Prodano was investigated by Prof. J. O. Arnold. He found that the 
brazing was originally sound, but that it had deteriorated by oxidatiou 
of the zinc in the brazing alloy by electrolysis, which was due to the 
presence of fatty acids produced by decomposition of the oil used in the 
engines. A full account of the investigation is given in The Engineer, 
April 15, 1898. 

Reinforcing Steam-pipes. (Eng,, Aug. 11, 1893.) — In the Italian 
Navy copper pipes above 8 in. diam. are reinforced by wrapping them with 
a close spiral of copper or Delta-metal wire. Two or three independent 
spirals are used for s'afety in case one wire breaks. They are wound at a 
tension of about IV2 tons per sq. in. 

Materials for Pipes and Valves for Superheated Steam. (M. TV. 
Kellogg, Trans. A. S. M. E., 1907.) — The latest practice is to do away 
with fittings entirely on high-pressure steam lines and put what are known 
as "nozzles" on the piping itself. This is accompUshed by welding 
wrought-steel pipe on the side of another section, so as to accomphsh 
the same result as a fitting. In this way rolled or cast steel flanges and a 
Rockwood or welded joint can be used. Tliis method has three distinct 
advantages: 1. The quaUty of the metal used. 2. The hghtening of the 
entire work. 3. The doing away with a great many joints. 

As a general average, at least 50% of the joints can be left out; some- 
times the proportion runs up as high as 70%. 

Above 575° F. the limit of elasticity in cast iron is reached with a 
pressure varying from 140 to 175 pounds. Under such conditions the 
material is strained and does not resume its former shape, eventually 
showing surface cracks which increase until the pipe breaks. [This state- 
ment concerning cast iron does not seem to agree with the one on page 
439, to the effect that no diminution in its strength takes place under 
900° F.] 

Tests by Bach on cast steel show that at 572° F. the reduction in break- 
' ing strength amounts only to 1.1% and at 752° F. to about 8%. 

The effect of temperature on nickel is similar to that on cast steel and 
in consequence this material is very suitable for use in connection with 



STEAM-PIPES. 883 

highly superheated steam. Bach recommends that bronze alloys be 
done awaj^ with for use on steam lines above a temperature of about 
390° F. 

The old-fashioned screwed joint, no matter how well made, is not 
suitable for superheated steam work. 

In making up a joint, the face of all flanges or pipe where a joint is made 
should be given a fine tool finish and a plane surface, and a gasket should 
be used. The best results have been obtained with a corrugated soft 
Swedish steel gasket with "Smooth-on" appUed, and with the McKim 
gasket, which is of copper or bronze surrounding asbestos. On super- 
heated steam fines a corrugated copper gasket will in time pit out in 
some part of the flange nearly through the entire gasket. 

Specifications for pipes ana fittings for superheated steam service were 
pubhshed by Crane Co., Chicago, in the Valve Woj^ld, 1907. 

Riveted Steel Steam-pipes have been used for high pressures. See 
paper on A Method of Manufacture of Large Steam-pipes, by Chas. H. 
Manning, Titans. A. S. M. E., vol. xv. 

Valves in Steam-pipes. — Should a globe- valve on a steam-pipe have 
the steam-pressure on top or underneath the valve is a disputed question. 
With the steam-pressure on top, the stuffing-box around the valve-stem 
cannot be repacked ^^1thout shutting off steam from the whole line of 
pipe; on the other hand, if the steam-pressure is on the bottom of the 
valve it all has to be sustained by the screw-thread on the valve-stem, 
and there is danger of stripping the thread. 

A correspondent of the American Machinist, 1892, says that it is a very 
uncommon thing in the ordinary globe-valve to have the thread give out, 
but by water-hammer and merciless screwing the seat \\ill be crushed 
down quite frequently. Therefore with plants where only one boiler is 
used he ad\ises placing the valve \vith the boiler-pressure underneath it. 
On plants where several boilers are connected to one main steam-pipe 
he would reverse the position of the valve, then when one of the valves 
needs repacking the valve can be closed and the pressure in the boiler 
whose pipe it controls can be reduced to atmospheric by lifting the safety- 
valve. The repacking can then be done without interfering with the 
operation of the other boilers of the plant. 

He proposes also the following other rules for locating valves: Place 
valves with the stems horizontal to avoid the formation of a water-pocket. 
Never put the junction-valve close to the boiler if the main pipe is above 
the boiler, but put it on the highest point of the junction-pipe. If the other 
plan is followed, the pipe fills with water wiienever this boiler is stopped 
and the others are running, and breakage of the pipe may cause serious 
results. Never let a junction-pipe run into the bottom of the main pipe, 
but into the side or top. Always use an angle-valve where convenient, 
as there is more room in them.. Never use a gate valve under high pressure 
unless a by-pass is used with it. Never open a blow^-off valve on a boiler 
a little and then shut it; it is sure to catch the sediment and ruin the 
valve; throw it well open before closing. Never use a globe-valve on an 
indicator-pipe. For water, always use gate or angle valves or stop-cocks 
to obtain a clear passage. Buy if possible valves with renew^able disks. 
Lastly, never let a man go inside a boiler to work, especially if he is to 
hammer on it, unless you break the joint between the boiler and the 
valve and put a plate of steel betw^een the flanges. 

The " Steam-Loop " is a system of piping by wiiich w^ater of con- 
densation in steam-pipes is automatically returned to the boiler. In its 
simplest form it consists of three pipes, which are called the riser, the 
horizontal, and the drop-leg. When the steam-loop is used for returning 
to the boiler the water of condensation and entrainment from the steam- 
pipe through which the steam flows to the cylinder of an engine, the riser 
is generally attached to a separator; tliis riser empties at a suitable 
height into the horizontal, and from thence the w^ater of condensation is 
led into the drop-leg, which is connected to the boiler, into which the 
water of condensation is fed as soon as the hydrostatic pressure in the 
drop-leg in connection with the steam-pressure in the pipes is sufficient to 
overcome the boiler-pressure. The action of the device depends on the 
following principles: Difference of pressure may be balanced by a water- 
column; vapors or liquids tend to flow to the point of lowest pressure; 
rate of flow depends on difference of pressure and mass; decrease of static 
pressure in a steam-pipe or chamber is proportional to rate of conden- 



884 



STEAM. 






sation; in a steam-current water will be carried or swept along rapidlv 
by friction. (Illustrated in Modern Mechanism, p. 807. Patented by 
J. H. Blessing, Feb. 13, 1872, Dec. 28, 1883.) Mr. Blessing thus describes 
the operation of the loop in Eng. Review, Sept., 1907. 

The heating system is so arranged that the water of condensation from 
the radiators gravitates towards some low point and thence is led into the 
top of a receiver. After this is done it is found that owing to friction 
caused by the velocity of the steam passing through the different pipes 
and cendensation due to radiation, the steam pressure in the small drip 
receiver is much less than that in the boiler. This difference will deter- 
mine the height, or the length of the loop, that must be employed so that 
the water will gravitate through it into the boiler: that is to say, if there is 
10 lbs. difference in pressure, the descending leg of the loop should extend 
about 30 feet above the water-level in the boiler, since a column of water 
2.3 ft. is equal to 1 lb. pressure, and a difference in pressure of 10 lbs. 
would require a column 23 ft. high. If we make the loop 30 feet high 
we shall have an additional length of 7 ft. with which to overcome fric- 
tion. The water, after it reaches the top of the loop, composed of a 
larger section of pipe, will flow into the boiler through the descending 
leg with a velocity due to the extra 7 ft. added to the discharging leg. 

Loss from an Uncovered Steam-pipe. (Bjorling on Pumping- 
engines.) — The amount of loss by condensation in a steam-pipe carried 
down a deep mine-shaft has been ascertained by actual practice at the 
Clay Cross ColUery, near Chesterfield, where there is a pipe 71/2 in. internal 
diam., 1100 ft. long. The loss of steam by condensation was ascertained 
by direct measurement of the water deposited in a receiver, and was found 
to be equivalent to about 1 lb. of coal per I.H.P. per hour for every 100 ft. 
of steam-pipe; but there is no doubt that if the pipes had been in the up- 
cast shaft, and well covered with a good non-conducting material, the loss 
would have been less. (For Steam-pipe Coverings, see p. 584, ante.) 

Condensation in an Underground Pipe Line. (vV. W. Christie, 
Eng. Rec, 1904.) — A length of 300 ft. of 4-in. pipe, enclosed in a box 
of 11/4-in. planks, 10 ins. square inside, and packed with mineral wool, 
was laid in a trench, the upper end being 1 ft. and the lower end 5 ft. below 
the surface. With 80 lbs. gauge pressure in the pipe the condensation 
was equivalent to 0.275 B.T.U. per mjnute per sq. ft. of pipe surface 
when the outside temperature was 31° F., and 0.222 per min. when the 
temperature was 62° F. 

Steam Receivers on Pipe Lines. (W. Andrews, Steam Eng'g, Dec. 
10, 1902.) — In the four large power houses in New York City, with 
an ultimate capacity of 60,000 to 100,000 H.P. each, the largest steam 
mains are not over 20 ins. in diameter. Some of the best plants have 
pipes which run from the header to the engine two sizes smaller than that 
called for by the engine builders. These pipes before reaching the engine 
are carried into a steel receiver, which acts also as a separator. This 
receiver has a cubical capacity of three times that of the high-pressure 
cylinder and is placed as close as possible to the cylinder. The pipe from 
the receiver to the cylinder is of the full size called for by the engine 
builder. The objects of this arrangement are: First, to have a full supply 
of steam to the throttle; second, to provide a cushion near the engine on 
which the cut-off in the steam chest may be spent, thereby preventing 
vibrations from being transmitted through the piping system; and 
third, to produce a steady and rapid flow of steam in one direction only, 
by having a small pipe leading into the receiver. The steam flows 
rapidly enough to make good the loss caused during the first quarter of 
the stroke. Plants fitted up in this way are successfully running where 
the drop in steam pressure is not greater than 4 lbs., although the engines 
are 500 ft. away from the boilers. 

Equation of Pipes. — For determining the number of small sized 
pipes that are equal in carrying capacity to one of greater size the table 
given under Flo w of Air, page 625, is commonly used. It is based on the 
equation N = '^dP^di^, in which A^ is the number of smaller pipes of 
diameter d\ equal in capacity to one pipe of diameter d. A more 
accu rate equ ation, based on Unwin's formula for flow of fluids, is A^ = 

, I ' ' ■ ; {d and c/i in inches). For d= 2di, the first formula gives 

rfi* Vd + 3.6 



THE STEAM-BOILER. 



885 



N =* 5.7, and the second N =» 6.15, an unimportant difference, but for 
d = 8di, the first gives iV = 181 and the second N = 274, a considerable 
difference. (G. F. Gebhardt, Power, June, 1907). 

Identification of Power House Piping by Different Colors. (W. 

H. Bryan, Trans. A. S. M, E., 1908.) —In large power plants the multi- 
plicity of pipe lines carrying different fluids causes confusion and may 
lead to danger by an operator opening a wrong valve. It has therefore 
become customary to paint the different hues of different colors. The 
paper gives several tables showing color schemes that have been adopted 
in different plants. The following scheme, adopted at the New York 
Edison Co.'s Waterside Station, is selected as an example. 



Pipe Lines. 



Steam, high pressure to engines, boiler 

cross-overs, leaders and headers 

All other steam lines 

Steam, exhaust 

Steam, drips including traps 

Steam trap discharge 

Blow-offs, drips from water columns 

and low-pressure drips 

Drains from crank pits 

Cold water to primary heaters and 

jacket pumps 

Feed-water, pumps to boilers 

Hot-water mains, primary heaters to 

pumps, and cooling-water returns. . . . 

Air pump discharge to hot well 

Cooling water, pumps to engines 

Fire lines 

Cylinder oil, high pressure 

Cylinder oil, low pressure 

Engine oil 

Pneumatic system 





Bands, Cou- 


Colors of Pipe. 


plings, Valves, 




etc. 


Black 


Brass 


Buff 


Black 


Orange 


Red 


Orange 


Black 


Green 


Black 


Slate 


Red 


Dark Brown 


Blue 


Blue 


Red 


Maroon 


Same 


Green 


Red 


Slate 


Black 


Blue 


Black 


Vermilion 


Same 


Brown 


Black 


Brown 


Green 


Brown 


Red 


Black 


Same 



THE STEAM-BOILER. 

The Horse-power of a Steam-boiler. — The term horse-power has 
two meanings in engineering: First, an absolute unit or measure of the rati 
of work, that is, of the work done in a certain definite period of time, by 
a source ot energy, as a steam-boiler, a waterfall, a current of air or water, 
or by a prime mover, as a steam-engine, a water-wheel, or a wind-mill. 
The value of this unit, whenever it can be expressed in foot-pounds ol 
energy, as in the case of steam-engines, water-wheels, and waterfalls, is 
33,000 foot-pounds per minute. In the case of boilers, where the work 
done, the conversion of water into steam, cannot be expressed in foot- 
pounds of available energy, the usual value given to the term horse-power 
is the evaporation of 30 lbs. of water of a temperature of 100° F. into 
steam at 70 lbs. pressure above the atmosphere. Both of these units are 
arbitrary; the first. 33,000 foot-pounds per minute, first adopted by James 
Watt, being considered equivalent to the power exerted by a good London 
draught-horse, and the 30 lbs. of water evaporated per hour being con- 
sidered to be the steam reauirement per indicated horse-power of an 
average engine (in 1876). 

The Committee of Jutlges of the Centennial Exhibition, 1876, in report- 
ing the trials of competing boilers at that exhibition adopted the unit, 
30 lb. of water evaporated into dry steam per hour from feed-water at 
100° F., and under a pressure of 70 lb. per square inch above the atmos- 
phere, these conditions being considered by them to represent fairly 
average practice. 

The A. S. M. E. Committee on Boiler Tests, 1884, accepted the sarne 
unit, and defined it as equivalent to 34.5 lb. evaporated per hour from a 



886 THE STEAM-BOILER. 

feed-water temperature of 212° into steam at the same temperature. 
The committee of 1899 adopted 34.5 lb. per hour, from and at 212°, as 
the unit of commercial horse-power, and it was reaffirmed in the Boiler 
Code of the Power Test Committee, 1915. Using the figures for 
total heat of steam given in Marks and Davis's steam tables (1909), 
34 Yi lb. from and at 212°, is equivalent to 33,479 B.T.U. per hour, or to 
an evaporation of 30.018 lb. from 100° feed-water temperature into 
steam at 70 lb. pressure. 

The second definition of the term horse-power is an approxijnate meas- 
ure of the size, capacity, value, or ''rating" of a boiler, engine, water- 
wheel, or other source or conveyer of energy, by which measure it may be 
described, bought and sold, advertised, etc. No definite value can be 
given to this measure, which varies largely with local custom or indivi- 
dual opinion of makers and users of machinery. The nearest 
approach to uniformity which can be arrived at in the term "horse- 
power,' ' used in this sense, is to say that a boiler, engine, water-wheel, 
or other macliine, "rated" at a certain horse-power, should be capable 
of steadily developing that horse-power for a long period of time under 
ordinary conditions of use and practice, leaving to local custom, to the 
judgment of the buyer and seller, to written contracts of purchase and 
sale, or to legal decisions upon such contracts, the interpretation of 
what is meant by the term "ordinary conditions of use and practice." 
{Trans. A. S. M. E., vol. vii, p. 226.) 

Contracts for power-plant apparatus should specify the leading 
dimensions of the apparatus and its rated capacity. If a specific 
guarantee of capacity is made, either working or maximum capacity, 
the operating conditions under which the guarantee is to be met should 
be clearly set forth; such, for example, as steam pressure, speed, vacuum, 
quality of fuel, force of draft, etc. I^ikewise if a contract contains a 
guarantee of economy all the conditions should be fully specified. 

The commercial rating of capacity determined on for power-plant 
apparatus, whether for the purpose of contracts for sale or otherwise, 
should be such that a sufficient reserve capacity beyond the rating 
is available to meet the contingencies of practical operation; such con- 
tingencies, for example, as the loss of steam pressure and capacity due 
to cleaning fires, inferior coal, oversight of the attendants, sudden de- 
mand for an unusual output of steam or power, etc. 

The Committee of 1899 says: A boiler rated at any stated capacity 
should develop that capacity when using the best coal ordinarily sold in 
the market where the boiler is located .when fired by an ordinary fireman, 
without forcing the fires, while exhibiting good economy: and further, the 
boiler should develop at least one-third more than the stated capacity 
when using the same fuel and operated by the same fireman, the full 
draught being employed and the fires being crowded; the available draught 
at the damper, unless otherwise understood, being not less than 1/2 inch 
water column. 

Unit of Evaporation. (Abbreviation, U. E.) — It is the custom to 
reduce results of boiler-tests to the common standard of the equivalent 
evaporation from and at the boiling-point at atmospheric pressure, or 
" from and at 212° F." This unit of evaporation, or one pound of water 
evaporated from and at 212°. is equivalent to 970.4 British thermal 
units. 1 B.T.U. = the mean quantity of heat required to raise 1 lb. of 
water 1° F. between 32° and 212°. 

Measures for Comparing the Duty of Boilers. — The measure of 
the efficiency of a boiler is the number of pounds of water evaporated per 
pound of combustible (coal less moisture and ash), the evaporation 
being reduced to the standard of "from and at 212°." 

The measure of the capacity of a boiler is the amount of " boiler horse- 
power" developed, a horse-power being defined as the evaporation of 
34.5 lb. per hour from and at 212°. 

The measure of relative rapidity of steaming of boilers is the number 
of pounds of water evaporated from and at 212° per hour per square 
foot of water-heating surface. 

The measure of relative rapidity of combustion of fuel in boiler- 
furnaces is the number of pounds of coal burned per hour per square 
foot of grate-surface. 



STEAM-BOILER PROPORTIONS. 887 

STEAM-BOILER PROPORTIONS. 

Proportions of Grate and Heating Surface required for a given 
Horse-power. — The term horse-power here means capacity to evap- 
orate 34.5 lb. of water from and at 212° F. 

Average proportions for maximum economy for land boilers fired with 
good anthracite coal (ordinary hand firing) : 

Heating sm*face per horse-power 11 . 5 sq. ft. 

Grate surface per horse-power 1/3 " 

Ratio of heating to grate surface 34 . 5 

Water evap'd from and at 212° per sq. ft. H.S. per hr. . . 3 lb. 

Combustible burned per H.P. per hour 3 

Coal with 1/6 refuse, lb. per H.P. per hour 3.6 

Combustible burned per sq. ft. grate per hour 9 

Coal with 1/6 refuse, lb. per sq. ft. grate per hour 10.8 

Water evap'd from and at 212° per lb. combustible. ... 11.5 
Water evap'd from and at 212° per lb. coal (i/e refuse). 9 . 6 
Heating-surface. — For maximum economy with any kind of fuel a 
boiler should be proportioned so that at least one square foot of heating- 
surface should be given for every 3 lbs. of water to be evaporated from 
and at 212° F. per hour. Still more hberal proportions are required if a 
portion of the heating-surface has its efficiency reduced by: 1. Tendency 
of the heated gases to short-circuit, that is, to select passages of least 
resistance and flow through them with high velocity, to the neglect of 
other passages. 2. Deposition of soot from smoky fuel. 3. Incrusta- 
tion. If the heating-surfaces are clean, and the heated gases pass over 
It uniformly, httle if any increase in economy can be obtained by increasing 
the heating-surface beyond the proportion of 1 sq. ft. to every 3 lbs. of 
water to be evaporated, and with all conditions favorable but little 
decrease of economy will take place if the proportion is 1 sq. ft. to every 
4 lbs. evaporated; but in order to provide for driving of the boiler beyond 
Its rated capacity, and for possible decrease of efficiency due to the causes 
above named, it is better to adopt 1 sq. ft. to 3 lbs. evaporation per hour 
as the minimum standard proportion. 

Where economy may be sacrified to capacity, as where fuel is very 
cheap, it is customary to proportion the heating-surface much less liber- 
ally. The following table show^s approximately the relative results that 
may be expected with different rates of evaporation, with anthracite coal. 
Lbs. water evapor'd from and at 21 2° per sq. f t . heating-surface per hour: 
2 2.5 3 3.5 4 5 6 7 8 9 10 

Sq. ft. heating-surface required per horse-power: 
17.3 13.8 11.5 9.8 8.6 6.8 5.8 4.9 4.3 3.8 3.5 

Ratio of heating to grate surface if 1/3 sq. ft. of G.S. is required per H.P.: 
52 41.4 34.5 29.4 25.8 20.4 17.4 13.7 12.9 11.4 10.5 

Probable relative economy: 
100 100 100 95 90 85 80 75 70 65 60 

Probable temperature of chimney gases, degrees F.: 
450 450 450 518 585 652 720 787 855 922 990 

The relative economy will vary not only with the amount of heating- 
surface per horse-power, but with the efficiency of that heating-surface as 
regards its capacity for transfer of heat from the heated gases to the w^ater, 
which will depend on its freedom from soot and incrustation, and upon the 
circulation of the water and the heated gases. 

With bituminous coal the efficiency will larerely depend upon the 
thoroughness with w^hich the combustion is effected in the furnace. 

The efficiency with any kind of fuel will greatly depend upon the amount 
of air supplied to the furnace in excess of that required to support com- 
bustion. With strong draught and tliin fires this excess may be great, 
causing a serious loss of economy. The subject is further discussed below. 

Measurement of Heating-surface. — The usual rule is to consider as 
heating-surface all the surfaces that are surroimded by water on one side 
and by flame or heated gases on the other, using the external instead of 
the internal diameter of tubes, for greater convenience in calculation, 
external diameters of boiler-tubes usually being made in even inches or 
half inches. This method, how^ever, is inaccurate, for the true heating- 
surface of a tube is the side exposed to the hot gases, the inner surf ace in a 
fire-tube boiler and the outer surface in a water-tube boiler. The re- 



888 



THE STEAM-BOILER. 



sistance to the passage of heat from the hot gases on one side of a tube or 
plate to the water on the other consists almost entirely of the resistance to 
the passage of the heat from the gases into the metal, the resistance of the 
metal itself and that of the wetted surface being practically nothing. 
See paper by C. W. Baker, Trans. A. S. M. E., vol. xix. 

Rule for finding the heating-surface of vertical tubular boilers: Multiply 
the circumference of the fire-box (in inches) by its height above the grate; 
multiply the combined circumference of all the tubes by their length, and 
to these two products add the area of the lower tube-sheet; from this sum 
subtract the area of all the tubes, and divide by 144: the quotient is the 
number of square feet of heating-surface. 

Rule for finding the heating-surface of horizontal tubular boilers: Take 
the dimensions in Inches. Multiply two-thirds of the circumference of the 
shell by its length; multiply the sum of the circumferences of all the tubes 
by their common length; to the sum ot tnese products aaa two thirds of 
the area of both tube-sheets; from this sum subtract twice the combined 
area of all the tubes; divide the remainder by 144 to obtain the result in 
square feet. 

Rule for finding the square feet of heating-surface in tubes: Multiply 
the number of tubes by the diameter of a tube in inches, by its length in 
feet, and by 0.2618. 

Horse-power, Builder's Rating. Heating-surface per Horse- 
power. — It is a general practice among builders to furnish about 10 
square feet of heating-surface per horse-power, but as the practice is not 
uniform, bids and contracts should always specify the amount of heating- 
surface to be furnished. Not less than one-third square foot of grate-sur- 
face should be furnished per horse-power with ordinary chimney draught, 
not exceeding 0.3 in. of water column at the damper, for anthracite coal, 
and for poor varieties of soft coal high in ash, with ordinary furnaces. A 
smaller ratio of grate surface may be allowed for liigh grade soft coal and 
for forced draught. 

Horse-power of Marine and Locomotive Boilers. — The term horse- 
power is not generally used in connection with boilers in marine practice, 
or with locomotives. The boilers are designed to suit the engines, and 
are rated by extent of grate and heating-surface only. 

Grate-surface. — The amount of grate-surface required per horse- 
power, and the proper ratio of heating-surface to grate-surface are ex- 
tremely variable, depending cliiefly upon the character of the coal and 
upon the rate of draught. With good coal, low in ash, approximatelj?- 
equal results may be obtained with large grate-surface and light draught 
and \\1th smaU grate-surface and strong draught, the total amount of coal 
burned per hour being the same in both cases. With good l^ituminous 
coal, like Pittsburgh, low in ash, the best results apparently are obtained 
with strong draught and high rates of combustion, pro\ided the grate- 
surfaces are cut down so that the total coal burned per hour is not too great 
for the capacity of the heating-surface to absorb the heat produced. 

With coals high in ash, especially if the ash is easily fusible, tending to 
choke the grates, large grate-surface and a slow rate of combustion are 
required, unless means, such as shaking grates, are provided to get rid of 
the ash as fast as it is made. The amount of grate-surface required per 
horse-power under various conditions may be estimated as follows: 





ajTj 




Pounds of Coal burned per square 




Lbs. Wat 
from an 
at 212° 
per lb.. 
Coal. 


Lbs. Coa 
per H.P 
per houi 


foot of Grate per hour. 




8 ! 10 1 


12 1 15 I 20 I 25 1 30 1 35 I 40 
3q. Ft. Grate per H.P. 






Good coal and 


no 

9 


3.45 


.43 


.35 


.28 


.23 


.17 


.14 


.11 


.10 


.09 


boiler, 


3.83 


.48 


.38 


.32 


.25 


.19 


.15 


.13 


.11 


.10 




( 8.61 


4. 


.50 


.40 


.33 


.26 


.20 


.16 


.13 


.12 


.10 


Fair coal or boiler, 


4.31 


.54 


.43 


.36 


.29 


.22 


.17 


.14 


.13 






4.93 


.62 


.49 


.41 


.33 


.24 


.20 


.17 


.14 


.12 




( 6.9 


5. 


.63 


.50 


.42 


.34 


.25 


.20 


.17 


.15 


.13 


Poor coal or boiler, 


6 


5.75 


.72 


.58 


.48 


.38 


.29 


.23 


.19 


.17 


.14 




\ 5 


6.9 


.86 


.69 


.58 


.46 


.35 


.28 


.23 


.22 


.17 


Lignite and poor 
boiler, 


} 3.45 


10. 


1.25 


1.00 


.83 


.67 


.50 


.40 


.33 


.29 


.25 



PERFORMANCE OF BOILERS. 889 

In designinpr a boiler for a given set of conditions, the grate-surface 
should be made as liberal as possible, say sufficient for a rate of combus- 
tion of 10 lbs. per square foot of grate for anthracite, and 15 lbs. per square 
foot for bituminous coal, and in practice a portion of the grate-surface 
may be bricked over if it is found that the draught, fuel, or other condi- 
tions render it ad\isable. 

Proportions of Areas of Flues and other Gas-passages. — Rules 
are usually given making the area of gas-passages bear a certain ratio to 
the area of the grate-surface; thus a common rule for horizontal tubular 
boilers is to make the area over the bridge wall 1/7 of the grate-surface, 
the flue area Vs, and the chimney area 1/9. 

For average conditions with anthracite coal and moderate draught, say 
a rate of combustion of 12 lbs. coal per square foot of grate per hour, and a 
ratio of heating to grate surface of 30 to 1, this rule is as good as any, but 
it is evident that if the draught were increased so as to cause a rate of com- 
bustion of 24 lbs., requiring the grate-surface to be cut down to a ratio of 
60 to 1, the areas of gas-passages should not be reduced in proportion. 
The amount of coal burned per hour being the same under the changed 
conditions, and there being no reason why the gases should travel at a 
higher velocity, the actual areas of the passages should remain as before, 
but the ratio of the area to the grate-surface would in that case be 
doubled. 

Mr. Barrus states that the highest efficiency with anthracite coal is 
obtained when the tube area is 1/9 to Vio of the grate-surface, and with 
bituminous coal when it is 1/6 to 1/7, for the conditions of medium rates of 
combustion, such as 10 to 12 lbs. per square foot of grate per hour, and 12 
square feet of heating-surface allowed to the horse-power. 

The tube area should be made large enough not to choke the draught 
and so lessen the capacity of the boiler; if made too large the gases are apt 
to select the passages of least resistance and escape from them at a high 
velocity and high temperature. 

This condition is very commonly found in horizontal tubular boilers 
where the gases go chiefly through the upper rows of tubes; sometimes 
also in vertical tubular boilers, where the gases are apt to pass most rapidly 
through the tubes nearest to the center. It may to some extent be 
remedied by placing retarders in those tubes in which the gases travel the 
quickest. 

Air-passages through Grate-bars. — The usual practice is, air- 
opening = 30% to 50% of area of the grate; the larger the better, to avoid 
stoppage of the air-supply by clinker; but with coal free from clinker much 
smaller air-space may be used without detriment. See paper by F. A. 
Scheffler. Trans. A. S. M. E., vol. xv, p. 503. 

Distance from Dead Plate to Shell in Horizontal Tubular Boiler 
Settings. — Rules of the Department of Smoke Inspection, Chicago, 
1912. 

Diameter of shell, in 72 66 60 54 48 42 36 

Dead plate to shell, in. . . 42 40 38 36 34 32 30 

The department has required that all boilers be set higher than has 
formerly been the practice in order to provide greater combustion 
space and to allow the installation of proper furnaces. 
PERFORMANCE OF BOILERS. 

The performance of a steam-boiler comprises both its capacity for gener- 
ating steam and its economy of fuel. Capacity depends upon size, both of 
grate-surface and of heating-surface, upon the kind of coal burned, upon the 
draught, and also upon the economy. Economy of fuel depends upon the 
completeness with which the coal is burned in the furnace, on the proper 
regulation of the air-supply to the amount of coal burned, and upon the 
thoroughness with which the boiler absorbs the heat generated in the 
furnace. The absorption of heat depends on the extent of heating-sur- 
face in relation to the amount of coal burned or of water evaporated, upon 
the arrangement of the gas-passages, and upon the cleanness of the sur- 
faces. The capacity of a boiler may increase with increase of economy 
when this is due to more thorough combustion of the coal or to better regu- 
lation of the air-supply, or it may increase at the expense of economy 
when the increased capacity is due to overdriving, causing an increased 
loss of heat in the chimney gases. The relation of capacity to economy 
is therefore a complex one, depending on many variable conditions. 



890 THE STEAM-BOILER. 

'' A formula expressing the relation between capacity, rate of driving, 
or evaporation per square foot of heating-surface, to the economy, or 
evaporation per pound of combustible is given on page 893. 

Selecting the highest results obtained at different rates of driving with 
anthracite coal in the Centennial tests (in 1876) and the highest results 
with anthracite reported by Mr. Barrus in his book on Boiler Tests, the 
author has plotted two curves showing the maximum results which may 
be expected with anthracite coal, the first under exceptional conditions 
such as obtained in the Centennial tests, and the second imaer the best 
conditions of ordinary practice. {Trans. A. S. M. E., xviii, 354). 
From these curves the following figures are obtained. 

Lbs. water evaporated from and at 212° per sq. ft. heating-surface 
per hour: 

1.6 1.7 2 2.6 3 3.5 4 4.5 5 6 7 8 

Lbs. water evaporated from and at 212° per lb. combustible: 
Centennial... 11.8 11.9 12.0 12.1 12.05 12 11.85 11.7 11.5 10.85 9.8 8.5 

Barrus 11.4 11.5 11.55 11.6 11.6 11.5 11.2 10.9 10.6 9.9 9.2 8.5 

Avg. Cent'1 12.0 11.6 11.2 10.8 10.4 10.0 9.6 8.8 8.0 7.2 

The figures in the last line are taken from a straight line drawn as nearly 
as possible through the average of the plotting of all the Centennial tests. 
The poorest results are far below these figures. It is evident that no for- 
mula can be constructed that will express the relation of economy to rate oj 
driving as well as do the three lines of figures given above. 

For semi-bituminous and bituminous coals the relation of economy tc 
the rate of driving no doubt follows the same general law that it does with 
anthracite, i.e., that bej^ond a rate of evaporation of 3 or 4 lbs. persq. ft. oJ 
heating-surface per hour there is a decrease of economy, but the figures 
obtained in different tests will show a wider range between maximum and 
average results on account of the fact that it is more difficult with bitumi- 
nous than with anthracite coal to secure complete combustion in the 
furnace. 

The amount of the decrease in economy due to driving at rates exceeding 
4 lbs. of water evaporated per square foot of heating-surface per houi 
differs greatly with different boilers, and with the same boiler it may diffei 
with different settings and with different coal. The arrangement and size 
of the gas-passages seem to have an important effect upon the relation ol 
economy to rate of driving. 

A comparison of results obtained from different types of boilers leads to 
the general conclusion that the economy with wliich different types ol 
boilers operate depends much more upon their proportions and the con- 
ditions under wliich they work, than upon their type; and, moreover, 
that when the proportions are correct, and when the conditions are favor- 
able, the various types of boilers give substantially the same economic 
result. 

Conditions of Fuel Economy in Steam-boilers. — 1. That the boiler 
has sufficient heating surface to absorb from 75 to 80% of all the heat 
generated by the fuel. 2. That this surface is so placed, and the gas pas- 
sages so controlled by baffles, that the hot gases are forced to pass uni- 
formly over the surface, not being short-circuited. 3. That the furnace is 
of such a kind, and operated in such a manner, that the fuel is completely 
burned in it, and that no unburned gases reach the heating surface of the 
boiler. 4. That the fuel is burned with the minimum supply of air re- 
quired to insure complete combustion, thereby avoiding the carrying of an 
excessive quantitj^ of heated air out of the chimney. 

There are two indices of high economj^ 1. High temperature, ap- 
proaching 3000° F. in the furnace, combined with low temperature, below 
600° F., in the flue. 2. Analysis of the flue gases showing between 4 and 
8% of free oxygen. Unfortunately neither of these indices is available 
to the ordinary fireman; he cannot distinguish by the eye any temperature 
above 2000°, and he cannot know whether or not an excessive amount oi 
oxygen is passing through the fuel. The ordinary haphazard way of firing 
therefore gives an average of about 10% lower economy than can be 
obtained when the firing is controlled, as it is in many large plants, by re- 
cording furnace pyrometers, or by continuous g.:s analysis, or by both. 
Low CO2 in the flue gases may indicate either excessive air supply in the 
furnace, or leaks of air into the setting, or deficient air supply with the 
presence of CO. and therefore imperfect combustion. The latter, if exces- 



PERFORMANCE OF BOILERS. 891 

sive, is indicated by low furnace temperature. The analysis for CO2 should 
be made both of the gas sampled just beyond the furnace and of the gas 
sampled at the flue. Diminished CO2 in the latter indicates air-leakage. 

Less than 4% of free oxygen in the gases is usually accompanied with 
CO, and it therefore indicates imperfect combustion from deficient air 
supply. More than 8% means excessive air supply and corresponding 
waste of heat. 

Air Leakage or infiltration of air through the firebrick setting is a 
common cause of poor economy. It may be detected by analysis as above 
stated, and shoula De prevented by stopping all visible cracks in the brick- 
work, and by covering it with a coating impervious to air. 

Autographic CO2 Recorders are used in many large boiler plants for 
the continuous recording of the percentage of carbon dioxide in the gases. 
When the percentage of C02is between 12 and 16.it indicates good fur-- 
nace conditions, when below 12 the reverse. 

Continuous Records are an important element in securing maximum 
economy in modern boiler plants. They include records of coal and 
water consumption, of draft at the furnace and the chimney, of the 
analyses of the gases, of the flue temperature, and of the steam de- 
livered. For description of steam flow meters and other recording 
apparatus see Steam Boiler Economy, 2d edition. 

Efficiency of a Steam-boiler. — The efficiency of a boiler is the 
percentage of the total heat generated by the comoustion of the fuel 
which is utiUzed in heating the water and in raising steam. With anthra- 
cite coal the heating-value of the combustible portion is very nearly 
14,800 B.T.U. per lb., equal to an evaporation from and at 212° of 14,800 
-5- 970 = 15.26 lbs. of water. A boiler which when tested with anthra- 
cite coal shows an evaporation of 12 lbs. of water per lb. of combustible, 
has an efficiency of 12 -^ 15.26 = 78.6%, a figure wliich is approximated, 
but scarcely ever quite reached, in the best practice. With bituminous 
coal it is necessary to have a determination of its heating-power made 
by a coal calorimeter before the efficiency of the boiler using it can be 
determined, but a close estimate may be made from the chemical analysis 
of the coal. (See Coal.) 

The difference between the efficiency obtained by test and 100% is 
the sum of the numerous wastes of heat, the chief of which is the necessary 
loss due to the temperature of the chimney-gases. If we have an analysis 
and a calorimetric determination of the heating-power of the coal (properiy 
sampled), and an average analysis of the chimney-gases, the amounts 
of the several losses may be determined with approximate accuracy by 
the method described below. 

Data given: 

1. Analysis of the Coal. 2. Analysis of the Dry Chimney- 
Cumberland Semi-bituminous. gases, by Weight. 

Carbon 80.55 C. O. N. 

Hydrogen 4.50 002=13.6 = 3.71 9.89 

Oxygen 2.70 CO = 0.2 = 0.09 0.11 

Nitrogen 1.08 O = 11.2 = 11.20 

Moisture 2.92 N = 75.0= 75.00 

Ash 8 . 25 



■ 100.0 3.80 21.20 75.00 

100.00 
Heating-value of the coal by Dulong's formula, 14.243 heat-units. 
The gases being collected over water, the moisture in them is not deter- 
mined. 

3. Ash and refuse as determined by boiler-test, 10.25, or 2% more than 
that found by analysis, the difference representing carbon in the ashes 
obtained in the boiler-test. 

4. Temperature of external atmosphere, 60° F. 

5. Relative humidity of air, 60%, corresponding (see air tables) to 
0.007 lb. of vapor in each lb. of air. 

6. Temperature of chimney-gases, 560° F. 
/^o Ipi ]1 Q 1" aH TPm il t s * 

The carbon in the* chimney-gases being 3.8% of their weight, the total 
weight of dry gases per lb. of carbon burned is 100 -^ 3.8 = 26.32 lbs. 
Since the carbon burned is 80.55 - 2 = 78.55% of the weight of the coal, 
the weight of the dry gases per lb. of coal is 26.32 x 78.55 -h 100 = 
20.67 lbs. 



892 THE STEAM-BOILER. 

Each pound of coal furnishes to the dry chimney-gases 0.7855 lb. C, 

0.0108 N, and (2.70-^) -> 100 = 0.0214 lb, O; a total of 0.8177, say 

82 lb. This subtracted from 20.67 lbs. leaves 19.85 lbs. as the quantity 
of dry air (not including moisture) wliich enters the furnace per pound 
of coal, not counting the air required to burn the available hydrogen, 
that IS, the hydrogen minus one-eighth of the oxygen chemicallv combined 
in the coal. Each lb. of coal burned contained 0.045 lb. H, which requirea 
0.045 X 8 = 0.36 lb. O for its combustion. Of this, 0.027 lb. is furnished 
by the coal itself, leaving 0.333 lb. to come from the air. The quantity 
of air needed to supply this oxygen (air containing 23% by weight of 
oxygen) is 0.333 -♦• 0.23 = 1.45 lb., which added to the 19.85 lbs. already 
• found gives 21.30 lbs. as the quantity of dry air supplied to the furnace 
per lb. of coal burned. 

The air carried in as vapor is 0.0071 lb. for each lb. of dry air, or 21.3 X 
0.0071= 0.151b. for each lb. of coal. Each lb. of coal contained 0.029 lb. 
of moisture, which was evaporated and carried into the chimney -gases. 
The 0.045 lb. of H per lb. of coal when burned formed 0.045 X 9 = 
0.405 lb. of H2O. 

From the analysis of the chimney-gas it appears that 0.09 -^ 3.80 = 
2.37% of the carbon in the coal was burned to CO instead of to CO2. 

We now have the data for calculating the various losses of heat, as 
follows, for each pound of coal burned: 

Heat- Per cent of 

units. Heat-value 
of the Coal. 

20.67 lbs. dry gas X (560° - 60°) X sp. heat 0.24 = 2480.4 17.41 

0.151b.vaporinairX(560° -60°) Xsp. ht. 0.48 = 36.0 0.25 

0.029 lb. moist, in coal heated from 60° to 212° = 4.4 0.03 

0.0291b. evap. from and at 212°; 0.029 X 966 = 28.0 0.20 

0.029 lb. steam (heated 212° to 560°) X348X 0.48= 4.8 0.03 
0.405 lb. H2O from H in coal X (152 + 966 4- 

348X0.48) = 520.4 3.65 
0.0237 lb. C burned to CO; loss by incomplete 

combustion, 0.0237 X (14544- 4451) = 239.2 1.68 

0.02 1b. coal lost in ashes; 0.02 X 14544 = 290.9 2.04 

Radiation and unaccounted for, by difference = 624.0 4.38 



4228.1 29.69 

Utilized in making steam, equivalent evapora- 
tion 10.37 lbs. from and at 212° per lb. of coal = 10,014.9 70.31 

14.243.0 100.00 
The heat lost by radiation from the boiler and furnace is not easily 
determined directly, especially if the boiler is enclosed in brickwork, or 
is protected by non-conducting covering. It is customary to estimate 
the heat lost by radiation by difference, that is, to charge radiation with 
all the heat lost which is not otherwise accounted for. One method of 
determining the loss by radiation is to block off a portion of the grate- 
surface and build a small fire on the remainder, and drive this fire with 
just enough draught to keep up the steam-pressure and supply the heat 
lost by radiation without allowing any steam to be discharged, weighing 
the coal consumed for this purpose during a test of several hours' duration. 
Estimates of radiation by difference are apt to be greatly in error, as 
in this difference are accumulated all the errors of tlie analyses of the 
coal and of the gases. An average value of the heat lost by radiation 
from a boiler set in brickwork is about 3 % . When several boilers are in 
a battery and enclosed in a boiler-house the loss by radiation may be very 
much less, since much of the heat radiated from the boiler is returned to 
it in the air supplied to the furnace, which is taken from the boiler-room. 
An important source of error in making a "heat balance" such as the 
one above given, especially when highly bituminous coal is used, may be 
due to the non-combustion of part of the hydrocarbon gases distilled from 
the coal immediately after firing, when the temperature of the furnace may 
be reduced below the point of ignition of the gases. Each pound of hydro- 
gen which escapes burning is equivalent to a loss of heat in the furnace of 



PERFORMANCE OF BOILERS. 893 

62,000 heat-units. Another source of error, especially with bituminous slack 
coal ni2:ti in moisture, is due to the tormation ot water-gas, CO + H, by the 
decomposition of the water, and the consequent absorption of heat, this 
water-gas escaping unbiirned on account of the choking of the air supply 
when fine fresh coal is suppUed to the fire. 

In analyzing the chimney-gases by the usual method the percentages of 
the constituent gases are obtained by volume instead of by weight. To 
reduce percentages by volume to percentages by weight, multiply the per- 
centage by volume of each gas by its specific gravity as compared with air, 
and divide each product by the sum of the products. 

Instead of using the percentages by weight of the gases, the percentage 
by volume may be used directly to find the weight of gas per pound of 
carbon by the formula given below. 

If O, CO, CO2, and N represent the percentages by volume of oxygen, 
carbonic oxide, carbonic acid, and nitrogen, respectively, in the gases of 
combustion: 

Lb. of air required to burn ) ^ 3.032 N 
one pound of carbon ) CO2 4-CO' 

N 
Ratio of total air to the theoretical requirement = 



Lb. of air per pound [ ^ < Lb. of air per pound ) ^ j Per cent of car- ) 
of coal \ \ of carbon j ^ 1 bon in coal j 



Lb. dry gas produced per pound of carbon = 



N- 3.782 (O- 1/2 CO) 
) y j Per cent of car- ) 
j ^ 1 bon in coal j 
11 C02+80+7(CO+N) 



3(C02 + CO) 



Relation of Boiler Efficiency to the Rate of Driving, Air Supply, 
etc. — In the author's Steam Boiler Economy (p. 294) a formula is de- 
veloped showing the efficiency that may be expected, when the com- 
bustion of the coal is complete, under different conditions. The 
formula is 

Ba_ K - tcf 970 ac^P W^ 

E^~ K (1 + RS/W) ~'K {K- tcf) 'S" 

K = heating value per lb. of combustible; Ea= actual evaporation from 
and at 212° per lb. of combustible; Ep = possible evaporation = K -i- 
970; t = elevation of the temperature of the water in the boiler above 
the atmospheric temperature; c = specific heat of the chimney gases, 
taken at 0.24;/ = weight of flue gases per lb. of combustible; S = square 
feet of heating surface; W = pounds of water evaporated per hour; 
W/S = rate of driving; R= radiation loss, in units of evaporation per 
sq. ft. of heating-surface per hour; a is a coefficient found by experiment; 
it may be calleci a coefficient of inefficiency of the boiler, and it depends 
on and increases with the resistance to the passage of heat through the 
metal, soot or scale on the metal, imperfect combustion, short-circuiting, 
air leakage, or any other defective condition, not expressed in terms in 
the formula, which may tend to low^er the efficiency. Its value is between 
200 and 400 when records of tests show liigh efficiency, and above 400 for 
lower efficiencies. 

The coefficient a is a criterion of performance of a boiler when all the 
other terms of the formula are known as the results of a test. By trans- 
position its value is 

r K-tcf ] . c2/2 w 

1970 a -^ RS/W) ""J • {K-tcnS 

On the diagram below (Fig. 159), with abscissas representing rates of 
driving and ordinates representing efficiencies are plotted curves showing 
the relation of the efficiency to rate of driving for values of a= 100 to 
400 and values of f from 20 to 35, together with a broken line showing 
the maximum efficiencies obtained by six boilers at the Centennial Exhi- 
bition, and other lines showing the poor results obtained from five other 
boilers. The Curves are also based on the following values, K = 14.800; 
c = 0.24; t=300 (except one curve, t = 250); R = 0.1. 

An inspection of the curves shows the following. 1. The maximum 
Centennial results all he below the curve/ = 20, a = 200, by 2 to 4%, 
but they follow the general direction of the curve. This curve may 



894 



THE STEAM-BOILER. 



therefore be taken as representing the maximum possible boiler per- 
formance with anthracite coal, as the results obtained in 1876 have never 
been exceeded with anthracite. 

2. With/ = 20 and a = 200 the efficiency for maximum performance, 
according to the curve, is a httle less than 82% at 2 lbs. evaporation per 
sq. ft. of heating-surface per hour, but it decreases very slowly at higher 
rates, so that it is 80% at 31/2 lbs., and 76% at 53/4 lbs. 

With a = 200 and / greater than 20, the efficiency has a lower maxi- 
mum, reaches the maximum at a lower rate of driving, and falls off 
rapidly as the rate increases, the more rapidly the higher the value of /. 
showing excessive air supply to be a potent cause of low economy. 



62 
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123456-7 8 

Xbs. of Water Evaporated.f com and at 212" F. per sq. ft. of Heating Surface per Hour 
Fig. 159. 

3. An increase in the value of a from 200 to 400 with / = 20 is much 
less detrimental to efficiency than an increase in / from 20 to 30. 

In the diagram, Fig. 160, are plotted, together with the curve for/ = 20, 
c= 200, t = 300, and K = 15,750, marked R = 0.1, a straight Une, R = 0, 
showing the theoretical maximum efficiency when there is no loss by 
radiation, land the plottings of the results of two series of tests, one of a 
Thomycroft boiler, with WIS from 1.24 to 8.5, and the other of a Babcock 
& Wilcox marine boiler with WIS from 5.18 to 13.67, together with the 
maximum Centennial tests. The calculated value of a in all these tests 
except one ranged from 191 to 454, the highest values being those show- 
ing the largest departure from the curve 11= 0.1. The one exception 
IS the Thornycroft test showing over 86% efficiency; this gives a value 
of a = 57, which indicates an error in the test, as such a low value is far 
below the lowest recorded in any other test. 

In the second edition of Steam Boiler Economy (page 316), there is 
developed a modification of the efficiency formula, so that it takes 



PERFORMANCE OF BOILERS. 



895 



account, in addition to the other variables, of hydrogen and moisture in 

the coal and of incomplete combustion. It is 

^^ _ ^M - tcfi _ 970.4 Qi c2/i2 W 
E^~K+aRS/W) K K{Ki-tcfi) S' 

The notation is the same as ui the original formula except that Ki = 

K - 101.5 C r^^ r^r^ - 970.4 (0.09 H + 0.01 M) in which C, H and 

M are respectively the percentages of carbon, hydrogen and moisture 
in the coal, and CO and CO 2 percentages by volume of the dry flue 
gases, and /i = /+ 0.28H + 0.03 M.^ .^ . . . „ 

Computing the results of six series of boiler tests, 47 tests m all, 
which have given high efficiencies, the value of Oi is found to average 
about 200. Values from 160 to 240 may be obtained in duplicate tests 



S 84 

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o 80 

ft 78 

c 74 

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66 

C4 

1 2 3 4 5 6 7 8 9 10 11 12 13 14 

Lbs. of Water Evaporated from and at 212" P« per sq. ft. of Heating Surface per Hour. 

Fig. 160. 

in which all the conditions, as far as known, are identical, the dif- 
ference between individual and average values being probably due to 
errors. Values above 300, if not due to errors, represent defective per- 
formance which may be due to short-circuiting or to unclean heating 

Effect of Quality of Coal upon Efficiency. — Calculations have been 
made, using the formula given above, of the theoretical efficiencies 
obtainable from five different kinds of coal and an average fuel oil, the 
analyses of which are given below, on the assumption of complete com- 
bustion with 20% excess air supply, ax = 200, t = 300, c = 0.24 and rates 
of driving WJS from 1 to 14 lb. The results are shown in the table. 
Analyses of Fuels. 



Anthracite 

Dry and Free 

from Ash. 


Semi-bitum. 


Pittsburgh 
Ash and 
Sul. Free. 


Illinois 


Lignite. 


California 
Fuel Oil. 


C 94.3 
H 2.3 
2.4 
N 1.0 

B.T.U. per 
lb. 15.000 


Moist. 1.7 

N.S.Ash 4.6 

C 85.0 

H 4.5 

3.2 

14.950 


Moist. 2.0 
C 83.0 
H 5.5 
8.0 
N 1.0 

14.908 


Moist. 10.8 
C 61.0 
H 4.2 
9.6 
N 1.2 

Ash, SI 3.2 

10.640 


Moist.27.0 
C 47.4 
H 3.3 
12.0 
N 1.0 

8.250 


0.2 

84.9 

11.9 

1.9 

S 1.1 

19,600 



Relation of Efficiency to Quality of Coal. 



Rate of 
Driving, TF/S. 


1 


2 


3 


4 


6 


8 


10 


12 


14 


Anthracite 

Semi-bitum 

Pittsburgh bitum . . 
Illinois 


81.85 
80.41 
79.78 
78.28 


84.56 
82.96 
82.30 
80.59 


Ef 
84.71 
83.00 
82.34 
80.44 


Hcienc 
84.16 
82.38 
81.71 
79.64 
76.52 


es 

82.39 
80.42 
79.76 
77.34 


80.25 
78.10 
77.45 
74.71 


77.95 
75.64 
75.01 
71.93 


75.59 
73.12 
72.48 
69.09 


73.19 
70.54 
69.92 
66.20 


Lignite 


75.83 77.76 77.51 


73.98 70.90 67.79 64.62 61.40 


Fuel Oil 


78.78 


81.61 


82.01 


81.74 


80.52 


78.97 


77.26 


75.48 


73.58 



896 



THE STEAM-BOILER. 



Effect of Imperfect Combustion and Excess Air Supply. — Taking 
a Pittsburgh bituminous coal, having a composition, free from sul- 
phur and ash. of 83 C, 5.5 H, 8 O, 1.5 N. and 2 IMoisture, and a heating 
value of 14,908 B.T.U. per lb. fuel = 15.222 B.T.U. per lb. combustible, 
and assuming it to be burned with different quantities of air, as in the 
table below, we may compute the weight of air supplied per pomid of 
fuel and per pound of carbon, and the analysis by volume of the gases, 
giving results as follows: 





Per 

Cent 

of C 

Burned 

to CO. 


Per 

Cent 

Excess 

Air. 


Dry 
Gas 
per lb. 
Fuel 
= /. 


Dry 
Gas 
per lb. 
Car- 
bon. 


Analysis of Dry Gas by Volume. 


Case, 


CO2. 


CO. 


0. 


N. 


(1) 

(2) 

(3) 

(4) 

A 

B 

C 

D 






5 
5 
10 
20 



20 
50 
100 


20 






11.60 
13.83 
17.16 
22.72 
11.36 
13.23 
11.12 
10.65 


13.98 
16.66 
20.67 
27.37 
13.69 
15.93 
13.40 
12.83 


18.45 
15.30 
12.18 
9.10 
17.85 
15.18 
17.21 
15.88 










0.94 

0.80 

1.92 

3.97 



3.56 
7.09 
10.57 


3.12 






81.55 
81.14 
80.73 
80.33 
81.21 
80.90 
80.87 
80.15 



H2O in gases per lb. fuel = 0.09 H + 0.01 M, in all cases = 0.515 lb. 
Case (X) is an ideal but not a practicable case, since it is not possible 
in practice to burn all the C to CO2 without excess of air. Cases 
(2), (3), (4), A and B are all within the range of ordinary practice 
(which sometimes shows 200% or more excess air) and cases C and D 
represent either the condition of too heavy firing and choked air supply, 
or the conditiori existing for a minute or two after firing of fine moist 
slack coal, which temporarily chokes the air supply and causes the for- 
mation of a great volume of smoky gas. 

Cases 2 and A represent tlie best possible practice, reached only 
when all conditions are most favorable. 

Applying the formula given above, we take K= 14,908; i = 300: 
c = 0.24; i^ = 0.1; Oi = 200; /= the values given in the table; Ki and 
/i = values given by the formulae in the preceding paragraph, and 
W/S different values from 0.5 to 14, and obtain the theoretical efficiencies 
given below: 

Theoretical Efficiencies with Pittsburgh Coal Under Dif- 
ferent Conditions. 



Per cent C to CO. 
Per cent excess air 

W/S = 

0.5 

1 

2 

3 

4 

6 

8 
10 
12 
14 



(1) 





74.76 
81.13 
84.06 
84.49 
84.24 
83.03 
81.47 
79.77 
77.99 
76.16 



(2) 


(3) 


(4) 


A 


B 


C 











5 


5 


10 


20 


50 


100 





20 






Efficiencies, Per Cent. 



73.68 
79.78 
82.30 
82.34 
81.71 
79.76 
77.45 
75.01 
72.48 
69.92 



72.05 
77.7.3 
79.60 
79.02 
77.79 
74.65 
71.17 
67.55 
63.86 
60.12 



68.97 
73.72 
73.90 
71.72 
68.91 
62.60 
55.87 
49.20 
42.37 
35.48 



72.53 
78.69 
81.53 
81.91 
81.64 
80.43 
78.87 
77.17 
75.41 
73.58 



71.61 
77.54 
80.02 
80.09 
79.50 
77.65 
75.48 
73.15 
70.76 
68.32 



69.77 
76.23 
78.98 
79.35 
79.09 
77.91 
76.39 
74.74 
73.02 
71.27 



D 
20 


65.79 
71.34 
73.87 
74.16 
73.85 
72.64 
71.11 
69.45 
67.72 
65.97 



The figures in the table show the great falling off in efficiency at high 
rates of driving Aviien the air supply is excessive, and the necessity of 
gas analysis (or of a CO2 or an oxygen indicator) if high efficiencies are 
to be obtained at high rates of driving. 

The Straight-line Formula for Efficiency. — An examination of the 
curves i)lotted from the table given above shows that when the rate of 
driving is in excess of ;^ lb. per sq. ft. of heating surface per hour, and 
the effect of the radiation lo.ss is therefore of small importance, the 
curves become approximately straight lines, the formula of which is 



PERFORMANCE OF BOILERS. 



897 



E = E jfidx — C{W/S — 3), in which E is the eflBciency at any rate of 
driving above W/S = 3, i? ^^^^ is the efficiency when W/S = 3, and C 
is a constant which depends on the quahty of the coal and on the 
furnace conditions. Taking from the above table the efficiencies at 
W/S = 3 and W/S = 14 and calculating the value of C in the above 
equation of a straight line between these points, we obtain the following 
formulae for efficiency for the several cases named: 



Cases. 


Per Cent 
C to CO2 


Per Cent 
Excess Air. 


Formula. 


1 
2 
3 
4 
A 
B 
C 
D 






5 
5 
10 
20 




20 

50 

100 



20 






E = 84.5 - 0.76(W/S - 3) 
E =82.3 - \.\3{W/S - 3) 
E = 79.0 - \.72{W/S -3) 
E =7\.7 - 3.39{W/S -3) 
£- = 81.9 - 0.76{W/S -3) 
E = 80.1 - \.07{W/S - 3) 
E = 79.4 - 0.74(W/S -3) 
E = 74.2 - 0.75(W/S - 3) 



The efficiencies ca^lculated by these formulae in every case in which 
W/S is between 3 and 14 are slightly lower than those calculated from 
the complex formula, but in no case is the difference as great as 1%. 
It must be noted that all the efficiencies are theoretical ones, based on 
the assiunptions that there are no leaks of air into the boiler setting, no 
loss due to imbumed hydrocarbons, and no short circuiting or deposit 
of soot on the tubes. In cases 1, A, C and D, in which there is no excess 
air supply, there would in practice be probably some loss from unburned 
hydrocarbons. 

The straight hne formulae obtained from the figures in the table 
showing the relation of quality of coal to efficiency, assuming complete 
combustion and 20% excess air supply, are 

Antliracite E= 84.7 - 1.05(W/S - 3) 

Semi-bituminous jE = 83 . - 1 . 13 ( W/S - 3) 

Pittsburgh bituminous J5;=82.3-l. ISiW/S - 3) 

Ilhnois bituminous E = 80.4:- 1. 29{W/S - 3) 

Lignite E= 77.5- 1.46(T^/S- 3) 

Fuel oil E = 82.0- 0.77(W*S- 3) 

Efficiencies Obtained in Practice. — In the best modem practice, 
imder the most favorable furnace conditions, the highest figures in 
the above tables have almost been reached. A few tests with fuel oil 
have shown figures sUghtly liigher than those given above. The best 
record yet obtained with coal is that of the ten best out of the sixteen 
tests at the Delray station of the Detroit Edison Co., reported by D. 
S. Jacobus in Trans, A. S. M. £;., 1911. A straight hne drawn through 
the plotting of these tests corresponds to the formula 
E = 81 - 1.33 {W/S- 3). 
No account is taken in the above calculation of any loss due to un- 
consumed hydrogen or hydrocarbons, nor of absorption of heat by 
decomposition of moisture in the coal by the reaction C + H2O = 2H 
-|- CO. Serious losses may be due to these causes if the air supply is 
deficient and the furnace temperature low from the firing of a thick 
layer of fresh and moist coal, or if the combustible gases are chilled by 
the surface of the boiler to a temperature below that of ignition. No 
account, either, has been taken of the loss due to moisture in the air, 
which loss is usually not over 0.5%, but may reach 2% with excessive 
air supply of high temperature and humidity. 

The highest efficiencies are obtained with low rates of driving, say 
3 to 4 lb. evaporated from and at 212° per sq. ft. of heating surface 
per hour. With higher rates of driving high efficiencies can be obtained 
only when the air supply is carefully regulated according to the in- 
dications of gas analyses, when the coal is nearly dry, when it is fed at 
a regular rate by a mechanical stoker, and when the gases from the 
coal are completely burned in a large fire-brick combustion chamber 
before they are chiUed by the comparatively cool surfaces of the boiler. 
Modern practice tends to extremely large combustion chambers. 



898 THE STEAM-BOILER. 

With water-tube boilers of the Babcock & Wilcox type the tubes are 
often placed 12 feet or more above the grate bars. In the Stirling 
boilers of the Detroit Edison Co. the combustion chambers are over 
25 ft. high. 

The range of efficiency between the highest possible and that which 
may be found in ordinary practice is very large. AVhile 80 per cent 
efficiency is possible with anthracite and semi-bituminous coals, and 
with bituminous coals containing not over 3% moisture and not over 
35% volatile matter in the combustible, it is difficult to get over 65% 
with Illinois coals, high in volatile matter and in moisture, even with 
mechanical stokers and with gas analysis. With ordinary hand- 
firing the average efficiency is apt to be at least 15 % lower than these 
figures. For numerous records of boiler tests under various conditions, 
with a discussion of the results, see "Steam Boiler Economy," 2d 
edition. 

Maximum Boiler Efficiencies at Diflferent Rates of Driving. — The 
ten best tests of the large boilers of the Detroit Edison Co., reported 
by D. S. Jacobus in Jour. A.. S. M. E., Nov., 1911, with rates of driving 
from 3.24 to 7.29 lb. water evaporated from and at 212° per sq. ft. of 
heating surface per hour gave efficiencies which are represented (within 
1 %) by the formula ^ = 81 - 1.33 {R- S), in which E is the efficiency 
per cent and R the rate of driving. Eight tests of Babcock & Wilcos 
marine boilers built for the U. S. war-vessels Cincinnati and Wyoming 
(Indust. Eng'g, March, 1911), at rates of driving from 8.42 to 14.76 
lb. correspond within 3% with the formula ^ = 80- 1.43 (R-S). 
The Detroit tests were made with bituminous coal, low in moisture, 
containing about 30% volatile matter, with mechanical stokers and 
very large combustion chambers. The marine boiler tests were made 
with semi-bituminous coal containing about 20% volatile matter, with 
hand-firing. These tests establish a world's record for boiler efficiencies. 
The formulae give the following efficiencies for the several rates of 
driving named, the first being used for rates of driving of 3 to 7 lb. and 
the second for rates of 7 to 15 lb. 

R = S 4 5 6 7 8 10 12 14 15 

E = 81 79.7 78.3 77.0 75.7 72.9 70.0 67.1 64.3 62.8 

Some Higli Rates of Evaporation. — Eng'g, May 9, 1884, p. 415. 

Locomotive. Torpedo-boat. 

Waterevap. per sq.ft. H.S. per hour. 12.57 13.73 12.54 20.74 
Water evap. per lb. fuel from and at 

212° 8.22 8.94 8.37 7.04- 

Thermal units transf 'd per sq. ft. of 

H.S 12,142 13,263 12,113 20,034 

Efficiency . , 0.586 0.637 0.542 0.468 

It is doubtful if these figures were corrected for moisture in the steam. 
BOILERS USING WASTE GASES. 

Steam-boilers Fired with Waste Gases from Puddling and Heat- 
ing-Fm-naces. — ^The Iron Age, April 6, 1893, contains a report of a 
number of tests of steam-boilers utilizing the waste heat from puddhng 
and heating-furnaces in rolling-mills. The following principal data are 
selected: in Nos. 1,2, and 4 the boiler is a Babcock & AVilcox water-tube 
boiler, and in No. 3 it is a plain cylinder boiler, 42 in. diam. and 26 ft. 
long. No. 4 boiler was connected with a heating-fiunace, the others 
with puddling furnaces. 

No. 1 No. 2 No. 3 No. 4 

Heating-surface, sq. ft 1026 1196 143 1380 

Grate-surface, sq. ft 19 . 9 13 . 6 13 . 6 16 . 7 

Ratio H.S. to G.S 52 87.2 10.5 82.8 

Water evap. per hour, lbs 3358 2159 1812 3055 

Water evap. per sq. ft. H.S. per hr. lbs. . . 3.3 1.8 12.7 2.2 
Water evap. per lb. coal from and at 212° 5.9 6.24 3.76 6.34 
Water evap. per lb. combustible from 

and at 212° 7.20 4.31 8.34 

In No. 2, 1.38 lb. of iron were puddled per lb. of coal. 

In No. 3, 1.14 lb. of iron were puddled per lb. of coal. 

No. 3 shows that an insufficient amount of heating-surface was 
provided for the amount of waste heat available. 



ETTLES FOR CONDUCTING BOILER TESTS. 



899 



Water-tube Boilers using Blast-furnace Gases. — D. S. Jacobus 
(Trans. A. I. M. E., xvii, 50) reports a test of a water-tube boiler using 
blast-furnace gas as fuel. The heating-surface was 2535 sq. ft. It 
developed 328 H.P., or 5.01 lb. of water from and at 212° per sq. ft. of 
heating-surface per hour. Some of the principal data obtained w^ere as 
follows: Calorific value of 1 lb. of the gas. 1413 B.T.U., including the 
effect of its initial temperature, w^iich was 650° F. Amount of air used 
to burn 1 lb. of the gas = 0.9 lb. Chimney draught, II/3 in. of water. 
Area of gas inlet 300 sq. in. ; of air inlet, 100 sq. in. Temperature of the 
chimney gases, 775° F. Efficiency of the boiler calculated from the 
temperatures and analyses of the gases at exit and entrance, 61 %. The 
average analyses were as follows, hydrocarbons being included in the 
nitrogen : 





By Weight. 


By Volume. 




At Entrance. 


At Exit. 


At Entrance. 


At Exit. 


C02 


10.69 
0.11 
26.71 
62.48 
2.92 
11.45 
14.37 


26.37 
3.05 
1.78 

68.80 
7.19 
0.76 
7.95 


7.08 
0.10 

27.80 
65.02 


18.64 


0. ..::::::::.:.:.. 


2.96 


CO 


1.98 


Nitrogen 


76.42 


C in CO2 




C in CO 






Total C 








RULES FOR CONDUCTING BOILER TESTS. 

Object of an Evaporation Test. — The principal object of an 
evaporation test of a steam-boiler is to find out how many pounds 
of water it evaporates under a certain set of conditions in a given 
time and how many pounds of coal are required to effect this evapo- 
ration. The test may be made for one or more of several purposes, 
viz: 

1. To determine whether or not the stipulations of a contract 
between the seller and the buyer of a boiler (or of an appendage to 
the boiler, such as a furnace) have been performed. 

2. To determine the relative economy of different kinds of fuel, of 
different kinds of larnaces, or of different methods of driving. 

3. To determine whether or not the boilers, as ordinarily run under 
the every-day conditions of the plant, are operated as economically 
as they should be. 

4. To determine, in case the boilers either fail to furnish easily the- 
quantity of steam desired, or else furnish it at what is supposed to be 
an excessive cost for fuel, whether any additional boilers are needed 
or whether some change in the conditions of running is a sufficient 
remedy for the difficulty. 

.For the first of the above-named purposes, it is necessary that the 
test should be made with every precaution to insure accuracy, such 
as those described in the Code of the Committee of the American 
Society of Mechanical Engineers,* which is printed in abridged form 
below. 

Instructions Regarding Tests in General. 
(Code of 1915). 

OBJECT. 

Ascertain the specific object of the test, and keep this in view not 
only in the work of preparation, but also during the progress of the 
test. 

If questions of fulfillment of contract are involved, there should be 

* Trans. A.S.M.E., 1914, Reprinted in pamphlet form by the 
Society. The first committee of the society on boiler-tests reported 
in 1885, the second in 1899. In 1909 a committee on Tests of Power 
Plant Apparatus was appointed; its preliminary report was published 
in 1912. andjts final reoort in 1914. 



900 THE STEAM-BOILER. 

a clear understanding between all the parties, preferably in writing, 
as to the operating conditions which should obtain during the trial, 
the methods of testing to be followed, corrections to be made in case 
the conditions actually existing during the test differ from those 
specified, and all other matters about which dispute may arise, unless 
these are already expressed in the contract itself. 

PREPARATIONS. 

Dimensions. — Measure the dimensions of the principal parts of 
the apparatus to be tested, so far as they bear on the objects in view, 
or determine them from working drawings. Notice the general 
features of the apparatus, both exterior and interior, and make sketches, 
if needed, to show unusual points of design. 

The areas of the heating surfaces of boilers and superheaters to be 
found are those of surfaces in contact with the fire or hot gases. 
The submerged surfaces in boilers at the mean water level should 
be considered as water-heating surfaces, and other surfaces which 
are exposed to the gases as superheating surfaces. 

Examination of Plant. — Make a thorough examination of the phys- 
ical condition of all parts of the plant or apparatus which concern 
the object in view, and record the conditions found. 

In boilers examine for leakage of tubes and riveted or other metal 
joints. Note the condition of brick furnaces, grates and baffles. 
Examine brick w^alls and cleaning doors for air leaks, either by shut- 
ting the damper and observing the escaping smoke or by candle- 
flame test. Determine the condition of heating surfaces with refer- 
ence to exterior deposits of soot and interior deposits of mud or scale. 

If the object of the test is to determine the highest efiBciencj^ or 
capacity obtainable, any physical defects, or defects of operation, 
tending to make the result unfavorable should first be remedied; all 
fouled parts being cleaned, and the whole put in first-class condition. 
If, on the other hand, the object is to ascertain the performance under 
existing conditions, no such preparation is either required or desired. 

Precautions against Leakage. — In steam tests make sure that there 
is no leakage through blow-offs, drips, etc., or any steam or water con- 
nections, wriich would in any way affect the results. All such con- 
nections should be blanked off, or satisfactory assurance should be 
obtained that there is leakage neither out nor in. -, . . 

Apparatus and Instruments.— ^qq that the apparatus and instru- 
ments are substantially reliable, and arrange them in such a way 
as to obtain correct data. 

Weighing Scales. — For determining the weight of coal, oil, water, etc., 
ordinary platform scales serve every purpose. Too much depend- 
ence, however, should not be placed upon their reliability without 
first cahbrating them bv the use of standard weights, and carefully 
examining the knife-edges, bearing plates, and ring suspensions, 
to see that thev are all in good order. 

For testing locomotives and some classes of marine boilers, where 
room is lacking, sacks or bags are sometimes required to facilitate 
the handUng of coal, the sacks being weighed at the time of filling. 

SAMPLING AND DRYING COAL,. 

Select a representative shovelful from each barrow-load as it is 
drawn from the coal-pile or other source of supply, and store the 
samples in a cool place in a covered metal receptacle. When all 
the coal has thus been sampled, break up the lumps, thoroughly mix 
the whole quantity, and finally reduce it by the process of repeated 
quartering and crushing to a sample weighing about 5 lbs., the largest 
pieces being about the size of a pea. From this sample two 1-qt. 
air-tight glass fruit-jars, or other air-tight vessels, are to be promptly 
filled and preserved for subsequent determinations of moisture, calorific 
value, and chemical composition. 

When the sample lot of coal has been reduced by quartering to 



RULES FOR CONDUCTING BOILER TESTS. 901 

say 100 lbs., a portion weighing say 15 to 20 lbs. should be with- 
drawn for the purpose of immediate moisture determination. This 
is placed in a shallow iron pan and dried on the hot iron boiler flue 
for at least 12 hours, being weighed before and after drying on scales 
reading to quarter ounces. 

The moisture thus determined is approximately rehable for an- 
thracite and semi-bituminous coals, but not for coals containing much 
inherent moisture. For such coals, and for all absolutely reliable 
determinations the method to be pursued is as follows: 
Take one of the samples contained in the glass jars, and subject it 
to a thorough air drying, by spreading it in a thin layer and exposing 
it for several hours*^to the atmosphere of a warm room, weighing it 
before and after, thereby determining the quantity of surface moisture 
it contains. Then crush the whole of it by running it through an 
ordinary coffee mill or other suitable crusher adjusted so as to pro- 
duce somewhat coarse grains (less than Vie in.), thoroughly mix the 
crushed sample, select from it a portion of from 10 to 50 grams 
(say 3^^ oz. to 2 6z.), weigh it in a balance which will easily show a 
variation as small as 1 part in 1000, and dry it for one hour in an 
air or sand bath at a temperature between 240 and 280° F. Weigh 
it and record the loss, then heat and weigh again until the minimum 
weight has been reached. The difference between the original and 
the minimum weight is the moisture in the air-dried coal. The 
sum of the moisture thus found and that of the surface moisture 
is the total moisture. 

If a larger drying oven is available the moisture may be deter- 
mined by heating one of the glass jars full of coal, the cover being 
removed, at a temperature between 240° and 280° F. until it reaches 
the minimum weight. 

SAMPLING STEAM. 

Construct a sampling pipe or nozzle made of V2-ln. iron pipe and 
insert it in the steam main at a point where the entrained moisture 
is likely to be most thoroughly mixed. The inner end of the pipe, 
which should extend nearly across to the opposite side of the main, 
should be closed and the interior portion perforated with not less 
than twenty Vs-in. holes equally distributed from end to end and 
preferably drilled in irregular or spiral rows, with the first hole not 
less than half an inch from the wall of the pipe. 
The sampling pipe should not be placed near a point where water may 

pocket or where such water may affect the amount of moisture 

contained in the sample. 

Rules for Conducting Evaporative Tests of Boilers. 

object and preparations. 

Determine the object of the test, take the dimensions, note the 
physical conditions, examine for leakages, install the testing appli- 
ances, etc., as pointed out in the general instructions and make prep- 
arations for the test accordingly. 



Determine the character of fuel to be used. For tests of maximum 
efficiency or capacity of the boiler to compare with other boilers, 
the coal should be of some kind which is commercially regarded as 
a standard for the locality where the test is made. 

A coal selected for maximum efficiency and capacity tests should 
be the best of its class, and especially free from slagging and unusual 
clinker-forming impurities. 

For guarantee and other tests with a specified coal containing not 
^ore than a certain amount of ash and moisture, the coal selected 
should not be higher in ash and in moisture than the stated amounts 



902 THE STEAM-BOILER. 

because any increase is liable to reduce the efficiency and capacity 
more than the equivalent proportion of such increase. 

OPERATING CONDITIONS. 

Determine what the operating conditions and method of firing 
should be to conform to the object in view, and see that they prevail 
throughout the trial, as nearly as possible. 

DURATION. 

The duration of tests to determine the efficiency of a hand-fired 
boiler should be at least ten consecutive hours. In case the rate of 
combustion is less than 25 lbs. per sq. ft. of grate per hour the tests 
should be continued for such a time as may be required to burn a total 
of 250 lbs. of coal per square foot of grate. Tests of longer ^duration 
than 10 hours are advisable in order to obtain greater accuracy. 

In the case of a boiler using a mechanical stoker, the duration, 
where practicable, should be at least 24 hours. If the stoker is of 
a type that permits the quantity and condition of the fuel bed at 
beginning and end of the test to be accurately estimated, the dura- 
tion may- be reduced to 10 hours, or such time as may be required 
to burn the total of 250 lbs. per square foot. 

STARTING AND STOPPING. 

The conditions regarding the temperature of the furnace and 
boiler, the quantity and quality of the live coal and ash on the grates, 
the water level, and the steam pressure, should be as nearly as pos- 
sible the same at the end as at the beginning of the test. 

To secure the desired equality of conditions with hand-fired boilers, 
the following method should be employed: 

The furnace being well heated by a prehminary run, burn the fire low, 
and thoroughly clean it. leaving enough hve coal spread evenly 
over the grate (say 2 to 4 ins.),* to serve as a foundation for the 
new fire. Note quickly the thickness of the coal bed as nearly as 
it can be estimated or measured, also the water level, t the steam 
pressure, and the time, and record the latter as the starting time. 
Fresh coal should then be fired from that weighed for the test, the ash-pit 
thoroughly cleaned and the regular work of the test proceeded with. 

Before the end of the test the tire should again be burned low 
and cleaned in such a manner as to leave the same amount of live 
coal on the grate as at the start. When this condition is reached, 
observe quickly the water level, f the steam pressure, and the 
time, and record the latter as the stopping time. If the water 
level is lower than at the beginning, a correction should be made 
by computation, ratlier than by feeding additional water. Finally 
remove the ashes and refuse from the ashpit. 

In a plant containing several boilers where it is not practicable 
to clean them simultaneously, the fires should be cleaned one after 
the other as rapidly as may be, and ea.ch one after cleaning charged 
with enough coal to maintain a thin fire in good working condition. 
After the last fire is cleaned and in working condition, bum all 
the fires low (say 4 to 6 ins.), note quickly the thickness of each, 
also the water levels, steam pressure, and time, which last is taken 
as the starting time. Likewise when the time arrives for closing 
the test, the fires should be quickly cleaned one by one, and when 
this work is completed they should all be burned low the same 
as at the start and the various observations made as noted. 

* 1 to 2 ins. for small anthracite coals. 

t Do not blow down the water-glass column for at least one hour 
before these readings are taken. An erroneous indication may other- 
wise be caused by a change of temperature and density of the water 
within the column and connecting pipe. 



RULES FOR CONDUCTING BOILER TESTS. 903 

In the case of a large boiler having several furnace doors requiring 
the fire to be cleaned in sections one after the other, the above 
directions pertaining to starting and stopping in a plant of several 
boilers may be followed. 
To obtain the desired equality of conditions of the Are when a 

mechanical stoker other than a chain grate is used, the procedure 

should be modified where practicable as follows: 

Regulate the coal feed so as to burn the fire to the low condition 
required for cleaning. Shut off the coal-feeding mechanism and 
fill the hoppers level full. Clean the ash or dump plate, note quicl<:ly 
the depth and condition of the coal on the grate, the water level, 
the steam pressure, and the time, and record the latter as the 
starting time. Then start the coal-feeding mechanism, clean the 
ashpit, and proceed with the regular work of the test. 

When the time arrives for the close of the test, shut off the coal- 
feeding mechanism, fill the hoppers and burn the fire to the same 
low point as at the beginning. When this condition is reached, 
note the water level, the steam pressure, and the time, and record 
the latter as the stopping time. Finally clean the ash plate and 
haul the ashes. 

In the case of chain-grate stokers, the desired operating conditions 
should be maintained for half an hour before starting a test and 
for a like period before its close, the height of the stoker gate or 
throat plate and the speed of the grate being the same during both 
these periods. 

RECORDS. 

Half-hourly readings of the instruments are usually sufQcient. If 
there are sudden and wide fluctuations, the readings in such cases 
should be taken every fifteen minutes, and in some instances oftener. 
The coal should be weighed and delivered to the firemen in portions 
sufficient for one hour's run, thereby ascertaining the degree of 
uniformity of firing. An ample supply of coal should be maintained 
at all times, but the quantity on the fioor at the end of each hour 
should be as small as practicable, so that the same may be readily 
estimated and deducted from the total weight. 

The records should be such as to ascertain also the consumption 
of feed-water each hour, and thereby determine the degree of uni- 
formity of evaporation. 

QUALITY OF STEAM. 

If the boiler does not produce superheated steam the percentage 
of moisture in the steam should be determined by the use of a throttling 
or separating calorimeter. If the boiler has superheating surface, 
the temperature of the steam should be determined by the use of 
a thermometer inserted in a thermometer well. 

SAMPLING AND DRYING COAL. 

During the progress of the test the coal should be regularly sampled 
for the purpose of analysis and determination of moisture. 

ASHES AND REFUSE. 

The ashes and refuse withdrawn from the furnace and ash-pit 
during the progress of the test and at its close should be weighed so 
far as possible in a dry state. If wet, the amount of moisture should 
be ascertained and allowed for, a sample being taken and dried for 
this purpose. This sample may serve also foi: analysis and the deter- 
mination of unburned carbon. 

CALORIFIC TESTS AND ANALYSES OF COAL. 

The quality of the fuel should be determined by calorific tests and 
analyses of the coal sample above referred to. 



904 THE STEAM-BOILER. 

ANALYSES OF FLUE GASES. 

For approximate determinations of the composition of the flue 
gases, the Orsat apparatus, or some modification thereof, should 
be employed. If momentary samples are obtained the analyses 
should be made as frequently as possible, say every 15 to 30 minutes, 
depending on the skill of the operator, noting at the time the sample 
is drawn the furnace and firing conditions. If the sample drawn 
Is a continuous one, the intervals may be made longer. 

SMOKE OBSERVATIONS. 

In tests of bituminous coals requiring a determination of the amount 
of smoke produced, observations should be made regularly through- 
out the trial at intervals of five minutes (or if necessary every minute), 
noting at the same time the furnace and firing conditions. For tests 
of furnaces, methods of firing, or smoke prevention devices, observations 
every 10 or 15 seconds, continued during an hour, are advisable. 

CALCULATION OF RESULTS. 

(a) Corrections for Quality of Steam. — When the percentage of moisture 
is less than 2 per cent it is sufficient merely to deduct the percentage 
from the weight of water fed, in which case the factor of correction 
for quality is 

_ % moistu re 

100 "• 

When the percentage is greater than 2 per cent, or if extreme accu- 
racy is required, the factor of correction is 

1 _ p H-hi 
H-h 

in which P is the proportion of moisture, H the total heat of 1 lb. 
of saturated steam, hi the heat in water at the temperature of satu- 
rated steam, and h the heat in water at the feed temperature. 

When the steam is superheated the factor of correction for quality 
of steam is 

Hs-h 



H-h 
in which Hg is the total heat of 1 lb. of superheated steam of the 
observed temperature and pressure. 
(6) Correction for Live Steam, if any, used for Aiding Combustion. — The 
quantity of steam or power, if any, used for producing blast, inject- 
ing fuel, or aiding combustion should be determined and recorded in 
the table of data and results. 

(c) Equivalent Evaporation. — The equivalent evaporation from and 
at 212° is obtained by multiplying the weight of water evaporated, 
corrected for moisture in steam, by the "factor of evaporation." 
The latter equals 

H-h 
970. 4 

in which H and h are respectively the total heat of satiu-ated steam 
and of the feed-water entering the boiler. 

The "factor of evaporation" and the "factor of correction for 
quality of steam" may be combined into one expression in the 
case of superheated steam as follows : 

Hs-h 

970A" 

(d) Efficiency . — The "efficiency of boiler, furnace and grate" is the 
relation between the heat absorbed per pound of coal fired, and 
the calorific value of 1 lb. of coal. 

The "efficiency based on combustible" is the relation between 



RULES FOR CONDUCTING BOILER TESTS. 905 

the heat absorbed per pound of combustible burned, and the 
calorific value of 1 lb. of combustible. This expression of efficiency 
furnishes a means for comparing the results of different tests, 
when the losses of unburned coal due to grates, cleanings, etc., are 
eliminated. 

The '"combustible burned" is determined by subtracting from 
the Aveight of coal supplied to the boiler, the moisture in the coal, 
the weight of ash and unburned coal withdrawn from the furnace 
and ash-pit, and the weight of dust, soot, and refuse, if any, with- 
drawn from the tubes, flues, and combustion chambers, including ash 
carried away in the gases, if any, determined from the analyses of 
coal and ash. The "combustible" used for determining the cal- 
orific value is the weight of coal less the moisture and ash found by 
analysis. 

The "heat absorbed" per pound of coal or combustible is cal- 
culated by multiplying the equivalent evaporation from and at 
212° per pound of coal or combustible by 970.4. 

CHART. 

In trials having for an object the determination and exposition 
of the complete boiler performance, the entire log of readings and 
data should be plotted on a chart and represented graphically. 

Data and Results of Evaporative Test."!" 

1. Test of boiler located at 

2. Number and kind of boilers 

3. Kind of furnace 

4. Grate surface (width length ) sq. ft. 

5. Water heating surface sq. ft. 

6. Superheating surface sq. ft. 

7. Total heating surface sq. ft. 

e. Distance from center of grate to nearest heating 

surface ft. 

DATE, DURATION, ETC. 

8. Date , 

9. Duration hrs. 

10. Kind and size of coal 

AVERAGE PRESSURES, TEMPER^VTURES, ETC. 

11. Steam pressure by gage lbs. per sq. in. 

12. Temperature of steam, if superheated degs. 

13. Temperature of feed-water entering boiler degs. 

14. Temperature of escaping gases leaving boiler degs. 

15. Force of draft between damper and boiler ins. 

c. Draft in furnace ins. 

d. Draft or blast in ash-pit ins. 

16. State of weather 

a. Temperature of external air degs. 

b. Temperature of air entering ash-pit degs. 

c. Relative humidity of air entering ash-pit degs 

QUALITY OF STEAAI 

17. Percentage of moisture in steam or degrees of super- 

heating % or degs. 

18. Factor of correction for quality of steam % or degs. 

TOTAL QUANTITIES. 

19. Total weight of copl as fired lbs. 

20. Percentage of moisture in coal as fired- per cent . 

21. Total weight of dry coal fired lbs. 

* This table contains the principal items of the tab^e in the Code 
of 1915 of the A.S.M.E. Committee on Power Tests. 



906 THE STEAM-BOILER. 

22. Total ash, clinkers, and refuse (dry) lbs. 

23. Total combustible burned (Item 21 — Item 22) lbs. 

24. Percentage of ash and refuse in dry coal per cent. 

25. Total weight of water fed to boiler lbs. 

26. Total water evaporated, corrected for quality of steam 

(Item 25 X Item 18) lbs. 

27. Factor of evaporation based on temperature of water 

entering boiler 

28. Total equivalent evaporation from and at 212° (Item 

26 X Item 27) lbs. 

HOURLY QUANTITIES AND RATES. 

29. Dry coal per hour lbs. 

30. Dry coal per square foot of grate surface per hour lbs. 

31. Water evaporated per hour, corrected for quahty of 

steam lbs. 

32. Equivalent evaporation per hour from and at 212°. . . . lbs. 

33. Equivalent evaporation per hour from and at 212° per 

square foot of water-heating surface lbs. 

CAPACITY. 

34. Evaporation per hr. from and at 212° (same as Item 32) lbs. 

a. Boiler horse-power developed (Item 34 -f- 341/2) ... Bl. H.P. 

35. Rated capacity per hour, from and at 212° lbs. 

a. Rated boiler horse-power Bl. H.P. 

36. Percentage of rated capacity developed per cent. 

ECONOMY. 

37. Water fed per pound of coal as fired (Item 25 -^ Item 19) lbs. 

38. Water evaporated per pound of dry coal (Item 26 -^ 

Item 21) lbs. 

39. Equivalent evaporation from and at 212° per pound of 

coal as fired (Item 28 -r- Item 19) lbs. 

40. Equivalent evaporation from and at 212° per pound of 

dry coal (Item 28 ^ Item 21) lbs. 

41. Equivalent evaporation from and at 212° per pound of 

combustible (Item 28 -r- Item 23) lbs. 

EFFICIENCY. 

42. Calorific value of 1 lb. of dry coal by calorimeter B.T.U. 

43. Calorific value of 1 lb. of combustible by calorimeter. . B.T.U. 

44. EflQciency of boiler, furnace and grate per cent. 

-if^r^^. Item 40 X 970.4 
^^^ ^ Item 42 * 

45. Efficiency based on combustible per cent. 

Item 41 X 970.4 



100 X 



Item 43 



COST OF EVAPORATION. 

46. Cost of coal per ton of . . . .lbs. delivered in boiler room, dollars. 

47. Cost of coal required for evaporating 1000 lbs. of water 

under observed conditions dollars. 

48. Cost of coal required for evaporating 1000 lbs. of water 

from 'and at 212° dollars. 

SMOKE DATA. 

49. Percentage of smoke as observed per cent. 

FIRING DATA. 

50. Kind of firing, whether spreading, alternate, or coking 

a. Average interval between times of leveling or 

breaking up min. 



KULES FOR CONDUCTING BOILER TESTS. 



907 



ANALYSES AND HEAT BALANCE, 

51. Analysis of dry gases by volume. 

a. Carbon dioxide (CO2) per cent. 

6. Oxygen (O) per cent. 

c. Carbon monoxide (CO) per cent. 

d. Hydrogen and hydrocarbons per cent. 

C. Nitrogen, by difference (N) per cent. 



52. Proximate analysis of coal 



a. Moisture 

b. Volatile Matter 

c. Fixed carbon 

d. Ash 



54. 



55. 



As Fired. 



Dry Coal. 



Combustible. 



100% 100% 100% 

e. Sulphur, separately determined, referred to dry coal, percent. 

53. Ultimate analysis of dry coal. 

a. Carbon (C) per cent. 

6. Hydrogen (H) per cent. 

c. Oxygen (O) per cent. 

d. Nitrogen (N) per cent. 

e. Sulphur (S) per cent. 

/. Ash per cent. 

Analysis of ash and refuse, etc 



Heat balance, based on dry coal and com 
bustible. 

a. Heat absorbed by the boiler (Item 40 

or 41 X 970.4) 

b. Loss due to evaporation of moisture 

In coal 

C. Loss due to heat carried away by 
steam formed by the burning of 
hydrogen 

d. Loss due to heat carried away in the 

dry flue gases 

e. Loss due to carbon monoxide .... 
/. Loss due to combustible in ash and 

refuse. .- 

g. Loss due to heating moisture in air. 

h* Loss due to unconsumed hydrogen 
and hydrocarbons, to radiation, 
and unaccounted for 

i. Total calorific value of 1 lb. of dry 
coal or combustible. (Items 42 
and 43) 



Dry Coal. I 



B.T.U. 



Per cent. 



100 



If it is desired that the heat balance be based on coal "as fired," or 
on combustible burned, the items in the first column are multiplied by 
(100 - Item 20) -^ 100 for coal as fired or by 100 -f- ( 100 - Item 55/, 
per cent) for combustible. 

Principal Data and Results of Boiler Test. 

1. Grate surface (width length ) sq. ft. 

2. Total heating surface sq. ft. 

3. Date 

4. Duration hrs. 

5. Kind and size of coal 



908 THE STEAM-BOILER. 

6. Steam pressure by gage lbs. per sq. in. 

7. Temperature of feed water entering boiler degs. 

8. Percentage of moisture in steam or number of degrees 

of superheating % or deg. 

9. Percentage of moisture in coal per cent. 

10. Dry coal consumed per hour lbs. 

11. Dry coal consumed per square foot of grate surface per 

hour lbs. 

12. Equivalent evaporation per hour from and at 212° .... lbs. 

13. Equivalent evaporation per hour from and at 212° per 

square foot of heating surface lbs. 

14. Rated capacity per hour, from and at 212° lbs. 

15. Percentage of rated capacity developed. . . .' per cent. 

16. Equivalent evaporation from and at 212° per pound 

of dry coal lbs. 

17. Equivalent evaporation from and at 212° per pound 

of combustible lbs. 

18. Calorific value of 1 lb. of dry coal by calorimeter B.T.U. 

19. Calorific value of 1 lb. of combustible by calorimeter. . B.T.U. 

20. Efficiency of boiler, furnace and grate per cent. 

21. Efficiency based on combustible per cent. 

FACTORS OF EVAPORATION. 

The figures in the table on the next four pages are calculated from the 
formula F =(i/ — /i) -r- 970.4, in which H is the total heat above 32° of 
1 lb. of steam of the observed pressure, h the total heat above 32° of the 
feed-water, and 970.4 the heat of vaporization, or latent heat, of steam at 
212° F. The values of these total heats and of the latent heat are those 
given in Marks and Davis's steam tables. 

The factors are given for every 3° of feed -water temperature between 
32^ and 212®, and for every 5 or 10 lbs. steam pressure within the ordinarv 
working Hmits of pressure. Intermediate values correct to the thirS 
decimal place may easily be found by interpolation. 

The factors in the table are for dry saturated steam only. 

STRENGTH OF STEAM-BOILERS. VARIOUS RULES FOR 
CONSTRUCTION. 

There is a great lack of uniformity in the rules prescribed by different 
writers and by legislation governing the construction of steam-boilers. 
In the United States, boilers for merchant vessels must be constructed 
according to the rules and regulations prescribed by the Board of Super- 
vising Inspectors of Steam Vessels; in the U. S. Navy, according to rules 
of the Navy Department, and in some cases according to special acts of 
Congress. On land, in some States, such as Massachusetts and Ohio, 
and in some cities in other States, the construction of boilers is governed 
by local laws; but in many places there are no laws upon the subject, 
and boilers are constructed according to the idea of individual en- 
gineers and boiler-makers. In recent years, however, there has been a 
great improvement in this matter. The wide publication of the 
]\1 assachusetts boiler rules, the activity of the American Boiler Manu- 
facturers' Association, of the American Society for Testing IVIaterials, 
and the work of a committee of the American Society of Mecha^nical 
Engineers, which completed its "Boiler Code" in 1915 (issued in pam- 
phlet form by the Society), have all tended to bring about a great 
degree of uniformity in the materials and the methods of boiler con- 
struction. The matter on the following pages consists chiefly of ex- 
tracts from the Massachusetts rules and the A. S. M. E. Boiler Code, 
and is condensed from a fuller treatment of the subject in the second 
edition of the author's " Steam Boiler Economy." 

Materials Used in Boilers. — For the shells, tubes, rivets and braces 
the material now in almost universal use is a special kind of soft open- 
hearth steel, low in sulphur and phosphorus and of a tensile strength 
not exceeding 65,000 lb. per sq. in. for shell plates and not exceeding 
55,000 lb. per sq. in. for rivets. 

Cast iron is used for fire-doors, grate-bars, manhole and handhole 

(Continued on p, 913.) 



FACTORS OP EVAPORATION. 



909 





Lbs 




















Gauge press. . OJ 


10.3 


20.3 


30.3 


40.3 


50.3 


60.3 


70.3 


80.3 


85.3 


Abs. press. . . .15. 


25. 


35. 


45. 


55. 


65. 


75. 


85. 


95. 


100. 


Feed 
water. 


Factors of Evaporation. 


212° F. 


1.0003 


1.0103 


1.0169 


1.0218 


1.0258 


1.0290 


1.0316 


1.0340 


1.0361 


1.0370 


209 


34 


34 


1.0200 


50 


89 


1.0321 


47 


71 


92 


1.0401 


206 


65 


65 


31 


81 


1 .0320 


52 


79 


1.0402 


1.0423 


32 


203 


96 


96 


62 


1.0312 


51 


83 


1.0410 


33 


54 


63 


200 


1.0127 


1.0227 


93 


43 


82 


1.0414 


41 


64 


85 


94 


197 


58 


58 


1.0324 


74 


1.0413 


45 


72 


95 


1.0516 


1.0525 


194 


89 


89 


55 


1.0405 


44 


76 


1.0503 


1.0526 


47 


56 


191 


1.0220 


1.0320 


86 


36 


75 


1 .0507 


34 


57 


78 


87 


188 


51 


51 


1.0417 


67 


1.0506 


38 


65 


88 


1.0609 


1.0618 


185 


82 


82 


48 


98 


37 


69 


96 


1.0619 


40 


49 


182 


1.0313 


1.0413 


79 


1.0529 


68 


1 .0600 


1.0627 


50 


71 


80 


179 


44 


44 


1.0510 


60 


99 


31 


58 


81 


1.0702 


1.0711 


176 


75 


75 


41 


91 


1.0630 


62 


89 


1.0712 


33 


42 


173 


1.0406 


1.0506 


72 


1.0622 


61 


93 


1.0720 


43 


64 


73 


170 


37 


^1 


1.0603 


53 


92 


1.0724 


51 


74 


95 


1 .0804 


167 


68 


68 


34 


84 


1.0723 


55 


82 


1.0805 


1.0826 


35 


164 


99 


99 


65 


1.0715 


54 


86 


1.0812 


36 


57 


66 


161 


1.0530 


1.0630 


96 


45 


85 


1.0817 


43 


67 


88 


97 


158 


61 


61 


1.0727 


76 


1.0816 


47 


74 


98 


1.0919 


1.0928 


155 


92 


92 


58 


1.0807 


46 


78 


1.0905 


1 .0929 


50 


59 


152 


1.0623 


1.0723 


89 


38 


77 


1.0909 


36 


60 


80 


90 


149 


54 


54 


1.0820 


69 


1.0908 


40 


67 


91 


1.1011 


1.1021 


146 


85 


85 


51 


1.0900 


39 


71 


98 


1.1022 


42 


52 


143 


1.0715 


1.0815 


81 


31 


70 


1.1002 


1.1029 


52 


73 


82 


140 


46 


46 


1.0912 


62 


1.1001 


33 


60 


83 


1.1104 


1.1113 


137 


77 


77 


43 


93 


32 


64 


91 


1.1114 


35 


44 


134 


1 .0808 


1.0908 


74 


1.1023 


63 


95 


1.1121 


45 


66 


75 


131 


39 


39 


1.1005 


54 


93 


1.1125 


52 


76 


97 


1.1206 


128 


70 


70 


36 


85 


1.1124 


56 


83 


1.1207 


1.1227 


37 


125 


1.0901 


I.IOOI 


67 


1.1116 


55 


87 


1.1214 


38 


58 


68 


122 


31 


31 


97 


47 


86 


1.1218 


45 


69 


89 


98 


119 


62 


62 


1.1128 


78 


1.1217 


49 


76 


99 


1.1320 


1.1329 


116 


93 


93 


59 


1.1209 


48 


80 


1.1306 


1.1330 


51 


60 


113 


1.1024 


1.1124 


90 


39 


79 


1.1310 


37 


61 


82 


91 


no 


55 


55 


1.1221 


70 


1.1309 


41 


68 


92 


1.1412 


1.1422 


107 


86 


86 


52 


1.1301 


40 


72 


99 


1.1423 


43 


53 


104 


1.1116 


1.1216 


82 


32 


71 


1.1403 


1.1430 


53 


74 


83 


101 


47 


47 


1.1313 


63 


1.1402 


34 


61 


84 


1.1505 


1.1514 


98 


78 


78 


44 


93 


33 


65 


91 


1.1515 


36 


45 


95 


1.1209 


1.1309 


75 


1.1424 


63 


95 


1.1522 


46 


66 


76 


92 


40 


40 


1.1406 


55 


94 


1.1526 


53 


77 


97 


1.1607 


89 


71 


71 


37 


86 


1.1525 


57 


84 


1.1608 


1.1628 


37 


86 


1.1301 


1.1401 


67 


1.1518 


56 


88 


1.1615 


38 


59 


68 


83 


32 


32 


98 


48 


87 


1.1619 


46 


69 


90 


99 


80 


63 


63 


1.1529 


78 


1.1618 


50 


76 


1.1700 


1.1721 


1.1730 


77 


94 


94 


60 


1.1609 


48 


80 


1.1707 


31 


51 


61 


74 


1.1425 


1.1525 


91 


40 


79 


1.1711 


38 


62 


82 


92 


71 


55 


55 


1.1621 


71 


1.1710 


42 


69 


92 


1.1813 


1.1822 


68 


86 


86 


52 


1.1702 


41 


73 


1.1800 


1.1823 


44 


53 


65 


1.1517 


1.1617 


83 


33 


72 


1.1804 


30 


54 


75 


84 


62 


48 


48 


1.1714 


63 


1.1803 


35 


61 


85 


1.1906 


1.1915 


59 


79 


79 


45 


94 


33 


65 


92 


1.1916 


37 


46 


56 


1.1610 


1.1710 


76 


1.1825 


64 


96 


1 . 1923 


47 


67 


77 


53 


41 


41 


1.1807 


56 


95 


1.1927 


54 


78 


98 


1.2008 


50 


72 


72 


38 


87 


1.1926 


58 


85 


1.2009 


1.2029 


39 


47 


1.1703 


1.1803 


69 


1.1918 


57 


89 


1.2016 


40 


60 


70 


44 


34 


34 


1.1900 


49 


88 


1.2020 


47 


71 


91 


1.2101 


41 


65 


65 


31 


80 


1.2019 


51 


78 


1.2102 


1.2122 


32 


38 


96 


96 


62 


1.2011 


50 


82 


1.2109 


33 


53 


63 


35 


1.1827 


1.1927 


93 


42 


81 


1.2113 


40 


64 


84 


94 


32 


58 


58 


1.2024 


73 


1.2113 


44 


71 


95 


1.2216 


1.2225 



THE STEAM-BOILER. 





Lbs. 






















Gauge press. 90.3 


95.3 


100.3 


105.3 


110.3 


115.3 


120.3 


125.3 


130.3 


135 3 


140 3 


Abs. press 


..105. 


110. 


115. 


120. 


125. 


130. 


135. 


140. 


145. 


150. 


155. 


Feed 
water. 


Factors of Evaporation. 


212^ F. 


1.0379 


1.0387 


1.0396 


1.0404 


1.0411 


1.0418 


1.0425 


1.0431 


1.0437 


1.0443 


1.0449 


209 


1.0410 


1.0419 


1 .0427 


35 


42 


49 


56 


62 


68 


74 


80 


206 


41 


50 


58 


66 


73 


81 


87 


93 


99 


1.0505 


1.0511 


203 


72 


81 


89 


97 


1.0504 


1.0512 


1.0518 


1.0524 


1.0530 


36 


43 


200 


1.0504 


1.0512 


1.0520 


1.0528 


35 


43 


49 


55 


61 


67 


74 


197 


35 


43 


51 


59 


66 


74 


80 


86 


92 


98 


1.0605 


194 


66 


74 


82 


90 


97 


1.0605 


1.0611 


1.0517 


1.0623 


1.0629 


36 


191 


97 


1.0605 


1.0613 


1.0621 


1.0629 


36 


42 


48 


54 


60 


67 


188 


1.0628 


36 


44 


52 


60 


67 


73 


79 


85 


91 


98 


185 


59 


67 


75 


83 


91 


98 


1.0704 


1.0710 


1.0716 


1.0722 


1.0729 


182 


90 


98 


1 .0706 


1.0714 


1.0721 


1.0729 


35 


41 


47 


53 


60 


179 


1.0721 


1.0729 


37 


45 


52 


60 


66 


72 


78 


84 


91 


176 


52 


60 


68 


76 


83 


91 


97 


1.0803 


1.0809 


1.0815 


1.0822 


173 


82 


91 


99 


1 .0807 


1.0814 


1.0822 


1.0828 


34 


40 


46 


53 


170 


1.0813 


1 .0822 


1.0830 


38 


45 


53 


59 


65 


71 


77 


83 


167 


44 


53 


61 


69 


76 


84 


90 


96 


1 .0902 


1.0908 


1.0914 


164 


75 


84 


92 


1 .0900 


1.0907 


1.0914 


1.0921 


1.0927 


33 


39 


45 


161 


1.0906 


1.0914 


1.0923 


31 


38 


45 


52 


58 


64 


70 


76 


158 


37 


45 


54 


62 


69 


76 


82 


89 


95 


1.1001 


1.1007 


155 


68 


76 


85 


93 


1.1000 


1.1007 


1.1013 


1.1020 


1.1025 


32 


38 


152 


99 


1.1007 


1.1015 


1.1024 


31 


38 


44 


51 


57 


63 


69 


149 


1.1030 


38 


46 


55 


62 


69 


75 


81 


88 


94 


1.1100 


146 


61 


69 


77 


86 


93 


1.1100 


1.1106 


1.1112 


1.1119 


1.1125 


31 


143 


92 


I. 1100 


1.1108 


1.1116 


1.1124 


31 


37 


43 


49 


56 


62 


140 


1.1123 


31 


39 


47 


54 


62 


68 


74 


80 


86 


93 


137 


53 


62 


70 


78 


85 


93 


99 


1.1205 


1.1211 


1.1217 


1.1224 


134 


84 


93 


1.1201 


1.1209 


1.1216 


1.1223 


1.1230 


36 


42 


48 


54 


131 


1.1215 


1.1223 


32 


40 


47 


54 


60 


67 


73 


79 


85 


128 


46 


54 


62 


71 


78 


85 


91 


98 


1 . 1304 


1.1310 


1.1316 


125 


77 


85 


93 


1.1302 


1.1309 


1.1316 


1.1322 


1.1328 


35 


41 


47 


122 


1.1308 


1.1316 


1.1324 


32 


. 40 


47 


53 


59 


65 


71 


78 


119 


39 


47 


55 


63 


70 


78 


84 


90 


96 


1.1402 


1.1409 


116 


69 


78 


86 


94 


1.1401 


1.1408 


1.1415 


1.1421 


1.1427 


33 


39 


113 


1.1400 


1.1408 


1.1417 


1.1425 


32 


39 


45 


52 


58 


64 


70 


110 


31 


39 


47 


56 


63 


70 


76 


82 


89 


95 


1.1501 


107 


62 


70 


78 


87 


94 


1.1501 


1.1507 


1.1513 


1.1519 


1.1526 


32 


104 


92 


1.1501 


1.1509 


1.1517 


1.1525 


32 


38 


44 


50 


56 


63 


101 


1.1523 


32 


40 


48 


55 


63 


69 


75 


81 


87 


93 


98 


54 


62 


71 


79 


86 


93 


1.1600 


1.1606 


1.1612 


1.1618 


1.1624 


95 


85 


93 


1.1602 


1.1610 


1.1617 


1.1624 


30 


37 


43 


49 


Jj 


92 


1.1616 


1.1624 


32 


41 


48 


55 


61 


67 


74 


80 


86 


89 


47 


55 


63 


71 


79 


86 


92 


98 


1.1704 


1.1711 


1.1717 


86 


78 


86 


94 


1.1702 


1.1710 


1.1717 


1.1723 


1.1729 


35 


41 


48 


83 


1.1708 


1.1717 


1.1725 


33 


40 


48 


54 


60 


66 


72 


78 


SO 


39 


47 


56 


64 


71 


78 


85 


91 


97 


1.1803 


1.1809 


77 


70 


78 


86 


95 


1.1802 


1.1809 


1.1815 


1.1822 


1.1823 


34 


40 


74 


1.1801 


1.1809 


1.1817 


1.1826 


33 


40 


45 


52 


59 


t5 


71 


71 


32 


40 


48 


56 


64 


71 


77 


83 


89 


96 


1.1902 


68 


62 


71 


79 


87 


94 


1.1902 


1.1908 


1.1914 


1.1920 


1.1925 


33 


65 


93 


1.1902 


1.1910 


1.1918 


1.1925 


33 


39 


45 


51 


57 


63 


62 


1.1924 


32 


41 


49 


56 


63 


70 


76 


82 


88 


94 


59 


55 


63 


72 


80 


87 


94 


1.2000 


1.2007 


1.2013 


1.2019 


1.2025 


56 


86 


94 


1.2002 


1.2011 


1.2018 


1.2025 


31 


38 


44 


50 


56 


53 


1.2017 


1.2025 


33 


42 


49 


56 


62 


68 


75 


81 


87 


50 


48 


56 


64 


73 


80 


87 


93 


99 


1.2106 


1.2112 


1.2118 


47 


79 


87 


95 


1.2104 


1.2111 


1.2118 


1.2124 


1.2130 


37 


43 


49 


44 


1.2110 


1.2118 


1.2126 


35 


42 


49 


55 


61 


68 


74 


80 


41 


41 


49 


57 


66 


73 


80 


86 


92 


99 


1.2205 


1.2211 


38 


72 


80 


88 


97 


1.2204 


1.2211 


1.2217 


1 . 2223 


1.2230 


36 


42 


35 


1.2203 


1.2211 


1.2219 


1.2228 


35 


42 


48 


55 


61 


67 


73 


32 


34 


42 


51 


59 


66 


73 


79 


86 


92 


98 


1.2304 



FACTORS OF EVAPORATION. 



911 





Lbs. 






















Gauge press. 1 45. 3 


150.3 


155.3 


160.3 


165.3 


170.3 


175.3 


180.3 


185.3 


190.3 


195.3 


Abs. pres 


3 .160. 


165. 


170. 


175. 


180. 


185. 


190. 


195. 


200. 


205. 


210 


Feed 
water. 


Factors of Evaporation. 


212° F. 


1.0454 


1.0460 


1.0464 


1 .0469 


1.0474 


1.0478 


1.0483 


1.048711.0492 


1 . 0496 


1 .0499 


209 


86 


91 


95 


1 .0500 


I .0505 


1 .0509 


1.0514 


1.0519 


1.0523 


1.0527 


1.0530 


206 


1.0517 


1 .0522 


1 .0526 


31 


36 


40 


45 


50 


54 


58 


61 


203 


48 


53 


57 


62 


67 


71 


77 


81 


85 


89 


92 


200 


79 


84 


88 


93 


98 


1 .0602 


1.0608 


1.0612 


1.0616 


1.0620 


1.0623 


197 


1.0610 


1.0615 


1.0619 


1.0624 


1.0629 


33 


39 


43 


47 


51 


54 


194 


41 


46 


50 


55 


60 


64 


70 


74 


78 


82 


85 


191 


72 


77 


81 


86 


91 


95 


1.0701 


1.0705 


1.0709 


1.0713 


1.0716 


188 


1.0703 


1.0708 


1.0712 


1.0717 


1.0722 


1.0727 


32 


36 


40 


44 


47 


185 


34 


39 


43 


48 


53 


58 


63 


67 


71 


75 


78 


182 


65 


70 


74 


79 


84 


88 


94 


98 


1.0802 


1.0806 


1.0809 


179 


96 


1.0801 


1.0805 


1.0810 


1.0815 


1.0819 


1.0825 


1.0829 


33 


37 


40 


176 


1 .0827 


32 


36 


41 


46 


50 


56 


60 


64 


68 


71 


173 


58 


63 


67 


72 


77 


81 


87 


91 


95 


99 


1.0902 


170 


89 


94 


98 


1 .0903 


1.0908 


1.0912 


1.0917 


1 0922 


1.0926 


1.0930 


33 


167 


1 .0920 


1 .0925 


1 .0929 


34 


39 


43 


48 


53 


57 


61 


64 


164 


51 


56 


60 


65 


70 


74 


79 


84 


88 


92 


95 


161 


81 


87 


91 


96 


1.1001 


1.1005 


1.1010 


1 1014 


1.1019 


1.1023 


1.1026 


158 


1.1012 


1.1018 


1.1022 


1.1027 


32 


36 


41 


45 


49 


54 


57 


155 


43 


48 


53 


58 


63 


67 


72 


76 


80 


85 


88 


152 


74 


79 


83 


89 


94 


98 


1.1103 


1.1107 


1.1111 


1.1115 


1.1119 


149 


1.1105 


1.1110 


1.1114 


1.1120 


1.1125 


1.1129 


34 


38 


42 


46 


49 


146 


36 


41 


45 


50 


56 


60 


65 


69 


73 


77 


80 


143 


67 


72 


76 


81 


86 


91 


96 


1.1200 


1.1204 


1.1208 


1.1211 


140 


98 


1.1203 


1.1207 


1.1212 


1.1217 


1.1221 


1.1227 


31 


35 


39 


42 


137 


1.1229 


34 


38 


43 


48 


52 


58 


62 


66 


70 


73 


134 


59 


65 


69 


74 


79 


83 


88 


92 


97 


1.1301 


1.1304 


131 


90 


95 


1.1300 


1.1305 


1.1310 


1.1314 


1.1319 


1.1323 


1.1327 


32 


35 


128 


1.1321 


1.1326 


30 


36 


41 


45 


50 


54 


58 


62 


66 


125 


52 


57 


61 


66 


72 


76 


81 


85 


89 


93 


96 


122 


83 


88 


92 


97 


1.1402 


1.1407 


1.1412 


1.1416 


1.1420 


1.1424 


1.1427 


119 


1.1414 


1.1419 


1.1423 


1.1428 


33 


37 


43 


47 


51 


55 


58 


116 


45 


50 


54 


59 


64 


68 


73 


78 


82 


86 


89 


113 


75 


81 


85 


90 


95 


99 


1.1504 


1.1508 


1.1512 


1.1515 


1.1520 


110 


1.1506 


1.1511 


1.1515 


1.1521 


1.1526 


1.1530 


35 


39 


43 


47 


50 


107 


37 


42 


46 


51 


57 


61 


66 


70 


74 


78 


81 


104 


68 


73 


77 


82 


87 


92 


97 


1.1601 


1.1605 


1.1609 


1.1612 


101 


99 


1.1604 


1.1608 


1.1613 


1.1618 


1.1622 


1.1627 


32 


36 


40 


43 


98 


1.1629 


35 


39 


44 


49 


53 


58 


62 


67 


71 


74 


95 


60 


65 


70 


75 


80 


84 


89 


93 


97 


1.1701 


1.1705 


92 


91 


96 


1.1700 


1.1705 


1.1711 


1.1715 


1.1720 


1.1724 


1.1728 


32 


35 


89 


1.1722 


1.1727 


31 


36 


42 


46 


51 


55 


59 


63 


66 


86 


53 


58 


62 


67 


72 


76 


82 


86 


90 


94 


97 


83 


84 


89 


93 


98 


1.1803 


1.1807 


1.1812 


1.1817 


1.1821 


1.1825 


1.1828 


80 


1.1814 


1.1820 


1.1824 


1.1829 


34 


38 


43 


47 


52 


56 


59 


77 


45 


50 


54 


60 


65 


69 


74 


78 


82 


86 


90 


74 


76 


81 


85 


90 


96 


1.1900 


1.1905 


1.1909 


1.1913 


1.1917 


1.1920 


71 


1.1907 


1.1912 


1.1916 


1.1921 


1.1926 


31 


36 


40 


44 


48 


51 


68 


38 


43 


47 


52 


57 


61 


67 


71 


75 


79 


82 


65 


69 


74 


78 


83 


88 


92 


97 


1.2002 


1.2006 


1.2010 


1.2013 


62 


99 


1.2005 


1.2009 


1.2014 


1.2019 


1.2023 


1.2028 


32 


36 


41 


44 


59 


1.2030 


35 


40 


45 


50 


54 


59 


63 


67 


72 


75 


56 


61 


66 


70 


76 


81 


85 


90 


94 


98 


1.2102 


1.2106 


53 


92 


97 


1.2101 


1.2107 


1.2112 


1.2116 


1.2121 


1.2125 


1.2129 


33 


36 


50 


1.2123 


1.2128 


32 


37 


43 


47 


52 


56 


60 


64 


67 


47 


54 


59 


63 


68 


74 


78 


83 


87 


91 


95 


98 


44 


85 


90 


94 


1.2200 


1.2205 


1.2209 


1.2214 


1.2218 


1.2222 


1.2226 


1.2229 


41 


1.2216 


1.2221 


1.2225 


31 


36 


40 


45 


49 


53 


57 


60 


38 


47 


52 


56 


62 


67 


71 


76 


80 


84 


88 


91 


35 


78 


83 


88 


93 


98 


1.2302 


1.2307 


1.2311 


1.2315 


1 . 2320 


1.2323 


32 


1.2309 


1.2315 


1.2319 


1.2324 


1.2329 


33 


38 


42 


46 


51 


54 



THE STEAM-BOILER. 





Lbs. 




1 


1 


1 


1 


1 










Gauge press. 200.3 


205.31 210.31 215.31 220. 3| 225. 3| 230. J 


235.3 


240.3 


245.3 


250.3 


Abs. press. . .215. 


220. 


1 225. 


1 230. 


1 235. 


1 240. 


1 245. 


250. 


255. 


260. 


265. 


Feed 
water. 


Factors of Evaporation. 


212° F. 


1.0503 


1.0507 


1.051C 


1.0513 


1.0517 


1.0520 


1.0523 


1.0527 


1.0529 


1.0533 


1 .0535 


209 


34 


38 


41 


4A 


48 


52 


55 


58 


60 


64 


66 


206 


65 


69 


72 


75 


79 


83 


86 


89 


91 


95 


97 


203 


96 


1.0600 


1.0603 


1.0606 


1.0611 


1.0614 


1.0617 


1 .0620 


1.0622 


1.0626 


1.0629 


200 


1.0627 


31 


34 


37 


42 


45 


48 


51 


53 


57 


60 


197 


58 


62 


65 


6fi 


73 


76 


79 


82 


84 


88 


91 


194 


89 


93 


96 


1 .0700 


1 .0704 


1 .0707 


1.0710 


1.0713 


1.0715 


1.0719 


1 .0722 


191 


1.0720 


1 .0724 


1 .0727 


31 


35 


38 


41 


44 


46 


50 


53 


188 


51 


55 


58 


62 


66 


69 


72 


75 


78 


81 


84 


185 


82 


86 


89 


93 


97 


1.0800 


1.0803 


1.0806 


1.0809 


1.0812 


1.0815 


182 


1.0813 


1.0817 


1.0820 


1 .0823 


1 .0828 


31 


34 


37 


39 


43 


46 


179 


44 


48 


51 


54 


59 


62 


65 


68 


70 


74 


77 


176 


75 


79 


82 


86 


90 


93 


96 


99 


1.0901 


1.0905 


1.0908 


173 


1.0906 


1.0910 


1.0913 


1.0916 


1 .0921 


1 .0924 


1.0927 


1.0930 


32 


36 


39 


170 


37 


41 


44 


47 


51 


55 


58 


61 


63 


67 


69 


167 


68 


72 


75 


78 


82 


86 


89 


92 


94 


98 


I. 1001 


164 


99 


1.1003 


1.1006 


1.1009 


1.1013 


1.1016 


1.1019 


1.1023 


1.1025 


1.1029 


31 


161 


1.1030 


34 


37 


40 


44 


47 


50 


54 


56 


60 


62 


158 


61 


65 


68 


71 


75 


78 


81 


85 


87 


91 


93 


155 


92 


96 


99 


1.1102 


1.1106 


1.1109 


1.1112 


1.1115 


1.1118 


1.1122 


1.1124 


152 


1.1123 


1.1127 


1.1130 


33 


37 


40 


43 


46 


49 


53 


55 


149 


54 


58 


61 


64 


68 


71 


74 


77 


80 


83 


86 


146 


84 


89 


92 


95 


99 


1.1202 


1.1205 


1.1208 


1.1211 


1.1214 


1.1217 


143 


1.1215 


1.1219 


1.1223 


1.1226 


1.1230 


33 


36 


39 


42 


45 


48 


140 


46 


50 


53 


56 


61 


64 


67 


70 


72 


76 


79 


137 


77 


81 


84 


87 


92 


95 


98 


1.1301 


1.1303 


1.1307 


1.1310 


134 


1.1308 


1.1312 


1.1315 


1.1318 


1.1322 


1.1326 


1.1329 


32 


34 


38 


40 


131 


39 


43 


46 


49 


53 


56 


59 


62 


65 


69 


71 


128 


70 


74 


77 


80 


84 


87 


90 


93 


96 


1.1400 


1.1402 


125 


1.1400 


1.1405 


1.1408 


1.1411 


1.1415 


1.1418 


1.1421 


1.1424 


1.1427 


30 


33 


122 


31 


35 


39 


42 


. 46 


49 


52 


55 


58 


61 


64 


119 


62 


66 


69 


72 


77 


80 


83 


86 


88 


92 


95 


116 


93 


97 


1.1500 


1.1503 


1.1507 


1.1511 


1.1514 


1.1517 


1.1519 


1.1523 


1.1525 


113 


1.1524 


1.1528 


31 


34 


38 


41 


44 


48 


50 


54 


56 


110 


55 


59 


62 


65 


69 


72 


75 


78 


81 


85 


87 


107 


85 


90 


93 


96 


1.1600 


1.1603 


1.1606 


1.1609 


1.1612 


1.1615 


1.1618 


104 


1.1616 


1.1620 


1.1624 


1.1627 


31 


34 


37 


40 


43 


46 


49 


101 


47 


51 


54 


57 


61 


65 


68 


71 


73 


77 


80 


98 


78 


82 


85 


88 


92 


95 


98 


1.1702 


1.1704 


1.1708 


1.1710 


95 


1.1709 


1.1713 


1.1716 


1.1719 


1.1723 


1.1726 


1.1729 


32 


35 


39 


41 


92 


39 


44 


47 


50 


54 


57 


60 


63 


66 


69 


72 


89 


70 


75 


78 


81 


85 


88 


91 


94 


97 


1.1800 


1.1803 


86 


1.1801 


1.1805 


1.1808 


1.1812 


1.1816 


1.1819 


1.1822 


1.1825 


1.1827 


31 


34 


83 


32 


36 


39 


42 


46 


50 


53 


56 


58 


62 


64 


80 


63 


67 


70 


73 


77 


80 


83 


87 


89 


93 


95 


77 


94 


98 


1.1901 


1.1904 


1.1908 


1.1911 


1.1914 


1.1917 


1.1920 


1.1924 


1.1926 


74 


1.1924 


1.1929 


32 


35 


39 


42 


45 


48 


51 


54 


57 


71 


55 


59 


63 


66 


70 


73 


76 


79 


82 


85 


88 


68 


86 


90 


93 


96 


1.2001 


1.2004 


1.2007 


1.2010 


1.2012 


1.2016 


1.2019 


65 


1.2017 


1.2021 


1.2024 


1.2027 


31 


35 


38 


41 


43 


47 


49 


62 


48 


52 


55 


58 


62 


65 


68 


72 


74 


78 


80 


59 


79 


83 


86 


89 


93 


96 


99 


1.2102 


1.2105 


1.2109 


1.2111 


56 


1.2110 


1.2114 


1.2117 


1.2120 


1.2124 


1.2127 


1.2130 


33 


36 


40 


42 


53 


41 


45 


48 


51 


55 


58 


61 


64 


67 


70 


73 


50 


71 


76 


79 


82 


86 


89 


92 


95 


98 


1.2201 


1.2204 


47 


1.2202 


1.2207 


1.2210 


1.2213 


1.2217 


1.2220 


1.2223 


1.2226 


1.2229 


32 


35 


44 


34 


38 


41 


44 


48 


51 


54 


57 


60 


63 


66 


41 


65 


69 


72 


75 


79 


82 


85 


88 


91 


94 


97 


38 


96 


1.2300 


1.2303 


1.2306 


1.2310 


1.2313 


1.2316 


1.2319 


1.2322 


1.2325 


1.2328 


35 


1.2327 


31 


34 


37 


41 


44 


47 


50 


53 


57 


59 


32 


58 


62 


65 


68 


72 


75 


78 


82 


84 


88 


90 



STRENGTH^ OF STEAM-BOILERS. 913 

plates, headers of water-tube boilers (for pressures under 160 lb.), mud 
drums (not exceeding 18 in. diameter), and nozzles for pipe attach- 
ments, but there is a tendency to substitute rolled or forged steel for all 
these purposes excej^t grate-bars. 

Quality of Steel. (A. S. M. E. Boiler Code, 1915.) 

Flange. Firebox. 

( Plates 3/4 in. thick 

Carbon \ ^,^^^ "«^^^- ?/ 12— 0.25% 

j Plates over 3/4 m. 

( thick 0.12 — 0.30 

Manganese 0.30 — 0.60% 0.30 — 0.50 

Phn«r»Vinrn«i Acid . . . . Not over 0.05 Not over 0.04 

i-nospnorus ^ g^^j^ -^^^ ^^^^ q ^^ -j^^^ ^^^j. 0.035 

Sulphur Not over 0. 05 Not over . 04 

Copper Not over . 05 

Tensile strength, lb. per sq. in. . . . 55,000 — 65,000 55,000 — 63,000 

Yield point, min., lb. per sq. in. . . 0.5 tens. str. 0.5 tens. str. 

T., ^. . o • . ^ 1,500,000 1,500,000 
Elongation m 8-m., mm., per cent ^ens. str. Tens. str. 

For material over 3/4 in. in thickness a deduction of 0.5 from the 
percentage of elongation shall be made for each increase of l/s in. in 
thickness above 3/4 in., to a minimum of 20%. 

Cold bending and quench bending tests are also required, and for fire- 
box steel a homogeneity test (see page 507). 

Rivet steel: Tensile strength, 45,000-55,000, Elongation in 8 in. 
1,500,000 ^tensile strength, but need not exceed 30%. Stay bolt steel, 
T. S., 50,000-60,000. 

Quench-bend Tests. — The test specimen, when heated to a light 
cherry red as seen in the dark (not less than 1200° F.), and quenched 
at once in water the temperature of which is between 80° and 90°, shall 
bend through 180° without cracking on the outside of the bent portion, 
as follows: For material 1 in. or under in thickness, flat on itself; for 
material over 1 in. in thickness, around a pin of a diameter equal to 
the thickness. 

Boiler tubes are now generally made of soft steel, but charcoal iron 
tubes are still preferred by some users. 

Shells; Water and Steam Drums. — The , cylindrical structure, in- 
cluding the ends, of a fire- tube boiler, is usually called the shell. The 
cylinder superposed on the tubes of a water-tube boiler is called a 
water and steam drum. Shells of marine boilers of the Scotch type 
have been built of diameters as large as 16 ft. Water and steam drums 
of water-tube boilers are rarely made of greater diameter than 42 in. 

The thickness of shell for a given pressure is found from the common 
formula for safe strength of thin cyhnders, 

P = 2tTf -.eZF; whence ^ = PclF-r-2Tf. 
P = safe working pressure; T = tensile strength of plate, both in lb. 
per sq. in., t = thickness of plate in inches: / = ratio of the strength of a 
riveted joint to that of the soUd plate; F = factor of safety allowed; and 
d = diameter of shell or drum in inches. 

The value taken for T is commonly that stamped on the plates by the 
manufacturer, / is taken from tables of strength of riveted joints or is 
computed, and F must be taken at a figure not less than is prescribed 
by local or State laws, or, in the case of marine boilers, by the rules 
of the U. S. Board of Supervising Inspectors, and may be more than uhis 
figure if a greater margin of safety is desired. 

Strength of Circumferential Seam. — Safe working pressure P = 
4tT f -^dF; t = PdF~4:Tf, notation as above. The strength of a 
shell against rupture on a circumferential line is twice that against 
rupture on a longitudinal line, therefore single riveting is sufficient 
on the circumferential seams while double, triple or quadruple rivet- 
ing is used for the longitudinal seams. 

Thickness of Plates; Riveting. (Mass. Boiler Rules, 1910). — The 
longitudinal joints of a boiler, the shell or drum of which exceeds 36 in. 
diameter, shall be of butt and double strap construction; if it does not 



914 THE STEAM-BOILER. 

exceed 36 in. lap-riveted construction may be used, the maximum 
pressure on such shells being 100 lb. per sq. in. 

Aliniirum thickness of plates in flat-stayed surfaces, S/ig in. 

The ends of stay bolts shall be riveted over or upset. 

Rivets shall be of sufficient length to completely fill the rivet holes 
and form a head equal in strength to the body of the rivet. 

Rivets shall be macliine driven wherever possible, with sufficient 
pressure to fill the rivet holes, and shall be allowed to cool and shrink 
under pressure. 

Rivet holes shall be drilled full size with plates, butt straps and 
heads bolted in position; or they may be punched not to exceed 1/4 in. 
less than full size for plates over s/ie in. thick, and i/s in. or less for 
plates not exceeding 5/iq in. thick, and then drilled or reamed to full 
size with plates, butt straps and heads bolted up in position. 

The longitudinal joints of horizontal return-tubular boilers shall be 
located above the fire-line of the setting. 

The thickness of plates in a shell or drmn shall be of the same gage. 
Minimum thickness of shell plates (Mass. Rules and A. S. M. E. Code) : 
Diam. 36 in. or under, 1/4 in.; over 36 to 54 in., 5/i6 in.; over 54 to 72 
in., 3/8 in.; over 72 in., 1/2 in. 

Minimiun thickness of butt straps: 



Plates, in . I/4 to II/32 



Straps, in . 



l/4_ 



V16 I 3/8 



3/8 to 13/32 7/16 to 15/32 I/2 to 9/i6 U/g tO 3/4 7/81 1 to U/g HA 



7/16 I 1/2 IVsl 3/4 I 7/8 



Minimum thickness of tube sheets: 



Diam. of tube 

sheet, in. . . . 
Thickness, in . . 



42 or under 

3/8 



Over 42 to 54 

7/16 



Over 54 to 72 

1/2 



Over 72 

9/16 



Convex or Bumped Heads. — Minimum thickness of convex heads, 
t = i/4d F P -i- T\ d = diameter in inches; F = 5 = factor of safety; P = 
working pressure, lb. per sq. in. ; T = tensile strength stamped on the 
head. 

When a convex head has a manhole opening the thicioiess is to be 
increased not less than i/g in. 

When the head is of material of the same quahty and tliickness as 
that of the shell, the head is of -equal strength with the shell when the 
radius of curvature of the head equals the diameter of the shell, or when 
the rise of the curve = 0.134 diam. of shell. 

[The A. S. M. E. Boiler Code specifies a higher factor of .safety, 5.5, 
and adds i/s in. to the thickness, making the formula t = 2.7 d PR/T 
+ 1/8 in., R being the radius to which the head is dished, in inches. 
When R is less than 0.8 d the thickness shall be at least that found by 
the formula when R = 0.8 d. Dished heads with the pressure on the 
convex side are allowed a maximum worldng pressure equal to 60% 
of that for heads of the same dimensions with the pressure on the 
concave side. When the dished head has a manhole opening the thick- 
ness as found by these rules shall be increased by not less than i/s in. 
The corner radius of a dished head shall be not less than 1 H in. nor 
more than 4 in., and not less than O.OSii. A manhole opening in a 
dished head shall be fianged to a depth not less than three times the 
thickness of the head measured fvom the outside.] 

Efficiency of Riveted Joints. (INIass. Boiler Rules, 1910.)* 
X = efficiency = ratio of strength of unit length of riveted joint to 

the strength of the same length of a solid plate. 
T = tensile strength of tiie material, in pomids per square inch. 
t — thickness of plate, in inches. 
b — thickness of butt strap, in inches. 

P = pitch of rivets, in inches, on the row having the greatest pitch. 
d — diameter of rivet, after driving, in inches. 
a = cross-section of rivet after driving, in square inches, 
s = strength of rivet in single shear, in pounds per square inch. 
S = strength of rivet in double shear, in pounds per square inch. 

* The same rules are given in the A. S. M. E. Boiler Code of 1914, 
which was modeled on the Massachusetts Rules. 



A 



STRENGTH OF STEAM-BOILERS. 915 

c = crushing strength of rivet, in pounds per square inch. 
n = number of rivets in single sliear in a length of joint equal to P. 
N = number of rivets in double shear in the same length of joint. 
For single-riveted lap joints: 

A = strength of solid plate = PtT. 

B = strength of plate between rivet holes = (P — d)tT. 

C = shearing strength of one rivet = nsa. 

D = crushing strength of plate in front of one rivet = dtc. 

X = -r or-r or -r, whichever is least. 
A A A 

For double-riveted lap joints: 

A and B as above, C and D to be taken for two rivets. 
X = B, C, or D (whichever is least) divided by A, 
For butt and double strap joint, double-riveted: 
A = strength of solid plate = PtT. 
B = strength of plate between rivet holes in the outer row = 

(P - d)tT. 
C = shearing strength of two rivets in double shear, plus shearing 

strength of one rivet in single shear = NSa + nsa. 
D = strength of plate between rivet holes in the second row, plus 
the shearing strength of one rivet in single shear in the outer 
row = (P - 2d)tT + nsa. 
E = strength of plate between rivet holes in the second row, plus 
the crushing strength of butt strap in front of one rivet in 
the outer row = (P - 2d)tT + dbc. 
F = crushing strength of plate in front of two rivets, plus the 
crushing strength of butt strap in front of one rivet = 
Ndtc + ndbc. 
G = crushing strength of plate in front of two rivets, plus the 

shearing strength of one rivet in single shear = Ndtc + nsa. 
X= B,C, D, E, F, or G (whichever is least) divided by A. 
For butt and double strap joint, triple-riveted: 

The same as for double-riveted, except that four rivets instead of 
two are taken for N in computing C, P, and G. 
For butt and double strap joint, quadruple-riveted: 
A, B, and D the same as for double-riveted joints. 
C = shearing strength of eight rivets in double shear and three 

rivets in single shear = NSa + nsa. 
E = strength of plate between rivet holes in the third row (the 
outer row being the first) plus the shearing strength in single 
shear of two rivets in the second row and one rivet in the 
outer row = (P — 4d)tT + nsa. 
F z= strength of plate between rivet holes in the second row, plus 
the crushing strength of butt strap in front of one rivet m 
the outer row = (P - 2d)tT + dhc. 
G = strength of plate between rivet holes in the third row, plus 
the crushing strength of butt strap in front of two rivets 
in the second row and one rivet in the outer row = 
(P -4d)tT+ ndbc. 
H = crushing strength of plate in front of eight rivets, plus the 
crushing strength of butt strap in front of three rivets = 
Ndtc + ndbc. 
I = crushing strength of plate in front of eight rivets, plus the 
shearing strength in single shear of two rivets in the second 
row and one in the outer row = Ndtc -\- nsa. 
X^B,C, D, E, F, G, H, or I (whichever is least) divided by A. 
The Massachusetts Rules allow the crushing strength of mild steel to 
be taken at 95,000 lb. per sq. in. The maximum shearing strength of 
rivets, in lb. per sq. in. of cross-section, is taken as follows: 
In single shear, iron, 38,000; steel, 42,000. 
In double shear, iron, 70,000; steel, 78,000. 

The A. S. M. Boiler Code aiso allows 95,000 lb. per sq. in. for crash- 
ing strength, but for shearing strength of rivets allows: 
In single shear, iron 38,000; steel 44,000. 
In double shear, iron 76,000; steel 88,000. 



916 



THE STEAM-BOILER. 



Allowable Stresses on Braces and Staybolts. (Massachusetts Rules.) 
— The maximum allowable stress per square inch net cross-sectional 
area of stays and staybolts shall be as follows: Weldless mild steel, 
head to head or through stays, 8000 lb., 9000 lb.; diagonal or crow- 
foot stays, 7500 lb., 8000 lb.; mild steel or wrought-iron staybolts 
6500 lb., 7000 lb. The first figure in each case is for size up to 1 1/4 
in. diameter or equivalent area, the second for size over 1 1/4 in. or 
equivalent area. 

The A. S. M. E. Boiler Code allows for welded stays 6000 lb. per sq. 
in.; for unwelded stays (a) 7500; (b) 9500; (c) 8500. (a) less than 20 
diameters long, screwed tlu"ough plates with ends riveted over; (b) 
lengths between supports not exceeding 120 diameters; (c) exceeding 120 
diameters. 

Allowable Pressure on Staybolted Surfaces. — The U. S. Supervising 
Inspectors' rule (for steamboat service) is: 

P = kt^-i- S2 

P = allowable pressure, lb. per sq. in., S = maximmn pitch in inches, 
t = thickness in sixteenths of an inch, k = 112 for plates up to 7/i6 in., 
and 120 for plates over 7/i6 in. 

The A. S. M. E. Boiler Code gtves the same formula with the follow- 
ing values of the constants: For stays screwed through plates with 
ends riveted over, plates^not over t/iq in. thick, C = 112; over T/u in. 
thick, C = 120; for stays"screwed tlirough plates and fitted with single 
nuts outside of plate, C = 135; for stays fitted with inside nuts and 
outside washers, the diameters of washers not less than 0.4 »S and 
thickness not less than t, C = 175. 

Staybolts. — Staybolts in water-legs are subject not only to longi- 
tudinal stress due to the boiler pressiu-e, and to corrosion, but also to 
bending stress caused by relative motions of the outer and inner sheets 
of the furnace or waterleg due to the variations in temperature to 
which the two are subjected. A staybolt usually fails by transverse 
fractiu-e close to the outer sheet, wliich is supposed to be due to the 
fact that the fire-box sheet is generally thinner than the outer sheet, and 
therefore holds the end of the stay less rigidly. Staybolts are some- 
times driUed with a small hole at one end through winch water will be 
blown out as soon as a fracture extends far enough across the section 
to reach the hole, thus calling attention to the failure of the stay. A 
better form is one in which the hole extends the whole length of the stay. 
The inner portion of the stay is turned to i/s in. smaller diameter than 
the ends, in order to make the stay more flexible and diminish the 
chances of fracture. 

Tube Spacing in Horizontal Tubular Boilers. — In modern practice 
the tubes are arranged in vertical and horizontal rows (not staggered 
as in earher practice), with not less than 1 in. space between adjacent 
tubes, not less than 2 in. between the two central vertical rows, and 
not less than 2 H in. between the shell and the nearest tube. In boilers 
60 in. diameter and larger a manhole is put in the front head beneath 
the central rows of tubes. 

Tubes and Tube Holes. (Mass. Boiler Rules). — Tube holes shall be 
drilled full size, or they may be punched not to exceed H in. less than 
the full size, and then drilled, reamed or finished full size with a rotating 
cutter. The edge of tube holes shall be chamfered to a radius of about 
1/16 in. A fire-tube boiler shall have the ends of the tubes substantially 
beaded. The ends of all tubes, suspension tubes and nipples shall be 
flared not less than i/g in. over the diameter of the tube hole on all 
water-tube boilers and superheaters, and shall project through the tube 
sheets or headers not less than 1/4 in. nor more than 1/2 in. Separately 
fired superheaters shall have the tube ends protected by refractory ma- 
terial where they connect with drums or headers. 

Holding Power of Expanded Tubes. (The Locomotive, Sept., 1893.) 
■ — Tubes 3 in. external diameter, 0.109 in. thick were expanded in a 
3/8-in. plate by rolling with a Dudgeon expander, without the pro- 
jecting part being flared or beaded. Stress was applied to draw the 
tubes out of the plates. The observed stress which caused yielding 
was, in three specimens, 6500, 5000 and 7500 lb. Two other specimens 
were flared so that the diameter of the extreme end of the tube pro- 



STRENGTH OF STEAM-BOILERS. 



917 



jecting 3/i6 in. beyond the plate was 3.2 in., the diameter of the tube 
where it entered the plate being 3.1 in. The observed stres.s which 
caused the yielding of these specimens was 21,000 and 19,500 lb. 
The Locomotiue estimates that the factor of safety of the plain rolled 
tubes is nearly 4 and that of the flared tubes about 15 against the stress 
to which they are subjected in a boiler at 100 lb. gage pressure. It is 
considered that the tubes act as stays for that portion of the flat head 
that is within two inches of the upper row of tubes, and that the seg- 
ment above this (except that portion that Ues with 3 in. of the shell) re- 
quires to be braced. 

Size of Boiler Tubes. — The following table gives the dimensions of 
the tubes commonly used in steam-boilers, together with their calculated 
surface per foot of length, and the length per square foot of surface, 
internal and external: 





Dimensions of Standard Boiler Tubes 






IS 
Is 


m 


1— i 


Inside Sur- 
face per 
Foot of 
Length. 


Length per 
Sq. ft. of 
Inside 
Surface. 


Outside Sur- 
face per Foot 
of Length, 
Sq. ft. 


Length, per 
Sq. ft. Out- 
side Surface, 
Ft. 


Internal 
Area, Sq. ft. 


External 
Area, Sq. ft. 


2 


0.095 


1.810 


0.4738 


2.110 


0.5236 


1.910 


0.0179 


0.0218 


21/4 


.095 


2.060 


.5393 


1.854 


.5890 


1.698 


.0231 


.0276 


2V2 


.109 


2.282 


.5974 


1.674 


.6545 


1.528 


.0284 


.0341 


2 3/4 


.109 


2.532 


.6629 


1.508 


.7199 


1.389 


.0350 


.0412 


3 


.109 


2.782 


.7283 


1.373 


.7854 


1.273 


.0422 


.0491 


3 1/4 


.120 


3.010 


.7880 


1.269 


.8508 


1.175 


.0494 


.0576 


31/2 


.120 


3.260 


.8535 


1.172 


.9163 


1.091 


.0580 


.0668 


33/4 


.120 


3.510 


.9189 


1.088 


.9817 


1.018 


.0672 


.0767 


4 


.134 


3.732 


.9770 


1.024 


1.0472 


0.955 


.0760 


.0873 



Flues Subjected to External Pressure. — The rules of the U. S. Board 
of Supervising Inspectors, Steamboat Inspection Service, 1909, give the 
following rules for flues subjected to external pressure only: 

Plain lap-Avelded flues 7 to 13 in. diameter. 

Furnaces. — The tensile strength of steel used in the construction of 
corrugated or ribbed furnaces shall not exceed 67,000, and be not less 
than 54,000 lb.; and in all other furnaces the minimum tensile strength 
shall not be less than 58,000, and the maximum not more than 67,000 
lb. The minimum elongation in 8 inches shall be 20%. 

All corrugated furnaces having plain parts at the ends not ex- 
ceeding 9 inches ^n length (except flues especially provided for), when 
new, and made to practically true circles, shall be allowed a steam 
pressure in accordance with the formula P = C X T -^ D. 

P = pressure in lb. per sq. in., T = thickness in inches, C = a con- 
stant, as below. 

Leeds suspension biflb furnace. . . C = 17,000, T not less than 5/i6 in. 

Morison corrugated type O = 15,600, T not less than 5/i6 in. 

Fox corrugated type C = 14,000, T not less than V16 in. 

Purves type, rib projections C = 14,000, T not less than t/iq in. 

Brown corrugated type C = 14,000, T not less than 5/i6 in. 

Type having sections 18 ins. long C = 10,000, T not less than t/iq in. 

Limiting dimensions from center of the corrugations or projecting 
ribs, and of their depth, are given for each furnace. 

Working Pressure on Boilers with Triple Riveted Joints. — ^A triple 
riveted double butt and strap joint, carefully designed, may be made 
to have an efficiency something higher than 85 per cent. Good boiler 
plate steel may be considered to have a tensile strength of 55,000 lb. 
per sq. in. Taking these flgures and a factor of safety of 5, we have 
safe working pressure 

2Ttf ^ 2X55.000X^X0.85 ^ 18700^ 
dF 5d d * 

from which the following table is calculated. 



P = 



I 



918 



THE STEAM-BOILER. 



Safe Working Pressure for Shells with Joints of 85% 


Efficiency. 


Thickness, In. . . 


1/4 


Vl6 


3/8 


Vl6 


1/2 


9/16 


5/8 


11/16 


3/4 

233 
212 
195 
180 
167 
156 
146 


13/16 

230 
211 
195 
181 
169 
158 


V8 

227 
210 
195 
182 
170 


15/16 

225 
209 
195 
183 


1 


Diameter, In. 
24 


195 
156 
130 
111 


247 
195 
162 
139 
122 
108 


234 
195 
167 
146 
130 
117 
106 


227 
195 
170 
151 
136 
124 
114 


260 
223 
195 
173 
156 
142 
130 
120 


250 
219 
195 
175 
159 
146 
135 
125 
117 


243 
216 
195 
177 
162 
150 
139 
130 
121 


238 
214 
195 
179 
165 
153 
143 
134 




30 




36 




42 




48 




54 






60 






66 








72 








78 










84 










??3 


90 












?08 


96 












195 



Shells of externally fired boilers are rarely made over 9/i6 in. thick. 

Pressures Allowed on Boilers. (Mass. Boiler Rules.) — The pressure 
allowed on a boiler constructed wholly of cast iron shall not exceed 
25 lb. per sq. in. 

The pressure allowed on a boiler the tubes of which are secured to 
cast-iron headers shall not exceed 160 lb. per sq. in. 

The maximum pressure to be allowed on a shell or drum of a boiler 
shall be determined from the minimum thickness of the shell plates, the 
lowest tensile strength stamped on the plates by the manufacturer, the 
efficiency of the longitudinal joint or of the ligament between the tube 
holes, whichever is least, the inside diameter of the outside course, and 
a factor of safety not less than five. 

The lowest factor of safety to be used for boilers the shells or drums 
of which are exposed to the products of combustion, and the longi- 
tudinal joints of which are lap riveted, shall be as follows: 5 for boilers 
not over 10 years old; 5.5 for boilers over 10 and not over 15 years old; 
5.75 for boilers over 15 and not over 20 years old; 6 for boilers over 20 
years old. The lowest factor of safety to be used for boilers the longi- 
tudinal joints of which are of butt and double strap construction is 4.5. 

A hydrostatic test is to be applied if in the judgment of the in- 
spector or of the insurance company it is advisable. The maximum 
pressure in a hydrostatic test shall not exceed 1 3^ times the maximum 
allowable working pressure, except that twice the maximum allowable 
working pressure may be applied on boilers permitted to carry not 
over 25 lb. pressure, or on pipe boilers. 

Fusible Plugs. — (A. S. M. E. Code.) Fusible plugs, if used, shall be 
filled with tin with a melting point between 400 and 500° F. The least 
diameter of fusible metal shall be not less>than 3^ in. , except for maximum 
allowable working pressures of over 175 lb. per sq. in. or when it is 
necessary to place a fusible plug in a tube, in which case the least 
diameter of fusible metal shall be not less than s/g in. 

Steam-domes. — Steam-domes or drums were formerly almost uni- 
versally used on horizontal boilers ^ but their use is now generally discon- 
tinued, as they are considered a useless appendage to a steam-boiler, and 
unless properly designed and constructed are an element of weakness. 



IMPEOVED METHODS OF FEEDING COAL. 

Mechanical Stokers. (William R. Roney, Trans. A. S. M. E., vol. 
xii.) — Mechanical stokers have been used in England to a limited extent 
since 1785. In that year one was patented by James Watt. (See D. K. 
Clark's Treatise on the Steam-engine.) 

After 1840 many styles of mechanical stokers were patented in England, 
but nearly all were variations and modifications of the two forms of 
stokers patented by John Jukes in 1841 and by E. Henderson in 184.3. 

The Jukes stoker consisted of longitudinal fire-bars, connected by 



IMPROVED METHODS OF FEEDING COAL. 919 

links, so as to form an endless chain. The small coal was delivered from 
a hopper on the front of the boiler, on to the grate, which, slowly movmg 
from front to rear, gradually advanced the fuel into the furnace and 
discharged the ash and clinker at the back. 

The Henderson stoker consists primarily of two horizontal fans revolv- 
ing on vertical spindles, which scatter the coal over the fire. 

The first American stoker was the Murphy stoker, brought out in 
1878. It consists of two coal magazines placed in the side walls of the 
boiler furnace, and extending back from the boiler front 6 or 7 feet. In 
the bottom of these magazines are rectangular iron boxes, which are 
moved from side to side by means of a rack and pinion, and serve to 
push the coal upon the grates, which incline at an angle of about 35 
from the inner edge of the coal magazines, forming a V-shaped recep- 
tacle for the burning coal. The grates are composed of narrow parallel 
bars, so arranged that each alternate bar hfts about an inch at the lower 
end, w^hile at the bottom of the V, and filling the space between the ends 
of the grate-bars, is placed a cast-iron toothed bar, arranged to be 
turned by a crank. The purpose of this bar is to grind the chnker com- 
ing in contact with it. Over this V-shaped receptacle Ls sprung a fire- 
brick arch 

In the Roney mechanical stoker the fuel to be burned is dumped into a 
hopper on the boiler front Set in the lower part of the hopper is a 
"pujher," which, by a vibratory motion, gradually forces the fuel over 
the ' dead-plate' ' and on the grate. The grate-bars in their normal C9n- 
dition form a series of steps. Each bar is capable of a rocking motion 
through an adjustable angle. All the grate-bars are coupled together by 
a "rocker-bar." A variable back-and-forth motion being given to the 
"rocker-bar," through a connecting-rod, the grate-bars rock m unison, 
now forming a series of steps, and now approximating to an inclined 
plane, with the grates partly overlapping, like shingles on a roof. \\ hen 
the grate-bars rock forward the fire will tend to work down m a body. 
But before the coal can move too far the bars rock back to the stepped 
position, checking the downward motion. The rocking motion is slow, 
being from 7 to 10 strokes per minute, according to the kind of coal. 
This alternate starting and checking motion is continuous, and finally 
lands the cinder and ash on the dumping-grate below. 

The Hawley Down-draught Furnace.— A foot or more above the 
ordinary grate there is carried a second grate, composed of a series of 
water-tubes, opening at both ends into steel drums or headers, through 
which water is circulated. The coal is fed on this upper grate, and as it 
is partially consumed falls through it upon the lower grate, where the 
combustion is completed in the ordinary manner. The draught through 
the coal on the upper grate is downward through the coal and the grate. 
The volatile gases are therefore carried down through the bed of coal, 
where they are thoroughly heated, and are burned in the space beneath, 
where they meet the excess of hot air drawn through the fire on the lower 
grate. In tests in Chicago, from 30 to 45 lb. of coal were burned per 
square foot of grate upon this system, with good economical results. 
(See catalogue of the Hawley Down-draught Furnace Co., Chicago.) 

The Chain Grate Stoker, made by Jukes in 1841, is now (1909) widely 
used in the United States. It is made by the Babcock & Wilcox Co., 
Green Engineering Co., and others. 

Under-feed Stokers. — Results similar to those that may be obtained 
with downward draught are obtained by feeding the coal at the bottom 
of the bed, pushing upward the coal already on the bed which has had 
its volatile matter distilled from it. The volatile matter of the freshly 
fired coal then has to pass through a body of ignited coke, where it 
meets a supply of hot air. (See circular of The Underfeed Stoker Co., 
Chicago.) 

The Taylor Gravity Stoker is a combination of an underfeed stoker 
containing two horizontal rows of pushers wath an inclined or step grate 
through which air is blown by a fan. 

The Riley Stoker is an underfeed stoker with a single horizontal row 
of pushers in combination with moving grate-bars, and moving pushers 
at the rear of the furnace for continuously dumping the refuse. 



I 



920 THE STEAM-BOILER 

SMOKE PREVENTION. 

The following article was contributed by the author to a "Report on 
Smoke Abatement," presented by a committee to the Syracuse Cham- 
ber of Commerce, published by the Chamber in 1907. 

Smoke may be made in two ways: (1) By direct distillation of tarry 
condensible vapors from coal without burning; (2) By the partial burn- 
ing or splitting up of hydrocarbon gases, the hydrogen burning and the 
carDon being lett unburned as smoke or soot. These causes usually act 
conjointly. 

The direct cause of smoke is that the gases distilled from the coal are 
not completely burned in the furnace before coming in contact with the 
surface of the boiler, which chills them below the temperature of ignition. 

The amount and quality of smoke discharged from a chimney may 
vary all the way from a dense cloud of jet-black smoke, which may be . 
carried by a Ught wind for a distance of a mile or more before it is finally 
dispersed into the atmosphere, to a thin cloud, which becomes invisible 
a few feet from the chimney. Often the same chimney will for a few 
minutes immediately after firing give off a dense black cloud and then a ' 
few minutes later the smoke will have entirely disappeared. 

The quantity and density of smoke depend upon many variable causes. 
Anthracite coal produces no smoke under any conditions of furnace. Semi- 
bituminous, containing 12.5 to 25% of volatile matter in the combustible 
part of the coal, will give off more or less smoke, depending on the con- 
ditions under which it is burned, and bituminous coal, containing from 
25 to 50% of volatile matter, will give off great quantities of smoke with 
all of the usual old-style furnaces, even with skillful firing, and this smoke 
can only be prevented by the use of special devices, together with proper 
methods of firing the fuel and of admission of air. 

Practically the whole theory of smoke production and prevention may 
be illustrated by the flame of an ordinary gas burner or gas stove. 
When the gas is turned down very low every particle of gas, as it emerges 
from the burner, is brought in contact with a sufficient supply of hot air to 
effect its complete and instantaneous combustion, with a pale blue or 
almost invisible flame. Turn on the gas a little more and a white flame 
appears. The gas is imperfectly burned in the center of the flame. Par- 
ticles of carbon have been separated which are heated to a white heat. 
If a cold plate is brought in contact with the white flame, these carbon 
particles are deposited as soot. Turn on the gas still higher, and it burns 
with a dull, smoky flame, although it is surrounded with an unlimited 
quantity of air. Now, carry this smoky flame into a hot fire-brick or 
porcelain chamber, where it is brought in contact with very hot air, and 
it \\ill be made smokeless by the complete burning of the particles. 

We thus see: (1) That smoke may be prevented from forming if each 
particle of gas, as it is made by distillation from coal, is immediately 
mixed thoroughly with hot air, and (2) That even if smoke is formed 
by the absence of conditions for preventing it, it may afterwards be 
burned if it is thoroughly mixed with air at a sufficiently high temperature. 
It is easy to burn smoke when it is made in small quantities, but when 
made in great volumes it is difficult to get the hot air mixed with it unless 
special apparatus is used. In boiler firing the formation of smoke must 
be prevented, as the conditions do not usually permit of its being burned. 
The essential conditions for preventing smoke in boiler fires may be 
enumerated as follows: 

1. The gases must be distilled from the coal at a uniform rate. 

2. The gases, when distilled, must be brought into intimate mixture 
with sufficient hot air to burn them completely. 

3. The mixing should be done in a fire-brick chamber. 

4. The gases should not be allowed to touch the comparatively cold 
surfaces of the boiler until they are completely burned. This means that 
the gases shall have sufficient space and time in which to burn before they 
are allowed to come in contact with the boiler surface. 

Every one of these four conditions is violated in the ordinary method 
of burning coal imder a steam boiler. (1) The coal is fired intermittently 
and often in large quantities at a time, and the distillation proceeds at so 
rapid a rate that enoucrh air cannot be introduced into the furnace to burn 
the gas. (2) The piling of fresh coal on the grate in itself chokes the air 



SMOKE PREVENTION. 921 

supply. (3) The roof of the furnace is the cold shell, or tubes, of the 
boiler, instead of a fire-brick arch, as it should be, and the fui-nace is not of 
a sufficient size to allow the gases time and space in which to be thoroughly 
mixed with the air supply. 

In order to obtain the conditions for preventing smoke it is necessary: 
(1) That the coal be delivered into the furnace in small quantities at a 
time. (2) That the draught be sufficient *o carry enough air into the 
furnace to burn the gases as fast as they are distilled. (3) That the air 
itself be thoroughly heated either by passing through a bed of white-hot 
coke or by passing through channels in hot brickwork, or by contact with 
hot fire-brick surfaces. (4) That the gas and the air be brought into 
the most complete and intimate mixture, so that each particle of carbon 
in the gas meets, before it escapes from the furnace, its necessary supply 
ot air. (5) That the flame produced by the burning shall be completely 
extinguished by the burning of every particle of the carbon into invisible 
carbon dioxide- 

If a white flame touches the surface of a boiler, it is apt to deposit 
soot and to produce smoke. A white flame itself is the visible evidence 
of incomplete combustion. 

The first remedy for smoke is to obtain anthracite coal. If this is not 
commercially practicable, then obtain, if possible, coal with the smallest 
amount of volatile matter. Coal of from 15 to 25% of volatile matter 
makes much less smoke than coals containing higher percentages. Pro- 
vide a proper furnace for burning coal. Any furnace is a proper furnace 
which secures the conditions named in the preceding paragraphs. Next, 
compel the firemen to follow instructions concerning the method of 
firing. 

It is impossible with coal containing over 30% of volatile matter and 
with a water-tube boiler, with tubes set close to the grate and vertical 
gas passages, as in an anthracite setting, to prevent smoke even by the 
njost skillful firing. This style of setting for a water-tube boiler should 
be absolutely condemned. A Dutch oven setting, or a longitudinal 
setting with fire-brick baffle walls, is highly recommended as a smoke- 
preventing furnace, but with such a furnace it is necessary to use con- 
siderable skill in firing. 

Mechanical mixing of the gases and the air by steam jets is sometimes 
successful in preventing smoke, but it is not a universal preventive, 
especially when the coal is very high in volatile matter, when the firing 
is done unskillfully, or when the boiler is being driven beyond its normal 
capacity. It is essential to have sufficient draught to burn the coal prop- 
erly and this draught may be obtained either from a chimney or a fan. 
There is no especial merit in forced draught. except that it enables a larger 
quantity of coal to be burned and the boiler to be driven harder in case 
of emergency, and usually the harder the boiler is driven, the more 
difficult it is to suppress smoke. 

Down-draught furnaces and mechanical stokers of many different kinds 
are successfully used for smoke prevention, and when properly designed 
and installed and handled skillfully, and usually at a rate not beyond 
that for which they are designed, prevent all smoke. If these appliances 
are found giving smoke, it is always due either to overdriving or to un- 
skillful handling. It is necessary, however, that the design of these 
stokers be suited to the quality of the coal and the quantity to be burned, 
and great care should be taken to provide a sufficient size of furnace with 
a fire-brick roof and means of introducing air to make them completely 
successful. 

Burninj? Illinois Coal without Smoke. (L. P. Breckenridge, 
Bulletin No. 15 of the Univ. of III. Eng'g Experiment Station, 1907.) 
— Any fuel may be burned economically and without smoke if it is 
mixed with the proper amount of air at a proper temperature. The 
boiler plant of the University of Illinois consists of nine units aggregating 
2000 H.P. Over 200 separate tests have been made. The following is a 
condensed statement of the results in regard to smoke prevention. 

Boilers Nos. 1 and 2. Babcock & Wilcox. Chain-grate stoker. Usual 
vertical baffling. Can be run without smoke at from 50 to 120 % of rated 
capacity. 

No. 3. Stirling boiler. Chain-grate stoker. Usual baffling and com- 



922 THE STEAM-BOILEE. 

bustion arches. Can be run without smoke at capacities of 50 to 
140%. 

No. 4. National water-tube. Chain-grate stoker. Vertical baffling. 
No smoke at capacities of 50 to 120 <J^. With the Murphy furnace it was 
smokeless except when cleaning fires. 

No. 5. Babcock & Wilcox. Roney stoker. Vertical baffling. Nearly 
smokeless (maximum No. 2 on a chart in which 5 represents black smoke) 
up to 100% of rating, but cannot be run above 100% without objection- 
able smoke. 

No. 6. Babcock & Wilcox. Roney stoker. Horizontal tile-roof baf- 
fling. Can be run without smoke at capacities of 50 to 100% of rating. 

Nos. 7 and 8. Stirling, equipped with Stirling bar-grate stoker. Usual 
baffling and combustion arches. Can be run without smoke at 50 to 
140 7o of rating. 

No. 9. Heine boiler. Chain-grate stoker. Combustion arch and tile- 
roof furnace. Can be run without smoke at capacities of 50 to 140%. 
It is almost impossible to make smoke with this setting under any con- 
dition of operation. As much as 46 lbs. of coal per sq. ft. of grate surface 
has been burned without smoke. 

Conditions of Smoke Prevention. — Bulletin No. 373 of the U. S. 
Geological Survey, 1909 (188 pages), contains a report of an extensive 
research by D. T. Randall and J. T. Weeks on The Smokeless Combustion 
of Coal in Boiler Plants. A brief summary of the conclusions reached is 
as follows: 

Smoke prevention is both possible and economical. There are many 
types of furnaces and stokers that are operated smokelessly. 

Stokers or furnaces must be set so that combustion will be complete 
before the gases strike the heating surfaces of the boiler. When partly 
burned gases at a temperature of say 2500° F. strike the tubes of a 
boiler at say 350° F., combustion may be entirely arrested. 

The most economical hand-fired plants are those that approach most 
nearly to the continuous feed of the mechanical stoker. The fireman is 
so variable a factor that the ultimate solution of the problem depends on 
the mechanical stoker — in other words, the personal element must be 
ehminated. 

A well designed and operated furnace will burn many coals without 
smoke up to a certain number of pounds per hour, the ra'^te varying with 
different coals. If more than this amount is burned, the efficiency will 
decrease and smoke will be made, owing to the lack of furnace capacity 
to supply air and mix gases. 

High volatile matter in the coal gives low efficiency, and vice versa. 
When the furnace was forced the efficiency decreased. 

With a hand-fired furnace the best results were obtained when firing 
was done most frequently, with the smallest charge. 

Small sizes of coal burned with less smoke than large sizes, but developed 
lower capacities. 

Peat, lignite, and sub-bituminous coal burned readily in the tile-roofed 
furnace and developed the rated capacity, with practically no smoke. 

Coals which smoked badly gave efficiencies three to five per cent lower 
than the coals burning with little smoke. 

Briquets were found to be an excellent form for using slack coal in a 
hand-fired plant. 

In the average hand-fired furnace washed coal burns with lower effi- 
ciency and makes more smoke than raw coal. Moreover, washed coal 
offers a means of running at high capacity, ^\ith good- efficiency, in a 
well-designed furnace. 

Forced draught did not burn coal any more efficiently than natural 
drauerht. It supplied enough air for high rates of combustion, but as the 
capacity of the boiler increased, the efficiency decreased and the per- 
centage of black smoke increased. 

Fire-brick furnaces of sufficient length and a continuous, or nearly 
continuous, supply of coal and air to the fire make it possible to burn 
most coals efficiently and without smoke. 

Coals containing a large percentage of tar and heavy hydrocarbons 
are difficult to burn without smoke and require special furnaces and more 
than ordinary care in firing. 



FORCED COMBUSTION IN STEAM-BOILERS. 923 

FORCED COMBUSTION IN STEAM-BOILERS. 

For the purpose of increasing the amount of steam that can be gener- 
ated by a boiler of a given size, forced draught is of great importance. 
It is universally used in the locomotive, the draught being obtained by a 
steam-jet in the smoke-stack. It is now largely used in ocean steamers, 
especially in ships of war, and to a small extent in stationary boilers. 
Economy of fuel is generally not attained by its use, its advantages be- 
ing confined to the securing of increased capacity from a boiler of a 
given bulk, weight, or cost. 

There are three different modes of using the fan for promoting com- 
bustion: 1, blowing direct into a closed ash-pit; 2, exhausting the gases 
by the suction of the fan; 3, forcing air into an air-tight boiler-room 
or stoke-hold. Each of these three methods has its advantages and dis- 
advantages. 

In the use of the closed ash-pit the blast-pressure frequently forces 
the gases of combustion from the joint around the furnace doors in so 
great a quantity as to affect both the efficiency of the boiler and the 
health of the firemen. 

The chief defect of the second plan is the great size of the fan required 
to produce the necessary exhaustion, on account of the higher exit tem- 
perature enlarging the volume of the waste gases. 

The third method that of forcing cold air by the fan into an air-tight 
boiler-room — the closed stoke-hold system — though it overcame the 
difficulties in working belonging to the two forms first tried, has serious 
defects of its own, as it cannot be worked, even with modern high-class 
boiler-construction, much, if at all, above the power of a good chimney 
draught, in most boilers, without damaging them. (J. Howden, Proc. 
Eng'g Congress at Chicago, in 1893.) 

In 18S0 Mr. Howden designed an arrangement intended to overcome 
the defects of both the closed ash-pit and the closed stoke-hold systems. 

An air-tight chamber is placed on the front end of the boiler and sur- 
rounding the furnaces. Tliis reservoir, which projects from. 8 to 10 
inches from the end of the boiler, receives the air under pressure, which 
is passed by valves into the ash-pits and over the fires in proportions 
suited to the kind of fuel and the rate of combustion. The air used above 
the fires is admitted to a space between the outer and inner furnace- 
doors, the inner having perforations and an air-distributing box through 
which the air passes under pressure. By means of the balance of pres- 
sure above and below the fires all tendency of the fire to blow out at 
the door is removed. 

A feature of the system is the combination of the heating of the air of 
combustion by the waste gases with the controlled and regulated admis- 
sion of air to the furnaces. This arrangement is effected most conve- 
niently by passing the hot fire-gases after they leave the boiler through 
stacks of vertical tubes enclosed in the uptake, their lower ends being 
immediately above the smoke-box doors. Installations on Howden's 
system have been arranged for a rate of combustion to give an average 
of from 18 to 22 I.H.P. per square foot of fire-grate with fire-bars from 
5 to 5 ^ ft. in length. It is believed that with suitable arrangement of 
proportions even 30 I.H.P. per square foot can be obtained. 

For an account of uses of exhaust-fans for increasing draught, see 
paper by W. R. Roney, Trans. A. S. M. E., vol. xv. 

Calculations for Forced Draft. — In designing a forced draft installa- 
tion the principal data needed are: 1, The maximum number of pounds 
of coal that will have to be burned per hour at the most rapid rate of 
driving, when the efficiency of the boiler, furnace and grate is lowest; 
2, the number of pounds of air used per pound of coal. If C, H and O 
are respectively the carbon, hydrogen and oxygen in 1 lb. of coal, then 
the number of pounds of air required, theoretically, for complete com- 
bustion is 34.56 (C/3 + H + 0/8). With mechanical stokers and CO2 
apparatus for control of the air supply 50% excess air supply is ample, 
but with ordinary hand-firing the actual air supply may be 100% or 
more in excess. In the author's " Steam Boiler Economy," 2d ed. 1915, 
p. 242, there is given a calculation of the number of cubic feet of air 
per minute required per boiler horsepower developed, giving results as 
follows: 



924 THE STEAM-BOILER. 

Cubic Feet of Air per Minute at 70° F. per Boiler Horsepower. 

Semi- East. West. 
Fuel Anth. bit. Bitu. Bitu. Lignite Oil 

Air 50% excess 11.52 11.30 10.99 11.86 13.63 11.13 

Air 100% excess 15.36 15.07 14.65 15.82 16.17 14.84 

Note that these figures are based not upon the rated horse-power of 
the boiler, but upon that actually developed, which may be far in excess 
of the rated power. For induced draft the figures given should be 
multiplied by (T-f- 460) -- 530, in which T is the temperature of the 
gases to be handled by the induced draft fan. 

FUEL ECONOMIZERS. 

Economizers for boiler plants are usually made of vertical cast-iron 
tubes contained in a long rectangular chamber of brickwork. The feed- 
water enters the bank of tubes at one end, while the hot gases enter the 
chamber at the other end and travel in the opposite direction to the 
water. The tubes are made of cast iron because it is more non-corrosive 
than wrought iron or steel when exposed to gases of combustion at low 
temperatures. An automatic scraping device is usually provided for 
the piu-pose of removing dust from the outer surface of the tubes. 

The amount of saving of fuel that may be made by an economizer ♦ 
varies greatly according to the conditions of operation. With a given 
quantity of cliimney gases to be passed through it, its economy will be 
greater (1) the higher the temperature of these gases; (2) the lower the 
temperature of the water fed into it ; and (3) the greater the amount of its 
heating surface. From (1) it is seen that an economizer will save more 
fuel if added to a boiler that is overdriven than if added to one driven at 
a nominal rate. From (2) it appears that less saving can be expected 
from an economizer in a power plant in which the feed-water is heated by 
exhaust steam from auxiliary engines than when the feed-water entering 
it is taken directly from the condenser hot-well. The amount of heat- 
ing surface that should be used in any given case depends not only on 
the saving of fuel that may be made, but also on the cost of coal, and on 
the annual costs of maintenance, including interest, depreciation, etc. 

The following table shows the theoretical results possibly attainable 
from economizers under the conditions specified. It is assumed that the 
coal has a heating value of 15,000 B.T.U. per lb. of combustible; that it 
is completely burned in the furnace at a temnerature of 2500° F. ; that 
the boiler gives efficiencies ranging from 60 to 75% according to the rate 
of driving; and that sufficient economizer surface is provided to reduce 
the temperature of the gases in all cases to 300° F. Assuming the specific 
heat of the gases to be constant, and neglecting the loss of heat by radi- 
ation, the temperature of the gases leaving the boiler and entering the 
economizer is directly proportional to (100— % of boiler efficiency), 
and the combined efficiency of boiler and economizer is (2500 — 300) 
-f- 2500 = 88%, which corresponds to an evaporation of (15.000 -^ 970) 
X 0.88 = 13.608 lb. from and at 212° per lb. of combustible; or as- 
suming the feed-water enters the economizer at 100° F. and the boiler 
makes steam of 150 lb. absolute pressure, to an evaporation of 11.729 
lb. under these conditions. Dividing this figure into the number of 
heat units utilized by the economizer per lb. of combustible gives the 
heat-units added to the water, from which, by reference to a steam 
table, the temperature may be found. With these data we obtain the 
results given in the table below. 



Boiler Efficiency, per cent. 



60 I 65 70 75 



B.T.U. absorbed by boiler per lb. combustible. . 

B.T.U. in chimney gases leaving boiler , 

Estimated temp, of gases leaving boiler 

Estimated temp, of gases leaving economizer. . . 

B.T.U. saved by economizer 

Efficiency gained by economizer, per cent ...... 

Equivalent water evap. per lb. comb, in boiler . . 
B.T.U. saved by econ. equivalent to evap. of lb., 

Temp, of water leaving economizer 

Efficiency of the economizer, per cent 



9000 9750 10500 11250 

6000 5250 4500 3750 

1000° 875°! 750° 625° 

300° 300°, 300° I 300° 

4200 3450l 27001 1950 

28' 23 18 13 

9.278 10.051 10.824 11.598 

4.3301 3.557 2.884 2.010 

448° I 389° I 327° 1 265° 

70 65.7 601 52 



FUEL ECONOMIZERS. 



925 



Equation of the Economizer. — Let W= lb. of water evaporated 
by the boiler, under actual conditions of feed-water temperature and 
steam pressure, per lb. of combustible; G = lb. of flue-gas per lb. 
combustible; Ti and Ti = temperatures of gas entering and leaving 
the economizer; ti and tz = temperatures of water entering and leaving 
the economizer; then assuming no loss by radiation and leakage, and 
taking the specific heat of the gas at 0.24 and that of the water at 1, 



t2-'tl- 



0.24G 
W 



(Ti- T2) = F(ri- T2), 



in which F has the values in the following table for given values of 
W and G. 



W = 



10 







F 


= 0.24 G/W, 




G = 18 


0.54 


0.48 


0.43 


0.39 


0.36 


21 


0.63 


0.56 


0.50 


0.46 


0.42 


24 


0.72 


0.64 


0.58 


0.52 


0.48 


27 


0.81 


0.72 


0.65 


0.59 


0.54 


30 


0.90 


0.80 


0.72 


0.65 


0.60 



Ti is usually fixed by the operating conditions of the boiler, and h 
by tlie condenser and feed-water heater conditions. 

Taking Ti at 800°, 700° and 600°, corresponding values of F at 0.49, 
0.39 and 0.36, and ti = 100°, 

t2 - 100 = 0.43(800 - T2) ; let T2 = 300, then ^2 = 0.43(500) -|- 100 =315° 
0.39(700 - T2); 250, 0.39(450) + 100 =266° 

0.36(600 - T2) ; 220, 0.36(380) -\- 100 =237° 

The mean temperature difference between the flue gas and the 
water, 

t ^ Ti + T2 _ 12+ h _ Ti-h-\-T2- h 



For the three cases given tm = 343°, 292°, 242°. 

If w = lb. of water heated by the economizer per hour from h to ^2, 
•S = sq. ft. of economizer surface, and C = heat-units transmitted per 
square foot of surface per hour per degree of mean temperature dif- 
ference, then w{t2— t\) = SCtm. The value of C is given by manu- 
facturers as ranging between 2 and 4 for different conditions of practice. 
It probably increases in some proportion to the increase of tm^ but no 
records of experiments have been pubhshed from which the law of this 
increase may be determined. 

Amount of Heating Surface. — The Fuel Economizer Co. says: We 
have found in practice that by allowing 4 sq. ft. of heating surface per 
boiler H.P. (34 M lb. evap. from and at 212° = 1 H.P.) we are able to 
raise the feed-water 60° F. for every 100' reduction in the temperature, 
the gases entering the economizer at 450° to 600°. With gases at 600° 
to 700° we have allowed a heating surface of 4 V2 to 5 sq. ft. per H.P., 
and for every 100° reduction in temperature of the gases we have 
obtained about 65° rise in temperature of the water; the feed-water 
entering at 60 to 120°. AYith 5000 sq. ft. of boiler-heating surface (plain 
cylinder boilers) developing 1000 H.P. we should recommend 5 sq. ft. of 
economizer surface per boiler H. P. developed, or an economizer of about 
500 tubes, and it should heat the feed-water about 300°. 

Heat Transmission in Economizers. (Carl S. Dow, Indust. Eng'g, 
April, 1909.) — The rate of lieat transmission (C) per sq. ft. per hour per 
degree of difference between the average temperatures of the gases and 
the water passing through the economizer varies with the mean tem- 
perature of the gas about as follows: Gas, 600°, C= 3.25; gas 500°, 
C = 3; gas 400°, C = 2.75; gas 300°, C = 2.25. 

Calculation of the Saving made by an Economizer. — The usual 
method of calculating the saving of fuel by an economizer when the 
boiler and the economizer are tested together as a unit is by the formula 
{Hi - h) -r- {Hi - h), m which h is the total heat above 32° of 1 lb. of 



926 



THE STEAM-BOILER. 



water entering, Hi the total heat of 1 lb. of water leaving the economizer, 
and H2 the total heat above 32° of 1 lb. of steam at the boiler pressure. 
If h = 100, Hi = 210, H2 = 1200, then the saving accordmg to the for- 
mula is (210 - 100) -r 1100 = 10%. This is correct if the saving is 
defined as the ratio of the heat absorbed by the economizer to the total 
heat absorbed by the boiler and economizer together, but it is not 
correct if the saving is defined as the saving of fuel made by running the 
combined unit as compared with running the boiler alone making the 
same quantity of steam from feed-water at the low temperature, so as to 
cause the boiler to furnish H2 — h heat-units per lb. instead of H2 — Hi, 
In this case the boiler is called on to do more work, and in doing it it may 
be overdriven and work with lower efficiency. 

In a test made by F. G. Gasche, in Kansas City in 1897, using Mis- 
souri coal analyzing moisture 7.58; volatile matter, 36.69; fixed carbon, 
35.02; ash, 15.69; sulphur, 5.12, he obtained an evaporation of 5.17 lb. 
from and at 212° per lb. of coal with the boiler alone, and when the 
boiler and economizer were tested together the equivalent evaporation 
credited to the boiler was 5.55, to the economizer 0.72, and to the com- 
bined unit 6.27, the saving by the combined unit as compared with the 
boiler alone being (6.27- 5.17) -v- 6.27= 17.5%, while the saving of 
heat shown by the economizer in the combined test is only (6.27 — 
5.55) -f- 6.27 = 11.5%, or as calculated by IMr. Gasche from the formula 
(Hi - h) ^ {H2 - h), (172.1 - 39.3) -^ (1181.8 -- 39.3) = 11.6%. 

The maximum saving of fuel which may be made by the use of an 
economizer when attached to boilers that are working with reasonable 
economy is about 15 % . Take the case of a condensing engine using 
steam of 125 lb. gage pressure, and with a hot-well or feed-water 
temperature of 100° F. The economizer may be expected under the 
best conditions to raise this temperature about 170° or to 270°. Then 
h = 68, Hi = 239, ^2 = 1190. (Hi- h). -^1{H 2 - h) = 171 -i- 1122 = 15.24%. 

If the boilers are not working with fair economy on account of being 
overdriven, then the saving made by the addition of an economizer may 
be much greater. 

Test of a Large Economizer. (R. D. Tomlinson, Power, Feb., 1904.) 
— Two tests were made of one of the sixteen Green economizers at the 
74th St. Station of the Rapid Transit Railway, New York City. Four 
520-H.P. B. & W. boilers were connected to the economizer. It had 512 
tubes, 10 ft. long, 4 9/15 in. external diam. ; total heating surface 6760 sq. 
ft., or 3.25 sq. ft. per rated H.P. of the boilers. Draught area through 
economizer, 3 sq. in. per H. P. The stack for each 16 boilers and four 
economizers was 280 ft. high, 17 ft. internal diam. The first test was 
made with the boilers driven at 94% of rating, the second at 113%. 
The results are given below, the figures of the second test being in 
parentheses. 

Water entering economizer 96° (93.5°) ; leaving 200° (203.8°) ; rise 
104 (110.3). 

Gases entering economizer 548° (603°) ; leaving 295 (325) ; 
(278). 

Steam, gage pressure, 166 (165). Total B. T.U. per lb. from feed 
temp. 1132 (1134). 

Saving of heat by economizer, per cent, 9.17 (9.73). 

Reduction of draught in passing through economizer, in. of water, 
0.16 (0.23). 

Results from Seven Tests of Sturtevant Economizers (Catalogue of 
B. F. Sturtevant Co.) 



(203.8°) ; : 
drop 253 



Plants 
Tested, 


Gases 


Gases 


Water 


Water 


Increase in 


Entering. 


Leaving. 


Entering. 


Leaving. 


Tempera- 


Deg. F. 


Deg. F. 


Deg. F. 


Deg. F. 


ture. 


I 


650 


275 


]80 


340 


160 


2 


575 


290 


160 


320 


160 


3 


470 


230 


130 


260 


130 


4 


500 


240 


110 


230 


120 


5 


460 


200 


90 


230 


140 


6 


440 


220 


120 


236 


116 


7 


525 


225 


180 


320 


140 



INCRUSTATION AND CORROSION. 927 

Explosions of Economizers. — Explosions of economizers are rare, 
but their possibility sbould be recognized and guarded against. They 
may occur from over-pres.sure, due to closing of the outlet valve or 
other causes, wliich may be prevented by means of a safety valve. 
When the gas inlet damper is closed there is a possibility that it may 
leak combustible gas into the economizer flue, making an explosive 
mixture which might be ignited by a lighted torch. The headers or 
tubes may be weakened by internal or external corrosion, and a rup- 
ture might occur at the normal working pressure. This should be 
guarded against by annual inspection and hydraulic test at 50 per 
cent in excess of the working pressure. 

THERMAL STORAGE. 

In Druitt Halpin's steam storage system (Industries and Iron, Mar. 22, 
1895) he employs only sufficient boilers to supply the mean demand, and 
storage tanks sufficient to supply the maximum demand. These latter 
not being subjected to the fire sutfer but httle deterioration. The boilers 
working continuously at their most economical rate have their excess of 
energy during light load stored up in the water of the tank, from which 
it may be drawn at will during heavy load. He proposes that the boilers 
and tanks shall work under a pressure of 265 lbs. per square inch when 
fully charged, which corresponds to a temperature of 406° F., and that 
the engines be worked at 130 lbs. per square inch, which corresponds to 
347° F. The total available heat stored when the reservoirs are charged 
is that due to a range of 59°. The falUng in temperature of 141/4 lbs. of 
water from 407° to 347° will yield 1 lb. of steam. To allow for radia- 
tion of loss and imperfect working, this may be taken at 16 lbs. of water 
per pound of steam. The steam consumption per effective H.P. maybe 
taken at 18 lbs. per hour in condensing, and 25 lbs. per hour in non-con- 
densing engines. The storage-room per effective H.P. by this method 
would, therefore, be (16 X 18) -J- 62.5= 4.06 cu. ft. for condensing and 
(16 X 25) -i- 62.5 = 6.4 cu. ft. for non-condensing engines. 

Gas storage, assuming that illuminating gas is used, would require 
about 20 cu. ft. of storage room per effective H.P. hour stored, and if 
ordinary fuel gas were stored it would require about four times tliis 
capacity. In water storage 317 cu. ft. would be required at an elevation 
of 100 ft. to store one H.P. hour, so that of the three methods of storing 
energy the thermal method is by far the most economical of space. 

In the steam storage method the boiler is completely filled with water 
and the storage tank nearly so. The two are in free communication by 
means of pipes, and a constant circulation of water is maintained between 
the two, but the steam for the engines is taken only from the top of the 
storage tank through a reducing valve. 

In the feed storage system, the excess of energy during light load is 
stored in the tank as before, but the boilers are not completely filled. In 
this system the steam is taken exclusively from the boilers, the super- 
heated water of the storage tanks being used during heavy load as feed- 
water to the boilers. 

A third method is a combination of these two. In the "combined" 
feed and steam storage system the pressure in boiler and storage tank is 
equahzed by connecting the steam spaces in both by pipe, and the steam 
for the engines is, therefore, taken from both. In other words th^y work 
in parallel. 

liNCRUSTATIGN AND CORROSION. 

Incrustation or Scale. — Incrustation (as distinguished from mere 
sediments due to dirty water, which are easily blown out, or gathered 
up, by means of sediment-collectors) is due to the presence of salts in the 
feed-water (carbonates and sulphates of lime and magnesia for the most 
part), which are precipitated when the water is heated, and form hard 
deposits upon the boiler-plates. (See Impurities in Water, p. 720, ante.) 

Where the quantity of these salts is not very large (12 grains per 
gallon, say) scale preventives may be found effective. The chemical 
preventives either form with the salts other salts soluble in hot water; 
or precipitate them in the form of soft mud, which does not adhere to 
the plates, and can be washed out from time to time. The selection of 
the chemical must depend upon the composition of the water, and it 
should be introduced regularly with the feed. 



928 THE STEAM-BOILER. 

Examples. — Sulphate-of-lime scale prevented by carbonate of soda: 
The sulphate of soda produced is soluble in water; and the carbonate of 
lime falls down in grains, does not adhere to the plates, and may there- 
fore be blown out or gathered into sediment-collectors. The chemical 
reaction is: 

Sulphate of lime + Carbonate of soda = Sulphate of soda + Carbonate of lime 
CaS04 Na2C03 Na2S04 CaCOs 

Where the quantity of salts is large, scale preventives are not of much 
use. Some other source of supply must be sought, or the bad water 
purified before it is allowed to enter the boilers. The damage done to 
boilers by unsuitable water is enormous. 

Pure water may be obtained by collecting rain, or condensing steam 
by means of surface condensers. The water thus obtained should be 
mixed with a Uttle bad water, or treated with a little alkali, as undiluted, 
pure water corrodes iron; or, after each periodic cleaning, the bad water 
may be used for a day or two to put a skin upon the plates. 

Carbonate of lime and magnesia may be precipitated either by heat- 
ing the water or by mixing milk of hme (Porter-Clark process) with it, 
the water being then filtered. 

Corrosion may be produced by the use of pure water, or by the presence 
of acids in the water, caused perhaps in the engine-cylinder by the ac- 
tion of high-pressure steam upon the grease, resulting in the production 
of fatty acids. Acid water may be neutralized by the addition of lime. 

Amount of Sediment which may collect in a 100-H.P. steam-boiler, 
evaporating 3000 lbs. of water per hour, the water containing different 
amounts of impurity in solution provided that no water is blown off : 

Grains of solid impurities per U. S. gallon: 

5 10 20 30 40 50 60 70 80 90 100 

Equivalent parts per 100,000: 

8.57 17.14 34.28 51.42 68.56 85.71 102.85 120 137.1 154.3 171.4 
Sediment deposited in 1 hour, pounds: 

0.257 0.514 1.028 1.542 2.056 2.571 3.085 3.6 4.11 4.63 5.14 
In one day of 10 hours, pounds: 

2.57 5.14 10.28 15.42 20.56. 25.71 30.85 36.0 41.1 46.3 51.4 
In one week of 6 days, pounds: 
15.43 30.85 61.7 92.55 123.4 154.3 185.1 216.0 246.8 277.6 308.5 

If a 100-H.P. boiler has 1200 sq. ft. heating-surface, one week's running 
without blowing off, with water containing 100 grains of solid matter per 
gallon in solution, would make a scale nearly 0.02 in. thick, if evenly depos- 
ited all over the heating-surface, assuming the scale to have a sp. gr. of 
2.5 = 156 lbs. Der cu. ft.: 0.02 X 1200 X 156 X Vis = 312 lbs. 

Effect of Scale on Boiler Efficiency. — The following statement, 
or a similar one, has been pubhshed and repubUshed for 40 years or more 
by makers of "boiler compounds," feed-water heaters and water-puri- 
fying apparatus, but the author has not been able to trace it to its original 
source:* 

*' It has been estimated that scale V.'so of an inch thick requires the 
burning of 5 Der cent of additional fuel: scale V25 of an inch thick 
requires 10 per cent more fuel; Vie of an inch of scale requires 15 per 
cent additional fuel; 1/8 of an inch, 30 per cent., and 1/4 of an inch» ob per 
cent." 

The absurdity of the last statement may be shown by a simple calcu- 
lation. Suppose a clean boiler is giving 75% efficiency with a furnace 
temperature of 2400° F. above the atmospheric temperature, Neglecting 
the radiation and assuming a constant specific heat for the gases, the 
temuerature of the chimney gases will be 600°. A certain amount of 
fuel and air supply will furnish 100 lbs. of gas. In the boiler with 1/4 in. 

' A committee of the Am. Ky. Mast. Mechs. Assn. in 1872 quoted 
from a paper by Dr. Jos. G. Rodgers before the Am. Assn. for Adv. of 
Science (date not stated): "It has been demonstrated [how and by 
whom not stated] that a scale Vie in. thick requires the expenditure of 
15% more fuel As the scale thickens the ratio increases; thus when it 
18 1/4 in. thick, 60% more is required." 



INCRUSTATION AND CORROSION. 929 

scale 66% more fuel will make 66 lbs. more gas. As the extra fuel does 
no work in evaporating water, its heat must all go into the chimney 
gas. We have then in the chimney gases 

100 lbs. at 600° F., product 60,000 
66 lbs. at 2400° F., product 158,400 

which divided by 166 gives 1370° above atmosphere as the temperature 
of the chimney gas, or more than enough to make the flue connection and 
damper red hot. (Makers of boiler compounds, etc., please copy.) 

Another writer says: "Scale of i/ie inch thickness will reduce boiler 
efficiency Vs, and the reduction of efficiency increases as the square of 
the thickness of the scale." 

This is still more absurd, for according to it if i/i8 in. scale reduces the 
efficiency Vs. then 3/ig in. will reduce it 9/8, or to below zero. 

From a series of tests of locomotive tubes covered with different thick- 
nesses of scale up to Vs in. Prof. E. C. Schmidt (Bull. No. 11 Univ. of 
111. Experiment Station, 1907) draws the following conclusions: 

1. Considering scale of ordinary thickness, say varying up to Vs inch, 
the loss in heat transmission due to scale may vary in individual cases 
from insignificant amounts to as much as 10 or 12 per cent. 

2. The loss increases somewhat with the thickness of the scale. 

3. The mechanical structure of the scale is of as much or more impor- 
tance than the thickness in producing this loss. 

4. Chemical composition, except in so far as it affects the structure 
of the scale, has no direct influence on its heat-transmitting qualities. 

In 1896 the author made a test of a water-tube boiler at Aurora. III., 
which had a coating of scale about 1/4 in. thick throughout its whole 
heating surface, and obtained practically the same evaporation as in 
another test, a few days later, after the boiler had been cleaned. This 
is only one case, but the result is not unreasonable when it is known 
that the scale was very soft and porous, and was easily removed from the 
tubes by scraping. 

Prof. R. C. Carpenter {Am. Electrician, Aug., 1900) says: So far as I am 
able to determine by tests, a lime scale, even of great thickness, has no 
appreciable effect on the efficiency of a boiler, as in a test which was 
conducted by myself the results were practically as good when the boiler 
was thickly covered with lime scale as when perfectly clean. . . . Ob- 
servations and experim.ents have shown that any scale porous to water 
has httle or no detrimental effect on economy of the boiler. There 
is, I think, good philosophy for this statement; the heating capacity is 
affected principally by the rapidity vvlth which the heated gases will 
surrender heat, as the water and the metal have capacities for absorbing 
heat more than a hundred times faster than the air will surrender heat. 

A thin film of grease, being impermeable to water, keeps the latter 
from contact with the metal and generally produces disastrous results. 
It is much more harmful than a very thick scale of carbonate of lime.^ 

Boiler-scale Compounds. — The Bavarian Steam-boiler Inspection 
Assn. in 1885 reported as follows: 

Generally the unusual substances in water can be retained in soluble 
form or precipitated as mud by adding caustic soda or hme. This la 
especially desirable when the boilers have small interior spaces. 

It is necessary to have a chemical analysis of the water in order to fully 
determine the kind and quantity of the preparation to be used for the 
above purpose. 

All secret compounds for removing boiler-scale should be avoided. 
(A list of 27 such compounds manufactured and sold by German firms is 
then given wliich have been analyzed by the association.) 

Such secret preparations are either nonsensical or fraudulent, or 
contain either one of the two substances recommended by the association 
for removing scale, generally soda, which is colored to conceal its presence, 
and sometimes adulterated with useless or even injurious matter. 

These additions as well as giving the compound some strange, fanciful 
name, are meant simply to deceive the boiler owner and conceal from him 
the fact that he is buying colored soda or similar substances, for which 
he is paying an exorbitant price. 

Kerosene and other Petroleum Oils: Foaming. — Kerosene has 
been recommended as a scale preventive. See paper by L. F. Lyne 



930 THE STEAM-BOILER. 

(Trans. A, S. M, E., ix. 247). The Am. Mach., May 22, 1890, says: 
Kerosene used in moderate quantities will not make the boiler foam; 
it is recommended and used for loosening the scale and for preventing th© 
formation of scale. The presence of oil in combination with other im- 
purities increases the tendency of many boilers to foam, as the oil with the 
impurities impedes the free escape of steam from the water surface. 
The use of common oil not only tends to cause foaming, but is dangerous 
otherwise. The grease appears to combine with the impurities of the 
water, and when the boiler is at rest this compound sinks to the plates 
and cUngs to them in a loose, spongy mass, preventing the water from 
coming in contact with the plates, and thereby producing overheating, 
which may lead to an explosion. Foaming may also be caused by forcing 
the fire, or by taking the steam from a point over the furnace ox where 
the ebullition is violent ; the greasy and dirty state of new boilers is another 
good cause for foaming. Kerosene should be used at first in small quan- 
tities, the effect carefully noted, and the quantity increased if necessary 
fol obtaining the desired results. 

R. C. Carpenter (Trans. A. S. M. E., vol. xi) says: The boilers of the 
State Argicultural College at Lansing, Mich., were badly incrusted with 
a hard scale. It was fully s/g in. thick in many places. The first appli- 
cation of the oil was made while the boilers were being but little used, 
by inserting a gallon of oil, filling with w^ater, heating to the boiling-point 
and allowing the water to stand in the boiler two or three weeks before 
removal. By this method fully one-half the scale was removed during 
the warm season and before the boilers were needed for heavy firing. 
The oil was then added in small quantities when the boiler was in actual 
use. For boilers 4 ft. in diam. and 12 ft. long the best results were 
obtained by the use of 2 qts. for each boiler per week, and for each boiler 
6 ft. in diam, 3 qts. per week. The water used in the boilers has the fol- 
lowing analysis: CaCOs, 206 parts in a milUon; MgCOs, 78 parts; Fe2C03, 
22 parts; traces of sulphates and chlorides of potash and soda. Total 
solids, 325 parts in 1,000,000. 

Petroleum Oils heavier than kerosene have been used with good re- 
sults. Crude oil should never be used. The more volatile oils it contains 
make explosive gases, and its tarry constituents are apt to form a spongy 
incrustation. 

Removal of Hard Scale. — When boilers are coated with a hard scale 
difficult to remove the addition of 1/4 lb. caustic soda per horse-power, 
and steaming for some hours, according to the tliickness of the scale, just 
before cleaning, will greatly facilitate that operation, rendering the scale 
soft and loose. This should be done, if possible, when the boilers are not 
otherwise in use. (Steam.) 

Corrosion in Marine Boilers. (Proc. Inst. M. E., Aug., 1884.) — 
The investigations of the Committee on Boilers served to show that the 
Internal corrosion of boilers is greatly due to the combined action of air 
and sea-water when under steam, and when not under steam to the com- 
bined action of air and moisture upon the unprotected surfaces of the 
metal. There are other deleterious influences at work, such as the corro- 
sive action of fatty acids, the galvanic action of copper and brass, and the 
inequalities of temperature; these latter, however, are considered to be of 
minor importance. 

Of the several methods recomm.ended for protecting the internal sur- 
faces of boilers, the three found most effectual are: First, the formation 
of a thin layer of hard scale, deposited by working the boiler with sea- 
water; second, the coating of the surfaces with a thin wash of Portland 
cement, particularly wherever there are signs of decay; third, the use of 
Einc slabs suspended in the water and steam spaces. 

As to general treatment for the preservation of boilers when laid up 
In the reserve, either of the two following methods is adopted. First, 
the boilers are dried as much as possible by airing-stoves, after wliich 
2 to 3 cwt. of quicklime is placed on trays at the bottom of the boiler and 
3n the tubes. The boiler is then closed and made as air-tight as possible, 
[nspection is made every six months, when if the lime be found slacked 
t is renewed. Second, the boilers are filled with sea or fresh water, 
laving added soda to it in the proportion of 1 lb. to every 100 or 120 lbs. 
if water. The sufficiency of the saturation can be tested by introducing 
a piece of clean new iron and leaving it in the boiler for ten or twelve 



INCRUSTATION AND CORROSION. 931 

hours: if it shows signs of rusting, more soda should be added. It is 
essential that the boilers be entirely filled, to the complete exclusion of 
air. 

Mineral oil has for many years been exclusively used for internal 
lubrication of engines, with the view of avoiding the effects of fatty acid, 
as this oil does not readily decompose and possesses no acid properties. 

Of all the preservative methods adopted in the British service, the use 
of zinc properly distributed and fixed has been found the most effectual 
in saving the iron and steel surfaces from corrosion, and also in neutral- 
izing by its own deterioration the hurtful influences met with in water as 
ordinarily suppUed to boilers. The zinc slabs now used in the navy 
boilers are 12 in. long, 6 in. wide, and M in. thick; this size being foimd 
convenient for general apphcation. The amount of zinc used in new 
boilers at present is one slab of the above size for every 20 I.H.P., or 
about 1 sq. ft. of zinc surface to 2 sq. ft. of grate surface. Rolled zinc is 
found the most suitable for the purpose. Especial care must be taken 
to insure perfect metalUc contact between the slabs and the stays or 
plates to which they are attached. The slabs should be placed in such 
positions that all the surfaces in the boiler are protected. Each slab 
should be periodically examined to see that its connection remains per- 
fect, and to renew any that may have decayed; this examination is 
usually made at intervals not exceeding three months. Under ordinary 
circumstances of working these zinc slabs may be expected to last in fit 
condition from 60 to 90 days, immersed in hot sea-water; but in new 
boilers they at first decay more rapidly. The slabs are generally 
secured by means of iron straps 2 in. X 3/8 in., and long enough to 
reach the nearest stay, to which the strap is attached by screw-bolts. 

To promote the proper care of boilers when not in use the following 
order has been issued to the French Navy by the Government: On board 
all sliips in the reserve, as well as those which are laid up, the boilers will 
be completely filled with fresh water. In the case of large boilers with 
large tubes there will be added to the water a certain amount of milk of 
lime, or a solution of soda. In the case of tubulous boilers with small 
tubes milk of Ume or soda may be added, but the solution will not be 
so strong as in the case of the larger tube, so as to avoid any danger of 
contracting the elfective area by deposit from the solution; but the 
strength of the solution will be just sufficient to neutraUze any acidity of 
the water. (Iron Age, Nov. 2, 1893.) 

Use of Zinc. — Zinc is often used in boilers to prevent the corrosive 
action of water on the metal. The action appears to be an electrical 
one, the iron being one pole of the battery and the zinc being the other. 
The hydrogen goes to the iron shell and escapes as a gas into the steam. 
The oxygen goes to the zinc. 

On account of tliis action it is generally beUeved that zinc will always 
prevent corrosion, and that it cannot be harmful to the boiler or tank. 
Some experiences go to disprove this belief, and in numerous cases zinc 
has not only been of no use, but has even been harmful. In one case a 
tubular boiler had been troubled with a deposit of scale consisting chiefly 
of organic matter and lime, and zinc was tried as a preventive. The 
beneficial action of the zinc was so obvious that its continued use was 
advised, with frequent opening of the boiler and cleaning out of detached 
scale until all the old scale shoifld be removed and the boiler become 
clean. Eight or ten months later the water-supply was changed, it be- 
ing now obtained from another stream supposed to be free from lime 
and to contain only organic matter. Two or three months after its 
introduction the tubes and shell were found to be coated with an ob- 
stinate adhesive scale, composed of zinc oxide and the organic matter 
or sediment of the water used. The deposit had become so heavy in 
places as to cause overheating and bulging of the plates over the fire. 
(The Locomotive.) 

Effect of Deposit on tlie Fire-surface of Flues. (Rankine.) — An 
external crust of a carbonaceous kind is often deposited from the flame 
and smoke of the furnaces in the flues and tubes, and if allowed to accu- 
mulate, serioiLsly impairs the economy of fuel. It is removed from time 
to time by means of scrapers and wire brushes. The accumulation of 
this crust is the probable cause of the fact that in some steamships the 
consumption of coal per I.H.P. per hour goes on gradually increasing 



932 



THE STEAM-BOILER. 



until it reaches one and a half times its original amount, and sometimes 
more. 

Dangerous Steam-boilers discovered by Inspection. — The Hartford 

Steam-boiler Inspection and Insurance Co. reported in The Locomotive 
the following summary of defects in boilers discovered by its inspectcws 
in the year 1912: 

Number of visits of inspection made 183,519 

Total number of boilers examined 337,178 

Niunber found uninsurable 977 

Whole 

Nature of Defects Number Dangerous 

Cases of sediment or loose scale 26,299 1,553 

Cases of adhering scale 40,336 1,436 

Cases of grooving 2,700 252 

Cases of internal corrosion 15,403 823 

Cases of external corrosion 10,411 895 

Cases of defective bracing 1,391 331 

Cases of defective staybolting 1,712 345 

Settings defective 8,119 768 

Fractured plates and heads 3,288 510 

Bui-ned plates 4,965 517 

Laminated plates 445 55 

Cases of defective riveting 1,816 405 

Cases of leakage around tubes 10,159 1,607 

Cases of defective tubes or flues 11,488 4,780 

Cases of leakage at seams 5,304 401 

Water-gages defective 3,663 816 

Blow-offs defective 4,429 1,398 

Cases of low water 447 151 

Safety-valves overloaded 1,349 380 

Safety-valves defective 1,534 419 

Pressure-gages defective 6,765 568 

Boilers without pressure-gages 633 102 

Miscellaneous defects 2,268 420 

Total 164,924 18,932 

The above-named company publishes annually a summary like the 
above, and also a classified list of boiler-explosions, compiled chiefly from 
newspaper reports, showing that from 200 to 300 explosions take place in 
the United States every year, killing frorh 200 to 300 persons, and in- 
juring from 300 to 450. The Usts are not pretended to be complete, and 
may include only a fraction of the actual number of explosions. 

Steam-boilers as Magazines of Explosive Energy. — Prof. R. H, 
Thurston {Trans. A. S. M. E., vol. vi), in a paper with the above title, 
presents calculations showing the stored energy in tlie hot water and 
steam of various boilers. Concerning the plain tubular boiler of average 
form and dimensions he says: It is 60 in. in diameter, containing 66 
3-in. tubes, and is 15 ft. long. It has 850 sq. ft. of heating and 30 sq. ft. of 
grate surface; is rated at 60 H.P., but is oftener driven up to 75; weighs 
9500 lb., and contains nearly its own weight of water, but only 21 lb. 
of steam when under a pressure of 75 lb. per sq. in., which is below its 
safe allowance. It stores 52,000,000 foot-pounds of energy, of which 
but 4% is in the steam, and this is enough to drive the boiler just about 
one mile into the air, with an initial velocity of nearly 600 ft. per second. 

SAFETY-VALVES. 

Calculation of Weight, etc., for Lever Safety-valves. 

Let W = weight of ball at end of lever; w = weight of lever itself; V = 
weight of valve and spindle, all in poimds; L = distance between fid- 
crum and center of ball; I = distance between fulcrum and center of 
valve; g = distance between fulcrum and center of gravity of lever, all in 
inches; A = area of valve, in sq. in.; P = pressure of steam, in lb. per 
sq. in., at which valve will open. 



SAFETY-VALVES. 933 

Then PAX I = WX L+ wx 9+ VX I; ,^. ^ ^ 

whence P = {WL -^ wg -\- VI) -- Al; W = {PAl - w.'^ - VO ^ L; L = 
{PAl -wg- VI) -r W. 

EXAMPLE. — Diameter of valve, 4 in. ; distance from fulcrum to center 
of ball, 36 in. ; to center of valve, 4 in. ; to center of gravity of lever, 
15 3^^ in.; weight of valve and spindle, 3 lb.; weight of lever, 7 lb.; re- 
quired the weight of ball to make the bio wing-off pressure 80 lib. per sq. 
in.; area of 4-in- valve = 12.566 sq. in. Then 

^ PAl -wg -Vl ^ SOX 12.566x4-7X151/2-3X4 ^ ^^g ^ „ 
L 36 ' ' 

By the rules of the U. S. Supervising Inspectors of Steam Vessels the 
use of lever safety-valves is prohibited on all boilers built for steam 
vessels after Jime 30, 1906, 

A method for calculating the size of safety-valve is given in The Loco- 
motive, July, 1892, based on the assumption that the actual opening 
should be sufficient to discharge all the steam generated by the boiler. 
Napier's rule for flow of steam is taken, viz., flow through aperture of one 
sq. in. in lbs. per second = absolute pressure -^ 70, or in lbs. per hour = 
51.43 X absolute pressure. 

If the angle of the seat is 45°, the area of opening in sq. m. = circum- 
ference of the disk X the lift X 0.71, 0.71 being the cosine of 45°; or 
diameter of disk X hft X 2.23. 

Spring-loaded Safety-Valtes. 

Spring-loaded safety-valves to be used on U. S. merchant vessels must 
conform to the rules prescribed by the Board of Supervising Inspectors, 
and on vessels for the U. S. Navy to specifications made by the Bureau 
of Steam Engineering, U. S. N. Valves to be used on stationary boilers 
must conform in many cases to the special laws made by various states. 
Few of these rules are on a logical basis, in that they take no account of 
the lift of the valve, and it is quite clear that the rate of steam discharge 
through a safety-valve depends upon the area of opening, which varies 
with the circumference of the valve and the lift. Experiments made by 
the ConsoUdated Safety Valve Co. showed that valves made by the differ- 
ent manufacturers and employing various combinations of springs with 
different designs of valve lips and huddling chambers give widely different 
lifts. Lifts at popping point of different makes of safety-valves, at 200 
lbs. pressure, are as follows: 

4-in. stationary valves, in., 0.031, 0.056, 0.064, 0.082, 0.094, 0.094, 0.137. 

Av. 0.079 in. 
3V2-in. locomotive valves, in., 0.040, 0.051, 0.065, 0.072, 0.076, 0.140 ins. 

Av. 0.074 in. 

United States Supervising Inspectors* Rule (adopted in 1904). A = 
0.2074 W/P. A = area of safety valve in sq. in. per sq. ft. of grate 
surface; W = lbs. of water evaporated per sq. ft. of grate surface per 
hour; P = boiler pressure, absolute, lbs. per sq. in. This rule assumes 
a lift of 1/32 of the nominal diameter, and 75% of the flow calculated by 
Napier's rule. This 75% corresponds nearly to the cosine of 45°, or 0.707. 

Massachusetts Rule of 1909. A = 770 W/P, in which W = lbs. evapo- 
rated per sq. ft. of grate per second; A and P as above. This is the 
same as the U. S. rule with o. 3.2% larger constant. 

Philadelphia Rule. — A = 22.5 (? -J- (P+ 8.62). A = total area of 
valve or valves, sq. in.; G = grate area, sq. ft.; P = boiler pressure 
(gauge). This rule came from France in 1868. It was recommended 
to the city of Philadelphia by a committee of the Franklin Institute, 
although the committee "had not found the reasoning upon which the 
rule had been based." 

Philip G. Darling (Trans. A. S. M. E., 1909) commenting on the above 
rules says: The principal defect of these rules is that they assume that 
valves of the same nominal size have the same capacity, and they rate 
them the same without distinction, in spite of the fact that in actual prac- 
tice some have but one-third of the capacity of others. There are other 
defects, such as varying the assumed lift as the valve diameter, while in 



934 



THE STEAM-BOILER. 



reality with a given design the lifts are more nearly the same in the dif- 
ferent sizes, not varying nearly as rapidly as the diameters. And 
further than this, the actual hfts assumed for the larger valves are 
nearly double the actual average obtained in practice. The direct con- 
clusion is that existing rules and statutes are not safe to follow. 

Rules of the A. S. M. E. Boiler Code Committee.— In 1914 the Com- 
mittee had several conferences with the principal safety-valve manu- 
facturers of the country and an agreement was finally reached on the 
rules given in condensed form below. The discharging capacity of a 
valve is based on Napier's rule with a coefficient of discharge of 0.96. 
The formula being W = 3600 X 3.1416 XDLX 0.96 X 0.707 X P/70 
or W = 109.66 Z) L P pounds per hour for a 45° bevel seat valve. 
For flat seat valves the factor 0.707 is omitted and the formula becomes 
W = 155.11 DLP pounds per hour. The following table is calcu- 
lated from the first formula. 

Discharge Capacities of Direct Spring -Loaded Pop Safety- Valves with 
45° Bevel Seats. Pounds per Hour. 



o5.S 


Diam. 1 in. 


Diam. IV2 in. 


Diam. 2 in. 


Diam. 2^^ in. 


2 a- 
















^flP 


Lift, in. 


/^rO 


Min. 


Int. 


Max. 


Min. 


Int. 


Max. 


Min. 


Int. 


Max. 


Min. 


Int. 


Max. 


0=5 


0.02 


0.04 


0.05 


0.03 


0.05 


0.06 


0.04 


0.06 


0.07 


0.04 


0.06 


0.08 


15 


65 


131 


163 


146 


245 


293 


261 


391 


456 


326 


488 


651 


25 


87 


174 


218 


196 


326 


392 


349 


523 


610 


435 


653 


871 


50 


142 


284 


354 


320 


532 


639 


568 


851 


994 


710 


1064 


1419 


75 


197 


393 


492 


443 


738 


886 


787 


1181 


1377 


984 


1475 


1968 


100 


252 


503 


629 


566 


944 


1133 


1007 


1510 


1761 


1258 


1887 


2516 


125 


307 


613 


767 


689 


1149 


1379 


1224 


1836 


2145 


1532 


2299 


3064 


150 


362 


723 


904 


813 


1355 


1625 


1438 


2158 


2529 


1806 


2710 


3613 


175 


416 


833 


1040 


936 


1561 


1872 


1664 


2497 


2913 


2081 


3121 


4161 


200 


471 


941 


1178 


1060 


1766 


2119 


1884 


2826 


3296 


2354 


3532 


4709 


225 


526 


1052 


1315 


1183 


1972 


2366 


2104 


3154 


3680 


2629 


3944 


5258 


250 


581 


1161 


1451 


1307 


2177 


2613 


2322 


3484 


4064 


2903 


4355 


5807 


275 


635 


1271 


1589 


1430 


2383 


2860 


2542 


3813 


4448 


3177 


4766 


6355 


300 


698 


1397 


1746 


3155 


2589 


3107 


2762 


4143 


4832 


3452 


5177 


6903 









Capacities of Safety- Valves. — Continued. 






•.2 


Diam. 3 in. 


Diam. 3 V2 in. 


Diam. 4 in. 


Diam. 4i^ in. 


i w 
^ J 


Lift, in. 


f5 


Min. 


Int. 


Max. 


Min. 


Int. 


Max. 


Min. 


Int. 


Max. 


Min. 


Int. 


Max. 


0:ti 


0.05 


0.08 


0.10 


0.06 


0.09 


0.11 


0.07 


0.10 


0.12 


0.08 


0.11 


0.13 


15 


489 


782 


977 


684 


1026 


1254 


912 


1303 


1564 


1173 


1613 


1906 


25 


653 


1046 


1307 


914 


1372 


1676 


1219 


1742 


2090 


1568 


2156 


2547 


50 


1064 


1703 


2129 


1490 


2235 


2732 


1987 


2839 


3406 


2555 


3513 


4151 


75 


1475 


2361 


2951 


2066 


3099 


3788 


2754 


3935 


4722 


3542 


4870 


5756 


100 


1887 


3019 


3774 


2642 


3963 


4843 


3522 


5032 


6038 


4529 


6227 


7358 


125 


2299 


3677 


4596 


3218 


4826 


5899 


4290 


6128 


7354 


5516 


7583 


8963 


150 


2710 


4335 


5419 


3794 


5690 


6954 


5058 


7226 


8670 


6503 


8940 


10566 


175 


3121 


4993 


6242 


4369 


6553 


8010 


5824 


8320 


9984 


7490 


10298 


12173 


200 


3532 


5651 


7064 


4946 


7418 


9068 


6593 


9420 


11305 


8475 


11655 


13773 


225 


3944 


6310 


7890 


5521 


8280 


10120 


7361 


10514 


12616 


9465 


13013 


15383 


250 


4355 


6968 


8708 


6097 


9143 


11175 


8130 


11614 


13938 


10448 


14366 


16980 


275 


4766 


7620 


9533 


6672 


10005 


12333 


8895 


12707 


15248 


11438 


15728 


18585 


300 


5177 


8280 


10358 


7248 


10875 


13290 


9668 


13807 


16568 


12428 


17088 


20195 



Safety-Valve Requirements. — Each boiler shall have two or more 
safety-valves, except a boiler for wliich one safety-valve 3-in. size or 
smaller is required by these Rules. 

The safety-valve capacity for each boiler shall be such that the 
safety-valve or valves will discharge all the steam that can be generated 



SAFETY-VALVES. 935 

by the boiler without allowing the pressure to rise more than 6 % above 
the maximum allowable working pressure, or more than 6 % above the 
highest pressure to which any valve is set. 

One or more safety-valves on every boiler shall be set at or below 
the maximum allowable working pressure. The remaining valves may 
be set within a range of 3% above the maximum allowable working 
pressure, but the range of setting of all of the valves on a boiler shall 
not exceed 10% of the highest pressure to which any valve is set. 

Safety-valves shall be of the direct spring-loaded pop type. The 
vertical lift of the valve disk may be made any amount desired up to a 
maximum of 0.15 in. The diameter measured at the inner edge of the 
valve seat shall be not less than 1 in. or more than 4 3^ in. 

Each safety-valve shall have plainly stamped or cast on the body: 
(a) The name or trade-mark of the manufacturer, (b) The nominal 
diameter with the words " Bevel Seat" or " Flat Seat." (c) The steam 
pressure at which it is set to blow, (d) The lift of the valve disk from 
its seat, measured immediately after .the sudden lift due to the pop. 
(e) The weight of steam discharged in pounds per hour at the pressure 
for which it is set to blow. 

The minimum capacity of a safety-valve or valves to be placed on a 
boiler shall be determined on the basis of 6 lb. of steam per hour per 
sq. ft. of boiler heating surface for water tube boilers, and 5 lb. for all 
other types of power boilers, and upon the relieving capacity marked 
on the valves by the manufacturer, provided such marked capacity 
does not exceed that given in the table, in which case the minimum 
safety-valve capacity shall be determined on the basis of the maximum 
relieving capacity given in the table for the particular size of valve and 
working pressure for which it was constructed. The heating surface 
shall be computed for that side of the boiler surface exposed to the 
products of combustion, exclusive of the superheating surface. 

Valves 1 }4 in. diam. with Ufts 0.03, 0.04 and 0.05 in. give a discharge 
for 0.04-in. lift the same as that of a 1-in. valve with 0.05-in. lift; with 
0.03-in. Uft 25% less and with 0.05-in. lift 25% greater. 

The discharge capacity of a fl^t seat valve is 1.41 times that of a 
45° bevel seat valve of the same diameter and Uft. 

Safety-valves for Locomotives.— A CommitteeoftheAmericanRailway 
Master Mechanics Association presented a report on safety-valves in 
1912, giving the following formula for 45° bevel seat valves: D L P = 
0.036 H, in which D = total of the diameters of the inner edge of 
the seats of the valves required; L = vertical lift in inches; P = 
absolute pressure, lb. per sq. in. ; H = total heating surface of boiler, 
sq. ft. (superheating surface not Included). Every locomotive should 
be equipped with not less than two and not more than three safety- 
valves, the size to be determined by the formula. The valves are to 
be set as follows: The first at boiler pressure, second 2 lb. in excess, 
third 3 lb. in excess of the second. Manufacturers should be required 
to stamp on the valve the Uft in inches as determined by actual test. 

The formula corresponds to the discharge calculated by Napier's 
rule with a coefficient of flow of 0.973 and an evaporation of 4 lb. per 
square foot of heating surface per hour. It is evident that safety- 
valves proportioned according to this formula will have a relieving 
capacity much less than the evaporative capacity of locomotive 
boilers with large fire-boxes and short flues. The Consolidated Safety 
Valve Co. suggests the formula D L P = Ci Hi -i- C2 H2 in which Hi is 
fire-box and H2 flue heating-surface, sq. ft., and Ci and C2 are constants 
to be determined by experiment. Ci being considerably larger than C2. 

Unequal expansion of safety-valve parts under steam temperatures 
tends to cause leakage, and as this temperature effect becomes more 
serious in the large sizes the manufacturers do not recommend the use 
of valves larger than 4 1/2 ins. If greater relieving capacity be required 
it is the best practice to use duplex valves or additional single valves. 

For an extended discussion on safety-valves, see Trans. A. S. M. E , 



936 



THE STEAM-BOILER. 



THE EVJECTOE. 

Equation of the Injector. 

Let S be the number of pounds of steam used; , , . *v u n^« 

W the number of pounds of water lifted and forced into the boiler; 

h the height in feet of a column of water, equivalent to the absolute 

pressure in the boiler; 
ho the height in feet the water is lifted to the injector; 
ti the temperature of the water before it enters the injector; 
t2 the temperature of the water after leaving the injector; 
H the total heat above 32° F. in one pound of steam in the boiler, 
in heat-units: , , ^ , ■, x ^i *i ^ 

L the work in friction and the equivalent lost work due to radiation 

and lost heat; 
778 the mechanical equivalent of heat. 
Then 

S[H- a.-32»)] = TF((.- h) + ^^±^if^^^^^^. 
An equivalent formula, neglecting Who + L as small, is 



or S = 



[17(^2 
W{{t2- 



-ii) + 



W-\- S 



1441 



1 



■tx) d + 0.1851 y] 



778J /f-((2-32°) 



[/i^ - ^2 - 32°)] d - 0.1851 p * 
In which d = weight of 1 cu. ft. of water at temperature t2', p = absolute 
pressure of steam, lbs. per sq. in. 

The rule for finding the proper sectional area for the narrowest part of 
the nozzles is given as follows by Rankine, S. E., p. 477: 



Area in square inches = 



cubic feet per hour gross feed-water 
800 >/pressure in atmospheres 



An important condition which must be fulfilled in order that the injec- 
tor will work is that the supply of water must be sufficient to condense 
the steam. As the temperature of the supply or feed-water is higher, 
the amount of water required for condensing purposes will be greater. 

The table below gives the calculated value of the maximum ratio of 
water to the steam, and the values obtained on actual trial, also the 
highest admissible temperature of the feed-water as shown by theory 
and the highest actually found by trial with several injectors. 





Maximum Ratio Water 
to Steam. 


Gauge- 
pres- 
sure, 

pounds 
per 

sq. in. 


Maximum Temperature 
of Feed- Water. 


Gauge- 
pres- 
sure, 
pounds 


Calculated 

from 

Theory. 


Actual Ex- 
periment. 


Theoreti- 
cal. 


Experimental 
Results. 


73 


. to 

■'3 


H. 


p. 


M. 




per 
sq. in. 


H. 


P. 


M. 


S. 


10 


36.5 

25.6 

20.9 

17.87 

16.2 

14.7 

13.7 

12.9 

12.1 

11.5 


30.9 
22.5 
19.0 
15.8 
13.3 
11.2 
12.3 
11.4 






10 
20 
30 
40 
50 
60 
70 
80 
90 
100 
120 
150 








137° 


20 
30 


19.9 21.5 
17 2| 19 


142° 
132 
126 
120 
114 
109 
105 
99 
95 
87 
77 


173° 

162 

156 

150 

143 

139 

134 

129 

125 

117 

107 


135° 


120° 


130° 


134 
134 


40 
50 


15.0 
14.0 
11.2 
11.7 
11.2 


15.86 
13.3 
12.6 
12.9 


140 


113 


125 


132 
131 


60 
70 
80 
90 


141* 


115 
1*18 


123 
123 
122 


130 
130 
131 
13?* 


100 














13?* 
















134* 










121* 



* Temperature of delivery above 212°. Waste-valve closed. 
H, Hancock inspirator; P, Park injector; M, Metropolitan injector; 
S, Sellers 1876 injector. 



THE INJECTOR. 937 

Efficiency of the Injector. — Experiments at Cornell University 
described by Prof. R. C. Carpenter, in Cassier^s Magazine, Feb., 1892 
show that the injector, when considered merely as a pump, has an exceed- 
ingly low efficiency, the duty ranging from 161,000 to 2,752,000 undei 
different circumstances of steam and delivery pressure. Small direct- 
acting pumps, such as are used for feeding boilers, show a duty of from 
4 to 8 million ft .-lbs., and the best pumping-engines from 100 to 140 mil- 
lion. When used for feeding water into a boiler, however, the injector 
has a thermal efficiency of 100%, less the trifling loss due to radiation, 
since all the heat rejected passes into the water which is carried into the 
boiler. 

The loss of work in the injector due to friction reappears as heat which 
is carried into the boiler, and the heat which is converted into useful 
work in the injector appears in the boiler as stored-up energy. 

Although the injector thus has a perfect efficiency as a boiler-feeder, it 
is not the most economical means for feeding a boiler, since it can draw 
only cold or moderately warm water, while a pump can feed water which 
has been heated by exhaust steam which would otherwise be wasted. 

Performance of Injectors. — In Am. Mach., April 13, 1893, are a 
number of letters from different manufacturers of injectors in reply to the 
question: "What is the best performance of the injector in raising or 
lifting water to any height?" Some of the replies are tabulated below. 

W. Sellers & Co. — 25.51 lbs. water delivered to boiler per lb. of steam; 
temperature of water, 64°; steam pressure, 65 lbs. 

Schaeffer & Budenberg — 1 gal. water delivered to boiler for 0.4 to 
0.8 lb. steam. 

Injector will lift by suction water of 

140° F. 136° to 133° 122° to 118° 113° to 107® 

If boiler pres. is 30 to 60 lbs. 60 to 90 lbs. 90 to 120 lbs. 120 to 150 lbs. 
If the water is not over 80° F., the injector will force against a pres- 
sure 75 lbs. higher than that of the steam. 

Hancock Inspirator Co.; 

Lift in feet 22 22 22 11 

Boiler pressure, absolute, lbs 75.8 54.1 95.5 75.4 

Temperature of suction 34 . 9° 35 . 4*^ 47 . 3° 53 . 2'' 

Temperature of deUvery 134° 117.4° 173 .7° 131 . 1^ 

Waterfedperlb. of steam. lbs 11.02 13.67 8.18 13.3 

The theory of the injector is discussed in Wood's, Peabody's, and 
Rontgen's treatises on Thermodynamics. See also " Theory and Practice 
of the Injector," by Strickland L. Kneass, New York, 1910. 

Boiler-feeding Pumps. — Since the direct-acting pump, commonly 
used for feeding boilers, has a very low efficiency, or less than one-tenth 
that of a good engine, it is generally better to use a pump driven by belt 
from the main engine or driving shaft. The mechanical work needed to 
feed a boiler may be estimated as follows: If the combination of boiler 
and engine is such that half a cubic foot, say 32 lbs. of water, is needed 
per horse-power, and the boiler-pressure is 100 lbs. per sq. in., then the 
work of feeding the quantity of water is 100 lbs. X 144 sq. in. X V2 ft.- 
Ib. per hour = 120 ft.-lbs. per min. = 120/33,000 = .0036 H.P., or less 
than 4/10 of 1% of the power exerted by the engine. If a direct-acting 
pump, which discharges its exhaust steam into the atmosphere, is used 
for feeding, and it has only 1/10 the efficiency of the main engine, then the 
steam used by the pump will be equal to nearly 4% of that generated by 
the boiler. 

The low efficiency of boiler-feeding pumps, and of other small auxiliary 
steam-driven machinery, is, however, of no importance if all the exhaust 
steam from these pumps is utilized in heating the feed-water. 

The following table by Prof. D. S. Jacobus gives the relative steam 
consumption of steam and power pumps and injector, with and with- 
out heater, as used upon a boiler with 80 lbs. gauge-pressure, the pump 
having a duty of 10,000,000 ft.-lbs. per 100 lbs. of coal when no heater 
Is used; the injector heating the water from 60° to 150° F. 

Direct-acting pump feeding water at 60°, without a heater 1 .000 

Injector feeding water at 150°, without a heater 0.985 

Injector feeding water through a heater in which it is heated from 

, 160° to 200° 0.938 



938 



THE STEAM-BOILER. 



Direct-actinp: pump feeding water through a heater, in which it Is 

heated from 60° to 200° . 879 

Geared pump, run from the engine, feeding water through a heater, 

in which it is heated from 60° to 200° .868 

Gravity Boiler-feeders. — If a closed tank be placed above the level 
of the water in a boiler and the tank be filled or partly filled with water, 
then on shutting off the supply to the tank, admitting steam from the 
boiler to the upper part of the tank, so as to equalize the steam-pressure 
in the boiler and in the tank, and opening a valve in a pipe leading from 
the tank to the boiler, the water will run into the boiler. An apparatus 
of this kind may be made to work with practically perfect efficiency as a 
boiler-feeder, as an injector does, when the feed-supply is at ordinary 
atmospheric temperature, since after the tank is emptied of water and the 
valves in the pipes connecting it with the boiler are closed the conden- 
sation of the steam remaining in the tank will create a vacuum which will 
lift a fresh supply of water into the tank. The only loss of energy in the 
cycle of operations is the radiation from the tank and pipes, which may 
be made very small by proper covering. 

When the feed-water supply is hot, such as the return water from a 
heating system, the gravity apparatus may be made to work by having 
two receivers, one at a low level, which receives the returns or other 
feed-supply, and the other at a point above the boilers. A partial vacuum 
being created in the upper tank, steam-pressure is applied above the 
water in the lower tank by which it is elevated into the upper. The 
operation of such a machine may be made automatic by suitable arrange- 
ment of valves. 

FEED-WATER HEATERS. 

Percentage of Saving for Each Degree of Increase in Temperature 
of Feed-water Heated by Waste Steam. 



Initial 


Steam Pressure in Boiler, lbs. per sq. in. above Atmosphere. 




Temp. 

of 
Feed. 




Initial 





20 


40 


60 


80 


100 


120 


140 


160 


180 


200 


Temp. 


32° 


0877. 


.0861 


.0855 


.0851 


.0847 


.0844 


.0841 


.0839 


.0837 


.0835 


.0833 


32^ 


40 


0878 


.0867 


.0861 


.0856 


.0853 


.0850 


.0847 


.0845 


.0843 


.0841 


.0839 


40 


50 


0886 


.0875 


.0868 


.0864 


.08o0 


.0857 


.0854 


.0852 


.0850 


.0848 


.0846 


50 


60 


0894 


,0883 


.0876 


.0872 


.0807 


.0864 


.0862 


.0859 


.0856 


.0855 


.0853 


60 


70 


090?. 


.0890 


.0884 


.0879 


.0875 


.0872 


.0869 


.0867 


.0864 


.0862 


.0860 


70 


80 • 


0910 


0898 


.0891 


.0887 


.0883 


.0879 


.0877 


.0874 


.0872 


.0870 


,0868 


60 


90 


0919 


,0907 


.0900 


.0895 


.0888 


.0887 


.0884 


.0883 


.0879 


.0877 


.0875 


90 


100 


097,7 


.0915 


.0908 


.0903 


.0899 


.0895 


.0892 


.0890 


.0887 


.0885 


.0883 


100 


110 


0936 


.0923 


.0916 


.0911 


.0907 


.0903 


.0900 


.0898 


.0895 


.0893 


.0891 


110 


120 


0945 


.0932 


.0925 


.0919 


.0915 


.0911 


.0908 


.0906 


.0903 


.0901 


.0899 


120 


130 


0954 


.0941 


.0934 


.0928 


.0924 


.0920 


.0917 


.0914 


.0912 


.0909 


.0907 


130 


MO- 


0963 


.0950 


.0943 


.0937 


.0932 


.0929 


.0925 


.0923 


.0920 


.0918 


.0916 


140 


ISO 


0973 


.0959 


.0951 


.0946 


.0941 


.0937 


.0934 


.0931 


.0929 


.0926 


.0924 


150 


160 


0982 


.0968 


.0961 


.0955 


.0950 


.0946 


.0943 


.0940 


.0937 


.0935 


.0933 


160 


170 


0992 


.0978 


.0970 


.0964 


.0959 


.0955 


.0952 


.0949 


.0946 


.0944 


.0941 


170 


180 


1002 


.0988 


.0981 


.0973 


.0969 


.0965 


.0961 


.0958 


.0955 


.0953 


.0951 


180 


190 


1012 


.0998 


.0989 


.0983 


.0978 


.0974 


.0971 


.0968 


.0964 


.0962 


.0960 


190 


200 


,1022 


.1008 


.0999 


.0993 


.0988 


.0984 


.0980 


.0977 


.0974 


.0972 


.0969 


200 


210 


,1033 


.1018 


.1009 


.1003 


.0998 


.0994 


.0990 


.0987 


.0984 


.0981 


.0979 


210 


220 




.1029 


.1019 


.1013 


.1008 


.1004 


.1000 


.0997 


.0994 


.0991 


.0989 


220 


230 




.1039 


.1031 


.1024 


.1018 


.1012 


.1010 


.1007 


.1003 


.1001 


.0999 


230 


240 




,1050 


.1041 


,1034 


.1029 


.1024 


.1020 


,1017 


.1014 


.1011 


,1009 


240 


250 




.1062 


.1052 


.1045 


.1040 


.1035 


.1031 


.1027 


.1025 


.1022 


.1019 


250 



An approximate rule for the conditions of ordinary practice is that a 
saving of 1% is made by each increase of 11° in the temperature of the 
feed-water. This corresponds to 0.0909% per degree. 

The calculation of saving is made as follows: Boiler-pressure, 100 lbs. 
gauge; total heat in steam above 32° = 1185 B.T.U. Feed-water, original 
temperature 60°, final temperature 209° F. Increase in heat-units, 150. 



FEED-WATER HEATERS. 939 

Heat-units above 32° in feed-water of original temperature = 28. Heat- 
units in steam above that in cold feed-water, 1185 — 28 = 1157. Saving 
by the feed-water heater = 150/1157 = 12.96%. The same result is 
obtained by the use of the table. Increase in temperature 150° X 
tabular figure 0.0864 = 12.96%. Let total heat of 1 lb. of steam at the 
boiler-pressure = H\ total heat of 1 lb. of feed-water before entering the 
heater = hi, and after passing through the heater = h2\ then the saving 

made by the heater is tt _ j. * 

Strains Caused by Cold Feed-water. — A calculation is made in 
The Locomotive of March, 1893, of the possible strains caused in the sec- 
tion of the shell of a boiler by cooUng it by the injection of cold feed- 
water. Assuming the plate to be cooled 200° F., and the coefficient of 
expansion of steel to be 0.0000067 per degree, a strip 10 in. long would 
contract 0.013 in., if it were free to contract. To resist this contraction, 
assuming that the strip is firmly held at the ends and that the modulus 
of elasticity is 29,000,000, would require a force of 37,700 lbs. per sq. in. 
Of course this amount of strain cannot actually take place, since the strip 
Is not firmlv held at the ends, but is allowed to contract to some extent 
by the elasticity of the surrounding metal. But, says The Locomotive, 
we may feel pretty confident that in the case considered a longitudinal 
strain of somewhere in the neighborhood of 8,000 or 10,000 lbs. per sq. in. 
may be produced by the feed-water striking directly upon the plates; 
and this, in addition to the normal strain produced by the steam-pressure, 
is quite enough to tax the girth-seams beyond their elastic limit, if the 
feed-pipe discharges anywhere near them. Hence it is not surprising that 
the girth-seams develop leaks and cracks in 99 cases out of every 100 in 
wliich the feed discharges directly upon the fire-sheets. 

Capacity of Feed-water Heaters. (W. R. Billings, Eng. Rec, 
Feb., 1898.) — Closed feed-water heaters are seldom provided with 
sufficient surface to raise the feed temperature to more than 200°. The 
rate of heat transmission may be measured by the number of British 
thermal units which pass through a square foot of tubular surface in one 
hour for each degree of difference in temperature between the water and 
the steam. One set of experiments gave results as below: 





r 5°F... 


... 67 B.T.U. 


Transmitted in one 


Difference between 


6° ".... 


...79 


hour by each sq. ft. 


final temperatures 


8° ".... 


...89 " 


of surface for each 


of water and 


11° ".... 


...114 '* 


degree of average 


steam 


15° •'.... 


...129 


difference in temper- 




L 18° ".... 


...139 " J 


atures. 



Even with the rate of transmission as low as 67 B.T.U. the water was 
still 5° from the temperature of the steam. At what rate would the heat 
have been transmitted if the water could have been brought to within 
2° of the temperature of the steam, or to 210° when the steam is at 212°? 

For commercial purposes feed-water heaters are given a H.P. rating 
which allows about one-third of a square foot of surface per H.P. — a 
boiler H.P. being 30 lbs. of water per hour. If the figures given in the 
table above are accepted as substantially correct, a heater which is to 
raise 3000 lbs. of water per hour from 60° to 207°, using exhaust steam 
at 212° as a heating medium, should have nearly 84 sq. ft. of heating 
surface or nearly a square foot of surface per H.P. That feed-water 
heaters do not carry this amount of heating surface is well known. 

Calculation of Surface of Heaters and Condensers. — (B.. L. Hep^ 
burn, Power, April, 1902.) Let W = lbs. of water per hour; A = area of 
surface in sq. ft.; Ts = temperature of the steam; / = initial tempera- 
ture of the water; F = final temperature of the water; S = lbs. of steam 
per hour; H = B.T.U. above 32° P. in 1 lb. of steam; N = B.T.U. in 
1 lb. of condensed steam; U = B.T.U. transmitted per sq. ft. per hr. per 
deg. of mean difference of temperature between the steam and the water. 

m r 

Then AU = W loge ^ ^ , for heaters. 



Ts 

• N 



„H - N Ts - I 

AU — S -^ z- X loge 7i^ B . for condensers. 



940 



THE STEAM-BOILER. 



The value of U varies widely according to the condition of the surface 

whether clean or coated with grease or scale, and also with the velocity 
of the water over the surfaces. Values of 300 to 350 have been obtained 
in experiments with corrugated copper tubes, but ordinary heaters give 
much lower values. From the experiments of Loring and Emery on the 
U. S. S. Dallas, Mr. Hepburn finds U = 192. Using this value he finds 
the number of square feet of heating surface required per 1000 lbs. of 
feed-water per hour to be as follows, the temperature of the entering 
water being 60° F. 



Steam Temperature, 212°. 


Steam 25 in. Vacuum. 


F 


S 


F S 


F 


s 


F 


S 


194 
196 
198 
200 
202 


11.11 
11.73 
12.44 
13.20 
14.17 


204 
206 
208 
210 
212 


15.34 
16.85 
18.93 
22.52 
Infinite 


90 
95 
100 
105 
110 


2.38 
3.03 
3.76 
4.62 
5.65 


115 
120 
125 
130 
133 


6.78 
8.60 
11.15 

16.25 
Infinite 



F = final temperature of feed- water, S = sq. ft. of surface. From this 
table it is seen that if 30 lbs. of water per hour is taken to equal 1 H.P. 
and a feed-water heater is made with 1/3 sq. tt. per H.P., it may be ex- 
pected to heat the feed-water from 60° to something less than 194°, or ii 
made with 1/2 sq. ft. per H.P. it may heat the water to 204° F. 

For a further discussion of this subject, see Heat, pages 587 to 591. 

Proportions of Open Type Feed-water Heaters. — C. L. Hubbard 
{Practical Engineer, Jan. 1, 1909) gives the fohowing: 

Exhaust heaters should be proportioned according to the quality of 
the water to be used, the size being increased with the amount of mud 
or scale-producing properties which the water contains regardless of the 
quantity of water to be heated. The general proportions of an open 
heater will depend somewhat upon the arrangement of the trays or pans, 
but an approximation of the size of sheU for a cyhndrical heater is as 
follows: A = H -T- aL; L = H -^ a^; in which A == sectional area of shell 
in sq. ft.; L = length of sheU in hnear ft.; // = total weight of water to 
be heated per hour divided by the weight of steam used per horse-power 
per hour by the engine; a = 2.15 for very muddy water, 6.0 for shghtly 
muddy water, and 8.0 for clear water. 

The pan or tray surface varies according to the quality of the water, 
both as regards the amount of mud and the scale-making ingredients. 
The surface in square feet for each 1000 lbs. of water heated per hour 
may be taken as follows, for the vertical and horizontal types respectively: 

Very bad water 8.5 and 9 . 1 

Medium muddy water 6 and 6.5 

Clear and little scale 2 and 2 . 2 

The space between the pans is made not less than 0.1 the width for 
rectangular and 0.25 the diameter for round pans. Under ordinary 
circumstances it is not customary to use more than six pans in a tier, 
in order to obtain a low velocity over each pan. The size of the storage 
or setthng chamber in the horizontal type varies from 0.25 to 0.4 of the 
volume of the shell, depending on the quahty of the water; 0.33 is about 
the average. In the case of vertical heaters, this varies from 0.4 to 0.6 
of the volume of the shell. Filters occupy from 10 to 15% of the volume 
of the sheU in the horizontal type and from 15 to 20% in the vertical. 

Open versus Closed Feed-water Heaters. (W. E. Harrington, St. 
Rwy. Jour., July 22, 1905.) — There still exists some difference of opinion 
as to the relative desirability of open or closed type of feed-water heater, 
but the degree of perfection which the open heater has attained has ehml- 
nated formerly objectionable features. The chief objection which attended 
the early use of the open heater, namely, that the oil from the exhaust 
steam was carried into the boiler, did much to discourage its more general 
adoption. This objection does not hold good against the better designs 
of open heaters now on the market. There are thousands of installations 
in wiiich the open heater is now being used where no difficulty is experi- 
enced from the contamination of the feed-water by oil. The perfection of 
oil separators for use in the exhaust steam connection to the heater has 
rendered this possible. 



STEAM SEPARATORS. 



941 



STEAM SEPAKATOES. 

If moist steam flowing at a high velocity in a pipe has its direction 
suddenly changed, the particles of water are by their momentum pro- 
jected in their original direction against the bend in the pipe or wall of 
the chamber in which the change of direction takes place. By making 
proper provision for drawing off the water thus separated the steam may 
be dried to a greater or less extent. For long steam-pipes a large drum 
should be provided near the engine for trapping the water condensed in 
the pipe. A drum 3 ft. diameter, 15 ft. high, has given good results in 
separating the water of condensation of a steam-pipe 10 in. diameter 
and 800 ft. long. 

Efficiency of Steam Separators. — Prof. R. C. Carpenter, in 1891, 
made a series of tests of six steam separators, furnishing them with 
steam containing different percentages of moisture, and testing the 
Quality of steam before entering and after passing the separator. A 
condensed table of the principal results is given below. 





Test with Steam of about 10% 
of Moisture. 


Tests with Varying Moisture. 


P 


Quality 
of Steam 
before. 


Quality 

of Steam 

after. 


Efficiency, 
per cent. 


Quality of 
Steam 
before. 


Quality of 
Steam after. 


Av'ge 
Effi- 
ciency. 


B 
A 
D 
C 
E 
F 


87.0% 

90.1 

89.6 

90.6 

88.4 

88.9 


98.8% 

98.0 

95.8 

93.7 

90.2 

92.1 


90.8 
80.0 
59.6 
33.0 
15.5 
28.8 


66.1 to 97.5% 
51.9 " 98 

72.2 '' 96.1 
67.1 " 96.8 
68.6 " 98.1 
70.4 '* 97.7 


97.8 to 99% 

97.9 " 99.1 
95.5 '* 98.2 
93.7 " 98.4 
79.3 " 98.5 
84.1 " 97.9 


87.6 
76.4 
71.7 
63.4 
36.9 
28.4 



Conclusions from the tests were: 1. That no relation existed between 
the volume of the several separators and their efhciency. 2. No marked 
decrease in pressure was shown by any of the separators, the most being 
1.7 lbs. in E. 3. Although changed direction, reduced velocity, and per- 
haps centrifugal force are necessary for good separation, still some means 
must be provided to lead the water out of the current of the steam. The 
high efficiency obtained from B and A was largely due to this feature. In 
B the interior surfaces are corrugated and thus catch the water thrown 
out of the steam and readily lead it to the bottom. In A, as so on as the 
water falls or is precipitated from the steam, it comes in contact with the 
perforated diaphragm through which it runs into the space below, where 
it is not subjected to the action of the steam. Experiments made by 
Prof. Carpenter on a "Stratton" separator in 1894 showed that the 
moisture in the steam leaving the separator was less than 1% when that 
in the steam supplied ranged from 6% to 21 %o. 

Experiments by Prof. G. F. Gebhardt {Power, May 11, 1909) on six 
separators of different makes led to the following conclusions; (1) The 
efficiency of separation decreases as the velocity of the steam increases. 
(2) The efficiency increases as the percentage of moisture in the enter- 
ing steam increases. (3) The drop in pressure increases rapidly with the 
increase in velocity. The six separators are described as foUows: 

U: 2-in. vertical; no baffles; current reversed once. 

V: 4-in. horizontal with single bafiQe plate of the fluted type; current 
reversed once. 

W: 4-in. vertical with two baffle plates of the smooth type; current 
reversed once. 

X: 3-in. horizontal; several fluted baffle plates; no reversal of current. 

Y: 6-in. vertical; centrifugal type; current reversed once. 

Z: 3-in. horizontal; current reversed twice; steam impinges on hori- 
zontal fluted baffle during reversal. 

The efflciency is defined as the ratio of the water removed from the 
steam by the separator to the water injected into the dry steam for the 
purpose of the test. With steam at 100 lbs. pressure containing 10% 
water, the efficiencies, taken from plotted curves, were as follows: 

U V W X Y Z 

At 2000 ft. per min 64 69 86 88 79 66 

At 3000 ft. per min 37 45 80 60 61 48 



942 THE STEAM-BOILER. 

DETER3IIXATIOX OF THE MOISTURE IN STEA3I — STEAM 
CALORI3IETERS. 

In all boiler-tests it is important to ascertain the quality of the steam, 
i.e., 1st, whether the steam is "saturated" or contains the quantity of 
heat due to the pressure according to standard experiments; 2d, whether 
the quantity of heat is deficient, so that the steam is wet; and 3d, whether 
the heat is in excess and the steam superheated. The best method of 
ascertaining the quality of the steam is undoubtedly that employed by a 
committee which tested the boilers at the American Institute Exhibition 
of 1871-2, of which Prof. Thurston was chairman, i.e., condensing all the 
water evaporated by the boiler by means of a surface condenser, weighing 
the condensing water, and taking its temperature as it enters ana as it 
leaves the condenser; but this plan cannot always be adopted. 

A substitute for this method is the barrel calorimeter, wiiich with careful 
operation and fairiy accurate instruments may generally be relied on to 
give results within two per cent of accuracy (that is, a sample of steam 
which gives the apparent result of 2% of moisture mpy contain anywhere 
between and 4%). This calorimeter is described as follows: A sample 
of the steam is taken by inserting a perforated 1/2-inch pipe into and 
through the main pipe near the boiler, and led by a hose, thoroughly 
felted, to a barrel, holding preferably 400 lbs. of water, which is set upon 
a platform scale and provided with a cock or valve for allowing the water 
to flow to waste, and with a small propeller for stirring the w^ater. 

To operate the calorimeter the barrel is filled with water, the weight 
and temperature ascertained, steam blown through the hose outside the 
barrel until the pipe is thoroughly warmed, when the hose is suddenly 
thrust into the water, and the propeller operated until the temperature 
of the water is increased to the desired point, say about 110° usually. 
The hose is then withdrawn quickly, the temperature noted, and the 
weight again taken. 

An error of 1/10 of a pound in weighing the condensed steam, or an 
error of 1/2 degree in the temperature, v;ill cause an error of over 1% in 
the calculated percentage of moisture. See Trans. A. S, M. E., vi, 293, 

The calculation of the percentage of moisture is made as below ; 

Q = quality of the steam, dry saturated steam being unity. 
H = total heat of 1 lb. of steam at the observed pressure. 
T = total heat of 1 lb. of water at the temperature of steam of the 

observed pressure. . . 

h = total heat of 1 lb. of condensing water, original. 
hi = total heat of 1 lb. of condensing water, final. . . . r 

W = weight of condensing water, corrected for water-equivalent of 

the apparatus. 
w = weight of the steam condensed. 
Percentage of moisture = 1 — ^. 

If Q is greater than unity, the steam is superheated, and the degrees of 
euperhearing = 2.0833 (H - T) (Q - 1). 

Difficulty of Obtaining a Correct Sample. — Experiments by Prof. 
D. S. Jacobus (Trans. A. S. M. E., xvi, 1017), show that it is practically 
impossible to obtain a true average sample of the steam flowing in a pipe. 
For accurate determinations all the steam made by the boiler should be 
passed through a separator, the water separated should be weighed and 
a calorimeter test made of the steam just after it has passed the separator. 
Coil Calorimeters. — Instead of the open barrel in which the steam 
is condensed, a coil acting as a surface-condenser may be used, which is 
placed in the barrel, the water in coil and barrel being weighed separately. 
For a description of an apparatus of this kind designed by the author, 
which he has found to give results with a probable error not exceeding 
1/2 per cent of moisture, see Trans. A. S. M. E., vi, 294. This calorimeter 
may be used continuously, if desired, instead of intermittently. In this 
case a continuous flow of condensing water into and out of the barrel 
must be established, and the temperature of inflow and outflow and of 
the condensed steam read at short intervals of time 



LETERMINATION OF THE MOISTURE IN STEAM. 



943 



Throttling Calorimeter. — For percentages of moisture not exceed- 
ing* 3 per cent the throttling calorimeter is most useful and convenient 
and remarkably accurate. In this instrument the steam which reaches 
it in a 1/2-inch pipe is throttled by an orifice Vi6 inch diameter, opening 
into a chamber which has an outlet to the atmosphere. The steam in 
this chamber has its pressure reduced nearly or quite to the pressure of the 
atmosphere, but the total heat in the steam before throttling causes the 
steam in the chamber to be superheated more or less according to whether 
the steam before throttling was dry or contained moisture. The only 
observations required are those of the temperature and pressure of the 
steam on each side of the orifice. 

The autlior's formula for reducing the observations of the throttling 
calorimeter is as follows (Experiments on Throttling Calorimeters, Am, 

Mach., Aug. 4, 1892): w = 100 X "^ ~ ^ ~ ^ ^X~l)^ in which w = 

percentage of moisture in the steam; H = total heat, and L = latent 
heat of steam in the main pipe ; h = total heat due the pressure in 
the discharge side of the calorimeter, = 1150.4 at atmospheric pressure; 
K = specific heat of superheated steam ; T = temperature of the 
throttled and superheated steam in the calorimeter; t = temperature due 
to the pressiu-e in the calorimeter, = 212° at atmospheric pressure. 

Taking K at 0.46 and the pressure in the discharge side of the calo- 
rimeter as atmospheric pressure, the formula becomes 

^ = 100 X g- 11504 -0.46(7-212°). 

From this formula the following table is calculated: 
IMoiSTURE IN Steam — Determinations by throttling calorimeter. 



Degree of 
Super- 
heating 

T - 212°. 


Gauge-pressures. 


5 1 10 1 20 1 30 1 40 1 50 1 60 1 70 1 75 1 80 1 85 1 90 


Per Cent of Moisture in Steam. 


0° 


0.51 


0.901 1.54 


2.06 


2.50 


2.90 


3.24 


3.56 


3.71 


3.86 


3.99 


4.13 


10° 


0.01 


0.39 


1.02 


1.54 


1.97 


2.36 


2.71 


3.02 


3.17 


3.32 


3.45 


3.58 


20° 






0.51 


1.02 


1.45 


1.83 


2.17 


2.48 


2.63 


2.77 


2.90 


3.03 


30° 






0.00 


0.50 


0.92 


1.30 


1.64 


1.94 


2.09 


2.23 


2.35 


2.49 


40° 










0.39 


0.77 


1. 10 


1.40 


1.55 


1.69 


1.80 


1.94 


50° 
60° 
70° 












0.24 


0.57 
0.03 


0.87 
0.33 


I.Ol 
0.47 


1.15 
0.60 
0.06 


1.26 
0.72 
0.17 


1.40 












0.85 














31 






















Dif. p. deg. . . 


.0503 


.0507 


.0515 


.0521 


.0526 


.0531 


.0535 


.0539 


.0541 


.0542 


.0544 


.0546 


Degree ot 
^' Super- 
B_ heating 
^LT -212°. 


Gauge-pressures. 


100 1 110 1 120 ! 130 1 140 1 150 I 160 | 170 | 180 j 190 \ 200 [ 250 


Per Cent of Moisture in Steam. 


B U° 


4.39 


4.63 


4.85 


5.08 


5.29 


5.49 


5.68 


5.87 


6.05 


6.22 


6.39 


7.16 


^m 


3.84 


4.08 


4.29 


4.52 


4.73 


4.93 


5.12 


5.30 


5.48 


5.65 


5.82 


6.58 


H 20° 


3.29 


3.52 


3.74 


3.96 


4.17 


4.37 


4.56 


4.74 


4.91 


5.08 


5.25 


6.00 


^m 30° 


2.74 


2.97 


3.18 


3.41 


3.61 


3.80 


3.99 


4.17 


4.34 


4.51 


4.67 


5.41 


^K 40° 


2.19 


2.42 


2.63 


2.85 


3.05 


3.24 


3.43 


3.61 


3.78 


3.94 


4.10 


4.83 


.r 5QO 


1.64 


1.87 


2.08 


2.29 


2.49 


2.68 


2.87 


3.04 


3.21 


3.37 


3.53 


4.25 


60° 


1.09 


1.32 


1.52 


1.74 


1.93 


2.12 


2.30 


2.48 


2.64 


2.80 


2.96 


3.67 


JL 70° 

m 80° 

■ 90° 


0.55 


0.77 


0.97 


1.18 


1.38 


1.56 


1.74 


1.91 


2.07 


2.23 


2.38 


3.09 


0.00 


0.22 


0.42 


0.63 


0.82 


1.00 


1.18 


1.34 


1.50 


1.66 


1.81 


2.51 








0.07 


0.26 


0.44 


0.61 


0.78 


0.94 


1.09 


1.24 


1.93 


100° 
110° 














0.05 


0.21 


0.37 


0.52 


0.67 
O.IO 


1 34 














0.76 


Dif. p. deg. . . 


.0549 


.0551 


.0554 


.0556 


.0559 


.0561 


.0564 


.0566 


.0568 


.0570 


.0572 


.0581 



Separating Calorimeters. — For percentages of moisture beyond the 
range of the throttling calorimeter the separating calorimeter is used, 



944 CHIMNEYS. 

which is simply a steam separator on a small scale. An improved form 
of this calorimeter is described by Prof. Carpenter in Power, Feb., 1893. 

For fuller information on various kinds oi calorimeters, see papers by 
Prof. Peabody, Prof. Carpenter, and Mr. Barrus in Trans. A. S. M. E., 
vols. X, xi, xii, 1889 to 1891; Appendix to Report of Com. on Boiler Tests, 
A. S. M. E., vol. vi, 1884; Circular of Schaeffer & Budenberg, N. Y., 
"Calorimeters, Throttling and Separating." 

Identification of Dry Steam by Appearance of a Jet. — Prof. 
Denton {Trans. A. S. M. E., vol. x) found that jets of steam show un- 
mistakable change of appearance to the eye when steam varies less than 
1% from the condition of saturation in the direction of either wetness 
or of superheating. 

If a jet of steam flow from a boiler into the atmosphere under circum- 
stances such that very little loss of heat occurs through radiation, etc., 
and the jet be transparent close to the orifice, or be even a grayish-white 
color, the steam may be assumed to be so nearly dry that no portable 
condensing calorimeter will be capable of measuring the amount of water 
in the steam. If the jet be strongly w^hite, the amount of water may be 
roughly judged up to about 2%, but beyond this only a calorimeter can 
deterrriine the exact amount of moisture. 

A common brass pet-cock may be used as an orifice, but it should. If 
possible, be set into the steam-drum of the boiler and never be plated 
further away from the latter than 4 feet, and then only when the inter- 
mediate reservoir or pipe is well covered. 

Usual Amount of 3Ioisture in Steam Escaping from a Boiler. — 
In the common forms of horizontal tubular land boilers and water-tube 
boilers with ample horizontal drums, and supplied with water free from 
substances likely to cause foaming, the moisture in the steam does not 
generallv exceed 2% unless the boiler is overdriven or the water-level is 
carried too high. 

CHIMNEYS. 

Chimney Draught Theory. — The commonly accepted theory of 
Chimney draught, based on Peclet's and Rankine's hypotheses (Rankine, 
S. E.), is discussed by Prof. De Volson Wood, Trans. A. S, M, £., vol. xi. 

Peclet represented the law of draught by the formula 



^2 / 
^==2^1 



1 + 0+^"^ 



mj 
in which Ji is the **head," defined as such a height of hot gases as, if added 

to the column of gases in the chimney, would produce the 
same pressure at the furnace as a column of outside air, of 
the same area of base, and a height equal to that of the 
chimney; 
u is the required velocity of gases in the chimney; 
G a constant to represent the resistance to the passage of air 

through the coal; 
I the length of the flues and chimney; 
m the mean hydraulic depth or the area of a cross-section divided 

by the perimeter; _, , 

/ a constant depending upon the nature of the surfaces over 
which the gases pass, whether smooth, or sooty and rough. 
Rankine's formula (Steam Engine, p. 288), derived by giving certain 
values to the constants (so-called) in Peclet's formula, is 

-°f 0.080?) J r \ 

h = ^4 H-H= (0.96 ^-i)H; 

in which H = the height of the chimney in feet; 

To= 493° F., absolute (temperature of melting ice); 
Ti= absolute temperature of the gases in the chimney; 
T2= absolute temperature of the external air. 



CHIMNEYS. 



945 



Prof. Wood derives from this a still more complex formula which gives 
the height of chimney required for burning a given quantity of coal per 
second, and from it he calculates the following table, showing the height 
of chimney required to burn respectively 24, 20, and 16 lbs. of coal per 
square foot of grate per hour, for the several temperatures of the chimney 
gases given. 





Chimney Gas. 


Coal per sq. ft. of grate per hour, lbs. 


Outside Air. 






24 


20 


16 


T2. 


Absolute. 


Temp. 
Fahr. 










Height H, feet. 


520° 


700 


239 


250.9 


157.6 


67.8 


absolute or 


800 


339 


172.4 


115.8 


55.7 


59° F. 


1000 


539 


149.1 


100.0 


48.7 




1100 


639 


148.8 


98.9 


48.2 




1200 


739 


152.0 


100.9 


49.1 




1400 


939 


159.9 


105.7 


51.2 




1600 


1139 


168.8 


111.0 


53.5 




2000 


1539 


206.5 


132.2 


63.0 



Rankine's formula gives a maximum draught when t = 21/12^2, or 
622° F., when the outside temperature is 60°. Prof. Wood says: "This 
result is not a fixed value, but departures from theory in practice do not 
affect the result largely. There is, then, in a properly constructed chimney 
properly working, a temperature giving a maximum draught,* and that 
temperature is not far from the value given by Rankine, although in 
special cases it may be 50° or 75° more or less." 

All attempts to base a practical formula for chimneys upon the theoret- 
ical formula of Peclet and Rankine have failed on account of the impos- 
sibihtv of assigning correct values to the so-called "constants" G and/. 
(See trans. A. S. M. E., xi, 984.) 

Force or Intensity of Draught. — The force of the draught is equal 
to the difference between the weight of the column of hot gases inside of 
the chimney and the weight of a column of the external air of the same 
height. It is measured by a draught-gauge, usually a U-tube partly 
filled with water, one leg connected by a pipe to the interior of the flue, 
and the other open to the external air. 

If D is the density of the air outside, d the density of the hot gas inside, 

in lbs. per cubic foot, h the height of the chimney in feet, and 0.192 the 

factor for converting pressure in lbs. per sq. ft. into inches of water column, 

then the formula for the force of draught expressed in inches of water is, 

F = 0.192 h {D - d). 

The density varies with the absolute temperature (see Rankine). 

d= ^0.084; 7) = 0.0807 -, 

Tl T2 

where tq is the absolute temperature at 32° F., = 493, ti the absolute 
temperature of the chimney gases and t2 that of the external air. Sub- 
stituting these values the formula for force of draught becomes 
F = 0.W2 ft (M:!? _ 41^N ^^ /7^ _ 7^5y 

\ T2 Tl / \ T2 Tl / 



* Much confusion to students of the theory of chimneys has resulted 
from their understanding the words maximum draught to mean maxi- 
mum intensity or pressure of draught, as measured by a draught-gauge. 
It here means maximum quantity or weight of gases passed up the 
chimney. The maximum intensity is found only with maximum tem- 
perature, but after the temperature reaches about 622° F. the density of 
the gas decreases more rapidly than its velocity increases, so that the 
weight is a maximum about 622° F., as shown by Rankine. — W. K. 



946 



CHIMNEYS. 



To find the maximum intensity of draught for any given chimney, the 
heated column being 600° F., and the external air 60°, multiply the height 
above grate in feet by 0.0073, and the product is the draught in inches 
of water. 

Height of Water Column Due to Unbalanced Pressure in Chimney 
100 Feet High. (The Locomotive, 1884.) 



Temp, in 

the 
Chimney. 


Temperature of the External Air — Barometer, 14.7 lbs 


per sq. in. 


0° 


10° 


20° 


30° 


40° 


50° 


60° 


70° 


80° 


90° 


100° 


200 


0.453 


0.419 


0.384 


0.353 


0.321 


0.292 


0.263 


0.234 


0.209 


0.182 


0.157 


220 


.488 


.453 


.419 1 .388 


.355 


.326 


.298 


.269 


.244 


.217 


.192 


240 


.520 


.488 


.451 


.421 


.388 


.359 


.330 


.301 


.276 


.250 


.225 


260 


.555. 


.528 


.484 


.453 


.420 


.392 


.363 


.334 


.309 


.282 


.257 


280 


.584 


.549 


.515 


.482 


.451 


.422 


.394 


.365 


.340 


.313 


.288 


300 


.611 


.576 


.541 


.511 


.478 


.449 


.420 


.392 


.367 


.340 


.315 


320 


.637 


.603 


.568 


.538 


.505 


.476 


.447 


.419 


.394 


.367 


.342 


340 


.662 


.638 


.593 


.563 


.530 


.501 


.472 


.443 


.419 


.392 


.367 


360 


.687 


.653 


.618 


.588 


.555 


.526 


.497 


.468 


.444 


.417 


.392 


380 


.710 


.676 


.641 


.611 


.578 


.549 


.520 


.492 


.467 


.440 


.415 


400 


.732 


.697 


.662 


.632 


.598 


.570 


.541 


.513 


.488 


.461 


.436 


420 


.753 


.718 


.684 


.653 


.620 


.591 


.563 


.534 


.509 


.482 


.457 


440 


.774 


.739 


.705 


.674 


.641 


.612 


.584 


.555 


.530 


.503 


.478 


460 


.793 


.758 


.724 


.694 


.660 


.632 


.603 


.574 


.549 


.522 


.497 


480 


.810 


.776 


.741 


.710 


.678 


.649 


.620 


.591 


.566 


.540 


.515 


500 


.829 


.791 


.760 


.730 


.697 


.669 


.639 


.610 


.586 


.559 


.534 



For any other height of chimney than 100 ft. the height of water column 
is found by simple proportion, the height of water column being directly 
proportioned to the height of chimney. 

The calculations have been made for a chimney 100 ft. high, \nth 
various temperatures outside and'inside of the flue, and on the supposition 
that the temperature of the chimney is uniform from top to bottom. 
This is the basis on which all calculations respecting the draught-power 
of chimneys have been made by Rankine and other writers, but it is very 
far from the truth in most cases. The difference will be shown by com- 
paring the reading of the draught-gauge ^Aith the table given. In one 
case a chimney 122 ft. high showed a temperature at the base of 320°, 
and at the top of 230°. 

Box, in his "Treatise on Heat," gives the following table: 

Draught Powers of Chimneys, etc., with the Internal Air at 552° 
AND THE External Air at 62°, and with the Damper nearly 
Closed. 



•*- fl 


tn 


Theoretical Velocity 


c 


en 


Theoretical Velocity 


li. 




in feet pei 


' second. 


2^ . 

•III 




in feet pei 


second. 


Ill 


Cold Air 


Hot Air 


Cold Air 


Hot Air 


«6 


Entering. 


at Exit. 


Kg 


Entering. 


at Exit. 


10 


0.073 


17.8 


35.6 


80 


0.585 


50.6 


101.2 


20 


0.146 


25.3 


50.6 


90 


0.657 


53.7 


107.4 


30 


0.219 


31.0 


62.0 


100 


0.730 


56.5 


113.0 


40 


0.292 


35.7 


71.4 


120 


0.876 


62.0 


124.0 


50 


0.365 


40.0 


80.0 


150 


1.095 


69.3 


138.6 


60 


0.438 


43.8 


87.6 


175 


1.277 


74.3 


149.6 


70 


0.511 


47.3 


94.6 


200 


1.460 


80.0 


160.0 



CHIMNEYS. 



947 



Rate of Combustion Due to Height of Chimney. — Trowbridge's 

"Heat and Heat Engines" gives the following figures for the heights of 
chimney for producing certain rates of combustion per sq. ft. of grate. 
They may be approximately true for anthracite in moderate and large 
sizes, but greater heights than are given in the table are needed to secure 
the given rates of combustion with small sizes of anthracite, and for 
bituminous coal smaller heights will suffice if the coal is reasonably free 
from ash — 5% or less. 





Lbs. of 




Lbs. of 




Lbs. of 




Lbs. of 


Height, 


Coal per 


Height, 


Coal per 


Height, 


Coal per 


Height, 


Coal per 


feet. 


Sq. Ft. of 


feet. 


Sq. Ft.of 


feet. 


Sq. Ft. of 


feet. 


Sq. Ft. of 




Grate. 




Grate. 




Grate. 




Grate. 


20 


7.5 


45 


12.4 


70 


15.8 


95 


18.5 


25 


8.5 


50 


13.1 


75 


16.4 


100 


19.0 


r 30 


9.5 


55 


13.8 


80 


16.9 


105 


19.5 


F 35 


10.5 


60 


14.5 


85 


17.4 


110 


20.0 


^ 40 


11.6 


65 


15.1 


90 


18.0 













2\/h- 



W. D. Ennis (Eng. Mag., Nov., 1907), gives the following as the force 
of draught required for burning No. 1 buckwheat coal: 

Draught, in. of water 0.3 0.45 0.7 1.0 

Lbs. coal per sq. ft. grate per hour 10 15 20 25 

Thurston's rule for rate of combustion effected by a given height of 
chimney (Trans. A. S. M. E., xi, 991) is: Subtract 1 from twice the square 
root of the height, and the result is the rate of combustion in pounds per 
square foot of grate per hour, for anthracite. Or rate = 2 V/i — 1, in 
which h is the height in feet. This rule gives the following: 

h = 50 60 70 80 90 100 110 125 150 175 200 
-1 = 13.14 14.49 15.73 16.89 17.97 19 19.97 21.36 23.49 25.45 27.28 

The results agree closely with Trowbridge's table given above. In 
practice the high rates of combustion for high chimneys given by the 
formula are not generally obtained, for the reason that with high chimneys 
there are usually long horizontal flues, serving many boilers, and the 
friction and the interference of currents from the several boilers are apt to 
cause the intensity of draught in the branch flues leading to each boiler 
to be much less than that at the base of the chimney. The draught of 
each boiler is also usually restricted by a damper and by bends in the gas- 
passages. In a battery of several boilers connected to a chimney 150 ft. 
high, the author found a draught of 3/4.inch water-column at the boiler 
nearest the chimney, and only 1/4-inch at the boiler farthest away. The 
first boiler was wasting fuel from too high temperature of the chimney- 
gases, 900°, having too large a grate-surface for the draught, and the last 
boiler was working below its rated capacity and with poor economy, on 
account of insufficient draught. 

The effect of changing the length of the flue leading into a chimney 
60 ft. high and 2 ft. 9 in. square is given in the following fable, from Box 
on "Heat": 



Length of Flue in 
feet. 


Horse-power. 


Length of Flue in 
feet. 


Horse-power. 


50 
^ 100 

m 200 

■ 600 


107.6 
100.0 
85.3 
70.8 
62.5 


800 
1,000 
1,500 
2,000 
3,000 


56.1 
51.4 
43.3 
38.2 
31.7 



The temperature of the gases in this chimney was assumed to be 552° F . 
and that of the atmosphere 62°. 



948 SIZE OF CHIMNEYS. 

High Chimneys not Necessary. — Chimneys above 150 ft. in height 
are very costly, and their increased cost is rarely justified by increased effi- 
ciency. In recent practice it has become somewhat common to build two 
or more smaller cliimneys instead of one large one. A notable example 
is the Spreckels Sugar Refinery in Pliiladelphia, where three separate 
cliimneys are used for one boiler-plant of 7500 H.P. The three cliimneys 
are said to have cost several thousand dollars less than a single chimney 
of their combined capacity would have cost. Very tall cliimneys have 
been characterized by one writer as "monuments to the folly of their 
builders." 

Heights of Chimney required for Different Fuels. — The minimum 
height necessary varies with the fuel, wood requiring the least, then good 
bituminous coal, and fine sizes of anthracite the greatest. It also varies 
with the character of the boiler — the smaller and more circuitous the 
gas-passages the higher the stack required ; also with the number of boilers, 
a single boiler requiring less height than several that discharge into a 
horizontal flue. No general rule can be given. 

C. L. Hubbard (Am. Electrician, Mar., 1904) says: The following heights 
have been found to give good results in plants of moderate size, and to 
produce sufficient draught to force the boilers from 20 to 30 per cent 
above their rating: 

With free-burning bituminous coal, 75 feet; with anthracite of medium 
and large size, 100 feet: with slow-burning bituminous coal, 120 feet; with 
anthracite pea coal, 130 feet; with anthracite buckwheat coal, 150 feet. 
For plants of 700 or 800 horse-power and over, the chimney should not 
be less than 150 feet liigh regardless of the kind of coal to be used. 

SIZE OF CHIMNEYS. 

The formula given below, and the table calculated therefrom for chim- 
neys up to 96 in. diameter and 200 ft. high, were first pubhshed by the 
author in 1884 (Trans. A. S. M. E., vi, 81). They have met with much 
approval since that date by engineers who have used them, and have been 
frequently published in boiler-makers' catalogues and elsewhere. The 
table is now extended to cover cliimneys up to 12 ft. diameter and 300 ft. 
high. The sizes corresponding to the given commercial horse-powers 
are believed to be ample for all cases in which the draught areas through 
the boiler-flues and connections are sufficient, say not less than 20% 
greater than the area of the chimney, and in which the draught between 
the boilers and chimney is not checked by long horizontal passages and 
right-angled bends. 

Note that the figures in the table correspond to a coal consumption of 5 lbs. 
of coal per horse-pdwer per hour. This hberal allowance is made to cover 
the contingencies of poor coal being used, and of the boilers being driven 
beyond their rated capacity. In large plants, with economical boilers 
and engines, good fuel and other favorable conditions, wiiich will reduce 
the maximum rate of coal consumption at any one time to less than 5 lbs. 
per H.P. per hour, the figures in the table may be multipHed by the ratio 
of 5 to the maximum expected coal consumption per H.P. per hour. 
Thus, with conditions which make the maximum coal consumption only 
2.5 lbs. per hour, the chimnev 300 ft. high X 12 ft. diameter should be 
sufficient for 6155 X 2 = 12,310 horse-power. The formula is based on 
the following data: 

1. The draught power of the chimney varies as the square root of the 
height. .^ ^ 

2. The retarding of the ascending gases by friction may be considered 
as equivalent to a diminution of the area of the chimney, or to a hning of 
the chimney by a layer of gas which has no velocity. The thickness of 
this lining is assumed to be 2 inches for all chimneys, or the diminution 
of area equal to the perimeter X 2 inches (neglecting the overlapping of 
the corners of the lining). Let D = diameter in feet, A = area, and E = 
effective area in square feet: 

8 D 2 /~~ 

For square chimneys, E = D* — = A - - ^ A. 

For round chimneys, E = '^{^D^ - %^\ = A - 0.591 v^. 



CHIMNEYS. 949 

For simplifying calculations, the coefficient of ^^A may be taken as 0.6 
for both square and round chimneys, and the formula becomes 

£: = ^ - 0.6 VI. 

3. The power varies directly as this effective area E. 

4. A chimney should be proportioned so as to be capable of giving 
sufficient draught to cause the boiler to develop much more than its rated 
power, in case of emergencies, or to cause the combustion of 5 lbs. of fuel 
per rated horse-power of boiler per hour. 

5. The powder of the chimney varying directly as the effective area, E, 
and as the square root of the height, H, the formula for horse-pow^r of 
boiler for a given size of chimney will take the form H.P. = CE ^H, in 
which C is a constant, the average value of which, obtained by plotting 
the results obtained from numerous examples in practice, the author 
finds to be 3.33. 

The formula for horse-power then is 

H.P. = 3.33 E Vh, or H.P. = 3.33 {A - 0.6 V3) \^H. 

If the horse-power of boiler is given, to find the size of chimney, the 
height being assumed, 

E = 0.3 H.P. -^ ^H; = A - 0.6 ^/J. 

For round chimneys, diameter of chimney = diam. of ^ + 4''. 
For square chimneys, side of chimney = ^E + 4". 
If effective area E is taken in square feet, the diameter in inches is c? = 
13.54jy^£7 + V, and the side of a square chimney in inches is s = 

12 ^E + V. 

/O 3 H P \2 
If horse-power is given and area assumed, the height H = ( ' ' j • 

An approximate formula for chimneys above 1000 H.P. is H.P. = 
2.5 D^ ^ H. This gives the H.P. somewhat greater than the figures in 
the table. 

In proportioning chimneys the height should first be assumed, with due 
consideration of the heights of surrounding buildings or hills near to the 

Eroposed chimney, the length of horizontal flues, the character of coal to 
e used, etc. ; then the diameter required for the assumed height and horse- 
power is calculated by the formula or taken from the table. 

For Height of Chimneys see pages 947 and 948. No formula for 
height can be given which will be satisfactory for different classes of coal, 
kinds and amounts of ash, styles of grate-bars, etc. A formula in " Ingeni- 
eurs Taschenbuch," translated into EngUsh measures, ish = 0.21QR^-i-6d. 
h= height in ft; i^ = lbs. coal burned per sq. ft. of grate per hour; d = 
diam. in ft. This formula gives an insufficient height for small sizes of 
anthracite, and a height greater than is necessary for free-burning bitu- 
minous coal low in ash. 

The Protection of Tall Chimney-shafts from Lightning. — C. 
Molyneux and J. M. Wood (Industries, March 28, 1890) recommend for 
tall chimneys the use of a coronal or heavy band at the top of the chimney, 
with copper points 1 ft. in height at intervals of 2 ft. throughout the cir- 
cumference. The points should be gilded to prevent oxidation. The 
most approved form of conductor is a copper tape about 3/4 in. by i/s in. 
thick, weighing 6 ozs. per ft. If iron is used it should weigh not less than 
21/4 lbs. per ft. There must be no insulation, and the copper tape should 
be fastened to the chimney with holdfasts of the same material, to pre- 
vent voltaic action. An allowance for expansion and contraction should 
be made, say 1 in. in 40 ft. Slight bends in the tape, not too abrupt, 
answer the purpose. For an earth terminal a plate of metal at least 3 ft. 
sq. and V16 in. thick should be buried as deep as possible in a damp spot. 
The plate should be of the same metal as the conductor, to which it 
should be soldered. The best earth terminal is water, and when a deep 
well or other large body of water is at hand, the conductor should be 
carried down into it. Right-angled bends in the conductor should b« 
avoided. No bend in it should be over 30°. 



950 



SIZE OF CHIMNEYS. 



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CHIMNEYS. 



951 



Velocity of Gas in Chimneys. — The velocity of the heated gas, based 
on the cliininey porportions given in the table, may be found from the 
following data: 

A = Lb. coal per hour = boiler horsepower X 5 ; 
B = Lb. gas per lb. coal = say 20 lb. ; 

C = Cu. ft. of gas per lb. of gas = 12.4 X (temp, of gas + 460) -r- 492; 

- 25 cu. ft. for 532° F. = 500 cu. ft. 
per lb. coal; 

yl X B X O 

V = Velocity of gas, feet per second = 7^^-^ t „^ , ,^ o^^ t^- 

'' ^ ' ^ Chimney area (sq. ft.) X 3600 

Based on a gas temperature of 532° F., 5 lb. coal per hour per rated 
H.P., and 20 lb. gas per lb. of coal we have 

Cu. ft. gas per second per lb. of coal per hour = 0.1389; 

Cu. ft. gas per second per boiler horse-power = 0.6944; 
and the velocities in feet per second, based on the effective areas given 
in the table, corresponding to different heights of chimney are: 



Height, ft. . 

Velocity, ft. 

per sec... 



50 
16.3 



60 70 80 90 100| 110 125. 150 175, 200. 225 
17.8!l9.4 20.7!22.0,23.2|24.3!25.9|28.3|30.6|32.7|34.7 



250 300 
36.6140.1 



Chimney Table for Oil Fuel. (C. R. Weymouth, Journal A. S. M.E., 
October, 1912.) — Conditions: Sea level; atmospheric temperature, 
80° F. ; draught at chimney side of damper, 0.30 in. ; excess air, less than 
50 % » assumed 50 % for calculations of efficiency and chimney dimensions ; 
temperature of gases leaving chimney, 500° F. ; boiler efficiency, 73 % ; 
actual boiler horse-power, 150 per cent of rated; lb. gas per actual 
boiler H. P. ,54. 6; height of chimney above point of draught measurement, 
12 ft. less than tabulated height. When building conditions permit 
select chimneys of least height in table for minimum cost of chimney. 
Chimney capacities stated are maximum for continuous load equally 
divided on all boilers. For large plants or swinging load, reduce capacity 
10 to 20 % . Breeching 20 % in excess of stack area ; length not exceed- 
ing 10 chimney diameters. 





Size of Chimneys for Oil Fuel 










Area, 

Sq. ft. 


Height in Feet above Boiler Room Floor. 


Diam., 
In. 


80 


90 


100 1 110 


120 1 130 1 140 1 150 1 160 




Actual Horse-power 


= 1 50 Per cent of Rated. 


18 


1.77 


63 


75 


84 


91 


96 


101 


104 


108 


110 


24 


3.14 


123 


148 


166 


180 


191 


201 


208 


215 


221 


30 


4.91 


206 


249 


280 


304 


324 


340 


354 


366 


377 


36 


7.07 


312 


379 


427 


466 


497 


523 


545 


564 


581 


42 


9.62 


443 


539 


609 


665 


711 


749 


782 


810 


830 


48 


12.57 


599 


729 


827 


904 


967 


1.020 


1.070 


1.110 


1,145 


54 


15.90 


779 


951 


1.080 


1.180 


1.270 


1.340 


1,400 


1.460 


1.500 


60 


19.64 


985 


1.200 


1.370 


1.500 


1.610 


1,710 


1.790 


1.860 


1.920 


66 


23.76 


1.220 


1.490 


1.700 


1.860 


2.000 


2.120 


2.220 


2.310 


2.390 


72 


28.27 


1.470 


1.810 


2.060 


2.260 


2.430 


2.580 


2.710 


2.820 


2.910 


78 


33.18 


1.750 


2.150 


2.460 


2.710 


2.910 


3.000 


3.250 


3.380 


3.500 


84 


38.49 


2.060 


2.530 


2,900 


3.190 


3.440 


3.650 


3.840 


4.000 


4.150 


96 


50.27 


2.750 


3.390 


3,880 


4.290 


4.630 


4.920 


5.180 


5.400 


5.610 


108 


63.62 


3.550 


4.380 


5.020 


5.550 


6.000 


6.390 


6.730 


7.030 


7.300 


120 


78.54 


4.440 


5.490 


6.310 


6.990 


7.560 


8.060 


8.490 


8.890 


9.240 


132 


95.03 


5.450 


6.740 


7.760 


8.600 


9.310 


9.930 


10.500 


11.000 


1 1 .400 


144 


113.1 


6.550 


8.120 


9.350 


10.400 


1 1 .200 


12,000 


12.700 


13.300 


13.800 


156 


132.7 


7.760 


9.630 


11.100 


12.300 


13.400 


14.300 


15.100 


15.800 


16.500 


168 


153.9 


9.060 


11.300 


13.000 


14.400 


15.700 


16.800 


17.700 


18.600 


19.400 


180 


176.7 


10.500 


13.000 


15.100 


16.700 


18.200 


19.500 


20.600 


21.600 


22.600 



In using the above table it must be noted that the conditions upon 
which it is based are all fairly good. With unskilful handling of oil 



952 CHIMNEYS. 

fuel the excess air is apt to be much more than 50% and the eflBciency 
much less than 73%. In that case the actual horse-power developed 
by a given size of chimney may be much less than the figure given in 
the table 

Draught of Chimneys 100 Ft. High — Oil Fuel. 

Temp^of gases enter- 
ing chimney 300 400 500 600 700 

Net chimney draught, inches of water 

f 60° F. 0.367 0.460 0.534 0.593 0.642 

Temp, of outside air. -I 80 0.325 0.417 0.490 0.550 0.599 

[100 0.284 0.377 0.451 0.510 0.559 

The net draught is the theoretical draught due to the difference in 
weight of atmospheric air and chimney gases at the stated temperatures, 
multiplied by a> coefficient, 0.95, for temperature drop in stack, and by 
5/6 as a correction for friction. For high altitudes the draught varies 
directly as the normal barometer. For other heights than 100 feet 
(measured above the level of entrance of the gases) the draught varies 
as the square root of the height. 

Chimneys with Forced Draught. — ^When natural, or chimney, draught 
only is used, the function of the chimney is 1, to produce such a dif- 
ference of pressure, or intensity of draught, between the bottom of the 
chimney and the ash-pit as will cause the flow of the required quantity 
of air through the grate-bars and the fuel bed, and the flow of the gases 
of combustion through the gas passages, the damper and the breeching; 
and 2, to convey the gases above the tops of surrounding buildings and 
to such a height that they will not become a nuisance. With forced 
draught the blower produces the difference of pressure, and the only use 
of the chimney is that of conveying the gases to a place where they will 
cause no inconvenience; and in that case the height of the chimney may 
be much less than that of a chimney for natural draught. 

With oil or natural gas for fuel, the resistance of the grates and of the 
fuel bed is ehminated, and the height of the chimney may be much less 
than that of one desired for coal firing. When oil or gas is substituted 
for coal, and the chimney is a high one, it may be necessary to restrict 
its draught power by a damper or other means, in order to prevent its 
creating too greata negative pressure in the furnace and thereby too great 
an admission of air, which will cause a decrease in efficiency. 

The Largest Chimney in the World, in 1908, is that of the Montana 
smelter, at Great Falls, Mont. Height 506 ft. Internal diam. at top 
50 ft. Built of Custodis radial brick. Designed to remove 4,000,000 cu. 
ft. of gases per minute at an average temperature of 600° F. Erected on 
top of a hill 500 ft. above the city, and 246 ft. above the floor of the fur- 
naces, which are about 2000 ft. distant. Designed for a wind pressure of 
331/3 lbs. per sq. ft. of projected area; bearing pressure limited to 21 tons 
per sq. ft. at any section. Foundation: 111 ft. max. diam., 221/2 ft. deep; 
bearing pressure on bottom (shale rock) 4.83 tons per sq. ft.; octagonal 
outside, 103 ft. across at bottom, 81 ft. at top. with inner circular open- 
ing 47 ft. diam. at bottom, 64 ft. at top; made of 1 cement, 3 sand, 5 
crushed slag. Four flue openings in the base, each 15 ft. \^ide, 36 ft. 
high. The stack proper consists of an octagonal base, 46 ft. in height, 
which has a taper of 8%, and above this a circular barrel, the first 180 ft. 
above the base having a taper of 7%, the next 100 ft. of 4%, and the 
remaining 180 ft. to the cap 2%. 

The chimney wall varies from 66 in. at the base to 181/8 in. at the top 
bv uniform decrements of 2 in. per section, excepting at the section imme- 
diately above the top of the base, where the thickness decreases from 60 in. 
to 54 in. The outside diameters of the stack are 78 1/2 ft. at the base, 
53 ft. 9 in. at the base of the cap; the inside diameters range from 66 1/2 ft. 
at the foundation line to 50 ft. at the top. The chimney is lined with 4- 
inch acid-proof brick, laid in sections carried on corbels from the main 
shell. A description of the methods of design and of erection of the 
Great Falls chimney is given in Eng. JRec, Nov. 28, 1908. 



CHIMNEYS. 



953 



Some Tall Brick Chimneys (1895). 



1. Hallsbruckner Hiitte, 

Saxony 

2. Townsend's, Glasgow. . . . 

3. Tennant's, Glasgow 

4. Dobson & Barlow, Bol- 

ton, Eng 

5. Fall River Iron Co., Bos- 

ton 

6. Clark Thread Co., New- 

ark, N. J 

7. Merrimac Mills, Lowell, 

Mass 

8. Washington Mills, Law- 

rence, Mass 

9. Amoskeag Mills, Man- 

chester, N. H 

10. Narragansett E. L. Co., 

Providence, R. I 

1 1 . Lower Pacific Mills, Law- 

rence, Mass 

12. Passaic Print Works, 

Passaic, N. J 

13. Edison Station Brooklyn, 

Two each 



460 
454 
435 

3671/2 

350 

335 

282^9' 

250 

250 

238 

214 

200 

150 



s 
5 



Outside 
Diameter. 



15.7' 

13' 2" 
11 
]] 
12 
10 
10 
14 

8 

9 
50'' X 120" 



W 



33' 
32 
40 

33' 10' 

30 

28' 6" 



a 
o 



21 
14 



each 



Capacity by the 
Author's 
Formula. 



H. P. 



13,221 



9,795 
8,245 
5,558 
5.435 
5,980 
3,839 
3,839 
7,515 
2,248 
2,771 
1,541 



Pounds 
Coal 



ifoi 



66,105 



48,975 
41.225 
27.790 
27,175 
29,900 
19.195 
19,195 
37,575 
11,240 
13,855 
7,705 



Notes on the Above Chimneys. — 1. This chimney is situated near 
Freiberg, at an elevp.tion of 219 ft. above that of the foundry works, so 
that its total height above the sea will be 7113/4 ft. The furnace-gases 
are conveyed across river to the chimney on a bridge, through a pipe 
3227 ft. long. It is built of brick, and cost about S40,000. — Mfr. & Bldr. 

2. Owing to the fact that it was struck by lightning, and somewhat 
damaged, as a precautionary measure a copper extension subsequently 
was added to it, making its entire height 488 feet. 

1, 2, 3, and 4 were built of these great heights to remove deleterious 
gases from the neighborhood, as well as for draught for boilers. 

5. The structure rests on a solid granite foundation, 55 X 30 feet, and 
16 feet deep. In its construction there were used 1,700,000 bricks, 
2000 tons of stone, 2000 barrels of mortar, 1000 loads of sand, 1000 barrels 
of Portland cement, and the estimated cost is $40,000. It is arranged for 
two flues, 9 feet 6 inches by 6 feet, connecting with 40 boilers, which are 
to be run in connection with four triple-expansion engines of 1350 horse- 
power each. 

6. It has a uniform batter of 2.85 ins. to every 10 ft. Designed for 
21 boilers of 200 H.P. each. It is surmounted by a cast-iron coping 
which weighs six tons, and is composed of 32 sections bolted together 
by inside flanges so as to present a smooth exterior. The foundation 
is 40 ft. square and 5 ft. deep. Two qualities of brick were used; the 
outer portions were of the first quality North River, and the backing up 
was of good quality New Jersey brick. Every twenty feet in vertical 
measurement an iron ring, 4 ins.\vide and 3/4 to 1/2 in. thick, placed edge- 
wise, was built into the walls about 8 ins. from the outer circle. As the 
chimney starts from the base it is double. The outer wall is 5 ft. 2 Ins. 
in thickness, and inside of this is a second wall 20 ins. thick and spaced 



954 CHIMNEYS. 

off about 20 ins. from main wall. From the interior surface of the main 
wall eight buttresses are carried, nearly touching this inner or main flue 
wall in order to keep it in Une should it tend to sag. The interior wall, 
starting with the thickness described, is gradually reduced until a height 
of about 90 ft. is reached, when it is diminished to 8 inches. _ At 165 ft. 
it ceases, and the rest of the chimney is without lining. The total weight 
of the chimney and foundation is 5000 tons. It was completed in Sep- 
tember, 1888. 

7. Connected to 12 boilers, with 1200 sq. ft. of grate. Draught 1 9/i6 ins. 

8. Connected to 8 boilers, 6 ft. 8 in. diam, X 18 ft. Grate 448 sq. ft. 

9. Connected to 64 Manning vertical boilers, total grate surface 1810 
sq. ft. Designed to burn 18,000 lbs. anthracite per hour. 

10. Designed for 12,000 H.P. of engines; (compound condensing). 

11. Grate-surface 434 square feet; H.P. of boilers about 2500. 

13. Eight boilers (water-tube) each 450 H.P.; 12 engines, each 300 
H.P. For the first 60 feet the exterior wall is 28 ins. thick, then 24 ins. for 
20 ft., 20 ins. for 30 ft., 16 ins. for 20 ft., and 12 ins. for 20 ft. The inte- 
rior wall is 9 ins. thick of fire-brick for 50 ft., and then 8 ins. thick of red 
brick for the next 30 ft. Illustrated in Iron Age, Jan. 2, 1890. 

A number of the above chimneys are illustrated in Pou'cr,. Dec, 1890. 

More Recent Brick Chimneys (1909). —Heller & Merz Co., Newark, 
N. J. 350 ft. high, inside diam., 8 ft. Outside diam., top 9 ft. 10 1/4 in., 
bottom 27 ft. 6V2 in. Outside taper 5.2 in 100. Outer shell 71/8 in. at 
the top, 38 in. at the bottom. Custodis radial brick laid in mortar of 
1 cement, 2 lime, 5 sand. The changes in thickness are made by 2-in. 
offsets on the inside every 20 ft. Iron band 31/2 X s/ie in., three courses 
below the top. Lined with 4 in. of special brick to resist acids. The 
lining is sectional, being carried on corbels projecting from the shell every 
20 ft. An air space of 2 ins. is left between the Uning and the shell. 
The lining bricks are laid in a m.ortar made of silicate of soda and white 
asbestos wool, tempered to the consistency of fire-clay mortar. This 
mortar is acid-proof, and its binding power, which is considerable in 
comparison to that of fire-clay mortar, is unaffected by temperatures up 
to 2000° F. {Eng. News, Feb. 15, 1906.) Supported on 324 piles driven 
60 ft. to soUd rock, and covering an area 45 ft. square. Total cost $32,000. 
The standard Custodis radial brick is 41/2 in. thick and 6V2 in. wide; 
radial lengths are 4, 51/2. 7i/8, 85/8 and lO-Vs ins. The smallest size has 
six vertical perforations, 1 in. square, and the largest fifteen. 

Eastman Kodak Co., Rochester, N. Y. Height 366 ft,; internal diam. 
at top 9 ft. 10 ins., at bottom 20 ft. 10 ins.; outside diam., top 11 ft., bottom 
27 ft. 10 ins. Radial brick, with 4-in. acid-resisting brick lining. 

Some notable tall chimneys built by the Alphonse Custodis Chimney 
Construction Co. are: Dolgeville, N. Y., 6 X 175 ft.; Camden, N. J., 7 X 210 
ft.; Newark, N. J., 8X 350 ft.; Rochester, N. Y., 9X 366 ft.; Constable 
Hook, N. J., 10 X 365 ft.; Pro\ddence. R. I.. 16 X 308 ft.; Garfield. Utah. 
30 X 300 ft. ; Great Falls Mont., 50 X 506 ft. 

Interior Stack of the Equitable Building, New York City (Eng. 
News, Nov. 12, 1914). — The stack is 11 ft. outside diam., 596 ft. high, 
made of steel plates 5/iq in. thick. It is supported on the steelwork of 
the building at every other story. It has a 2-in. lining of J. & ISI. 
Vitribestos, alternate layers of plain and corrugated asbestos board 
coated with a supposedly vitrified compound. The rated H.P. of this 
chimney, taking 10 ft. 7 in. as the inside. diameter, is 6710, equivalent 
to the burning of 33,550 lb. of coal per hour. 

Stability of Chimneys. — Chimneys must be designed to resist the 
maximum force of the wind in the locahty in which they are built. A 
general rule for diameter of base of brick chimneys, approved by many 
years of practice in England and the United States, is to make the diam- 
eter of the base one-tenth of the height. If the chimney is square or 
rectangular, make the diameter of the inscribed circle of the base one- 
tenth of the height. The "batter" or taper of a chimney should be 
from 1/16 to 1/4 inch to the foot on each side. The brickwork should be 
one brick (8 or 9 inches) thick for the first 25 feet from the top, increasing 
1/2 brick (4 or 41/2 inches) for each 25 feet from the top downwards. If 
the inside diameter exceeds 5 feet, the top length should be IV2 bricki; 
and if under 3 teet. it mav be 1/2 brick for ten feet. 

(From The Locomotive, 1884 and 1886.) For chimneys of four feet in 



STABILITY OF CHIMNEYS. 955 

diameter and one hundred feet high, and upwards, the best form is cir- 
cular wim a straignt oatter on tne outside. 

Chimneys of any considerable height are not built up of uniform 
thickness from top to bottom, nor with a uniformly varying thickness of 
wall, but the wall, heaviest of course at the base, is reduced by a series 
of steps. 

Where practicable the load on a chimney foundation should not exceed 
two tons per square foot in compact sand, gravel, or loam. Where a 
solid rock-bottom is available for foundation, the load may be greatly 
increased. If the rock is sloping, all unsound portions should be removed, 
and the face dressed to a series of horizontal steps, so that there shall be 
no tendency to shde after the structure is finished. 

All boiler-chimneys of any considerable size should consist of an outer 
stack of sufficient strength to give stability to the structure, and an inner 
stack or core independent of the outer one. This core is by many engineers 
extended up to a height of but 50 or 60 feet from the base of the chimney, 
but the better practice is to run it up the whole height of the chimney; it 
may be stopped off, say, a couple of feet below the top, and the outer shell 
contracted to the area of the core, but the better way is to run it up to 
about 8 or 12 inches of the top and not contract the outer shell. But 
under no circumstances should the core at its upper end be built into or 
connected with the outer stack. This has been done in several instances 
by bricklayers, and the result has been the expansion of the inner core 
which lifted the top of the outer stack squarely up and cracked the brick- 
work. 

For a height of 100 feet v/e would make the outer shell in three steps, the 
first 20 feet high, 16 inches thick, the second 30 feet high, 12 inches thick, 
the third 50 feet high and 8 inches thick. These are the minimum 
thicknesses admissible for chimneys of tliis height, and the batter should 
be not less than 1 in 36 to give stabihty. The core should also be built 
In three steps, each of which may be about one-third the height of the 
chimney, the lowest 12 inches, the middle 8 inches, and the upper step 
4 inches thick. This will insure a good sound core. The top of a chimney 
may be protected by a cast-iron cap; or perhaps a cheaper and equally 
good plan is to lay the ornamental part in some good cement, and plaster 
the top with the same material. 

C. L. Hubbard (Am. Electrician, Mar., 1904) says: The following 
approximate method may be used for determining the thickness of walls. 
If the inside diameter at the top is less than 3 ft. the walls may be 4 ins. 
thick for the first 10 ft., and increased 4 ins. for each 25 ft. downward. 
If the inside diameter is more than 3 ft. and less than 5 ft., begin with a 
waU 8 ins. thick, increasing 4 ins. for each 25 ft. downward. If the diam- 
eter Is over 5 ft., begin with a 12-in. waH, increasing below the first 10 ft. 
as before. The lining or core may be 4 ins. thick for the first 20 ft. from 
the top, 8 ins. for the next 30 ft., 12 ins. for the next 40 ft., 16 Ins. for 
the next 50 ft., and 20 ins. for the next 50 ft. .Using this method for an 
outer wall 200 ft. high and assuming a cubic foot of brickwork to weigh 
130 lbs., it gives a maximum pressure of 8.2 tons per sq. ft. of section at 
the base; while a Uning 190 ft. high would have a maximum pressure of 
8.6 tons per sq. ft. The safe load for brickwork may be taken at from 
8 to 10 tons per sq. ft., although the strength of best pressed brick will run 
much higher. 

James B. Francis, in a report to the Lawrence Mfg. Co. in 1873 {Eng. 
News, Aug. 28, 1880), concerning the probable effects of wind on that 
company's chimney as then constructed, says: 

The stability of the chimney to resist the force of the wind depends 
mainly on the weight of its outer shell, and the width of its base. The 
cohesion of the mortar may add considerably to its strength; but it is too 
uncertain to be rehed upon. The inner shell will add a little to the 
stabihty, but it may be cracked by the heat, and its beneficial effect, if 
any, is too uncertain to be taken into account. 

The effect of the joint action of the vertical pressure due to the weight 
of the chimney, and the horizontal pressure due to the force of the wind is 
to shift the center of pressure at the base of the chimney, from the axis 
toward one side, the extent of the shifting depending on the relative 
magnitude of the two forces. If the center of pressure is brought too near 
the side of the chimney, it will crush the brickwork on that side, and the 



956 CHIMNEYS. 

chimney will fall. A line drawn through the center of pressure, perpen- 
dicular to the direction of the wind, must leave an area of brickwork 
between it and the side of the chimney , sufficient to support half the weight 
of the chimney: the other half of the weight being supported by the brick- 
work on the windward side of the line. 

Different experimenters on the strength of brickwork give very different 
results. Kirkaldy found the weights which caused several kinds of 
bricks, laid in hydraulic Ume mortar and in Roman and Portland cements, 
to fail sUghtly, to vary from 19 to 60 tons (of 2000 lbs.) per sq. ft. If 
we take in this case 25 tons per sq. ft. as the weight that would cause it 
to begin to fail, we shall not err greatly. 

Rankine, in a paper printed in the transactions of the Institution of 
Engineers, in Scotland, for 1867-68, says: "It had previously been ascer- 
tained by observation of the success and failure of actual chimneys, and 
especially of those which respectively stood and fell during the violent 
storms of 1856, that, in order that a round chimney may be sufficiently 
stable, its weight should be such that a pressure of wind, of about 55 lbs. per 
sq. ft. of a plane surface, directly facing the wind, or 271/2 lbs. per sq. ft. 
of the plane projection of a cylindrical surface, . . . shall not cause the 
resultant pressure at any bed-joint to deviate from the axis of the 
chimney by more than one-quarter of the outside diameter at that 
joint. *' 

Steel Chimneys are largely used, especially for tall chimneys of iron- 
works, from 150 to 300 feet in height. The advantages claimed are: 
greater strength and safety; smaller space required; smaller cost, by 
30 to 50 per cent, as compared with brick chimneys; avoidance of infiltra- 
tion of air and consequent checking of the draught, common in brick 
chimneys. They are usually made cylindrical in shape, with a wide curved 
flare for 10 to 25 feet at the bottom. A heavy cast-iron base-plate is 
provided, to which the chimney is riveted, and the plate is secured to a 
massive foundation by holding-down bolts. No guys are used. 

Design of Self-supporting Steel Chimneys. — John D. Adams 
(Eng. News, July 20, 1905) gives a very full discussion of the design of steel 
chimneys, from which the following is adapted. The bell-shaped bottom 
of the chimney is assumed to occupy one-seventh of the total height, and 
the point of maximum strain is taken to be at the top of this bell portion. 
Let D = diam. in inches, H = height in feet, T = thickness in inches, 
S = safe tensile stress, lbs. per sq. in. The general formula for moment 
of resistance of a hollow cylinder is Af = 1/32 tt (D<— Di^) S/D. When 
the thickness is a small fraction of the diameter this becomes approxi- 
mately M = 0.7854 D^TS. 

With steel plate of 60,000 lbs. tensile strength, riveting of 0.6 efficiency, 
and a factor of safety of 4, we have S = 9000 pounds per sq. in., and the 
safe moment of resistance = 7070 D'^T. 

The effect of the wind upon a cylinder is equal to the wind pressure 
multipUed by one-half the diametral plane, and taking the maximum 
wind pressure at 50 lbs. per sq. ft., we get 

Total wind pressure = 50 X 1/12 D X 1/2 X 6/7H = 25 DH/14:. 

The distance of the center of pressure above the top of the bell por- 
tion = 3/7 H, multiplied by the total wind pressure, gives us the bend- 
ing moment due to the wind, 

inch-pounds, 25 DH/14 X 3/7 if X 12 = 9.184 DH^. 

Equating the bending and the resisting moment we have T = 0.0013 

With this formula the maximum thickness of plates was calculated 
for different sizes of chimneys, as given in the table on p. 957. 

In the above formula, no attention has been paid to the weight of the 
steel in the stack above the bell portion, which weight has a tendency 
to decrease the tension on the windward side and increase the com- 
pression on the leeward side of the stack. A column of steel 150 ft. 
high would exert a pressure of approximately 500 lb. per sq. in., which, 
with steel of 60,000 lb. tensile strength, is less than 1 % of the ultimate 
strength, and may safely be neglected. 

From the table it appears that a chimney 12 X 120 ft. requires, as far 
as fracture by bending of a tubular section is concerned, a thickness of 
but little over i/s in. In designing a stack of such extreme proportions 



SIZE OF CHIMNEYS. 



957 



as 12 X 120 ft., there are other factors besides bending to take into con- 
sideration that ordinarily could be neglected. For instance, such a stack 
should be provided with stiffening angles, or else made heavier, to guard 
against lateral flattening. Ordinarily, however, the strength of the 
chimney determined as a tubular section will be the prime factor in deter- 
mining the maximum thickness of plates. 

Thickness of Base-ring Plates of Self-supporting Steel Stacks. 

For normal wind pressure of 50 lbs. per sq. ft. on half the diametral plane- 

Diameter of Stack in feet. 



4j 


3.5 


4 


5 


6 


7 


8 


8.5 


9 


9.5 


10 


", 


12 


70 


152| 133 


1.106 
.139 
.175 
.217 
.262 
.312 
.366 
.425 
.487 
.555 
676 




















80 


0.198 
0.224 
0.310 
0.375 
0.446 
0.523 
0.607 
0.696 


.182 
.219 
.271 

328 
.390 
.458 
.531 
.609 

693 


.... 

.116 
.146 
.181 
.218 
.260 
.305 
.354 
.406 
.462 
.522 
.585 
.652 


•.099 
.125 
.155 
.187 
.223 
.262 
.303 
.348 
.396 
.447 
.501 
.559 
.620 
.682 
















90 


.111 
.135 

.164 
.195 
.228 
.265 
.305 
.346 
.391 
.439 
.489 
.542 
.596 
.655 
.717 














100 


.127 
.154 

.183 
.215 
.250 
.286 
.326 
.368 
.413 
.460 
.510 
.562 
.617 
.674 
.734 


.120 
.146 
.173 
.203 
.236 
.271 
.308 
.348 
.390 
.434 
.481 
.531 
.582 
.637 
.693 
.752 










no 

120 
130 
140 
150 
160 


.138 
.164 
.193 
.223 
.257 
.292 
.330 
.370 
.411 
.456 
.503 
.552 
.603 
.657 
.713 


.131 
.156 
.183 
.212 
.244 
.277 
.313 
.351 
.391 
.433 
.478 
.524 
.573 
.624 
.677 


.119 
.142 
.166 
.193 
.222 
.252 
.285 
.319 
.356 
.394 
.434 
.476 
.521 
.567 
.615 


.153 
.180 
.203 
.231 


170 






.261 


lao 






.702 


.293 


IQO 






.326 


700 








.361 


710 










.398 


2:^0 










.437 


730 












477 


240 












.520 


250 














.564 



Foundation. — Neglecting the increase of wind area due to the flare 
at the base of the chimney, which has but a very small turning effect, 
if all dimensions be taken in feet, we have 

Total wind pressure = 1/2 D X H X 50 = 25 DH; lever-arm -^hH; 
hence, turning moment = 12.5 DH^. 

Let d = diameter and h = height of foundation. For average con- 
ditions h = 0.4 d, then volume of foundation = 0.7854 d'^h, and for 
concrete at 150 lbs. per cu. ft., weight of foundation = W ^ 0.7854 d^h 
X 150 = 47.124^3. 

The stability of the foundation or the tendency to resist overturning 
Is equal to the weight of the foundation multiplied by its radius or 1/2 Wd 
= 23.562 d^ Applying a factor of safety of 2 1/2, which is indicated by 
current practice, gives safe stability = 9.4 25 d ^. Equating this to the 
overturning moment we obtain d= 1.07 '\JdH^, in which all dimensions 
are in feet. 

Anchor-bolts. — The holding power of the bolts depends on three 
factors: the number of bolts, the diameter of the bolt circle, and the 
diameter of the bolts. The number of bolts is largely conventional and 
may be selected so as not to necessitate bolts of too large a diameter. The 
diameter of the bolt circle is also more or less arbitrary. The bolts will 
be stretched and therefore strained, in proportion to their distance from 
the axis of turning, assuming, as we must, that the cast-iron ring at the 
base of the chimney is rigid. The leverage at which any bolt acts is also 
directly proportional to its distance from the axis of turning. Therefore, 
since the effectiveness of any one bolt, as regards overturning, depends 
upon the strain in that bolt, multiplied by its leverage, it is evident that 
the effectiveness of any bolt varies as the square of its distance from the 
axis of turning. If we lay out, say, 12 or 24 bolts equidistant on a circle 
and add all the squares of these distances, we will find that we may con- 
sider the total as though the bolts were all placed at a distance of 3/3 
the diameter of the bolt circle from the axis of turning, which is the tan- 
gent to the bolt circle. 

Let & == diameter of bolt in inches, n = number of bolts, diameter 



958 



CHIMNEYS. 



of bolt circle = ilzd. Take safe working stress at 8000 pounds per sq. 
inch. Then resistance to overturning = 0.7854 h- X 8000 X ^zd X 3/8 X 
N = 6283 b^Nd/4. Equatmg this to the turning moment, 12.5 Dif 2, 
gives V = 0.0257 H\/W/'d for 12 bolts, 0.0222 H\/D7d for 18 bolts, 
and 0.0182 H \/D/d for 24 bolts. 

Reinforced Concrete Chimneys began extensively to come into use 
in the United States in 1901. Some hundreds of them are now (1909) 
in use. The following description of the method of construction of these 
chimneys is condensed from a circular of the Weber Chimney Co., Chicago. 

The foundation is comparatively light and made of concrete, consisting 
of 1 cement, 3 sand, and 5 gravel or macadam. The steel reenforcement 
consists of two networks usually made of T steel of small size. The bars 
for the lower network are placed diagonally and the bars for the second 
network (about 4 to 6 ins. above, the first one) run parallel to the sides. 
The vertical bars, forming the reenforcement of the chimney itself, also 
go down into the foundation and a number of these bars are bent in order 
to secure an anchorage for the chimney. 

The chimney shaft consists of two parts, the lower double shell and the 
single shell above, which are united at the offset. The inside shell is 
usually 4 ins. thick, while the thickness of the outer shell depends on the 
height and varies from 6 to 12 ins. The single shell is from 4 to 10 ins. 
thick. The height of the double shell depends upon the purpose of the 
chimney, nature and heat of the gases, etc. 

Between the two shells in the lower part there is a circular air space 4 
ins. in width. An expansion joint is provided where the two shells unite. 

The concrete above the ground level consists of one part Portland 
cement and three parts of sand. No gravel or macadam is used. 

The bending forces caused by wind pressure are taken up by the vertical 
steel reenforcement. The resistance of the concrete itself against tension 
is not considered in calculation. 

The vertical T bars are from 1 X 1 X Vs to 1 1/2 XI V2 X V2 in., the weight 
and number depending upon the dimensions of the chimney. The bars 
are from 16 to 30 ft. long and overlap not less than 24 ins. They are 
placed at regular intervals of 18 ins. and encircled by steel rings bent to 
the desired circle. 

The following is a list of some of the tallest concrete chimneys that 
have been built of their respective diameters: Butte, Mont., 350 X 18 
ft.; Seattle, Wash., 278 X 17 ft.; Portland, Ore., 230 X 12 ft.; Lawrence, 
Mass., 250 X 11 ft.; Cincinnati, Ohio, 200 X 10 ft.; Worcester, Mass, 
220 X 9 ft.; Atlanta, Ga., 225 X 8 ft.; Chicago. 175 X 7 ft.; Rockville, 
Conn., 175 X 6 ft.; Seymour, Ind., 150 X 5 ft.; lola, Kans., 143 X 4 ft.; 
St. Louis, Mo., 130 X 3 ft. 4 in.; Dayton, Ohio, 94 X 3 ft. 

Sizes of Foundations for Steel Chimneys. 

(Selected from circular of Phila. Engineering Works.) 
Half-Lined Chimneys. 

Diameter, clear, feet 3 

Height, feet 100 

Least diam. foundation.. 15'9'' 
Least depth foundation.. 6' 

Height, feet 125 

Least diam. foundation 18'5 

Least depth foundation 

Weight of Sheet-iron Smolce-staclis per Foot. 
(Porter Mfg. Co.) 



4 


5 


6 


7 


9 


11 


100 


150 


150 


150 


150 


150 


16'4" 


20'4" 


2rio" 


22'7" 


23'8" 


24'8' 


6' 


9' 


8' 


9' 


10' 


10' 


125 


200 


200 


250 


275 


300 


18'5'' 


23'8'' 


25' 


29'8" 


33'6" 


36' 


7' 


10' 


10' 


12' 


12' 


14' 



Diam. 


Thick- 


Weight 


Diam. 


Thick- 


Weight 


Diam. 


Thick- 
ness. 
W. G. 


Weight 


inches. 


ness. 
W. G. 


per ft. 


inches. 


W. G. 


per ft. 


inches. 


per ft. 


10 


No. 16 


7.20 


26 


No. 16 


17.50 


20 


No. 14 


18.33 


12 




8.66 


28 




18.75 


22 


•* 


20.00 


14 




9.58 


30 


•' 


20.00 


24 


'• 


21.66 


16 




11.68 


10 


No. 14 


9.40 


26 


*• 


23.33 


20 




13.75 


12 


** 


11.11 


28 


" 


25.00 


22 




15.00 


14 


" 


13.69 


30 


" 


26.66 


24 




16.25 


16 




15.00 







THE STEAM-ENGINE; 



959 



THE STEAM-ENGINE. 

Expansion of Steam. Isothermal and Adiabatic. — According to 

Mariotte's law, the volume of a perfect gas, the temperature being kept 
constant, varies inversely as its pressure, or p oc l/v\ p2; = a constant. The 
curve constructed from tliis formula is called the isothermal curve, or 
curve of equal temperatures, and is a comm.on or rectangular hyperbola. 
The expansion of steam in an engine is not isothermal, since the temper- 
ature decreases with increase of volume, but its expansion curve approxi- 
mates the curve of pi; = a constant. The relation of the pressure and 
volume of saturated steam, as deduced from Regnault's experiments, and 
as given in steam tables, is approximately, according to Rankine (S. E., 
p. 403), for pressures not exceeding 120 lbs., pocl/i;il, or p ocyis orpvis = 
25i;i.o625 = a constant. Zeuner has found that the exponent 1.0646 gives a 
closer approximation. 

When steam expands in a closed cylinder, as in an engine, according to 
Rankine (S. E., p. 385), the approximate law of the expansion is p oc l/i;V*, 
orpocf"^^^' or pi;i*"i= a constant. The curve constructed from this 
formula is called the adiabatic curve, or curve of no transmission of heat. 

Peabody (Therm., p. 112) says: "It is probable that this equation was 
obtained by comparing the expansion lines on a large number of indicator- 
diagrams. . . . There does not appear to be any good reason for using an 
exponential equation in this connection, . . . and the action of a lagged 
steam-engine cyUnder is far from being adiabatic. . . . For general pur- 
poses the hyperbola is the best curve for comparison with the expansion 
curve of an indicator-card. ..." Wolff and Denton, Trans. A. S. M. E., 
ii, 175, say: " From a number of cards examined from a variety of steam- 
engines in current use, w^e find that the actual expansion line varies between 
the 10/9 adiabatic curve and the Mariotte curve." 

Prof. Thurston (Trans. A.S. M. E.,i\, 203) says he doubts if the exponent 
ever becomes the same in any two engines, or even in the same engine 
at different times of the day and under varying conditions of the day. 

Expansion of Steam according to Mariotte's Law and to the 
Adiabatic Law. {Trans, A. S. M. E., ii, 156.) — Mariotte's law pv^ 

pi-yi; values calculated from formula — "^ p ^-^ + ^^P ^^^ '^)' ^^ which 

R = V2 -^ vi, pi = absolute initial pressure, P^ = absolute mean pressure, 

vi = initial volume of steam in cylinder at pressure pi, V2 = final volume 

of steam at final pressure. Adiabatic law: p-yV = pivi^^; values calcu- 
p 

lated from formula -^=10 R~^-9R~^^' 

Pi 



Ratio 
of Ex- 


Ratio of Mean 
to Initial 
Pressure. 


Ratio 

of Ex- 


Ratio of Mean 
to Initial 


Ratio 
of Ex- 


Ratio of Mean 
to Initial 
Pressure. 


pansion 
R. 


pansion 
R. 


Pres 


sure. 


pansion 
R. 


Mar. 


Adiab. 


Mar. 


Adiab. 


Mar. 


Adiab. 


1.00 


1.000 


1.000 


3.7 


0.624 


0.600 


6. 


0.465 


0.438 


1.25 


.978 


.976 


3.8 


.614 


.590 


6.25 


.453 


.425 


1.50 


.937 


.931 


3.9 


.605 


.580 


6.5 


.442 


.413 


1.75 


.891 


.881 


4. 


.597 


.571 


6.75 


.431 


.403 


2. 


.847 


.834 


4.1 


.588 


.562 


7. 


.421 


.393 


2.2 


.813 


.798 


4.2 


.580 


.554 


7.25 


.411 


.383 


2.4 


.781 


.765 


4.3 


.572 


.546 


7.5 


.402 


.374 


2.5 


.766 


.748 


4.4 


.564 


.538 


7.75 


.393 


.365 


2.6 


.752 


.733 


4.5 


.556 


.530 


8. 


.385 


.357 


2.8 


.725 


.704 


4.6 


.549 


.523 


8.25 


.377 


.349 


3. 


.700 


.678 


4.7 


.542 


.516 


8.5 


.369 


.342 


3.1 


.688 


.666 


4.8 


.535 


.509 


8.75 


.362 


.335 


3.2 


.676 


.654 


4.9 


.528 


.502 


9. 


.355 


.328 


3.3 


.665 


.642 


5.0 


.522 


.495 


9.25 


.349 


.321 


3.4 


.654 


.630 


5.25 


.506 


.479 


9.5 


.342 


.315 


3.5 


.644 


.620 


5.5 


.492 


.464 


9.75 


.336 


.309 


3.6 


.634 


.610 


5.75 


.478 


.450 


10. 


.330 


.303 



960 



THE STEAM-ENGINE. 



Mean Pressure of Expanded Steam. — For calculations of engines 
it is generally assumed that steam expands according to Mariotte's law, 
the curve of the expansion line being a hyperbola. The mean pressure, 
measured above vacuum, is then obtained from the formula 



Pm-P- 



1 + hyp log R 
R 



or P^ = P^(l + hyplogie), 



in which P^ is the absolute mean pressure, pi the absolute imtial pressure 
taken as uniform up to the point of cut-off, P^ the terminal pressure, and 
R the ratio of expansion. If I = length of stroke to the cut-off, L = total 
stroke. j^ 

p,Z+ piZ hyp log-7- r -. , u 1 Ti 

_ ^^ ^ "^^ ^ ^ . if p - ^. P =x) 1 + hyp log R 

Mean and Terminal Absolute Pressures. — 3Iariotte's Law. — The 

values in the following table are based on Mariotte's law, except those 
In the last column, wliich give the mean pressure of superheated steam, 
which, according to Rankine, expands in a cylinder according to the 
law pccv~ii. These latter values are calculated from the formula 

^m 17-16P~xs 1 , 4. ^ V. ^ ^- ^u 

— = ^ R 16 may be found by extracting the square root 

of — four times. From the mean absolute pressures given deduct the mean 
R 



back pressure (absolute) to obtain the 


mean effective pressure. 


Rate 

of 
Expan- 
sion. 


Cut- 
off. 


Ratio of 

Mean to 

Initial 

Pressure. 


Ratio of 
Mean to 
Terminal 
Pressure. 


Ratio of 
Terminal 
to Mean 
Pressure. 


Ratio of 

Initial 

to Mean 

Pressure. 


Ratio of 

Mean to 

Initial 

Dry Steam. 


30 

28 


0.033 
0.036 
0.038 
0.042 
0.045 
0.050 
0.055 
0.062 
0.066 
0.071 
0.075 
0.077 
0.083 
0.091 
0.100 
0.111 
0.125 
0.143 
0.150 
0.166 
0.175 
0.200 
0.225 
0.250 
0.275 
0.300 
0.333 
0.350 
0.375 
0.400 
0.450 
0.500 
0.550 
0.600 
0.625 
0.650 
0.675 


0.1467 
0.1547 
0.1638 
0.1741 
0.1860 
0.1998 
0.2161 
0.2358 
0.2472 
0.2599 
0.2690 
0.2742 
0.2904 
0.3089 
0.3303 
0.3552 
0.3849 
0.4210 
0.4347 
0.4653 
0.4807 
0.5218 
0.5608 
0.5965 
0.6308 
0.6615 
0.6995 
0.7171 
0.7440 
0.7664 
0.8095 
0.8465 
0.8786 
0.9066 
0.9187 
0.9292 
0.9405 


4.40 
4.33 
4.26 
4.18 
4.09 
4.00 
3.89 
3.77 
3.71 
3.64 
3.59 
3.56 
3.48 
3.40 
3.30 
3.20 
3.08 
2.95 
2.90 
2.79 
2.74 
2.61 
2.50 
2.39 
2.29 
2.20 
2.10 
2.05 
1.98 
1.91 
1.80 
1.69 
1.60 
1.51 
1.47 
1.43 
1.39 


0.227 
0.231 
0.235 
0.239 
0.244 
0.250 
0.256 
0.265 
0.269 
0.275 
0.279 
0.280 
0.287 
0.294 
0.303 
0.312 
0.321 
0.339 
0.345 
0.360 
0.364 
0.383 
0.400 
0.419 
0.437 
0.454 
0.476 
0.488 
0.505 
0.523 
0.556 
0.591 
0.626 
0.662 
0.680 
0.699 
0.718 


6.82 
6.46 
6.11 
5.75 
5.38 
5.00 
4.63 
4.24 
4.05 
3.85 
3.72 
3.65 
3.44 
3.24 
3.03 
2.81 
2.60 
2.37 
2.30 
2.15 
2.08 
1.92 
1.78 
1.68 
1.58 
1.51 
1.43 
1.39 
1.34 
1.31 
1.24 
1.18 
1.14 
1.10 
1.09 
1.07 
1.06 


0.136 


26 




24 




22 




20 
18 


0.186 


16 




15 




14 




13.33 
13 


0.254 


12 




11 




10 
9 


0.314 


8 
7 


0.370 


6.66 
6.00 


6.4i7 


5.71 




5.00 
4.44 


0.506 


4.00 
3.63 


0.582 


3.33 
3.00 


0.6-.8 


2.86 
2.66 


0.707 


2.50 
2.22 
2.00 
1.82 
1.66 
1.60 


0.756 
0.800 
0.840 
0.874 
0.900 


1.54 

1.48 


0.926 



THE STEAM-ENGINE. 



961 




Calculation of Mean Effective Pressure, Clearance and Com- 
pression Considered. — In the above tables no account is taken of 

clearance, which in actual 

u-eY I ^ steam-engines modifies the 

' ratio of expansion and the 

mean pressure ; nor of com- 
pression and back-pressure, 
which diminish the mean 
effective pressure. In the 
following calculation these 
elements are considered. 

L = length of stroke, I = 
length before cut-off, x = 
length of compression part of 
stroke, c = clearance, pi = 
initial pressure, p^ = back 
pressure, Pc = pressure of 
clearance steam at end of 
compression. All pressures 
are absolute, that is, measured 
from a perfect vacuum. 

Area of ABCD = Pi a + c) (l 4- hyp log y^) ; 
B = pt,{L-x); 

C = PcC (l + hyp log ^-T-^) =Pb {x+c) \l + hyp log —7-^); 
D = (Pi-Pc) c = pic-pb {x + c). 
Area of A = ABCD - (B + C + D) 

= Pia+c) (i+hyplog^^) 

- \vb (L -x) +Pb(x + c) (1 + hyp log ^ ^ ^^ + pic-pj) {x 4-c)J 

»2?ia+c)(l+hyplog|^) 

- Pb HL - x) + (^x-hc) hyp log — —J -piC. 

^ ^. area of A 
Mean effective pressure = j 

Example. — Let L = l, 2 = 0.25, a; = 0.25, c = 0.1, pi = 60 lbs., P6 = 2 lbs. 
Area A = 60 (0.25 4- 0.1) (l + hyp log ^) 



--2 [(l- 



0.25)^-0.35hyplog 



60 X 0.1. 



0.35 1 _ 
0.1 J 

21 (1+ 1.145) -2 [0.75+ 0.35X1.2531 - 6 
45.045 -2.377 -6 = 36.668 = mean effective pressure. 



The actual indicator-diagram generally shows a mean pressure con- 
siderably less than that due to the initial pressure and the rate of expan- 
sion. The causes of loss of pressure are: 1. Friction in the stop- valves 
and steam-pipes. 2. Friction or wire-dramng of the steam during 
admission and cut-off. due chiefly to defective valve-gear and contracted 
steam-passages. 3. Liquefaction during expansion. 4. Exhausting 
before the engine has completed its stroke. 5. Compression due to early 
closure of exhaust. 6. Friction in the exhaust-ports, passages, ana 
pipes. 



962 THE STEAM-ENGINE. 

Re-evaporation during expansion of the steam condensed during admis- 
sion, and valve-leakage alter cut-off, tend to elevate the expansion hne 
of the diagram ana increase the mean pressure. . . . , 

If the theoretical mean pressure be calculated from the initial pressure 
and the rate of expansion on the supposition that the expansion curve 
follows Mariotte's law, pv = sl constant, and the necessary corrections 
are made for clearance and compression, the expected mean pressure in 
Dractice may be found by multiplying the calculated results by the factor 
(commonly called the "diagram factor") in the following table, according 
to Seaton. 

Particulars of Engine. Factor. 

Expansive engine, special valve-gear or with a sepa- 

rate cut-off valve, cyhnder jacketed . . 94 

Expansive engine having large ports, etc., and good 

ordinary valves, cyUnders jacketed. . 0.9 to 0.9 J 

Expansive engines with the ordinary valves and gear 

as in general practice, and unjacketed . 0.8 to 0.85 

Compound engines, with expansion valve to h p. 

cyhnder; cyhnders jacketed, and with large ports, ^^^^^92 

Compound engines," with'ordinary sUde-valves, cyhn- . ^ . ^ ^^ 

ders jacketed, and good ports, etc 0.8 to u.»d 

Compound engines as in general practice in the 

merchant service, with eariy cut-off in both cyhn- _ _ . ^ o 

ders, without jackets and expansion-valves . . 7 to u . » 

Fast-running engines of the type and design usually 

fitted in war-ships O.b to 0.8 

If no correction be made for clearance and compression and the engine 
Is in accordance with genera modern practice, the theoretical mean 
pressu^fmay be multiplied by 0.96, and the product by the proper factor 
in the table, to obtain the expected mean pressure. 

Given the Initial Pressure and the Average Pressure, to Find the 
Ratio of Expansion and the Period of Admission. 

P = initial absolute pressure in lbs. per sq. in.; 

p = average total pressure during stroke in lbs. per sq. in., 

L = length of stroke in inches; v, • • f +.m.^. 

I = period of admission measured from beginmng of stroke, 

c = clearance in inches; 

L-\-c /-ix 

R = actual ratio of expansion = ^ ^ ^^^ 



V 



P(14-hyplogfi) 
R 



To find average pressure p, taking account of clearance, 

pg^c^ ^Pq + c) hyp log R-Pc /2) 

Tp = ~~r 

whence pL + Pc = P (i + c) (1 4- hyp log R) ; 

admission ?. substitute it in equation (3) and solve for R. Substitute tms- 
value of R in the formula (1), or I = ^^ - c, obtained from formula^ 
ri), and find I. If the result is .greater than, the assumed value of J 
then the assumed value of the period of admission is too lo^^- f, ff :/^^ 
assumed value is too short. Assume a new value of .^'.substitute it in 
formula (3) as before, and continue by this method of trial and error lui 
the required values of R and I are obtained. 



THE STEAM-ENGINE. 



963 



¥ 



Example. — P — 70, p = 42.78, L= 60 in., c = 3 in., to find I. Assume 
I = 21 in. 

U + c '-If X 60+ 3 

hyp log /? = ^-j+~c 1= -n + 3 1 = 1.653- 1« 0.653; 

hyp log 72 = 0.653, whence 72 = 1.92. 

^~ R ^"1.92 "^-^^.S. 

which Is erreater than the assumed value, 21 inches. 
l*Jovv assume I = 15 inches: 

l|fx60 + 3 
hyp log 72 = \^^^ 1 = 1.204, whence /e = 3.5; 

I = — TT^ — c= r-^— 3 = 18 — 3 = 15 inches, the value assumed, 
K o.o 

Therefore R = 3.5, and Z = 15 inches. 

Period of Admission Required for a Given Actual Ratio of Expansion: 

1= — ~ c, in inches (4) 

K 

- ^ * ^ 1 7 100 + p. ct. clearance ^ , 

In percentage of stroke, I = — ^ p. ct. clearance . (5) 

P (l-\-c) P 
Terminal pressure = -y— — ■ = -^ (6) 

Pressure at any other Point of the Expansion. — Let Li = length of 
stroke up to the given point. 

P(l-\- c) 
Pressure at the given point = ^ — (7) 

Li\ ~r C 

Mechanical Energy of Steam Expanded Adiabatically to Various 
Pressures. — The figures in the following table are taken from a chart 
constructed by R. M. Neilson in Power, Mar. 16, 1909. The pressures 
are absolute, lbs per sq. in. 



mm . . 


























1" 


20 


25 


40 


60 


80 


100 


120 


140 


170 


200 


250 




Mechanical Energy, Thousands of Foot-Pounds p 


3r Lb- of Steam. 


fei 






15 





f >7 


29.5 


55.5 


77.5 


94.5 


107 


116.5 


121 


136,5 


146 


160 


12 


12 


29 


41 


66.5 


88 


104 


116 


126 


135 


145 


154.5 


168.5 


10 


22 


39 


50.5 


75.5 


97 


113 


125 


135.5 


144 


154 


163.5 


176 


8 


34 


50 


62 


86.5 


109 


124 


136 


147 


155 


165.5 


174.5 


186 


6 


49 


64 


76 


101 


123 


138 


150 


160 


168.5 


179 5 


188 


199 


4 


68 


85 


95.5 


120 


142 


157 


168 


177.5 


186 


196 


204.5 


216 


2 


100 


116 


128 


151 


171 


186.5 


197.5 


207 


215 


224 


232.5 


244 


1 


131 


147 


157 5 


181 5 


200.5 


215 


225 


234.5 


243 


250.5 


260.5 


270.5 



Measures for Comparins: the Duty of Enffines. — Capncitv is meas- 
ured in horse-powers, pxpressed bv the initials, H.P.: 1 H.P. = 33,000 
ft.-lbs. per minute, =550 ft.-lbs. perse-ond, = 1,980,000 ft.-lbs. per hour. 
1 ft.-lb. = a pressure of 1 lb. exerted through a space of 1 ft. 

Economy is measured, 1, in pounds of coal per horse-power per hour; 
2, in pounds of steam per horse-power per hour. The second of these 
measures is the more accurate and scientific, since thn pnsnne uses steam 
and not coal, and it is independent of the economy of the boiler. A still 
more accurate measure is the heat units per minute (or per hour) per 
horse-power. 



964 



THE STEAM-ENGINE. 



In gas-engine tests the common measure is the number of cubic feet 
of gas (measured at atmospheric pressure) per horse-power, but as all gas 
is not of the same quality, it is necessary for comparison of tests to give 
the analysis of the gas. When the gas for one engine is made in one 
gas-producer, then the number of pounds of coal used in the producer per 
hour per horse-power of the engine is a measure of economy. Since 
different coals vary in heating value, a more accurate measure is the 
number of heat units required per horse-power per hour. 

Economy, or duty of an engine, is also measured in the number of foot- 
pounds of work done per pound of fuel. As 1 horse-power is equal to 
1,980,000 ft .-lbs. of work in an hour, a dutv of 1 lb. of coal per H.P. per 
hour would be equal to 1,980,000 ft .-lbs. per lb. of fuel; 2 lbs. per H.P. 
per hour equals 990,000 ft. -lbs. per lb. of fuel, etc. 

The duty of pumping-engines is expressed by the number of foot- 
pounds of work done per 100 lbs. of coal, per 1000 lbs. of steam, or per 
million heat units, 

When the duty of a pumping-engine is given, in ft. -lbs. per 100 lbs. of 
coal, the equivalent number of pounds of fuel consumed per horse-power 
per hour is found by dividing 198 by the number of millions of foot-pounds 
of duty. Thus a pumping-engine giving a duty of 99 millions is equiva- 
lent to 198/99 = 2 lbs. of fuel per horse-power per hour. 

Efficiencj^ Measured in Thermal Units per Minute. — The efficiency 
of an engine is sometimes expressed in terms of the number of thermal 
units used by the engine per minute for each indicated horse-power, instead 
of by the number of pounds of steam used per hour. 

The heat chargeable to an engine per pound of steam is the difference 
between the total heat in a pound of steam at the boiler-pressure and that 
in a pound of the feed-water entering the boiler. In the case of con- 
densing engines, suppose we have a temperature in the hot-well of 100° F., 
corresponding to a vacuum of 28 in. of mercury; we may feed the water 
into the boiler at that temperature. In the case of a non-condensing 
engine, by using a portion of the exhaust steam in a good feed-water 
heater, at a pressure a trifle above the atmosphere (due to the resistance, 
of the exhaust passages through the heater), we may obtain feed-water 
at 212°. One pound of steam used by the engine then would be equivalent 
to thermal units as follows: 

Gauge pressure 50 75 100 125 150 175 200 

Absolute pressure. ...65 90 115 140 165 190 215 

Total heat in steam above 32°: 

1178.5 1184.4 1188.8 1192.2 1195.0 1197.3 1199.2 

Subtracting 68 and 180 heat-units, respectively, the heat above 32° in 
feed-water of 100° and 212° F., we have — 

Heat given by boiler per pound of steam: 

Feed at 100° 1110.5 1116.4 1120.8 1124.2 1127.0 1129.3 1131.2 

Feed at 212° 998.5 1004.4 1008.8 1012.2 1015.0 1017.3 1019.2 

Thermal units per minute used by an engine for each pound of steam 
used per indicated horse-power per hour: 

Feed at 100° 18.51 18.61 18.68 18.74 18.78 18.82 18.85 

Feed at 212° 16.64 16.76 16.78 16.87 16.92 16.96 16.99 

Examples. — A triple-expansion engine, condensing, with steam at 
175 lbs. gauge, and vacuum 28 in., uses 13 lbs. of water per I. H.P. per hour, 
and a high-speed non-condensing engine, with steam at 100 lbs. gauge, 
uses 30 lbs. How many thermal units per minute does each consume? 

Ans. — 13 X 18.82 = 244.7, and 30 X 16.78 = 503.4 thermal units 
per minute. 

A perfect engine converting all the heat-energy of the steam into 
work would reauire 33,000 ft.-lbs. ^ 777.54 = 42.44 thermal units per 
minute per indicated horse-power. This figure, 42.44, therefore, divided 
by the number of thermal units per minute per I. H.P. consumed by an 
engine, gives its efficiency as compared with an ideally perfect engine. 
In the examples above, 42.44 divided by 244.7 and by 503.4 gives 
17.34% and 8.43% eflaciency, respectively. 



ACTUAL EXPANSIONS. 



965 



ACTUAL, EXPANSIONS 

With Different Clearances and Cut-offs. 

Computed by A. F. Nagle. 







Per Cent of Clearance. 


Cut- 
off. 











1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


.01 


100.00 


50.5 


34.0 


25.75 


20.8 


17.5 


15.14 


13.38 


12.00 


10.9 


10 


.02 


50.00 


33.67 


25.50 


20.60 


17.33 


15.00 


13.25 


11.89 


10.80 


9.91 


9.17 


.03 


33.33 


25.25 


20.40 


17.16 


14.86 


13.12 


11.78 


10.70 


9.82 


9.08 


8.46 


.04 


25.00 


20.20 


17.00 


14.71 


13.00 


11.66 


10.60 


9.73 


9.00 


8.39 


7.86 


.05 


20.00 


16.83 


14.57 


12.87 


11.55 


10.50 


9.64 


8.92 


8.31 


7.79 


7.33 


.06 


16.67 


14.43 


12.75 


11.44 


10.40 


9.55 


8.83 


8.23 


7.71 


7.27 


6.88 


.07 


14.28 


12.62 


11.33 


10.30 


9.46 


8.75 


8.15 


7.64 


7.20 


6.81 


6.47 


.08 


12.50 


11.22 


10.2 


9.36 


8.67 


8.08 


7.57 


7.13 


6.75 


6.41 


6.11 


.09 


11.11 


10.10 


9.27 


8.58 


8.00 


7.50 


7.07 


6.69 


6.35 


6.06 


5.79 


.10 


10.00 


9.18 


8.50 


7.92 


7.43 


7.00 


6.62 


6.30 


6.00 


5.74 


5.50 


.11 


9.09 


8.42 


7.84 


7.36 


6.93 


6.56 


6.24 


5.94 


5.68 


5.45 


5.24 


.12 


8.33 


7.78 


7.29 


6.86 


6.50 


6.18 


5.89 


5.63 


5.40 


5.19 


5.00 


.14 


7.14 


6.73 


6.37 


6.06 


5.78 


5.53 


5.30 


5.10 


4.91 


4.74 


4.58 


.16 


6.25 


5.94 


5.67 


5.42 


5.20 


5.00 


4.82 


4.65 


4.50 


4.36 


4.23 


.20 


5.00 


4.81 


4.64 


4.48 


4.33 


4.20 


4.08 


3.96 


3.86 


3.76 


3.67 


.25 


4.00 


3.88 


3.77 


3.68 


3.58 


3.50 


3.42 


3.34 


3.27 


3.21 


3.14 


.30 


3.33 


3.26 


3.19 


3.12 


3.06 


3.00 


2.94 


2.90 


2.84 


2.80 


2.75 


.40 


2.50 


2.46 


2.43 


2.40 


2.36 


2.33 


2.30 


2.28 


2.25 


2.22 


2.20 


.50 


2.00 


1.98 


1.96 


1.94 


1.92 


1.90 


1.89 


1.88 


1.86 


1.85 


1.83 


.60 


1.67 


1.66 


1.65 


1.64 


1.63 


1.615 


1.606 


1.597 


1.588 


1.580 


1.571 


.70 


1.43 


1.42 


1.42 


1.41 


1.41 


1.400 


1.395 


1.390 


1.385 


1.380 


1.375 


.80 


1.25 


1.25 


1.244 


1.241 


1.238 


1.235 


1.233 


1.230 


1.227 


1.224 


1.222 


.90 


1.111 


1.11 


1.109 


1.108 


1.106 


1.105 


1.104 


1.103 


1.102 


1.101 


1.100 


1.00 


1.00 


1.00 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 


1.000 



Relative Eflficiency of 1 lb. of Steam with and without Clearance; 

back pressure and compression not considered. 



- - -P (^ + c) + P (Z + c) hyp log R - Pc 
Let P = 1;L = 100; Z = 25; c = 7. 



Mean total pressure 



107 

32 + 32 hyp log -^-7 



32+ 32X 1.207- 7 



= 0.636. 



100 100 

If the clearance be added to the stroke, so that clearance becomes 
zero, the same quantity of steam being used, admission I being then 
= / + c = 32, and stroke L +,c = 107, 



107 107 

The work of one stroke = pi{L + c) = 0.660 X 107 = 70.6. The 
amount of the clearance 7 being added to both admission and the 
stroke, the same quantity of steam will do more work than when the 
clearance is 7 in the ratio 706 : 636, or 11% more. 

Back Pressure Considered. — If backpressure =0.10ofP, thisamount 
has to be subtracted from p and pi giving p = 0.536, pi = 0.560, the 
work of a given quantity of steam used without clearance being greater 
than when clearance is 7% in the ratio (560 X 1.07) : 536, or 12% more. 

Effect of Compression. — By early closure of the exhaust, so that a 
portion of the exhaust-steam is compressed into the clearance-space, 
much of the loss due to clearance may be avoided. If expansion is con- 
tinued down tothe back pressure, if the back pressure is uniform through- 
out the exhaust-stroke, and if compression begins at such point that the 



966 



THE STEAM-ENGINE. 



exhaust-steam remaining in the cylinder is compressed to the initial 
pressure at the end of the back stroke, then the work of compression of the 
exhaust-steam equals the work done during expansion by the clearance- 
steam. The clearance-space being filled by the exhaust-steam thus com- 
pressed, no new steam is required to fill the clearance-space for the next 
forward stroke, and the work and efficiency of the steam used in the 
cylinder are just the same as If there were no clearance and no compression. 
When, however, there is a drop in pressure from the final pressure of the 
expansion, or the terminal pressure, to the exhaust or back pressure (the 
usual case), the work of compression to the initial pressure is greater than 
the work done by the expansion of the clearance-steam, so that a loss of 
efficiency results. In this case a greater efficiency can be attained by 
inclosing for compression a less quantity of steam than that needed to fill 
the clearance-space with steam of the initial pressure. (See Clark, 
S. E., p. 399, et seq. ; also F. H. Ball, Trans. A. S. M. E., xiv, 1067.) It is 
shown by Clark that a somewhat greater efficiency is thus attained 
whether or not the pressure of the steam be carried down by expansion 
to the back exhaust-pressure. 

Cylinder-condensation may have considerable effect upon the best 
point of compression, but it has not yet (1893) been determined by 
experiment. (Trans. A. S. M. E., xiv, 1078.) 

Clearance in Low- and High-speed Engines. (Harris Tabor, Am. 
Mack., Sept. 17, 1891.) — The construction of the high-speed engine is 
such, \\ith its relatively short stroke, that the clearance must be much 
larger than in the releasing-valve type. The short-stroke engine is, 
of necessity, an engine with large clearance, which is aggravated when 
variable compression is a feature. Conversely, the engine with releasing- 
valve gear is, from necessity, an engine of slow rotative speed, where 
great power is obtainable from long stroke, and small clearance is a 
feature in its construction. In one case the clearance will vary f^-om 
8% to 12% of the piston-displacement, and in the other from 2% to 3%. 
In the case of an engine with a clearance equaling 10% of the piston- 
displacement the waste room becomes enormous when considered in con- 
nection with an early cut-off. The system of compounding reduces the 
waste due to clearance in proportion as the steam is expanded to a lower 
pressure. The farther expansion is carried through a train of cyfinders 
the greater will be the reduction of waste due to clearance. This is shown 
from the fact that the high-speed engine, expanding steam much less than 
the Corliss, will show a greater gain when changed from simple to com- 
pound than its rival under similar conditions. 

Cylinder-condensation. — Rankine, S. E., p. 421, says: Conduction 
of heat to and from the metal of the cyUnder, or to and from liquid water 
contained in the cylinder, has the effect of lowering the pressure at the 
beginning and raising it at the end of the stroke, the lowering effect being 
on the whole greater than the raising effect. In some experiments the 
quantity of steam wasted through alternate liquefaction and evaporation 
in the cylinder has been found to be greater than the quantity which 
performed the work. 

Percentage of Loss by Cylinder-condensation, taken at Cut-off. 

(From circular of the Ashcroft Mfg. Co. on the Tabor Indicator, 1889.) 



Is. 



5 
10 
15 
20 
30 
40 
50 



Per cent of Feed-water ac- 
counted for by the Indicator. 



Simple 
Engines. 

58 
66 
71 
74 
78 
82 
86 



Compound 
Engines, 
h.p. cyl. 



74 
76 
78 
82 
85 
88 



Triple-ex- 
pansion 

Engines, 
h.p. cyl. 



78 
80 
84 
87 
90 



Per cent of Feed-water due 
to Cylinder-condensation. 



Simple 
Engines. 

42 
34 
29 
26 
22 
18 
14 



Compound 
Engines, 
h.p. cyl. 



26 
24 
22 
18 
15 
12 



Triple-ex- 
pansion 
Engines, 
h.p. cyl. 



22 
20 
16 
13 
10 



CYLINDER CONDENSATION. 



967 



Theoretical Compared with Actual Water-consumption, Single- 
cylinder Automatic Cut-off Engines. (From the catalogue of the 
Buckeye Engine Co.) — The following table has been prepared on the 
basis of the pressures that result in practice with a constant boiler-pressure 
of 80 lbs. and ditferent points of cut-oif, with Buckeye engines and others 
with similar clearance. Fractions are omitted, except in the percentage 
column, as the degree of accuracy their use would seem to imply is not 
attained or aimed at. 





Mean 


Total 


Indicated 


Assun"*''^ 




Cut-off 


Effective 


Terminal 


Rate, lbs. 






Product 


Part of 


Pressure. 


Pressure, 


Water per 






of Cols. 






Stroke. 


lbs. per 
sq. in. 


lbs. per 
sq. in. 


I.H.P. per 
hour. 


Act'lRate. 


% Loss. 


1 and 6. 


0.10 


18 


11 


20 


32 


58 


3.8 


0.15 


27 


15 


19 


27 


41 


6.15 


0.20 


35 


20 


19 


25 


31.5 


6.3 


0.25 


42 


25 


20 


25 


25 


6.25 


C.30 


48 


30 


20 


24 


21.8 


6.54 


0.35 


53 


35 


21 


25 


19 


6.65 


0.40 


57 


38 


22 


26 


16.7 


6.68 


0.45 


61 


43 


23 


27 


15 


6.75 


0.50 


64 


48 


24 


27 


13.6 


6.8 



It will be seen that while the best indicated economy is when the cut-off 
is about at 0.15 or 0.20 of the stroke, giving about 30 lbs. M.E.P., and a 
terminal 3 or 4 lbs. above atmosphere, when we come to add the per- 
centages due to a constant amount of unindicated loss, as per sixth 
column, the most economical point of cut-off is found to be about 0.30 of 
the stroke, giving 48 lbs. M.E.P. and 30 lbs. terminal pressure. This 
showing agrees substantially with modern experience under automatic 
cut-off regulation. 

The last column shows that the actual amount of cylinder condensation 
is nearly a constant quantity, increasing only from 5.8% of the cylinder 
volume at 0.10 cut-off to 6.8% at 0.50 cut-off. 

Experiments on Cylinder-condensation. — Experiments by Major 
Thos. English (Eng'g, Oct. 7, 1887, p. 386) with an engine 10 X 14 in., 
jacketed in the sides but not on the ends, indicate that the net initial 
condensation (or excess of condensation over re-evaporation) by the 
clearance surface varies directly as the initial density of the steam, and 
Inversely as the square root of the number of revolutions per unit of time. 
The mean results gave for the net initial condensation by clearance-space 
per sq. ft. of surface at one rev. per second 6.06 thermal units in the engine 
when run non-condensing and 5.75 units when condensing. 

G. R. Bodmer (Eng'g, March 4, 1892, p. 299) says: Within the ordinary 
limits of expansion desirable in one cyUnder the expansion ratio has 
practically no influence on the amount of condensation per stroke, which 
for simple engines can be expressed by the following formula for the 
weight of water condensed [per minute, probably; the original does not 



state]: 



O ( fp +\ 

W = C ^ — . where T denotes the mean admission temper- 



L ^J^2 

ature, t the mean exhaust temperature, S clearance-surface (square feet). 
N the number of revolutions per second, L latent heat of steam at the 
mean admission temperature, and C a constant for any given type of 
engine. 

Mr. Bodmer found from experimental data that for high-pressure non- 
jacketed engines C = about 0.11, for condensing non-jacketed engines 
0.085 to 0.11, for condensing jacketed engines 0.085 to 0.053. The 
figures for jacketed engines apply to those jacketed in the usual way, 
and not at the ends. 

C varies for different engines of the same class, but is practically con- 
stant for any given engine. For simple high-pressure non-jacketed 
engines it was found to range from 0.1 to 0.112. 

Applying Mr, Bodmer's formula to the case of a Corliss non-jacketed 



968 



THE STEAM-ENGINE. 



non-condensing engine, 4-ft. stroke, 24 in. diam., 60 revs, per min., initial 
pressure 90 lbs. gauge, exhaust pressure 2 lbs., we have T - i =- 112°, 
iV = 1, L = 880, 6' = 7 sq. ft.; and, taking C = 0.112 and W= lbs. 



water condensed per minute, W = 



0.112X 112X7 



= 0.09 lb. per 




1 X 880 

minute, or 5.4 lbs. per hour. If the steam used per I.H.P. per hour 
according to the diagram is 20 lbs., the actual water consumption is 
25.4 lbs., corresponding to a cyUnder condensation of 27%. 

INDICATOR-DIAGRA3I OF A SINGLE-CYLINDER ENGINE. 

Deflnitions. — The Atmospheric Line, AS, is a line drawn by the pencil 
of the indicator when the connections with the engine are closed and both 

sides of the piston 
are open to the 
atmosphere. 

The Vacuum Line, 
OX, is a reference 
line usually drawn 
about 14.7*^ pounds 
by scale below the 
atmospheric line. 

The Clearance 
Line, OF, is a refer- 
ence line drawn at a 
distance from the 
end of the diagram 
equal to the same 
per cent of its length 
as the clearance and 
B waste room is of the 
piston-displacement. 
-X^ The Line of Boiler- 
"pressure, JK, is 
^iG- io2. • drawn parallel to the 

atmospheric line, and at a distance from it by scale equal to the boiler- 
pressure shown by the gauge. 

The Admission Line, CD, shows the rise of pressure due to the admission 
of steam to the cylinder by opening the steam-valve. 

The Steam Line, DE, is drawn when the steam-valve is open and steam 
is being admitted to the cylinder. 

The Point of Cut-off, E, is the point where the admission of steam is 
stopped by the closing of the valve. It is often difficult to determine 
the exact point at wliich the cut-off takes place. It is usually located 
where the outUne of the diagram changes its curvature from convex to 
concave. 

The Expansion Curve, EF, shows the fall in pressure as the steam in the 
cylinder expands doing work. 

The Point of Release, F, shows when the exhaust-valve opens. 
The Exhaust Line, FG, represents the change in pressure that takes 
place when the exhaust-valve opens. 

The Back-pressure Line, GH, shows the pressure against which the 
piston acts during its return stroke. 

The Point of Exhaust Closure, H, is the point where the exhaust-valve 
closes. It cannot be located definitely, as the change in pressure is at first 
due to the gradual closing of the valve. 

The Compression Curve, HC, shows the rise in pressure due to the com- 
pression of the steam remaining in the cylinder after the exhaust-valve 
has closed. 

The Mean Height of the Diagram equals its area divided by its length. 
The Mean Effective Pressure is the mean net pressure urging the piston 
forward = the mean height X the scale of the indicator-spring. 

To find the Mean Effective Pressure from the Diagram. — Divide the 
length. LB, into a number, say 10, equal parts, setting off half a part at 
L, half a part at B, and nine other parts between; erect ordinates perpen- 
dicular to the atmospheric line at the points of division of LB, cutting 
the diagram; add together the lengths of these ordinates intercepted 



INDICATOR-DIAGRAMS. 



969 



between the upper and lower lines of the diagram and divide by their 
number. Tliis gives the mean height, whicli muitiphed by the scale ol 
the indicator-spring gives the M.E.ir*. Or tiiid the area by a planimeter, 
or other means (see Mensuration, p. 56), and aiviae by the length LB 
to obtain the mean height. 

The Initial Pressure is the pressure acting on the piston at the beginning 
of the stroke. 

The Terminal Pressure is the pressure above the line of perfect vacuum 
that would exist at the end of the stroke if the steam had not been released 
earher. It is found by continuing the expansion-curve to the end of the 
diagram. 

A single indicator card shows the pressure exerted by the steam at 
each instant on one side of the piston; a card taken simultaneously from 
the opposite end of the engine shows the pressure exerted on the other 
side. By superposing these cards the pres'sure or tension on the piston 
rod may be determined. The pressure or pull on the crank pin at any 
instant is the pressure or tension in the rod modified by the angle of the 
connecting rod and by the effect of the inertia of the reciprocating parts. 
For discussion of this subject see Klein's "High-speed Steam Engine," 
also papers by S. A. Moss, Trans. A. S. M. E., 1904, and by F. W. Holl- 
mann, in Power, April 6, 1909. 

Errors of Indicators. — The most common error is that of the spring, 
which may vary from its normal rating; the error may be determined by 
proper testing apparatus and allowed for. But after making this correc- 
tion, even with the best work, the results are liable to variable errors 
which may amount to 2 or 3 per cent. See Barrus, Trans. A. S. M. E., 
v, 310: Denton, Trans. A. S. M. E., xi, 329; David Smith, U. S. N., Proc. 
Eng'g Congress, 1893, Marine Division. 

Other errors of indicator diagrams are those due to inaccuracy of the 
straight-line motion of the indicator, to the incorrect design or position 
of the "rig" or reducing motion, to long pipes between the indicator and 
the engine, to throtthng of these pipes, to friction or lost motion in the 
indicator mechanism, and to drum-motion distortion. For discussion of 
the last named see Power, April, 1909. For methods of testing indicators, 
see paper by D. S. Jacobus, Trans. A. S. M. E., 1898. 

Indicator "Rigs," or Reducing-motions; Interpretation of Diagrams 
for Errors of Steam-distribution, etc. For these see circulars of manu- 
facturers of Indicators; also works on the Indicator. 

Pendulum Indicator Rig. —Pow;er (Feb., 1S93) gives a graphical 
representation of the errors in indicator-diagrams, caused by the use ol 
incorrect forms of the pendulum rigging. It 
is shown that the "brumbo" pulley on the c E 

pendulum, to which the cord is attached, 
does not generally give as good a reduction 
as a simple pin attachment. When the end 
of the pendulum is slotted, working in a pin 
on the crosshead, the error is apt to be con- 
siderable at both ends of the card. With a 
vertical slot in a plate fixed to the cross- 
head, and a pin on the pendulum working in 
this slot, the reduction is perfect, when the 
cord is attached to a pin on the pendulum, 
a shght error being introduced if the brumbo 
pulley is used. With the connection be- 
tween the pendulum and the crosshead made 
by means of a horizontal hnk, the reduction 
is nearly perfect, if the construction is such that the connecting link 
vibrates equally above and below the horizontal, and the cord is attached 
by a pin. If the link is horizontal at mid-stroke a serious error is intro- 
duced, which is magnified if a brumbo pulley also is used. The adjoin- 
ing figures show the two forms recommended. 

The Manograph, for indicating engines of very liigh speed, invented 
by Prof. Hospitaller, is described by Howard Greene in Power, June, 1907. 
It is made by Carpentier, of Paris. A small mirror is tilted upward and 
downward by a diaphragm which responds to the pressure variations in 
the cylinder, and the same mirror is rocked from side to side by a reducing 
mechanism which is geared to the engine and reproduces the reaprocations 



Fig. 163. 



970 THE STEAM-ENGINE. 

of the engine piston on a smaller scale. A beam of light is reflected by 
the mirror to the ground-glass screen, and this beam, by the oscillations 
of the mirror, is made to traverse a path corresponding to that of the 
pencil point of an ordinary indicator. The diagram, therefore, is made 
continuously but varies with varying conditions in the cylinder. 

A plate-holder carrying a photograpliic dry plate can be substituted for 
the ground-glass screen, and the diagram photographed, the exposure 
required varying from half a second to three seconds. By the use of 
special diaphragms and springs the effects of low pressures and vacuums 
can be magnified, and thus the instrument can be made to show with 
remarkable clearness the action of the valves of a gas engine on the suction 
and exhaust strokes. 

The Lea Continuous Recorder, for recording the steam consiimptign 
of an engine, is described by W. H. Booth in Power, Aug. 31, 1909. It 
comprises a tank into which flows the condensed steam from a condenser, 
a triangular notch through which the water flows from the tank, and a 
mechanical device through which the variations in the level of the water 
in the tank are translated into the motion of a pencil, which motion is 
made proportionate to the quantity flowing, and is recorded on paper 
moved by clockwork. 

INDICATED HORSE-POWER OF ENGINES, SINGIJE-CYLINDER. 

Indicated Horse-power, I.H.P.= , 

oo,yJ\)\J 

in which P = mean effective pressure in lbs. per sq. in.; L = length of 
stroke in feet; a = area of piston in square inches. For accuracy, one 
half of the sectional area of the piston-rod must be subtracted from the 
area of the piston if the rod passes through one head, or the whole area of 
the rod if it passes through both heads: n = No. of single strokes per min. 
= 2 X No. of revolutions of a double-acting engine. 

PfiQ 

I.H.P. =;5^-7r7rp: . in wluch <S = piston speed in feet per minute. 
I.H.P. = ^^^ = Sn^ = 0.0000238 PLd2n = 0.0000238Pd2^, 

in which d = diam. of cyl. in inches. (The flgures 238 are exact, since 
7854 -i- 33 = 23.8 exactly.) If product of piston-speed X mean effec- 
tive pressure = 42,017, then the horse-power would equal the square of 
the diameter in inches. 

Handy Rule for Estimating the Horse-power of a Single-cylinder 
Engine. — Square the diameter and divide by 2. This is correct whenever 
the product of the mean effective pressure and the piston-speed = V? 
of 42,017, or, say, 21,000, viz., when M.E.P. = 30 and i5 = 700: when 
M.E.P. = 35 and 5 = 600: when M.E.P. = 38.2 and 5 = 550: and when 
M.E.P. = 42 and S = 500. These conditions correspond to those of 
ordinary practice with both Corliss engines and shaft-governor high-speed 
engines! 

Given Horse-power, Mean Effective Pressure, and Piston-speed, 
to find Size of Cylinder. — 

33,000 XI.H.P -^. ^ ^^. ./l.H.P. 

Area = — — pj • Diameter = 205 y p^ • 

Brake Horse-power is the actual horse-power of the engine as measured 
at the fly-wheel by a friction-brake or dynamometer. It is the indicated 
horse-power minus the friction of the engine. 

Electrical Horse-power is the power in an electric current, usually 
measured in kilowatts, translated into horse-power. 1 H.P. = 33,000 
ft. lbs. per min.; 1 K.W.= 1.3405 H.P.; 1 H.P. = 0.746 kilowatts, or 
746 watts. 

Example. — A 100-H.P. engine, with a friction loss of 10% at rated 
load, drives a generator whose efficiency is 90%, furnishing current to a 
motor of 90% effy., through a line whose loss is 5%. I. H.P. = 100; 
B.H.P. = 90: E.H.P. at generator 81, at end of line 76.95. H.P. delivered 
by motor 69.26. 



INDICATED HORSE-POWER OF ENGINES. 



971 



Table for Roughly Approximating the Horse-power of a Com- 
pound Engine from the Diameter of its Low-pressure Cylinder. — 



The indicated horse-power of an engine being 



PsiP- 



in which P = 



42.017' 

mean effective pressure per sq, in.. 5 = piston-speed in ft. per min., and 
d = diam. of cylinder in inches; if s = 600 ft. per min., wliich is approxi- 
mately the speed of modern stationary engines, and P = 35 lbs., which is 
an approximately average figure for the M.E.P. of single-cylinder engines, 
and of compound engines referred to the low-pressure cylinder, then 
I.H.P. = V2C/2; hence the rough-and-ready rule for horse-power given 
above: Square the diameter in inches and divide by 2. This appUes to 
triple and quadruple expansion engines as well as to single cylinder and 
compound. For most economical loading, the M.E.P. referred to the 
low-pressure cylinder of compound engines is usually not greater than 
that of simiple engines; for the greater economy is obtained by a greater 
number of expansions of steam of higher pressures, and the greater the 
number of expansions for a given initial pressure the lower the mean 
effective pressure. The following table gives approximately the figures 
of mean total and effective pressures for the different types of engines, 
together with the factor by wliich the square of the diameter is to be 
multiplied to obtain the horse-power at most economical loading, for a 
piston-speed of 600 ft. per minute. 



Type of Engine. 



:^Ph 



O) c3 73 
C K O 



- 9 (« 
fl s 1^ 



c3 o 



(D 






cs oT 


^gi 


:3 


^ 3 , 


H^^ 




^?,^ 


^flH£ 


^^% 


% 


H 



(D !» 



a^ 
c a 



0) X 

aS 
o N 



Non-condensing. 



Single Cylinder 

Compound 

Triple 

Quadruple 

Single Cylinder 

Compound 

Triple 

Quadruple 



100 


5. 


20 


0.522 


52.2 


15.5 


36.7 


600 


120 


7.5 


16 


.402 


48.2 


15.5 


32.7 


'* 


160 


10. 


16 


.330 


52.8 


15.5 


37.3 


*• 


200 


12.5 


16 


.282 


56.4 


15.5 


40.9 


*' 



0.524 
467 
533 
584 



Condensing Engines. 



100 


10. 


10 


0.330 


33.0 


2 


31.0 


600 


120 


15. 


8 


.247 


29.6 


2 


27.6 


•* 


160 


20. 


8 


.200 


32.0 


2 


30.0 


" 


200 


25. 


8 


.169 


33.8 


2 


31.8 


" 



0.443 
.590 
.429 
.454 



For any other piston-speed than 600 ft. per min., multiply the figures 
in the last column by the ratio of the piston-speed to 600 ft. 

Horse-power Constant of a given Engine for a Fixed Speed =» 

product of its area of piston in square inches, length of stroke in feet 

and number of single strokes per minute divided by 33,000, or ^^ 

«= C. The product of the mean effective pressure as found by the dia- 
gram and this constant is the indicated horse-power. 

Horse-power Constant of any Engine of a given Diameter of 
Cylinder, whatever the length of stroke, = area of piston -^ 33,000 = square 
of the diameter of piston in inches X 0.0000238. A table of constants 
derived from tliis form.ula is given on page 943. 

The constant multiplied bv the piston-speed in feet per minute and 
by the M.E.P. gives the I.H.P. 

Table of Engine Constants for Use in Figuring Horse-power. — 
"Horse-power constant" for cylinders from 1 inch to 60 inches in diam- 
eter, advanrine by Sth?;. for one foot of piston-speed per minute and one 
pound of M.E.P. " Find the diameter of the cylinder in the column at the 
side. If the diameter contains no fraction the constant will be found in 
the cohimn headed Even Inches. If the diameter is not in even inches, 
follow the line horizontally to the column corresponding to the required 
fraction. The constants multiplied by the piston-speed and by the 
M.E.P. give the horse-power. 



972 



THE STEAM-ENGINE. 



Engine Constants, Constant X Piston Speed X M.E.P. =H.P. 



Diam.of 


Even 
Inches. 
















Cylin- 
der. 


+ 1/8 


+ 1/4 


+ 3/8 


+ 1/2 


+ 5/8 


+ 3/4 


+ 7/8 


I 


.0000238 


.0000301 


.0000372 


.0000450 


.0000535 


.0000628 


.0000729 


.0000837 


2 


.0000952 


.0001074 


1.0001205 .0001342 


.0001487 


.0001640 .0001800 


.0001967 


3 


.0002142 


.0002324 


1.0002514 .0002711 


.0002915 


.0003127 


.0003347 


.0003574 


4 


.0003808 


.0004050 


.0004299 


.0004554 


.0004819 


.0005091 


.0005370 


.0005556 


5 


.0005950 


.0006251 


.0006560 


.0006876 


.0007199 


.0007530 


.0007869 


.0008215 


6 


.0008568 


.0008929 


.0009297 


.0009672 


.0010055 


.0010445 


.0010844 


.0011249 


7 


.0011662 


.0012082 


.0012510 


.0012944 


.0013387 


.0013837 


.0014295 


.0014759 


8 


.0015232 


.0015711 


.0016198 


.0016693 


.0017195 


.0017705 


.0018222 


.0018746 


9 


.0019278 


.0019817 


.0020363 


.0020916 


.0021479 


.0022048 


.0022625 


.0023209 


10 


.0023800 


.0024398 


.0025004 


.0025618 


.0026239 


.0026867 


.0027502 


.0028147 


11 


.0028798 


.0029456 


.0030121 


.0030794 


.0031475 


.0032163 


.0032859 


.0033551 


12 


.0034272 


. 0034990 


.0035714 


.0036447 


.0037187 


.0037934 


.0038690 


.0039452 


13 


.0040222 


.0040999 


.0041783 


.0042576 


.0043375 


.0044182 


.0044997 


.0045819 


14 


.0046648 


.0047484 


.0048328 


.0049181 


.0050039 


. 0050906 


.0051780 


.0052661 


15 


.0053550 


.0054446 


.0055349 


.0056261 


.0057179 


.0058105 


.0059039 


.0059979 


15 


.0060928 


.0061884 


.0062847 


.0063817 


.0064795 


.0065780 


.0066774 


.0067774 


17 


.0068782 


.0069797 


.0070819 


.0071850 


.0072887 


.0073932 


.0074985 


.0075044 


18 


.0077112 


.0078187 


.0079268 


.0080360 


.0081452 


.0082560 


.0083672 


.0084791 


19 


.0085918 


.0087052 


.0088193 


.0089343 


.0090499 


.0091663 


.0092835 .0094013 


20 


.0095200 


.0096393 


.0097594 


.0098803 


.0100019 


.0101243 


.0102474;. 0103712 


21 


.0104958 


.0106211 


.0107472 


.0108739 


.0110015 


.0111299 


.0112589 .0113885 


22 


.0115192 


.0116505 


.0117825 


.0119152 


.0120487 


.0121830 


.0123179!. 0124537 


23 


.0125902 


.0127274 


.0128654 


.0130040 


.0131435 


.0132837 


.01 342471 01 35664 


24 


.0137088 


.0138519 


.0139959 


.0141405 


.0142859 


.0144321 


.0145789;. 0147265 


25 


.0148750 


.0150241 


.0151739 


.0153246 


.0154759 


.0156280 


.0157809 


.0159345 


26 


.0160888 


.0162439 


.0163997 


.0165563 


.0167135 


.0168716 


.0170304 


.0171899 


27 


.0173502 


.0175112 


.0176729 


.0178355 


.0179988 


.0181627 


.0183275 


.0184929 


28 


.0186592 


.0188262 


.0189939 


.0191624 


.0193316 


.0195015 


.0196722 


.0198435 


29 


.0200158 


.0201887 


.0203634 


.0205368 


.0207119 


.0208879 


.0210645 


.0212418 


30 


.0214200 


.0215988 


.0217785 


.0219588 


.0221399 


.0223218 


.0225044 


.0226877 


31 


.0228718 


.0230566 


.0232422 


.0234285 


.0236155 


.0238033 


.0239919 


.0241812 


32 


.0243712 


.0245619 


.0247535 


.0249457 


.0251387 


.0253325 


.0255269 


.0257222 


33 


.0259182 


.0261149 


.0263124 


.0265106 


.0267095 


.0269092 


.02710971.0273109 


34 


.0275128 


.0277155 


.0279189 


.0281231 


.0283279 


.0285336 


.0287399 .0289471 


35 


.0291550! 


.0293636 


.0295729 


.0297831 


.0299939 


.0302056 


.0304179 .0306309 


35 


.0308448 


.0310594 


.0312747 


.0314908 


.0317075 


.0319251 


.0321434 .0323524 


37 


.0325822 


.0328027 


.0330239 


.0332460 


.0334687 


.0336922 


.0339165 


.0341415 


38 


.0343672 


.0345937 


.0348209 


.0350489 


.0352775 


.0355070 


.0357372 


.0359581 


39 


.0361998 


.0364322 


.0366654 


.0368993 


.8371339 


.0373694 


.0376055 


.0378424 


40 


.0380800 


.0383184 


.0385575 


.0387973 


.0390379 


.0392793 


.0395214 


.0397542 


41 


.0400078 


.0402521 


.0404972 


.0407430 


.0409895 


.0412368 


.0414849 


.0417337 


42 


.0419832 


.0422335 


.0424845 


.0427362 


.0429887 


.0432420 


.0434959 


.0437507 


43 


.0440062 


.0442624 


.0445194 


.0447771 


.0450355 


.0452947 


.0455547 


.0458154 


44 


.0460768 


.0463389 


.0466019 


.0468655 


.0471299 


.0473951 


.0476609 


.0479276 


45 


.0481950 


.0484631 


.0487320 


.0490016 


.0492719 


.0495430 


0498149 


.0500875 


45 


.0503608 


.0506349 


.0509097 


.0511853 


.0514615 


.0517386 


.0520164 


.0522949 


47 


.0525742 


.0528542 


.0531349 


.0534165 


.0536988 


.0539818 


.0542655 


.0545499 


48 


.0548352 


.0551212 


.0554079 


.0556953 


.0559835 


.0562725 


.0565622 


.0568525 


49 


.0571438 


.0574357 


.0577284 


.0580218 


.0583159 


.0586109 


.0589065 


.0592029 


50 


.0595000 


.0597979 


.0600965 


.0603959 


.0606959 


.0609969 


.0612984 


.0515007 


51 


.0619038 


.0622076 


.0625122 


.0628175 


.0632235 


.0634304 


.0637379 


.0540452 


52 


.0643552 


.0646649 


.0549753 


.0652867 


.0655987 


.0659115 


.0662250 


.0655392 


53 


.0668542 


.0671699 


.0674864 


.0678036 


.0681215 


.0684402 


.0687597 


.0690799 


54 


.0694008 


.0697225 


.0700449 


.0703681 


.0705293 .0710166 


.0713419 


.0715581 


55 


.0719950 


.0724226 


.0726510 


.0729801 


.0733099 .0736406 


.0739719 


.0743039 


55 


.0746368 


.0749704 


.0753047 


.0756398 


.0759755 


.0763120 


.0765494 


.0759874 


57 


.0773262 


.0776657 


.0780060 


.0783476 


.0786887 


.0790312 


.0793745 


.0797185 


58 


.0800632 


.0804087 


.0807549 


.0811019 


.0814495 


.0817980 


.0821472 


.0824971 


59 


.0828478 


.0831992 


.0835514 


.0839043 


.0842579 


.0846123 .0849675 


.0853234 


60 


.0856800 


.0860374 


.0863955 


.0867543 


.0871139 


.0874743|. 0878354 


.0881973 



INDICATED HORSE-POWER OF ENGINES. 



973 



Horse-power per Pound Mean Effective Pressure. 

Formula, Area in sq. in. X piston-speed ^ 33,000. 



Diam of 

Cylinder, 
inches. 




Speed of Pist( 


3n in feet per minute. 




100 


200 


300 


400 


500 


600 


700 


800 


900 


4 


.0381 


.0762 


.1142 


.1523 


.1904 


.2285 


.2666 


.3046 


.3427 


41/2 


.0482 


.0964 


.1446 


.1928 


.2410 


.2892 


.3374 


.3856 


.4338 


5 


.0595 


.1190 


.1785 


.2380 


.2975 


.3570 


.4165 


.4760 


.5355 


51/2 


.0720 


.1440 


.2160 


.2880 


.3600 


.4320 


.5040 


.5760 


.6480 


6 


.0857 


.1714 


.2570 


.3427 


.4284 


.5141 


.5998 


.6854 


.7711 


61/2 


.1006 


.2011 


.3017 


.4022 


.5028 


.6033 


.7039 


.8044 


.9050 


7 


.1166 


.2332 


.3499 


.4665 


.5831 


.6997 


.8163 


.9330 


1.0496 


71/2 


.1339 


.2678 


.4016 


.5355 


.6694 


.8033 


.9371 


1.0710 


1.2049 


8 


.1523 


.3046 


.4570 


.6093 


.7616 


.9139 


1.0662 


1.2186 


1.3709 


81/2 


.1720 


.3439 


.5159 


.6878 


.8598 


1.0317 


1.2037 


1.3756 


1.5476 


9 


.1928 


.3856 


.5783 


.7711 


.9639 


1.1567 


1 .3495 


1.5422 


1.7350 


91/2 


.2148 


.4296 


.6444 


.8592 


1.0740 


1.2888 


1.5036 


1.7184 


1.9532 


10 


.2380 


.4760 


.7140 


.9520 


1.1900 


1.4280 


1.6660 


1.9040 


2.1420 


n 


.2880 


.5760 


.8639 


1.1519 


1.4399 


1.7279 


2.0159 


2.3038 


2.5818 


12 


.3427 


.6854 


1.0282 


1.3709 


1.7136 


2.0563 


2.3990 


2.7418 


3.0845 


13 


.4022 


.8044 


1.2067 


1.6089 


2.0111 


2.4133 


2.8155 


3.2178 


3.6200 


14 


.4665 


.9330 


1.3994 


1.8659 


2.3324 


2.7989 


3.2654 


3.7318 


4.1983 


15 


.5355 


1.0710 


1.6065 


2.1420 


2.6775 


3.2130 


3.7485 


4.2840 


4.8195 


16 


.6093 


1.2186 


1.8278 


2.4371 


3.0464 


3.6557 


4.2650 


4.8742 


5.4835 


17 


.6878 


1.3756 


2.0635 


2.7513 


3.4391 


4.1269 


4.8147 


5.5026 


6.1904 


18 


.7711 


1.5422 


2.3134 


3.0845 


3.8556 


4.6267 


5.3978 


6.1690 


6.9401 


19 


.8592 


1.7184 


2.5775 


3.4367 


4.2959 


5.1551 


6.0143 


6.8734 


7.7326 


20 


.9520 


1.9040 


2.8560 


3.8080 


4.7600 


5.7120 


6.6640 


7.6160 


8.5680 


21 


1.0496 


2.0992 


3.1488 


4.1983 


5.2479 


6.2975 


7.3471 


8.3966 


9.4462 


22 


1.1519 


2.3038 


3.4558 


4.6077 


5.7596 


6.9115 


8.0634 


9.2154 


10.367 


23 


1.2590 


2.5180 


3.7771 


5.0361 


6.2951 


7.5541 


8.8131 


10.072 


11.331 


24 


1 .3709 


2.7418 


4.1126 


5.4835 


6.8544 


8.2253 


9.5962 


10.967 


12.338 


25 


1.4875 


2.9750 


4.4625 


5.9500 


7.4375 


8.9250 


10.413 


11.900 


13.388 


26 


1.6089 


3.2178 


4.8266 


6.4355 


8.0444 


9.6534 


11.262 


12.871 


14.480 


27 


1.7350 


3.4700 


5.2051 


6.9401 


8.6751 


10.410 


12.145 


13.880 


15.615 


28 


1.8659 


3.7318 


5.5978 


7.4637 


9.3296 


11.196 


13.061 


14.927 


16.793 


29 


2.0016 


4.0032 


6.0047 


8.0063 


10.008 


12.009 


14.011 


16.013 


18.014 


30 


2.1420 


4.2840 


6.4260 


8.5680 


10.710 


12.852 


14.994 


17.136 


19.278 


31 


2.2872 


4.5744 


6.8615 


9.1487 


11.436 


13.723 


16.010 


18.297 


20.585 


32 


2.4371 


4.8742 


7.3114 


9.7485 


12.186 


14.623 


17.060 


14.497 


21.934 


33 


2.5918 


5.1836 


7.7755 


10.367 


12.959 


15.551 


18.143 


20.735 


23.326 


34 


2.7513 


5.5026 


8.2538 


11.005 


13.756 


16.508 


19.259 


22.010 


24.762 


35 


2.9155 


5.8310 


8.7465 


11.662 


14.578 


17.493 


20.409 


23.324 


26.240 


36 


3.0845 


6.1690 


9.2534 


12.338 


15.422 


18.507 


21.591 


24.676 


27.760 


37 


3.2582 


6.5164 


9.7747 


13.033 


16.291 


19.549 


22.808 


26.066 


29.324 


38 


3.4367 


6.8734 


10.310 


13.747 


17.184 


20.620 


24.057 


27.494 


30.930 


39 


3.6200 


7.2400 


10.860 


14.480 


18.100 


21.720 


25.340 


28.960 


32.580 


40 


3.8080 


7.6160 


11.424 


15.232 


19.040 


22.848 


26.656 


30.464 


34.272 


41 


4.0008 


8.0016 


12.002 


16.003 


20.004 


24.005 


28.005 


32.006 


36.007 


42 


4.1983 


8.3866 


12.585 


16.783 


20.982 


25.180 


29.378 


33.577 


37.775 


43 


4.4006 


8.8012 


13.202 


17.602 


22.003 


26.404 


30.804 


35.205 


39.606 


44 


4.6077 


9.2154 


13.823 


18.431 


23.038 


27.646 


32.254 


36.861 


41.469 


45 


4.8195 


9.6390 


14.459 


19.278 


24.098 


28.917 


33.737 


38.556 


43.376 


46 


5.0361 


10.072 


15.108 


20.144 


25.180 


30.216 


35.253 


40.289 


45.325 


47 


5.2574 


10.515 


15.772 


21.030 


26.287 


31.545 


36.802 


42.059 


47.317 


48 


5.4835 


10.967 


16.451 


21.934 


27.418 


32.901 


38.385 


43.868 


49.352 


49 


5.7144 


11.429 


17.143 


22.858 


28.572 


34.286 


40.001 


45.715 


51.429 


50 


5.9:oo 


11.900 


17.850 


23.800 


29.750 


35.700 


41.650 


47.600 


53.550 


51 


6.1904 


12.381 


18.571 


24.762 


30.952 


37.142 


43.333 


49.523 


55.713 


52 


6.4355 


12.871 


19.307 


25.742 


32.178 


38.613 


45.049 


51.484 


57.920 


53 


6.6854 


13.371 


20.056 


26.742 


33.427 


40.113 


46.798 


53.483 


60.169 


54 


6.9401 


13.880 


20.820 


27.760 


34.700 


41.640 


48.581 


55.521 


62.461 


55 


7.1995 


14.399 


21.599 


28.798 


35.998 


43.197 


50.397 


57.596 


64.796 


56 


7.4637 


14.927 


22.391 


29.855 


37.318 


44.782 


52.246 


59.709 


67.173 


57 


7.7326 


15.465 


23.198 


30.930 


38.663 


46.396 


54.128 


61.861 


69.597 


58 


8.0063 


16.013 


24.019 


32.025 


40.032 


48.038 


56.044 


64.051 


72.054 


59 


8.2848 


16.570 


24.854 


33.139 


41.424 


49.709 


57.993 


66.278 


74.563 


60 


8.5680 


17.136 


25.704 


34.272 


42.840 


51.408 


59.976 


68.544 


77.112 



974 



THE STEAM-ENGINE. 



Nominal Horse-power, — The term "nominal horse-power "originated 
in tiie time ot Watt, and was used to express approximately the power 
01 an engine as calculated from its diameter, estimating the mean pressure 
in the cylinder at 7 lbs. above the atmospuere. it has long been obsolete. 

Horse-power Constant of a given li^ngine for Varying Speeds = 
product of its area of piston anj length oi stroke aivided by 33,000. 
This multiplied by the mean effective pressure and by the number of 
single strokes per minute is the indicated horse-power. 

To draw the Clearance-line on the Indicator-diagram, the ac- 
tual clearance not being known. — The clearance-hne may be obtained 
approximately by drawing a straight line, chad, across the compression 

Y 




Fig. 164. 
curve, first having drawn OX parallel to the atmospheric Une and 14.7 
lbs. below. Measure from a the. distance ad, equal to cb, and draw YO 
perpendicular to OX through d; then will TB divided by ^T be the per- 
centage of clearance. The clearance may also be found from the expan- 
sion-hne by constructing a rectangle efhg, and dra\^dng a diagonal gj 
to intersect the hne XO. This wiU give the point 0, and by erecting a 
perpendicular to ZO we obtain a clearance-Une OY. 

Both these methods for finding the clearance require that the expan- 
sion and compression curves be hyperbolas. Prof. Carpenter (Power, 
Sept., 1893) says that with good diagrams the methods are usually very 
accurate, and give r^^sults which check substantially. 

The Buckeye Engine Co., however, says that, as the results obtained are 
seldom correct, being sometimes too little, but more frequently too much, 
and as the indications from the two curves seldom agree, the operation 
has httle practical value, though when a clearly defined and apparently 
undistorted compression curve exists of sufficient extent to admit of the 
application of the process, it may be relied on to give much more correct 
res'ilts than the expansion curve. 

To draw the Hyperbolic Curve on the Indicator-diagram. — Select 

any point / in the actual curve, and 
from this point draw a Une perpen- 
dicular to the Une JB, meeting the 
latter in the point J. The Une JB 
may be the line of boiler-pressure, 
but this is not material: it may be 
drawn at anv convenient height near 
the top of the diagram and parallel 
to the atmospheric Une. From J 
draw a diagonal to K, the latter 
point being the intersection of the 
^ vacuum and clearance lines; from / 
Fig. 165. draw IL parallel with the atmos- 

pheric line. From L, the point of 
Intersection of the diagonal JK and the horizontal Une IL, draw the verti- 



J 3 2 1 M 


E 






^..^f^^rz ^lNX>C - \/ 


C 


^^~^^s 



WATER-CONSUMPTION OF ENGINES. 975 

cal line LM. The point M is the theoretical point of cut-off, and LM the 
cut-off line. Fix upon any number of points 1, 2, 3, etc., on the line JB, 
and from these points draw diagonals to K. From the intersection ot these 
diagonals with LM draw horizontal hues, and from 1,2, 3, etc., vertical 
lines. Where these lines meet will be points in the hyperboUc curve. 

Theoretical Water-consumption calculated from the Indicator- 
card. — The following method is given by Prof. Carpenter (Power, 
Sept., 1893): p = mean effective pressure, I = length of stroke in feet, 
a = area of piston in square inches, a -i- 144 = area in square feet, c = 
percentage of clearance to the stroke, b = percentage of stroke at point 
where water rate is to be computed, n = number of strokes per minute, 
60 n = number per hour, w = weight of a cubic foot of steam having a 
pressure as show^n by the diagram corresponding to that at the point where 
water rate is required, w' = that corresponding to pressure at end of 
compression. 



Number of cubic feet per stroke =Z ( Tqq-) ttt* 

Corresponding weight of steam per stroke in lbs. =Z (tq^) ttt ^* 



Volume of clearance 



Weight of steam in clearance = 



14,400 

Icav/ 



14,400 



Total weight of I , / ?>+ c \ wa _ Icaw' ^ la . ,, . 

steam per stroke j *" V 100 / 144 14,400 14,400 ^^ "^ ^^ w-^qw j. 

Total weight of steam ) _ 60 nZa w^cw'} 

from diagram per hour/ " 14,400 ^^ ^ -^ •'• 

The indicated horse-power is plan -4- 33,000. Hence the steam-COD- 
sumption per hour per indicated horse-power is 

^^^l(b + c)w-cw] 137.50,,,^ ^ 

p fan H- 33.000 ■ = -^-[O + c)w - cw]. 

Changing the formula to a rule, we have: To find the water rate from 
the indicator diagram at any point in the stroke. 

Rule. — To the percentage of the entire stroke which has been com- 
pleted by the piston at the point under consideration add the percentage 
of clearance. Multiply this result by the weight of a cubic foot of steam, 
having a pressure of that at the required point. Subtract from this the 
product of percentage of clearance multipUed by weight of a cubic foot 
of steam having a pressure equal to that at the end of the compression. 
Multiply this result by 137.50 divided by the mean effective pressure.* 

Note. — This method applies only to points in the expansion curve 
or between cut-off and release. 

The beneficial effect of compression in reducing the water-consumption 
of an engine is clearly shown by the formula. If the compression is 
carried to such a point that it produces a pressure equal to that at the 
point under consideration, the weight of steam per cubic foot is equal, 
and w = w\ In this case the effect of clearance entirely disappears, and 
the formula becomes 137.5 (bw) -^ p. 

In case of no compression, w' becomes zero, and the water-rate = 
137.5 [(b-hc) w] -^p. 

Prof. R. C. Carpenter (Sibley Jour, of Eng'g, Dec, 1910) states that 
tests of engines show that economy is really decreased by high com- 
pression. Armand Duchesne (Power, Jan. 10, 1911) gives as a reason 
for this that the steam undergoing compression is superheated and 
the work of compressing the superheated steam is greater than the work 
which it gives out later when it is in the condition of saturated steam. 

* For compound or triple-expansion engines read : divided by the 
equivalent mean effective pressure, on the supposition that all work is 
done in one cylinder. 



976 



THE STEAM-ENGINE. 



Prof. Denton (Trans. A. S. M. E., xiv, 1363) gives the following tabU 
of theoretical water-consumption for a perfect Mariotte expansion with 
steam at 150 lbs. above atmosphere, and 2 lbs. absolute back pressure: 



Ratio of Expansion, r. 



10 
15 

20 
25 
30 
35 



M.E.P., lbs. per sq. in. 



52.4 
38.7 
30.9 
25.9 

22.2 
19.5 



Lbs. of Water per hour 
per horse-power, W. 



9.68 
8.74 
8.20 

7.84 
7.63 
7.45 



The difference between the theoretical water-consumption found by the 
formula and the actual consumption as found by test represents *' water 
not accounted for by the indicator," due to cylinder condensation, leak- 
age through ports, radiation, etc. 

Leakage of Steam. — Leakage of steam, except in rare instances, has 
so little effect upon the lines of the diagram that it can scarcely be 
detected. The only satisfactory way to determine the tightness of an 
engine is to take it wiien not in motion, apply a full boiler-pressure to 
the valve, placed in a closed position, and to the piston as weU, which 
is blocked for the purpose at some point away from the end of the stroke, 
and see by the eye whether leakage occurs. The indicator-cocks provide 
means for bringing into view steam which leaks through the steam- 
valves, and in most cases that which leaks by tlie piston, and an opening 
made in the exhaust-pipe or observations at the atmospheric escape- 
pipe, are generally sufficient to determine the fact with regard to the 
exhaust-valves. 

The steam accounted for by the indicator should be computed for both 
the cut-off and the release points of the diagram. If the expansion-line 
departs much from the hyperbolic curve a very different result is shown 
at one point from that shown at the other. In such cases the extent of 
the loss occasioned by cylinder condensation and leakage is indicated in a 
much more truthful manner at the cut-off than at the release. (Tabor 
Indicator Circular.) 



COMPOUND ENGINES. 

Compound, Triple- and Quadruple-expansion Engines. — A com- 
pound engine is one having two or more cylinders, and in which the steam 
after doing work in the first or high-pressure cylinder completes its 
expansion in the other cylinder or cylinders. 

The term "compound" is commonly restricted, however, to engines in 
which the expansion takes place in two stages only — high and low 
pressure, the terms triple-expansion and quadruple-expansion engines 
being used when the expansion takes place respectively in three and 
four stages. The number of cylinders may be greater than tlie number 
of stages of expansion, for constructive reasons; thus in the compound or 
two-stage expansion engine the low-pressure stage may be effected in two 
cylinders so as to obtain the advantages of nearly equal sizes of cylinders 
and of three cranks at angles of 120°. In triple-expansion engines there 
are frequently two low-pressure cylinders, one of them being placed 
tandem with the high-pressure, and the other with the intermediate 
cylinder, as in mill engines with two cranks at 90°. In the triple-expan- 
sion engines of the steamers Carm^ania and Lucania, with three cranks at 
120°, there were five cylinders, two high, one intermediate, and two low, 
the high-pressure cylinders being tandem with the low. 

Advantages of Compounding. — The advantages secured by divid- 
mg the (expansion into two or more stages are twofold: 1. Reduction 
of wastes of steam by cylinder-condensation, clearance, and leakage; 
2. Dividing the pressures on the cranks, shafts, etc., in large engines so 
as to avoid excessive pressures and consequent friction. The diminished 



COMPOUND ENGINES. 



977 



loss by cylinder-condensation is effected by decreasing the range of tem- 
perature of the metal surfaces of the cyUnders, or the difference of tempera- 
ture of the steam at admission and exhaust. When high-pressure steam 
is admitted into a single-cyUnder engine a large portion is condensed by 
the comparatively cold metal surfaces; at the end of the stroke and during 
the exhaust the water is re-evaporated, but the steam so formed escapes 
into the atmosphere or into the condenser, doing no work; while if it is 
taken into a second cyUnder, as in a compound engine, it does work. 
The steam lost in the first cylinder by leakage and clearance also does 
work in the second cylinder. Also, if there is a second cylinder, the 
temperature of the steam exhausted from the first cylinder is higher than 
if there is only one cylinder, and the metal surfaces therefore are not 
cooled to the same degree. The difference in temperatures and in pres- 
sures corresponding to the work of steam of 150 lbs. gauge-pressure ex- 
panded 20 times, in one, two, and three cylinders, is shown in the 
following table, by W. H. Weightman, Am. Mach., July 28, 1892: 



Diameter of cylinders, in. . 

Area ratios 

Expansions 

Initial steam-pressures — 

absolute — pounds 

Mean pressures, pounds. . . 
Mean effective pressures, 

pounds 

Steam temperatures into 

cylinders 

Steam temperatures out 

of the cylinders 

Difference in temperatures 



Single 
Cyl- 
inder. 



60 

20 

165 
32.96 

28.96 

366° 

184.2° 
181.8 



Compound 
Cylinders. 



33 

1 
5 

165 
86.11 

53.11 

366° 

259.9° 
106.1 



61 

3.416 
4 

33 
19.68 

15.68 

259.9° 

184.2° 
75.7 



Triple-expansion 
Cylinders. 



28 
1 
2.714 

165 
121.44 

60.64 

366° 

293.5° 
72.5 



46 

2.70 
2.714 

60.8 
44.75 

22.35 

293.5° 

234.1° 
59.4 



61 
4.740 
2.714 

22.4 
16.49 

12.49 

234.1° 

184.2° 
49.9 



**Woolf " and Receiver Types of Compound Engines. — The 

compound steam-engine, consisting of two cylinders, is reducible to two 
forms, 1, in which the steam from the h.p. cylinder is exhausted direct 
into the l.p. cylinder, as in the Woolf engine; and 2, in wiiich the steam 
from the h.p. cylinder is exhausted into an intermediate reservoir, whence 
the steam is supplied to, and expanded in, the l.p. cylinder, as in the 
" receiver-engine. " 

If the steam be cut off in the first cylinder before the end of the stroke, 
the total ratio of expansion is the product of the two ratios of expansion; 
that is, the product of the ratio of expansion in the first cylinder, into the 
ratio of the volume of the second to that of the first cylinder. 

Thus, let the areas of the first and second cylinders be as 1 to 3V2, the 
strokes being equal, and let the steam be cut off in the first at 1/2 stroke; 
then 

Expansion in the 1 st cylinder 1 to 2 

Expansion in the 2d cylinder 1 to 3V2 

Total or combined expansion, the product of the two ratios 1 to 7 

Woolf Engine, without Clearance — Ideal Diagrams. — The 

diagrams of pressure of an ideal Woolf engine are shown in Fig. 166, as 
they would be described by the indicator, according to the arrows.- In 
these diagrams pq is the atmospheric line, mn the vacuum line, cd the 
admission line, dg the hyperboHc curve of expansion in the first cylinder, 
and gh the consecutive expansion-line of back pressure for the return- 
Btroke of the first piston, and of positive pressure for the steam-stroke 
of the second piston. At the point h. at the end of the stroke of the 
second piston, the steam is exhausted into the condenser, and the pressure 
falls to the level of perfect vacuum, mn. 



978 



THE STEAM-ENGINE. 



The diagram of the second cylinder, below gh, is characterized by the 
absence of any specific period of admission; the whole of the steam-Hne 

gh being expansional, generated by the 
expansion of the initial body of steam 
d fin IK contained in the first cylinder into the 
-buibs. second. When the return-stroke is 
completed, the whole of the steam 
transferred from the first is shut into 
the second cylinder. The final pres- 
sure and volume of the steam in the 
second cylinder are the same as if the 
whole of the initial steam had been 
admitted at once into the second cylin- 
der, and then expanded to the end of 
the stroke in the manner of a single- 
cyUnder engine. The net work of the 
steam is also the same, according to 
both distributions. 

Receiver-engine, vrithout Clear- 
ance — Ideal Diagrams. — In the 
166. — WooLF Engine, Ideal j^^al receiver-engine the pistons of the 
Indicator-diagrams. two cylinders are connected to cranks 

at right angles to each other on the 
same shaft. The receiver takes the steam exhausted from the first cyUn- 
der and supphes it to the second, in which the steam is cut off and then 
expanded to the end of the stroke. On the assumption that the initial 
pressure in the second cylinder is equal to the final pressure in the first, 
and of course eaual to the pressure in the receiver, the volume cut off in 
the second cyUnder must be equal to the volume of the first cyhnder, for 
the second cyUnder must admit as much steam at each stroke as is dis- 
charged from the first cylinder. 

In Fig. 167, cd is the fine of admission and hg the exhaust-line for the 
first cylinder; and dg is the expansion-curve and pq the atmospheric line. 
d c ^ dc 




Fig. 




^0 lbs 








-%-h 




-40 


tk 


-%— 


._-, 


^-hJ—^ 




-20 






i 


/ 


h 




k 
-0 I 


--^ 







Fig. 167. — Receiver-engine, Fig. 168. — Receiver Engine, Ideal 
Ideal Indicator-diagram. Diagrams Reduced and Combined. 

In the region below the exhaust-line of the first cylinder, between it and 
the line of perfect vacuum, ol, the diagram of the second cylinder is 
formed; hi, the second line of admission, coincides with the exhaust-line 
hg of the first cylinder, showing in the ideal diagram no intermediate 
fall of pressure, and ik is the expansion-curve. The arrows indicate 
the order in which the diagrams are formed. 

In the action of the receiver-engine, the expansive working of the 
Bteam, though clearly divided into two consecutive stages, is, as in the 
Woolf engine, essentially continuous from the point of cut-off in the first 
cylinder to the end of the stroke of the second cylinder, where it is 
delivered to the condenser; and the first and second diagrams may be 
placed together and combined to form a continuous diagram. For this 
purpose take the second diagram as the basis of the combined diagram, 
namely, hiklo, Fig. 168. The period of admission, hi, is one-third of the 
stroke, and as the ratios of the cylinders areas 1 to 3, hi is also the propor- 



COMPOUND ENGINES. 



979 



tional length of the first diagram as applied to the second. Produce oh up- 
wards, and set ort oc equal to tne total neight ot the ftrst diagram above the 
vacuuin-hne, and, upon tne shortened base/ii, and tne heignt he, complete 
the hrst aiagram vvitn ttie steam-line cd and tne expansion line di. 

It is snovvn by ClarK (ri. E., p. 43J et seq.) in a series of arithmetical calcu- 
lations, tnat the recei srer-engine is an elastic system of compound engine, in 
whicn considerable latitude is aiforded for adapting the pressure in the re- 
ceiver to tne demands of the second cylinder, without considerably dimin- 
istiing the effective work of the engine. In the Woolf engine, on the 
contrary, it is of much importance that the intermediate volume of space 
between the first and second cylinders, which is the cause of an interme- 
diate fall of pressure, should be reduced to the lowest practicable amount. 

Supposing that there is no loss of steam in passing through the engine, 
by cooling and condensation, it is obvious that whatever steam passes 
through the first cylinder must also find its way through the second 
cylinder. By varying, therefore, in the receiver-engine, the period of 
admission in the second cylinder, and thus also the volume of steam ad- 
mitted for each stroke, the steam will be measured into it at a higher 
pressure and of a less bulk, or at a lower pressure and of a greater bulk; 
the pressure and density naturally adjusting themselves to the volume 
that the steam from the receiver is permitted to occupy in the second 
cyhnder. With a sufficiently restricted admission, the pressure in the 
receiver may be maintained at the pressure of the steam as exhausted 
from the first cyhnder. On the contrary, with a wider admission, the 
pressure in the receiver may fall or "drop" to three-fourths or even one- 
half of the pressure of the exhaust steam from the first cyhnder. 

(For a more complete discussion of the action of steam in the Woolf 
and receiver engines, see Clark on the Steam-engine.) 

Combined Diagrams of Compound Engines. — The only way of 
making a correct combined diagram from the indicator-diagrams of 
the several cyhnders 
in a compound engine 
is to set off all the 
diagrams on the same 
horizontal scale of vol- 
umes, adding the 
clearances to the cyl- 
inder capacities prop- 
er. When this is 
attended to, the suc- 
cessive diagrams fall 
exactly into their right 
places relatively to one 
another, and would 
compare properly with 
any theroretical ex- 
pansion-curve, (Prof. 
A. B. W. Kennedy, 
Proc, InsLM. E., Oct., 
1886.) 

This method of com- 
bining diagrams is 
commonly adopted, 
but there are objec- 
tions to its accuracy, 
since the whole quan- 
tity of steam con- Fig. 169. 
sumed in the first cyhnder at the end of the stroke is not carried forward 
to the second, but a part of it is retained in the first cyhnder for com- 
pression, i^or a method of combining diagrams in which compression 
is taken account of, see discussions by Thomas Mudd and others, in Proc. 
Inst M. E., Feb., 1887, p. 48. The usual method of combining diagrams 
is also criticised by Frank H. Bah as inaccurate and misleading (Am. 
Mach., April 12, 1894: Trans. A. S. M. E., xiv, 1405, and xv, 403). 

Figure 169 shows a combined diagram of a quadruple-expansion engine, 
drawn according to the usual method, that is, the diagrams are first 
reduced in length to relative scales that correspond with the relative 




980 



THE STEAM-ENGINE. 



piston-displacement of the three cylinders. Then the diagrams are 
placed at such distances from the clearance-Une of the proposed combined 
diagram as to represent correctly the clearance in each cylinder. 

Proportions of Cylinders in Compound Engines. — Authorities 
differ as to the proportions by volume of the liigh and lo_w pressure 

cylinders v and V._ Thus Grashof gives V -r- v = 0.85 ^r; Hrabak, 
0.90 v^r; Werner, v^r; and Rankine, ^r^, r being the ratio of expansion. 
Busley makes the ratio dependent on the boiler-pressure thus: 

Lbs. per sq. in 60 90 105 120 

V -^ V =3 4 4.5 5 

(See Seaton's Manual, p. 95, etc., for analytical method; Sennett, p. 496, 
etc.; Clark's Steam-engine, p. 445, etc.; Clark's Rules, Tables, Data, p. 849, 
etc.) 

Mr. J. McFarlane Gray states that he finds the mean effective pressure 
in the compound engine reduced to the low-pressure cylinder to be approx- 
imately the square root of 6 times the boiler-pressure. 

Ratio of Cylinder Capacity in Compound 3Iarine Engines. (Sea- 
ton.) — The low-pressure cylinder is the measure of the power of a com- 
pound engine, for so long as the initial steam-pressure and rate of expansion 
are the same, it signifies very little, so far as total power only is concerned, 
whether the ratio between the low and high pressure cylinders is 3 or 
4; but as the power developed should be nearly equally divided between 
the two cylinders, in order to get a good and steady working engine, 
there is a necessity for exercising a considerable amount of discretion 
in fixing on the ratio. 

In choosing a particular ratio the objects are to divide the power evenly 
and to avoid as much as possible "drop" and liigh initial strain. [Some 
writers advocate drop in the high-pressure cylinder making it smaller 
than is the usual practice and making the cylinder ratio as high as 6 or 7.] 

If increased economy is to be obtained by increased boiler-pressures 
the rate of expansion should vary with the initial pressure, so that the 
pressure at which the steam enters the condenser should remain constant. 
In this case, with the ratio of cylinders constant, the cut-off in the high- 
pressure cylinder will vary inversely as the initial pressure. 

Let R be the ratio of the cylinders; r the rate of expansion; pt the 
initial pressure: then cut-off in liigh-pressure cylinder = R -^ r; r varies 
with pi, so that the terminal pressure p^ is constant, and consequently 
r = Pi-i- p^; therefore, cut-off in high-pressure cylinder = R X p^ -^ pi. 

Ratios of Cylinders as Found in Marine Practice. — The rate of 
expansion may be taken at one-tenth of the boiler-pressure (or about one- 
twelfth the absolute pressure), to work economically at full speed. There- 
fore, when the diameter of the low-pressure cylinder does not exceed 
100 inches, and the boiler-pressure 70 lbs., the ratio of the low-pressure 
to the high-pressure cylinder should be 3.5; for a boiler-pressure of 80 lbs., 
3.75; for 90 lbs., 4.0; for 100 lbs., 4.5. If these proportions are adhered 
to, there will be no need of an expansion-valve to either cylinder. If, 
however, to avoid "drop," the ratio be reduced, an expansion-valve 
should be fitted to the high-pressure cylinder. 

Where economy of steam is not of first importance, but rather a large 
power, the ratio of cylinder capacities may with advantage be decreased, 
so that with a boiler-pressure of 100 lbs. it may be 3.75 to 4. 

In tandem engines there is no necessity to divide the work equally. 
The ratio is generally 4, but when the steam-pressure exceeds 90 lbs. 
absolute 4.5 is better, and for 100 lbs. 5.0. 

When the power requires that the l.p. cylinder shall be more than 100 in. 
diameter, it should be divided in two cylinders. In this case the ratio of the 
combined capacity of the two l.p. cyUnders to that of the h.p. may be 
3.0 for 85 lbs. absolute, 3.4 for 95 lbs., 3.7 for 105 lbs., and 4.0 for 115 lbs. 

Receiver Space in Compound Engines should be from 1 to 1.5 times 
the capacity of the high-pressure cylinder, when the cranks are at an 
angle of from 90° to 120°. When the cranks are at 180° or nearly this, 
the space may be very much reduced. In the case of triple-compound 
engines, with cranks at 120°, and the intermediate cylinder leading the 
high-pressure, a very small receiver will do. The pressure in the receiver 
should never exceed half the boiler-pressure. (Seaton.) 



COMPOUND ENGINES. 981 



Formula for Calculating the Expansion and the Work of Steam 
in Compound Engines. 

(Condensed from Clark on the "Steam-engine.") 

a = area of the first cylinder in square inches; 

a' = area of the second cylinder in square inches; 

r = ratio of the capacity of the second cylinder to that of the first; 

L = length of stroke in feet, supposed to be the same for both cylinders; 
I = period of admission to the first cylinder in feet, excluding clearance; 

c = clearance at each end of the cylinders, in feet; 

U = length of the stroke plus the clearance, in feet; 
V= period of admission plus the clearance, in feet; 

s = length of a given part of the stroke of the second cylinder, in feet; 

P = total initial pressure in the first cylinder, in lbs. per square inch, 

supposed to be uniform during admission; 
P' = total pressure at the end of the given part of the stroke s; 

p = average total pressure for the whole stroke; 

R = nominal ratio of expansion in the first cylinder, or L -4- Z; 
R' = actual ratio of expansion in the first cylinder, or U -^ V; 
R" = actual combined ratio of expansion, in the first and second cylin- 
ders together; 

n = ratio of the final pressure in the first cyhnder to any intermediate 
fall of pressure between the first and second cylinders; 

N = ratio of the volume of the intermediate space in the Woolf engine, 
reckoned up to, and including the clearance of, the second pis- 
ton, to the capacity of the first cylinder plus its clearance. The 
value of N is correctly expressed by the actual ratio of the 
volumes as stated, on the assumption that the intermediate space 
is a vacuum when it receives the exhaust-steam from the first 
cylinder. In point of fact, there is a residuum of unexhausted 
steam in the intermediate space, at low pressure, and the value 
of N is thereby practically reduced below the ratio here stated. 

n— 1 



w = whole net work in one stroke, in foot-pounds. 
Ratio of expansion in the second cylinder: 

In the Woolf engine 



In the receiver-engine. 



1 + A^ ' 
(n-l)r 



Total actual ratio of expansion = product of the ratios of the three 
consecutive expansions, in the first cyUnder, in the intermediate space, 
and in the second cylinder, 

In the Woolf engine, R' (r ■=-, + n\; 

In the receiver-engine, r -^t or rR' , 

Combined ratio of expansion behind the pistons = ^^— - vR' ^R'\ 

Work done in the two cylinders for one stroke, with a given eut-ofif 
and a given combined actual ratio of expansion: 

Woolf engine, w = aP [V{1 + hyp log R") -c]; 
Receiver engine, w = aP \U (1 + hyp log R")-c (l + ^-^ ) It 
when there Is no intermediate fall of pressure. 



982 THE STEAM-ENGINE. 

When there is an intermediate fall, when the pressure falls to 3/4, 2/3, 
1/2 of the final pressure in the 1st cyUnder, the reduction of work is 0.290, 
1.0%, 4.6% of that when there is no fall. 

Total work in the two cyhnders of a receiver-engine, for one stroke 
for any intermediate fall of pressure, 

. = aP[.(!i±l..ypIo..")-c(l:-<ii..^|:->)J. 

Example. — Let a = 1 sq. in., P = 63 lbs., V = 2.42 ft., n = A, R" = 
5.969, c = 0.42 ft., r = S, R' = 2.653; 

w; = l X 63 [2.42 (5/4 hyp log 5.969) -.42 (1 + 4^2653 )] =^21. 55 ft .-lbs. . 

Calculation of Diameters of Cylinders of a compound condensing 
engine of 2000 H.P. at a speed of 700 feet per minute, with 100 lbs. boiler- 
pressure. 

100 lbs. gauge-pressure = 115 absolute, less drop of 5 lbs. between 
boiler and cylinder = 110 lbs. initial absolute pressure. Assuming 
terminal pressure in l.p. cyUnder = 6 lbs., the total expansion of steam 
in both cyhnders = 110 -^- 6 = 18.33. Hyp log 18.33 = 2.909. Back 
pressure in l.p. cylinder, 3 lbs. absolute. 

The following formulae are used in the calculation of each cyUnder: 

,,, ^ - ,. , H.P. X 33,000 

(1) Area of cylinder = , , ^ „ ,, — — -^ -. 

' "^ M.E.P. X piston-speed 

(2) Mean effective pressure = mean total pressure — back pressure. 

(3) Mean total pressure = terminal pressure X (1+ hyp log R). 

(4) Absolute initial pressure = absolute terminal pressure X ratio of 
expansion. 

First calculate the area of the low-pressure cyUnder as if aU the work 
were done in that cylinder. 

From (3), mean total pressure = 6 X (1 + hyp log 18.33) = 23.454 \ 
lbs. 

From (2), mean effective pressure = 23.454 — 3 = 20.454 lbs. 
2000 X 33 000 

From (1), area of cyUnder = ■ ' =4610sq.ins. = 76.6ins.diam. 

If half the work, or 1000 H.P.', is done in the l.p. cyUnder the M.E.P. 
will be half that found above, or 10.227 lbs., and the mean total pressure 
10.227+ 3 = 13.227 lbs. 

From (3), 1 + hyp log R = 13.227 -h 6 = 2.2045. 

Hyp log R = 1.2045, whence R in l.p. cyl. = 3.335. 

From (4), 3.335 X 6 = 20.01 lbs. initial pressure in l.p. cyl. and ter- 
minal pressure in h.p. cyl., assuming no drop between cylinders. 

110 -4- 20.01 = 18.33 -^ 3.335 = 5.497, R'm. h.p. cyl. 

From (3), mean total pres. in h.p. cyl. = 20.01 X (1 + hyp log 5.497) ) 
= 54.11. 

From (2), 54.11 - 20.01 = 34.10, M.E.P. in h.p. cyl. 

/-.N *u I 1000X33,000 ,^0^ . Ac^' A- 

From (1), area of h.p. cyl. = — =1382 sq. ins. = 42ins. diam. 

CyUnder ratio = 4610 -^- 1382 = 3.336. 

The area of the h.p. cylinder may be found more directly by dividing 
the area of the l.p. cyl. by the ratio of expansion in that cyUnder. 4610 
■^ 3.335 = 1382 sq. ins. 

In the above calculation no account is taken of clearance, of com- 
pression, of drop between cylinders, nor of area of piston-rods. It also 
assumes that the diagram in each cylinder is the full theoretical diagram, 
with a horizontal steam-line and a hyperbolic expansion line, with no 
allowance for rounding of the corners. To make allowance for these, , 
the mean effective pressure in each cvlinder must be multiplied by a i 
diagram factor, or the ratio of the area of an actual diagram of the rlass 1 
of engine considered, with the given initial and terminal pressures, to the 
area of the theoretical diagram . S'lch diagram factors will range from 
0.6 to 0.94, as in the table on p. 962. 

Best Ratios of Cylinders. — The question what is the best ratio of 
areas of the two cylinders of a compv^und pugine is still (1901) a disputed 
one, but there appears to be an increasing tendency in favor of large 



TRIPLE-EXPANSION ENGINES. 983 

ratios, even as great as 7 or 8 to 1, with considerable terminal drop in 
the high-pressui-e cyUnder. A discussion oi" the subject, together with a 
description of a new method of drawing theoretical diagrams of multiple- 
expansion engines, taking into consideration drop, clearance, and com- 
pression will be found in a paper by Bert C. Ball, in Trans, A. S, M. E., 
xxi, 1002. 

TRIPLE-EXPANSION ENGINES. 

Proportions of Cylinders. — H. H. Suplee, Mechanics, Nov., 1887, 
gives the foUowing method of proportioning cylinders of triple-expansion 
engines: 

As in the case of compound engines the diameter of the low-pressure 
cyUnder is first determined, being made large enough to furnish the entire 
power required at the mean pressure due to the initial pressure and 
expansion ratio given; and then this cyhnder is given only pressure enough 
to perform one-third of the work, and the other cylinders are proportioned 
so as to divide the other two-thirds between them. 

Let us suppose that an initial pressure of 150 lbs. is used and that 
000 H.P. is to be developed at a piston-speed of 800 ft. per min., and that 
an expansion ratio of 16 is to be reached with an absolute back-pressure 
of 2 lbs. 

The theoretical M.E.P. with an absolute initial pressure of 150 + 14.7 =» 
164.7 lbs. initial at 16 expansions is 

P (14- hyp log 16) _ 164 7 X 5:ZI?6 _ 33 33^ 
16 * 16 

less 2 lbs. back pressure, = 38.83 - 2 = 36.83. 

In practice only about 0.7 of this pressure is actually attained, so that 
36.83 X 0.7 = 25.781 lbs. is the M.E.P. upon which the engine is to be 
proportioned. 

To obtain 900 H.P. we must have 33,000 X 900 = 29,700,000 foot- 
pounds, and this divided by the mean pressure (25.78) and by the speed 
in feet (800) mil give 1440 sq. in. as the area of the l.p. cylinder, about 
equivalent to 43 in. diam. 

Now as one-third of the work is to be done in the l.p. cylinder, the 
M.E.P. in it will be 25.78 -j- 3 = 8.59 lbs. 

The cut-off in the high-pressure cylinder is generally arranged to cut off 
at 0.6 of the stroke, and so the ratio of the h.p. to the l.p. cylinder is equal 
to 16 X 0.6 = 9.6, and the h.p. cyhnder will be 1440 -^ 9.6 = 150 sq. 
in. area, or about 14 in. diameter, and the M.E.P. in the h.p. cylinder is 
equal to 9.6 X 8.59 = 82.46 lbs. 

If the intermediate cylinder is made a mean size between the other two, 
its size would be determined by di\dding the area of the l.p. cylinder by 
the square root of the ratio between the low and the high: but in practice 
this is found to give a result too large to equalize the stresses, so that 
instead the area of the int. cylinder is found by di\iding the area of the 
l.p. piston by 1.1 times the square ro ot of the ratio of l.p. to h.p. cylinder, 
which in this case is 1440 -§- (1.1 V9.6) = 422.5 sq. in., or a little more 
than 23 in. diam. 

The choice of expansion ratio is governed by the initial pressure, and is 
generally chosen so that the terminal pressure in the l.p. cylinder shall be 
about 10 lbs. absolute. 

Formulae for Proportioning Cylinder Areas of Triple-Expansion 
Engines. — The following formulae are based on the method of first 
finding the cylinder areas that would be required if an ideal hyperbohc dia- 
gram were obtainable from each cylinder, with no clearance, compression, 
wire-drawing, drop by free expansion in receivers, or loss by cyhnder 
condensation, assuming equal work to be done in each cylinder, and 
then dividing the areas thus found by a suitable diagram factor, such as 
those given on page 962, expressing the ratio which the area of an actual 
diagram, obtained in practice from an engine of the type under consider- 
ation, bears to the ideal or theoretical diagram. It will vary in different 
classes of engine and in different cylinders of the same engine, usual 
values ranging from 0.6 to 0.9. When any one of the three stages of 
expansion takes place in two cylinders, the combined area of these 
cylinders equals the area foimd by the formulae. 



984 



THE STEAM-ENGINE. 



Notation. 

Pi = initial pressure in the high-pressure cylinder. 
Pl = terminal pressure in the low-pressure cylinder. 
Pfy = back pressure in the low-pressure cylinder. 

2?2 = term, press, in h.p. cyl. and initial press, in intermediate cyl. 

P3=' term, press, in int. cyl. and initial press, in l.p. cyl. 

Ri, R'i, Rs, ratio of exp. in h.p. int. and l.p. cyls. 

R = total ratio of exp. = i^i x -B2 X -Rs. 

P = M.E.P. of the combined ideal diagram, referred to the l.p. cyl. 

Pi, P2, Ps = M.E.P. in the h.p., int., and l.p. cyls. 

H P = horse-power of the engine = PLAzN -^ 33,000. 

L = length of stroke in feet; N = number of single strokes per min. 

Ai, A2, A3, areas (sq. ins.) of h.p. int. and l.p. cyls. (ideal). 

W = work done in one cylinder per foot of stroke. 

r-z = ratio of A2 to Ai; rz = ratio of Az to A\. 

Fu F'2, F3, diagram factors of h.p. int. and l.p. cyl. 

fli, a2, as, areas (actual) of h.p. int. and l.p. cyl. 

Formulce. 

(1) ;? = pi -s- p^, 

(2) P = p^ (1 + hyp log R) - p^,. 

(3) P3 = 1/3 P. 

(4) Hyp log R3 = (P3 - Pf^ Pb) - ^ Pt' 

(5) R1R2 = R -^ Rs; Ri = R2 = '^RiR^ 

(6) Pz = PtX Rs. 

(7) P2 = P3 y R2. 

(8) pi = P2 X Ri. 

(9) P2 = P3 (hyp log R2) = P3R3. 

(10) Pi = P2 (hyp log Ri) = P2R2. 

(11) W = 11,000 i/P -^ LN. 

(12) Ai = W -^ Pi', A2 = W -^ P2: As = W -^ Ps. 

(13) r2 = ^2 -^ ^1 = Pi H- P2 = Ri or R2; rz = Az ^ Ai ^ Pi ^ P3. 

(14) ai = -4.1 -^ Pi; a2 = ^2 -^ P2; 03 = A3 -^ P3. 

From these formulae the figures in the following tables have been 
calculated; 

Theoretical Mean Effectr^e Pressures, Cylinder Ratios, Etc., 

OF Triple-Expansion Engines. 

Back pressure, 3 lbs. Terminal pressure, 8 lbs. (absolute). 



Pi- 


R. 


P. 


P3. 


Rz, 


Ru R2, 
or ra. 


P3. 


P2. 


P2. 


Pi. 


rz. 


120 


15 


26.66 


8.89 


1.626 


3.037 


13.01 


39.51 


14.45 


43.89 


4.939 


140 


17.5 


27.90 


9.30 


1.712 


3.197 


13.70 


43.79 


15.92 


50.89 


5.472 


160 


20 


28.97 


9.66 


1.790 


3.343 


14.32 


47.86 


17.29 


57.76 


5.980 


180 


22.5 


29.91 


9.97 


1.861 


3.477 


14.89 


51.77 


18.55 


64.52 


6.471 


200 


25 


30.75 


10.25 


1.928 


3.601 


15.42 


55.54 


19.76 


71.16 


6.942 


220 


27.5 


31.51 


10.50 


1.990 


3.718 


15.91 


59.16 


20.90 


77.69 


7.397 


240 


30 


32.21 


10.74 


2.049 


3.826 


16.39 


62.72 


22.00 


84.16 


7.839 



Theoretical Mean Effective Pressures, Cylinder Ratios, Etc., 
OF Triple-Expansion Engines. 
Back pressure, 3 lbs. Terminal pressure, 10 lbs. (absolute). 



pl- 


R. 


P. 


P3. 


Rz. 


Ru R2, 
or n. 


P3. 


V2. 


P2. 


Pi. 


rz. 


120 


12 


31.85 


10.62 


1.436 


2.890 


14.36 


41.50 


15.24 


44.04 


4.148 


140 


14 


33.39 


11.13 


1.511 


3.044 


15.11 


45.99 


16.82 


51.20 


4.600 


160 


16 


34.73 


11.58 


1.580 


3.182 


15.80 


50.28 


18.29 


58.20 


5.027 


180 


18 


35.90 


11.97 


1.643 


3.310 


16.43 


54.38 


19.66 


65.09 


5.439 


200 


20 


36.96 


12.32 


1.702 


3.428 


17.02 


58.34 


20.97 


71.88 


5.834 


220 


22 


37.91 


12.64 


1.757 


3.538 


17.57 


62.15 


22.20 


78.54 


6.215 


240 


24 


38.78 


12.93 


1.809 


3.642 


18.09 


65.88 


23.38 


85.15 


6.587 



Given the required H.P. of an engine, its speed and length of stroke, 



TRIPLE-EXPANSION ENGINES. 



985 



and the assumed diagram factors t'l, ti, tz lor tne inree cynnuers, me 
areas of the cylinders may be found by using formulae (11), (12), and 
(14), and the values of Pi, Pi, and Ps in the above table. 

A Common Rule for Proportioning the Cylinders of multiple- 
expansion engines is: for two-cylinder compound engines, the cylinder 
ratio is the square root of the number of expansions, and for triple- 
expansion engines the ratios of the high to the intermediate and of the 
intermediate to the low are each equal to the cube root of the number of 
expansions, the ratio of the high to the low being the product of the two 
ratios, that is, the square of the cube root of the number of expansions. 
Applying this rule to the pressures above given, assuming a terminal 
pressure (absolute) of 10 lbs. and 8 lbs. respectively, we have, for triple- 
expansion engines: 



Boiler- 


Terminal Pressure, 10 lbs. 


Terminal Pressure, 8 lbs. 


pressure 
(Absolute) . 


No. of Ex- 
pansions. 


Cylinder Ratios, 
areas. 


Nc.ofEx- 
pansions. 


Cylinder Ratios, 
areas. 


130 
140 
150 
160 


13 
14 
15 

16 


1 to 2.35 to 5.53 
I to 2.41 to 5.81 
1 to 2.47 to 6.08 
1 to 2.52 to 6.35 


161/4 

171/2 
,83/. 


1 to 2.53 to 6.42 
1 to 2.60 to 6.74 
I to 2.66 to 7.06 
1 to 2.71 to 7.37 



The ratio of the diameters is the square root of the ratios of the areas, 
and the ratio of the diameters of the first and third cylinders is the same 
as the ratio of the areas of first and second. 

Seaton, in his Marine Engineering, says: When the pressure of steam 
employed exceeds 115 lbs. absolute, it is advisable to employ three 
cylinders, through each of which the steam expands in turn. The ratio 
of the low-pressure to liigh-pressure cylinder in this system should be 5, 
when the steam-pressure is 125 lbs. absolute; when 135 lbs., 5.4; when 
145 lbs., 5.8; when 155 lbs., 6.2; when 165 lbs., 6.6. The ratio of low- 
pressure to intermediate cylinder should be about one-half that between 
low-pressure and high-pressure, as given above. That is, if the ratio 
of l.p. to h.p. is 6, that of l.p. to int. should be about 3, and consequently 
that of int. to h.p. about 2. In practice the ratio of int. to h.p. is nearly 
2.25, so that the diameter of the int. cyhnder is 1.5 that of the h.p. The 
introduction of the triple-compound engine has admitted of ships being 
propelled at higher rates of speed than formerly obtained without exceed- 
ing the consumption of fuel of similar ships fitted with ordinary com- 
pound engines; in such cases the higher power to obtain the speed has been 
developed, by decreasing the rate of expp.nsion, the low-pressure cylin- 
der being only 6 times the capacity of the high-pressure, with a working 
pressure of 170 lbs. absolute. It is now a very general practice to make 
the diameter of the low-pressure cylinder equal to the sum of the diameters 
of the h.p. and int. cyUnders; hence, 

Diameter of int. cylinder =1.5 diameter of h.p. cylinder; 
Diameter of l.p. cyUnder = 2.5 diameter of h.p. cylinder. 

In this case the ratio of l.p. to h.p. is 6.25; the ratio of int. to h.p. is 2.26; 
and ratio of l.p. to int. is 2.78. 

Ratios of Cylinders for Different Classes of Engines. (Proc. Inst. 
M. E.y Feb., 1887, p. 36.) — As to the best ratios for the cylinders in a 
triple engine there seems to be great difference of opinion. Considerable 
latitude, however, is due to the requirements of the case, inasmuch as 
ii would not be expected that the same ratio would be suitable for an 
economical land engine, where the space occupied and the weight were of 
minor importance, as in a war-ship, w^here the conditions were reversed. 
In the land engine, for example, a theoretical terminal pressure of about 
7 lbs. above absolute vacuum would probably be aimed at, which would 
give a ratio of capacity of high pressure to low pressure of 1 to 8 1/2 or 1 to 
9; whilst in a war-ship a terminal pressure would be required of 12 to 13 
lbs. which would need a ratio of capacity of 1 to 5; yet in both these 
instances the cyUnders were correctly proportioned and suitable to the 
requirements of the case. It is obviously unwise, therefore, to introduce 
any hard-and-fast rule. 

Types of Three-stage Expansion Engines. — 1. Three cranks at 



i 



986 



THE STEAM-ENGINE. 



120 (leg. 2. Two cranks with 1st and 2d cylinders tandem. 3. Two ) 

cranks with 1st and 3d cylinders tandem. The most common type is the ' 
first, with cyUnders arranged in the sequence high, intermediate, low. 

Sequence of Cranks. — Mr. WylUe (Proc. Inst M. E., 1887) favors, 
the sequence high, low, intermediate, while Mr. Mudd favors high, inter- - 
mediate, low. The former sequence, high, low, intermediate, gave an i 
approximately horizontal exhaust-line, and thus minimizes the range of I 
temperature and the initial load; the latter sequence high, intermediate, , 
low, increased the range and also the load. 

Mr. Morrison, in discussing the question of sequence of cranks, pre- • 
sented a diagram showing that with the cranks arranged in the sequence 
high, low, intermediate, the mean compression into the receiver was 
191/2 per cent of the stroke; with the sequence high, intermediate, low, 
it was 57 per cent. 

In the former case the compression was just what was required to keep 
the receiver-pressure practically uniform; in the latter case the compression 
caused a variation in the receiver-pressure to the extent sometimes of 
221/2 lbs. 

Velocity of Steam through Passages in Compound Engines. 
{Proc. Inst. M. E., Feb., 1887.) — In the SS. Para, taking the area of the 
cyUnder multiplied by the piston-speed in feet per second and dividing 
by the area of the port the velocity of the initial steam through the high- 
pressure cyUnder port would be about 100 feet per second; the exhaust 
would be about 90. In the intermediate cylinder the initial steam had 
a velocity of about 180, and the exhaust of 120. In the low-pressure 
cylinder, the initial steam entered through the port with a velocity of 250, 
and in the exhaust-port the velocity was about 140 feet per second. 

A Double-tandem Triple-expansion Engine, built by Watts, 
Campbell & Co., Newark, N. J., is described in Am. Mach., April 26, 1894. 
It is two three-cylinder tandem engines coupled to one shaft, cranks at 
90°, cylinders 21, 32 and 48 by 60 in. stroke, 65 revolutions per minute, 
rated H.P. 2000; fly-wheel 28 ft. diameter, 12 ft. face, weight 174,000 
lbs.; main shaft 22 in. diameter at the swell; main journals 19 X 38 in.; 
crank-pins 91/2 X 10 in.; distance between center hues of two engines 
24 ft. 71/2 in.; CorHss valves, .with separate eccentrics for the exhaust- 
valves of the l.p. cylinder. 



QUADRUPLE-EXPANSION ENGINES. 

H. H. Suplee (Trans. A. S. M. E., x, 583) states that a study of 14; 
different quadruple-expansion engines, nearly all intended to be operated 
at a pressure of 180 lbs. per sq. in., gave average cyUnder ratios of 1 to 2, 
to 3.78, to 7.70, or nearly in the proportions 1, 2, 4, 8. 

If we take the ratio of areas of any two adjoining cyhnders as the fourth 
root of the number of expansions, the ratio of the 1st to the 4th will be ^ 
the cube of the fourth root. On this basis the ratios of areas for different t 
pressures and rates of expansion will be as follows: 



Gauge- 


Absolute 


Terminal 


Ratio of 


Ratios of Areas 


pressures. 


Pressures. 


Pressures. 


Expansion. 


of Cylinders. 






12 


14.6 1 


: 1.95: 3.81 : 7.43 


160 


175 


10 


17.5 1 


2.05:4.18: 8.55 






( 8 


21.9 1 


2.16: 4.68: 10.12 






12 


16.2 1 


2.01 : 4.02: 8.07 


180 


195 


10 


19.5 1 


2.10: 4.42: 9.28 






( 8 


24.4 1 


2.22: 4.94: 10.98 






(12 


17.9 1 


2.06:4.23: 8.70 


200 


215 


no 


21.5 1 


2.15: 4.64: 9.98 






( 8 


26.9 1 


2.28: 5.19: 11.81 






12 


19.6 I 


2.10:4.43: 9.31 


220 


235 


10 


23.5 1 


2.20: 4.85: 10.67 






( 8 


29.4 1 • 


2.33 : 5.42: 12.62 



Seaton says: When the pressure of steam employed exceeds 190 lbs. 
absolute, four cylinders should be employed, with the steam expanding 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 987 

through each successively ; and the ratio of l.p. to h.p. should be at least 
y.5, and if economy oi i'uel is of prime confeiaeratioii it snould be 8; then 
the ratio of first intermediate to h.p. should be 1.8, that of second inter- 
mediate to first int. 2, and that of l.p. to second int. 2.2. 

In a paper read before the North East Coast Institution of Engineers 
and Shipbuilders, 1890, WiUiam Russell Cummins advocates the use of a 
four-cylinder engine with four cranks as being more suitable for high 
speeds than the three-cylinder three-crank engine. The cyhnder ratios, 
he claims, should be designed so as to obtain equal initial loads in each 
cyhnder. The ratios determined for the triple engine are 1, 2.04, 6.54, 
and for the quadruple, 1, 2.08, 4.46, 10.47. He advocates long stroke, 
high piston-speed, 100 revolutions per minute, and 250 lbs. boiler-pressure, 
unjacketed cyUnders, and separate steam and exhaust valves. 

ECONOMIC PERFORMANCE OF STEAM-ENGINES. 

Economy of Expansive Working under Various Conditions, Single 

Cylinder. 

(Abridged from Clark on the Steam Engine.) 

1 Single Cylinders with Superheated Steam, Non-condensing. — 
Inside cyhnder locomotive, cyhnders and steam-pipes enveloped by the 
hot gases in the smoke-box. Net boiler pressure 100 lbs.; net maximum 
pressure in cyhnders 80 lbs. per sq. in. 

Cut-off, per cent ..... 20 25 30 35 40 50 60 70 80 

Actual ratio of expan- 
sion 3.91 3.31 2.87 2.53 2.26 1.86 1.59 1.39 1.23 

Water per i.H.P. per 

hour, lbs 18.5 19.4 20 21.2 22.2 24.5 27 30 33 

2 Single Cylinders with Superheated Steam, Condensing. ^ 
The best results obtained by Hirn, with a cyhnder 233/4 x 67 in. and steam 
superheated 150° F., expansion ratio 33/4 to 41/2, total maximum pressure 
in cylinder 63 to 69 lbs., were 15.63 and 15.69 lbs. of water per I.H.P. per 
hour. 

3. Single Cylinders, not Steam-jacketed, Condensing. — The best 
result is from a Corhss-Wheelock engine 18 X 48 in.; cut-off, 12.5%; 
actual expansion ratio, 6.95: maximum absolute pressure in cyhnder, 
104 lbs.; steam per I.H.P. hour, 19.58 lbs. Other engines, with lower 
steam pressures, gave a steam consumption as high as 26.7 lbs. 

Feed-water Consumption of Different Types of Engines. — The 
following tables are taken from the circular of the Tabor Iridicator (Ash- 
croft Mfg. Co., 1889). In the first of the two columns under Feed-water 
required, in the tables for simple engines, the figures are obtained by 
computatiOii from nearly perfect indicator diagrams, with allowance 
for cylinder condensation according to the table on page 936, but without 
allowance for leakage, with back-pressure in the non-condensing table 
taken at 16 lbs. above zero, and in the condensing table at 3 lbs. above zero. 
The compression curve is supposed to be hyperbolic, and commences at 
0.91 of the return-stroke, with a clearance of 3% of the piston-displace- 
ment. 

Table No. 2 gives the feed-water consumption for jacketed compound- 
condensing engines of the best class. The water condensed in the jackets 
is included in the quantities given. The ratio of areas of the two cylinders 
is as 1 to 4 for 120 lbs. pressure: the clear?nce of each cylinder is 3% 
and the cut-off in the two cylinders occurs at the same point of stroke. 
The initial pressure in the l.p. cylinder is 1 lb. per sq. in. below the back- 
pressure of the h.p. cyhnder. The average back-pressure of the whole 
stroke in the l.p. cyhnder is 4.5 lbs. for 10% cut-off; 4.75 lbs. for 20% 
cut-off; and 5 lbs. for 30% cut-off. The steam accounted for by the 
indicator at cut-off in the h.p. cyhnder (allowing a small amount for leak- 
age) is 0.74 at 10 7o cut-off, 0.78 at 20%, and 0.82 at 30% cut-off. The 
loss by condensation between the cylinders is such that the steam ac- 
counted for at cut-off in the l.p. cyhnder, expressed in proportion of that 
shown at release in the h.p. cyhnder^ is 0.85 at 10% cut-off, 0.87 at 20% 
cut-off, and 0.89 at 30% cut-off. 



988 



THE STEAM-ENGINE. 



TABLE No. 1. 

Feed-water Consumption, Simple Engines. 
Non-condensing Engines. Condensing Engines. 



dJ CO 

£=2 



Ph 






Feed-water Re- 
quired per I.H.P. 
per Hour, 



CD 2 
C 






•< fl S 0) 



O 



2 






Feed-water Re- 
quired per I.H.P. 
per Hour. 







s^ 


Oc.|_3 


"*^ 


-^ c3 oj 


bCfl 


W)<J « 


c I! 


C 03 a)HH 


'-^-a 


^-S--- 


c-5 


C 3 t^j 






CD Sr. 


^^fi.^^ 


Corr 
gra 
age 




17.30 


18.89 


17.15 


18.70 


17.02 


18.56 


17.60 


19.09 


17.45 


18.91 


17.32 


18.74 


18.27 


19.69 


18.14 


19.51 


18.02 


19.36 


19.91 


21.25 


19.78 


21.06 


19.67 


20.93 


21.36 


22.56 


21.24 


22.41 


21.13 


22.24 



10 



20 



30 



40 



"i 



80 
90 
100 

80 
90 
100 

80 
90 
100 

80 
90 
100 



90 
100 



16.07 
19.76 
23.45 

32.02 
37.47 
42.92 

43.97 
50.73 
57.49 

53.25 
61.01 
68.76 

60.44 
68.96 
77.48 



27.61 
25.43 
23.90 

21.04 
23.00 
22.25 

24.71 
23.91 
23.27 

25.76 
25.03 
24.47 

26.99 
26.32 
25.78 



29.88 
27.43 
25.73 

25.68 
24.57 
23.77 

26.29 
25.38 
24.68 

27.17 
,26.35 
25.73 

28.38 
27.62 
26.99 



20 



30 



40 



80 
90 
100 

80 
90 
100 

80 
90 
100 

80 
90 
100 

80 
90 
100 



29.72 
33.41 
37.10 

38.28 
42.92 
47.56 

45.63 
51.08 
56.53 

57.57 
64.32 
71.08 

66:85 
74.60 
82.36 



TABLE No. 2 
Feed-water Consumption for Compound Condensing Engines. 



Cut-oflF 
per cent. 


Initial Pressure above 
Atmosphere. 


Mean Effective Press. 


Feed-water 

Required 

per I.H.P. per 

Hour, lb. 


h.p.Cyl., lb. 


l.p.Cyl.,lb. 


h.p.Cyl., lb. 


l.p.Cyl.,lb. 


10 


80 
100 
120 


4.0 
7.3 
11.0 


11.07 
15.33 
18.54 


2.65 
3.87 
5.23 


16.92 
15.00 
13.86 


20 


80 
100 
120 


4.3 
8.1 
12.1 


26.73 
33.13 
39.29 


5.48 
7.56 
9.74 


14.60 
13.67 
13.09 


„ j 


80 
100 
120 


4.6 

8.5 
11.7 


37.61 
46.41 
56.00 


7.48 
10.10 
12.26 


14.99 
14.21 
13.87 



Sizes and Calculated Performances of Vertical High-speed 
EngineSo — The following tables are taken from an old circular, describ- 
ing: the en^nes made by the Lake Erie Enpineerin? Works, Buffalo, N. Y. 
The engines are fair representatives of the type largely used for drivinf: 
dynamos directly without belts. The tables were calculated by E. F. 
WiUiams, designer of the engines. They are here somewhat abridged to 
save space. 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 989 









Simple Engines — 


- Non-condensing. 








'>> r^ 


01 




H.P. when 


H.P. when 


H.P. when 


Dimen- 
sions of 
Wheels, 
dia. face 


. 




O^^ 


fl 


u . 


cutting off 


cutting off 


cutting off 


a 




o ^- 


2 


^ 


at 1/5 stroke. 


at 1/4 stroke. 


at 1/3 stroke 


S 


to 
13 . 


03 c 


70 


80 


90 


70 


80 


90 


70 


80 


90 


Ft. 




JS 


15- 


cc 


lbs. 
20 


lbs. 
25 


lbs. 
30 


lbs. 
26 


lbs. 
31 


lbs. 
36 


lbs. 
32 


lbs. 
37 


lbs. 
43 


In. 

4 


21/0 


wS 


71/7 


10 


370 


4 


3 


81/?, 


12 


318 


27 


32 


39 


34 


41 


47 


41 


48 


56 


41/9 


5 


23/J 


^1/2 


101/7, 


14 


277 


41 


49 


60 


52 


62 


71 


63 


74 


85 


5/9// 


6 1/9 


31/0 


4 


12 


16 


246 


53 


64 


77 


67 


81 


93 


82 


96 


11] 


6' 8" 


9 


4 


41/2 


131/7 


18 


222 


66 


80 


96 


84 


100 


116 


102 


120 


138 


71/9 


11 


4 


5 '" 


16 


20 


181 


95 


115 


138 


120 


144 


166 


146 


172 


198 


8M" 


15 


Alio 


6 


18 


24 


138 


119 


144 


173 


151 


181 


208 


183 


215 


248 


10 


19 


5 '^ 


7 


22 


28 


138 


179 


216 


261 


227 


272 


313 


276 


324 


373 


ir8" 


28 


6 


8 


241/7, 


32 


120 


221 


267 


322 


281 


336 


386 


340 


400 


460 


13' 4" 


34 


7 


9 


27 


34 


112 


269 


325 


392 


342 


409 


470 


414 


487 


560 


14' 2'' 


41 


8 


10 


M.E. 


P., lbs 
of exp 


... 


24 


29 


35 


30.5 


36.5 


42 


37 


43.5 


50 


Note. — The 


Ratio 


5 


4 


3 


nominal-power 




1*1 pr 


ess. 








rating of the en- 


Tern 




















gines is at 80 lbs. 


(abc 


)i]t), lb 


s. . 


17.9 


20 


22.3 


22.4 


25 


27.6 


29.8 


33.3 


36.8 


gauge pressure, 


Cvl. r 


ond'n, 


%- 


26 


26 


26 


24 


24 


24 


21 


21 


21 


steam cut-off at 


Steax 


nperl. 
'.lbs.. 


H.P. 




















1/4 stroke. 


houi 




32.9 


30 


27.4 


31.2 


29.0 


27.9 


32 


31.4 


30 





Compound Engines 


— Non-condensing - 


-H 


igh. 


pressure Cylinder 




and Receiver Jaclieted. 








H.P., cutting off 


H.P., cutting off 


H.P., cutting off 


Diam. 
Cylinder, 




5^ 


at 1/4 Stroke 


at 1/3 Stroke 


at 1/2 Stroke 


c5 

1 


a 

m 

.2 


in h.p. Cylinder. 


in h.p. Cylinder. 


in h.p. Cylinder. 


inches. 


Cyls. 


Cyls. 


Cyls. 


Cyls. 


Cyls. 


Cyls. 







3-2 


31/3: 1. 


41/2: 1. 


31/3: 1. 


41/2: 1. 


31/3:1. 


41/2: 1. 


Pi 


^ 


Pk 


80 


90 


130 


150 


80 


90 


130 


150 


80 


90 


130 


150 


w 


W 


^ 




lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


53/4 


61/? 


12 


10 


370 


7 


15 


19 


32 


23 


31 


35 


46 


44 


55 


64 


79 


63/8 


71/?, 


131/7 


12 


318 


9 


19 


24 


40 


29 


39 


45 


59 


56 


70 


81 


101 


;3/4 


9 


16 1/0 


14 


277 


14 


28 


36 


60 


43 


58 


67 


87 


83 


104 


121 


159 


9 


101/7 


19 


16 


246 


18 


37 


47 


78 


57 


76 


87 


114 


109 


136 


158 


196 


101/2 


12 


221/? 


18 


222 


26 


53 


68 


112 


81 


109 


125 


164 


156 


195 


226 


281 


12 


131/, 


25 


20 


185 


32 


65 


84 


139 


100 


135 


154 


202 


192 


241 


279 


346 


131/2 


151/, 


281/9 


24 


158 


43 


88 


112 


186 


135 


181 


206 


271 


258 


323 


374 


464 


16 


181/7 


331/? 


28 


138 


57 


118 


151 


249 


180 


242 


277 


363 


346 


433 


502 


623 


18 


201/7 


38 


32 


120 


74 


152 


194 


321 


232 


312 


357 


468 


446 


558 


647 


803 


20 


221/, 


43 


34 


112 


94 


194 


249 


412 


297 


400 


457 


601 


572 


715 


829 


1030 


:^4i/2 


281/2 


52 


42 


93 


138 


285 


365 


603 


436 


587 


670 


880 


838 


1048 


1215 


1508 


281/2 


33 


60 


48 


80 


180 


374 


477 


789 


570 


767 


877 


1151 


1096 


1370 


1589 


1973 


Mean eff. pressure, lbs.. 


3.3 


6.8 


8.7 


14.4 


10.4 


14.0 


16 


21 


20 


25 


29 


36 


Ratio of expansion 


131/2 


181/4 


101/4 


133/4 


63/4 


91/4 


Cyl. condensation, %.. 


14 


14 


16 


16 


12 


12 


13 


13 


10 


10 


11 


11 


Ter.pres. (abt.), lbs... 


7.3 


7.7 


7.9 


9 


9.2 


10.4 


10.5 


12 


14 


15.5 


14 6 


17,8 


Loss from expanding 


























below atmosphere, % 


34 


15 


17 


3 


5 























St.perI.H.P.hour,lbs. 


55 


42 


47 


29 


33.3 


27.7 


28.7 25. 4| 30 


26.2 


21 


20 



990 



THE steam-engine. 





Compound Engines — 


- Condensing — 


Steam-jack 


Bted 












H.P. when 


H.P. when 


H.P. when 








cutting off at 


cutting off at 


cutting off at 


Diam. 




u, 


1/4 Stroke 


1/3 Stroke 


1/2 Stroke 


Cylinder, 
inches. 


S 


s 


in h.p. Cylinder. 


in h.p. Cylinder. 


in h.p. Cylinder. 














c 


C 

o q3 


Ratio, 


Ratio, 


Ratio, 


Ratio, 


Eatio, 


Ratio. 




2 


33 

"o.S 


31/3: 1. 


4: 1. 


31/3: 1. 


4: 1. 


31/3: 1. 


4: 1. 


^ 


^. 


P^ 


80 


no 


115 


125 


80 


110 


115 


125 


80 


no 


115 


125 


a 


S 


iJ 


02 


P^ 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


6 


61/9 


12 


10 


370 


44 


59 


53 


62 


55 


70 


68 


75 


70 


97 


95 


106 


61/9 


71/9 


131/9 


12 


318 


56 


76 


67 


78 


70 


90 


87 


95 


90 


123 


120 


134 


81/4 


9 


161/?, 


14 


277 


83 


112 


100 


lit 


104 


133 


129 


141 


133 


183 


m 


200 


Ql/'' 


10 1/9 


19 


16 


246 


109 


147 


131 


152 


136 


174 


169 


185 


174 


239 


234 


261 


11 


12 


221/9 


18 


222 


156 


210 


187 


218 


195 


250 


242 


265 


250 


343 


335 


374 


l?l/? 


131/9 


23 


20 


185 


192 


260 


231 


269 


241 


308 


298 


327 


308 


423 


414 


462 


14 


151/9 


281/9 


24 


158 


258 


348 


310 


36i 


323 


413 


400 


439 


413 


568 


555 


619 


17 


181/9 


331/9 


28 


138 


346 


467 


415 


484 


433 


554 


536 


588 


554 


761 


744 


830 


19 


201/9 


38 


32 


120 


446 


602 


535 


624 


558 


714 


691 


758 


714 


981 


959 


1070 


21 


221/9 


43 


34 


112 


572 


772 


686 


801 


715 


915 


887 


972 


915 


125^ 


1230 


1373 


26 
30 


281/9 


52 


42 


93 


838 


1131 


1006 


1174 


1048 


1341 


1299 


1425 


1341 


1844 


1801 


2012 


33 


60 


48 


80 


1096 


1480 


1316 


1534 


1370 


1757 


1699 


1863 


1757 


2411 


2356 


2632 


Mean efiF. press., lbs 


Vo... 


20 


27 


24 


28 


25 


32 


31 


34 


32 


44 


43 


48 


Ratio of expansion 


131/2 


161/4 


10 


121/4 


63/4 


8 1/4 


Cyl. condensation, ^ 


18 


18 


20 


20 


15 


15 


18 


18 


12 


12 i 14 1 14 


St. per I.H.P. hour 


lbs. 


17.3 


16.6 


16.6 


15.2 


17.0 


16.4 


16.3 


15.8 


17.5|17.0I16.8|16.C 



Triple-expansion Engines, Non-condensing — Be 
Jacketed. 


ceiver 


only 






(h 


Horse-power 


Horse-power 


Horse-power 


Diameter 


",i 


a 


when cutting 


when cutting 


TNhen cutting 


Cylinders, 


j3 


CQ 


off at 42% of 
Stroke in First 


off at 50% of 


cff at 67% of 


inches. 


c 


. 


Stroke in First 


Stroke in First 









Cylinder. 


Cylinder. 


Cylinder. 


H.P. 


LP. 


L.P. 


180 lbs. 


200 lbs. 


180 lbs. 


200 lbs. 


180 lbs. 


200 lbs. 


43/4 


71/9 


12 


10 


370 


55 


64 


70 


84 


95 


108 


51/?, 


81/? 


131/9 


12 


318 


70 


81 


90 


106 


120 


137 


6 1/2 


101/2 


16 1/2 


14 


277 


104 


121 


133 


158 


179 


204 


71/2 


12 


19 


16 


246 


136 


158 


174 


207 


234 


267 


9 


141/? 


221/2 


18 


222 


195 


226 


250 


296 


335 


382 


10 


16 


25 


20 


185 


241 


279 


308 


366 


414 


471 


11V?- 


18 


281/? 


24 


158 


323 


374 


413 


490 


555 


632 


13 


22 


331/? 


28 


138 


433 


502 


554 


657 


744 


848 


15 


241/2 


38 


32 


120 


558 


647 


714 


847 


959 


1093 


17 


27 


43 


34 


112 


715 


829 


915 


1089 


1230 


1401 


20 


33 


52 


42 


93 


1048 


1215 


1341 


1592 


1801 


2053 


231/2 


38 


60 


48 


80 


1370 


1589 


1754 


2082 


2356 


2685 


Mean eff. press., lbs 


25 


29 


32 


38 


43 


49 


No. of expansions 


16 


13 


10 


Cyl. condensation, % 


14 


12 


10 


Steam p. I.H.P.p.hr., lbs. 


20 76 


19.36 


19.25 17.00 


17.89 


17.20 


Lbs. coal at 8 lb. evap., lbs. 


2.59 


2.39 ] 


2.40 2.12 


2.23 


2.15 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 991 





Triple-expansion 


Engines — 


Condensing - 


— Steam-jacketed. 










Horse- 


Horse- 


Horse- 


Horse- 


Diameter 


^ 


Pi 


power when 


power when 


power when 


power when 


Cylinders, 


J3 


06 


cutting off 


cutting ofif 


cutting off 


cutting ofif 


inches. 


C 


at 1/4 Stroke 


at 1/3 Stroke 


at 1/2 Stroke 


at 3/4 Stroke 




6 

2 


'o.S 


in First Cyl. 


in First Cyl. 


in First Cyl. 


in First CyL 


^ 


Ph 


^ 


120 


140 


160 


120 


140 


160 


120 


140 


160 


120 


140 


160 


W 


HH 


h^I 


02 


P^ 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


43/<i 


71/? 


12 


10 


370 


35 


42 


48 


44 


53 


59 


57 


72 


84 


81 


97 


no 


51/9 


81/9 


131/9 


12 


318 


45 


53 


62 


56 


67 


76 


73 


92 


107 


104 


123 


140 


61/0 


101/? 


161/9 


14 


277 


67 


79 


92 


83 


100 


112 


108 


137 


159 


154 


183 


208 


71/2 


12 


19 


16 


246 


87 


103 


120 


109 


131 


147 


141 


180 


208 


201 


239 


272 


9 


141/9 


221/9 


18 


222 


125 


148 


172 


156 


187 


211 


203 


257 


299 


289 


343 


390 


10 


16 


25 


20 


185 


154 


183 


212 


192 


231 


260 


250 


317 


368 


356 


423 


481 


111/9 


18 


281/9 


24 


158 


206 


245 


284 


258 


310 


348 


335 


426 


494 


477 


568 


645 


13 


22 


331/9 


28 


138 


277 


329 


381 


346 


415 


467 


450 


571 


663 


640 


761 


865 


15 


241/9 


38 


32 


120 


357 


424 


491 


446 


535 


602 


580 


736 


854 


825 


981 


1115 


17 


27 


43 


34 


112 


458 


543 


629 


572 


686 


772 


744 


944 


1095 


1058 


1258 


1430 


20 


33 


52 


42 


93 


670 


796 


922 


838 


1006 


1131 


1089 


1383 


1605 


1551 


1844 


2096 


231/2 


38 


60 


48 


80 


877 


1041 
19 


1206 
22 


1096 
20 


1316 
24 


1480 
27 


1424 
26 


1808 
33 


2099 
38.3 


2028 
37 


2411 

44 


2740 


Mean eff. press., lbs 


.... 


16 


50 


No. of expansio 


ns.. 


26.8 


20.1 


13.4 


8.9 




^0..- 




Cyl. condensation, ^ 


19 


19 


19 


16 


16 


16 


12 


12 


12 


8 


8 


8 


St.p. I.H.P. p. hr.. 


lbs.. 


14.7 


13.9 


13.3 


14.3 


13.9 


13.2 


14.3 


13.6 


13.0 


15.7114.9114.7 


Coal at 8 lbs. evap., 


lbs. 


1.8 


1.73 


1.66 


1.78 


1.7 


41.65 


1.78 


1.70 


1.62 


1.96 


1.8611.72 



The Willans Law. Total Steam Consumption at Different Loads. 

— Mr. Willans found with his engine that when the total steam consump- 
tion at different loads was plotted as ordinates, the loads being abscissas, 
the result would be a straight incUned Hne cutting the axis of ordinates at 
some distance above the origin of coordinates, this distance representing 
the steam consumption due to cylinder condensation at zero load. This 
statement applies generally to throttling engines, and is known as the 
Willans law. It applies also approximately to automatic cut-off engines 
of the Corliss, and probably of other types, up to the most economical 
load. In Mr. Barrus's book there is a record of six tests of a 16 X 42-in. 
Corliss twin-cylinder non-condensing engine, which gave results as follows: 

I.H.P 37 100 146 222 250* 287 342 

Feed-waterper I.H.P. hour. 73.63 38.28 31.47 25.83 25.0* 25.39 25.91 

Total feed-water per hour... 2724 3825 4595 5734 6250 7287 8861 

* Interpolated from the plotted curve. 

The first five figures in the last line plot in a straight line whose equa- 
tion is y = 2122 + 16.55 H.P., and a straight Hne through the plotted 
position of the last two figures has the equation y = 28.62 H.P. — 927. 
These two lines cross at 253 H.P., which is the most economical load, the 
water rate being 24.96 lbs. and the total feed 6314 lbs. The figure 2122 
represents the constant loss due to cylinder condensation, which is just 
over one-third of the total feed-water at the most economical load. 

In Geo. H. Barrus's book on "Engine Tests " there is a diagram of 
condensation and leakage in tight or fairly tight simple engines usine: sat- 
urated steam. The average curve drawn through the several observations 
shows the condensation and leakage to be about as follows for different 
percentages of cut-off: 

Cut-off, % of stroke = I 

Condens. and leakage, % = p. . . 
c = IXP -^ (100 - p) = 

The figures in the last line represent the condensation and leakage as 
a Dercentage of the volume of the stroke of the piston, that is, in the same 



5 


10 


15 


20 


25 


30 


35 


42 


60 


43 


35 


29 


24 


20 


17 


15 


7.5 


7.5 


8 


8.2 


7.9 


7.5 


7.2 


7.4 



992 THE STEAM-ENGINE. 

terms as the first line, instead of as a percentage of the total steam sup- 
plied, in which terms the figures of the second line are expressed. They 
indicate that the amount of cylinder condensation is nearly a constant 
quantity for a given engine with a given steam pressure and speed, what- 
ever may be the point of cut-off. 

Economy of Engines under Varying Loads. (From Prof. W. C. 
Unwin's lecture before the Society of Arts, London, 1892.) — The general 
result of numerous trials with large engines was that with a constant load an 
indicated horse-power should be obtained with a consumption of 1 1/2 lbs. 
of coal per I.H.P. for a condensing engine, and 13/4 lbs. tor a non-conden- 
sing engine, corresponding to about 13/4 lbs. to 21/8 lbs. per effective H. P. 

In electric-lighting stations the engines work under a very fluctuating 
load, and the results are far more unfavorable. An excellent Willans 
non-condensing engine, which on full-load trials worked with under 
2 lbs. per effective H.P. hour, in the ordinary daily working of the station 
used 7 1/2 lbs. in 1886, which was reduced to 4.3 lbs. in 1890 and 3.8 lbs. in 
1891. Probably in very few cases were the engines at electric-light stations 
working under a consumption of 41/2 lbs. per effective H.P. hour. In the 
case of small isolated motors working with a fluctuating load, still more 
extravagant results were obtained. 

At electric-lighting stations the load factor, viz., the ratio of the average 
load to the maximum, is extremly smah, and the engines worked under 
very unfavorable conditions, which largely accounted for the excessive 
fuel consumption at these stations. 

In steam-engines the fuel consumption has generally been reckoned on 
the indicated horse-power. At full-power trials tliis was satisfactory 
enough, as the internal friction is then usually a smaU fraction of the total. 

Experiment has, however, shown that tlie internal friction is nearly 
constant, and hence, when the engine is lightly loaded, its mechanical 
efficiency is greatly reduced. At full load small engines have a mechan- 
ical efficiency of 0.8 to 0.85, and large engines might reach at least 0.9, 
but if the internal friction remained constant this efficiency would be 
much reduced at low powers. Thus, if an engine working at 100 I.H.P. 
had an efficiency of 0.85, then when the I.H.P. fell to 50 the effective H.P. 
would be 35 H.P. and the efficiency only 0.7. Similarly, at 25 H.P= the 
effective H.P. would be 10 and the efficiency 0.4. 

Experiments on a Corliss engine at Creusot gave the following results: 

Effective power at full load 1.0 0.75 0.50 0.25 0.125 

Condensing, mechanical efficiency . 82 . 79 . 74 . 63 . 48 

Non-condensing, mechanical efficiency. . 86 . 83 . 78 . 67 . 52 

Steam Consumption of Engines of Various Sizes. — W. C. Unwln 
(Cassier's Magazine, 1894) gives a table showing results of 49 tests of 
engines of different types. In non-condensing simple engines, the steam 
consumption ranged from 65 lbs. per hour in a 5-horse-power engine to 22 
lbs. in a 134-H.P, Harris-Corliss engine. In non-condensing compound 
engines, the only type tested was the Willans, which ranged from 27 lbs. 
in a 10-H.P. slow-speed engine, 122 ft. per minute, with steam-pressure 
of 84 lbs., to 19.2 lbs. in a 40-H.P. engine, 401 ft. per minute, with steam- 
pressure 165 lbs. A Willans triple-expansion non-condensing engine, 
39 H.P., 172 lbs. pressure, and 400 ft. piston speed per minute, gave a 
consumption of 18.5 lbs. In condensing engines, nine tests of simple 
engines gave results ranging only from 18,4 to 22 lbs. In compound- 
condensing engines over 100 H.P., in 13 tests the range is from 13.9 to 
20 lbs. In three triple-expansion engines the figures are 11.7, 12.2, and 
12.45 lbs., the lowest being a Sulzer engine of 360 H.P. In marine com- 
pound engines, the Fusiyama and Colchester, tested by Prof. Kennedy, 
gave steam consumption of 21.2 and 21.7 lbs.; and the Meteor and Tartar 
triple-expansion engines gave 15.0 and 19.8 lbs. 

Taking the most favorable results which can be regarded as not excep- 
tional it appears that in test trials, with constant and full load, the ex- 
penditure of steam and coal is about as follows: 

l bs. Per I.H.P. hour . Per EfYective H.P.h r. 

Kind of Engine. ^—^^ Steam,* C^^i; Steam,' 

Non-condensing 1.80 16.5 2.00 18.0 

Condensing 1.50 13.5 1.75 15.8 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 993 



These may be regarded as minimum values, rarely surpassed by the 
most efficient machinery, and only reached with very good machinery in 
the favorable conditions of a test trial. 

Small Engines and Engines with Fluctuating Loads are usually 
very wasteful of fuel. The following figures, illustrating their low econ- 
omy, are given by Prof. Unwin, Cassier's Magazine, 1894. Small engines 
in workshops in Birmingham, Eng. 

Probable I.H.P. at full 

load 

Average I.H.P. during 

observation 

Coal per I.H.P. per hour 

during observation, lbs. 36.0 21.25 22.61 18.13 11.68 9.53 8.50 

It is largely to replace such engines as the above that power will be 
distributed from central stations. 

Tests at Royal Agricultural Society's show at Plymouth, Eng. Engi- 
neering, June 27, 1890. 



12 


45 


60 


45 


75 


60 


60 


2.96 


7.37 


8.2 


8.6 


23.64 


19.08 


20.08 



Rated 
H.P. 


Com- 
pound or 
Simple. 


Diam. of 
Cylinders. 


Stroke, 
ins. 


Max. 

Steam- 
pressure. 


Per Brake H.P. 
per hour. 


5:213 

C3 t- O 


h.p. 


l.p. 


Coal. 


Water. 


^s,^ 


5 
3 
2 


simple 

compound 

simple 


7 
3 
41/2 


"'6' 


10 
6 

71/2 


75 
110 

75 


12.12 
4.82 
11.77 


78.1 lbs. 
42.03 " 
89.9 •' 


6.1 lb. 
8.72 " 
7.64" 



Steam-consumption of Engines at Various Speeds. (Profs. Den- 
ton and Jacobus, Trans. A. S. M. E., x, 722.) — 17 X 30 in. engine, 
non-condensing, fixed cut-off, Meyer valve. (From plotted diagrams.) 



Revs, per min . 


8 12 16 


20 


24 


32 


40 


48 


56 


72 


88 


1/8 cut-off, lbs. . 


. 39 35 32 


30 


29.3 


29 


28.7 


28.5 


28.3 


28 


27.7 


1/4 cut-off, lbs.. 


39 34 31 


29.5 


29 


28.4 


28 


27.5 


27.1 


26.3 


25.6 


1/2 cut-off, lbs. . 


39 36 34 


33 


32 


30.8 


29.8 


29.2 


28.8 


28.7 


. . . . 



Steam-consumption of same engine: fixed speed, 60 revs, per minute. 
Varying cut-off compared with throttling-engine for same horse-power 
and boiler-pressures: 
Cut-off, fraction 

of stroke 0.1 0.15 0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.8 

Steam, 90 lbs.. . 29 27.5 27 27 27.2 27.8 28.5 

Steam, 60 lbs.. . 39 34.2 32.2 31.5 31.4 31.6 32.2 34.1 36.5 39 

Throttling-engine, 7/8 cut-off, for corresponding horse-powers. 

Steam, 90 lbs... 42 37 33.8 31.5 29.8 „ ... , 

Steam, 60 lbs 50.1 49 46.8 44.6 41 ... „ ... 

Some of the principal conclusions from this series of tests are as follows: 

1. There is a distinct gain in economy of steam as the speed increases 
for 1/2. 1/8. and 1/4 cut-off at 90 lbs. pressure. The loss in economy for 
about 1/4 cut-off is at the rate of 1/12 lb. of water per I.H.P. per hour for each 
decrease of a revolution per minute from 86 to 26 revolutions, and at the 
rate of s/g lb. of water below 26 revolutions. Also, at all speeds the 1/4 
cut-off is more economical than either the 1/2 or i/s cut-off. 

2. At 90 lbs. boiler-pressure and above 1/3 cut-off, to produce a given 
H.P. requires about 20% less steam than to cut off at T/s stroke and regu- 
late by the throttle. 

3. For the same conditions T^ith 60 lbs. boiler-pressure, to obtain, by 
throttling, the same mean effective pressure at 7/8 cut-off that is obtained 
by cutting off about 1/3, requires about 30% more steam than for the 
latter condition. 

Capacity and Economy of Steam Fire Engines. (Eng. News, 
Mar. 28, 1895.) — Tests of fire engines by Dexter Brackett for the Board 
of Fire Commissioners, Boston, Mass. are tabulated on p. 994. 



994 



THE STEAM-ENGINE. 



Results of Tests of Steam Fire Engines. 



No. of 
engine. 



I. 
1. 

2. 

3. 

4. 

5. 

5. 

6. 

7. 

8. 

9. 
10. 
10. 
11. 






101.0 



85.0 
74.0 
86.5 
86.0 



86.0 
112.0 
140.5 
174.0 
225.0 



229.0 






lbs. 
191.0 
184.0 
191.0 
141.6 
138.4 
163.7 
103.3 
181.6 
117.3 
172.1 
142.5 
91.1 
151.4 
148.4 






S^ So* 



lbs. 
2.26 



2.66 
3.57 
2.88 



5.87 
3.45 
4.94 
3.51 
4.49 
4.22 
4.10 
3.76 







.^ OQ 




02 CC 




. o 


<v 


^- 


i- 


lbs. 


lbs. 


90.2 


143.2 


92.3 


124.0 


78.4 


123.3 


75.7 


113.8 


71.5 


136.4 


102.7 


121.2 


72.1 


119.6 


92.7 


143.0 


68.8 


119.2 


101.3 


112.8 


76.5 


111.5 


59.0 


102.1 


87.8 


126.8 


74.7 


128.1 






7,619,800 
9,632,700 
5,900,000 
5,882,000 
8,112,900 
8,736,300 

14,026,000 
9,678,400 

10,201,600 
7,758,300 
7,187,400 
6,482,100 
7,993,400 
7,265,000 






galls. 
549 
499 
535 
482 
459 
449 
545 
536 
596 
910 
482 
419 
564 
572 



Nos. 1, 2, 3 and 4, Amoskeag engines; Nos. 5, 6, 7 and 8, Clapp & 
Jones; Nos. 9, 10, 11, Siisby. The engines all show an exceedingly high 
rate of combustion, and correspondingly low boiler efficiency and pump 
duty. 

Economy Tests of High-speed Engines. (F. W. Dean and A. C. 
Wood, Jour. A. S. M. E., June, 1908.) — Some of these engines had been in 
service for a long time, and therefore their valves may not have been in 
the best condition. The results may be taken as fairly representing the 
economy of average engines of the type, under usual working conditions. 
The engines w^ere all non-condensing. The 16 X 15-in. engine was 
vertical, the others horizontal. They were all direct-connected to gen- 
erators. 



No. of Test. 

Size of engine, ins 

Hours in service 

Revs, permin 

Valves 

Generator, K.W 

Steam per I.H.P.-hr. 
Steam per K.W.-hr . 



1 

15 X 14 

15,216 

240 

Iflat 

100 

37.2,t 36.2* 

60.2, 58.4 



2 

16X15 
20,000 

240 

1 flat 

2-50 

36.7.t 35.8 

61.0 59.7 



3 

14X12 

28,644 
300 

1 flat 

2-40 
31.7,t 32.0 
57.1, 57.4 



4 

16X M 

719 

270 

4 flat 

125 

37.5,* 36.7 

54.9. 54.7 



No. of Test. 
Size of engine, ins. 
Hours in service. . . 
Revs, per min 

Valves 



Generator, K.W 

Steam per I.H.P.-hr.. 
Steam per K.W.-hr.., 




7 

12X 18 

10,800 

190 

2 flat inlet 

2 Corliss exh. 

75 

44.0,t 36.7, 34.1 § 

79.3. 60.5. 53.7 



* 3/4 load ; 1 1/2 load ; $ 1 1/4 load ; §1 V2 load ; the others full load. 

Some of the conclusions of the authors from, the results of these tests 
are as follows: 

The performances of the perfectly balanced flat valve engines are so 
relatively poor as to disqualify them, unless this type of valve can be made 
with some mechanism by which wear will not increase leakage. The four 
valve engines, which were built to be more economical than single- valye 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 995 

engines, have utterly failed in their object. The duplication of valves 
used in both four- valve engines simply increased the opportunity for leak- 
age. The most economical result was obtained from a piston valve engine, 
No. 5, hea\ily loaded. With the lighter loads that are comparable the 
flat valve engine. No. 3, surpassed No. 5 in economy. The hat valve 
engines give a flatter load cm ve than the piston valve engines. Compar- 
ing the results of the fiat valve engines, the most economical results were 
obtained from engine No. 3, which had a valve which automatically takes 
up wear, and if it does not cut, must maintain itself tigiit for long periods. 

From the results we are justified in thinking that most high-speed en- 
gines rapidly deteriorate in economy. On the contrary, slower running 
Corliss or gridiron valve engines improve in economy for some time and 
then maintain the economy for many years. It is difficult to see that 
the speed is the cause of this, and it must depend on the nature of the 
valve. 

The steam consumption of small single-valve high-speed engines non- 
condensing, is not often less than 30 lbs. per I.H.P. per hour. Tw^o Water- 
town engines, 10 X 12 tested by J. W. Hill for the Philadelphia Dept. of 
PubUc Works in 1904, gave respectively 30.67 and 29.70 lbs. at full load, 
61.8 and 63.9 I.H.P., and 28.87 and 29.54 lbs. at approximately half-load, 
37.63 and 36.36 I.H.P. 

High Piston-speed in Engines. {Proc. Inst. M. E., July, 1883, p. 
321.) — The torpedo boat is an excellent example of the advance towards 
high speeds, and shows w^hat can be accomplished by studying lightness 
and strength in combination. In running at 22 1/2 knots an hour, an engine 
with cylinders of 16 in. stroke will make 480 revolutions per minute, which 
gives 1280 ft. per minute for piston-speed; and it is remarked that engines 
running at that high rate work much more smoothly than at lower speeds, 
and that the difficulty of lubrication diminishes as the speed increases. 

A High-speed Corliss Engine. — A Corliss engine, 20 X 42 in., has 
been running a wire-rod mill at the Trenton Iron Co.'s works since 1877, at 
160 revolutions or 1120 ft. piston-speed per minute {Trans. A. S. M. E.,n, 
72). A piston-speed of 1200 ft. per min. has been realized in locomotive 
practice. 

The Limitation of Engine-speed. (Chas. T. Porter, in a paper on the 
Limitation of Engine-speed, Trans. A. S. M. E., xiv, 806.) — The practical 
limitation to high rotative speed in stationary reciprocating steam-engines 
is not found in the danger of heating or of excessive wear, nor, as is gen- 
erally believed, in the centrifugal force of the fly-wheel, nor in the tendency 
to knock in the centers, nor in vibration. He gives two objections to very 
high speeds: First, that "engines ought not to be run as fast as they can 
be; " second, the large amount of waste room in the port, which is required 
for proper steam distribution. In the important respect of economy of 
steam, the high-speed engine has thus far proved a failure. Large gain 
was looked for from high speed, because the loss by condensation on a 
given surface would be divided into a greater weight of steam, but this 
expectation has not been realized. For this unsatisfactory result we have 
to lay the blame chiefly on the excessive amount of waste room. The 
ordinary method of expressing the amount of waste room in the percentage 
added by it to the total piston displacement, is a misleading one. It 
should be expressed as the percentage which it adds to the length of 
steam admission. For example, if the steam is cut off at 1/5 of the stroke, 
8% added by the waste room to the total piston displacement means 
40% added to the volume of steam admitted. Engines of four, five and 
six feet stroke may properly be run at from 700 to 800 ft. of piston travel 
per minute, but for ordinary sizes, says Mr. Porter, 600 ft. per minute 
should be the limit. 

British High-speed Engines. (John Davidson. Power, Feb. 9, 1909.) 
— The following figures show the general practice of leading builders: 

I.H.P. 50 100 200 500 750 1000 1500 2000 

Revs, per min.. 

600-700 550-600 500 350-375 325 250 200 160-180 
Piston speed, ft. per min. 

600 650 675 750 775 800 900 1000 

Rapid strides have been made during the last few years, despite the 



996 



THE STEAM-ENGINE. 



0.7 0.8 0.9 1.0 
10.75 10.75 10.8 11.0 



competition of the steam turbine. The single-acting type (Brotherhood, 
Wiilans and others) has been superseded by double-acting engines with 
forced lubrication. There is less wear in a high-speed than in a low-speed 
engine. A 500-H.P. 3-crank engine after running 7 years, 12 hours per 
day and 300 days per year, showed the greatest wear to be as follows: 
crank pins, 0.003 in. ; maiii bearings, 0.003 in. ; eccentric sheaves, 0.015 in.; 
crosshead pins, 0.005 in. All pins, where possible, are of steel, case- 
hardened. High-speed engines have at least as high economy and effi- 
ciency as any other type of engine manufactured. A triple-expansion 
mill engine, with steam at 175 lbs., vacuum 26 ins., superheat 100° F., 
gave results as shown below, [figures taken from curves in the original]. 

Fraction of full 

load 0.1 0.2 0.3 0.4 0.5 0.6 

Lbs. steam per 

I.H.P. hour.. 12.7 11.85 11.4 11.1 10.9 lO.S 
Lbs. steam per 

B.H.P. hour.. 16.0 14.8 13.7 12.9 12.4 12.05 11.85 11.8 11.8 11.8 

0^\1ng to the forced lubrication and throttle-governing, the economical 
performance at Hght loads is relatively much better than in slow-speed 
engines. The piston valves render the use of superheat practicable. 
At 200° superheat the saving in steam consumption of a triple-expansion 
engine is 26%. [A curve of the relation ot superheat to saving shows 
that the percentage of saving is almost uniformly IA% for each additional 
10° from 0° to 160° of superheat.] 

The method of governing small high-speed engines is by means of a 
plain centrifugal governor fixed to the crank shaft and acting -directly 
on a throttle. Several makers use a governor which at light Toads acts 
by throttling, and at heavy loads by altering the expansion in the high- 
pressure cylinder. The crank-shaft governor used in America has been 
found impracticable for high speeds, except perhaps for small engines. 

Advantage of High Initial and Low Back Pressure. — The theoretical 
advantage due to the use of high steam pressure and low back pressure 
or high vacuum is shown in the following table, which gives the cflB- 
ciencies of an ideal engine operating on the Rankine cycle with different 
initial and back pressures, using dry saturated steam. The method 
of calculating the Rankine cycle eflSciency, and a table showing the 
efficiencies with superheated steam will be found under Steam Turbines, 
page 1089. 



Rankine Cycle Efficiencies — Saturated Steam. 



Initial 




Vacuum, In. 


of Mercury. 




Pressure, 
Absolute, 





26 


27 


28 


28.5 


29 


Lb. 




Efficiencies 


, Per Cent 






100 


13.9 
16.7 
18.7 
19.4 
20.0 


23.6 
25.9 
27.4 
28.0 
28.6 


24.8 
27.0 
. 28.5 
29.1 
29.7 


26.3 
28.4 
29.9 
30.5 
31.0 


27.4 
29.4 
.30.9 
31.4 
32.0 


28.9 


150 


30.8 


200 


32.2 


225 


32.7 


250 


33.2 







In practice the efficiencies given in the above table cannot be reached 
on account of the imperfection of the engine and its losses due to 
cylinder condensation, leakage, radiation and friction. The relative 
advantages of high pressure and low back pressure are probably pro- 
portional to the figures in the table, provided the expansion is divided 
into two or more stages at pressures above 100 lb. The possibility of 
obtaining very high vacua is Umited by the temperature of the con- 
densing water available and by the imperfections of the air pump. 
The use of high initial pressures is limited by the safe working pressure 
of the boiler and engine. 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 997 

Cromparison of the Economy of Compound and Single-cylinder Corliss 
Condensing Engines, each expanding about Sixteen Times. (D. S. 

Jacobus, Trans,, A. S. M. E., xii, 943.) 

The engines used in obtaining comparative results are located at 
Stations I and II of the Pawtucket Water Co. 

vThe tests show that the compound engine is about 30% more economical 
than the single-cylinder engine. The dimensions of the two engines are 
as follows: Single 20 X 48 ins.; compound 15 and 301/8 X 30 ins. The 
steam used per I.H.P. hour was: single 20.35 lbs., compound 13.73 lbs. 

Both of the engines are steam-jacketed, practically on the barrels only, 
with steam at full boiler-pressure, viz., single 106.3 lbs., compound 127.5 lbs. 

The steam-pressure in the case of the compound engine is 127 lbs., or 
21 lbs. higher than for the single engine. If the steam-pressure be raised 
this amount in the case of the single engine, and the indicator-cards be 
increased accordingly, the consumption for the single-cylinder engine 
would be 19.97 lbs. per hour per horse-power. 

Two-cylinder vs. Three-cylinder Compound Engine. — A Wheelock 
triple-expansion engine, built for the Merrick Thread Co., Holyoke, Mass., 
is constructed so that the intermediate cylinder may be cut out of the 
circuit and the high-pressure and low-pressure cyUnders run as a two- 
cylinder compound, using the same conditions of initial steam-pressure 
and load. The diameters of the cylinders are 12, 16, and 2413/32 ins., the 
stroke of the first two being 36 ins. and that of the low-pressure cylinder 
48 ins. The results of a test reported by S. M. Green and G. I. Rockwood, 
Trans. A. S. M. E., vol. xiii, 647, are as follows: In lbs. of dry steam used 
per I.H.P. per hour, 12 and 2413/32 in. cyUnders only used, two tests 13.06 
and 12,76 lbs., average 12.91. All three C34inders used, two tests 12.67 
and 12.90 lbs., average 12.79. The difference is only 1%, and would 
indicate that more than two cylinders are unnecessary in a compound 
engine, but it is pointed out by Prof. Jacobus, that the conditions of the 
test were especially favorable for the two-cylinder engine, and not rela- 
tively so favorable for the three cylinders. The steam-pressure was 142 
lbs. and the number of expansions about 25. (See also discussion on 
the Rockwood type of engine, Trans. A. S. M. E., vol. xvi.) 

Economy of a Compound Engine. (D. S. Jacobus, Trans. A. S. M. E., 
1903.) — A Rice & Sargent engine, 20 and 40 X 42 ins., was tested with 
steam about 149 lbs., vacuum 27.3 to 28.8 ins. or 0.82 to 1.16 lbs. abso- 
lute. r.D.m. 120 to 122. with results as follows: 

I.H.P 1004 853 820 627 491 340 

Water per I.H.P. per hr. . . 12.75 12.33 12.55 12.10 13.92 14.58 
B.T.U. per I.H.P. per min. 231.8 226.3 229.9 222.7 256.8 267.7 

The Lentz Compound Engine is described in The Engineer (London), 
July 10, 1908. It is the latest development of the reciprocating engine 
with four double-seated poppet valves to each cylinder, each valve op- 
erated by a separate eccentric mounted on a lay-shaft driven by bevel- 
gearing from the main shaft. The throw of the high-pressure steam 
eccentrics is varied by slide-blocks which are caused to slide along the lay- 
shaft by the action of a centrifugal inertia governor, which is also mounted 
on the lay-shaft. No elastic packing is used in the engine, the piston-rod 
stuffing box being fitted with ground cast-iron rings, and the valve stems 
being provided with grooves and ground to fit long bushings to 0.001 in. 
Two tests of a Lentz engine built in England, 14 1/2 and 243/4 by 271/2 in., 
gave results as follows: 

Saturated steam, 170 lbs., vacuum 26 in., I.H.P. 366, steam per I.H.P. 
per hour 12.3 lbs. Steam 170 lbs. superheated 150° F., vac. 26 in., I.H.P. 
366, steam oer I.H.P. per hour, 10.4 lbs. Revs, per min. in both cases 
167. Piston speed 767 ft. per min. Engines are built for speeds up to 
900 ft. per min., and up to 350 r.p.m. The Lentz engine is built in the 
United States by the Erie City Iron Works. 

The Stumpf Uniflow Engine is a single cylinder engine with a very 
long piston and with exhaust ports in the middle of the cylinder which 
are uncovered as the piston travels beyond them. The inlet ports are 
at the ends. The exhaust steam therefore does not have to flow back 
to the ends of the cylinder in order to escape, and the cooling of the 
ends and of the ports is thereby avoided. It is claimed that this single 
cylinder engine gives a steam economy equal to that of a compound 
engine. Uniflpw engines are built by Nordberg Mfg. Ck>., Milwaukee. 



998 



THE STEAM-ENGINE. 



Steam Consumption of Sulzer Compound and Triple-expansion 
Engines with Superheated Steam. 

The figures in the table below were furnished to the author in 1902 
by Sulzer Bros., Winterthur, Switzerland. Results of official tests: 



Saturated Steam. 




Superheated Steam. 


i 




s« 




ii 


3 




u 

> 




i4 


'^s 


AS 


1^ 


111 


B^. 


fl 


'43 ^ 


42 


P^ 


SP4 








^S3 


to 






1^3 


130 


356 


26.4 


850 


13.30 


^ { 


132 
122 


428 
482 


26. A 
26.6 


842 
1719 


12.05 
12.42 


136 


357 


28 


481 


13.00 


iH 


135 


547 


28 


515 


11.32 


134 


356 


28 


750 


13.10 


132 


533 


27.8 


788 


11.52 


135 


356 


27.6 


1078 


14.10 


134 


546 


27.2 


1100 


11.88 


130 


358 


28.2 


1076 


14.10 


\ ^ \ 


132 


496 


28.3 


1071 


11.73 


129 


358 


28 


1316 


14.50 


136 


527 


* 


1021 


15.37 


190 


397 


27.2 


2880 


11.28 


D 


188 


606 


28 


2860 


8.97 


196 


381 


26.2 


3040 


11.57 


E 


189 


613 


27 


2908 


9.41 


'^. Superheated Steam. 


) ( 


127 


655 


27.2 


788 


9.91' 


135 557 26.4 519 lO.SOf 


j.o] 


127 


664 


27.2 


797 


9.68t 
10.70- 


135 554 26.4 347 10.35t 


128 


572 


27.1 


788 


Normal, H.P. Cylinders, In. 




R.P.M. 


A 1500 to 1800 30.5 & 49.2 X 59.1 




83 


B 800 to 1000 24 & 40.4 X 51.2 




83 


C 950 to 1150 26 & 42.3 X 51.2 




86 


D 3000 triple expan. 321/4, 471/4, & 58 X 


59 


85 


E 3000 triple expan. 34, 49, & 61 X 


51 


83.5 


F 400 to 500 17.7 & 30.5 X 35.4 




110 


C 


^ 1( 


X)0 to 


1200 




26.9 & 4 


.7.2 X 


66.9 




65 



* Non-condensing, t With intermediate superheating. Tempera- 
ture of steam at entrance to low-pressure cyhnder, 307 to 349° F. 

Test of a Non-condensing Engine with Superheated Steam. — Prof. 
J. A. Moyer reports in Power, Dec. 2, 1913, the following results of tests 
of a simple Lentz horizontal engine, cyUnder, 191/32 in. X 20i5/i6 in. 
stroke, 207 to 211 r.p.m. Steam pressure, absolute, 170.1 to 171.9 lb. 
Back pressxu'e, to 0.34 in. of mercury. 

Indicated horse-power 162 . 7 

Steam per I. H.P. hour, lb 17 . 25 

Superheat, deg. F 98.3 

Saving of Steam due to Superheating. — The following figures are 
given by Power Specialty Co., makers of the Foster superheater. 

A 3300 horse-power Lentz cross-compound engine having 37 1/2-in. 
and 63-in. cylinders, 55-in. stroke, at Charlottenburg, Germany, with 
192-lb. gage pressure, 26-in. vacuum, 107 revs, per min., gave the follow- 
ing steam consiunption: 



227.6 


282.1 


322.5 


15.78 


15.24 


15.48 


139.4 


141.5 


159.7 



Temp. 

of 
Steam. 


Super- 
heat. 


Load. 


V4 


V2 


V4 


Vi 


5/4 


570° 
660° 


185° F. Steam per I.H.P. hr., lb 

275° F. Steam per I.H.P. hr.. lb. . . . 


11.1 
10.6 


10.1 
9.7 


9.5 
9.0 


9.2 

8.8 


9.7 
9.2 



The saving in steam effected by superheating 100 degrees, as com- 
pared with saturated steam, is, approximately, for steam turbines. 
10 per cent; triple-expansion engines, 12 per cent; compound engines, 
14 per cent; simple engines, 18 per cent and over. 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 999 



Tests of Buckeye engines, simple, 12 X 16 in., and compoimd, 10 and 
17V2 X 16 in., with steam at 100 to 110 lb. pressure, gave the following: 





Per 
Cent of 
Rated 
Load. 


Degrees of Superheat. 


Engine. 


1 50 100 1 150 1 200 




Lb. Steam per I.H.P. Hr. 


Simple, non-condensing 


30 
50 
100 
100 
100 


35 
31.5 

28.5 


28 

25.5 

24.0 


24 

22 

20 

17.5 

14 


21.5 

19 

18 

15.5 

12.5 


19.5 


Simple, non-condensing 


17 5 


Simple, non-condensing 


17.5 


Compound, non-condensing 


14.6 


Compound, condensing 


18 


16.5 


11.5 



Steam Consumption of Different Types of Engines. 

Tests of a Ridgway 4- valve non-condensing engine, 19 X 18 in., at 
200 r.p.m. and 100 lb. pressure, are reported in Power, June, 1909, as 
follows: 

Load 1/4 1/2 3/4 Fidl II/4 

Steam per I.H.P. hour. .. . 30.7 24.4 23.2 23.8 I 25.4 

The best result obtained at 130 lb. pressure was 21.6 lb.; at 115 lb. 
pressure, 22.6 lb. ; and at 85 lb. pressure, 24.3 lb. Maintained economy 
in this type of engine is dependent upon reduction of unnecessary over- 
travel, properly fitted valves, valves which do not span a wide arc, close 
approach of the movement of the valves to that of a Corliss engine, and 
good materials. 

The probable steam consumption of condensing engines of different 
types with different pressures of steam is given in a set of curves by 
E. H. Thurston and L. L. Brinsmade, Trans. A. S. M. E., 1897, from 
which curves the following approximate figures are derived. 

Steam pressure, absolute, lbs. per sq. in. 



Ideal Engine 

(Rankine cycle) 
Quadruple Exp. 

Wastes 20% 
Triple Exp. 

Wastes 25% 
Compound. 

Wastes 33% 
Simple Engine. 

Wastes 50% 


400 


300 


250 


200 


150 


100 


75 


50 


6.95 
8.75 


7.5 

9.15 


7.9 
9.75 


8.45 
10.50 


9.20 
11.60 


10.50 
13.0 


11.40 
14.0 


12.9 
15.6 


9.25 


9.95 


10.50 


11.15 


12.30 


14.0 


15.1 


16.7 


10.50 
14.00 


11.25 
15.00 


11.80 
15.80 


12.70 
16.80 


13.90 
18.40 


15.6 
20.4 


16.9 

22.7 


18.9 
25.2 



The same authors give the records of tests of a three-cylinder engine 
at Cornell University, cyhnders 9, 16 and 24 ins., 36-in. stroke, first as a 
tnple-expansion engine; second, with the intermediate cyhnder omitted, 
making a compound engine with a cylinder ratio of 7 to 1 • and third, 
omitting the third cyhnder, making a compound engine with a ratio of 
a nttle over 3 to 1. The boiler pressure in the first case was 119 lbs , 
m the second 115, and in the third 117 lbs. Charts are given showing 
the steam consumption per I.H.P. and per B.H.P. at different loads, 
from which the fohowing fisrures are taken. 

Indicated Horse-power 40 60 80 100 110 120 130 

Steam consumption per I.H.P. per hoiu*. 

Triple Exp 19.1 16.7 15.3 14.2 13.7 13.8 14.4 

Comp. 7 to 1 IP. 6 18.2 17.0 16.3 16. 15.8 15.8 

Comp. 3 to 1 19.7 18.4 18.1 18.5 

Steam consumption per B.H.P. hour. 

Triple Exp 30.5 23.0 19.6 17.1 16.2 16.2 16.7 

Comp. 7 to 1 26.2 21.7 19.3 18.7 18.5 18.4 18.5 

Comp. 3 to 1 23.4 20.6 20. 20 

The most economical performance was as follows: 

Triple Comp. 7 to 1 Comr). 3 to I 

Indicated Horse-power 112.7 130.0 67.7 

Steam per I.H.P. hour. . . , . 13.68 15.8 18.03 



1000 THE STEAM-ENGINE. 

A test of a 7500-F.P. enpine, at the 59th St. Station of the Interboroiigh 
Rapid Transit Co., New York, is reported in Power, Feb., 1906. _ It is a 
double cross compound en^ne, with horizontal h.p. and vertical l.p. 
cylinders. With steam at 175 lbs. grauere and vacnnm 25.02 ins., 75 r.p.m. 
it developed 7365 I.H.P., 5079 K.W. at switchboard. Friction and elec- 
trical losses 417.3 K.W. Dry steam per K.W. hour 17.34 lbs.; per I.H.P. 
hour, 11.96 lbs. 

A test of a Fleminer 4-valve enerine, 15 and 40.5 in. diam., 27-in. -stroke,, 
positive-driven Coriiss valves, fiv-wheel grovernor, is reported by B. T. 
Allen in Trans. A. S. M. E., 1903. The followiner results were obtained. 
The speed was above 150 r.p.m. and the vacuum 26 in. 

Fraction of full load about i/e s/g 7/io Full load 1.1 

Horse-power 87.1 321.5 348.3 501.6 553.5 

Steam per I.H.P. hour 14.42 13.59 12.33 12.66 12.7 

Relative Economy of Compound Non-condensing Engines 
Under Variable Loads. — F. M. Rites, in a paper on the Steam Dis- 
tribution in a Form of Single-acting Engine (Trans. A. S. M. E., xiii, 537), 
discusses an engine designed to meet the following problem: Given an 
extreme range of conditions as to load or steam-pressure, either or both, 
to fluctuate together or apart, violently or with easy gradations, to 
construct an engine whose economical performance should be as good as 
though the engine were specially designed for a momentary condition — 
the adjustment to be complete and automatic. In the ordinary non-con- 
densing compound engine with hght loads the high-pressure cyUnder is 
frequently forced to supply all the power and in addition drag along with 
it the low-pressure piston, whose cylinder indicates negative work. Mr. 
Rites shows the peculiar value of a receiver of predetermined volume 
which acts as a clearance chamber for compression in the high-pressure 
cyHnder. The Westinghouse com.pound single-acting engine is designed 
upon this principle. The following results of tests of one of these engines 
rated at 175 H.P. for most economical load are given: 

Water Rates under Varying Loads, lbs. per H.P. per Hour. 

Horse-power .210 170 140 115 100 80 50 

Non-condensing 22.6' 21.9 22.2 22.2 22.4 24.6 28.8 

Condensing 18.4 18.1 18.2 18.2 18.3 18.3 20.4 

Eflaciency of Non-condensing Compound Engines. (W. Lee 

Church, Am. Mach., Nov. 19, 1891.) — The compound engine, non-con- 
densingj at its best performance will exhaust from the low-pressure cylin- 
der at a pressure 2 to 6 pounds above atmosphere. Such an engine will 
be limited in its economy to a very short range of power, for the reason 
that its valve-motion will not permit of any great increase beyond its 
rated power, and any material decrease below its rated power at once 
brings the expansion curve in the low-pressure cylinder below atmos- 
phere. In other words, decrease of load tells upon the compound engine 
Somewhat sooner, and much more severely, than upon the non-compound 
engine. The loss commences the moment the expansion line crosses a 
line parallel to the atmospheric line, and at a distance above it repre- 
senting the mean effective pressure necessary to carry the frictional load 
of the engine. When expansion falls to this point the low-pressure 
cylinder becomes an air-pump over more or less of its stroke, the power 
to drive which must come from the liigh-pressure cylinder alone. Under 
the light loads common in many industries the low-pressure cylinder is 
thus a positive resistance for the greater portion of its stroke. A careful 
study of this problem revealed the functions of a fixed intermediate 
clearance, always in communication with the high-pressure cylinder, 
and having a volume bearing the same ratio to that ot the high-pressure 
cylinder that the high-pressure cylinder bears to the low-pressure. Engines 
laid down on these lines have fully confirmed the judgment of the de- 
signers. The effect of this constant clearance is to supply sufficient steam 
to the low-pressure cylinder under light loads to hold its expansion curve 
up to atmosphere, and at the same time leave a sufficient clearance volume 
in the high-pressure cylinder to permit of governing the engine on its 
compression under light loads. 

Tests, of two non-condensing Corliss engines by G. H. Barrus are re- 
ported m Power, April 27, 1909. The engines were built bv Rice & 
Sargent. One is a simple engine 22 X 30, and the other a tandem 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 1001 



compound 22 and 36 X 36 ins. Both engines are jacketed in both 
heads, and the compound enmne has a reheating receiver with 0.6 sq. ft. 
o{ brass pipes per rated H.P. (600). The pruarantees were: compound 
engine, not to exceed 19 lbs. of steam per I. H.P. per hour, with 130 lbs. 
steam pressure and 1 lb. back pressure in the exhaust pipe, and the 
simple engine not to exceed 23 lbs. The friction load, engine run with 
the brushes off the generator and the field not excited, was not to exceed 
41/2 H.P. in either engine. The results were: compound engine, 99.2 
r.p.m., 608.3 H.P.; 18.33 lbs. steam per I. H.P. per hour; friction load 
3.8% of 600 H.P.; simple engine, 98.5 r.p.m.; 306.2 I.H.P.; 20.98 lbs. per 
I. H.P. per hour; friction 3.6% of 300 H.Po 

A single-cylinder engine 12 X 12 Ins., made by the Buffalo Forge Co., 
was tested by Profs. Reeve and AUen. {El. World, May 23, 1903.) 
Some of the results were: 

I.H.P 16.39 37.20 56.00 69.00 74.10 81.4 89.3 125.9* 86.42t 

Water-rate... 52.3 35.3 33.3 31.9 30.6 34.6 33.1 27.6 37.5 

* Steam pressure 125 lbs. gauge, all the other tests 80 lbs. f Con- 
densing, other tests all non-condensing. 

Effect of Water contained in Steam on the Efficiency of the 
Steam-engine. (From a lecture by Walter C. Kerr, before the Franklin 
Institute, 1891.) — Standard writers make little mention of the effect 
of entrained moisture on the expansive properties of steam, but by 
common consent rather than any demonstration they seem to agree that 
moisture produces an ill effect simply proportional to the percentage 
amount of its presence. That is, 5% moisture will increase the water rate 
of an engine 5%. 

Experiments reported in 1893 by R. C. Carpenter and L. S. Marks, 
Trans. A. S. M. E., xv, in which water in varying quantity was intro- 
duced into the steam-pipe, causing the quality of the steam to range from 
99% to 58% dry, showed that throughout the range of quahties used the 
consumption of dry steam per indicated horse-power per hour remains 
practically constant, and indicated that the water was an inert quantity, 
doing neither good nor harm. 

Influence of Vacuum and Superheat on Steam Consumption. {Eng, 
Digest, Mar., 1909.) — Herr Roginsky (''Die Turbine") discusses the 
economies effected by the use of superheat and high vacuums. 

In a certain triple-expansion engine, working under good average 
conditions, there was found a saving of approximately 6% for each 10% 
increase in vacuum beyond 50%. 

The BatuUi-Tumhrz formula for superheated steam is: p (v + a) = RT. 
in which p = steam pressure in kgs. per s^. meter, v = cubic meters in 
1 kg. of superheated steam at pressure p^ a — 0.0084, R = 46.7, and 
T = absolute temperature in deg. C. 

Using this expression, it is found that, neglecting the fuel used for 
superheating, for each 10° C. of superheat at pressures ranging from 
100 to 185 lbs. per sq. in. there is an average increase of volume of 2.8%. 
The work done by the expansion of superheated steam, as shown by 
diagrams, is about 1.6% less for 10° of superheating, so that the net 
saving for each 10° of superheat is 2.8 «- 1.6 == 1.2%, approx. (0.66% 
for each 10° F.). 

Rateau's formula for the steam consumption (K) per H.P.-hr. of an 
ideal steam turbine, in which the steam expands from pressure pt to pa, i« 

K = 0.85 (6.95 - 0.92 log P2) /(log Pi - log P2), 
K being in kilograms and pi and p2 in kgs. per sq. meter. From this 
formula the following table is calculated, the values being transformed 
into British units. 



Pi 
Lbs. per 


Lbs. Steam 
at 50% 
Vacuum. 


Reduction of Steam Consumption (%) by 
using a Vacuum of 


sq. in. 


60% 


70% 


80% 


90% 


95% 


184.9 
156.5 
128 
99.6 


11.11 
11.75 
12.57 
13.84 


5. 

5.8 
6.6 
7.6 


11.1 
11.8 
12.9 
14.4 


18.1 
19.3 
20.5 
22. 


27.8 
28.8 
20.8 
33.3 


34.6 
36.4 
38.5 
40.6 



1002 



THE STEAM-ENGINE. 



From the entropy diagram it is seen that in expanding from pressm-es 
in excess of 100 lbs. per sq.in. down to 1.42 lbs. absolute, approximately 
1 % more work is performed for every 10° F. of superheat. The effect of 
increasing the degree of vacuum is summed up in the following table: 



Increasing 


Decreases Steam Consumption. 


the 
Vacuum from 


in Reciprocating 
Engines. 


in Steam 
Turbines. 


50% to 60% 
50% to 70% 
50% to 80% 
50% to 90% 
50% to 95% 


5.8% 
11.6% 
17.3% 
23.1% 
26.0% 


6.2% 
12.6% 
20.0% 
30.1% 
37.4% 



In the last case (from 50% to 95%) the decrease in steam consumption 
is 44% greater for a steam turbine than for a reciprocating engine. 

The following results of tests of a compound engine using superheated 
steam are reported in Power, Aug., 1905. The cyhnders were 21 and 
36 X 36 ins. The steam pressure was about 117 lbs. gauge. R.p.m. 100, 
vacuum 26.5 ins. 



Test No 1 

Indicated H.P 481 

Superheat of steam 

entering h.p. cyl. . . 253° F 
B.T.U. suppUed per 

I.H.P. per min.... 198.2 
B.T.U. theoretically 

required. Rankine 

cycle 142.4 

Efficiency ratio 0.72 

Thermal efficiency % 21.39 
Lbs. steam per I.H.P. 

hour 9.098 



2 
461 



242** 



3 

347 

221° 



4 
145 



202° 



5 
333 



232° 



6 

258 

210° 



201.7 197.6 192.1 194.0 194.0 



42.5 


130.2 


128.0 


126.0 


128.5 


0.71 


0.66 


0.67 


0.65 


0.66 


21.02 


21.46 


22.07 


21.86 


21.86 



9.267 8.886 8.585 8.682 8.742 



The Practical Application of Superheated Steam is discussed in a 
paper by G. A. Hutchinson in Trans. A. S. M. E., 1901. Many different 
forms of superheater are illustrated. 

Some results of tests on a 3000-H.P., four-cyUnder, vertical, triple-ex- 
pansion Sulzer engine, using steam from Schmidt independently fired 
superheaters, are as follows. {Eng. Rec, Oct. 13, 1900.) 



Tests Using Steam. 


Highly Superheated. 


Mod- 
erately 
Super- 
heated 


Saturated. 


Initial pressure in h.p. cyl. 
(absolute), lbs 


187.3 

582 
2,900 
9.64 
477 


195.5 

585 
2,779 
9.67 

482 


188.4 

614 
2,868 
9.56 
479 


190.3 

531 

2,850 
10.29 
447 


194.6 

381 
2,951 
11.77 
438 


195 9 


Temp, of steam in valve 
chest, deg. F 


381 


Total I.H.P 

Lbs. steam per I.H.P. hour 
Watt hours per lb. of coal. 


2,999 
11.75 
435 



The saving due to the use of highly superheated steam is (482-438) — 
482=9.1%. 

Tests of a 4000-H.P. double-compound engine (Van den Kerchove, of 
Brussels) with superheated steam are reported in Power, Dec. 29, 1908. 
The cyhnders are 341/4 and 60 ins., stroke 5 ft. Ratio of areas 2.97. The 
following are the principal results, the first figures given being for the full- 
load test and the second (in parpntheses) for the half-load test. Steam 
pressure at drier, 136.5 lbs. (137.9). R.p.m. 84.3 (84.06). Temp, of 
steam entering engine 519° F. (498), leaving l.p. cyl. 121.5° (121.5). 
Vacuum in condenser, ins., 27.5 (27). I.H.P. 3776 (2019). Steam per 
I.H.P. hour, lbs., 9.62 (9.60). 

The saving due to the use of superheated steam is reported in numerous 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 1003 

tests as being all the way from less than 10% to more than 40%. The 
greater saving is usually found with engines that are the most inefficient 
with saturated steam, such as single-cylinder engines with light loads, in 
which the cylinder condensation is excessive. 

R. P. Bolton (E7ig. Mag., May, 1907) states that tests of superheated 
steam in locomotives, by the Prussian Railway authorities in 1904, with 
50°, 104° and 158° F. superheat, showed a saving of water respectively 
of 2.5, 10 and 16%, and a saving of coal of 2, 7 and 12%. Mr. Bolton's 
paper concludes with a long list of references on the subject of super- 
heated steam. A paper by J. R. Bibbins in Elec. Jour., March, 1906, gives 
a series of charts showing the saving made by different degrees of super- 
heating in different types of engines, including steam turbines. 

For description of the Foster superheater, see catalogue of the Power 
Specialty Co., New York. 

The Wolf (French) semi-portable compound engine of 40 H.P. with 
superheater and reheater, the engine being mounted on the boiler, is 
reported by R. E. Mathot, Power, July, 1906, to have given a steam 
consumption as low as 9.9 lbs. per I. H.P. hour, and 10.98 lbs. per B.H.P. 
hour. The steam pressure in the boiler was 172.6 lbs., and was super- 
heated initially to 657° F., and reheated to 361° before entering the l.p. 
cylinder. This is a remarkable record for a small engine. 

A test of a Rice & Sargent cross-compound horizontal engine 16 and 
28X42 ins., with superheated steam, is reported by D. S. Jacobus in 
Trans. A. S. M. E. , 1904. The steam pressure at the throttle was 140 lbs. 
gauge, the superheating was 350 to 400°, and the vacuum 25 to 26 ins., 
r.p.m. 102. In three tests with superheated and one with saturated, 
steam the results were: 

I.H.P. developed 474.5 420.4 276.8 406.7 

Water consumption per I. H.P. hour 9.76 9.56 9.70 13.84 

Coal consumption per I.H.P. hour 1.265 1.257 1.288 1.497 

B.T.U. per min. per I.H.P 205.0 203.7 208.8 248.2 

Temp, of steam entering h. p. cyl 634 659 672 

Temp, of steam leaving h. p. cyl 346 331 288 262 

Temp, of steam entering l.p. cyl 408 396 354 269 

Temp, of steam leaving l.p. cyl 135 141 117 

Performance of a Quadruple Engine. — O. P. Hood (Trans. A. S, 
M. E., 1906) describes a test of a high-duty air compressor, with four 
steam cylinders, 14.5, 22, 38 and 54 in. diam., 48-in. stroke. The clear- 
ances were respectively 6, 5.7, 4.4 and 3.5%. R.p.m. 57. Steam pressure, 
gauge, near throttle, 242.8 lbs., in 1st. receiver 120.7 lbs., in 2d, 30.8 lbs., 
in 3d, vac, — 1.24 ins. Moisture in steam near throttle, 5.74%. Steam 
in No. 1 receiver, dry; in No. 2, 17° superheat; in No. 3, 9° superheat. 
The engine has poppet valves on the h.p. cylinder and Corliss valves on 
the other cylinders. The feed-water heaters are four in number, in series, 
on the Nordberg system; No. 1 receives its steam from the exhaust of 
No. 4 cylinder; No. 2 from the jacket of No. 4 cyl.: No. 3 from the jackets 
of No. 3 cylinder and No. 3 reheater; No. 4 from the jacket of No. 2 
cylinder. The reheaters are suppUed \sith steam from the boilers. The 
temperatures of steam and water were as follows: Temperatures of steam: 
Fed to No. 1 engine, 403°; leaving receivers. No. 1, 351°; No. 2, 291°; 
No. 3, 216°. Exhaust entering preheater, 114°. Temperature ccx-re- 
sponding to condenser pressure, 109.6°. Temperatures of water: Fed to 
preheater, 93°; fed to heaters, No. 1, 114°; No. 2, 173°; No. 3. 202°; No. 4, 
269°; leaving heater No. 4 as boiler feed, 334°. 

The principal results of the test are as follows: 

Cylinder : 1 • 2 3 4 

I.H.P. developed in steam cylinders 181.47 256.96 275.71 275.56 

I.H.P. used in the cyUnders 220.04 222.12 226.20 214.84 

Total indicated horse-power, steam cyhnders 989.7 

Total horse-power used in air cyUnders 883.2 

Total indicated horse-power of auxiUaries 11.0 

Horse-power representing friction of the 

machine 95.5 

Per cent of friction 9.65% 

Mechanical efficiency engine and compressor 90.35% 

Heat consumed bv engine per hour per I.H.P., 10,157 B.T.U. ; per 
B.H.P. , 11,382 B.T.U. Equivalent standard coal consumption per 



1004 THE STEAM-ENGINE. 

hour assuming 10,000 B.T.U. imparted to the boiler per pound coal, per 
I.H.P., 1,016 lbs.; per B.H.P., 1,138 lbs. Dry steam per hour per 
I.H.P., 11.23 lbs.; per B.H.P., 12.58 lbs. Heat units consumed per 
mmute, per I.H.P., 169.29 B.T.U. ; per B.H.P., 189.70 B.T.U. 
Efficiency of Carnot cycle between the temperature of incoming 

steam and that corresponding to pressure in the condenser... 34.0 % 

Actual heat efficiency attained by this engine . .• 25.05% 

Relative efficiency compared with Carnot cycle 73.69% 

Relative efficiency compared with Rankine'cycle 88.2 % 

Duty, ft.-lbs. per milUon B.T.U. supphed 194,930.000 

This engine establishes a new low record for the heat consumed per hour 
per I.H.P., being 9% lower than that used by the Wild wood pumping 
engine reported in 1900. (See Pumping Engines.) 

The Use of Reheaters in the receivers of multiple-expansion engines is 
discussed by R. H.Thurston in Trans. A.S.M.E. ,xxi,S9S. Heshowsthat 
such receivers improve the economy of an engine very little unless they 
are also superheaters; in which case marked economy may be effected 
by the reduction of cylinder condensation. The larger the amount of 
cyUnder condensation and the greater the losses, exterior and interior, 
the greater the effect of any given amount of superheating. The same 
statement will hold of the use of reheaters: the more wasteful the engine 
without them and the more effectively they superheat, the larger the 
gain by their use. A reheater should be given such area of heating surface 
as will insure at least moderate superheating. 

Influence of the Steam-jacket. — Tests of numerous engines with 
and without steam-jackets show an exceeding diversity of results, ranging 
all the way from 30% saving down to zero, or even in some cases showing 
an actual loss. The opinions of engineers at this date (1894) is also as 
diverse as the results, but there is a tendency towards a general belief 
that the jacket is not as valuable an appendage to an engine as was for- 
merly supposed. An extensive resumi of facts and opinions on the steam- 
jacket is given by Prof. Thurston in Trans. A. S. M. E., xiv, 462. See 
also Trans. A. S. M. E., xiv, 873 and 1340; xiii, 176; xii, 426 and 1340; 
and Jour. F. I., April, 1891, p. 276. The foUowing are a few statements 
selected from these papers. 

>The results of tests reported by the research committee on steam-jackets 
appointed by the British Institution of Mechanical Engineers in 1886, 
indicate an increased efficiency due to the use of the steam-jacket of from 
1% to over 30%, according to varying circumstances. 

Professor Unwin considers that "in all cases and bn all cylinders the 
jacket is useful; provided, of course, ordinary, not superheated, steam is 
used; but the advantages may diminish to an amount not worth the in- 
terest on extra cost." 

Professor Cotterill says: Experience show^s that a steam-jacket is advan- 
tageous, but the amount to be gained will vary according to circumstances. 
In many cases it may be that the advantage is small. Great caution is 
necessary in drawing conclusions from any special set of experiments on 
the influence of jacketing. 

In the Pawtucket pumping-engine, 15 and 30V8X 30 in., 50 revs, per 
min., steam-pressure 125 lbs. gauge, cut-off i/4in h.p. and 1/3 in l.p. cyhnder, 
the barrels only jacketed, the saving by the jackets was from 1% to 4%. 

The superintendent of the Holly Mfg. Co. (compound pumping-engines) 
says: " In regard to the benefits derived from steam-jackets on our steam- 
cylinders, I am somewhat of a skeptic. From data taken on our own 
engir)es and tests made I am yet to be convinced that there is any practical 
value in the steam-jacket." 

Professor Schrooter from his work on the triple-expansion engines at 
Augsburg, and frlm the resuUs of his tests of the jacket efficiency on a 
small engine of the Sulzer type in his own laboratory, concludes: (1) The 
value of the jacket may vary within very wide limits, or even become 
negative. (2) The shorter the cut-off the greater the gain by the use of a 
jacket. (3) The use of higher pressure in the jacket than in the cyhnder 
produces an advantage. The greater this difference the better. (4) The . 
high-pressure cylinder maybe left unjacketed without great loss, but the 
other should always be jacketed. 

The test of the Laketon triple-expansion pumping-engine showed a gain 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 1005 



of 8.3 % by the use of the jackets, but Prof. Denton points out {Trans. 
A. S. M, E., xiv, 1412) that all but 1.9% of the gain was ascribable to the 
greater range of expansion used with the jackets. 

Test of a Compound Condensing Engine with and without Jackets 
at different Loads. (R. C. Carpenter, Trans. A. S. M. E., xiv, 428.) — 
Cvhnders 9 and 16 in. X 14 in. stroke; 112 lbs. boiler- pressure; rated 
capacity 100 H.P.; 265 revs, per min. Vacuum, 23 in. From the results 
of several tests curves are plotted, from which the foUowing principal 
figures are taken. 



Indicated H.P 


30 
22.6 


40 

21.4 


50 

20.3 


60 

19.6 
22 
10 Q 


70 

19 

20.5 
7 3 


80 

18.7 
19.6 
4.6 


90 

18.6 
19.2 
3.1 


100 

18.9 
19.1 
1.0 


110 

19.5 

19.3 

-1.0 


120 

20.4 

20.1 

-1.5 


125 


Steam per I.H.P. per hr. 

With jackets, lbs 

Without jackets, lbs. . . . 


21.0 


Saving by jacket, % 

























This table gives a clue to the great variation in the apparent saving 
due to the steam-jacket as reported by different experimenters. With 
this particular engine it appears that when running at its most econom- 
ical rate of 100 H.P. , without jackets, very little saving is made by use 
of the jackets. When running hght the jacket makes a considerable 
saving, but when overloaded it is a detriment. 

At the load which corresponds to the most economical rate, with no 
steam in jackets, or 100 H.P., the use of the jacket makes a saving of 
only 1%; but at a load of 60 H.P. the saving by use of the jacket is 
about 11%, and the shape of the curve indicates that the relative ad- 
vantage of the jacket would be still greater at lighter loads than 60 H.P. 

The Best Economy of the Piston Steam-Engine at the Advent of 
the Steam Turbine is the subject of a paper by J. E. Denton at the 
International Congress of Arts and Sciences, St. Louis, 1904. {Power 
Oct. 26, 1905.) Prof. Denton says: 

During the last two years the following records have been established: 

(1) With an 850-H.P. Rice & Sargent compound Corhss engine, running 
at 120 r.p.m., having a 4 to 1 cyUnder ratio, clearances of 4% and 7%, 
live jackets on cyhnder heads and hve steam in reheater. Prof. Jacobus 
found for 600 H.P. of load, with 150 lbs. saturated steam, 28.6 ins. vacuum, 
and 33 expansions, 12.1 lbs. of water per I.H.P., with a cyhnder-conden- 
sation loss of 22%, and a jacket consumption of 10.7% of the total steam 
consumption. 

(2) With a 250-H.P. Belgian poppet-valve compound engine, 126 r.p.m.. 
with 2.97 to 1 cyhnder ratio, clearances of 4%, steam-chest jackets on 
barrels and head, and no reheater. Prof. Schroter, of Munich, found with 
117 H.P. of load, 130 lbs. saturated steam, 27.6 ins. of vacuum, and 32 ex- 
pansions, 11.98 lbs. of water per H.P. per hour, with a cyUnder-condensa- 
tionloss oi 23.5%, and a jacket consumption of 7% of the total steam 
consumption in the liigh cyhnder jacket and 7% in the low jacket. 

(3) With the Westinghouse twin compound combined poppet-valve 
and Corhss-valve engine, at the New York Edison plant, running 76 r.p.m. 
with 5.8 to 1 cyhnder ratio, clearances of 10.5% and 4%, without jackets 
or reheater, Messrs. Andrew, Wliitham and Wells found for the full load 
of 5400 H.P., 185 lbs. steam pressure, 27.3 ins. vacuum, and 29 expan- 
sions, 11.93 lbs. of water per I.H.P. per hour, with an initial condensation 
of about 32%. 

These facts show that the minimum water consumption of the compound 
engine of the present date, using saturated steam, is not dependent upon 
any particular cylinder ratio and clearance nor upon any system of jacket- 
ing, but that tne essential condition is the use of a ratio of expansion 
of about 30, above wliich the cyhnder-condensation loss is hable to prevail 
over the influence of the law of expansion. The conclusion appears 
warranted, therefore, that if this ratio of expansion is secured with any 
of the current cyhnder and clearance ratios, and with any existing system 
of jackets and reheaters, or without them, a water consumption of 12 4 lbs 
per horse-power is possible, and that a variation of 0,4 lb. below or above 
this figure may occur by the accidental favorable, or unfavorable jacket 
and cylinder-wall expenses which are beyond the control of the designer. 
Compound Piston Engine Economy vs. that of Steam Turbine. — In order 
to compare the economy of the piston engine with that of the steam tur- 



1006 THE STEAM-ENGINE. 

bine, we must use the water consumption per brake horse-power, since no 
mriicator card is possible from the turbine; and furthermore, we must use 
the average water consumption for the range of loads to which engines are 
subject in practice. 

In all of the public turbine tests to date, with one exception the output 
was measured tlirough the electric power of a dynamo whose efficienc\" is 
not given for the range of loading employed, so that the average brake 
horse-power is not known. This exception is the Dean and Main test of 
a 600-H.P. Westinghouse-Parsons turbine using saturated steam at 1 50 lbs. 
pressure, and a 28-in. vacuum. We may compare the results of this test 
with that of the 850-H.P. Rice & Sargent and of the 250-H.P. Belgian 
engine, by assiuning that the power absorbed by friction in these en- 
gines is 3 % of the indicated load plus the power shown by friction cards 
taken with the engine unloaded. The latter showed 5% of the rated 
power in the R .& S. engine and 8 % in the Belgian engine. The results are : 

Per cent of full load 41 75 100 125 Avg. 85% 

Lbs. Water per Brake H.P. Hour. 

600-H.P. Turbine 13.62 13.91 14.48 16.05 14.51 

800-H.P. Comp. Engine 13.78 13.44 13.66 17.36 14.56 

250 H.P. Belgian Engine 15.10 14.15 13.99 15.31 14.64 

These figures show practical equality in economy of the types of engines. 
The full report of the Van den Kerchove Belgian engine is given in Power ^ 
June, 1903. 

For large-sized units Prof. Denton compares the Elberfeld test of a 
Parsons turbine at the full load of 1500 electric H.P., allowing 5% for 
attached air pump, 95% for generator efficiency, with the 5400-H.P. 
Westinghouse compound engine at the New York Edison station, whose 
friction at full load was found to be 4%. The turbine with 150 lbs. steam 
and 28 ins. vacuum required 13.08 lbs. of saturated steam per B.H.P. 
hour, a gain of 4% over the 600-H.P. turbine. The engine with 18.5 lbs. 
boiler pressure gave 12.5 lbs. per B.H.P. hour. Crediting the turbine 
with the possible influence of the difference in size and steam pressure," 
there is again practical equality, in economy between it and the piston 
engine. 

Triple-expansion Pumping Engines. — The triple-expansion engine has 
failed to supplant the compound tor electric hght and mill service, be- 
cause the gain in fuel economy due to its use was not sufficient to over- 
come its higher first cost, depreciation, etc. It is, however, almost uni- 
versally used in marine practice, and also in large-sized pumping engines. 
Prof. Denton says: Pumping engines in the United States have been de- 
veloped in the triple-expansion fly-wheel type to a degree of economy 
superior to that afforded by any compound mill or electric engine, and, 
for saturated steam, superior to that of the pumping engines of any other 
country. This is because their slow speed permits of greater benefit 
from jackets and reheaters and of less losses from wire-drawing and back 
pressure. These causes, together with the greater subdivision of the range 
of expansion, have resulted in records made between 1894 and 1900 of 
11.22, 11.26 and 11.05 lbs. of saturated steam per I.H.P., with 175 lbs. 
steam pressure and from 25 to 33 expansions, in the cases of the Leavitt, 
Snow and Allis pumping engines, respectively, the corresponding heat 
consumption being by different dispositions of the jacket drainage, 204, 
208 and 212 thermal units per I. H.P. minute; while later the AlHs pump, 
with 185 lbs. steam pressure, has lowered the record to 10.33 lbs. of satu- 
rated steam per I.H.P., with 196 B.T.U. per H.P. minute. 

Gain from Superheating. — In the Belgian compound engine above de- 
scribed, with steam at 130 lbs., vacuum 27.6 ins., the average consumption 
of saturated steam, between 45 and 125% of load, was 12.45 lbs. per 
I.H.P. hour, or 225 B.T.U. per I.H.P. minute. With steam superheated 
224° F. the average consumption for the same loads was 10.09 lbs. per 
I.H.F. hour, computed to be equivalent to 209 B.T.U. per H.P. minute, 
a gain due to superheating of 7%. With steam superheated 307° and 
the load about 80% of rating the water consumption was 8.99 lbs. per 
I.H.P. hour, equivalent to 192 B.T.U. per H.P. minute. The same load 
with saturated steam requires 221 B.T.U., showing a gain due to super- 
heating of 13%. 

The best performance reported for superheated steam used in the tur- 



ECONOMIC PERFORMANCE OF STEAM-ENGINES. 1007 



bine is that of Brown & Boveri Parsons, Frankfort, 4000-H.P. machine, 

which, with 183 lbs. gauge pressure and 190° F. superheat, afforded 10.28 
lbs. per B.H.P. hour, assumins: a generator efficiency of 0.95. Reckoning 
from the feed temperature of its vacuum of 27.5 ins., the heat consumption 
is 214 B.T.U. per H.P. minute. 

The heat consumption of the 250-H.P. Belgian compound engine per 
B.H.P. hour at the highest superheating of 307° F. is 220 B.T.U. The 
turbine, therefore, probably holds the record for brake horse-power econ- 
omy over the piston engine for superheated steam by a margin of about 
3%, although had the compound engine been of the same horse-power as 
the turbine, so that its friction load would be only 8% of its power instead 
of the 13% here allowed, it would have excelled the turbine in brake 
horse-power economy by a margin of about 2.5%. 

The Sulphur-dioxide Addendum. — If the expansion in piston engines 
could continue until the pressure of 1 pound was attained before exhaust 
occurred, considerable more work could be obtained from the steam. 
Tliis cannot be done, for two reasons: first, because the low cylinder would 
have to be about hve times greater in volume, which is commercially 
impracticable; and, second, because the velocity of exit through the 
largest exhaust ports possible is so great that the frictional resistance of 
the steam makes the back pressure from 1 to 3 pounds higher than the 
condenser pressure in the best engines of ordinary piston speed. 

All the work due to tliis extra expansion can be obtained by exhausting 
the steam at 6 lbs. pressure against a nest of tubes containing sulphur 
dioxide wliich is thereby boiled to a vapor at about 170 lbs. pressure. 

Professor Josse, of Berlin, has perfected this sulphur-dioxide system 
of improvement, and reliable tests have shown that if cooling water of 
65° is available, and to the extent of about twice the quantity usuaUy em- 
ployed for condensing steam under 28 ins. of vacuum, a sulphur-dioxide 
cyUnder of about half the size of the high-pressure cylinder of a com- 
pound engine will do sufficient work to improve the best economy of 
such engines at least 15%. The steam turbine expands its steam to the 
pressure of its exhaust chamber, and as unlimited escape ports can be 
provided from tliis chamber to a condenser, it follows that the turbine 
can practically expand its steam to the pressure of the condenser. There- 
fore a steam turbine attached to a piston engine to operate with the latter's 
exhaust should effect the same saving as the sulphur-dioxide cyUnder. 

Standard Dimensions of Direct-connected Generator Sets. From 
a report by a committee of the A. S. M. E., 1901. 

Capacity of unit, K.W 25 35 50 75 100 150 200 

Revolutions per minute 310 300 290 275 260 225 200 

Armature bore, center crank engines. .. 4 4 41/2 51/2 6 7 8 
Armature bore, side-crank engines 41/2 51/2 6I/2 71/2 8I/2 10 11 

The diameter of the engine shaft at the armature fit is 0.001 in. 
greater than the bore, for bores up to and including 6 ins., and 0.002 
In. greater for bores 6 1/2 ins. and larger. 

Dimensions of Some Parts of Large Engines in Electric Plants. — 
The Electrical World, Sept. 27, 1902, gives a table of dimensions of 
the engines in the five large power stations in New York City at that 
date. The following figures are selected from the table. 



Name of station 


Metro- 
politan. 


Manhat- 
tan. 


Kings- 
bridge. 


Rapid 
Transit. 


Edison. 


Type of engine 


Vert. 
Cross- 
Comp. 


Double, 
2hor. 

2 vert. 
Cyls. 


Vert. 
Cross- 
Comp. 


Double 
2hor. 
2 vert. 
Cyls. 


3 Cyl. Vert. 


Rated H.P 

Cylinders, (60" stroke) 
Piston rods, diam., in. 
Crank pins 


4500 

46, 86 in. 

9. 10 

14 X 14 

14 X 14 

27 ft. 4 in. 

37 in. 

34 X60 


8000 
44. 88 in. 

8 

18 X 18 

12 X 12 

25 ft. 3 in. 

37 in. 

34 X60 


4500 
46, 86 in. 

9. 10 
14 X 14 
14 X 14 

27 ft. 

39 in. 
34 X60 


8900 
42, 86 in. 

8. 10 

20 X 18 

12 X 12 

25 ft. 3 in. 

37 in. 
34 X60 


5200 

43i/2,2-751/2in. 

9 
22 & 16 X 14 


Wrist pins 

Shaft length 


14 X 14 
35 ft 


max. diam 

bearings 


293/8 in. 
26 X60 



1008 



THE STEAM-ENGINE. 



The shafts are hollow, with a 16-in. hole, except the Edison which has 
10 in. The speed of all the engines is 75 r.p.m., or 750 ft. per min. The 
crank-pins of the Manhattan and Rapid Transit engines each are at- 
tached to two connecting-rods, side by side, hor. and vert., each rod hav- 
ing a bearing 9 in. long on the pin. The crank-pins of the Edison en- 
gine are 16 in. diam. for the side-cranks, and 22 in. for the center-crank. 

The four 8000- horse-power engines in the Manhattan station, new in 
1902, were replaced in 1914-15, although still as good as new, by four 
30,000 K.W. steam turbines occupying the same space. The turbines 
will have a water rate 30 per cent lower than the engines. (Power, 
April 27, 1915.) 

Some Large BoUing-Mill Engines. 



Cylinders. 






P^ 


44 & 82 X60 


65 


46 & 80 X60 


80 


52 <& 90X60. 




2 each 




42 & 70X54 




2 each 

44 & 70X60 


60 



Type. 



Cross-C . 
Tandem. 
Tandem. 



Double. 
Tandem. 



Double. 
Tandem. 



Fly-wheel. 



o-^ Diam. Wt. 
£^ Ft. Lbs. 



140 
150 



150 



150 



24 
24 
25 



150,000 
110,000 
250.000 



Location. 



Republic I. & S. 
Co., Youngs- 

town, Ohio. 

Carnegie S. Co., 
Donora, Pa. 

Carnegie S. Co., 
Youngstown, 
Ohio. 

Carnegie S. Co., 
S. Sharon, Pa. 

' Carnegie S. 
Co., Du- 
quesne. Pa. 
Jones & 
Laughlin 
Steel Co., 
Aliquippa,Pa. 



Builders. 



Filer & 
Stowell. 

Wiscon- 
sin Eng. 

Co. 
Wm. Tod 
Co. 

AUis 
Chal- 
mers Co. 

Mackin- 
tosh, 
Hemp- 
hill & 
Co. 



Some details: Main bearings, No. 1, 25 X 431/2 in.; No. 2, 30 X 52 in.; 
No. 3, 30 X 60 in. Shaft diam. at wheel pit, No. 1, 26 in.; No. 3, 36 in. 
Crank pins, No. 1, h.p. 14 X 14; l.p., 14 X 23 in.; No. 2, 18 X 18 in. 
Crosshead pins, No. 1, 12 X 14; No. 2, 16 X 20 in. No. 4 is a reversing 
engine, with the Marshall gear. No. 5 is a reversing engine with piston 
valves -below the cylinders. 

Counterbalancing En«:ines. — Prof. Unwin gives the formula for 

counterbahmcin^' vertical eh.^lnes: Wi = W-irlv, (1) 

in which U'l denotes the wdglit of the balance weight and p the radius to 
its center of gravity, TF2 the weight of the crank-pin and half the weight of 
the connecting-rod, and r the length of the crank. For horizontal engines: 



Wi = 2/3 (TF2 + TF3) rip to 3/4 (TFo + Wz) rlp, . . 



C2) 



in which TF3 denotes the weight of the piston, piston-rod, cross-head, and 
the other half of the weight of the connecting-rod. 

The American Machinist, commenting on these formulae, says: For 
horizontal engines formula (2) is often used; formula (1) will give a coun- 
terbalance too light for vertical engines. We should use formula (2) for 
computing the counterbalance for both horizontal and vertical engines, 
excepting locomotives, in which the counterbalance should be heavier. 

For an account of experiments on counterbalancing large engines, with 
a method of recording vibrations, see paper by D. S. Jacobus, Trans, 
A. S. M. E., 1905. 

Preventing Vibrations of Enejines. — Many suggestions have been 
made for remedying the vibration and noise attendant on the working 
of the big engines which are employed to run dynamos. A plan which has 
given great satisfaction is to build hair-felt into the foundations of the 
engine. An electric company has had a 9()-horse-power engine removed 
from its foundations, which were then taken up to the depth of 4 feet. A 



COMMERCIAL ECONOMY — COSTS OF POWER. 1009 

layer of felt 5 inches thick was then placed on the foundations and run 

up 2 feet on all sides, and on the top of this the brickwork was built up. — 
Safety Valve. 

Steam-engjine Foundations Embedded in Air. — In the sugar- 
refinery of Claus Spreckels, at Philadelphia, Pa., the engines are distrib- 
uted practically all over the buildings, a large proportion of them beinff 
on upper floors. Some are bolted to iron beams or girders, and are con- 
sequently Innocent of all foundation. Some of these engines ran noise- 
lessly and satisfactorily, while others produced more or less vibration and 
rattle. To correct the latter the engineers suspended foundations from 
the bottoms of the engines, so that, in looking at them from the lower 
floors, they were literally hanging in the air. — Iron Age, Mar. 13, 1890. 

COMMERCIAL. ECONOMY. —COSTS OF POWER. 

The Cost of Steam Power is an exceedingly variable quantity. The 
principal items to be considered in estimating total annual cost are: load 
factor ; hours run per year ; percentage of full load at different hours of 
the day ; cost and quaUty of fuel ; boiler efficiency and steam consumption 
of engines at different loads ; cost of water and other supphes ; cost of 
labor, first cost of plant, depreciation, repairs, interest, insurance and taxes. 

In figuring depreciation not only should the probable life of the several 
parts of the plant, such as buildings, boilers, engines, condensers, etc., be 
considered, but also the possibility of part of the plant, or the whole of it, 
depreciating rapidly in value on account of obsolescence of the machinery 
or of changes in the conditions of the business. 

When all of the heat in the exhaust steam from engines and pumps, in- 
cluding water of condensation, is used for heating purposes the fuel cost of 
steam-engine power may be practically nothing, since the exhaust contains 
all of the heat in the steam delivered to the engine except from 5 to 10 
per cent which is converted into work, and a trifling amount lost by 
radiation. 

Most Economical Point of Cut-off in Steam-engines. (See paper 
by Wolff and Denton, Trans. A. S. M. E., vol. ii, p. 147-281; also. Ratio 
of Expansion at Maximum Efficiency, R. H. Thurston, vol. ii, p. 128.) 
— The problem of the best ratio of expansion is not one of economy of con- 
sumption of fuel and economy of cost of boiler alone. The question of in- 
terest on cost of engine, depreciation of value of engine, repairs of engine, 
etc., enters as well; for as we increase the rate of expansion, and thus, 
within certain limits fixed by the back-pressure and condensation of 
steam, decrease the amount of fuel required and cost of boiler per unit of 
work, we have to increase the dimensions of the cylinder and the size 
of the engine, to attain the required power. 

Type of Engine to be used where Exhaust-steam is needed for 
Heating. — In many factories more or less of the steam exhausted from 
the engines is utilized for boiling, drying, heating, etc. Where all the 
exhaust-steam is so used the question of economical use of steam in the 
engine itself is eUminated, and the high-pressure simple engine is entirely 
suitable. Where only part of the exhaust-steam is used, and the quantity 
so used varies at different times, the question of adopting a simple, a 
condensing, or a compound engine becomes more complex. Tliis problem 
is treated by C. T. Main in Trans. A. S. M. E., vol. x, p. 48. He shows 
that the ratios of the volumes of the cylinders in compound engines should 
vary according to the amount of exhaust-steam that can be used for 
heating. A case is given in which three different pressures of steam are 
required or could be used, as in a worsted dye-house: the high or boiler 
pressure for the engine, an intermediate pressure for crabbing, and low- 
pressure for boiling, drying, etc. If it did not make too much compli- 
cation of parts in the engine, the boiler-pressure might be used in the high- 
pressure cylinder, exhausting into a receiver from which steam could be 
taken for running small engines and crabbing, the steam remaining in the 
receiver passing into the intermediate cylinder and expanded there to 
from 5 to 10 lbs. above the atmosphere and exhausted into a second 
receiver. From this receiver is drawn the low-pressure steam needed for 
drying, boiling, warming mills, etc., the steam remaining in the receiver 
passing into the condensing cylinder. 

Cost of Steam-power. (Chas. T. Main, Trans. A. S. M. E., x, 48.) — 
Estimated costs in New England in 1888, per horse-power, using com- 



1010 



THE STEAM-ENGINE. 



pound condensing, and non-condensing engines, and based on engines 
of 1000 H.P. are as follows: 

Compound Condens- Non-con- 

Engine. ing Engine, densing 

Engine. 

1. Cost engine and piping, complete $25.00 $20.00 $17.50 

2. Engine-house 8.00 7.50 7.50 

3. Engine foundations 7.00 5.50 4.50 

4. Total engine plant 40.00 33.00 29.50 

5. Depreciation, 4% on total cost i 60 1.32 ~Tl8 

6. Repairs, 2% on total cost 0.80 0.66 0.59 

7. Interest, 5% on total cost 2 00 1.65 1 475 

8. Taxation, 1.5% on 3/4 cost o]45 0.371 o!332 

9. Insurance on engine and house. ..... 0.165 0.138 0.125 

10. Total of lines 5, 6, 7, 8, 9 5.015 4.139 3.702 

11. Cost boilers, feed-pumps, etc 9.33 13.33 leToo" 

12. Boiler-house 2.92 4.17 5.00 

13. Chimney and flues 6.11 7.30 8.00 

14. Total boiler-plant 18.36 24.80 29.00 

15. Depreciation, 5% on total cost 0.918 1.240 1.450 

16. Repairs, 2% on total cost 0.367 0.496 0.580 

17. Interest, 5% on total cost 918 1 240 1 450 

18. Taxation, 1.5% on 3/4 cost 0.207 0.279 0.326 

19. Insurance, 0.5% on total cost 0.092 0.124 0.145 

20. Total of lines 15 to 19 ..... .. 2.502 3.379 3.951 

21. Coal used per I.H.P. per hour, lbs. . . 1.75 2.50 3.00 

22. Cost of coal per I.H.P. per day of 101/4 cts. cts. cts. 

hours at $5.00 per ton of 2240 lbs. . . . 4.00 5.72 6.86 

23. Attendance of engine per day 0.60 0.40 0.35 

24. Attendance of boilers per day 0.53 0.75 0.90 

25. Oil, waste, and supplies, per day. . » o 0.25 0.22 0.20 

26. Total daily expense 5.38 7.09 8.31 

27. Yearly running expense, 308 days, per 

_I.H.P.. $16,570 $21,837 $25,595 

28. Total yearly expense, lines 10, 20, 

and 27 24.087 29.355 33.248 

29. Total yearly expense per I.H.P. for 

power if 50% of exhaust-steam is 

used for heating 12.597 14.907 16.663 

30. Total if all exhaust-steam is used for 

heating 8.624 7.916 7.700 

When exhaust-steam or a part of the receiver-steam is used for heating, 
or if part of the steam in a condensing engine is diverted from the con- 
denser, and used for other purposes than power, the value of such steam 
should be deducted from the cost of the total amount of steam generated 
in order to arrive at the cost properly chargeable to power. The figures 
in lines 29 and 30 are based on an assumption made by Mr. Main of losses 
of heat amounting to 25% between the boiler and the exhaust-pipe, an 
allowance which is probably too large. 

See also two papers by Chas. E. Emery on "Cost of Steam Power," 
Trans. A. S, M. E., vol. xii, Nov., 1883, and Trans. A. I. E. E., vol. x. 
Mar., 1893. 

Cost of Coal for Steam-power. — The following table shows the 
amount and the cost of coal per day and per year for various horse-powers 
from 1 to 1000, based on the assumption of 4 lbs. of coal being used per 



COMMERCIAL ECONOMY — COSTS OF POWER. 1011 

hour per horse-power. It is useful, among other things, in estimating the 

saving that may oe made in fuel by substituting more economical boilers 
and engines for those already in use. Thus with coal at $3.00 per ton of 
2000 ibs., a saving of $9000 per year in fuel may be made by replacing a 
steam plant of 1000 H.P., requiring 4 lbs. of coal per hour per horse-power, 
with one requiring only 2 lbs. 





Coal Consumption, at 4 lbs. 
















per H.P hour; 10 hours a 














. 


day; 300 days per Year. 


$2 per 
Short 
Ton. 


$3 per 
Short 
Ton. 


s 

s 


4 per 
hort 


1 


Lbs. 


Long Tons. 


Short 
Tons. 


ron. 


& 












Cost in 


Cost in 


Cost in 


o 


Per 


Per 
Day. 


Per 

Year. 


Per 
Day. 


Per 
Yr. 


Dollars. 


Dollars. 


Dollars. 


Day. 


























Day. 


Yr. 


Day. 


Yr. 


Day. 


Yr. 


1 


40 


0.0179 


53.57 


0.02 


6 


0.04 


12 


0.06 


18 


0.08 


24 


10 


400 


0.1786 


53.57 


0.20 


60 


0.40 


120 


0.60 


180 


0.80 


240 


25 


1,000 


0.4464 


133.92 


0.50 


150 


1.00 


300 


1.50 


450 


2.00 


600 


50 


2,000 


0.8928 


267.85 


1. 00 


300 


2.00 


600 


3.00 


900 


4.00 


1,200 


75 


3,000 


1.3393 


401.78 


1.50 


450 


3.00 


900 


4.50 


1,350 


6.00 


1,800 


100 


4,000 


1.7857 


535.71 


2.00 


600 


4.00 


1,200 


6.00 


1.800 


8.00 


2,400 


150 


6,000 


2.6785 


803.56 


3.00 


900 


6.00 


1,800 


9.00 


2,700 


12.00 


3,600 


200 


8,000 


3.5714 


1,071.42 


4.00 


1,200 


8.00 


2,400 


12.00 


3,600 


16.00 


4,800 


250 


10,000 


4.4642 


1,339.27 


5.00 


1,500 


10.00 


3,000 


15.00 


4.500 


20.00 


6,000 


300 


12,000 


5.3571 


1,607.13 


6.00 


1,800 


12.00 


3,600 


18.00 


5,400 


24.00 


7,200 


350 


14,000 


6.2500 


1,874.98 


7.00 


2,100 


14.00 


4,200 


21.00 


6,200 


28.00 


8,400 


400 


16,000 


7.1428 


2,142.84 


8.00 


2,400 


16.00 


4,800 


24.00 


7,200 


32.00 


9.600 


450 


18,000 


8.0356 


2,410.69 


9.00 


2,700 


18.00 


5,400 


27.00 


8,100 


36.00 


10,800 


bOO 


20.000 


8.9285 


2,678.55 


10.00 


3,000 


20.00 


6,000 


30.00 


9,000 


40.00 


12,000 


600 


24,000 


10.7142 


3,214.26 


12.00 


3,600 


24.00 


7,200 


36.00 


10,800 


48.00 


14,400 


700 


28,000 


12.4999 


3,749.97 


14.00 


4,200 


28.00 


8,400 


42.00 


11,600 


56.00 


16,800 


«00 


32,000 


14.2856 


4,285.68 


16.00 


4,800 


32.00 


9,600 


48.00 


12,400 


64.00 


19,200 


900 


36,000 


16.0713 


4,821.39 


18.00 


5,400 


36.00 


10,800 


54.00 


14,200 


72.00 


21,600 


1000 


40,000 


17.8570 


5.357. 10 


20.00 


6,000 


40.00 


12,000 


60.00 


18,000 


80.00 


24,000 



It is usual to consider that a factory working 10 hours a day requires 
10 1/2 hours coal consumption on account of the coal used in banking or 
in starting the fires, and that there are 306 working days in the year. For 
these conditions multiply the costs given in the table by 1.071. For 
24 hours a day 365 days in the year, multiply them by 2.68. For other 
rates of coal consumption than 4 lbs. per H.P. hour, the figures are to be 
modified proportionately. 



Belative Cost of Different Sizes of Steam-engines. 

(From catalogue of the Buckeye Engine Co., Part III.) 



Horse-power.. . . 
CostperH.P.. $ 



75 

171/2 



150 

141/r 



200 
131/2 



300 
123/4 



350 
12.5 



400 500 
12.6 12.8 



600 
131/4 



800 
15 



Power Plant Economics. (H. G. Stott, Trans. A. I. E. E., 1906.) — 
The table on the following page gives an analysis of the heat losses found 
in a year's operation of one of the most efficient plants in existence. 

The following notes concerning power-plant economy are condensed 
from Mr. Stott's paper. 

Item 1. B.T.U. per lb. of coal. The coal is bought and paid for on 
the basis of the B.T.U. found by a bomb calorimeter. 



1012 THE STEAM-ENGINE. 

AVERAGE LOSSES IN THE CONVERSION OF 1 LB. OF COAL INTO ELECTRICITY. 

B.T.U. % B.T.U. % 

1. B.T.U. per lb. of coal supplied 14,160 100.0 

2. Loss in ashes 340 2.4 

3. Loss to stack , 3,212 22.7 

4. Loss in boiler radiation and air leakage 1,131 8.0 

5. Returned by feed-water heater 441 3.1 

6. Returned by economizer 960 6.8 

7. Loss in pipe radiation 28 0.2 

8. Delivered to circulator 223 1.6 

9. Delivered to feed pump 203 1.4 

10. Loss in leakage and high-pressure drips 152 1.1 

11. Delivered to small auxiliaries 51 0.4 

12. Heating 31 0.2 

13. Loss in engine friction Ill 0.8 

14. Electrical losses 36 0.3 

15. Engine radiation losses 28 0.2 

16. Rejected to condenser 8,524 60.1 

17. To house auxiliaries 29 0.2 



15,551 109.9 14,099 99.6 
14,099 99.6 



Delivered to bus bar 1.452 10.3 

Item 3. The chimney loss is very large, due to admitting too much air 
to the combustion chamber. This loss can be reduced about half by the 
use of a CO2 recorder and proper management of the fire. 

Item 4. This loss is largely due to infiltration of air into the brick 
setting. It can be saved by having an air-tight sheet-iron casing enclosing 
a magnesia lining outside of the brickwork. 

Item 5. All auxiUaries should be driven by steam, so that their exhaust 
may be utilized in the feed-water heater. 

Item 6. In all cases where the load factor exceeds 25% the investment 
in economizers will be justified* 

Item 7. The pipes are covered with two layers of covering, each about 
1.5 in. thick. 

Item 10. The high-pressure drips can be returned to the boiler, so 
practically all the loss under this heading is recoverable. 

Item 13. Recent tests of a 7500-H.P. reciprocating engine show a 
mechanical efficiency of 93.65%, or an engine friction of 6.35%. The 
engine is lubricated by the flushing system. 

Item 16. The maximum theoretical efficiency of an engine working 
between 175 lbs. gauge and 28 ins. vacuum is 

(Ti - T2) -^ Ti = (837 - 560) ^ 837 = 33%. 
The actual best efficiency of this engine is 17 lbs. per K.W.-hour — 16.7% 
thermal efficiency: dividing by 0.98, the generator efficiency, gives the net 
thermodynamic efficiency of the engine, = 17%. The difference between 
the theoretical and the actual efficiency is 33 — 17 = 16%, of which 6.35% 
is due to engine friction, and the balance, 9.65%, is due to cylinder con- 
densation, incomplete expansion, and radiation. [Some of this difference 
is due to the fact that the engine does not work on the Carnot cycle, in 
which the heat is all received at the liighest temperature, and part of this 
loss might be saved by the Nordberg feed-water heating system. There 
may also be a slight loss from leakage. W.KJ Superheated steam, to 
such an extent as to insure dry steam at the point of cut-off in the low- 
pressure cylinder, might save 5 or 6%. 

The present type of power plant using reciprocating engines can be im- 
proved in efficiency as follows: Reduction of stack losses, 12%; boiler 
radiation and leakage^ 5%; by superheating, 6%; resulting in a net in- 
crease of thermal efficiency of the entire plant of 4.14% and bringing the 
total from 10.3 to 14.44%. 

The Steam Turbine. — The best results from the steam turbine up to 
date show that its economy on dry saturated steam is practically equal 
to that of the reciprocating engine, and that 200° superheat reduces its 
steam consumption 13.5%. The shape of the economy curve is much 



COMMERCIAL ECONOMY — COSTS OF POWER. 1013 
Maintenance and Operation Costs of Different Types of Plant. 





Recip- 
rocating 
Engines. 


Steam 
Turbines 


Recip- 
rocating 
Engines 

and 

Steam 

Turbines. 


Gas- 
Engine 
Plant. 


Gas 

Engines 

and 

Steam 

Turbines. 


Maintenance. 
1. Engine room mechan- 
ical 


2.57 

4.61 

0.58 
1.12 

2.26 
1.06 
0.74 
7.15 

0.17 

61.30 

7.14 

6.71 
1.77 
0.30 
2.52 


0.51 

4.30 

0.54 
1.12 

2.11 
0.94 
0.74 
6.68 

0.17 
57.30 
0.71 

1.35 
0.35 
0.30 

2.52 


1.54 

3.52 

0.44 
1.12 

1.74 
0.80 
0.74 
5.46 

0.17 

46.87 

5.46 

4.03 
1.01 
0.30 
2.52 


2.57 

1.15 

0.29 
1.12 

1.13 
0.53 
0.74 
1.79 

0.17 

26.31 

3.57 

6.71 
1.77 
0.30 
2.52 


1.54 


2. Boiler room or pro- 

ducer room 

3. Coal- and ash-han- 

dling apparatus.. . 

4. Electrical apparatus 

Operation. 

5. Coal- and ash-han- 

dling labor 


1.95 

0.29 
1.12 

1.13 


6. Removal of ashes .... 

7. Dock rental 


0.53 
0.74 


8. Boiler-room labor 

9. Boiler-room oil,waste, 

etc 


3.03 
0.17 


10. Coal 


25.77 


1 1 . Water 


2.14 


32. Engine-room me- 
chanical labor 

13. Lubrication 


4.03 
1.06 


14. Waste, etc 


0.30 


15. Electrical labor 


2.52 


Relative cost of mainte- 
nance and operation . . 


100.00 


79.64 


75.72 


50.67 


46.32 


Relative investment in 
per cent 


100.00 


82.50 


77.00 


100.00 


91.20 







flatter [from 3300 to 8000 K. W. the range of steam consumption is between 
14.6 and 15.0 lbs. per K.W.-hour], so that the all-day efficiency would be 
considerably better than that of the reciprocating engine, and the cost 
would be about 33% less for the combined steam motor and electric 
generator. 

High-pressure Reciprocating Engine with Low-pressure Turbine. — The 
reciprocating engine is more efficient than the turbine in the higher pres- 
sures, while the turbine can expand to lower pressures and utilize the gain 
of full expansion. The combination of the two would therefore be more 
efficient than a turbine alone. 

The Gas Engine. — The best result up to date obtained from gas pro- 
ducers and gas engines is about as follows: Loss in producer and auxiliaries, 
20%; in jacket water, 19%; in exhaust gases, 30%: in engine friction, 
6.5%; in electric generator, 0.5%. Total losses, 76%. Converted into 
electric energy, 24%. Only one important objection can be raised to this 
motor, that its range of economical load is practically limited to between 
50% and full load. This lack of overload capacity is probably a fatal 
defect for the ordinary railway power plant acting under a violently 
fluctuating load, unless protected by a large storage-battery. 

At light loads the economy of gas and liquid fuel engines fell off even 
more rapidly than in steam-engines. The engine friction was large and 
nearly constant, and in some cases the combustion was also less perfect 
at hght loads. At the Dresden Central Station the gas-engines were kept 
working at nearly their full power by the use of storage-batteries. The 
results of some experiments are given below: 



1014 THE STEAM-ENGINE. 

Brake-load, per Gas-engine, cu. ft. Petroleum Eng., Petroleum Eng., , 
cent of full of Gas per Brake Lbs. of Oil per Lbs. of Oil per 

Power. H.P. per hour. B.H.P. per hr. B.H.P. per hr. 

100 22.2 0.96 0.88 

75 23.8 1.11 0.99 

59 28.0 1.44 1.20 

20 40.8 2.38 1.82 

121/2 66.3 4.25 3.07 

Comhination of Gas Engines and Turbines. — A steam turbine unit can i 
be designed to take care of 100% overload for a few seconds. If a plant 
were designed with 50% of its normal capacity in gas engines and 50% 
in steam turbines, any fluctuations in load likely to arise in practice could 
be taken care of. By utiUzing the waste heat of the gas engine in econ- 
omizers and superheaters there can be saved approximately 37% of this ' 
waste heat, to make steam for the turbines. The average total thermal 
efficiency of such a combination plant would be 24.5%. This combina- 
tion offers the possibility of producing the kilowatt-hour for less than one- 
half its present cost. 

The table on p. 1013 shows the distribution of estimated relative main- 
tenance and operation costs of five different types of plant, the total costt 
Of current with the reciprocating engine plant being taken at 100. 

Storing Heat in Hot Water. — (See also p. 927.) There is no satisfac- 
tory method for equahzing the load on the engines and boilers in electric- 
light stations. Storage-batteries have been used, but they are expensive 
in first cost, repairs, and attention. Mr. Halpin, of London, proposes to 
store heat during the day in specially constructed reservoirs. As the 
water in the boilers is raised to 250 lbs. pressure, it is conducted to cylin- 
drical reservoirs resembling English horizontal boilers, and stored there 
for use when wanted. In this way a comparatively small boiler-plant 
can be used for heating the water to 250 lbs. pressure all through the 
twenty-four hours of the day, and the stored water may be drawn on at 
any time, according to the magnitude of the demand. The steam-engines 
are to be worked by the steam generated by the release of pressure from 
this water, and the valves are to be arranged in such a way that the steam 
shall work at 130 lbs. pressure. A reservoir 8 ft. in diameter and 30 ft. 
long, containing 84,000 lbs. of heated water at 250 lbs. pressure, would 
supply 5250 lbs. of steam at 130 lbs. pressure. As the steam consump- 
tion of a condensing electric-light engine is about 18 lbs. per horse-power 
hour, such a reservoir would supply 286 effective horse-power hours. In 
1878, in France, this method of storing steam was used on a tramway. 
M. Francq, the engineer, designed a smokeless locomotive to work by 
steam-power supplied by a reservoir containing 400 gallons of water at 
220 lbs. pressure. The reservoir was charged with steam from a stationary 
boiler at one end of the tramway. 

An installation of the Rateau low-pressure turbine and regenerator 
system at the rolling mill of the International Harvester Co., in Chicago, 
is described in Power, June, 1907. The regenerator is a cylindrical shell 
11 1/2 ft. diam., 30 ft. long, containing six large elliptical tubes perforated 
with many 3/4-in. holes through which exhaust steam from a reversing 
blooming-mill engine enters the water contained in the shell. A large 
steam pipe leads from the shell to the turbine. A series of tests of the 
combination was made, giving results as follows: The 42 X 60 in. blooming 
mill engine developed 820 I. H.P. on the average, with a water rate of 64 
lbs. per I. H.P. hour. It delivered its exhaust, averaging a Uttle above at- 
mospheric pressure, to the regenerator, at an irregular rate corresponding 
to the varying work of the rolling-mill engine. The regenerator furnished 
steam to the turbine, which in four different tests developed 444, 544, 
727 and 869 brake H.P. at the turbine shaft, with a steam consumption 
of 47.7, 37.1, 30.7 and 33.7 lbs. of steam per B.H.P. hour at the turbine. 
Had the turbine been of sufficient capacity to use all the exhaust of the 
mill engine, 1510 H.P. might have been deUvered at the switchboard, 
which added to the 820 of the mill engine would make 2330 H.P. for 
62,400 lbs. of steam, or a steam rate of 22.5 lbs. per H.P. hour tor the 
combination. 



RULES FOR CONDUCTING ENGINE TESTS. 1015 

tJTILIZING THE SUN'S HEAT AS A SOURCE OF POWER. 

John Ericsson, 1868-1875, experimented on "solar engrines," in which 
reflecting surfaces concentrated the sun's rays at a central point causing 
them to boil water. A large motor of this type was built at Pasadena, 
Cal,, in 1898. The rays were concentrated upon a water heater through 
which ether or sulphur dioxide was pumped in pipes, and utiUzed in a 
vapor engine. The appara.tus was commercially unsuccessful on account 
of variable weather conditions. Eng. Neics, May 13, 1909, describes the 
solar heat systems of F. Shuman and of H. E. Willsie and John Boyle, Jr. 

In the Shuman invention a tract of land is rolled level, forming a shallow 
trough. This is lined -^ath asphaltum pitch and covered with about 
3 ins. of water. Over the water about i/ie in. of parafRne is flowed, leaving 
between this and a glass cover about 6 ins. of dead air space. It is esti- 
mated that a power plant of this type to cover a heat-absorption area of 
160,000 sq. ft., or nearly four acres, would develop about 1000 H.P. 
Provision is made for storing hot water in excess of the requirements of 
a low-pressure turbine during the day, to be utilized for running the 
turbine during the period when there is no absorption of heat. The 
heated water is run from the heat absorber to the storage tank, thence 
to the turbine, through a condenser and back to the heat absorber. The 
water enters the thermally insulated storage tank, or the turbine, at about 
202° F. With a vacuum of 28 ins. in the condenser, the boiling-point of 
the water is reduced to 102°, and as it enters the turbine nearly 10% 
explodes into steam. Mr. Shuman estimates that a 1000-H.P. plant built 
upon his plan would cost about $40,000. 

The Willsie and Boyle plant also utilizes the indirect system of absorb- 
ing solar heat and storing the hot water in tanks. This hot water cir- 
culates in a boiler containing some volatile liquid, and the vapor generated 
is used to operate the engine, is condensed, and returned to the boiler 
to be used again. Mr. Willsie compares the cost per H.P.-hour in a 
400-H.P. steam-electric and solar-electric power plant, and finds that the 
steam plant would have to obtain its coal for $0.66 a ton to compete with 
the sun power plant in districts favorable to the latter. 

RULES FOR CONDUCTING TESTS FOR RECffROCATING 
STEAM-ENGINES. 

(Abstract of the 1915 Code of the Power Test Committee of the 
Am. Soc. M. E.) 

The code for steam engine tests applies to tests for determining 
the performance of the engine alone (including reheaters and jackets, 
if any) apart from that of steam-driven auxiliaries which are neces- 
sary to its operation. For tests of engine and auxiliaries combined, 
and tests of multiple expansion engines from which steam is with- 
drawnjfor heating feed water or otherwise, refer to the Code for Com- 
plete Steam Power Plants. 

OBJECT AND PREPARATIONS. 

Determine the object of the test, take the dimensions, and note 
the physical conditions, not only of the engine, but of all parts of 
the plant that are concerned in the determinations, examine for 
leakages, install the testing appliances, etc., and prepare for the 
test accordingly . 

The determination of the heat and steam consumption of an engine 
by feed-water test requires the measurement of the various supplies 
of water fed to the boiler; that of the water w^asted by separators 
and drips on the main steam line, that of steam used for other purposes 
than the main engine cylinders, and that of water and steam which 
escape by leakage of the boiler and piping; all of these last being de- 
ducted from the total feed water measured. 

Where a surface condenser is provided and the steam consumption 
is determined from the water discharged by the air pump, no such 
measurement of drips and leakage is required, out assurance must 
be had that all the steam passing into the cy_mders finds its way 



1016 THE STEAM-ENGINE. 

into the condenser. If the condenser leaks, the defects causing i 
such leakage should be remedied, or suitable correction should be 'i 
made. 

When no other method is available the steam consumption may 
be determined by the use of a steam meter, bearing in mind the caution 
that it should be calibrated under the exact conditions of use. 

The " steam consumed by steam-driven auxiharies which are vo- 
quired for the operation of the engine should be included in the total I 
steam from which the heat consumption is calculated and the quan-. 
tity of steam thus used should be determined and reported. 

OPERATING CONDITIONS. 

Determine what the operating conditions should be to conform 
to the object in view, and see that they prevail throughout the trial, 

DURATION, 

A test for steam or heat consumption, with substantially constant 
load, should be continued for such time as may be necessary to obtain 
a number of successive hourly records, during which the results are 
reasonably uniform. For a test involving the measurement of feed- 
water for tills purpose, five hoiu^s' duration is suflQcient. Where a 
surface condenser is used, and the measurement is that of the water 
discharged by the air pump, the duration may be somewhat shorter. 
In this case, successive half-hoiu*ly records may be compared and the 
time correspondingly reduced. 

When the load varies widely at different times of the day, the 
duration should be such as to cover the entire period of variation. 

STARTING AND STOPPING. 

The engine and appurtenances having been set to work and thor'* 
oughly heated under the prescribed conditions of test (except in cases 
where the object is to obtain the performance under working condl' 
tions) note the water levels in the boilers and feed reservoir, take the 
tinje and consider this the starting time. Then begin the measure- 
ments and observations and carry them forward until the end of the 
period determined on. When this time arrives, the water levels and 
steam pressure should be brought as near as practicable to the same 
points as at the start. This being done, again note the time and 
consider it the stopping time of the test. If there are differences in 
the water levels, proper corrections are to be applied. 

Where a surface condenser is used, the collection of water dis- 
charged by the air pump begins at the starting time, and the water 
is thereafter^measured or weighed until the end of the test. 

EECORDJS. 

Half-hoiu*ly readings of the instruments are sufficient, excepting 
where there are wide fluctuations. A set of indicator diagrams should 
be obtained at intervals of 15 or 20 minutes, and oftener if the nature 
of the test makes it necessary. Mark on each card the cylinder and 
the end on which it was taken, also the time of day. Record on one 
card of each set the readings of the steam pressure and vacuum gages. 
These records should be subsequently entered on the general log. 
together with the areas, pressures, lengths, etc., measured from the 
diagrams, when these are worked up. 

CALCULATION OF RESULTS. 

Dry Steam. — The quantity of dry steam consumed is determined 
by deducting the moisture, if any, found by the calorimeter test 
from the total amount of feed-water (the latter being corrected 
for leakages and other losses) or from the amount of air-pump dis- 
charge, as the case may be. If the steam is superheated, no cor- 
rection is to be made for the superheat. 

Heat Consumption. — The number of heat-units consumed by the 
engine is found by multiplying the weight of feed-water consumed, 



RULES FOR CONDUCTING STEAM-ENGINE TESTS. 1017 

corrected for moisture in the steam, if any, and for plant leakages 
and other exterior losses, by the total heat of 1 lb. of steam (sat- 
urated or superheated) less the heat in 1 lb. of water at the tem- 
perature corresponding to the pressure in the exhaust pipe near 
the engine. 
Indicated Horse-power. — In a single double-acting cylinder the indi- 
cated horse-power is found by using the formula 

PLAN 
33,000' 

in which P represents the average mean effective pressure in pounds 
per square inch measured from the indicator diagrams, L the length 
of stroke in feet, A the area of the piston less one-half the area 
of the piston rod, or the mean area of the rod if it passes through 
both cylinder heads, in square inches, and N the number of single 
strokes"^ per minute. 

Brake Horse-power. — The brake horse-power is found by multiplying 
the net pressure or weight in poimds on the brake arm (the gross 
weight minus the weight when the brake is entirely free from the 
pulley) in pomids. the circiunference of the circle whose radius 
is the horizontal distance between the center of the shaft and the 
bearing point at the end of the brake arm in feet, and the number 
of revolutions of the brake shaft per minute; and dividing the 
product by 33,000. 

Electrical Horse-power. — The electrical horse-power of a direct-con- 
nected generator is foimd by dividing the output at the terminals 
expressed in kilowatts, by the decimal 0.7457. With alternating 
current generators the net output is to be used, this being the total 
output less that consimied for excitation and for separately-driven 
ventilating fans. 

Efficiency. — The thermal efficiency, that is, the percentage of the 
total heat consumption which is converted into work, is found 
by dividing the quantity 2546.5, which is the B.T.U. equivalent 
of one H. P. -hour, by the number of heat-units actually consumed 
per H.P.-hoiu*. 

The Rankine cycle efficiency is found by dividing the heat con- 
sumption of an ideal engine conforming to the Rankine cycle by 
the actual heat consumption. 

Steam Accounted for by Indicator Diagrams at Points Near Cut-off 
and Release. — The steam accounted for, expressed in pounds per 
I.H.P. per hour, may be found by using the formula 

~^[iC + E) Wc -iH + E) W^], 

in which 

M.E.P. = mean effective pressure; 

C = proportion of direct stroke completed at points on ex- 
pansion line near cut-off or release; 
E = proportion of clearance; 
H = proportion of return stroke uncompleted at point on 

compression line just after exhaust closure; 
Wq = weight of 1 cu. ft. steam at pressure shown at cut-off or 
. release point; 

I Wfi = weight of 1 cu. ft. steam at pressure shown at compres- 

sion point. 
In multiple expansion engines the mean effective pressure to be 
used in the above formula is the aggregate INI.E.P. referred to the 
cylinder under consideration. In a compound engine the aggregate 
M.E.P. for the h.p. cylinder is the sum of the actual M.E.P. of 
the h.p. cylinder and that of l.p. cylinder multiplied by the cyl- 
inder ratio. Likewise the aggregate M.E.P. for the l.p. cylinder 
is the sum of the actual M.E.P. of the l.p. cylinder and the M.E.P. 
of the h.p. cylinder divided by the cylinder ratio. 

The relation between the weight of steam shown by the indicator 
at any point in the expansion line and the weight of the mixture 
of steam and water in the cylinder, may be represented graphically 
by plotting on the diagram a saturated steam curve showing the 



1018 THE STEAM-ENGINE. 

total consumption per stroke (including steam retained at com- 
pression) and comparing the abscissae of this curve with the abscissae 
of the expansion line, both measured from the line of no clearance. 
Cut-off and Ratio of Expansion. — To find the percentage of cut-off, 
or what may best be termed the "commercial cut-off," the fol- 
lowing rule should be observed: 

Through the point of maximum pressure during admission 

draw a line parallel to the atmospheric line. Through a 

point on the expansion line where the cut-off is complete, 

draw a hyperbolic curve. The intersection of these two lines 

is the point of commercial cut-off, and the proportion of cut-off 

is found by dividing the length measured on the diagram 

up to this point by the total length. 

To find the ratio of expansion divide the volume corresponding 

to the piston displacement, including clearance, by the volume of 

the steam at the commercial cut-off, including clearance. 

In a multiple expansion engine the ratio of expansion is found 
by dividing the volume of the l.p. cylinder, including clearance, 
by the volume of the h.p. cylinder at the commercial cut-off, in- 
cluding clearance. 

DATA AND RESULTS. 

The data and results should be reported in accordance with the 
form given herewith, adding lines for data not provided for, or omitting 
those not required, as may conform to the object in view. If the 
principal data and results pertaining to steam consumption only are 
desired, the subjoined abbreviated table may be used. 

DATA AND RESULTS OF STEAM-ENGINE TEST 
Code of 1915. 

1. Test of engine located at 

To determine 

Test conducted by 

DIMENSIONS, ETC. 

2. Type of engine (simple or multiple expansion) 

3. Class of service (mill, marine, electric, etc.) 

4. Auxiliaries (steam or electric driven) 

5. Rated power of engine 

1st 2d 3d 

6. Diameter of cylinders in 

7. Stroke of pistons ft 

(a) Diameter of piston-rod, each end, 

in 

8. Clearance (average) in per cent of piston 

displacement 1 to — 

9. H. P. constant 1 lb. 1 rev H.P 

(a) Cylinder ratio (based on net pis- 
ton displacement 1 to — 

10. Capacity of generator or other apparatus 

consuming power of engine H.P 

DATE AND DURATION. 

11. Date 

12. Duration hr. 

Average Pressures and Temperatures. 

13. Pressure in steam pipe near throttle, by gage lbs. per sq, in. 

14. Barometric pressure ins. 

15. Pressure in 1st receiver, by gage lbs. per sq. in. 

16. Pressure in 2d receiver, by gage lbs. per sq. in. 

17. Vacuum in condenser ins. 

18. Pressure in jackets and reheaters lbs. per sq. in. 

19. Temperature of steam near throttle, if superheated degs. 

20. Temperature corresponding to pressure in exhaust pipe 

near engine . . , , degs. 



RULES FOR CONDUCTING STEAM-ENGINE TESTS. 1019 

QUALITY OF STEAM. 

21. Percentage of moisture in steam near throttle, or degrees 

of superheating % or deg. 

TOTAL QUANTITIES. 

22. Water fed to boilers, from main supply lbs. 

23. Water fed to boilers from additional supplies lbs. 

24. Total water fed to boilers lbs. 

25. Total condensed steam from surface condenser (corrected 

for condenser leakage) lbs. 

26. Total dry steam consumed (Item 24 to 25 less moisture 

in steam) lbs. 

HOURLY QUANTITIES. 

27. Water fed to boilers from main supply per hour lbs. 

28. Water fed to boilers from additional supphes per hour. . lbs. 

29. Total water fed to boilers or drawn from surface con- 

denser per hour lbs. 

30. Total dry steam consumed for all purposes per hour 

(Item 26 4- Item 12) lbs. 

31. Steam consumed per hour for all purposes foreign to the 

main engine (including drips and leakage of plant) . . . lbs. 

32. Dry steam consumed by engine per hour (Item 30 — 

Item 31) lbs. 

33. Heat units consumed by engine per hour (Item 32 X 

total heat of steam per lb. above exhaust temperature 

of Item 20) B.T.U. 

INDICATOR DIAGRAMS. 

1st Cyl. 2d Cyl. 3d Cyl. 

34. Commercial cut-off in per cent of stroke, 

per cent 

35. Initial pressure above atmosphere 

lbs. per sq. in 

36. Back pressure at lowest point above or 

below atmosphere lbs. per sq. in 

37. Mean effective pressure lbs. per sq. in 

38. Aggregate M.E.P. referred to each cyl- 

inder lbs. per sq. in 

39. Steam accounted for per I.H.P.-hr. at 

point on expansion line shortly after 

cut-off lbs 

40. Steam accounted for per I.H.P.-hr. at 

point on expansion lin^ just before 

release lbs 

SPEED. 

41. Revolutions per minute R.P.M. 

42. Piston speed per minute ft. 

(a) Variation of speed between no load and full load . per cent. 

(b) Momentary fluctuation of speed on suddenly 
changing from full load to half load per cent. 

POWER. 

43. Indicated H.P. developed, whole engine I.H.P. 

(a) I.H.P. developed by 1st cyhnder I.H.P. 

(b) I.H.P. developed by 2d cyhnder I.H.P. 

(c) I.H.P. developed by 3d cyhnder I.H.P. 

44. Brake H.P B.H.P. 

45. Friction of engine (Item 43 - Item 44) H.P. 

(a) Friction expressed in percentage of I.H.P. (Item 

45 ^ Item 43 X 100) per cent. 

(6) Indicated H.P. with no load, at normal speed. . . . I.H.P. 



1020 THE STEAM-ENGINE. 

ECONOMY RESULTS. 

46. Dry steam consumed by engine per I.H.P. per hr Ibg. 

47. Dry steam consumed by engine per brake H.P.-hr lbs. 

48. Percentage of steam consumed by engine accounted for 

by indicator at point near cut-off per cent. 

49. Percentage of steam consumed near release per cent. 

50. Heat-units consumed by engine per I. H.P.-hr. (Item 

33 ^ Item 43) B.T.U. 

51. Heat-units consumed by engine per brake H.P.-hr. (Item 

33 -^ Item 44) B.T.U. 

52. Heat-units consumed per H.P.-hr. by ideal engine, 

based on Rankine cycle B.T.U. 

EFFICIENCY RESULTS. 

53. Thermal efficiency of engine referred to I.H.P. (2546.5 -J- 

Item 50) percent. 

54. Thermal efficiency of engine referred to Brake H.P. 

(2546.5 -^ Item 51) per cent. 

55. Efficiency of engine based on Rankine cycle referred to 

I.H.P. (Item 52 -i- Item 50) per cent. 

56. Efliciency of engine referred to Brake H.P. (Item 52 h- 

Item 51) per cent. 

WORK DONE PER HEAT-UNIT. ^ 

57. Foot-pounds of net work per B.T.U. consumed by 

engine (1,980,000 -J- Item 51) ft.-lbs. 

SAMPLE DIAGRAMS. 

58. Sample diagrams from each cylinder 

Note: — For an engine driving an electric generator the form should 
be enlarged to include the electrical data, embracing the average 
voltage, number of amperes each phase, number of watts, number 
of watt-hours, average power factor, etc.; and the economy results 
based on the electric output embracing the heat-units and steam 
consumed per electric H.P. per hour and per kw.-hr., together with 
the efficiency of the generator. 

Likewise, in a marine engine having a shaft dynamometer, the 
form should include the data obtained from this instrument, in which 
case the Brake H.P. becomes the Shaft H.P. 

Principal Data and Results of Reciprocating Engine Test. 

1. Dimensions of cylinders 

2. Date , 

3. Duration hrs. 

4. Pressure in steam pipe near throttle by gage lbs. per sq. in. 

5. Pressure in receivers lbs. per sq. in. 

6. Vacuum in condenser ins. 

7. Percentage of moisture in steam near throttle or 

number of degrees of superheating % or deg. 

8. Net steam consumed per hour lbs. 

9. Mean effective pressure in each cylinder lbs. per sq. in. 

10. Revolutions per minute R.P.M. 

11. Indicated horse-power developed H.P. 

12. Steam consumed per I.H.P. per hr lbs. 

13. Steam accounted for at cut-off each cylinder lbs. 

14. Heat consumed per I.H.P. per hr B.T.U. 



DIMENSIONS OF PARTS OF ENGINES. 



1021 



DIMENSIONS OF PAETS OF ENGINES. 

The treatment of this subject by the leading authorities on the steam- 
engine is very unsatisfactory, being a confused mass of rules and for- 
mulae based partly upon theory and partly upon practice. The practice 
of builders shows an exceeding diversity of opinion as to correct dimen- 
sions. The treatment given below is chiefly the result of a study of the 
works of Rankine, Seaton, Unwin, Thurston, Marks, and Whitham, and 
is largelv a condensation of a series of articles by the author published 
in the American Machinist, in 1894, with many alterations and much 
additional matter. 

(Two notable papers on the subject, however, have appeared: 1, Cur- 
rent Practice in Engine Proportions, by Prof. John H. Barr, 1897; and 
2, Current Practice in Steam-engine Design, by Ole N. Trooien, 1909. 
Both of these are abstracted on pages 1039 and 1040.) 

Cylinder. (Whitham) — Length of bore = stroke + breadth of pis- 
ton-ring — i/s to 1/2 in. ; length between heads = stroke + tliickness of 
piston + sum of clearances at both ends ; thickness of piston = breadth 
of ring + thickness of flange on one side to carry the ring + thickness 
of follower-plate. 

Thickness of flange or follower. . . 3/8 to 1/2 in. 3/4 in. 1 in. 

For cylinder of diameter 8 to 10 in. 36 in. 60 to 100 in. 

Clearance of Piston. (Seaton.) — The clearance allowed varies with 
the size of the engine from i/g to s/g in. for roughness of castings and 
1/16 to 1/8 in. for each working joint. Naval and other very fast-running 
engines have a larger allowance. In a vertical direct-acting engine the 
parts which wear so as to bring the piston nearer the bottom are three, 
viz., the shaft journals, the crank-pin brasses, and piston-rod gudgeon- 
brasses. 

Thickness of Cylinder.— In the earlier editions of this book eleven 
formulae, from seven different authorities, were given for thickness of 
cylinders and they were applied to six engines, the dimensions of which, 
are given in the following table. 



Dimensions, etc. 


, OF Engines. 




Engine, No , 1 1 and 2. 


3 and 4. 


5 and. 6. 


Indicated horse-povver I.H.P. 

Diam. of cyl., in D 

Stroke, feet L 

Revs, per min r 


50 

10 

1 ...2 

250... 125 

500 

78.54 

42 

7854 

100 


450 

30 

21/2.^.5 

130 ... 65 

650 

706.86 
32.3 
70.686 
100 


1250 
50 
4 ...8 
90 . .45 


Piston speed, ft. per min S 

Area of piston, sq. in a 


700 
1963.5 


Mean effective pressure M.E.P. 

Max. total unbalanced pressure P 

Max. tojtal pressure per sq. in p 


30 

196.350 

100 



The thickness of the cyHnders of these engines, according to the 
eleven formulae, ranges for engines 1 and 2 from 0.33 to 1.13 in., for 
3 and 4 from 0.99 to 2.00 in., and for 5 and 6 from 1.56 to 3.00 in. 
The averages of the eleven are, for 1 and 2, 0.76 in.; for 3 and 4, 1.48 
in.; for 5 and 6, 2.26 in. 

The average corresponds nearly to the formula t = 0.00037 Dp -f 0.4 
in. A convenient approximation is ^ = 0.0004 Dp + 0.3 in., which gives 
for 

Diameters 10 20 30 40 50 60 in. 

Thicknesses 0.70 1.10 1.50 1.90 2.30 2,70 in. 

The last formula corresponds to a tensile strength of cast iron of 
12,500 lb., with a factor of safety of 10 and an allowance of 0.3 in. for 
reboring. 

'" Thickness of Cylinder and Its Connections for Marine Engines. 
(Seaton.) — D = the diam. of the cylinder in inches; p = load on the 
safety-valves in lb. per sq. in. ; /, a constant multiplier, = thickness of 
barrel + 0.25 in. 



1022 THE STEAM-ENGINE. 

Thickness of metal of cylinder barrel or liner, not to be less than 
pX D ^ 3000 when of cast iron.* 

Thickness of cyUnder-barrel = pX D ^ 5000 +0.6 in. 

Thickness of Jiner = 1.1 X / 

Thickness of hner when of steel = pXD ^ 6000 -f 0.5 in. 

Thickness of metal of steam-ports = 0.6 X/. 

Thickness of metal valve-box sides = 0.65 X /. 
Thickness of metal of valve-box covers = 0.7 X /. 

cylinder bottom =1.1 X /, if single thickness. 



= 0.65 X/. if double 



covers 



cylinder flange 

*' cover-flange 

*• valve-box flange =1.0 

*' door-flange 

*' face over ports 



false-face 



= 1.0 


X/, if single 


= 0.6 


X /, if double 


= 1.4 


x/. 


= 1.3 


x/. 


= 1.0 


Xf. 


= 0.9 


xf. 


= 1.2 


Xf. 


= 1.0 


X f, when there is a false- 




face. 


= 0.8 


X /, when cast iron. 


= 0.6 


X /, Avhen steel or bronze. 



Cylinder-heads. — Applying six different formulse to the engines of 10, 
30, and 50 inches diameter, with maximum unbalanced steam-pressure 
of 100 lb. per sq. in., we have 

For cylinder 10 in. diam., 0.35 to 1.15 in.; for 30 in. diam., 0.90 to 
1.75 in. ; for 50-in. diam., 1.50 to 2.75 in. The averages are respectively 
0.65, 1.38, and 2.10 in. 

The average is expressed by the formula t = 0.00036 Dp -{■ 0.31 inch. 

Web-stiffened Cylinder-covers. — Seaton objects to webs for 
stiffening cast-iron cylinder-covers as a source of danger. The strain on 
the web is one of tension, and if there should be a nick or defect in the 
outer edge of the web the sudden application of strain is apt to start 
a crack. He recommends that high-pressure cylinders over 24 in. and 
low-pressure cylinders over 40 in. diam. should have their covers cast 
hollow, with two thicknesses of metal. The depth of the cover at the 
middle should be about 1/4 the diam. of the piston for pressures of 80 lb. 
and upwards, and that of the low-pressiu*e cylinder-cover of a com- 
pound engine equal to that of the high-pressure cylinder. Another 
rule is to make the depth at the middle not less than 1.3 times the 
diameter of the piston-rod. In the British Navy the cylinder-covers 
are made of steel castings, 3/4 to 1 1/4 in. thick, generally cast without 
webs, stiffness being obtained by their form, which is often a series of 
corrugations. 

Cylinder-head Bolts. — Diameter of bolt-circle for cy Under-head = 
diameter of cyUnder + 2 X thickness of cyUnder + 2 X diameter of bolts. 
The bolts should not be more than 6 in. apart (Whitham). 

Marks gives for number of bolts b = 0.7854 D2p -h 5000 c, in which 
c = area of a single bolt, p = boiler-pressure in lb, per sq. in.; 5000 lb. 
Is taken as the safe strain per sq. in. on the nominal area of the bolt. 

Thurston says: Cylinder flanges are made a little thicker than the 
cyhnder, and usually of equal thickness with the flanges of the heads. 
CyUnder-bolts should be so closely spaced as not to allow springing of the 
flanges and leakage, say, 4 to 5 times the thickness of the flanges. Their 
diameter should be proportioned for a maximum stress of not over 4000 
to 5000 lb. per square inch. 

If D = diameter of cylinder, p = maximum steam-pressure, b = 
number of bolts, 5 = size or diameter of each bolt, and 5000 lb. be 
allowed per sq. in. of actual area at the root of the thread, 0.7854 D^p = 
3927 bs2; whence bs2 = 0.0002 D^p. 

b = .0002 -^ ; s = 0.01414 D^j |. For the three engines we have: 

* When made of exceedingly good material, at least twice melted, 
the thickness may be 0.8 of that given by the above rules. 



DIMENSIONS OF PARTS OF ENGINES. 1023 

Diameter of cylinder, inches 10 30 50 

Diameter of bolt-circle, approx 13 35 57 . 5 

Circumference of circle, approx 40.8 110 180 

Minimmn no. of bolts, circ. -j- 6 7 18 30 

Diam of bolts, s = 0.01414 D^/-^ 3/4 in. 1.00 1.29 



'^1 



The diameter of bolt for the 10-inch cylinder is 0.54 in. by the formula, 
but 3/4 inch is as small as should be taken, on account of possible over- 
strain by the wrench in screwing up the nut. 

The Piston. Details of Construction of Ordinary Pistons. (Seaton.) 
— Let D be the diameter of the piston in inches, p the effective pressure 
per square inch on it, x a constant multipUer, found as follows; 

3: = (D - 50) X Vp^ 1. 
The thickness of front of piston near the boss =0.2 X a:. 

" rim =0.17Xa:. 
back " = 0.18 X x, 

*' boss around the rod = 0.3 X x. 

** flange inside packing-ring = 0.23 X :r. 

" at edge = 0.25 X x. 

•* packing-ring = 0.15 X a;. 

•* junk-ring at edge = 0.23 X x. 

** " inside packing-ring = 0.21 X x. 

at bolt-holes = 0.35 X x. 

*• metal around piston edge = 0.25 X a:. 

The breadth of packing-ring = 0.63 X x. 

" depth of piston at center =1.4 X x, 

*' lap of junk-ring on the piston = 0.45 X x. 

*' space between piston body and packing-ring = 0.3 X x. 
*' diameter of junk-ring bolts =0.1 X x +0.25 in. 

*' pitch of junk-ring bolts =10 diameters. 

*' number of webs in the piston = (D + 20) -7-12. 

*' thickness of webs in the piston = 0.18 X x. 

Marks gives the approximate rule: Thickness of piston-head =^i/TD, 
in which I = length of stroke, and D = diameter of cylinder in inches. 
Whit ham says: In a horizontal engine the rings support the piston, or at 
least a part of it, under ordinary conditions. The pressure due to the 
weight of the piston upon an area equal to 0.7 the diameter of the 
cy Under X breadth of ring-face, should never exceed 200 lb. per sq. in. 
He also gives a formula much used in this country: Breadth of ring- 
face = 0.15 X diameter of cyhnder. 

For our engines we have diameter = 10 30 50 

Thickness of piston-head. 

Marks, 'i/lD; long stroke 3.31 

Marks, '^t/lD', short stroke 3 . 94 

Seaton, depth at center = 1.4 x 4.20 

Seaton, breadth of ring = 0.63 x 1 .89 

Whitham, breadth of ring = 0.15 Z) 1 . 50 

Diameter of Piston Packing-rings. — These are generally turned, 
before they are cut, about 1/4 inch diameter larger than the cylinder, 
for cylinders up to 20 inches diameter, and then enough is cut out of the 
rings to spring them to the diameter of the cylinder. For larger cyhn- 
ders the rings are turned proportionately larger. Seaton recommends 
an excess of 1 % of the diameter of the cyhnder. 

A theoretical paper on Piston Packing Rings of Modem Steam En- 
gines by O. C. Reymann wiU be found in Jour. Frank. Inst., Aug., 1897. 

Cross-section of tlie Rings. — The thickness is commonly made 
1/30 of the diam. of cyl. -\- i/g inch, and the width = thickness 4- i/ginch. 
For an eccentric ring the mean thickness may be the same as for a ring 
of uniform thickness, and the minimimi thickness = 2/3 the maximum. 

A circular issued by J. H. Dunbar, manufacturer of packing-rings, 
Youngstown, Ohio, says: Unless otherwise ordered, the thickness of 
rings wiU be made equal to 0.03 X their diameter. This thickness has 
been foimd to be satisfactory in practice. It admits of the ring being 



5.48 


7.00 


6.51 
9.80 
4.41 
4.50 


8.32 

15.40 

6.93 

7.50 



1024 THE STEAM-ENGINE. 

made about 3/i6 in. to the foot larger than the cylinder, and has, when 
new, a tension of about two pounds per inch of circumference, which is 
ample to prevent leakage if the surface of the ring and cylinder are 
smooth. 

As regards the width of rings, authorities "scatter" from very narrow 
to very wide, the latter being fully ten times the former. For instance, 
Unwin gives W = 0.014 rf + 0.08. Whitham's formula is PF = 0.15 d. 
In both formulae W is the width of the ring in inches, and d the diameter 
of the cylinder in inches. Unwin 's formula makes the width of a 20-in. 
ring W= 20X 0.014 + 0.08 = 0.36 in., while Whitham's is 20 X 0.15 = 
3 in. for the same diameter of ring. There is much less difference in the 
practice of engine-builders in this respect, but there is stiU room for a 
standard T\adth of ring. It is beUeved that for cyhnders over 16 in. 
diameter 3/4 in. is a popular and practical width, and 1/2 in. for cylinders 
of that size and under. 

Fit of Piston-rod into Piston. (Seaton.) — The most convenient 
and reUable practice is to turn the piston-rod end with a shoulder of i/ie 
inch for small engines, and i/g inch for large ones, make the taper 3 in. to 
the foot until the section of the rod is three-fourths of that of the body, 
then turn the remaining part parallel ; the rod should then fit into the 
piston so as to leave i/s in. between it and the shoulder for large pistons 
and 1/16 in. for small. The shoulder prevents the rod from splitting the 
piston, and allows of the rod being turned true after long wear without 
encroaching on the taper. 

The piston is secured to the rod by a nut, and the size of the rod should 
be such that the strain on the section at the bottom of the thread does 
not exceed 5500 lb. per sq. in. for iron, 7000 lb. for steel. The depth 
of this nut need not exceed the diameter which would be found by allow- 
ing these strains. The nut should be locked to prevent its working 
loose. 

Diameter of Piston-rods. — Taldng d = diam. of piston-rod, D — 
diam. of piston, I = length of stroke, p = maximum unbalanced pres- 
sure, lb. per_sq. in., Unwin gives, for iron rods, d = 0.0167 D\/p\ steel, 
0.0144 D\/p. Marks gives: (1) d = 0.0179 D^/pfov iron; (2) 0. 0105 
D\/p for steel; and (3) d = 0.0390 ^DH'^p "for iron; (4) 0.0352 ^DH'^p 
for steel. Deduce the diameter of the rod by (1) or (2) and if this 
diameter is less than 1/12^ then use (3) or (4). Applying these four 
formulae to the six engines and taking the average results, we have the 
following : 

Diameter of Piston-rods. 



Diameter of Cylinder, inches 


10 


30 


50 










Stroke, inches. 


12 

1.49 
1.33 


24 
1.82 
1.59 


30 

4.30 
3.83 


60 

5.26 
4.52 


48 96 


Diam. of rod, average for iron 

" " average for steel 


7.11 8.74 
6.33 7.46 



An empirical formula which gives results approximating the above 
averages is d'' = c \/Dlp, the values of c being for short stroke engines, 
iron, 0.0145; steel, 0.0129; and for long stroke engines, iron, 0.0126, 
steel, 0.0108. 

The calculated results for this formula, for the six engines, are, re- 
spectively : 

Iron 1.59 1.95 4.35 5.36 7.11 8.73 

Steel 1.31 1.67 3.87 4.58 6.32 7.48 

In considering an expansive engine, p, the effective pressure, should be 
taken as the absolute working pressure, or 15 lb. above that to which 
the boiler safety-valve is loaded ; for a compound engine the value of p 
for the high-pressure piston should be taken as the absolute pressure, 
less 15 lb., or the same as the load on the safety-valve; for the medium- 
pressure the load may be taken as that due to half the absolute boiler- 
pressure; and for the low-pressure cylinder the pressure to which the 
escape- valve is loaded + 15 lb., or the maximum absolute pressure 
which can be got in the receiver, or about 25 lb. It is an advantage to 
make all the rods of a compound engine alike, and this is now the rule. 

Piston-rod Guides. — The thrust on the guide, when the connecting- 



DIMENSIONS OP PARTS OF ENGINES. 



1023 



rod is at its maximum angle with the line of the piston-rod, is foimd from 
the formula: Thrust = total load on piston X tangent of maximum angle 
of connecting-rod = p tan 0. This angle, 9, is the angle whose sine = 
half stroke of piston -h length of connecting-rod. 

Ratio of length of connecting-rod to stroke. . 2 21/2 3 

Maximum angle of connecting-rod with line 

of piston-rod 14° 29' ll** 33' 9° 36' 

Tangent of the angle 0.258 0.204 0.169 

Secant of the angle 1.0327 1.0206 1.014 

Thurston says: The rubbing surfaces of guides are so proportioned 
that if V be their relative velocity in feet per minute, and p be the in- 
tensity of pressure on the guide in lb. per sq. in., pV < 60,000 and 
pV> 40,000. 

The lower is the safer hmit ; but for marine and stationary engines it 

is allowable to take p = 60,000 -^ V. According to Rankine, for loco- 

44,800 , . ^, . ,^ . ^ ,, 

motives, p = ^ , where p is the pressure m lb. per sq. m. and V 

the velocity of rubbing in feet per minute. This includes the sum of 
all pressures forcing the two rubbing surfaces together. 

Some British builders of portable engines restrict the pressure between 
the guides and cross-heads to less than 40, sometimes 35 lb. per sq. in. 

For a mean velocity of 600 feet per minute, Prof. Thurston's formulae 
give, p < 100, p > 66.7; Rankine's gives p = 72.2 lb. per sq. in. 

Whitham gives, 

A = area of sUdes in square inches = =rr = — ^ - 

po \/n2 - 1 po \/n2 - 1* 
in which P = total unbalanced pressure, pi = pressure per square inch 
on piston, d = diameter of cylinder, po = pressure allowable per square 
inch on sUdes, and n = length of connecting-rod -7- length of crank. 
This is equivalent to the formula, A = P tan -r- po. For n = 5, pi = 
100 and po = 80, A = 0.2004 dK For the three engines 10, 30, and 50 in. 
diam., this would give for area of sUdes, A = 20, 180, and 500 sq. in., 
respectively. Whitham says : The normal pressure on the shde may be 
as high as 500 lb. per sq. in., but this is when there is good lubrication 
and freedom from dust. Stationary and marine engines are usually 
designed to carry 100 lb. per sq. in., and the area in this case is reduced 
from 50% to 60% by grooves. In locomotive engines the pressure 
ranges from 40 to 50 lb. per sq. in. of sUde, on account of the inaccessi- 
bility of the shde, dirt, cinder, etc. 

The Connecting-rod. Ratio of length of connecting-rod to length of 
stroke. — Experience has led generally to the ratio of 2 or 2 1/2 to 1, the 
latter giving a long and easy- working rod, the former a rather short, but 
yet a manageable one (Thurston) . Whitham gives the ratio of from 2 
to 4 1/2 and Marks from 2 to 4. 

Dimensions of the Connecting-rod. — The calculation of the diameter 
of a connecting-rod on a theoretical basis, considering it as a strut sub- 
ject to both compressive and bending stresses, and also to stress due to 
its inertia, in high-speed engines, is quite complicated. See Whitham, 
Steam-engine Design, p. 217; Thurston, Manual of S. E., p. 100. 

Applying seven formulae given by different authorities to the six 
engines the average diameters (at the middle of the rod) are given 
below : 

Diameter of Connecting-rods. 



Diameter of Cylinder, inches 


10 


30 


50 










Stroke, inches 


12 

30 

2.24 


24 

60 

2.26 


30 

75 

6.38 


60 
150 
6.27 


48 
120 
10.52 


96 


Length of connecting-rod I 


240 


Diameter of rod, inches 


10.26 



The average figures show but little difference in diameter between 
long- and short-stroke engines; this is what might be expected, for while 
the connecting-rod, considered simply as a column, would require an 
increase of diameter for an increase of length, the load remaining the 



1026 THE STEAM-ENGINE. 

same, yet in an engine generally the shorter the connecting-rod the 
greater the number of revolutions, and consequently the greater the 
strains due to inertia. The influences tending to increase the diameter 
therefore tend to balance each other, and to render the diameter to 
some extent independent of the length. The^average figures correspond 
nearly to the simple formula d = 0.021 D\/p. The diameters of rod for 
the three diameters of engine by this formula are, respectively, 2.10, 
6.30, and 10.50 in. Since the total pressure on_the piston P = 0.7854 
D^p, the formula is equivalent to d = 0.0237 \/P. 

Seaton and Sennett give the diameter at the necks of a connecting- 
rod = 0.9 the diam. at the middle. Whitham gives it as 1.0 to 1.1 the 
diam. of the piston-rod. 

Connecting-rod Ends. — For a connecting-rod end of the marine 
type, where the end is secured with two bolts, each bolt should be pro- 
portioned for a safe tensile strength equal to two-thirds of the maximum 
pull or thrust in the connecting-rod. 

The cap is to be proportioned as a beam loaded with the maximum 
puU of the connecting-rod, and supported at both ends. The calcula- 
tion should be made for rigidity as weU as strength, allowing a maximum 
deflection of i/ioo inch. For a strap-and-key connecting-rod end the 
strap is designed for tensile strength, considering that two-tliirds of the 
pull on the connecting-rod may come on one arm. At the point where 
the metal is slotted for the key and gib, the straps must be tliickened to 
make the cross-section equal to that of the remainder of the strap. Be- 
tween the end of the strap and the slot the strap is Uable to fail in double 
shear, and sufficient metal must be provided at the end to prevent such 
failure. 

The breadth of the key is generally one-fourth of the width of the 
strap, and the length, parallel to the strap, should be such that the cross- 
section will have a shearing strength equal to the tensile strength of the 
section of the strap. The taper of the key is generaUy about 5/8 inch 
to the foot. 

Tapered Connecting-rods. — In modern high-speed engines it is cus- 
tomary to make the connecting-rods of rectangular instead of circular 
section, the sides being parallel, and the depth increasing regularly from 
the cross-head end to the crank-pin end. According to Grashof, the 
bending action on the rod due to its inertia is greatest at 6/io the length 
from the cross-head end, and, according to this theory, that is the point 
at which the section should be greatest, although in practice the section 
is made greatest at the crank-pin end. 

Professor Thurston furnished the author with the following rule for 
tapered connecting-rods of rectang ular sect ion: Take the section as com- 
puted by the formula cZ" =0.1 ■\lDL\/p'-\- 3/4 for a circular section, 
and for a rod 4/3 the actual length, placing the computed section at 
2/3 the length from the small end, and carrying the taper straight 
through this fixed section to the large end. This brings the computed 
section at the surge point and makes it heavier than the rod for which 
a tapered form is not required. 

Taking the above formula, m ultiplyin g L by Vs, and changing it to I 

in inches, it becomes d = 1/30 ^ Dl \/p'+ 3/4 in. Taking a rectangular 
section of the same area as the round section whose diameter is d, 
and making the depth of the section h = twice the th ickness t, we have 

0.7854 d2= ht = 2 /2, whence t = 0.627; d = 0.0209 -yj Dl\/~p + 0.47 in., 
which is the formula for the thickness or distance between the parallel 
sides of the rod. Making the depth at the cross-head end = 1.5 /, and 
at 2/3 the length = 2 t, the equivalent depth at the crank end is 2.25 /. 
Applying the formula to the short-stroke engines of our examples, we have 



Diameter of cylinder, inches 

Stroke, inches 

Length of connecting-rod 

Thickness, t = 0.0209 Vd/ \/p4- 0.47 = . 

Depth at cross-head end, 1.5^ = 

Depth at crank end, 21/4^ 



10 


30 


12 


30 


30 


75 


1.61 


3.60 


2.42 


5.41 


3,62 


8.11 



50 
48 
120 

5.59 
8.39 
12.58 



DIMENSIONS OF PARTS OF ENGINES. 



1027 



The thicknesses t, found by the formula t = 0.0209 V Dl\/v + 0.47, 
agree closely with the more simple formula t = 0,01 D\/~p + 0.60 in., the 
thicknesses calculated by this formula being respectively 1.6, 3.6, and 
5.6 in. 

The Crank-Pin. — A crank-pin should be designed (1) to avoid heat- 
ing, (2) for strength, (3) for rigidity. The heating of a crank-pin 
depends on the pressure on its rubbing surface, and on the coefficient 
of friction, which latter varies greatly, according to the effectiveness of 
the lubrication. It also depends upon the facility with which the heat 
produced may be carried away: thus it appears that locomotive crank- 
pins may be prevented to some degree from overheating by the cooUng 
action of the air through which they pass at a high speed. 

Marks states as a general law, within reasonable limits as to pressure 
and speed of rubbing, the longer a bearing is made, for a given pressure 
and number of revolutions, the cooler it will work; and its diameter has 
no effect upon its heating. 

Whitham recommends for pressure per square inch of projected area, 
for naval engines 500 pounds, for merchant marine engines 400 pounds, 
for paddle-wheel engines 800 to 900 pounds. 

Thurston says the pressure on a steel crank-pin should, in the steam- 
engine, never exceed 1000 or 1200 pounds per square inch. He gives 
the formula for length of a steel pin, in inches. 

1 = PR- 600,000, 

in which P and R are the mean total load on the pin in pounds, and the 
number of revolutions per minute. For locomotives, the divisor may be 
taken as 500,000. Pins so proportioned, if well made and well lubri- 
cated, may always be depended upon to run cool; if not well formed, 
perfectly cylindrical, well finished, and kept well oiled, no crank-pin 
can be rehed upon. It is assumed above that good bronze or white- 
metal bearings are used. 

By calculating lengths of iron crank-pins for the engines 10, 30, and 
50 inches diameter, long and short stroke, by the formulae given by dif- 
ferent writers, it is found that there is a great difference in the results, 
so that one formula in certain cases gives a length three times as great 
as another. 

The average of the calculated lengths of iron crank-pins for the 
several cases by five formulae are given in the table below, together 
with the calculated lengths by two formulae for steel. 





Length of Crank-pins 


• 








Diameter of cylinder . . . 

Stroke 

Revolutions per minute. 
Horse-power 




D 

L (ft.) 

R 

.I.H.P. 


10 

1 

250 

50 

7.854 

42 


10 

2 

125 

50 


30 

130 
450 


30 
5 

65 
450 


50! 50 

4, 8 

90! 45 

1.250^ K250 


Maximum pressure .... 
Mean pressure per cent 


of max . 


...lbs. 


7,854 70.686 70.686i 196.350 196.350 
42 32.3 32.3i 30 30 


Mean pressure 


P. 


3.299 22.832 22.8321 58.905, 58.905 


Length of crank-pin, average for iron. . 


2.72 


1.36. 9.86 4.93 I 17.12 | 8.56 


Unwin, best steel, l=0.\ 
Thurston, steel, l=PR- 


I.H.P.4 

-600,000 


-r 


0.83 
1.37 


0.42 
0.69 


3.0 
4.95 


1.5 

2.47 


5.21 

8.84 


2.61 
4.42 



The calculated lengths for the long-stroke engines are too low to pre- 
vent excessive pressures. See "Pressures on the Crank-pins," below. 

Tiie Strength of the Crank-pin is determined substantially as is that 
of the crank. In overhung cranks the load is usually assumed as 
carried at the middle of the pin, and, equating its moment with that of 
the resistance of the pin. 



1/2 PZ= V32tTrd\ and 



.= v/^. 



in which d = diameter of pin in inches, P = maximum load on the 
piston, t = the maximum allowable stress on a square inch of the metal. 
For iron it may be taken at 9000 lbs, For steel the diameters found by 
this formula may be reduced 10%. (Thurston.) 



1028 



THE STEAM-ENGINE. 



Unwin gives the same formula in another form, viz.: 



,= ^5^^, y/^V/p^. 



the last form to be used when the ratio of length to diameter is assumed. 
For wrought iron, t = 6000 to 9000 lbs. per sq. in., 



^5.1/t^ 0.0947 to 0.0827; V5.1/i == 0.0291 to 0.0238. 
For ste el, t == 9000 to 13,000 lbs. per sq. in., 

•^SoZt = 0.0827 to 0.0723: Vs.l/i = 0.0238 to 0.0194- 
Marks, calculating the diameter for rigidity, gives 
d = 0.066 \/pi3 



0.945 ^(H..F.)l^ ■+■ LN; 



p — maximum steam-pressure in pounds per square inch, D = diameter 
of cylinder in inches, L = length of stroke in feet, N = number of single 
strokes per minute. He says there is no need of an investigation of the 
strength of a crank-pin, as the condition of rigidity gives a great excess 
of strength. 

Marks's formula is based upon the assumption that the whole load 
may be concentrated at the outer end, and cause a deflection of 0.01 in. 
at that point. It is serviceable, he says, for steel and for wrought iron 
aUke. 

Using the average lengths of the crank-pins already found, we have 
the following for our six engines : 



Diameter of Crank-pins. 



Diameter of cylinder 

Stroke, ft 

Length of crank-pin 

tJnwin, d = tf -^-r — 

Marks. <f=0.066^pP52.. 



10 

1 

2.72 
2.29 
1.39 


10 

2 

1.36 

1.82 
0.85 


30 

21/2 

9.86 
7.34 
6.44 


30 

5 

4.93 

5.82 
3.78 


50 

4 

17.12 

12.40 
12.41 



50 

8 

8 56 

9.84 
7.39 



Pressures on the Crank-pins. — If we take the mean pressure upon 
the crank-pin = mean pressure on piston, neglecting the effect of the 
varying angle of the connecting-rod, we have the following, using the 
average lengths already found, and the diameters according to Unwin 
and Marks; 



Engine No 


1 


2 


3 


4 


5 


6 






Diameter of cylinder, inches 


10 

1 
3,299 
6.23 
3.78 
530 
873 


10 

2 
3,299 
2.36 
1.16 
1,398 
2,845 


30 

21/2 
22,832 
72.4 
63.5 
315 
360 


30 

5 

22,832 

28.7 

18.6 

796 

1.228 


50 
4 
58,905 
212.3 
212.5 
277 
277 


50 


Stroke, feet 


8 


Mean pressure on pin, pounds 


58,905 


Projected area of pin, Unwin 


84.2 


Projected area of pin, Marks 


63.3 


Pressure per square inch, IJnwin 

Pressure per square inch, Marks 


700 
930 



The results show that the application of the formulae for length and 
diameter of crank-pins give quite low pressures per square inch of pro- 
jected area for the short-stroke high-speed engines of the larger sizes, but 
too high pressures for all the other engines. It is therefore evident that 
after calculating the dimensions of a crank-pin according to the formulae 
given, the results should be modified, if necessary, to bring the pressure 
per square inch down to a reasonable figure. 

In order to bring the pressures down to 500 pounds per square inch, 
we divide the mean pressures by 500 to obtain the projected area, or 



DIMENSION'S OF PARTS OF ENGINES. 1029 

p^^'i^r.^A iT^*^ by diameter. Making ^ = 1.5 rf for engines Nos. 1, 
J, 4, and 6, the revised table for the six engines is as follows: 

Engine No 1 2 3 4 5 a 

Lengthof crank-pin, inches.. 3.15 3.15 9.86 8.37 17 12 13 30 
Diameter of crank-pin 2.10 2.10 7.34 5.58 12:40 sis" 

^.^f?^f**-®*^:P*"^.*^'' Wrist-pin.— Seaton says the area, calculated by 
multiplying the diameter of the journal by its length, Should be such 
that the pressure does not exceed 1200 lb. per sq. iS., taking the maxi- 
mum load on the piston as the total press^e on the pin^ 
n^.Hno.^?^H ^^|"ies with the gudgeon shrunk mto the jaws of the con- 
Pnd%"'^cAn^r''H ^«^k^^& in brasses fitted into a recess in the piston-rod 
end and secured by a wrought-iron cap and two bolts, Seaton gives: 
Diameter of gudgeon = 1.25 X diam. of piston-rod, 
Length of gudgeon = 1 . 4 X diam. of piston-rod. 

If the pressure on the section, as calculated by multiDlvine leneth hv 
diameter exceeds 1200 lbs. per sq. in. this length shoulc? be"acreased.^ 
cross^ekd^n r9H'?n^\'Q J^^"^^ Reference" book, gives for length of 
Hi«m of SiJ^S-^^o*^ ^'^ ^^^^- 9^ piston, and diam. =0.18 to 0.2 
H nS* ^/rP^f^"-v,-^l?.^^ ^^. ^^^s for diam. of piston-rod 0.14 to 17 
are ahnnF'f Tr;' .^in'^iT'i'-'"''" ^^/ diameter and length of crosshead-p n 
mLirS?,!iJ ^-1^^ ^u,^ ^'^ ^^^^' ^f piston-rod respectively. Taking the 
maximum allowable pressure at 1200 lbs. per sq. in. and making the 
length of the crosshead-pin= 4/3 of its diameter, we have cf= Vp^ 40, Z = 
ur^dT ^u.'J^,^^}^^ P= maximum total load on piston in lbs., d = diam. 
and I = length of pin in inches. For the engines of our example we have- 
Diameter of piston, inches 10 30 Ko 

Maximum load on piston, lbs 7854 70 686 196 3^0 

Diameter of crosshead-pin, inches 2. 22 6 65 11 08 

Length of crosshead-pin, inches 2.96 8 86 14 77 

Stanwood s rule gives diameter, ins.... 1.8 to 2 5 4 to 6 9 to 10 
Stanwood s rule gives length, inches. . . 2.5 to 3 7 5 to 9 12 5 to 15 
Stanwood's largest dimensions give ^.oiuy 1^.010 la 

pressure per sq. in., lbs 1309 1329 1309 

These pressures are greater than the maximum allowed by Seaton 
if /rio?h^f?S?.i ^"^^ —The crank-arm is to be treated as a lever, so that 
If i^l^n^il^i^^"-^'!''^ adirection parallel to the shaft-axis and 5 its breadth 

♦kPok^^'^^^I^w.^^^^S^P*^"^*^^ s^ that h varied as VJ (as given bv 
Jn m\H?,yf^ 7^^^ '* ''^^^^^ ^^ ^^ ^V^^ ^ ^^^ved form as to be inconvenient 
to manufacture, and consequently it is customary in practice to find the 
n.P^iTnTel^J''^ ^^ ^ ^^"^ draw tangent lines to the curve at the poin si 
tSe^c'rlXlr^r^^T^hTs^fe^^^^^^ *^^ ^^^^ -^-^' ^-^-^-^ to the Lss of 

«o3i,/i^^^•^^^^ ^^^^^^ ^^ th^ ^^^^ throughout the crank-arm; and, con- 
ntS^nni^^.'^-.^^""^^ compared with the bending strain close to the crank- 
pin; and so it is not sufficient to provide there onlv for bend in/st rains 

hvVhTn^^ni l^'' Pf^^"* !t^"l^ ^S-'""^^ that, in addition to whSt is given 
py the calculation from the bending moment there is an r^tra qmVnrp 
inch for every 8000 lbs. of thrust on^the connectin|-?od (Seaton) ^ 
1 n nf^tlTg- ^ ''V^'' 5^f ^ i^t^ ^^^^^h the shaft is fitted is from' 0.75 to 
^r»%1:!sTn7s?r^^^^^^^ ?L TL'iti^lfS^^^T'^' ^^ -^-^-^^ 

nesWfc^ir^&VyTel^to"^^ '' '^^ '""""^"^ ^^^^^^ ^' *^^^^- 

When h = D, then e = 0.35 D; if steel, 0.3. 
h = 0.9Z>, then e = 0.38 D; if steel, 0.32. 
h = 0.81), then e = 0.40 D; if steel, 0.33. 
h = 0.7 D, then e = 0.41 D\ if steel, 0.34. 



1030 



THE STEAM-ENGINE. 



The crank-eye or boss into which the pin is fitted should bear the same 
relation to the pin that the boss does to the shaft. 

The diameter of the shaft-end onto which the crank is fitted should 
be 1.1 X diameter of shaft. 

Thurston says: The empirical proportions adopted by builders will 
commonly be found to fall well within the calculated safe margin. 
These proportions are, from the practice of successful designers, about 
as follows: 

The hub is 1.75 to 1.8 times the least diameter of that part of the 
shaft carrying full load ; the eye is 2.0 to 2.25 the diameter of the inserted 
portion of the pin, and their depths are, for the hub, 1.0 to 1.2 the 
diameter of shaft, and for the eye, 1.25 to 1.5 the diameter of pin. The 
web is made 0.7 to 0.75 the width of the adjacent hub or eye, and is 
given a depth of 0.5 to 0.6 that of the adjacent hub or eye. 

The crank-shaft is usually enlarged at the seat of the crank to about 
1.1 its diameter at the journal. The size should be nicely adjusted to 
allow for the shrinkage or forcing on of the crank. A difference of 
diameter of 0.2 % wiU usually suffice. 

The formulae given by different writers for crank-arms practically 
agree, since they all consider the crank as a beam loaded at one end and 
fixed at the other. The relation of breadth to thickness may vary 
according to the taste of the designer. Calculated dimensions for our 
six engines are as follows: 

Dimensions of Crank-arms. 



Diam. of cylinder, ins.. 

Stroke S, ins 

Max. pressure on pin P 

(approx.), lbs 

Diam.. crank-pin d 

^. ^ ,, tVl.H.P. ^ 
Dia. shaft, a V — p — , D 

(a = 4.69. 5.09 and 5.22)... 

Length of boss, 0.8 D 

Thickness of boss, 0.4 D. . . 

Diam. of boss, 1 .8 D 

Length crank-pin eye, O.S d 
Thickness of crank-pin eye, 

O.Ad 

Max. mom. T at distance 

1/2 5- 1/2 O from center of 

pin, inch-lbs 

Thickness of crank-arm a = 

' 0.75 D 

Greatest breadth, 

6= VbT -i- 9000 a 
Min. mom. Tq at distance 

d from center of pin = Pd . 

Least breadth, 

bi='V6 To ^ 9000 a 



10 
12 


10 

24 


30 
30 


30 
60 


50 

48 


7854 
2.10 


7854 
2.10 


70,686 
7.34 


70,686 
5.58 


196,350 
12.40 


2.74 


3.46 


7.70 


9.70 


12.55 


2.19 
1. 10 
4.93 
1.76 


2.77 
1.39 
6.23 
1.76 


6.16 
3.08 
13.86 
5.87 


7.76 
3.88 
17.46 
4.46 


10.04 
5.02 

22.59 
9.92 


0.88 


0.88 


2.94 


2.23 


4.46 


37,149 


80,661 


788,149 


1,848,439 


3,479,322 


2.05 


2.60 


5.78 


7.28 


9.41 


3.48 


4.55 


9.54 


13.0 


15.7 


16,493 


16,493 


528,835 


394,428 


2,434,740 


2.32 


2.06 


7.81 


6.01 


13.13 



50 
96 

196,350 
8.87 



15.82 



12.65 
6.32 

28.47 
7.10 

3.55 



7,871,671 
11.87 
21.0 

1,741,625 
9.89 



The Shaft. — Twisting Resistance. — From the general formula 



for torsion, we have: T = -^-^ d^S = 0.19635 d^S, whence d = ^ ^, 

16 \ S 

in which T = torsional moment in inch-pounds, d = diameter in inches, 
and S = the shearing resistance of the material, lb. per sq. in. 

If a constant force P were applied to the crank-pin tangentially to its 
path, the work done per minute would be 

PXLX27r-M2X/2 = 33,000 X I.H.P., 
in which L = length of crank in inches, and R = revs, per min., and the 
mean twisting moment T = I.H.P. -^ RX 63,025. Therefore 

d= '\/5.1 T -^ 8== -^321,427 I.H.P. ^ RS, 



DIMENSIONS OF PARTS OF ENGINES. 



1031 



This may take the form 



d = ^I.H.P. X F/R, OT d = a \/l.H.P. -j- R, 
in which F and a are factors that depend on the strength of the material 
and on the factor of safety. Taking /S at 45,000 pounds per square inch 
for wrought iron, and at 60,000 for steel, we have, for simple twisting by 
a uniform tangential force, 
Factor of safety =568 10 5 6 810 

Iron F = 35.7 42.8 57.1 71.4 a = 3.3 3.5 3.85 4.15 

Steel F= 26.8 32.1 42.8 53.5 a = 3.0 3.18 3.5 3.77 

Unwin, taking for safe working strength of wrought iron 9000 lbs., 
steel 13,500 lbs., and cast iron 4500 lbs., gives a = 3.294 for wrought 
iron, 2.877 for steel, and 4.15 for cast iron. Thurston, for crank-axles 
of wrought iron, gives a = 4.15 or more. 

Seaton says: For wrought iron, /, the safe strain per square inch, should 
not exceed 9000 lbs., and when the shafts are more than 10 inches diameter, 
8000 lbs. Steel, when made from the ingot and of good materials, will 
admit of a stress of 12,000 lbs. for small shafts, and 10,000 lbs. for those 
above 10 inches diameter. 

The difference in the allowance between large and small shafts is to com- 
pensate for the defective material observable in the heart of large shaft- 
ing, owing to the hamm ering failing to affect it. 

The formula d = a -x/l.H.P. -r- R assumes the tangential force to be 
uniform and that it is the only acting force. For engines, in which the 
tangential force varies with the angle between the crank and the connect- 
ing-rod, and with the variation in steam-pressure in the cyhnder, and also 
is influenced by the inertia of the reciprocating parts, and in which also 
the shaft may be subjected to bending as well as torsion, the factor 
a must be increased, to provide for the maximum tangential force and 
for bending. 

Seaton gives the following table showing the relation between the 
maximum and mean twisting moments of engines working under various 
conditions, the momentum of the moving parts being neglected, which is 
allowable: 



Description of Engine. 



Single-crank expansive. . 



Steam Cut-off 
at 



Max. 

Twist 

Divided 

by 

Mean 

Twist. 
Moment 



Cube 
Root 
of the 
Ratio. 



Two-cylinder expansive, cranks at 90° 



Three-cylinder compound, cranks 120°. . 

Three-cylinder compound, l.p. cranksop- 

Dosite one another, and h.p. midway 



0.2 
0.4 
0.6 
0.8 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
h.p. 0.5, l.p.0.66 



2.625 
2.125 
1.835 
1.698 
1.616 
1.415 
1.298 
1.256 
1.270 
1.329 
1.357 
1.40 

1.26 



1.38 
1.29 
1.22 
1.20 
1.17 
1.12 
1.09 
1.08 
1.08 
1. 10 
1.11 
1.12 

1.08 



For the engines we are considering it will be a very liberal allowance for 
ratio of maximum to mean twisting moment if we take it as equal to the 
ratio of the maximum to the mean pressure on the piston. The factor a, 
then, in the formula for diameter of the shaft will be multiplied by the cube 

8/ 3/ 3 ■ 

root of this ratio, or t/^ = 1.34, \/^^= 1.45, 

for the 10, 30, and 50-in. engines, respectively. Taking «'= 3.5, which 
corresponds to a shearing strength of 60,000 and a factor of safety of 8 for 



V 30 



1.49 



1032 



THE STEAM-ENGINE. 



steel, or to 45,000 and a factor of 6 for iron, we have for the new coeflB- 
cient ai in the formula di = ai -v/I.H.P. -^ R, the values 4.69, 5.08, and 
5.22 from which we obtain the diameters of shafts of the six engines as 
follows: 

Engine No 1 2 

Diam. of cyl 10 10 

Horse-power, I. H.P 50 50 

Revs, per min., R 250 125 

Diam. of shaft d = 2 . 74 3 . 46 

These diameters are calculated for twisting only. When the shaft is 
also subjected to bending strain the calculation must be modified as 
below: 

Resistance to Bending. — The strength of a circular-section shaft 
to resist bending is one-half of that to resist twisting. If B is the bending 
moment in inch-lbs., and d the diameter of the shaft in inches, 



3 


4 


5 


6 


30 


30 


50 


50 


450 


450 


1250 


1250 


130 


65 


90 


45 


7.67 


9.70 


12.55 


15.82 



B = 



32 



X /; and d 



-{/f 



X 10.2; 



/ is the safe strain per square inch of the material of which the shaft is 
composed, and its value may be taken as given above for twisting (Seaton). 

Equivalent Twisting Moment. — When a shaft is subject to both 
twisting and bending simultaneously, the combined strain on any section 
of it may be measured by calculating what is called the equivalent twisting 
moment; that is, the two strains are so combined as to be treated as a 
twisting strain only of the same magnitude and the size of shaft calculated 
accordingly. Rarikine gave the following solution of the combined action 
of the two strains. 

If T = the twisting moment, and B = the bending moment on a sect ion 
of a shaft, then the equivalent twisting moment Ti = B -^ v^gM-T^. 

The two principal strains vary throughout the revolution, and the 
maximiun equivalent twisting moment can only be obtained acciu'ately 
by a series of calculations of bending and twisting moments taken at 
fixed intervals, and from them constructing a curve of strains. 

Considering the engines of our examples to have overhung cranks, the 
maximum bending moment resulting from the thrust of the connecting- 
rod on the crank-pin will take place when the engine is passing its centers 
(neglecting the effect of the inertia of the reciprocating parts), and it will 
be the product of the total pressure on the piston by the distance between 
two parallel lines passing through the centers of the crank-pin and of the 
shaft bearing, at right angles to their axes; which distance is equal to 
1/2 length of crank-pin bearing -I- length of hub + 1/2 length of shaft- 
bearing + any clearance that may be allowed between the crank and the 
two bearings. For our six engines we may take this distance as equal 
to 1/2 length of crank-pin + thickness of crank-arm -I- 1.5 X the diam- 
eter of the shaft as already found by the calculation for twisting. The 
calculation of diameter is then as below: 



Engine No. 


1 


2 


3 


4 


5 


6 


Diam. of cyl., in.... 


10 


10 


30 


30 


50 


50 


Horse-power 


50 


50 


450 


450 


1250 


1250 


Revs, per min 


250 


125 


130 


65 


90 


45 


Max. press, on pis.P 


7,854 


7,854 


70,686 


70,686 


1%,350 


1%,350 


Leverage,* L in 


6.32 


7.94 


22.20 


26.00 


36.80 


42.25 


Bd.mo.PL=5in.-lb 


49,637 


62,361 


1,569,222 


1,837,836 


7,225,680 


8,295,788 


Twist, mom. T .... 


47,124 


94,248 


1,060,290 


2,120,580 


4,712,400 


9,424,800 


Equiv. twist mom. 














Ti^ B+^B^+T^ 




(approx.) 


118.000 


175,000 


3.463,000 


4,647,000 


15,840.000 


20,850.000 



* Leverage = distance between centers of crank-pin and shaft bearing 
- V2i 4- 2.25 d. 

Having already found the diameters, on the assumption that the shafts 
were subjected to a twisting moment T only, we may find the diameter 



DIMENSIONS OF PARTS OF ENGINES. 1033 

for resisting combined bending and twisting by multiplying the diameters 
already found by the cube roots of the ratio Ti -^ T, or 

1.40 1.27 1.46 1.34 1.64 1.36 
Giving corrected diameters a'l = 3.84 4.39 11.35 12.99 20.58 21.52 

By plotting these results, using the diameters of the cylinders for abscis- 
sas and diameters of the shafts for ordinates, we find'^that for the long- 
stroke engines the results lie almost in a straight hne expressed by the 
formula, diameter of shaft =- 0.43 X diameter of cyUnder; for the short- 
stroke engines the Hne is sUghtly curved, but does not diverge far from a 
straight line whose equation is, diameter of shaft =0.4 diameter of 
cylinder. Using these two formulas, the diameters of the shafts will be 
4.0, 4.3, 12.0, 12.9, 20.0, 21.5. 

J. B. Stanwood, in Engineering, June 12, 1891, gives dimensions of 
shafts of Corliss engines in American practice for cylinders 10 to 30 in. 
diameter. The diameters range from 4l5/i6 to 1415/16, following precisely 
the equation, diameter of shaft = 1/2 diameter of cylinder — Vie inch. 

Fly-wheel Shafts. — Thus far we have considered the shaft as resist- 
ing the force of torsion and the bending moment produced by the pressure 
on the crank-pin. In the case of fly-wheel engines the shaft on the 
opposite side of the bearing from the crank-pin has to be designed with 
reference to the bending moment caused by the weight of the fly-wheel, 
the weight of the shaft itself, and the strain of the belt. For engines 
in which there is an outboard bearing, the weight of fly-wheel and shaft 
being supported by two bearings, the point of the shaft at which the 
bending moment is a maximum may be taken as the point midway 
between the two bearings or at the middle of the fly-wheel hub, and the 
amount of the moment is the product of the v/eight supported by one of 
the bearings into the distance from the center of that bearing to the 
middle point of the shaft. The shaft is thus to be treated as a beam 
supported at the ends and loaded in the middle. In the case of an over- 
hung fly-wheel, the shaft having only one bearing, the point of maximum 
moment should be taken as the middle of the bearing, and its amount is 
very nearly the product of half the weight of the fly-wheel and the shaft 
into the distance of the middle of its hub from the middle of the bear- 
ing. The bending moment should be calculated and combined with the 
twisting moment as above shown, to obtain the equivalent twisting 
moment, and the diameter necessary at the point of maximum moment 
calculated therefrom. 

In the case of our six engines we assume that the weights of the fly- 
wheels, together with the shaft, are double the weight of fly-wheel rim 

obtained from the formula W= 785,400 -^^ (given under Fly-wheels); 

that the shaft is supported by an outboard bearing, the distance between 
the two bearings being 2 V2, 5, and 10 feet for the 10-in., 30-in., and 50-in. 
engines, respectively. The diameters of the fly-wheels are taken such 
that their rim velocity will be a little less than 6000 feet per minute. 

Engine No 1 2 3 4 5 6 

Diam. of cyl., inches 10 10 30 30 60 50 

Diara. of fly-wheel, ft.... 7.5 15 14.5 29 21 42 

Revs, per mi n 250 125 130 65 90 45 

Half wt. fly-wheel and 

shaft, lbs 268 536 5,968 11,936 26,384 52,769 

Lever arm for maximum 

moment, in 15 15 30 30 60 60 

Maximum bending mo- 
ment, in.-lbs 4020 8040 179,040 358,080 1,583,070 3,166,140 

As these are very much less than the bending moments calculated from 
the pressures on the crank-pin, the diameters already found are sufficient 
for the diameter of the shaft at the fly-wheel hub. 

In the case of engines with heavy band fly-wheels and with long fly- 
wheel shafts it is of the utmost importance to calculate the diameter of 
the shaft with reference to the bending moment due to the weight of the 
fly-wheel and the shaft. 

B. H. Coffey (Power, October, 1892) gives the formula for combined 
be nding a nd twisting resistance, Ti = 0.196 d^S, in wliich Ti = B ■¥ 
^B^+T^; r being the maximum, not the mean twisting moment; and 



1034 



THE STEAM-ENGINE. 



finds empirical working values for 0.196 S as below. He says: Four 
points should be considered in determining this value: First, the nature 
of the material; second, the manner of applying the loads, with shock 
or otherwise; third, the ratio of the bending moment to the torsional 
moment — the bending moment in a revolving shaft produces reversed 
strains in the material, which tend to rupture ft; fourth, the size of the 
section. Inch for inch, large sections are weaker than small ones. He 
puts the dividing hne between large and small sections at 10 in. diameter, 
and gives the following safe values of *S X 0.196 for steel, wrought iron, 
and cast iron, for these conditions. 

Value of 5 X 0.196. 



Ratio. 


Heavy Shafts 
with Shock. 


Light Shafts 

with Shock. 

Heavy Shafts 

No Shock. 


Light Shafts 
No Shock. 


Bto T. 


Steel. 


Wro't 
Iron. 


Cast 
Iron. 


Steel . 


Wro't 
Iron. 


Cast 
Iron. 


Steel . 


Wro't 
Iron. 


Cast 
Iron. 


3 to 10 or less 

3 to 5 or less 

1 to 1 or less 

B greater than T. . . 


1045 
941 
855 

784 


880 
785 
715 
655 


440 
393 
358 
328 


1566 
1410 
1281 
1176 


1320 
1179 
1074 
984 


660 
589 
537 
492 


2090 
1882 
1710 
1568 


1760 
1570 
1430 
1310 


880 
785 
715 
655 



Mr. Coffey gives as an example of improper dimensions the fly-wheel 
shaft of a 1500 H.P. engine at Willimantic, Conn., which broke while the 
engine was running at 425 H.P. The shaft was 17 ft. 5 in. long between 
centers of bearings, 18 in. diam. for 8 ft. In the middle, and 15 in. diam. 
for the remainder, including the bearings. It broke at the base of the 
fillet connecting the two large diameters, or 561/2 in. from the center of 
the bearing. He calculates the mean torsional moment to be 446,654 
inch-pounds, and the maximum at twice the mean; and the total weight 
on one bearing at 87,530 lbs., which, multipUed by 561/2 in., gives 
4,945,445 i n.-lbs. b ending moment at the fillet. Applying the formula 
ri = B+'^/j52 4.2^2 gives for equivalent twisting moment 9,971,045 in.- 
lbs. Substituting this value in the formula Ti = 0.196 *Sd3 gives for S 
the shearing strain 15,070 lbs. persq. in., or if the metal had a shearing 
strength of 45,000 lb., a factor of safety of only 3. Mr. Coffey considers 
that 6000 lb. is all that should be allowed for »S under these circum- 
stances. This would give d = 20.35 in. If we take from Mr. Coffey's 
table a value of 0.196 S = 1100, we obtain d^ = 9000 nearly, or d = 20.8 
in. instead of 15 in., the actual diameter. 

Length of Shaft-bearings. — There is as great a difference of opinion 
among writers, and as great a variation in practice concerning length of 
journal-bearings, as there is concerning crank-pins. The length of a 
journal being determined from considerations of its heating, the observa- 
tions concerning heating of crank-pins apply also to shaft-bearings, and 
the formulae for length of crank-pins to avoid heating may also be used, 
using for the total load upon the bearing the resultant of all the pres- 
sures brought upon it, by the pressure on the crank, by the weight of the 
fly-wheel, and by the pull of the belt. After determining this pressure, 
however, we must resort to empirical values for the so-called constants 
of the formulae, really variables, which depend on the power of the 
bearing to carry away heat, and upon the quantity of heat generated, 
which latter depends on the pressure, on the number of square feet of 
rubbing surface passed over in a minute, and upon the coefficient of 
friction. This coefficient is an exceedingly variable quantity, ranging 
from 0.01 or less with perfectly polished journals, having end-play, and 
lubricated by a pad or oil-bath, to 0.10 or more with ordinary oil-cup 
lubrication. 

Thurston says that the maximum allowable mean intensity of pressure 
may be, for all cases, computed by his formula for journals, I = PV -r- 
60,000 d, or by Rankine's, 1 = P(V+ 20) ^ 44,800 d, in which P is the 
mean total pressure in pounds, V the velocity of rubbing surface in feet 
per minute, and d the diameter of the shaft in inches. It must be borne 
in mind, he says, that the friction work on the main bearing next the crank 
is the sum of that due the action of the piston on the pin and that due 



DIMENSIONS OF PARTS OF ENGINES. 



1035 



that portion of the weight of wheel and shaft and of pull of the b61t which 
is carried there. The outboard bearing carries practically only the 
latter two parts of the total. The crank-shaft journals will be made 
longer on one side, and perhaps shorter on the other, than that of the 
crank-pin, in proportion to the work fallmg upon each, i.e., to their 
respective products of mean total pressure, speed of rubbing surfaces, and 
coefficients of friction. 

Unwin says: Journals running at 150 revolutions per minute are often 
only one diameter long. Fan shafts running 150 revolutions per minute 
have journals six or eight diameters long. The ordinary empirical mode 
of proportioning the length of journals is to make the length proportional 
to the diameter, and to make the ratio of length to diameter increase 
with the speed. For wrought-iron journals: 

Revs, per min= 50 100 150 200 250 500 1000 Z/d = 0.004 i^ +1. 
Length -i- diam. = 1.2 1.4 1.6 1.8 2.0 3.0 5.0. 

Cast-iron journals may have l-^-d =^ 9/io, and steel journals l-^cf=lV4, 
of the above values. 

Unwin gives the following, calculated from the formula !=» .4 H.P. -h r, 
in which r is the crank radius in inches, and H.P. the horse-power trans- 
mitted to the crank-pin. 

Theoretical Journal Length in Inches. 



Load on 
Journal in 


Revolutions of Journal per minute. 


Pounds. 


50 1 100 1 200 1 300 1 500 | 1000 


1,000 
2,000 
4,000 
5,000 
10,000 
15,000 


0.2 
0.4 
0.8 
1.0 
2. 
3. 
4. 
6. 
8. 
10. 


0.4 

0.8 

1.6 

2. 

4. 

6. 

8. 
12. 
16. 
20. 


0.8 

1.6 

3.2 

4. 

8. 

12. 

16. 

24. 

32. 

40. 


1.2 
2.4 
4.8 
6. 

12. 

18. 

24. 

36. 


2. 

4. 

8. 
10. 
20. 
30. 
40. 


4. 

8. 
16. 
20. 
40. 


20,000 




30 000 




40,000 






50.000 










Applying six different formulae to our six engines, we have: 



Engine No 


1 


2 


3 


4 


5 


6 






Diam. cyl 


10 

50 
250 
3,299 
268 

3,310 
3.84 

5.38 
4.27 
3.61 
5.22 
7.68 
3.33 


10 

50 
125 
3.299 
536 

3,335 
4.39 

2.71 
2.15 
1.82 
2.78 
6.59 
1.60 


30 
450 
130 

23,185 
5,968 

23,924 
11.35 

20.87 
16.53 
14.00 
21.70 
17.25 
12.00 


30 
450 

65 
23,185 
11,936 

26.194 
12.99 

11.07 
8.77 
7.43 
10.85 
16.36 
6.00 


50 

1,250 

90 
58,905 
26,470 

64,580 
20.58 

37.78 
29.95 
25.36 
35.16 
27.99 
20.83 


50 


Horse-power 


1,250 
45 


Revs, per min 


Mean pressure on crank-pin = S 

Half wt. ot fly-wheel and shaft = Q 

Resultant pressure on bearing 


58,905 
52,940 


Diam. of shaft journal 


79,200 
21 52 


Length of shaft journal: 
Marks, Z = 0. 0000325 fR^NCf =0.]0) 
Whitham,Z = 0.00005 15 f RtR {/ =0.\0) 
Thurston, l-=PV^ (60,000 d) . 


23.17 

18.35 
15 55 


Rankine, Z= P (7+20) -- (44,806<i).. . 
Unwin, 1= (0.004 R+])d 


22.47 
25.39 
10.42 


Unwin, Z=0.4H.P.-^r 


Average 


4.92 


2.99 


17.05 


10.00 


29.54 


19.22 





If we divide the mean resultant pressure on the bearing by the pro- 
jected area, that is, by the product of the diameter and length of the 
journal, using the greatest and smallest lengths out of the seven lengths 



1036 



THE STEAM-ENGINE. 



for each 'journal given above, we obtain the pressure per square inch 
upon the bearing, as follows: 



Engine No 


1 


2 


3 


4 


5 


6 






Press, per sq. in., shortest journal 

Longest journal 


259 
112 
175 


455 
115 
254 
173 


176 
97 
124 


336 
123 
202 
155 


151 
83 
106 


353 
145 


Average journal 


191 


Journal of length = diam 


175 



Many of the formulae give for the long-stroke engines a length of journal 
less than the diameter, but such short journals are rarely used in practice. 
The last line in the above table has been calculated on the supposition 
that the journals of the long-stroke engines are made of a length equal 
to the diameter. 

In the dimensions of Corliss engines given by J. B. Stanwood (Eng., 
June 12, 1891), the lengths of the journals for engines of diam. of cyl. 
10 to 20 in. are the same as the diam. of the cylinder, and a little more 
than twice the diam. of the journal. For engines above 20 in. diam. of 
cyl. the ratio of length to diam. is decreased so that an engine of 30 in. 
diam. has a journal 26 in. long, its diameter being 14i5/i6 in. These 
lengths of journal are greater than those given by any of the formul© 
above quoted. 

There thus appears to be a hopeless confusion in the various formulae 
for length of shaft journals, but this is no more than is to be expected 
from the variation in the coefficient of friction, and in the heat-conducting 
power of journals in actual use, the coefficient varying from 0.10 (or 
even 0.16 as given by Marks) down to 0,01, according to the condition 
of the bearing surfaces and the efficiency of lubrication. Thurston's 

PV 
formula, I = ^^' , » reduces to the form I = 0.000004363 PR, in which 

dO,UOO a 
P — mean total load on journal, and R = revolutions per minute. This 
is of the same form as Marks's and Whitham's formulae, in which, if/, the 
coefficient of friction, be taken a,t 0.10, the coefficients of PR are, respec- 
tively, 0.0000065 and 0.00000515. Taking the mean of these three 
formulae, we have I = 0.0000053 PR, if / = 0.10 or I = 0.000053 fPR 
for any other value of /. The author beUeves this to be as safe a formula 
as any for length of journals, with the limitation that if it brings a result 
of length of journal less than the diameter, then the length should be 
made equal to the diameter. Whenever, with/ = 0.10 it gives a length 
which is inconvenient or impossible of construction on account of limited 
space, then provision should be made to reduce the value of the coefficient 
of friction below 0.10 by means of forced lubrication, end play, etc., and 
to carry away the heat, as by water-cooled journal-boxes. The value of 
P should be taken as the resultant of the mean pressure on the crank, 
and the load brought on the bearing by the weight of the shaf t, fly-wh eel, 

etc., as calculated by the formula already given, viz., Ri = ^Q^ + S^ for 
horizontal engines, and Ri == Q -h S for vertical engines. 

For our six engines the formula I = 0.0000053 PR gives, with the 
limitation for the long-stroke engines that the length shall not be leas 
than the diameter, the following: 

Engine No 12 3 

Length of journal 4.39 4.39 16.48 

Pressure per square inch 

on journal 196 173 128 

Crank-shafts with Center-crank and 

center-crank engines, one of the crank-arms, and its adjoining journal, 
called the after journal, usually transmit the power of the engine to the 
work to be done, and the journal resists both twisting and bending mo- 
ments, while the other journal is subjected to bending moment only. 
For the after crank-journal the diameter should be calculated the same 
as for an overhung crank, using the formula for combined bending and 
twisting moment, Ti = B + \/ B^ -\- T^, in which Ti is the equivalent 
twisting moment, B the bending moment, and T the twi sting mo ment. 
This value of Ti is to be used in the formula, diameter = ^^5.1 TIS. The 



4 
12.99 



5 

30.80 



6 
21.52 



155 102 171 

Double-crank Arms. — ^In 



DIMENSIONS OP PARTS OF ENGINES. 



1037 



bending moment is taken as the maximum load on piston multiplied Dy 
one-fourth of the length of the crank-shaft between middle points of the 
■ two journal bearings, if the center is midway between the bearings, or 
by one-half the distance measured parallel to the shaft from the middle 
of the crank-pin to the middle of the after bearing. This supposes the 
crank-shaft to be a beam loaded at its middle and supported at the ends, 
but Whitham would make the bending moment only one-half of this, 
considering the shaft to be a beam secured or fixed at the ends, with a 
point of contraflexure one-fourth of the length from the end. The first 
supposition is the safer, but since the bending moment will in any case 
be much less than the twisting moment, the resulting diameter will be 
but little greater than if Whitham's supposition is used. For the for- 
ward journ al which is subjected to bending moment only, diameter ol 

shaft = ^10.2 B/S, in which B is the maximum bending moment and 
S the safe shearing strength of the metal per square inch. 

For our six engines, assuming them to be center-crank engines, and 
considering the crank-shaft to be a beam supported at the ends and 
loaded in the middle, and assuming lengths between centers of shaft 
bearings as given below, we have: 



Engine No | 1 


2 


1 3 


1 4 


3 1 6 


Length of shaft, 














assumed, in., L.. 


20 


24 


48 


60 


76 


96 


Max. press. on 














crank-pin, P 


7,854 


7,854 


70,686 


70,686 


196,350 


196.350 


Max. bending mo- 














ment, 5 = y4PL, 


39,270 


49,637 


848,232 


1,060,290 


3,729,750 


4,712,400 


Twisting mom., T 


47,124 


94,248 


1,060,290 


2,120,580 


4,712,400 


9,424,800 


Equiv. twist, mom. 














B + V52 + 2^2 . . . 


101,000 


156,000 


2,208,000 


3,430,000 


9.740,000 


15,240.000 


Diam. of after jour. 














^= V 8000 - 
Diam. of forw. jour., 


3.98 


4.60 


11.15 


13.00 


18.25 


21.20 


3.68 


3.99 


10.28 


11.16 


16.82 




^^= V 8000 •••• 


18.18 



The lengths of the journals would be calculated in the same manner as 
in the case of overhung cranks, by the formula I = 0.000053 fPR, in 
which P is the resultant of the mean pressure due to pressure of steam on 
the piston, and the load of the fly-wheel, shaft, etc., on each of the two 
bearings. Unless the pressures are equally divided between the two 
bearings, the calculated lengths of the two will be different; but it is 
usually customary to make them both of the same length, and in no case 
to make the length less than the diameter. The diameters also are usually 
made alike for the two journals, using the largest diameter found by 
calculation. 

The crank-pin for a center crank should be of the same length as for 
an overhung crank, since the length is determined from considerations 
of heating, and not of strength. The diameter also will usually be the 
same, since it is made great enough to make the pressure per square inch 
on the projected area (product of length by diameter) small enough to 
allow of free lubrication, and the diameter so calculated will be greater 
than Is required for strength. 

Crank-shaft with Two Cranks coupled at 90°. — If the whole 
power of the engine is transmitted through the after journal of the after 
crank-shaft, the greatest twisting moment is equal to 1.414 times the 
maximum twisting moment due to the pressure on one of the crank-pins. 
If r = the maximum twisting moment produced by the steam-pressure 
on one of the pistons, then jTi, the maximum twisting moment on the 
after part of the crank-shaft, and on the Une-shaft produced, when each 
crank makes an angle of 45° with the center line of the engine, is 1.414 T, 
Substituting this va lue in the formula for dia meter to resist sim ple 
torsion, viz.. d = nJ/ 5.1 T -^ S, we have d = ^5.1 X 1.414 T -r 5. or 



1038 THE STEAM-ENGINE. 



d = 1.932 ^ TIS, in which T is the maximum twisting moment pro- 
duced by one of the pistons, d = diameter in inches, and /S = safe 
working shearing strength of the material. For the forward journal of 
the after crank, and the after journal of the forward crank, the torsional 
moment is that due to the pressure of steam on the forward piston only, 
and for the forward journal of the forward crank, if none of the power 
of the engine is transmitted through it. the torsional moment is zero, and 
its diameter is to be calculated for bending moment only. 

For Combined Torsion and Flexure. — Let Bi = bending moment 
on either journal of the forward crank due to maximum pressure on 
forward piston, B2 = bending moment on either journal of the after crank 
due to maximum pressure on after piston, Ti = maximum twisting 
moment on after journal of forward crank, and T2 = maximum twisting 
moment on after journal of after crank, due to pressure on the after 
piston. 

The n equivale nt twisting moment on after journal of forward crank = 

On forward journal of after crank = B2 + ^Bz^ + Ti^. 

On after journal of after crank = ^2 + ^B2^ -h (Ti-\- ^2)2. 

These values of equivalent twisting mo ment are to be used in the 

formula for diameter of journals d = \/5.1 T /S, For the forward 

Journal of the forward crank-shaft d = '\yi0.2 Bi/S. 

It is customary to make the two journals of the forward crank of one 
diameter, viz., that calculated for the after journal. 

For a Three-cylinder Engine with cranks at 120°, the greatest 
twisting moment on the after part of the shaft, if the mxaximum pressures 
on the three pistons are equal, is equal to twice the maximum pressure on 
any one piston, and it takes place when two of the cranks make angles 
of 30° with the center line, the third crank being at right angles to it. 
(For demonstration, see Whitham's "Steam-engine Design," p. 252.) 
For combined torsion and flexure the same method as above given for 
two crank engines is adopted for the first two cranks: and for the 
third, or after crank, if all the power of the three cylinders is transmitted 
through it, we have the equivalent twisting moment on the forward 

Jo urnal = P3 + ^B^^ + (Ti + 7^2)2, and on the after journal = B3 + 

^Bz^-h (Ti-{- T2-h r.3)2, ^3 and Ts being respectively the bending and 
twisting moments due to the pressure on the third piston. 

Crank-shafts for Triple-expansion 3farine Engines, according to 
an article in The Engineer, April 25, 1890, should be made larger than the 
formulse would call for, in order to provide for the stresses due to the 
racing of the propeller in a sea-v/ay, w^hich can scarcely be calculated. 
A kind of unwritten law has sprung up for fixing the size of a crank- 
shaft, according to which the diameter of the shaft is made about 0.45 D, 
where D is the diameter of the high-pressure cvlinder. This is for solid 
shafts. When the speeds are high, as in war-ships, and the stroke short, 
the formula becomes 0.4 D, even for hollow shafts. 

The Valve-stem or Valve-rod. — The valve-rod should be designed 
to move the valve under the most unfavorable conditions, which are when 
the stem acts bv thrusting, as a long column, when the valve is unbalanced 
(a balanced valve may become unbalanced bv the joint leakine:) and when 
It IS imperfectly lubricated. The load on the valve is the product of the 
area mto the greatest unbalanced pressure upon it per square inch, and 
the coefficient of friction mav be as high as 20%. The product of this 
coeflacient and the load is the force necessary to move the valve, which 
equals the maximum thrust on the valve-rod. From tliis force the 
diameter of the valve-rod may be calculated by the usual formula for 
colum ns. A n empirical formula given by Seaton is: Diam. of rod = 
d = Vlbp/F, in which I = length, and b = breadth of valve, in inches; 
p = maximum absolute pressure on the valve in lb. per sq. in., and 
F a coefficient whose values are, for iron: long rod 10,000, short 12,000; 
for steel: long rod 12,000, short 14.500. 

Whitham gives the short empirical rule; Diam. of valve-rod = 1/30 
diam. of cyl. = 1/3 diam. of piston-rod. 



DIMENSIONS OF PARTS OF ENGINES. 1039 

The Eccentric. — Diam. of eccentric-sheave = 2.4 X throw of eccen- 
tric + 1.2 X diam. of shaft. D = diam. of valve rod (Seaton). 

Breadth of the sheave at the shaft = 1.15 X D + 0.65 in. 

Breadth of the sheave at the strap = -D + 0.6 in. 

Thickness of metal around the shaft. . . . = 0.7 X D + 0.5 in. 
Thickness of metal at circmnference . . . . = 0.6 X -D -f 0.4 in. 

Breadth of key =0.7 X D + 0.5 in. 

Thickness of key = 0.25 X D + 0.5 in. 

Diam. of bolts connecting parts of strap. = 0.6 X £> 4- 0.1 in. 

Thickness of Eccentric-strap. 

When of bronze or malleable cast iron : 

Thickness of eccentric-strap at the middle. . . = 0.4 X JD + 0.6 in. 

Thickness of eccentric-strap at the sides =0.3 X D -\- 0.5 lq. 

When of wrought iron or cast steel : 

Thickness of eccentric-strap at the middle. . . = 0.4 X D -\- 0.5 in. 

Thickness of eccentric-strap at the sides = 0.27 X D -{- 0.4 in. 

The Eccentric-rod. — The diameter of the eccentric-rod in the body 
and at the eccentric end may be calculated in the same way as that of 
the connecting-rod, the length being taken from center of strap to 
center of pin. Diameter at the link end = 0.8D + 0.2 in. 

This is for wrought iron; no reduction in size should be made for steel. 

Eccentric-rods are often made of rectangular section. 

Reversing-gear should be so designed as to have more than sufficient 

strength to withstand the strain of both the valves and their gear at the 

same time under the most unfavorable circumstances; it will then have 

the stiffness requisite for good working. 

Assuming the work done in reversing the hnk-motion, TF, to be only 
that due to overcoming the friction of the valves themselves through their 
whole travel, then, if T be the travel of valves in inches, for a compound 
engine 

w = -^ /ZJ<_&X_P\ _r ( U Xbi XPi V 
12 \ 5 /'^12\ 5 y* 

Zi, 6i, and pi being length, breadth, and maximum steam-pressure on 
valve of the second cylinder; and for an expansive engine 

,.= .xX(iX|X_.).o.^ax6X.). 

To provide for the friction of link-motion, eccentrics, and other gear, 
and for abnormal conditions of the same, take the work at one and a half 
times the pbove amount. 

To find the strain at any part of the gear having motion. when reversing, 
divide the work so found by the space moved through by that part in 
feet ; the quotient is the strain in pounds ; the size may be found from the 
ordinary rules of construction for any of the parts of the gear. (Seaton.) 

Current Practice in Engine Proportions, 1897. (Compare pages 1021 
to 1039.) — A paper with this title by Prof. John H. Barr, in Trans, 
A. S. M. E., xviii, 737, gives the results of an examination of the propor- 
tions of parts of a great number of single-cylinder engines made by 
different builders. The engines classed as low speed (L. S.) are Corhss 
or other long-stroke engines usually making not more than 100 or 125 revs, 
per min. Those classed as high speed (H. S.) have a stroke generally of 
1 to 1 1/2 diameters and a speed of 200 to 300 revs, per min. The results 
are expressed in formulas of rational form with empirical coefficients, 
and are here abridged as follows (dimensions in inches): 

Thickness of Shell, L. S. only. — t = CD -\- B; D = diam. of piston in 
in. ; S = . 3 in. ; C varies from . 04 to . 06, mean = 0.05. 

Flanges and Cylinder-heads.^ 1 to 1.5 X thickness of shell, mean 1.2. 

Cylinder-head Studs. — No studs less than 3/4 in. nor greater than is/gin. 
diam. Least number, 8, for 10 in. diam. Average number = 0.7 D. 
Average diam. = D/40 -f 1/2 in 

Ports and Pipes. — a = area' of port (or pipe) in sq. in.: A = area of 
piston, sq. m.; F = mean piston-soeed. ft. per min.: a = AV /C,m which 
C=mean velocity of steam through the port or pipe in ft. per min. 



1040 THE STEAM-ENGINE. 

Ports, H. S. (same ports for steam as for exhaust). — C = 4500 to 
6500, mean SSOO. For ordinary piston-speed of 600 ft. per min. a = 
KA: K = 0.09 to 0.13, mean 11 

Steam-ports, L. S. — C = 5000 to 9000, mean 6800; K = 0.08 to 0.10, 
mean 0.09. 

Exhaust-ports, L. S. — C = 4000 to 7000, mean 5500; X = 0.10 to 0.125, 
mean 0. 11. 

Steam-pipes, n. S. — <? = 5800 to 7000, mean 6500. If rf = diam. of 
pipe and D = diam. of piston, rf = . 29 D to . 32 D, mean . 30 D. 

Steam-pipes, Jj.S. — C = 5000 to 8000, mean 6000; rf = 0.27 to 0.35 D; 
mean . 32 D. 

Exhaust-pipes, H. S. — C = 2500 to 5500, mean 4400; cf = 0.33 to 
0.50 D, mean 0.37 D. 

Exhaust-pipes, L. S. — C = 2800 to 4700, mean 3800; d = 0.35 to 
. 45 D, mean . 40 D 

n fr?f ?f fj^^^^^' — ^ = face; D = diameter. F = CD. H. S.: C = 
0.30to0.60, meanO.46. L. S.: C = 0.25 to 0.45. mean 0.32. 

fiston-rods, — c? = diam. of rod; D = diam. of piston; L = stroke, in.: 
d= (7 ^DL. H. S.: C= 0.12 to 0.175, mean 0.145. L. S.: C= 0.10 to 
0.13, mean 0.11. 

Connecting-rods. — H. S. (generally 6 cranks Ions:, rectansrular section): 

= breadth; h = height of section; Li = length of connecting-rod; 
D = diam. of piston; 5 = C ^DLv, (7 = 0.045 to 0.07, mean 0.057; 
h =» Kb: i? = 2.2 to 4, mean 2.7. L. S. (generally 5 cranks long, cir- 
cular sections only): C = 0.082 to 0. 105. mean 0.092. 

Cross-head Slides. — Maximum pressure in lbs. per sq. in. of shoe, due 
to the vertical component of the force on the connecting-rod. H. S.: 
10.5 to 38, mean 27. L. S.: 29 to 58, mean 40. 

Cross-head Pins. — I = length; d = diam.; projected area = a = dl = 
CA; A = area of piston; I = Kd. H. S.: C = 0.06 to 0.11, mean 0.08; 
/JL = 1 to2, mean 1.25. L. S.: C = 0.054 to 0.10, mean 0.07; K = 1 to 
1.5, mean 1.3. 

Crank-pin. — H.P.= horse-power of engine; L= length of stroke; 

1 = length of pin; I = C X H.P:/L+ B; d = diam. of pin; A= area of 
piston; dl == KA. H. S.: C = 0. 13 to 0.46, mean 0.30; B = 2.5 in.; 
K = 0.17 to 0.44, mean 0.24. L. S.: C = 0.4 to 0.8, mean 0.6; 5 = 

2 in.; K = 0.065 to 0.115, mean 0.09. 

Crank-shaft Main Journal. — d= C ^H.P. ^ N;d= diam.; Z = length; 
N = revs, per min.; projected area = MA; A = area of piston. H. S.: 
C = 6.5 to 8.5, mean 7 .3; l = Kd; K = 2 to S, mean 2.2; M = 0.37 to 
0.70, mean 0.46. L. S.: C = 6 to 8, mean 6.8; K= 1.7 to 2.1, mean 
1.9; Af = 0.46 to 0.64, mean 0.56. 

Piston-speed. — H. S.: 630 to 660, mean 600; L. S.: 500 to 850, mean 
600. 

Weight of Reciprocating Parts (piston, piston-rod, cross-head, and one- 
half of connecting-rod). — W = CD^ -^ LN^\ D = diam. of piston; 
L = length of stroke, in.; A^ = revs, per min. H. S. only: C = 1,200,009 
to 2,300,000, mean 1,860,000. 

Belt-surface per I.H.P. — S = CXB..F.+ B; 5 = product of width of 
belt in feet by velocity of belt in ft. per min. H. S.: C = 21 to 40, mean 
28;B = 1800. L. S.; S = CX H.P., C = 30 to 42, mean = 35. 

Fly-wheel (H. S. only). — Weight of rim in lbs.: W = C X H.P.-^ 
Di2iV3; Dl = diam. of wheel in in.; C = 65 X l-O^o to 2 X 10^2 mean = 
12 X 10", or 1,200,000,000,000. 

Weight of Engine per I.H.P. in lbs., including fly-wheel. — W = 
C X H.P. H. S.: C= 100 to 135, mean 115. L. S.: C = 135 to 240, 
mean 175. 

Current Practice in Steam-engine Design, 1909. (Ole N. Trooien, 
Bull. Univ'y of Wis., No. 252; Am. Mach., April 22, 1909.) — Practice in 
proportioning standard steam-engine parts has settled down to certain 
definite values, which have by long usage been found to give satisfactory 
results. These values can readily be expressed in formulas showing the 
relation between the more important factors entering the problem of 
design. 

These formulae may be considered as partly rational and partly em- 



DIMENSIONS OF PARTS OF ENGINES. 1041 

pirical; rational in the sense that the variables enter in the same manner 
as in a strict analysis, and empirical in the sense that the constants, 
instead of being obtained from assumed working strength, bearing 
pressures etc., are derived from actual practice and include elements 
whose values are not accurately known but which have been found safe 
and economical. 

The following symbols of notation are used in the formulas given: 
D = diameter of piston. A = area of piston. L = length of stroke. 
p = unit steam pressure, taken as 125 lbs. per sq. in. above exhaust as 
a standard pressure. H.P. = rated horse-power. N = revs, per min. 
Cand K, constants, and d = diam. and ? = length of unit under consider- 
ation. All dimensions in inches. 

The commercial point of cut-off is taken at 1/4 of the stroke. H. S., 
high-speed engines. L. S., low-speed, or long-stroke engines. 

Piston Rod. — d = C <^DL. H. S.t C = 0.15 (min., 0.125; max., 
0.187): L. S.: C = 0.114 (min., 0.1; max., 0.156). 

C2/h*n(fer. -— Thickness of wall in ins. = CD + 0.28. C =0.054 
(min., 0.035: max., 0.072). Clearance volume 5 to 11% for H.S. engines, 
and from 2 to 5% for Corliss engines. 

Stud Bolts. — Number =0 . 72 D for H. S. (0 . 65 D for Corliss.) Diam. 
in ins. = 0.04 D 4- 0.375. 

Batio (C) of Stroke to Cylinder Diameter (L/D). — For AT > 200, 
C = 1.07 (min., 0.82: max., 1.55): for N = 110 to 200, C = 136 (min.. 
1.03: max., 1.88); for AT < 110 (Corliss engines), C = (L - 8)/D = 1.63 
(min., 1.15; max., 2.4). 

Piston. — Width of face in ins. = CD +1. Mean value of C = 0.32 
for H. S. (0.26 for Corliss). Thickness of shell = thickness of cylinder 
wall X 0.6 (0.7 for Corliss). 

Piston Speeds. — H. S., 605 ft. per min. (min. 320; max., 920): Corliss, 
592 ft. per min. (min., 400; max., 800). 

Cross-head. — Area of shoes in sq. ins. =0.53 A (min., 0.37; max., 
0.72). 

Cross-head Pin. — Diameter = . 25 D (min., 0.17; max., 0.28). 
Length for H.S. = diam. X 1.25 (min., 1; max., 1.5); for Corliss =» 
diam. X 1.43 (min., 1; max., 1.9). 

Connecting-rods. — Breadth for H. S. =0.073 ^L^D (min., 0.55; max., 
0.094). Height = breadth X 2. 28 (min., 1.85; max., 3). For L. S., diam. 
of circular rod = . 092 V^^D (min., 0.081; max., 0.104). L^ = length 
center to center of bearings. 

Crank-pin. — Diam. for H.S. center-crank engines = . 4 D (min., 
0.28; max., 0.526). Diam. for side-crank Corliss = 0.27 D (min., 
0.21; max., 0.32). Length for H. S. = diam. X 0.87 (min., 0.66; 
max., 1.25). Length for Corliss = diam. X 1.14 (min., 1; max., 1.3). 

Main Journals of Crank-shaft. — For H. S. center-crank engines, diam. 
= 6.6 \Jb..F ./N (min., 5.4; max., 8.2). For Corliss, diameter = 7.2 
[^(H.P./A^)-0.3] (min., 6.4; max., 8). 

Fly-wheels. — Total weight in pounds for H.S. up to 175 H.P. 
= 1,300,000,000,000 H.P. /Di2A^^ where Di = diam. of wheel in ins. 
(min., 660,000,000,000; max., 2,800,000,000,000). For larger H.S. 
engines, weight = (C X B..F. /Di^m) + 1000, where C = 720,000,000,000 
(min., 330,000,000,000; max., 1,140,000,000,000). For Corliss engines, 
weight = (C X H.P. IDi^N^)-K, where C = 890,000,000,000 (min., 625,- 
000,000,000; max., 1,330,000,000,000), and K = 4000 (min., 2,800; max., 
6000). Diam. in ins.= 4.4X length of stroke. 

Belt Surface per I. H.P, — Square feet of belt surface per minute {S) 
for H. S. = H.P. X 26.5 (min., 10; max., 55). For Corliss engines, 
*S = 1000 + (21 X H.P.) (min., 18.2; max., 35). 

Velocity of Wheel Rim. — For H. S. 70 ft. per sec. (min., 48; max., 
70); for Corliss, 68 ft. per sec. (min., 40; max., 68). 

Weight of Reciprocating Parts (Piston + piston rod + crosshead + 1/2 
connecting-rod). — Weight in lbs. W = (D^ / LN^) X 2,000,000 (min., 
1,370,000; max., 3,400,000). Balance weight opposite crank-pin = 
0.75 TF. 

Weight of engine per I. H.P. —Lbs. per I. H.P. for belt-connected H. S. 



i 



1042 THE STEAM-ENGINE. 

engines = H.P. X 82 (min., 52; max., 120). Do., for Corliss = H.P. 
X 132 (min., 102; max., 164). 

Shafts and Bearings of Engines. (James Christie, Proc 
Engrs. Club of Phila., 1898.) — The dimensions are determined by two 
independent considerations: 1. Sufficient size to prevent excessive 
deflection or torsional yield. 2. To provide sufficient wearing surface; 
to prevent excessive wear of journals. Usually, when the first condi- 
tion is preserved, the other is provided for. When the bearings are 
flexible, — and excessive deflection within the limit of ordinary safety 
affects nothing external to the bearings, — considerable deflection can be 
tolerated. When bearings are rigid, or deflection may derange external 
mechanism, — for example, an overhung crank, — then the deflection 
must be more restricted. The effect of deflection is to concentrate 
pressure on the ends of journals, rendering the apparent bearing surface 
Inefficient. 

In direct-driven electric generators a deflection of 0.01 in. per foot of 
length has caused much trouble from hot bearings. I have proportioned 
such shafts so that the deflection will not exceed one-half this extent. 

In some shafts, especially those having an oscillating movement, 
torsional elasticity is a prime consideration, and the limits can be known 
only by experience. Reuleaux says: "Limit the torsional yield to 0.1 
degree per foot of length." This in some cases can be readily tolerated; 
in others, it has proved excessive. I have adopted the following as a 
general guide: Permissible twist per foot of length = 0.10 degree for 
easy service, without severe fluctuation of load; 0.075 degree for fluctu- 
ating loads suddenly applied; 0.050 degree for loads suddenly reversed. 

Sufficiency of wearing surface and the limitation of pressure per unit 
Of surface are determined by several conditions: 1. Speed of movement. 
2. Character of material. 3. Permissible wear of journals or bearings. 
4. Constancy of pressure in one direction. 5. Alternation of the direction 
of pressure. 

Taking the product of pressure per sq. in. of surface in lbs,, and speed 
of movement in ft. per min., we obtain a quantity, wiiich we can term 
the permissible foot-pounds per minute for each sq. in. of wearing surface. 
This product varies in good practice under various conditions from 
50,000 to 500,000 ft. -lbs. per min. For instance, good practice, in later 
years, has largely increased the area of crosshead slide surfaces. For 
crossheads having maximum speed of 1000 feet per minute, the pressure 
per inch of wearing surface should not exceed 50 pounds, giving 50,000 
ft .-lbs. per min.; whereas crank-pins of the requisite grade of steel, with 
good lining metal in the boxes and efficient lubrication, will endure 
200,000 ft.-lbs. per min. satisfactorily, and more than double this when 
speeds are very high and the pressure intermittent. On main shafts, 
with pressures constant in one direction, it is advisable not to exceed 
50,000 ft.-lbs. per min. for heavily loaded shafts at low velocity. This 
may be increased to 100,000 for lighter loads and higher velocities. It 
can be inferred, therefore, that the product of speed and pressure cannot 
be used, in any comprehensive way, as a rational basis for proportioning 
wearing surfaces. The pressure per unit of surface must be reduced as the 
speed is increased, but not in a constant ratio. A good example of 
journals severely tested are the recent 110,000-pound freight cars, wliich 
bear a pressure of 400 lbs. per sq. in. of journal bearing, and at a speed 
of ten miles per hour make about 60,000 foot-pounds per minute. 

Calculating the Dimensions of Bearings. (F. E. Cardullo, Mach'y, 
Feb., 1907.) — The durability of the lubricating lilm is affected in great 
measure by the character of the load that the bearing carries. When the 
load is unvarying in amount and direction, as in the case of a shaft carry- 
ing a heavy bandwheel, the film is easily ruptured. In those cases where 
the pressure is variable in amount and direction, as in railway journals 
and crank-pins, the film is much more durable. When the journal only 
rotates through a small arc, as with the wrist-pin of a steam-engine, the 
circumstances are most favorable. It has been found that when all other 
circumstances are exactly similar, a car journal v/ill stand about twice 
the unit pressure that a fly-wheel journal will. A crank-pin, since the 
load completely reverses every revolution, will stand three times, and a 
wrist-pin v\111 stand four times the unit pressure that the fly-wheel journal 
wilL 



DIMENSIONS OF PARTS OF ENGINES. 1043 

The amount of pressure that commercial oils will endure at low speeds 
without breaking down varies from 500 to 1000 lbs. per sq. in., where the 
load is steady. It is not safe, however, to load a bearing to this extent, 
since it is only under favorable circumstances that the film will stand this 
pressure without rupturing. On this account, journal bearings should 
not be required to stand more than two-thirds of tliis pressure at slow 
speeds, and the pressure should be reduced when the speed increases. 
The approximate unit pressure which a bearing will endure without 
seizing is p = PK -^ (D.Y + K) (1\ p = allowable pressure in lbs. per 
sq. in. of projected area, D = diam. of the bearing in ins., N = r.p.m. 
and P and K depend upon the kind of oil, manner of lubrication, etc. 

P is the maximum safe unit pressure for the given circumstances, at a 
very slow speed. In ordinary cases, its value is 200 for collar thrust 
bearings, 400 for shaft bearings, 800 for car journals, 1200 for crank-pins, 
and 1600 for wrist-pins. In exceptional circumstances, these values 
may be increased by as much as 50%. but only when the workmanship 
is of the best, the care the most skillful, the bearing readily accessible, 
and the oil of the best quality, and unusually viscous. In the great units 
of the Subway power plant in New York, the value of P for the crank- 
pins is 2000. 

The factot" K depends upon the method of oiling, the rapidity of cool- 
ing, and the care which the journal is likely to get. It will have about 
the following values: Ordinary work, drop-feed lubrication, 700; first- 
class care, drop-feed lubrication, 1000: force-feed lubrication or ring- 
oiling, 1200 to 1500; extreme Umit for perfect lubrication and air-cooled 
bearings, 2000. The value 2000 is seldom used, except in locomotive 
work where the rapid circulation of the air cools the journals. Higher 
values than ttiis may only be used in the case of water-cooled bearings. 

In case the bearing is some form of a sliding shoe, the quantity 240 V 
should be substituted for the quantity DN, V being the velocity of rubbing 
in feet per second. There are a few cases where a unit pressure sufficient 
to break down the oil film is allowable, such as the pins of puncliing and 
shearing machines, pivots of swing bridges, etc. 

In general, the diameter of a shaft or pin is fixed from considerations of 

strength or stiffness. Having obtained the proper diameter, we must 

next make the bearing long enough so that the unit pressure shall not 

exceed the required value. This length may be found by the equation: 

L == {W ^ PK) X{N + KID), (2) 

where L is the length of the bearing in ins., W the load upon it in lbs., 
and P, K, N, and D are as before. 

A bearing may give poor satisfaction because it is too long, as well as 
because it is too short. Almost every bearing is in the condition of a 
loaded beam, and therefore it has some deflection. 

Shafts and crank-pins must not be made so long that they will allow 
the load to concentrate at any point. A good rule for the length is to 
make the ratio of length to diameter about equal to Vs ^N. This 
quantity may be diminished by from 10 to 20% in the case of crank-pins 
and increased in the same proportion in the case of shaft bearings, but 
it is not wise to depart too far from it. In the case of an engine making 
100 r.p.m., the bearings would be by this rule from 1 1/4 to 1 1/2 diams. in 
length. In the case of a motor running at 1000 r.p.m., the bearings 
would be about 4 diams. long. 

The diameter of a shaft or pin must be such that it will be strong and 
stiff enough to do its work properly. In order to design it for strength 
and stiffness, it is first necessary to know its length. This may be assumed 
tentatively from the equation 

L = 20TFV^h-PK (3) 

The diameter may then be found by any of the standard equations for 
the strength of shafts or pins given in the different works on machine 
design. [See The Strength of the Crank-pin, page 1027.] The length is 
then recomputed from formula No. 2, taking tliis new value if it does 
not differ materially from the one first assumed. If it does, and espe- 
cially if it is greater than the assumed length, take the mean. value of the 
assumed and computed lengths, and try again. 
Example. — We will take the case of the crank-pin of an engine with a 



1044 THE STEAM-ENGINE. 

20-in. cylinder, ninning at 80 r.p.m., and having a maximum unbalanced 
steam pressure of 100 lbs. per sq. in. The total steam load on the piston 
is 31,400 pounds. P is taken at 1200, and K as 1000. We will therefore 
obtain for our trial length: 

L=(20X 31,400 X v^80)-i- (1200X1000) = 4. 7, or say 43/4 ins. 

In order that the deflection of the pin shall not be sufficient to destroy 

the lubricating film we have 

D = 0.09 ^WL^, 

which limits the deflection to 0.003 in. This gives D= 3.85 or say 37/8 i 
ins. With this diameter, formula No. 2 gives L = 8.9, say 9 ins ^ 

The mean of this value and the one obtained before is about 7 ins- 
Substituting this in the equation for the diameter, we get 51/4 ins bub- 
stituting this new diameter in equation No. 2 we have L = 7 . 05, say 

Probably most good designers would prefer to take about half an inch 
off the length of this pin, and add it to the diameter, making it 53/4 X6I/2 
inches, and this will bring the ratio of the length to the diameter nearer 

^Engine-frames or Bed-plates.— No definite rules for the design 
of engine-frames have been given by authors of works on the steam- 
engine. The proportions are left to the designer who uses * rule of ' 
thumb" or copies from existing engines. F. A. Halsey (Am. Mach., 
Feb. 14, 1895) has made a comparison of proportions of the frames of 
horizontal Corliss engines of several builders. The method of comparison 
is to compute from the measurements the number of square inches in the 
smallest cross-section of the frame, that is, immediately behind the 
pillow block, also to compute the total maximum pressure upon the piston, 
and to divide the latter quantity by the former. The result gives the 
number of pounds pressure upon the piston allowed for each square inch 
of metal in the frame. He finds that the number of lbs. per sq. in. of 
smallest section of frame ranges from 217 for a 10 X 30 in. engine up to 
575 for a 28 X 48 in. A 30 X 60 in. engine shows 350 lbs., and a 32-in. 
engine which has been running for many years shows 667 lbs. Generally 
the, strains increase with the size of the engine, and more cross-section of 
metal is allowed with relatively long strokes than with short ones. 

From the above Mr. Halsey formulates the general rule that in engines 
of moderate speed, and having strokes up to 1 1/2 times the diameter of the 
cylinder, the load per square inch of smallest section should be for a 10-in. 
engine 300 lbs., which figure should be increased for larger bores up to 500 
lbs. for a 30-in. cylinder of the same relative stroke. For high speeds or 
for longer strokes the load per square inch should be reduced. 

FLY-WHEELS. 

The function of a fly-wheel is to store up and to restore the periodical 
fluctuations of energy given to or taken from an engine or machine, and 
thus to keep approximately constant the velocity of rotation. Rankine 

AE 
calls the quantity r— pr the coefficient of fluctuation of speed or of un- 

steadiness, in which Eq is the mean actual energy, and AE the excess 
of energy received or of work performed, above the mean, during a 
given interval. The ratio of the periodical excess or deficiency of energy 
AE to the whole energy exerted in one period or revolution General 
Morin found to be from i/e to 1/4 for single-cylinder engines using expan- 
sion; the shorter the cut-off the higher the value. For a pair of engines 
with cranks coupled at 90° the value of the ratio is about 1/4, and for 
three engines with cranks at 120°, V12 of its value for single-cylinder 
engines. For tools working at intervals, such as punching, slotting and 
plate-cutting machines, coining-presses, etc., A^; is neariy equal to the 
whole work performed at each operation. 

A fly-wheel reduces the coefficient -r-^r to a certain fixed amount, being 

about 1/32 for ordinary machinery, and 1/50 or Voo for machinery for fine 
purposes. 



FLY-WHEELS. 1045 

If m be the reciprocal of the intended value of the coeflQcient of fluc- 
tuation of speed, aE the fluctuation ot energy, / the moment of inertia 

of the fly-wheel alone, and Gq its mean angular velocity, / = -^ — As 

the rim of a fly-wheel is usually heavy in comparison with the arms, 
/ may be taken to equal Wr^, in which W = weight of rim in pounds, and 

r the radius of the wheel; then W = —^yt "^ ~2 — , if v be the velocity 

of the rim in feet per second. The usual mean radius of the fly-wheel 
In steam-engines is from three to five times the length of the crank. The 
ordinary values of the product mg, the unit of time being the second, lie 
between 1000 and 2000 feet. (Abridged from Rankine, S. E., p. 62.) 
Thurston gives for engines with automatic valve-gear W = 250,000 

ASv 
• p,^ . in which A = area of piston in square inches, S = stroke in feet, 

p = mean steam-pressure in lbs. per sq. in., R = revolutions per minute, 
D = outside diameter of wheel in feet. Thurston also gives for ordinary 
forms of non-condensing engine with a ratio of expansion between 3 and 

aAS 
5, TF = 7^^-F^, in which a ranges from 10,000,000 to 15,000,000, averaging 

12,000.000. For gas-engines, in which the charge is fired with every 
revolution, the American Machinist gives this latter formula, with a 
doubled, or 24,000,000. Presumably, if the charge is fired every other 
revolution, a should be again doubled. 

Rankine ("Useful Rules and Tables," p. 247) gives 1^=475,000 

yj^^ni ' ^^ which V is the variation of speed, per cent of the mean speed. 

Thurston's first rule above given corresponds with this if we take V = 1.9. 

Hartnell {Proc. Inst. M. E., 1882, 427) says: The value of F, or the 
variation permissible in portable engines, should not exceed 3% with an 
ordinary load, and 4% when heavily loaded. In fixed engines, for ordi- 
nary purposes, F = 2V2 to 3%. For good governing or special purposes, 
such as cotton-spinning, the variation should not exceed 1 1/2 to 2%. 

F. M. Rites (Trans. A. S. M. E., xiv, 100) develops a new formula for 

^ y T TJ p 

weight of rim, viz., W =» — ^3 ' ^ ' ' ♦ and weight of rim per horse-power 

" -5^, in which C varies from 10,000,000,000 to 20,000,000,000; also 

using the latter value of C, he obtains for the energy of the fly-wheel 
Mv^ ^ _W_ (3.14)2 Z)2i^2 ^ CX H.F. (3.14)2 7)2/^2 ^ 850.000 H.P , pj 

2 64.4 3600 i^3i)2 x 64 . 4 X 3600 R 

wheel energy per H.P. = 850,000 -^ R. 

The Umit of variation of speed with such a weight of wheel from excess 
of power per fraction of revolution is less than 0.0023. 

The value of the constant C given by Mr. Rites was derived from 
practice of the Westinghouse single-acting engines used for electric- 
lighting. For double-acting engines in ordinary service a value of C — 
5,000,000,000 would probably be ample. 

From these formulae it appears that the weight of the fly-wheel for a 
given horse-power should vary inversely with the cube of the revolutions 
and the square of the diameter. 

J. B. Stanwood (Eng'g, June 12, 1891) says: Whenever 480 feet Is the 
lowest piston-speed probable for an engine of a certain size, the fly-wheel 
weight for that speed approximates closely to the formula 

W = 700,000 (Ps -^ D2/22. 
W = weight In pounds, d = diameter of cylinder In Inches, 8 =» stroke 
in inches, D = diameter of wheel in feet, R = revolutions per minute, 
corresponding to 480 feet piston-speed. 

In a Ready Reference Book published by Mr. Stanwood, Cincinnati, 
1892, he gives the same formula, with coefficients as follows: For slide- 
valve engines, ordinary dutv, 350,000; same, electric fighting, 700,000; 
for automatic high-speed engines. 1.000.000: for Corliss engines, ordinary 
duty 700,000, electric lighting 1,000,000. 



1046 



THE STEAM-ENGINE. 



Thurston's formula above given, W = aAS ^ RW^ with a =12,000,000 
if reduced to terms of d and s in ins., becomes W = 785,400 d^s -=- RW^. 
If we reduce it to terms of horse-power, we have I.H.P. = 2 ASPR -t- 
33,000, in which P = mean effective pressure. Taking this at 40 lbs., 
we obtain W = 5,000,000,000 I.H.P. ^ RW^. If mean effective pres- 
sure = 30 lbs., then W = 6,666,000,000 I.H.P. ^ RW^. 

Emil Theiss (A??!. Mach., Sept. 7 and 14, 1893) gives the following 
values of d, the coefficient of steadiness, which is the reciprocal of what 
Rankine calls the coefficient of fluctuation: 
For engines operating — 

Hammering and crushing machinery d = 5 

Pumping and shearing machinery rf = 20 to 30 

Weaving and paper-making machinery d = 40 

Milling machinery d = 50 

Spinning machinery d = 50 to 100 

Ordinary driving-engines (mounted on bed- 
plate) , belt transmission d = 35 

Gear-wheel transmission d = 50 

Mr. Theiss's formula for weight of fly-wheel in pounds is W = iX 
dXlHP 

T.^ ' — •*, where d is the coefficient of steadiness, V the mean velocity 

of the fly-wheel rim in feet per second, n the number of revolutions per 
minute, i = a coefficient obtained by graphical solution, the values of 
which for different conditions are given in the following table. In 
the lines under "cut-off," p means "compression to initial pressure," 
and O "no compression." 

Values of i. Single-cylinder Non-condensing Engines. 



Piston- 


Cut-off, 1/6. 


Cut-off, 1/4. 


f Cut-off, 1/3. 


Cut-off, 1/2. 


speed, ft. 
per min. 


Comp. 
P 





Comp. 

P 





Comp. 

P 





Comp. 
P 





200 
400 
600 


272.690 
240.810 
194,670 


218.580 
187.430 
145.400 


242.010 
208.200 
168.590 
162.070 


209.170 
179,460 
136.460 
135.260 


220,760 i 201.920 
188.510 170.040 
165,210 146.610 


193,340 
174.630 


182.840 
167.860 


800 


158.200 


108.690 











Single-cylinder Condensing Engines. 



*,^G Cut-off, 1/8. 



f^aS 



Comp. 
P 







Cut-off, 1/6. 



Comp.' 

P i 



Cut-off, 1/4. 



Comp. 
P 



Cut-off, 1/3. 



Comp. 
P 



Cut-off, 1/2. 



Comp. 
P 



200 
400 
600 



265.560 176.560 234.160 
194,550 117.870174.380 
148,780| 140,090 



173,660 204.210 
118,3501164.720 



167.140189.600 
133,080,174,630 



161.830172.690 
151.680: 



156.990 



Two-cylinder Engines, Cranks at 90°. 



Piston- 


Cut-off, 1/6. 


Cut-off, 1/4. 


Cut-off, 1/3. 


Cut-off, 1/2. 


speed, ft. 
per min. 


Comp. 
P 





Comp. 

P 





Comp. 

P 





Comp. 

P 





200 
400 
600 
800 


71.980 
70,160 
70.040 
70.040 


] 

[ Mean 

[60.140 


59,420 
57.000 
57.480 
60.140 


Mean 
f 54.340 

J 


49,272 
49,150 
49.220 


1 Mean 
[ 50.000 

J 


37.920 
35.000 


i Mean 
( 36.950 



Three-cylinder Engines, Cranks at 120°. 



Piston- 


Cut-off, 1/6. 


Cut-off, 1/4. 


Cut-off, 1/3. 


Cut-off, 1/2. 


speed, ft. 
per min. 


Comp. 

P 





Comp. 

.P 





Comp. 

P 





Comp. Q 

P 


200 
800 


33.810 
30.190 


32.240 
31.570 


33.810 
35.140 


35.500 
33.810 


34.540 
36,470 


33,450 
32.850 


35.260 32.370 
33.810 32.370 



As a mean value of i for these engines we may use 33,810, 



FLY-WHEELS. 1047 

Weight of Fly-wheels for Alternating-current Units. — (J. Begtrup, 
Am. Mach., July 10, 1902.)— 

TFI>2+mi).2= 14.000.000 Jfl/ _ 

In which W= weight of rim of fly-wheel in pounds, D = mean diameter 
of rim in feet, Wi = weight of armature in pounds, Di= mean diameter 
of armature in feet, H = rated horse-power of engine, (7 = a factor of 
steadiness, N = number of revolutions per minute, V == maximum 
instantaneous displacement in degrees, not to exceed 5 degrees divided 
by the number of poles on the generator, according to the rule of the 
General Electric Company. 

For simple horizontal engines, length of connecting-rod = 5 cranks, 
C7 = 90; (ditto, no account being taken of angularity of connecting-rod, 
U = 64) ; cross-compound horizontal engines, connecting-rod = 5 cranks, 
U = 51; ditto, vertical engines, heavy reciprocating parts, unbalanced, 
U = 78; vertical compound engines, cranks 180 degrees apart, recipro- 
cating parts balanced, U = 60. 

The small periodical variation in velocity (not angular displacement) 
can be determined from the following formula: 

p = 387,700.000 HZ 
NHWD^-i-WiDi^y 

in which H = rated horse-power, Z = a factor of steadiness, N = revs, 
per min., D = mean diameter of fly-wheel rim in feet, W= weight of fly- 
wheel rim in pounds, Di = mean diameter of armature or field in feet, 
Wi = weight of armature, F = variation in per cent of mean speed. 

For simple engines and tandem compounds, Z = 16; for horizontal 
cross-compounds, Z = 8.5; for vertical cross-compounds, heavy recip- 
rocating parts, Z = 12.5; for vertical compounds, cranks opposite, 
weights balanced, Z = 14. F represents here the entire variation, 
between extremes — not variation from mean speed. It generally varies 
from 0.25% of mean speed to 0.75% — evidently a negligible quantity. 

A mathematical treatment of this subject will be found in a paper 
by J. L. Astrom, in Trans. A. S. M. E., 1901. 

Centrifugal Force in Fly-wheels. — Let W = weight of rim in 
pounds; R = mean radius of rim in feet; r = revolutions per minute, 
g = 32.16; V = velocity of rim in feet per second = 2TrRr h- 60. 

Centnfugal force of whole rim = 2^ = -^ = '' ^ =0.000341 WRrK 

gR 3600 g 

The resultant, acting at right angles to a diameter, of half of this force 
tends to disrupt one half of the wheel from the other half, and is resisted 
by the section of the rim at each end of the diameter. The resultant of 
half the radial forces taken at right angles to the diameter is 1 ^ i/27r = 
2/7r of the sxmi of these forces ; hence the total force F is to be divided by 
2X2X1. 5708 = 6. 2832 to obtain the tensile strain on the cross-section 
of the rim, or, total strain on the cross-section = S = 0.00005427 WRr^. 
The weight TFi of a rim of cast iron 1 inch square in section is 2 nR x 
3.125 = 19.635 i? pounds, whence strain per square inch of sectional 
area of rim = Si = 0.0010656 R^r^ = 0.0002664 2)^2 = 0.0000270 V^, 
In which D = diameter of wheel in feet, and V is velocity of rim in feet 
per minute. ^Si = . 0972 v^, if v is taken in feet per second. 

For wrought iron; 

Si = 0.0011366 R^r^ = 0.0002842 DV^ = 0.0000288 V^. 

For steel: 

Si = 0.0011593 i?V = 0.0002901 DV" = 0.0000294 V^. 

For wood; 

Si = 0.0000888 R'-r^ = 0.0000222 DV^ = 0.00000225 V^. 
The specific gravity of the wood being taken at 0.6 = 37.5 lbs. per cu. 
ft., or i/i2 the weight of cast iron. 

Example. — Required the strain per square inch in the rim of a cast- 
iron wheel 30 ft. diameter, 60 revolutions per minute. 

Answer.— 15'- X 6O2 x 0.0010656 = 831.1 lbs. 

Required the j?train per square inch in a cast-iron wheel-rim running 
a mile a minute. Answer. — 0.000027 X 52802 = 752.7 lbs. 



1048 THE STEAM-ENGINE. 

In cast-iron fly-wheel rims, on account of their thickness, there is 
diflSculty in securing soundness, and a tensile strength of 10,000 lbs. 
per sq. in. is as much as can be assumed with safety. Using a factor of 
safety of 10 gives a maximum allowable strain in the rim of 1000 lbs. 
per sq. in., which corresponds to a rim velocity of 6085 ft. per minute. 

For any given material, as cast iron, the strength to resist centrifugal 
force depends only on the velocity of the rim, and not upon its bulk or 
weight. 

Chas. E. Emery {Cass. Mag., 1892) says: It does not appear that fly- 
wheels of customary construction should be unsafe at the comparatively 
low speeds now in common use if proper materials are used in con- , 
struction. The cause of rupture of fly-wheels that have failed is usually 
either the "running away" of the engine, such as may be caused by 
the breaking or slackness of a governor-belt, or incorrect design or de- 
fective materials of the fly-wheel. 

Chas. T. Porter (Trans. A. S. M. E., xiv, 808) states that no case of the 
bursting of a fly-wheel with a solid rim in a high-speed engine is known. 
He attributes the bursting of wheels built in segments to insufficient 
strength of the flanges and bolts by which the segments are held together. 
[The author, however, since the above was written, saw a solid rim fly- 
wheel of a high-speed engine which had burst, the cause being a large 
shrinkage hole at the junction between one of the arms and the rim. The 
wheel was about 6 ft. diam. Fortunately no one was injured by the 
accident.] (See also Thurston, "Manual of the Steam-engine," Part II, 
page 413.) 

Diameters of Fly-wheels for Various Speeds. — If 6000 feet per 
minute be the maximum velocity of rim allowable, then 6000 = ttRD^ 
in which R = revolutions per minute, and D= diameter of wheel in feet, 
whence D = 6000 -^ tt/^ == 1910 -f- R. 

W. H. Boehm, Supt. of the Fly-wheel Dept. of the FideUty and Casu- 
alty Co. {Eng. News, Oct. 2, 1902), says: For a given material there is a 
definite speed at which disruption will occur, regardless of the amount 
of material used. This mathematical truth is expressed by the formula: 

V ^ i.eVs/w, 

In which V is the velocity of the rim of the wheel in feet per second at 
which disruption will occur, W the weight of a cubic inch of the material 
used, and S the tensile strength of 1 square inch of the material. 

For cast-iron wheels made in one piece, assuming 20,000 lbs. per sq. 
in. as the strength of small test bars, and 10,000 lbs. per s q. in. in lar ge 
castings, and applying a factor of safety of 10, F = 1.6 VlOOO/0.26 = 
100 ft. per second for the safe speed. For cast steel of 60,000 lbs. per 
sq. in., V = 1.6 V6000 -i- 0.28 = 233 ft. per second. This is for wheels 
made in one piece. If the wheel is made in halves, or sections, the 
efficiency of the rim joint must be taken into consideration. For belt 
wheels with flanged and bolted rim joints located between the arms, the 
joints average only one-fifth the strength of the rim, and no such joint 
can be designed having a strength greater than one-fourth the strength 
of the rim. If the rim is thick enough to allow the joint to be reinforced 
by steel links shrunk on, as in heavy balance wheels, one-third the 
strength of the rim may be secured in the joint; but this construction can 
not be applied to belt wheels having thin rims. 

For hard maple, having a tensile strength of 10,500 lbs. per sq. in., 
and weigliing 0.0283 lb. per cu. in., we have, using a factor of safety of 
20, and remembering that the strength is reduced one-ha lf because the 
wheel is built up of segments, y = 1.6 ^262.5 -^ 0.0283 = 154 ft. per 
second. The stress in a wheel varies as the square of the speed, and the 
factor of safety on speed is the square root of the factor of safety on 
strength. 

Mr. Boehm gives the following table of safe revolutions per minute 
of cast-iron wheels of different diameters. The- flange joint is taken at 
. 25 of the strength of a wheel with no joint, the pad joint, that is a wheel 
made in six segments, with bolted flanges or pads on the arms, = 0.50» 
and the link joint =« 0.60 of the strength of a soUd rim. 



FLY-WHEELS. 



1049 





Safe Revolutions peb 


Minute of Cast-Iron Fly- 


JVHEELS. 






No 


Flange 


Pad 


Link 




No 


Flange 


Pad 


Link 




joint. 


joint. 


joint. 


joint. 




joint. 


joint. 


joint. 


joint. 


Diam. 










Diam. 










in 


R.P.M. 


R.P.M. 


R.P.M. 


R.P.M. 


in 


R.P.M. 


R.P.M. 


R.P.M. 


R.P.M. 


Ft. 










Ft. 










1 


1910 


955 


1350 


1480 


16 


120 


60 


84 


92 


2 


953 


478 


675 


740 


17 


112 


56 


79 


87 


3 


637 


318 


450 


493 


18 


106 


53 


75 


82 


4 


478 


239 


338 


370 


19 


100 


50 


71 


78 


5 


382 


191 


270 


296 


20 


95 


48 


68 


74 


6 


318 


159 


225 


247 


21 


91 


46 


65 


70 


7 


273 


136 


193 


212 


22 


87 


44 


62 


67 


8 


239 


119 


169 


185 


23 


84 


42 


59 


64 


9 


212 


106 


130 


164 


24 


80 


40 


56 


62 


10 


191 


96 


135 


148 


25 


76 


38 


54 


59 


11 


174 


87 


123 


135 


26 


74 


37 


52 


57 


12 


159 


80 


113 


124 


27 


71 


35 


50 


55 


13 


147 


73 


104 


114 


28 


68 


34 


48 


53 


14 


136 


68 


96 


106 


29 


66 


33 


47 


51 


15 


128 


64 


90 


99 


30 


64 


32 


45 


49 



The table is figured for a margin of safety on speed of approximately 
3, which is equivalent to a margin on stress developed, or factor of safety 
in the usual sense, of 9. {Am. Mach., Nov. 17, 1904.) 

Strains in the Rims of Fly-band Wheels Produced by Centrif- 
ugal Force. (James B. Stanwood, Trans. A. S. M. E., xiv, 251.) — • 
Mr. Stanwood mentions one case of a fly-band wheel where the periphery 
velocity on a 17 ft. 9 in. wheel is over 7500 ft. per minute. 

In band-saw mills the blade of the saw is operated successfully over 
wheels 8 and 9 ft. in diameter, at a periphery velocity of 9000 to 10,000 ft. 
per minute. These wheels are of cast iron throughout, of heavy thick- 
ness, with a large number of arms. 

In shingle-machines and chipping-machines where ca.st-iron disks 
from 2 to 5 ft. in diameter are employed, with knives inserted radially, 
the speed is frequently 10,000 to 11,000 ft. per minute at the periphery. 

If the rim of a fly-wheel alone be considered, the tensile strain in pounds 
per square inch of the rim section is 7" = 72/10 neariv, in which V = 
velocity in feet per second; but this strain is modified by the resistance 
of the arms, which prevent the uniform circumferential expansion of the 
rim, and induce a bending as well as a tensile strain. Mr. Stanwood 
discusses the strains in band-wheels due to transverse bending of a section 
of the rim between a pair of arms. 

When the arms are few in number, and of large cross-section, the rim 
will be strained transversely to a greater degree than with a greater num- 
ber of lighter arms. To illustrate the necessary rim thicknesses for vari- 
ous rim velocities, pulley diameters, number of arms, etc., the following 
table is given, based upon the formula 



f = 0.475<i^iV«(|,-±), 



in which f = thickness of rim in inches, rf= diameter of pulley in inches, 
N = number of arms, V = velocity of rim in feet per second, and F= the 

Greatest strain in pounds per square inch to which any fiber is subjected, 
'he value of F is taken at 6000 lbs. per sq. in. 



1050 



THE STEAM-ENGINE. 



Thickness of Rims in Solid Wheels. 



Diameter of 
Pulley in 
inches. 


Velocity of 

Rim in feet per 

second. 


Velocity of 

Rim in feet per 

minute. 


No. of Arms. 


Thickness m 
inches. 


24 
24 
48 
108 
108 


50 
88 
88 
184 
184 


3,000 
5,280 
5,280 
11,040 
11,040 


6 
6 
6 
16 
36 


2/10 
15/32 

21/2 
1/3 



c^J^ y^^ limit of rim velocity for all wheels be assumed to be 88 ft. per 
second, equal to 1 mile per minute, F = 6000 lbs., the formula becomes 

t = 0.475 d -i- 0.67 A^2 = o.7d -&- iV2. 

When wheels are made in halves or in sections, the bending strain mav 
be such as to make t greater than that given above. Thus, when the 
joint comes half way between the arms, the bending action is similar to 
a beam supported simply at the ends, uniformly loaded, and t is 50% 
greater. Then the formula becomes t = 0.712 d-^ A' 2^— - J^Y or for a 

fixed maximum rim velocity of 88 ft. per second and /= 6000 lbs ^- 
1.05^ -hV2. In segmental wheels it is preferable to have the ioints 
opposite the arms. Wheels in halves, if very tliin rims are to be em! 
ployed, should have double arms along the line of separation 

Attention should be given to the proportions of large recei\ing and 
Hl^^^'^^^HP''^^•^y'• 1^^^ thickness of'^rim for a 484n. wheel shSln^n 
table) with a nm velocity of 88 ft. per second, is 15/i6 in. Many wrecks 
ha^^e been caused by the failure of receiving or tightening pulleys whose 
^nL^^^^ ^^^"^ \'''' ^^^^S Ply-^^'heels calculated for a |ven coefficient 
?/f'r,?ol'''^'' T frequently lighter than the minimum safe weight. This 
nf whPPiFno'rfK^ ^^ large wheels. A rough guide to the minimum weight 
ntr^Mv fnr^^^'fr^t'^^^'''^'^^ ^^^^ ^^^ formul^. The arms, hub, lugs, etc., 
K ^ ;pnrP«T.f l 'i^oT^"'^''?'"^^^ ?^ one-third the entire weight of thi wheel 
lLJ^r.%1 ^ ^^f ^^^^ ^/ ^ "^'^'^^^ ^^ i^^hes, the weight of the rim (con- 
of sneed f. «l'fTPl^..^''''"^^S "Vl^^ V^^ be ^ = . 82 dtb lbs. If the limit 
^iptPnn.,! ^.h? P' P^- 5^?.^?^' *^^^ f^^ solid Wheels t == 0.7d -^ A2. For 
sectional wheels (joint between arms) ^ = i.05 d -^ A2. Weight of rim 

Tnt^Twl^^bf J^^t ^f""}^ between arms, w = 0.86^25 ^ a^2, in pounds. 

10^%^ .4^; ^^o S^l^^^^i^y ^'^eels ^Ith joint between arms, W = 

•9^u^^ ~"^-^ to 1 . 3 rf2& -. m^ in pounds. 
Prnf r jy.^^'^T '^ f^^ther discussed by Mr. Stanwood. in vol. xv, and by 
J^ror. Gaetano Lanza, in vol. xvi, Trans A S M E ) 
TnH.^n ^iUA^"^^^^ll and Pulleys. — Professor* Torrey (Am. Mach,. 
c^^fLn aA V-^^^^u*^^ following formula for arms of eUiptical cross- 
section of cast-iron wheels: 

TleT?in7h^';^f^„l?HPv?^''1^ ^^ti?^,P^ one arm: ;S = strain on belt in pounds 
wtdth^nf SLf^^^-^' i^^^'^ ^^ ^^ fo^ single and 112 for double belts: v =^ 
h-^Z{^?}^ ^? inches; n ~ number of arms: L = length of arm in feet; 
- Dreadth of arm at hub: d = depth of arm at hub, both in inches: 
ZrZrTJr.^ ^' ?» = ^^< - 30 c/2. The breadth of the arm is its least 
ThTcf?nr?^„;: ^T^^ ?^^s of the elhpse, and the depth the major axis. 
Ihis formula is based on a factor of safety of 10 

lat J^thp ^rL. -^ !?T^"^^v^^st assume some depth for the arm, and calcu- 
as^nmp fha^H"^^.1^^^^.1J^ *^ ^^ with it. If it gives too round an arm, 
triaT^^Mi nlr^^H^^i^ httle greater, and repeat the calculation. A second 

-Tho • a^"l.ost always give a good section, 
somewhnf rpHn!J!/T'l^* t^^ ^"^ h^"'^"^ b^^" calculated, they may be 
Sed aVthprS^o^.^^ *^^ ''"" ^"^- The actual amount cannot be cal- 
cuiaiea, as there are too many unknown quantities. However, the depth 



FLY-WHEELS. 



1051 



and breadth can be reduced about one-third at the rim without danger, 
and this will give a well-shaped arm. 

Pulleys are often cast in halves, and bolted together. When this is 
done the greatest care should be taken to provide sufficient metal in the 
bolts. This is apt to be the very w^eakest point in such pulleys. The 
combined area of the bolts at each joint should be about 28/100 the 
cross-section of the pulley at that point. (Torrey.) 

Unwin gives d = 0.6337 ^ BD/?i for single belts; 

d = . 798 ^BD/n for double belts ; 

D being the diameter of the pulley, and B the breadth of the rim, both in 
inches. These formulae are based on an eUiptical section of arm in which 
b = 0.4 dor d = 2.5&ona width of belt = 4/5 the width of the pulley 
rim, a maximum driving force transmitted by the belt of 56 lbs. per inch 
of width for a single belt and 112 lbs. for a double belt, and a safe working 
stress of cast iron of 2250 lbs. per square inch. 

If in Torrey's formula we make 6 = 0.4 d, it reduces to 



^=Vii^'^= V' 



WL 
12" 



Example. — Given a pulley 10 feet diameter; 8 arms, each 4 feet long; 
face, 36 inches wide; belt, 30 inches; required the breadth and depth of the 
arm at the hub. According to Unwin, 

d = 0.6337 -^BDIn =0.633^36X120/8 = 5.16 for single belt, 6 = 2.06; 

d = 0.798 -^BD/n = 0.798 -^36 X 120/8 = 6.50 for double belt, & = 2.60. 

According to Torrey, if we take the formula b = WL -^ 30 d^ and 
assume rf = 5 and 6.5 inches, respectively, for single and double belts, 
we obtain b = 1.08 and 1.33, respectively, or practically only one-half 
of the breadth according to Unwin, and, since transverse strength is pro- 
portional to breadth, an arm only one-half as strong. 

Torrey's formula is said to be based on a factor of safety of 10, but this 
factor can be only apparent and not real, since the assumption that the 
strain on each arm is equal to the strain on the belt divided by the num- 
ber of arms, is, to say the least, inaccurate. It would be more nearly 
correct to say that the strain of the belt is divided among half the number 
of arms. Unmn makes the same assumption in developing his formula, 
but says it is only in a rough sense true, and that a large factor of safety 
must be allowed. He therefore takes the low figure of 2250 lbs. per square 
inch for the safe working strength of cast iron. Unmn says that his 
equations agree well with practice. 

A Wooden-rim Fly-wheel, built in 1891 for a pair of Corliss engines 
at the Amoskeag Mfg. Co.'s mill, Manchester, N.H., is described by 
C. H. Manning in Trans. A. S. M. E., xiii, 618. It is 30 ft. diam. and 
108 in. face. The rim is 12 inches thick, and is built up of 44 courses of 
ash plank, 2, 3, and 4 inches thick, reduced about 1/2 inch in dressing, 
set edgewise, so as to break joints, and glued and bolted together. There 
are two hubs and two sets of arms, 12 in each, all of cast iron. The weights 
are as follows: 

Weight (calculated) of ash rim 31,855 lbs. 

Weight of 24 arms (foundry 45,020) 40,349 

Weight of 2 hubs (foundry 35,030) 31,394 ± " 

Counter-weights in 6 arms 664 

Total, excluding bolts and screws 104,262 ± " 

The wheel was tested at 76 revs, per min., being a surface speed of 
nearly 7200 feet per minute. 

Wooden Fly-wheel of the Willimantic Linen Co. (Illustrated in 
Power, March, 1893.) — Rim 28 ft. diam., 110 in. face. The rim is 
carried upon three sets of arms, one under the center of each belt, with 
12 arms in each set. 

The material of the rim is ordinary whitewood, 7/3 in. in thickness, cut 
into segments not exceeding 4 feet in length, and either 5 or 8 inches in 



1052 THE STEAM-ENGINE. 



width. These were assembled by building a complete circle 13 inches in 
width, first with the 8-inch inside and the 5-inch outside, and then beside 
it another circle with the widths reversed, so as to break joints. Each 
piece as it was added was brushed over with glue and nailed with three- 
inch wire nails to the pieces already in position. The nails pass through 
three and into the fourth thickness. At the end of each arm four 14- 
inch bolts secure the rim, the ends being covered by wooden plugs glued 
and driven into the face of the wheel. 

Wire-wound Fly-wheels for Extreme Speeds. {Eng^g News, 
August 2, 1890.) — The power required to produce the Mannesmann 
tubes is very large, varjing from 2000 to 10,000 H.P., according to the 
dimensions of the tube. Since this power is needed for only a short time 
(it takes only 30 to 45 seconds to convert a bar 10 to 12 ft. long and 4 in. 
in diameter into a tube), and then some time elapses before the next bar 
is ready, an engine of 1200 H.P. provided with a large fly-wheel for stor- 
ing the energy will supply power enough for one set of rolls. These 
fly-wheels are so large and run at such great speeds that the ordinary 
method of constructing them cannot be followed. A wheel at the Mannes- 
mann Works, made in Komotau, Hungary, in the usual manner, broke at 
a tangential velocity of 125 ft. per second. The fly-wheels designed to 
hold at more than double this speed consist of a cast-iron hub to which 
two steel disks, 20 ft. in diameter, are bolted; around the circumference 
of the wheel thus formed 70 tons of No. 5 wire are wound under a tension 
of 60 lbs. In the Mannesmann Works at Landore, Wales, such a wheel 
makes 240 revolutions a minute, corresponding to a tangential velocity 
of 15,080 ft. or 2.85 miles per minute. 

THE SLIDE-VALVE. 

Definitions. — Travel = total distance moved by the valve. 

Throw of the Eccentric = eccentricity of the eccentric = distance from 
the center of the shaft to the center of the eccentric disk = 1/2 the travel 
of the valve. 

Lap of the valve, also called outside lap or steam-lap = distance the 
outer or steam edge of the valve extends beyond or laps over the steam 
edge of the port when the valve is in its central position. 

Inside lap, or exhaust-lap = distance the inner or exhaust edge of the 
valve extends beyond or laps over the exhaust edge of the port w^hen the 
valve is in its central position. The inside lap is sometimes made zero, 
or even negative, in which latter case the distance between the edge of 
the valve and the edge of the port is sometimes called exhaust clearance, 
or inside clearance. 

Lead of the valve = the distance the steam-port is opened when the 
engine is on its center and the piston is at the beginning of the stroke. 

Lead-angle = the angle between the position of the crank when the 
valve begins to be opened and its position when the piston is at the 
beginning of the stroke. 

The valve is said to have lead when the steam-port opens before the 
piston begins its stroke. If the piston begins its stroke before the admis- 
sion of steam begins, the valve is said to have negative lead, and its amount 
is the lap of the edge of the valve over the edge of the port at the instant 
when the piston stroke begins. 

Lap-angle = the angle through which the eccentric must be rotated to 
cause the steam edge to travel from its central position the distance of 
the lap. 

Angular advance of the eccentric = lap-angle 4- lead-angle. 

Linear advance = lap 4- lead. 

Effect of Lap, Lead, etc., upon the Steam Distribution, — Given 
valve-travel 2 3/4 in., lap 3/4 in., lead V16 in., exhaust-lap Vs in., required 
crank position for admission, cut-off, release and compression, and 
greatest port-opening. (Halsey on Slide-valve Gears.) Draw a circle 
of diameter fh = travel of valve. From O the center set off Oa = lap 
and ah = lead, erect perpendiculars Oe, ac, bd: then ec is the lap-angle 
and cd the lead-angle, measured as arcs. Set off fg = cd, the lead- 
angle; then Og is the position of the crank for steam admission. Set off 
2ec -h cd from h to i; then Oi is the crank-angle for cut-off, and fk -^ fh 
Is the fraction of stroke completed at cut-off. Set off 01 = exhaust- 



THE SUDE- VALVE. 



1053 



lap and draw Im; em is the exhaust-lap angle. Set off hn= ec -{■ cd - em, 
and On is the position of crank at release. Set off fp = ec-^cd-\- em^ 
and Op is the position of crank for compression, fo -j- fh is the fraction 
of stroke completed at release, and hq -h hf is the fraction of the return 
stroke completed when compression begins; Oh, the throw of the eccentric, 
minus Oa the lap, equals ah the maximum port-opening. 



ICut-off 



Release 




• Fig. 170. 

If a valve has neither lap nor lead, the line joining the center of the 
eccentric disk and the center of the snaft being at right angles to the line 
of the crank, the engine would follow full stroke, admission of steam 
beginning at the beginning of the stroke and ending at the end of the 
stroke. 

Adding lap to the valve enables us to cut off steam before the end of 
the stroke. The eccentric being advanced on the shaft an amount equal 
to the lap-angle enables steam to be admitted at the beginning of the 
stroke, as before lap was added, and advancing it a further amount equal 
to the lead-angle causes steam to be admitted before the beginning of the 
stroke. 

Having given lap to the valve, and having advanced the eccentric 
on the shaft from its central position at right angles to the crank, 
through the angular advance = lap-angle + lead-angle, the four events, 
admission, cut-off, release or exhaust-opening, and compression or exhaust- 
closure, take place as follows: Admission, when the crank lacks the lead- 
angle of having reached the center; cut-off, when the crank lacks two 
lap-angles and one lead-angle of having reached the center. During 
the admission of steam the crank turns through a semicircle less twice 
the lap-angle. The greatest port-opening is equal to half the travel of the 
valve less the lap. Therefore for a given port-opening the travel of the 
valve must be increased if the lap is increased. When exhaust-lap is 
added to the valve it delays the opening of the exhaust and hastens its 
closing by an angle of rotation equal to the exhaust-lap angle, which is 
the angle through which the eccentric rotates from its middle position 



1054 



THE STEAM-ENGINE. 



while the exhaust edge of the valve uncovers its lap. Release then 
takes place when the crank lacks one lap-angle and one lead-angle minus 
one exhaust-lap angle of having reached the center, and compression when 
the crank lacks lap-angle -f lead-angle + exhaust-lap angle of having 
reached the center. 

The above discussion of the relative position of the crank, piston, and 
valve for the different points of the stroke is accurate only with a con- 
necting-rod of infinite length. 

For actual connecting-rods the angular position of the rod causes a 
distortion of the position of the valve, causing the events to take place too 
late in the forward stroke and too early in the return. The correction of 
this distortion may be accomplished to some extent by setting the valve 
so as to give equal lead on both forward and return stroke, and by alter- 
ing the exhaust-lap on one end so as to equalize the release ana com- 
pression. F. A. Halsey, in his SUde-valve Gears, describes a method of 
equahzing the cut-off without at the same time affecting the equality of 
the lead. In designing slide-valves the effect of angularity of the con- 
necting-rod should be studied on the drawing-board, and preferably by 
the use of a model. 

Sweet's Valve-dia.^ram. — To find outside and inside lap of valve 
for different cut-off's and compressions (see Fig. 171): Draw a circle 
whose diameter equals travel of valve. Draw diameter BA and con- 
tinue to A^, so that the length AA^ bears the same ratio to XA as the 




Fig. 171. — Sweet's Valve Diagram, 
length of connecting-rod does to length of engine-crank. Draw small 
circle K with a radius equal to lead. Lay off AC so that ratio of AC to 
AB = cut-off in parts of the stroke. Erect perpendicular CD. Draw 
DL tangent to K', draw XS perpendicular to DL; XS is then outside lap 
of valve. 

To find release and compression: If there is no inside lap, draw FE 
through X parallel to DL. F and E will be position of crank for release 
and compression. If there is an inside lap, draw a circle about X, in 
which radius XY equals inside lap. Draw HG tangent to this circle and 
parallel to DL; then H and G are crank positions for release and for com- 
pression. Draw HN and MG, then AN is piston position at release and 
A'M piston position at compression, AB being considered stroke of 
engine. 

To make compression alike on each stroke it is necessary to increase 
the inside lap on crank end of valve, and to decrease by the same amount 
the inside lap on back end of valve. To determine this amount, through 
M with a radius MM^ = AA^, draw arc MP, from P draw PT perpen- 
dicular to AB, then TM is the amount to be added to inside lap on crank 
end, and to be deducted from inside lap on back end of valve, inside lap 
being XY. 

For the Bilgram Valve-Diagram, see Halsey on Slide-valve Gears. 

The Zeuner Valve-diagram is given in most of the works on the 
steam-engine, and in treatises on valve-gears, as Zeuner's, Peabody's, and 
Spangler's. The following paragraphs show how the Zeuner valve-diagram 
may be employed as a convenient means (1) for finding the lap, lead, 
etc., of a slide-valve when the points of admission, cut-off, and release 



THE SLIDE-VALVE. 



1055 



are given; and (2) for obtaining the points of admission, cut-off, release, 
and compression, etc., when the travel, the laps, and the lead of the valve 
are given. In working out these two problems, the connecting-rod is 
supposed to be of infinite length. 

Determination of the Lap, Lead, etc., of a Slide-valve for Given Steam 
Distribution. — Given the points of admission, cut-off, and release, to find 
the point of compression, the lap, the lead, the exhaust lap, the angular 
advance, and the port-openings at different fractions of the stroke. 

Draw a straight line AA\ Fig. 172, to represent on any scale the travel 
of the valve, and on it draw a circle, with the center O, to represent the 
path of the center of the eccentric. The fine and the circle will also repre- 
sent on a different scale the length of stroke of the piston and the path 
of the crank-pin. On the circle, which is called the crank circle, mark B, 






E Fl P' 









Cut-off 



Center of x*' 
Eccentric 



Kelease\L 



B\AdmiBSi'on 



CompressiX)ii 



.WT 



.\^ 



^-^ye Circle 



^ra; 



i2^ Circle 



Fig. 172. — Zeuner's Valve Diagram. 

the position of the crank-pin when admission of steam begins, the direc- 
tion of motion of the crank being shown by the arrow; C, the position of 
the crank-pin at cut-off; and L, its position at release. From these points 
draw perpendiculars BM, CN, and LV, to the line AA'; AI, N, and V 
will then represent the positions of the piston at admission, cut-off, and 
release respectively, the admission taking place, as shown, before the 
piston reaches the end of the stroke in the direction OA, and release 
taking place before the end of the stroke in the direction OA'. 

Bisect the arc BC at D, and draw the diameter DOD'. On DO draw 
he circle DHOGE, called the valve circle. Draw OB, cutting the valve 
lircle at G; and OC, cutting it at H. Then OG = OH is the lap of the 
valve, measured on the scale in which OA is the half-travel of the valve. 
With OG as radius draw the arc GFH, calle4 the steam-lap circle, or, for 
■"ihort, the lQ,p circle. 



1056 THE STEAM-ENGINE. 

Mark the point E, at which the valve circle cuts the line OA. The 
distance FE represents the lead of the valve, and BG = AF is the max^ 
imum port-opening. A perpendicular drawn from OA at E will cut the 
valve circle and the crank circle at D, since the triangle DEO is a right- 
angled triangle drawn in the semicircle DEGO. 

Erect the perpendicular FJ, then angle DOJ = AOB is the lead-angle 
and JOK is the lap-angle, OK being a perpendicular to AA' drawn from 
O. DOK is the sura of the lap and lead angles, that is, the angular 
advance, by which the eccentric must be set beyond 90° ahead of the 
crank. Set off Xy = KD\ then Y is the position of the center of the 
eccentric when the crank is in the position OA. 

To find the point of compression, set off D'P = D'L\ then P is the 
point of compression. 

Draw OP and OL. On OD' draw the valve circle ORD'S, cutting 
OL at R and OP at S. With OR as a radius draw the arc of the exhaust- 
lap circle,, RTS, OR = OS is the exhaust lap. 

The port-oj>ening at any part of the stroke, or corresponding position 
of the crank, is represented by the radial distances, as EF, DW, and J'X, 
intercepted between the lap and the valve circles on radii drawn from O. 
Thus, on the radius OB, the port-opening is zero when steam admission is 
about to begin; on the radius OA, when the crank is on the dead center 
the opening is EF, or equal to the lead of the valve; on the radius DO, 
midway between the point of admission and the point of cut-off, the 
opening is a maximum DW = AF = BG; on the radius OC it is zero 
again when steam has just been cut off. 

In like manner the exhaust opening is represented by the radial dis- 
tances intercepted between the exhaust-lap circle, RR'TS, and the valve 
circle, ORD'S. On the radius OL it is zero when release begins; on OD' 
it is TD', a maximum; and on OP it is zero again when compression begins. 

Determination of the Steam Distribution, etc., for a Given Valve. — Given 
the valve travel, the lap, the lead, and the exhaust lap, to find the maxi- 
mum port-opening, the angular advance, and the points of admission, 
cut-off, release, and compression. 

This problem is the reverse of the preceding. Draw AOA* to represent 
the valve travel on a certain scale, O being the middle point, and on this 
line on the same scale set off OF = the lap, FE = the lead, and OR' = 
the exhaust lap. AF then will be the maximum port-opening. Draw the 
perpendiculars OK and ED. DOK is the angular advance. 

Draw the diameter DOD', and on DO and D'O draw the two valve 
circles. From O, the center, with a radius OF, the lap, draw the arc of 
the steam-lap circle cutting the valve circle in G and H. Through G 
draw OB, and through H draw 0C\ B then is the point of admission, 
and C the point of cut-off. With OR, the exhaust lap, as a radius, draw 
the arc of the exhaust-lap circle, RTS, cutting the valve circle in R and 
S. Through R draw OL, and through S draw OP. Then L is the point 
of release and P the point of compression. Draw the perpendiculars 
BM, CN, LV, and PP\ to find M, N, V, and P', the respective positions 
on the stroke of the piston when admission, cut-off, release, and com- 
pression take place. 

Practical Application of Zeuner's Diagram. — In problems solved by 
means of the Zeuner diagram, the results obtained on the drawings are 
relative dimensions or the ratios of the several dimensions to a given 
dimension the scale of which is known, such as the valve travel, the 
maximum port-opening, or the length of stroke. In problems similar to 
the first problem given above, the known dimensions are usually the 
length of stroke, the maximum port-opening, AF, which is calculated 
from data of the dimensions of cylinder, the piston speed, and the allow- 
able velocity of steam through the port. The length of the stroke being 
represented on a certain scale by AA\ the points of admission, cut-off, 
release, and compression, in fractions of the stroke, are measured respec- 
tively by A'M, AN, AV, and A'P on the same scale. The actual dimen- 
Bion of the maximum port-opening is represented on a different scale by 
AF, therefore the actual dimensions of the lap, lead, and exhaust lap are 
measured respectively by OF, FE, and OR' on the same scale as AF; 
or, in other words, the lap, lead, and exhaust lap are respectively the 
OF FT* OR' 

latios j-=» -j^» and -j-^ • each multiplied by the maximum port-opening. 



THE SLIDE-VALVE. 



1057 



In problems similar to the second problem, the actual dimensions of 
the lap, the lead, the exhaust lap, and the valve travel are all known, 
and are laid down on the same scale on the line AA\ representing the 
valve travel; and the maximum port-opening is found by the solution of 
the problem to be AF, measured on the same scale; or the maximum 
port-opening = 1/2 valve travel minus the lap. Also in this problem 
AA' represents the known length of stroke on a certain scale, and the 
points of admission, cut-off, release, and compression, in fractions of the 
stroke, are represented by the ratios wliich A'M, AN, AV, and A'P, 
respectively, bear to AA\ 

Port-opening. — The area of port-opening is usually made such that 
the velocity of the steam in passing through it should not exceed 6000 ft. 
per min. The ratio of port area to piston area will vary with the piston- 
speed as follows: 

Forspeed^of^piston,| jqq 20O 300 400 500 600 700 800 900 1000 1200 
Port areaj=^piston|QQj7 q33 q^ ^g^ ^33 ^ ^q^ ^33 ^^ ^g^ 2 

For a velocity of 6000 ft. per min., 

Port area = sq. of diam. of cyl.X piston speed -^ 7639. 

The length of the port-opening may be equal to or sometliing less than 
the diameter of the cylinder, and the width = area of port-opening -»- 
its length. 

The bridge between steam and exhaust ports should be wide enough 
to prevent a leak of steam into the exhaust due to overtravel of the 
valve. 

The width of exhaust port = width of steam port 4- 1/2 travel of valve 
-f- inside lap — width of bridge. 

Lead. (From Peabody's Valve-gears.) — The lead, or the amount 
that the valve is open when the engine is on a dead point, varies, with the 
type and size of the engine, from a very small amount, or even nothing, 
up to 3/8 of an inch or more. Stationary-engines running at slow speed 
may have from 1/64 to 1/16 inch lead. The effect of compression is to fill 
the waste space at the end of the cylinder with steam; consequently, 
engines having much compression need less lead. Locomotive-engines 
having the valves controlled by the ordinary form of Stephenson link- 
motion may have a small lead when running slowlj^ and with a long 
cut-off, but when at speed with a short cut-off the lead is at least 1/4 inch; 
and locomotives that have valve-gear which gives constant lead com- 
monly have 1/4 inch lead. The lead-angle is the angle the crank makes 
with the line of dead points at admission. It may vary from 0° to 8°. 

Inside Lead. — Weisbach (vol. ii, p. 296) says: Experiment shows 
that the earlier opening of the exhaust ports is especially of advantage, 
and in the best engines the lead of the valve upon the side of the exhaust, 
or the inside lead, is 1/25 to 1/15; i.e., the slide-valve at the lowest or highest 
position of the piston has made an opening whose height is 1/25 to 1/15 of 
the whole throw of the slide-valve. The outside lead of the slide-valve 
or the lead on the steam side, on the other hand, is much smaller, and is 
often only 1/100 of the whole throw of the valve, 

EfTect of Changing Outside Lap, Inside Lap, Travel and 
Angular Advance. (Thurston.) 





Admission. 


Expansion. 


Exhaust. 


Compression. 


Incr. 
O.L. 


is later, 
ceases sooner 


occurs earlier, 
continues longer 


is unchanged 


begins at 
same point 


Incr. 
I.L. 


unchanged 


begins as before, 
continues longer 


occurs later, 
ceases earlier 


begins sooner, 
continues longer 


Incr. 
T. 


begins sooner, 
continues longer 


begins later, 
ceases sooner 


begins later, 
ceases later 


begins later, 
ends sooner 


Incr. 
A.A. 


begins earlier, 
period unaltered 


begins sooner, 
per. the same 


begins earlier, 
per. unchanged 


begins earlier, 
per. the same 



1058 



THE STEAM-ENGINE. 



Zeuner gives the following relations (Weisbach-Dubois, vol. ii,p. 307); 
It S = travel of valve, p = maximum port opening; 
L = steam-lap, I = exhaust-lap; 

T T-> 

R = ratio of steam-lap to half travel = „ _ ,. , L = — X 5; 



r = ratio of exhaust-lap to half travel = 

2v 



'0.5S • ^ 2 ^*^' 



S = 2p-\-2L=2p-\'RXS',S = 



1-R 



If a = angle BOC between positions of crank at admission and at 
cut-off, and ^ = angle LOP between positions of crank at release and at 

D ., sin (180°-a) ., sin(180°-^) 
compression, then R = 1/2 ■ — 77 -\ r = 1/2 



sin 1/2 a, 



sin 1/2/3 



Crank-angles for Connecting-rods of Different Lengths. 

Forward and Return Strokes. 



-1^ 

oil 

'3 <o a 




Ratio of Length of Connecting-rod to Length of Stroke. 




2 


21/2 


3 


31/2 


4 


5 


Infi- 


OM a> 














nite 


m 








































For. 


*^GQ§ 


For. 


Ret. 


For. 


Ret. 


For. 


Ret. 


For. 


Ret. 


For. 


Ret. 


For. 


Ret. 


or 





























Ret. 


.01 


10.3 


13.2 


10.5 


12.8 


10.6 


12.6 


10.7 


12.4 


10.8 


12.3 


10.9 


12.1 


11.5 


.02 


14.6 


18.7 


14.9 


18.1 


15.1 


17.8 


15.2 


17.5 


15.3 


17.4 


15.5 


17.1 


16.3 


.03 


17.9 


22.9 


18.2 


22.2 


18.5 


• 21.8 


18.7 


21.5 


18.8 


21.3 


19.0 


21.0 


19.9 


.04 


20.7 


26.5 


21.1 


25.7 


21.4 


25.2 


21.6 


24.9 


21.8 


24.6 


22.0 


24.3 


23.1 


.05 


23.2 


29.6 


23.6 


28.7 


24.0 


28.2 


24.2 


27.8 


24.4 


27.5 


24.7 


27.2 


25.8 


JO 


33.1 


41.9 


33.8 


40.8 


34.3 


40.1 


34.6 


39.6 


34.9 


39.2 


35.2 


38.7 


36.9 


.15 


41 


51.5 


41.9 


50.2 


42.4 


49.3 


42.9 


48.7 


43.2 


48.3 


43.6 


47.7 


45.6 


.20 


48 


59.6 


48.9 


58.2 


49.6 


57.3 


50.1 


56.6 


50.4 


56.2 


50.9 


55.5 


53.1 


.25 


54.3 


66.9 


55.4 


65.4 


56.1 


64.4 


56.6 


63.7 


57.0 


63.3 


57.6 


62.6 


60.0 


.30 


60.3 


73.5 


61.5 


72.0 


62.2 


71.0 


62.8 


70.3 


63.3 


69.8 


63.9 


69.1 


66.4 


.35 


66.1 


79.8 


67.3 


78.3 


68.1 


77.3 


68.8 


76.6 


69.2 


76.1 


69.9 


75.3 


72.5 


.40 


71.7 


85.8 


73.0 


84.3 


73.9 


83.3 


74.5 


82.6 


75.0 


82.0 


75.7 


81.3 


78.5 


.45 


77.2 


91.5 


78.6 


90.1 


79.6 


89.1 


80.2 


88.4 


80.7 


87.9 


81.4 


87.1 


84.3 


.50 


82.8 


97.2 


84.3 


95.7 


85.2 


94.8 


85.9 


94.1 


86.4 


93.6 


87.1 


92.9 


90.0 


.55 


88.5 


102.8 


89.9 


101.4 


90.9 


100.4 


91.6 


99.8 


92.1 


99.3 


92.9 


98.6 


95.7 


.60 


94.2 


108.3 


95.7 


107.0 


96.7 


106.1 


97.4 


105.5 


98.0 


105.0 


98.7 


104.3 


101.5 


.65 


100.2 


113.9 


101.7 


112.7 


102.7 


111.9 


103.4 


111.2 


103.9 


110.8 


104.7 


llO.l 


107.5 


.70 


106.5 


119.7 


108.0 


118.5 


109.0 


117.8 


109.7 


117.2 


110.2 


116.7 


no. 9 


116.1 


113.6 


.75 


113.1 


125.7 


114.6 


124.6 


115.6 


123.9 


116.3 


123.4 


116.7 


123.0 


117.4 


122.4 


120.0 


.80 


120.4 


132 


121.8 


131.1 


122.7 


130.4 


123.4 


129.9 


123.8 


129.6 


124.5 


129.1 


126.9 


.85 


128.5 


139 


129.8 


138.1 


130.7 


137.6 


131.3 


137.1 


131.7 


136.8 


132.3 


136.4 


134.4 


.90 


138.1 


146.9 


139.2 


146.2 


139.9 


145.7 


140.4 


145.4 


140.8 


145.1 


141.3 


144.8 


143.1 


.95 


150.4 


156.8 


151.3 


156.4 


151.8 


156.0 


152.2 


155.8 


152.5 


155.6 


152.8 


155.3 


154.2 


.96 


153.5 


159.3 


154.3 


158.9 


154.8 


158.6 


155.1 


158.4 


155.4 


158.2 


155.7 


158.0 


156.9 


.97 


157.1 


162.1 


157.8 


161.8 


158.2 


161.5 


158.5 


161.3 


158.7 


161.2 


159.0 


161.0 


160.1 


.98 


161.3 


165.4 


161.9 


165.1 


162.2 


164.9 


162.5 


164.8 


162.6 


164.7 


162.9 


164.5 


163.7 


.99 


166.8 


169.7 


167.2 


169.5 


167.4 


169.4 167.6 


169.3 


167.7 


169.2 


167.9 


169.1 


168.5 


1.00 


180 


180 


180 


180 


180 


180 180 


180 


180 


180 


180 


180 


180 



Ratio of Lap and of Port-opening to Valve-traveL — The table 
on page 1059, giving the ratio of lap to travel of valve and ratio of travel 
to port-opening, is abridged from one given by Buel in Weisbach-Dubois, 



THE SLIDE-VALVE. 



1059 



rol. ii. It is calculated from the above formulae. Intermediate values 
may be found by the formulae, or with sufficient accuracy by interpolation 
from the figures in the table. By the table on page 1058 the crank-angle 
may be found, that is, the angle between its position when the engine is 
on the center and its position at cut-off, release, or compression, when 
these are known in fractions of the stroke. To illustrate the use of the 
tables the following example is given by Buel: width of port = 2.2 in.; 
width of portropening = width of port + 0.3 in.; overtravel = 2.5 in.; 
length of connecting-rod = 21/2 times stroke; cut-off = 0.75 of stroke; 
release = 0.95 of stroke; lead-angle, 10°. From the first table we find 
crank-angle = 114.6; add lead-angle, making 124.6°. From the second 
table, for angle between admission and cut-off, 125°, we have ratio of 
travel to port-opening = 3.72, or for 124.6° = 3.74, which, multiphed 
by port-opening 2.5, gives 9.45 in. travel. The ratio of lap to travel, 
by the table, is 0.2324, or 9.45 X 0.2324 = 2.2 in. lap. For exhaust- 
lap, we have for release at 0.95, crank-angle = 151.3; add lead-angle 
10° = 161 .3°. From the second table, by interpolation, ratio of lap to 
travel = 0.0811, and 0.0811 X 9.45 = 0.77 in., the exhaust-lap. 

Lap-angle = 1/2(180° — lead-angle — crank-angle at cut-off); 

= 1/2(180° - 10 - 114.6) = 27.7°. 
Angular advance = lap-angle -I- lead-angle = 27.7 + 10 = 37.7°. 
Exhaust lap-angle = crank-angle at release + lap-angle + lead-angle — ISO® 

= 151. 3+27. 7+10-180° = 9°. 
Crank-angle at com- ) 
.pression measured [ =180° — lap-angle — lead-angle — exhaust lap-angle 
on return stroke ) 

= 180-27.7-10-9=133.3°; corresponding, by 
table, to a piston position of .81 of the return stroke; or 
Crank-angle at compression = 180°— (angle at release— angle at cut-off) 

+ lead-angle 
= 180 - (151. 3-114. 6) +10= 133.3°. 

The positions determined above for cut-off and release are for the 
forward stroke of the piston. On the return stroke the cut-off will take 
place at the same angle, 114.6°, corresponding by table to 66.6% of the 
return stroke, instead of 75%. By a slight adjustment of the angular 
advance and the length of the eccentric-rod the cut-off can be equalized. 
The width of the bridge should be at least 2.5 + .25 - 2.2 = .55 in. 







Lap and Travel of 


Valve 


. 






«3*»H-^ 1 




4) 1 


03 <♦-(,- 1 


tM 


(V 1 


i««f-(. ' 1 


V-, 


OJ ji. 


C5 ^'S S 

.2«?o 





> ^ 


.2 cn?0 


C 


> fl 


fl otc g 







"S 


c3 a 


% 


■^a 


2 „ ? 


'3 


— c 




> 


-1 


osit 
oint 
Cut 
d C 


> 

2 




P'50t3 


> 


'^ 


p^fi^-og 


H 


PL,flH-d G 


H 


-n^ 


^fS-^g 


H 


^0 




Q 


(uPh 


» " C M 





13 pL, 







cP-i 


D. 


do 




2^ 


a 


d 


S-S-s^d 


c3 
^_5 


H^ 


B-^-iSc 




^-B 


•>^ a "^ <i> 9 


s 


H^ 


ngle be 
of Crai 
Admisj 
or Rel 
pressio 




atio of 
to Wid 
ing. 


ngle be 
of Crai 
Admisj 
or Rel 
pressio 




atio of 
to Wid 
ing. 


ngle be 
of Crai 
Admis! 
or Rel 
pressio 




atio of 
f.o Wid 
ing. 


< 


c^ 


P^ 


< 


^ 


P^ 


< 


^ 


P^ 


30° 


0.4830 


58.70 


85° 


0.3686 


7.61 


135° 


0.1913 


3.24 


35 


.4769 


43.22 


90 


.3536 


6.83 


140 


.1710 


3.04 


40 


.4699 


33.17 


95 


.3378 


6.17 


145 


.1504 


2.86 


45 


.4619 


26.27 


100 


.3214 


5.60 


150 


.1294 


2.70 


50 


.4532 


21.34 


105 


.3044 


5.11 


155 


.1082 


2.55 


55 


.4435 


17.70 


110 


.2868 


4.69 


160 


.0868 


2.42 


60 


.4330 


14.93 


115 


.2687 


4.32 


165 


.0653 


2.30 


65 


.4217 


12.77 


120 


.2500 


4.00 


170 


.0436 


2.19 


70 


.4096 


11.06 


125 


.2309 


3.72 


175 


.0218 


2.09 


75 


.3967 


9.68 


130 


.2113 


3.46 


180 


.0000 


2.00 


80 


.3830 


8.55 





























1060 



THE STEAM-ENGINE. 



Relative Motions of Crosshead and Crank. — L = length of con. 
necting-rod, R = length of crank, 9 = angle of crank with center line of 
engine, D = displacement of crosshead from the beginning of its stroke, 
V — velocity of crank-pin, Fi = velocity of piston. 

For i2=*l, Z) = ver sin e± (L- ^L^-sin'^e), 



Fi=7sin0/1 db- 



cos Q 



"VL2-sin2 0/ 



From these formulae Mr. A. F. Nagle computes the following: 
Piston Displacement and Piston Velocity for each 10° of Motion 

OF Crank. Length of crank = 1. Length of connecting-rod = 5. 

Piston velocity Vi for vel. of crank-pin = 1. 



Angle 


Displacement. 


Veloc 


ty. 


Angle 

of 
Cr'nk 


Displacement. 


Velocity. 


of 
Cr'nk 


For- 
ward. 


Back. 


For- 
ward. 


Back. 


For- 
ward. 


Back. 


For- 
ward. 


Back. 


10° 
20° 
30° 
40° 
50° 


0.018 
0.072 
0.159 
0.276 
0.416 


0.012 
0.048 
0.109 
0.192 
0.298 


0.207 
0.406 
0.587 
0.742 
0.865 




60° 
70° 
80° 
84° 
90° 


0.576 
0.747 
0.924 
1.000 
1.101 


0.424 
0.569 
0.728 

■■6!899' 


954 
1.005 
1.019 
1.011 
1.000 


0.778 
0.875 
0.950 

i^ooo 



PERIODS OF ADMISSION, OR CUT-OFF, FOR VARIOUS LAPS 
AND TRAVELS OF SLIDE-VALVES. 

The two following tables are from Clark on the Steam-engine. In the 
first table are given the periods of admission corresponding to travels of 
valve of from 12 in. to 2 in., and laps of from 2 in. to 3/3 in., with 1/4 in. 
and 1/8 in. of lead. With greater leads than those tabulated, the steam 
would be cut off earlier than as shown in the table. 

The influence of a lead of ^Im in. for travels of from is/s in. to 6 in., 
and laps of from 1/2 in. to II/2 in., as calculated for in the second table, 
is exhibited by comparison of the periods of admission in the table, for 
the same lap and travel. The greater lead shortens the period of admis- 
sion, and increases the range for expansive working. 

Periods of Admission, or Points of Cut-off, for Given Travels and 
Laps of Slide-valves. 









Periods of Admissi 


on, or 


Points 


of Cut-off, for the 




5..-^ 








following L 


aps of Valves 


in inches. 






^'^ 


2 


13/4 


11/2 


11/4 


1 


7/8 


3/4 


5/8 


1/2 


3/8 


in. 


in. 


% 


% 


% 


% 


% 


% 


% 


% 


% 


% 


12 


1/4 


88 


90 


93 


95 


96 


97 


98 


98 


99 


99 


10 


1/4 


82 


87 


89 


92 


95 


96 


97 


98 


98 


99 


8 


V4 


72 


78 


84 


88 


92 


94 


95 


96 


98 


98 


6 


1/4 


50 


62 


71 


79 


86 


89 


91 


94 


96 


97 


5V? 


1/8 


43 


56 


68 


77 


85 


88 


91 


94 


96 


97 


5 


1/8 


32 


47 


61 


72 


82 


86 


89 


92 


95 


97 


4V? 


1/8 


14 


35 


51 


66 


78 


83 


87 


90 


94 


96 


4 


1/8 




17 


39 


57 


72 


78 


83 


88 


92 


95 


31/2 


1/8 
1/8 
1/8 
1/8 






20 


44 
23 


63 
50 
27 


71 
61 
43 


79 
71 
57 
33 


84 
79 
70 
52 


90 
86 
80 
70 


94 


3 






91 


21/2 








88 


2 










81 



















THE SLIDE-VALVE. 



1061 



Periods of Admission, or Points of Cut-off, for given Travels and 
Laps of Slide-valves. 

Constant lead, 5/i6. 



Travel. 








Lap. 










Inches. 


1/2 


5/8 


3/4 


7/8 


1 


11/8 


11/4 


13/8 


11/2 


15/8 


19 


















13/4 


39 


















17/8 


47 


17 
















2 


55 
61 


34 

41 
















21/8 


14 














21/4 


65 
68 
71 
74 
76 
78 
80 
81 
83 
84 


50 
55 
59 
63 
67 
70 
13 
74 
76 
78 


30 
38 
45 
49 
56 
59 
62 
65 
68 
71 














23/8 


13 
27 
36 
43 
47 
50 
55 
59 
62 












21/2 












25/8 


\i 

26 
32 
38 
44 
48 
51 










23/4 










27/8 


23 
30 
34 
40 














31/8 


10 

22 
29 






31/4 
33/8 






9 




31/2 


85 


80 


73 


64 


53 


45 


34 


20 




35/8 


86 


81 


75 


66 


57 


49 


38 


26 


9 


33/4 


87 


82 


76 


68 


60 


52 


42 


32 


19 


37/8 


87 


83 


78 


70 


63 


55 


46 


36 


25 


4 


88 


84 


79 


72 


66 


58 


49 


40 


29 


41/4 


89 


86 


81 


76 


70 


63 


56 


47 


37 


41/2 


90 


87 


83 


79 


73 


67 


61 


54 


45 


43/4 


92 


89 


85 


81 


76 


70 


65 


58 


51 


5 


93 


90 


87 


83 


78 


73 


67 


62 


56 


51/2 


94 


92 


89 


86 


82 


78 


73 


68 


63 


6 


95 


93 


91 


88 


85 


82 


78 


74 


69 



Piston-valve. — The piston-valve is a modified form of the slide- 
valve. The lap, lead, etc., are calculated in the same manner as for the 
common slide-valve. The diameter of valve and amount of port-opening 
are calculated on the basis that the most contracted portion of the steam- 
passage between the valve and the cylinder should have an area such that 
the velocity of steam through it will not exceed 6000 ft. per minute. The 
area of the opening around the circumference of the valve should be about 
double the area of the steam-passage, since that portion of the opening 
that is opposite from the steam-passage is of little effect. 

Setting the Valves of an Engine. — The principles discussed above 
are applicable not only to the designing of valves, but also to adjustment 
of valves that have been improperly set; but the final adjustment of the 
eccentric and of the length of the rod depends upon the amount of lost 
motion, temperature, etc.; and can be effected only after trial. After 
the valve has been set as accurately as possible when cold, the lead and 
lap for the forward and return strokes being equalized, indicator diagrams 
should be taken and the length of the eccentric-rod adjusted, if necessary, 
to correct slight irregularities. 

To Put an Engine on its Center. — Place the engine in a position 
where the piston will have nearly completed its outward stroke, and 
opposite some point on the crosshead. such as a corner, make a mark 
upon the guide. Against the rim of the pulley or crank-disk place a 
pointer and mark a line ^\ith it on the pulley. Then turn the engine over 
the center until the crosshead is again in the same position on its inward 
stroke. This will bring the crank as much below the center as it was 
above it before. With the pointer in the same position as before make 
a second mark on the pulley rim. Divide the distance between the marks 
in two and mark the middle point. Turn the engine until the pointer 
Is opposite this middle point, and it will then be on its center. To avoid 



1062 THE STEAM-ENGINE. 

the error that may arise from the looseness of crank-pin and wrist-pin 
bearings, the engine should be tm-ned a little above the center and 
then be brought up to it. so that the crank-pin will press against the 
same brass that it does when the first two marks are made. 

Link Motion. — Link-motions, of which the Stephenson hnk is the 
most conmaonlj^ used, are designed for two purposes: first, for reversing 
the motion of the engine, and second, for varying the point of cut-off 
by varying the travel of the valve. The Stephenson link-motion is a 
combination of two eccentrics, called forward and back eccentrics, with 
a Unk connecting the extremities of the eccentric-rods ; so that by vary- 
ing the position of the link the valve-rod may be put in direct connec- 
tion with either eccentric, or may be given a movement controlled in 
part by one and in part by the other eccentric. When the hnk is moved 
by the reversing lever into a position such that the block to which the 
valve-rod is attached is at either end of the hnk, the valve receives its 
maximum travel, and when the link is in mid-gear the travel is the 
least and cut-off takes place early in the stroke. 

In the ordinary shifting-hnk with open rods, that is, not crossed, the 
lead of the valve increases as the link is moved from full to mid-gear, 
that is, as the period of steam admission is shortened. The variationfof 
lead is equalized for the front and back strokes by curving the link to 
the radius of the eccentric-rods concavely to the axles. With crossed 
eccentric-rods the lead decreases as the hnk is moved from full to mid- 
gear. In a valve-motion with stationary link the lead is constant. 
(For illustration see Clark's "Steam-engine," vol. ii, p. 22.) 

The linear advance of each eccentric is equal to that of the valve in 
full gear, that is, to lap + lead of the valve, when the eccentric-rods 
are attached to the link in such position as to cause the half- travel of 
the valve to equal the eccentricity of the eccentric. 

The angle between the two eccentric radii, that is, between hnes 
drawn from the center of the eccentric disks to the center of the shaft, 
equals 180° less twice the angular advance. 

Buel, inAppleton's "Cyclopedia of Mechanics, "vol. ii, p. 316, discusses 
the Stephenson link as follows: "The Stephenson link does not give a 
perfectly correct distribution of steam; the lead varies for different 
points of cut-off. The period, of admission and the beginning of ex- 
haust are not alike for both ends of the cyhnder, and the forward 
motion varies from the backward. 

"The correctness of the distribution of steam by Stephenson's hnk- 
motion depends upon conditions which, as much as the circumstances 
will permit, ought to be fulfilled, namely: 1. The link should be curved 
in the arc of a circle whose radius is equal to the length of the eccentric- 
rod. 2. The eccentric-rods ought to be long, the longer they are in pro- 
portion to the eccentricity the more symmetrical will the travel of the 
valve be on both sides of the center of motion. 3. The link ought to be 
short. Each of its points describes a curve in a vertical plane, whose 
ordinates grow larger the farther the considered point is from the center 
of the link; and as the horizontal motion only is transmitted to the 
valve, vertical oscillation will cause irregularities. 4. The link-hanger 
ought to be long. The longer it is the nearer will be the arc in wliich 
the link swings to a straight line, and thus the less its vertical osciUation. 
If the link is suspended at its center, the curves that are described by 
points equidistant on both sides from the center are not alike, and 
hence results the variation between the forward and backward gears. 
If the link is suspended at its lower end. its lower half will have less 
vertical oscillation and the upper half more. 5. The center from which 
the link-hanger swings changes its position as the link is lowered or 
raised, and also causes irregularities. To reduce them to the smallest 
amount the arm of the lifting-shaft should be made as long as the 
eccentric-rod, and the center of the lifting-shaft should be placed at 
the height corresponding to the central position of the center on which 
the link-hanger swings." 

All these conditions can never be fulfilled in practice, and the variations 
in the lead and the period of admission can be somewhat regulated in an 
artificial way, but for one gear only. This is accomphshed by giving 
different lead to the two eccentrics, which difference will be smaller the 
longer the eccentric-rods are and the shorter the link, and by suspending 



THE STEPHENSON LINK-MOTION. 



1063 



the link not exactly on its center line but at a certain distance from it, 
giving what is called "the offset." 

For application of the Zeuner diagram to link-motion, see Holmes on 
the Steam-engine, p. 290. See also Clark's Railway Machinery (1855), 
Clark's Steam-engine, Zeuner's and Auchincloss's Treatises on Slide- 
valve Gears, and Halsey's Locomotive Link Motion. (See page 1119.) 

The following rules are given by the American Machinist for laying out 
a link for an upright sUde-valve engine. By the term radius of link is 
meant the radius of the link-arc, ah, Fig. 173, drawn through the center 
of the slot ; this radius is generally made equal to the distance from the 




Fig. 173. 



center of shaft to center of the link-block pin P when the latter stands 
midway of its travel. The distance between the centers of the eccentric- 
rod pins ei 62 should not be less than 21/2 times, and, when space will 
permit, three times the throw of the eccentric. By the throw we mean 
twice the eccentricity of the eccentric. The slot link is generally sus- 
pended from the end next to the forward eccentric at a point in the link- 
arc prolonged. This will give comparatively a small amount of slip to the 
link-block when the link is in forward gear; but this slip will be increased 
when the link is in backward gear. This increase of slip is, however, 
considered of little importance, because marine engines, as a rule, work 
but very little in the backward gear. When it is necessary that the 
motion shall be as efficient in backward gear as in forward gear, then the 
link should be suspended from a point midway between the two eccentric- 
rod pins; in marine engine practice this point is generally located on the 
link-arc; for equal cut-offs it is better to move the point of suspension 
a small amount towards the eccentrics. 

For obtaining the dimensions of the link in inches: Let L denote the 
length of the valve, B the breadth, p the absolute steam-pressure per sq. in ., 
and R a factor of computation used as below ; then R =0.01 ^L XB X p 

Breadth of the link = ie X 1 .6 

Thickness T of the bar = RX O.S 

Length of sUding-block = RX 2.5 

Diameter of eccentric-rod pins = (72 X 0.7) ^- 1/4 in. 

Diameter of suspension-rod pin = (i? X 0. 6) + 1/4 in. 

Diameter of suspension-rod pin when overhung. . . = (72 X 0. 8) + 1/4 in. 

Diameter of block-pin when overhung = 72 -f- 1/4 in. 

Diameter of block-pin when secured at both ends, = (RX 0.8) + 1/4 in. 



1064 



THE STEAM-ENGINE. 



The length of the link, that is, the distance from a to &, measured on a 
straight line joining the ends of the link-arc in the slot, should be such 
as to allow the center of the link-block pin P to be placed in a Hne with 
the eccentric-rod pins, leaving sufficient room for the shp of the block. 
Another type of hnk frequently used in marine engines is the double-bar 
link, and this type is again divided into two classes: one class embraces 
those Unks which have the eccentric-rod ends as well as the valve-spindle 
end between the bars, as shown at B (with these Unks the travel of the 
valve is less than the throw of the eccentric); the other class embraces 
those links, shown at C, for which the eccentric-rods are made with fork- 
ends, so as to connect to studs on the outside of the bars, allowing the 
block to sUde to the end of the hnk, so that the centers of the eccentric- 
rod ends and the block-pin are in hne when in full gear, making the travel 
of the valve equal to the throw of the eccentric. The dimensions of these 
links when the distance between the eccentric-rod pins is 21/2 to 23/4 times 
the throw of eccentrics can be found as follows; 

Depth of bars = (R X 1 . 25) 4- V2in. 

Thickness of bars = {R X . 5 ) + 1/4 in. 

Diameter of center of sliding-block = R X 1.3 

When the distance between the eccentric-rod pins is equal to 3 or 4 
times the throw of the eccentrics, then 

Depth of bars = (RX 1.25) + 3/4 in. 

Thickness of bars = {RX 0.5 ) + V4 in. 

All the other dimensions may be found by the first table. These are 
empirical rules, and the results may have to be slightly, changed to suit 
given conditions. In marine engines the eccentric-rod ends for all 
classes of links have adjustable brasses. In locomotives the slot-link is 
usually employed, and in these the pin-holes have case-hardened bushes 
driven into the pin-holes, and have no adjustable brasses in the ends of 
the eccentric-rods. The link in B is generally suspended by one of the 
eccentric-rod pins; and the link in C is suspended by one of the pins in 
the end of the hnk, or by one of the eccentric-rod pins. (See note on 
Locomotive Link Motion, p. 1119.) 

The Walschaerts Valve-gear. Fig. 174. — This gear, wliicli was 
invented in Belgium, has for many years been used on locomotives in 
Europe, and it has now (1909) come largely into use in the United States. 
The return crank Q, which takes the place of an eccentric, through the 
rod B oscillates the link on the fixed pin F. The block D is raised and 
lowered in the link by the reversing rod 7, operating through the bell* 

-.D 




Fig. 174*— The Walschaerts Valve-gear. 



crank leVefs H, H, and the supporting rod G. When the block is in its 
lowest position the radius rod U has a motion corresponding in direction 
to that of the rod B; when the block is at its upper position U moves in 
an opposite direction to B. The valve-rod E is moved by the combined 
action of U ahd a lever T whose lower end is connected through the 
rod S to the cross-head 7^. Constant lead is secured by this gear. (The 
main crank and the return crank should be shown in the cut as inclin- 
ing to the right to correspond with the position of the cross-head.) 



GOVERNORS. 1065 

Other Forms of Valve-gear, as the Joy, Marshall, Hackworth, 
Bremme, Walschaerts, Corliss, etc., are described in Clark's Steam- 
engine, vol. ii. Power, May 11, 1909, illustrates the Stephenson, Gooch, 
Allen, Polenceau, Marshall, Joy, Waldegg, Walschaerts, Fink, and 
Baker-PiUiod gears. The design of the Reynolds-CorUss valve-gear is 
discussed by A. H. Eldridge in Power, Sept., 1893, Bee also Henthorn 
on the Corliss Engine. Rules for laying down the center lines of the 
Joy valve-gear are given in American Machinist, Nov. 13, 1890. For 
Joy's "Fluid-pressure Reversing-valve," see Eng'g, May 25, 1894. 

GOVERNORS. 

Pendulum or Fly-ball Governor. — The inclination of the arms of a 
revolving pendulum to a vertical axis is such that the height of the point 
of suspension h above the horizontal plane in which the center of gravity 
of the balls revolves (assuming the weight of the rods to be small compared 
with the weight of the balls) bears to the radius r of the circle described 
by the centers of the bahs the ratio 

h _ weight _ w _ gr 

r ~ centrifugal force ~" wv^ ~ t;* 
gr 

which ratio is independent of the weight of the balls, v being the velocity 
of the centers of the balls in feet per second. 

If T = number of revolutions of the balls in 1 second, v == 2 tttT =^ or, 
in which a = the angular velocity, or 2 irT, and 

'^ ^ $ = 4^2» or ^ = ^^"P^ feet = ^^ inches, 

gf = 32.16. If iV = revs, per minute, h = 35,190 -^ NK 

For revolutions per minute .... 40 45 50 60 75 

The height in inches will be .. . 21.99 17.38 14.08 9.775 6.256 

Number of turns per minute required to cause the arms to take a givea 
angle with the vertical axis: Let I = length of the arm in inches from 
the center of suspension to the center of gyration, and a the required 
angle; then 

y I cos a 1 I cos a ^ h 

The simple governor is not isochronous; that is, it does not revolve 
at a uniform speed in all positions, the speed changing as the angle of th^ 
arms changes. To remedy this defect loaded governors, such as Porter's, 
are used. From the balls of a common governor whose coUectjve weight 
is A let there be hung by a pair of links of lengths equal to the pendulum 
arms a load B capable of shding on the spindle, having its center of gravity 
in the axis of rotation. Then the centrifugal force is that due to A alone, 
and the effect of gravity is that due to A + 2 B; consequently the alti- 
tude for a given speed is increased in the ratio {A + 2 B) : A, as com- 
pared with that of a simple revolving pendulum, and a given absolute 
variation in altitude produces a smaller proportionate variation in speed 
than in the common governor. (Rankine, S. E., p. 551.) 

For the weighted governor let 1= the length of the arm from the point 
of suspension to the center of gravity of the ball, and let the length of the 
suspending-Unk Zi = the length of the portion of the arm fr9m the point 
of suspension of the arm to the point of attachment of the link; G = the 
weight of one ball, Q = half the weight of the shding v>' eight, h = the 
height of the governor from the point of suspension to the plane of revolu* 
tion of the balls, a = the angular velocity = 2nT, T being the number oj 

1 *x A ^u ./32.I6A ^2ZiQ\ , 32.16 /, , 2^1 g\ 

revolutions per second ; then a = 4/ , (1 + -j- q)''^= ^2 \} ^ ~r g) 

in feet, or ft = ^^^(l + X i) ^^ inches, iV being the number of revo» . 
iutions per minute. 



1066 THE STEAM-ENGINE. 

(1R7 7\2 7? 4- 2 TV 
~^ j , in which B is the combined 

weight of the two balls and W the central weight. 

For various forms of governor see App. Cyl. Mech., vol. ii, 61, and 
Clark's Steam-engine, vol. ii, p. 65. 

To Change the Speed of an Engine Having a Fly-baii Governor. — 

A slight difference in the speed of a governor changes the position of its 
weights from that required for full load to that required for no load. 
It is evident therefore that, whatever the speed of the engine, the normal 
speed of the governor must be that for which the governor was designed; 
i.e., the speed of the governor must be kept the same. To change the 
speed of the engine the problem is to so adjust the pulleys which drive 
the governor that the engine at its new speed shall drive it just as fast as 
it was driven at its original speed. In order to increase the engine-speed 
we must decrease the pulley upon the shaft of the engine, i.e., the driver, 
or increase that on the governor, i.e., the driven, in the proportion that 
the speed of the engine is to be increased. 

Fly-wheel or Shaft-governors. — At the Centennial Exhibition in 
1876 there were shown a few steam-engines in which the governors were 
contained in the fly-wheel or band-wheel, the fly-balls or weights revolving 
around the shaft in a vertical plane with the wheel and shifting the eccen- 
tric so as automatically to vary the travel of the valve and the point of 
cut-off. This form of governor has since come into extensive use, espe- 
cially for high-speed engines. In its usual form two weights are carried on 
arms the ends of which are pivoted to two points on the pulley near its 
circumference, 180° apart. Links connect these arms to the eccentric. 
The eccentric is not rigidly keyed to the shaft but is free to move trans- 
versely across it for a certain distance, having an oblong hole which allows 
of this movement. Centrifugal force causes the weights to fly towards 
the circumference of the wheel and to pull the eccentric into a position of 
minimum eccentricity. This force is resisted by a spring attached to 
each arm which tends to pull the weights towards the shaft and shift the 
eccentric to the position of maximum eccentricity. The travel of the valve 
is thus varied, so that it tends to cut off earlier in the stroke as the engine 
increases its speed. Many modifications of this general form are in use. 
In the Buckeye and the Mcintosh & Seymour engines the governor shifts 
the eccentric around on the shaft so as to vary the angular advance 
In the Sweet " Straight -line " engine and in some others a single weight 
and a single spring are used. For discussions of this form of governor 
see Hartnell, Proc. Inst. M. E., 1882, p. 408: Trans. A. S. M. E., ix, 300; 
xi, 1081; xiv, 92; xv, 929; Modern Mechanism, p. 399: Whitham's Con- 
structive Steam Engineering: J. Begtrup, Am. Mach., Oct. 19 and Dec. 14, 
1893, Jan. 18 and March 1, 1894. 

More recent references are: J. Richardson, Proc. Inst. M. E., 1895 
(includes electrical regulation of steam-engines); A. K. Mansfield, Trans. 
A. S. M. E., 1894; F. H. Ball, Trans. A. S. M. E., 1896; R. C. Carpenter, 
Power, May and June, 1898; Thos. Hall, El. World, June 4, 1898; F. M. 
Rites, Power, July, 1902; E. R. Briggs, Am. Mach., Dec. 17, 1903 

The Rites Inertia Governor, which is the most common form of the 
shaft governor at this date (1909). has a long bar, usually made heavy at 
the ends, like a dumb-bell, instead of the usual weights. This is carried 
on an arm of the fly-wheel by a pin located at some distance from the 
center line of the bar, and also at some distance from its middle point. 
To pins located at two other points are attached the valve-rod and the 
spring. The bar acts both by inertia and by centrifugal force. When 
the wheel increases its speed the inertia of the bar tends to make it fall 
behind, and thus to change the relative position of the fly-wheel arm and 
the bar, and to change the travel of the valve. A small book on "Shaft 
Governors" (Hill Pub. Co., 1908) describes and illustrates this and many 
other forms of shaft governors, and gives practical directions for adjusting 
them. 

Calculation of Springs for Shaft-governors. (Wilson Hartnell, 
Proc. Inst. M. E., Aug.. 1882.) — The springs for shaft-governors may be 
conveniently calculated as follows, dimensions being in inches; 

Let W = weight of the balls or weights, in pounds; 

fi and r2 = the maximum and minimum radial distances of the 
center of the balls or of the centers of gravity of the weights; 



GOVERNORS. 1067 

h. and h = the leverages, i.e., the perpendicular distances from the 
center of the weight-pin to a line in the direction of the centrif- 
ugal force drawn through the center of gravity of the weights 
or balls at radii ri and 7-2; 

mi and 1712 = the corresponding leverages of the springs; 

Ci and C2 = the centrifugal forces, for 100 revolutions per minute, 
at radii ri and rz; 

Pi and P2 = the corresponding pressures on the spring; 

(It is convenient to calculate these and note them down for refer- 
ence.) 

Cs and C4 = maximum and minimum centrifugal forces; 

S = mean speed (revolutions per minute); 

Si and ^2 = the maximum and minimum number of revolutions 
per minute; 

Pa and P* = the pressures on the spring at the Umiting number 
of revolutions (Si and S2); 

P4 — P3 = jD = the difference of the maximum and minimum 
pressures on the springs; 

V = the percentage of variation from the mean speed, or the 
sensitiveness; 

t = the travel of the spring; 

u = the initial extension of the spring; 

V = the stiffness in pounds per inch; 
w = the maximum extension = u -{■ t. 

The mean speed and sensitiveness desired are supposed to be ^ven. 
Then 



«— iJ^ 






».— ii;^ 


Ci = 0.28XriX W; 




C2 = 0.28Xr2X W; 


mi 






P. = C.XA; 


^-^'X(S = 






^'-^'>^& 


D 


U 


V 


V 



It is usual to give the spring-maker the values of P4 and of v or w. 
To ensure proper space being provided, the dimensions of the spring should 
be calculated by the formulae for strength and extension of springs, and 
the least length of the spring as compressed be determined. 

rru P3+P4,, t 

The governor-power = — X j-^- 

With a straight centripetal line, the governor-power 
_ C3+C4, 



/ r2 — ri \ 
\ 12 /• 



For a preliminary determination of the governor-power it may be taken 
as equal to this in all cases, although it is evident that with a curved cen, 
tripetal line it will be slightly less. The difference D must be constant for 
the same spring, however great or little its initial compression. Let the 
spring be screwed up until its minimum pressure is P3. Then to find the 
speed Pe == P5 + I>, _ _ 

>S5 = 100y/|^; Se=100\^^' 

The speed at which the governor would be isochronous would be 
100 < 



Vk§k- 



Suppose the pressure on the spring with a speed of 100 revolutions, at 
the maximum and minimum radii, was 200 lbs. and 100 lbs., respectively, 



1068 



THE STEAM-ENGINE. 



then the pressure of the spring to suit a variation from 95 to 105 revolu- 
tions will be 100 X (^V= 90 .2 and 200 X (1^^ = 220. 5 That is, the 

increase of resistance from the minimum to the maximum radius must be 
220-90 = 130 lbs. 

The extreme speeds due to such a spring, screwed up to different 
pressures, are shown in the following table: 



Revolutions per minute, balls shut 

Pressure on springs, balls shut 

Increase of pressure when balls open fully 

Pressure on springs, balls open fully 

Revolutions per minute, balls open fully . . 
Variation, per cent of mean speed 



80 


90 


95 


100 


110 


64 


81 


90 


100 


121 


130 


130 


130 


130 


130 


194 


211 


220 


230 


251 


98 


102 


105 


107 


112 


10 


6 


5 


3 


1 



120 
144 
130 
274 
117 
-I 



The speed at which the governor would become isochronous is 114. 

Any spring will give the right variation at some speed; hence in experi- 
menting with a governor the correct spring may be found from any v/rong 
one by a very simple calculation. Thus, if a governor with a spring 
whose stiffness is 50 lbs. per inch acts best when the engine runs at 95, 90 

/go \ 2 
being its proper speed, then 50 X ( 5-^ ) =45 lbs. is the stiffness of spring 

required. 

To determine the speed at wliich the governor acts best, the spring 
may be screwed up until the governor begins to "hunt" and then be 
slackened until it is as sensitive as is compatible with steadiness. 



Another formula is: Q = 



WH 
R 



CONDENSERS, AIR-PUMPS, CIRCULATING-PTJMPS, ETC. 

The Jet Condenser. — In practice the temperature in the hot-well 
varies from 110° to 120°, and occasionally as much as 130° is maintained. 
To find the quantity of injection-water per pound of steam to be condensed: 
Let Ti = temperature of steam at the exhaust pressure; To = temper- 
ature of the cooling-water; T2 = temperature of the water after condensa- 
tion, or of the hot-well; Q = pounds of the cooling-water per lb. of steam 
condensed; then 

1114° + 0.3 7^1-^2 
^ T2-T0 

in which W is the weight of steam con- 
densed, H the units of heat given up by 1 lb. of steam in condensing, and 
R the rise in temperature of the cooling-water. This is applicable both 
to jet and to surface condensers. 

Quantity ojf Cooling-water. — The quantity depends chiefly upon 
its initial temperature, which in Atlantic practice may vary from 40° in 
the winter of temperate zone to 80° in subtropical seas. "To raise the 
temperature to 100° in the condenser will require three times as many 
thermal units in the former case as in the latter, and therefore only one- 
third as much cooling-water will be required in the former case as in the 
latter. It is usual to provide pumping power sufficient to supply 40 times 
the weight of steam for general traders, and as much as 50 times for sliips 
stationed in subtropical seas, when the engines are compound. If the 
circulating pump is double-acting, its capacity may be 1/53 in the former 
and 1/42 in the latter case of the capacity of the low-pressure cyhnder. 
(Seaton.) 

The following table, condensed from one given by W. V. Terry in Power, 
Nov. 30, 1909, shows the amount of circulating water required under 
different conditions of vacuum, temperature of water entering tlic con- 
denser, and drop. The "drop" is the difference between the temperature 
of steam due to a given vacuum and the temperature of the water leaving 
the condenser. 



CONDENSERS, AIR-PUMPS, ETC. 



1069 



Pounds of Circulating Water per Pound of Steam Condensed. 



Vac- 
uum. 
Ins. 


Drop. 

Deg. 

F. 






Inject 


on Water Temperature, Deg. F. 






45 


50 


55 


60 


65 


70 


75 


80 


85 


90 


29.0 


6 
12 

18 


37.5 

47.8 
65.7 


45.7 
61.8 
95.5 


58.3 
87.5 


80.8 














28.5 


6 

12 
18 


25.6 
30.0 
36.2 


29.2 
35.0 
43.8 


33.9 
42.0 
55.3 


40.3 
52.5 
75.0 


50.0 
70.0 


65.7 


95.5 








28.0 


6 

12 
18 


21.5 
24.4 
28.4 


23.9 
27.7 
32.8 


26.9 
31.8 
38.9 


30.9 
37.5 
47.8 


36.3 
45.7 
61.8 


43.8 
58.3 
87.5 


55.3 
80.8 


75.0 






27.0 


6 
12 
18 


16.4 
18.1 
20.2 


17.8 
19.8 
22.4 


19.5 
21.9 
25.0 


21.5 
24.4 
28.4 


23.9 
27.7 
32.8 


27.0 
31.8 
38.9 


30.9 
37.5 

47.8 


36.2 
45.7 
61.8 


43.8 
58.3 
87.5 


55.3 
80.8 


26.0 


6 

12 
18 


14.0 
15.2 
16.8 


15.0 
16.4 
18.1 


16.2 
17.8 
19.8 


17.5 
19.5 
21.9 


19.1 
21.5 
24.4 


21.0 
23.9 
27.7 


23.4 
26.9 
31.8 


26.3 
30.9 
37.5 


30.0 
36.3 

45.7 


35.0 

43.8 
58.3 



Ejector Condensers. — For ejector or injector condensers (Bulkley's, 
Schutte's, etc.) the calculations for quantity of condensing-water is the 
same as for jet condensers. 

The Barometric Condenser consists of a vertical cylindrical chamber 
mounted on top of a discharge pipe whose length is 34 ft. above the level 
of the hot well. The exhaust steam and the condensing water meet in the 
upper chamber, the w^ater being delivered in such a manner as to expose 
a large surface to the steam. The external atmosphere maintains a col- 
umn of water in the tube, as a column of mercury is maintained in a 
barometer, and no air pump is needed. The Bulkley condenser is the 
original form of the type. In some modern forms a small air pump draws 
from the chamber the residue of air which is not drawn out by the de- 
scending column of water, discharging it into the column below the 
chamber. 

The Surface Condenser — Cooling Surface. — In practice, with the 
compound engine, brass condenser-tubes, 18 B.W.G. tliick, 13 lbs. of 
steam per sq. ft. per hour, with the cooling-water at an initial temperature 
of 60°, is considered very fair work when the temperature of the feed- 
water is to be maintained at 120°. It has been found that the surface in 
the condenser may be half the heating surface of the boiler, and under 
some circumstances considerably less than this. In general practice the 
following holds good when the temperature of sea-water is about 60°: 
Terminal pres., lbs., abs. . 30 20 15 I21/2 10 8 6 

Sq. ft. per I.H.P 3 2.50 2.25 2.00 1.80 1.60 1.50 

For ships whose station is in the tropics the allowance should be in- 
creased by 20%, and for ships which occasionally visit the tropics 10% 
increase will give satisfactory results. If a ship is constantly employed 
in cold climates 10% less suffices. (Seaton, Marine Engineering.) 

Whitham (Steam-engine Design, p. 283, also Trans. A. S. M. E., ix, 431 ) 
WL 
gives the following: S= , _., , in which S = condensing-surface in 

sq. ft.; Ti = temperature Fahr. of steam of the pressure indicated by the 
vacuum-gauge; t = mean temperature of the circulating water, or the 
arithmetical mean of the initial and final temperatures; L = latent heat 
of saturated steam at temperature T\; k = perfect conductivity of 1 sq. 
ft. of the metal used for the condensing-surface for a range of 1° F. (or 
550 B.T.U. per hour for brass, according to Isherwood's experiments); 
c = fraction denoting the efficiency of the condensing-surface; W = 



1070 THE STEAM-ENGINE. 

pounds of steam condensed per hour. From experiments by Loring and 
Emery, on U.S.S. Dallas, c is found to be 0.323, and ck = 180; making 

the equation S = ^gQ (y^_^y 

Whitham recommends this formula for designing engines having inde- 
pendent circulating-pumps. When the pump is worked by the main 
engine the value of S should be increased about 10%. 

Taking Ti at 135° F., and L = 1020, corresponding to 25 in. vacuum, 

^ * * ^ * * ^ro V, o 1020 T^' 17 W 

and t for summer temperatures at 75°, we have : S = ., ^^ ,..„_ — ^r^\ =-7377- 

180 (135 — 75/ 180 
Much higher results than those quoted by Wliitham are obtained from 
modern forms of condensers. The literature on the subject of condensers 
from 1900 to 1909 has been quite voluminous, and much difference of 
opinion as to rules of proportioning condensers is shown. 

Coefficient of Heat Transference in Condensers. (Prof. E. Jesse 
of Berlin. Condensed from an abstract in Power, Feb. 2, 1909. See also 
Transmission of Heat from Steam to Water, pages 587 to 589.) 

The coefficient U , the number of heat units transferred per hourthrough 
1 sq. ft. of metallic condenser wall when the temperature of the steam is 
1° F. higher than that of the water, can be deduced from the formula 
IIU = IM1+ diL + IM2, 

in which iMi is the resistance to transmission from steam to metal, IM2 
the resistance to transmission from metal to water, and dIL the resistance 
to transmission of heat through the metal, d being the usual thickness of 
condenser tubes (1 m.m. or .0393 in.). For this thickness the value of 
L is fairly well known and may be given as 18,430 for brass, 6,500 for 
copper, 11,270 for iron, 5740 for zinc, 11,050 for tin and 2660 for alumi- 
num. The middle term dIL would have the value of 1/18,430 and be of 
comparatively^ little importance. 

The term II A2 is the most important and has been investigated with 
the aid of two concentric tubes, water being sent both through the inner 
tube and the annular jacket. The values of various experimenters differ 
greatly. Ser gives the approximate formula 

A - 2 = 510 Vy, 

where V is the velocity of water through the tubes in ft. per sec. This 
velocity is far more important than the material of the condenser tubes 
and their thickness, and also of greater consequence than the velocity 
of the steam, about which, or, rather, the term 1/Ai, there is even less 
agreement. Prof. Josse adopts the figure 3900. The velocity of the 
steam has its influence, but the whole term does not count for much. 
For water flowing at the rate of 1 .64 ft. per sec. Josse's formula would be: 
IIU = 1/3900 + 1/18,430 + 1/653 = 1/445, 

and U = 445. 

If A 1 be increased to twice its value U would rise only to 475, and if the 
tube thickness be doubled U wDuld hardly be affected. An increase, 
however, in the rate of flow of water from 1.64 to 5 feet per second would 
raise U to 625. As an increase of the steam flow is undesirable the best 
plan is to accelerate the flow of the circulating water, and by introducing 
the baffle strips or retarders into his condenser tubes, in order to break the 
water currents up into vortices, Josse raised the value of U at a velocity of 
3.28 feet per second from 614 to 922. 

Opinions differ concerning the increase of U with greater differences of 
temperature. According to some the heat transferred should increase 
proportionately to the difference; according to Weiss and others, pro- 
portionally to the square of the temperature differences. Josse's investi- 
gations were conducted by placing thermo couples in different portions 
of the condenser tubes. If the heat transferred increases as a linear 
function of the difference, then the rise of the temperature in the cool- 
ing water should follow an exponential law, and it was found to be so. 

Curves showing the relation of the extent of surface to the temperatures 
of steam and water show an agreement with the formula 

Surface = *S « § log^ J-Zf' 



CONDENSERS, AIR-PUMPS, ETC. 



1071 



where tg is the saturation temperature and t^the temperature of the cooling- 
water at entrance, t being the discharge temperature. 

Air Leakage. — Air passes into the condenser with the exhaust steam, 
the temperature of the air being that of the steam; the pressure of the 
mixture will be the sum of the partial steam pressure and of the partial 
air pressure. The air must be withdrawn by the air-pump. If the with- 
drawal takes place at the temperature corresponding to the condenser 
pressure the partial steam pressure would be equal to the condenser 
pressure, and the pump would have to deal with an enormous air volume. 
The air temperature should, therefore, be lowered, at the spot where the 
air is withdrawn, below the saturation temperature of the condenser 
pressure. 

In steam turbines it is more easy to keep air out than in reciprocating 
engines. Experiments with a 300-kw. Parsons turbine show that not more 
than 1/2 lb. of air was deUvered per hour when 6600 lbs. of steam was used 
per hour. 

Condenser Pumps. — The air and condensed water may either be 
removed separately, by a so-called dry-air pump, or both together, by 
a wet-air pump. As dry-air pumps have to deal with high compression 
ratios, with high vacua and single-stage pumps, the clearances must be 
small. When the clearance amounts to 5% the vacuum cannot be main- 
tained at more than 95%, and the clearance must be reduced, or other 
expedients adopted. Three are mentioned: (1) the air-pump may be 
built in two stages; (2) the pump may be fitted with an equalizing pipe 
so that the two sides of the piston are connected near the end of each 
stroke; the volumetric efficiency is raised by this expedient, but consider- 
ably more power is absorbed to accompUsh the result; (3) with the wet- 
air pump the clearance space is made to receive the condensed water, 
which will fill at least part of it. 

Contraflow and Ordinary Flow. — Prof. Josse questions the distinction 
between contraflow and ordinary flow. For the greater portion of the 
condenser there is a rise of temperature only on the water side; the tem- 
perature of the steam side remains that of the saturated steam, and the 
term "contraflow" should, strictly speaking, only be apphed if there is a 
temperature faU in the one direction and a corresponding temperature rise 
in the opposite direction. As far as the condensation is concerned, it is 
immaterial in which direction the water flows. The contraflow principle 
is, however, correct and necessary for the smaller portion of the condenser 
in which the condensed liquid is cooled together with the air; for the 
air must be withdrawn from the coldest spot. It seems inadvisable to 
attempt to direct the flow of the steam on the contraflow principle, as that 
would obstruct the steam flow and create a pressure difference between 
different portions of the condenser w^hich w^ould be injurious to the main- 
tenance of high vacua. 

The Power Used for Condensing Apparatus varies from about 
11/2 to 5% of the indicated power of the main engine, depending on the 
efficiency of the apparatus, on the degree of vacuum obtained, the tem- 
perature of the cooling-water, the load on the engine, etc. J. R. Bibbins 
(Power, Feb., 1905) gives the records of test of a 300-kw. plant from which 
the following figures are taken. Cooling-water per lb. of steam 32 to 37 
lbs. Vacuum 27.3 to 27.8 ins. Temp. cooUng-water 73. Hot-well 102 
to 105. 



Indicated H.P 

% of total power used . . 

% for air cylinder 

% for water pump 



151 


220 


238 


260 


291 


294 


457 


4.69 


3.51 


3.22 


3.22 


3.08 


2.97 


2.80 


1.63 


1.36 


1.27 


1.21 


1.19 


1.09 


0.95 


3.07 


2.14 


1.95 


2.00 


1.90 


1.89 


1.85 



589 
2.47 
0.85 
1.52 



Vacuum, ins. of Mercury, and Absolute Pressures. — The vacuum 
as shown by a mercury column is not a direct measure of pressure, but 
only of the difl:'erence between the atmospheric pressure and the absolute 
pressure in the vacuum chamber. Since the atmospheric pressure varies 
with the altitude and also with atmospheric conditions. It is necessary 
when accuracy is desired to give the reading of the barometer as well as 
that of the vacuum gauge, or preferably to give the absolute pressure in 
lbs. per sq. in. above a perfect vacuum. 



1072 



THE STEAM-ENGINE. 



Temperatures, Pressures and Volumes of Saturated Air.— (D. B. 

Morison, on the influence of Air on Vacuum in Surface Condensers, 
Eng'g, April 17, 1908.) 





Volume 


OF 


1 Lb. of Air with , 


A.CCOMP ANTING VAPOR. 








Vacuum, ins. of Mercury, and lbs. absolute. 


24 in., 
2.947. 


26 in., 
1.962. 


27 in., 
1.474. 


28 in., 
0.9823. 


28.5 in., 
0.7368. 


28.8 in., 
0.5894. 


29 in., 
0.4912. 


50 
60 
70 
80 


0.17 
0.25 
0.36 
0.50 
0.69 
0.94 
1.26 
1.68 


P 

2.78 
2.70 
2.59 
2.45 
2.26 
2.01 
1.69 
1.27 


V 
68 
71 
75 
81 
90 
103 
125 
170 


P 

1.79 
1.71 
1.60 
1.46 
1.27 
1.02 
0.70 
0.28 


V 
105 
113 
124 
137 
163 
203 
304 
770 


P 

1.30 

I:f? 

0.97 
0.78 
0.53 
0.21 


V 
147 
158 
178 
204 
260 
390 
(a) 


P 

0.81 
0.73 
0.62 
0.48 
0.29 
0.042 


V 

233 
263 
315 

420 
700 

(&) 


P 
0.57 
0.49 
0.38 
0.24 
0.05 


V 
336 
393 
520 
832 
(c) 


P 

0.42 
0.34 
0.23 
0.09 


V 
450 
566 
852 
id) 


P 
0.32 
0.24 
0.13 


V 
592 
800 
1536 


90 






100 










110 














170 







































P = partial pressure of air, lbs. per sq. in. V = volume of 1 lb. of 
air with accompanying vapor, cu. ft. (a) over 1000; (b) nearly 5000; 
(c) about 4000; (d) over 2000. 

Temperatures and Pressures of Saturated Air. 



Vacuum, Ins. 


Proportions of Air and Steam by Weight. 


with Barom. 


Saturated 


Air, 0.25. 


Air, 0.5. 


Air, 0.75. 


Air, 1. 


at 30 in. 


Steam. 


Steam, 1. 


Steam, 1. 


Steam, 1. 


Steam, 1. 


29 


79.5° F. 


75 


71 


67.5 


64.5 


28 


101.5 


96.5 


92.4 


88.8 


85.3 


27 


115 


110 


105.6 


101.7 


98.6 


26 


126 


120.2 


115.5 


111.5 


108.3 


25 


134 


128.4 


123.5 


119 2 


116.2 


24 


141 


135.2 


130.3 


125.8 


122.3 



From this table it is seen that a temperature of 126° F. corresponds to 
a 24-in. vacuum if the steam in the condenser has 75% of its weight of 
air mingled with it, and to a 26-in. vacuum if it is free from air. 

One cubic foot of air measured at 60° F. and atmospheric pressure 
becomes 10 cu. ft. at 27 in. and 30 cu. ft. at 29 in. vacuum at the same 
temperature; 10.9 cu. ft. at 105° and 27 in.; 30.5 cu. ft. at 70° F. and 
29 in. The same cu. ft. of air saturated with water vapor at 70° F. and 
29 in. becomes 124.3 cu. ft., or 44.9 cu. ft. at 105° and 27 in. vacuum* 
The temperatures 105° and 70° are about 10% below the temperatures 
of saturated steam at 27 in. and 29 in. respectively. 

Condenser Tubes are generally made of soUd-drawn brass tubes, and 
tested both by hydraulic pressure and steam. They are usually made of 
a composition of 68% of best selected copper and 32% of best Silesian 
spelter. The Admiralty, however, always specify the tubes to be made 
of 70% of best selected copper and to have 1% of tin in the composition, 
and test the tubes to a pressure of 300 lbs. per sq. in. (Seaton.) 

The diameter of the condenser tubes varies from 1/2 in. in small con- 
densers, when they are very short, to 1 in. in very large condensers and 
long tubes. In the mercantile marine the tubes are, as a rule, 3/4 in. 
diam. externally, and 18 B.W.G. thick (0.049 inch): and 16 B.W.G. 
(0 .065), under some exceptional circumstances. In the British Navy the 
tubes are also, as a rule, 3/4 in. diam., and 18 to 19 B.W.G.. tinned on 
both sides; when the condenser is brass the tubes are not required to be 
tinned. Some of the smaller engines have tubes s/g in. diam.. and 19 
B. W. G. The smaller the tubes, the larger is the surface which can be 
put in a certain space. (Seaton.) 

In the merchant service the almost universal practice is to circulate 
the water through the tubes. 

Whitham says the velocity of flow through the tubes should not be 
less than 400 nor more than 700 ft. per min. 



CONDENSERS, AIR-PUMPS, ETC. 



1073 



Tube-plates are usually made of brass. Rolled-brass tube-plates 
should be from 1.1 to 1.5 times the diameter of tubes in thickness, 
depending on the method of packing. When the packings go completely- 
through the pl-ates, the latter thickness, but when only partly through, 
the former, is sufficient. Hence, for 3/4-in. tubes the plates are usually 
7/8 to 1 in. thick with glands and tape-packings, and 1 to 1 1/4 ins. thick 
with wooden ferrules. The tube-plates should be secured to their seat- 
ings by brass studs and nuts, or brass screw-bolts: in fact there must be 
no wrought iron of any kind inside a condenser. When the tube-plates 
are of large area it is advisable to stay them by brass rods, to prevent 
them from collapsing. 

Spacing of Tubes, etc. — The holes for ferrules, glands, or india- 
rubber are usually 1/4 inch larger in diameter than the tubes; but when 
absolutely necessary the wood ferrules may be only 3/32 inch thick. 

The pitch of tubes when packed with wood ferrules is usuallv 1/4 inch 
more than the diameter of the ferrule-hole. For example, the tubes are 
generally arranged zigzag, and the number which may be fitted into a 
square foot of plate is as follows: 



Pitch of 

Tubes, 

In. 


No. in a 
Sq. Ft. 


Pitch of 

Tubes, 

In. 


No. in a 
Sq. Ft. 


Pitch of 

Tubes, 

In. 


No. in a 
Sq. Ft. 


1 

11/16 
1 1/8 


172 
150 
137 


1 5/32 
13/16 

1 7/32 


128 
121 
116 


1 1/4 
19/32 
1 5/16 


110 
106 
99 



Air-Pump. — The air-pump in all condensers abstracts the water con- 
densed and the air originally contained in the water when it entered the 
boiler. In the case of jet-condensers it also pumps out the water of con- 
densation and the air which it contained. The size of the pump is calcu- 
lated from these conditions, making allowance for efficiency of the pump. 

In surface condensation allowance must be made for the water oc- 
casionally admitted to the boilers to make up for waste, and the air 
contained in it, also for sUght leaks in the joints and glands, so that the 
air-pump is made about half as large as for jet-condensation. 

Seaton says: The efficiency of a single-acting air-pump is generally 
taken at 0.5 and that of a double-acting pump at 0.35. W^hen the 
temperature of the sea is 60°, and that of the (jet) condenser is 120°, 
Q being the volume of the cooling-water and q the volume of the con- 
densed water in cubic feet, and n the number of strokes per minute, 

The volume of the single-acting pump = 2.74 ((?+ Q) -^ n. 

The volume of the double-acting pump = 4: {Q -\- q) ^ n. 

W. H. Booth, in his "Treatise on Condensing Plant," says the 
volume to be generated by an air-pump bucket should not be less than 
0.75 cu. ft. per pound of steam dealt with by the condensing plant. 
Mr. R. W. Allen has made tests with as little air-pump capacity as 0.5 
cu. ft. and he gives 0.6 cu. ft. as a minimum. An Edwards pump with 
three 14-in. barrels, 12-in. stroke, single-acting, 150 r.p.m., is rated at 
45,000 lbs. of steam per hour from a surface condenser, which is equiva- 
lent to 0.66 cu. ft. per pound of feed- water. 

In the Edwards pump, the base of the pump and the bottom of the 
piston are conical in shape. The water from the condenser flows by 
gravity into the space below the piston, which descending projects it 
through ports into the space in the barrel above the piston, whence on 
the ascending stroke of the piston it is discharged through the outlet 
valves. There are no bucket or foot-valves, and the pump may be run 
at much higher speeds than older forms of pump. (See Catalogue of 
the Wheeler Condenser and Engineering Co.) 

The Area through Valve-seats and past the valves should not be 
less than will admit the full quantity 'of water for condensation at a 
velocity not exceeding 400 ft. per minute. In practice the area is gen- 
erally in excess of this. (Seaton.) 

Area tlirough foot- valves = D- X S ^ 1000 square inches. 
Area through head- valves = D~ X Sj^ 800 square inches. 
Diameter of discharge-pipe = D X \/S -r 35 inches. 
D = diam. of air-pump in inches, S = Its speed in ft. per min. 

James Tribe (Am. Mach., Oct. 8, 1891) gives the following rule for air- 



1074 



THE STEAM-ENGINE. 



prnnps used with jet-condensers : Volume of single-acting air-pump driven 

by main engine = volume of low-pressure cylinder in cubic feet, multiplied 
by 3.5 and divided by the number of cubic feet contained in one pound 
of exhaust steam of the given density. For a double-acting air-pump the 
same rule will apply, but the volume of steam for each stroke of the 
pump will be but one-half. Should the pump be driven independently 
of the engine, then the relative speed must be considered. Volume of jet- 
condenser = volume of air-pump X 4. Area of Injection valve = vol. of 
air-pump in cubic inches -?- 520. 

The Work done by an Air-pump, per stroke, is a maximum the- 
oretically, when the vacuum is between 21 and 22 ins. of mercury. As- 
suming adiabatic compression, the mean effective pressure per stroke 

r / r>2 \ 0*29 T 

is P = 3 .46 pi ( — 1 "" 1 ' where p = absolute pressure of the vacuum 

and P2 the terminal, or atmospheric, pressure, = 14 .7 lbs. per sq. in. The 
horse-power required to compress and deliver 1 cu. ft. of air per minute, 
measured at the lower pressure, is, neglecting friction, P X 144 -v- 33,000. 
The following table is calculated from these formulse (R. R. Pratt, Power 
Sept. 7, 1909). 



Vac. in 
Ins. of 
Mer- 


Abs. 
Press., 


'El 


Theo- 


Theo- 


V^ac. in 
Ins. of 
Mer- 


Abs. 
Press., 


V2 


Theo- 


Theo- 


Ins. of 


retic. 


retic. 


Ins. of 


retic. 


retic. 


Mer- 


Vi 


M.E.P. 


H.P. 


Mer- 


Vi 


M.E.P. 


H.P. 


cury. 


cury. 








cury. 


cury. 








29 


1 


30.00 


2.86 


0,0124 


18 


12 


2.50 


6.21 


0.0271 


26 


2 


15.00 


4.05 


0.0177 


16 


14 


2.14 


5.89 


0.0256 


27 


3 


10.00 


4.83 


0.0211 


14 


16 


1.87 


5.42 


0.0236 


26 


4 


7.50 


5.40 


0.0235 


12 


18 


1.67 


4.88 


0.0212 


25 


5 


6.00 


5.78 


0.0252 


10 


20 


1.50 


4.23 


0.0184 


24 


6 


5.00 


6.05 


0.0264 


8 


22 


1.36 


3.52 


0.0153 


23 


7 


4.28 


6.23 


0.0271 


6 


24 


1.25 


2.73 


0.0119 


22 


8 


3.75 


6.33 


0.0276 


4 


26 


1.15 


1.88 


0.0082 


21 


9 


3.33 


637 


0.0278 


2 


28 


1.07 


0.96 


0.0042 


20 


10 


3.00 


6.36 


0.0277 


1 


29 


1.03 


0.49 


0021 



The work done by the air-pump is to compress the saturated mixture 
of air and water vapor at the condenser pressure to atmospheric pressure 
and to discharge it into the atmosphere together with the water of 
condensation (and with the cooling water in the case of jet condensers 
operated a' ith an air-pump). The amount of air to be discharged 
varies with the amount of air in the feed-water and with the leakage of 
air through the stuflang-boxes. Geo. A. Orrok {Jour. A. S. M. E., 1912, 
p. 1625) found the volume of air in city water at 52 deg. F. to be over 4 
per cent; and in feed- water at 187 degrees less than 1 per cent. With 
turbines of from 5,000 to 20,000 kw. capacity the air discharged by 
the air-pump at atmospheric pressure and temperature varied from 
1 cu. ft. per min. with the units in the best condition to 15 or 20 when 
ordinary leakage was present, or to 30 to 50 when the units were in bad 
condition. Stodola states that we may ordinarily expect the air to 
amount to 1.5 to 2.5 cu. ft. per min. for each 1000 kw. capacity. 
T. C. McBride (Power, July 14, 1908) gives results of tests in which 
the amount of air varied from 18 to 74 volumes per 10,000 volumes of 
exhaust steam. C. L. W. Trinks (Proc. Engrs. Soc. of W. Penna., June, 
1914) gives the weight of air normally expected by builders of air- 
pumps as 0.25 to 0.50 per cent of the weight of steam. 

W. H. Herschel {Power, June 1, 1915), after quoting the above figiu*es, 
gives the results of calculations based upon assumed air leakages of 
20, 40, and 60 volumes of air per 10,000 volumes of steam, corresponding 
respectively to 0.31, 0.62, and 0.93 per cent of the weight of steam, or 
approximately to 15, 30, and 45 cu. ft. per min. for every 1000 kw. 
capacity, the smallest amount being that which may be obtained with 
stufling-boxes in the best condition, while the largest value may be 
reached, or even exceeded, with stuffing-boxes in poor condition. 
Following are his figures for the extreme conditions: 



CONDENSERS, AIR-PUMPS, ETC. 



1075 



Total Work of 


\N AlF 


.-PUMP 


, Including Discharge of 


Cooling Water. 


O M . 


Vacuum, In., Leakage 0,31 %. 




Vacuum, In., Leakage 0.93%. 




29 


28.5 


28 


27 


26 


29 


28.5 


28 


27 


26 


£ 2.5« 






















h^ 


Temperature of Condenser °F. 


Temperature of Condenser °F. 


32° 


63' 71 


78 


87 


96 


32° 


55 


62 


681 77 


77 


50° 


68 77 


83 


92 


100 


50° 


64 


71 


78 


85 


91 


60° 


71 


79 


86 


96 


104 


60° 


68 


75 


82 


88 


96 


70° 


76 


83 


89 


100 


109 


70° 


72 


80 


86 


95 


103 


80° 




86 


94 


104 


111 


80° 




82 


92 


99 


106 


Ft.-lb. Work per Lb. Steam Condensed^ 


Ft.-lb. Work per Lb. Steam Condensed. 


32° 


2150 


1560 


1280 


1000 


840 


32° 3840 


2880 


2380; 18401 1530 


50° 


3300 


2120 


1650 


1210 


990 


50° 


5760 


3730 


2920 


2150 


1760 


60° 


4820 


2740 


2000 


1410 


1120 


60° 


8440 


4720 


3450 


2440 


1960 


70° 


8220 


4010 


2670 


1700 


1280 


70° 


13250 


6610 


4410 


2850 


2210 


80° 




7750 


3930 


2110 


1530 


80° 




11330 


6960 


3520 


2560 


Lb. Cooling Water per Lb. Steam. 


Lb. Cooling Water per Lb. Steam. 


32° 


32.1 


25.6 


21.7 


18.2 


15.6 


32° 


42.7 


32.8 


28.0 


24.5 


21.5 


50° 


55.0 


36.7 


30.2 


24.7 


19.9 


50° 


70.8 


47.3 


35.5 


28.6 


24,5 


60° 


89.8 


52.3 


37.9 


27.5 


22.6 


60° 


123.8 


66.0 


45.1 


35.7 


27.8 


70° 


164.0 


75.8 


52.2 


32.8 


25.2 


70° 


494.0 


98.8 


61.8 


39.6 


30.1 


80° 




164.0 


70.0 


41.0 


31.8 


80° 




493.0 


82.0 


52.0 


38.1 



Most Economical Vacuum for Turbines. — Mr. Herschel, taking the 
air-pump work given in the above table for the several conditions 
named, an efficiency of 50 per cent for the air-pump, and assuming a 
turbine working with dry steam 150-lb. gage, without superheat, cal- 
culates the net work of the turbine in foot-pounds per lb. of steam 
with the most economical vacuum for different temperatures of cooling 
water. He compares the results with those calculated for the same 
air-pump conditions, but for a turbine using steam of 140 lb. super- 
heated 218° F. The results are tabulated below, the vacuum giving 
the best economy being given in parentheses. The lines marked 5 are 
for the superheated steam turbine. It appears that 29 in. vacuum is 
the most economical only for low temperatures of cooling water, and 
that the vacuum giving the best economy decreases with increase of 
leakage and with increasing temperature of the cooling water. 



Temperature of cooling water, °F. 32 I 50 | 60 I 70 
Net Work of Turbine, Ft.-lb. per Lb. of Steam. 



Leakage of [o.31% 

air, % I 
weight of 

steam. 



56000(29) I 
S. 76200(29) I 



53700(29) 
73900(29) 



152120(28.5) I 
171620(28.5) I 



n go^ j 52620(29) 
"•^^/'^ I 8.72820(29) 



50140(28.5) I 48800(28) 
69640(28.5) | 67660(28.5) | 



50360(28) 
69080(28.5) 

47500(27) 
64280(28) 



I 80 



I 48980(27) 
I 65240(28) 

I 46160(27) 
I 62060(27) 



Circulating-pump. — Let Q be the quantity of cooling-water in 
cubic feet, n the number of strokes per minute, and S the length of stroke 
in feet. 

Capacity of circulating-pump = Q -i- n c ubic fee t. 

Diameter of circulating-pump = 13.55 ^Q-i-nS inches. 

The clear area through the valve-seats" and past the valves should be 
such that the mean velocity of flow does not exceed 450 feet per minute. 
The flow through the pipes should not exceed 500 ft. per min. in small 
pipes and 600 in large pipes. (Seaton.) 

For Centrifugal Circulating-pumps, the velocity of flow in the inlet and 
outlet pipes should not exceed 400 ft. per min. The diameter of the fan- 
wheel is from 21/2 to 3 times the diam. of the pipe, and the speed at it? 
periphery 450 to 500 ft. per min. 



1076 THE STEAM-ENGINE. 

The Leblanc Condenser (made by the Westinghouse Machine Co.) 
accomplishes the separate removal of water and air by means of a pair of 
relatively smaU turbine-type rotors on a common shaft in a single casing, 
wliich is integral with or attached directly to the lower portion of the 
condensing chamber. The condensing chamber itself is but Uttle more 
than an enlargement of the exhaust pipe. The injection water is pro- 
jected downwards through a spray nozzle, and the combined injection 
water and condensed steam flow downward to a centrifugal discharge 
pump under a head of 2 or 3 ft., which insures the filling of the pump. 
The space above the water level in the condensing chamber is occupied 
by water vapor plus the air which entered with the injection water and 
\vith the exhaust steam, and tliis space communicates with the air-pump 
through a relatively small pipe. 

The air-pump differs from pumps of the ejector type in that the vanes 
in traversing the discharge nozzle at high speed constitute a series of 
pistons, each one of which forces ahead of it a small pocket of air, the 
high velocitj^ of which effectually prevents its return to the condenser. 
A small quantity of water is supplied to the suction side of the air-pump 
to assist in the performance of its functions. The power required for the 
pumps is said to approximate 2 to 3 per cent of the power generated by 
the main engine. 

Feed-pumps for Marine Engines. — With surface-condensing 
engines the amount of water to be fed by the pump is the amount con- 
densed from the main engine plus what may be needed to supply auxiliary 
engines and to supply leakage and waste. Since an accident may happen 
to the surface-condenser, requiring the use of jet-condensation, the pumps 
of engines fitted with surface-condensers must be sufficiently large to do 
duty under such circumstances. With jet-condensers and boilers using 
salt water the dense salt water in the boiler must be blown off at intervals 
to keep the density so low that deposits of salt wiU not be formed. Sea- 
water contains about 1/32 of its weight of solid matter in solution. The 
boiler of a surface-condensing engine may be worked with safety wiien 
the quantity of salt is four times that in sea-water. If Q = net quantity 
of feed-water required in a given time to make up for w^hat is used as 
steam, n = number of times the saltness of the water in the boiler is to 
that of sea-water, then the gross feed-water = ??QH-(n — 1). In order to be 
cauable of filling the boiler rapidly each feed-pump is made of a capacity 
equal to twice the gross feed-water. Two feed-pumps should be supplied 
so that one may be kept in reserve to be used while the other is out of 
repair. If Q be the quantity of net feed-water in cubic feet. I the length 
of stroke of feed-pump in feet, and n the number of strokes per minute, 

Diameter of each feed-pump plunger in inches' = v^550 Q-^nl, 

If W be the net feed-water in pounds, 

Diameter of each feed-pump plunger in inches = v^8.9 W -^nl. 

An Evaporative Surface Condenser built at the Virginia Agricul- 
tural CoUege is described by James H. Fitts (Trans. A.S. M. E., xiv, 690). 
It consists of two rectangular end chambers connected by a, series of 
horizontal rows of tubes, each row of tubes immersed in a pan of water. 
Through the spaces between the surface of the water in each pan and the 
bottom of the pan above air is drawn by means of an exhaust-fan. At 
the top of one of the end chambers is an inlet for steam, and a horizontal 
diaphragm about midway causes the steam to traverse the upper half 
of the tubes and back through the lower. An outlet at the bottom leads 
to the air-pump. The passage of air over the water surfaces removes 
the vapor as it rises and thus hastens evaporation. The heat necessary 
to produce evaporation is obtained from the steam in the tubes, causing 
the steam to condense. It was designed to condense 800 lbs. steam per 
hour and give a vacuum of 22 in,, with a terminal pressure in the cylinder 
of 20 lbs. absolute. Results of tests show that the cooUng-water required 
is practically equal in amount to the steam used by the engine. And 
since the consumption of steam is reduced by the application of a con- 
denser, its use will actually reduce the total quantity of water required. 

The Continuous Use of Condensing-water is described in a series 
of articles in Power, Aug.-Dec, 1892. It finds its apphcation in situations 
T^here water for condensing purposes is expensive or difficult to obtain. 



CONDENSERS, AIR-PUMPS, ETC. 



1077 



The different methods described include coohng pans on the roof; 

fountains and other spray pipes in ponds, fine spray discharged at an 
elevation above a pond; trickling the water discharged from the hot-well 
over parallel narrow metal tanks contained in a large wooden structure, 
while a fan blower drives a current of air against the lilms of water falling 
from the tanks, etc. These methods are suitable for small powers, but 
for large powers they are cumbersome and require too much space, and 
are practically supplanted by cooling towers. 

The Increase of Power that may be obtained by adding a condenser 
giving a vacuum of 26 inches of mercury to a non-condensing engine may 



_ N0..0t o| J oLUv^lo^l olJcolr-l col J ^1 c.\ c^l 

Expansions "1 H ~hhrkh-|l 1 III 1 ^1 1 


Points of 111111111^111 1 L /I 3^ 1 5 2 3- 
Cut-nff 30 25'20181614.12''i0'9 8' 7 "? 6" 4- 3 8 2 8 34rul 




10 20 3'0/4p/50'^0 770 gfo/go/lO 


Pressure^in Pouji'ds / / /// / \ 
0/1 1 120 1 30 1 40 1 1 60 1 7,0 1 SOylto^OO 1 




li-U^-t-i^ Ll t 








\\U 11 i : i i 


/ill ^^4- 




X t t-l-ll till t t 


7 -,^ I ^ ^2^^ 




t tltt-i-, t^^ 


I 1 J. J. aZ^ ^ 




±Jz ttuiiijit t 


T /^ / _/ 'A^ /. 




jnAiH-i ittt-,-f 


I -, J -/ A^ /- 




:tt^U4-i-i-i I ^ ^ 


7 Z Z yiz /. 




\ J 1 / / / / / / / 


J J. I ^vy /. 




fttht t'tri_t > 


-1 ^ A y/./-/. 


"Dicn 


tt-lttlnn T. t 


-7 -X J. J^tl/. 


C ' 


\ \ 1 J / / 


Z 7 / Z2z^ 




\m\i' ' I • / 


/ / 7/y 7~ 




IJlpL'irl-/ ' L J 


A^J-J^//. 




Jltm1''fl / 7^ 


^ 2. 22^ 




\ i \ 'i 1 / / / / / 


Z^22z 


2120- 


/ llh '' ' / / / / 


I Z^/. 


\ Mh J / ' / ^ -' 


2/^ 


^110- 
0) 


.iiLtLT-tij 1 J-/ ^"^ 


^2^ 


^mtuti-ii/ 4 /^Ja 


V.Z. 




ml PiiU f ^^ ^^^/ 


/ 




W J / / / / y yV/ 




* an 


lML7JlUy//i^'A. 




iWil^/T J ^ ^yj^/v 


-^80- 


4mE^0xS^ 


3 70- 




|eo- 

< 50- 
40 - 
80 - 
20 -j 
10 t 
^ 




mlMf/ r f{ 


will J ^z W 


^ 


~ 120 60 40 30 24 20 17 15 13 U 

PeTCen.t ot Powe 


\ 11 10 . 

r Gained by Vacuum 





Fig. 175. 
"be approximated by considering it to be equivalent to a net gain of 12 lbs. 
mean effective pr essure per sq. in. of piston area. If A — area of piston 
in sq ins., S = piston speed in ft. per min., then 12 AS -^ 33,000 = 
AS X 2750 = H.P. made available by the vacuum. If the vacuum = 
13.2 lbs. per sq. in. = 27.9 in. of mercury, then H.P. = AS j 2500. ^ 

The saving of steam for a given horse-power will be represented approxi- 
mately by the shortening of the cut-off when the engine is run with the 
condenser. Clearance should be included in the calculation. To the 
mean effective pressure non-condensing, with a given actual cut-off, 
clearance considered, add 3 lbs. to obtain the approximate mean total 
pressure condensing. From tables of expansion of steam find what 
actual cut-off will give tliis mean total pressure. The difference between 
this and the original actual cut-off, divided by the latter and by 100, will 
give the percentage of saving. .x-r -r, t^t xt • ^ n i. 

The diagram, Fig. 175 (from catalogue of H. R. Wortmngton) shows 
the percentage of power that may be gained by attaching a condenser 
to a non-condensing engine assuming that the vacuum is 12 lbs. per sq. 



1078 THE STEAM-ENGINE. 

in. The diagram also shows the mean pressure in the cylinder for a given 
initial pressure and cut-off, clearance and compression not considered. 

The pressures given in the diagram are absolute pressures above a 
vacuum. 

To find the mean effective pressure produced in an engine cylinder with 
90 lbs. gauge (= 105 lbs. absolute) pressure, cut-off at 1/4 stroke: find 
105 in the left-hand or initial-pressure column, follow the horizontal line 
to the right until it intersects the oblique line that corresponds to the V4 
cut-off, and read the mean total pressure from the row of figures directly 
above the point of intersection, wliich in this case is 63 lbs. From this 
subtract the mean absolute back pressure (say 3 lbs. for a condensing 
engine and 15 lbs. for a non-condensing engine exhausting into the 
atmosphere) to obtain the mean effective pressure, which in this case, for 
a non-condensing engine, gives 48 lbs. To find the gain of power by the 
use of a condenser with this engine, read on the lower scale the figures 
that correspond in position to 48 lbs. in the upper row, in this case 25%, 
As the diagram does not take into consideration clearance or compression, 
the results are only approximate. 

Advantage of High Vacuum in Reciprocating Engines. (R. D. 
Tomlinson, Power, Feb. 23, 1909.) — Among the transatlantic liners, 
the best ships with reciprocating engines are carrying from 26 to 28 and 
more inches of vacuum. Where the results are looked into, the engineers 
are required to keep the vacuum system tight and carry all the vacuum 
they can get, and while it is true that greater benefits can be derived 
from high vacua in a steam turbine than in a reciprocating engine, it is 
also true that, where primary heaters are not used, the higher the vacuum 
carried the greater is the justifiable economy which can be obtained from 
the plant. 

The Interborough Rapid Transit Company, New York City, changed 
the motor-driven air-pump and jet-condenser for a barometric type of 
condenser and increased the vacuum on each of the 8000-H.P. Allis- 
Chalmers horizontal vertical engines at the 74th Street station from 
26 to 28 ins., thereby increasing the power on each of the eight units 
approximately 275 H.P., and the economy of the station was increased 
nearly in the same ratio. This change was made about seven years ago 
and the plant is still operating with 28 ins. of vacuum, measured with 
mercury columns connected to the exhaust pipe at a point just below the 
exhaust nozzle of the low-pressure cylinders. 

A careful test made on the 59th Street station showed a decrease in 
steam consumption of 8% when the vacuum was raised from 25 to 28 ins. 
These engines drive 5000-kw. generators. 

The Choice of a Condenser. — Condensers may be divided into two 
general classes: 

First. — Jet condensers, including barometric condensers, siphon 
condensers, ejector condensers, etc., in which the cooling-water mingles 
with the steam to be condensed. 

Second. — Surface condensers, in which the cooling-water is separated 
from the steam, the coohng-water circulating on one side of this surface 
and the steam coming into contact with the other. 

In the jet-condenser the steam, as soon as condensed, becomes mixed 
with the cooling-water, and if the latter should be unsuitable for boiler- 
feed because of scale-forming impurities, acids, salt, etc., the pure distilled 
water represented by the condensed steam is wasted, and, if it were 
necessary to purchase other water for boiler-feeding, this might represent 
a considerable waste of money. On the other hand, if the cooling-water 
is suitable for boiler-feeding, or if a fresh supply of good water is easily 
obtainable, the jet-condenser, because of its simphcity and low cost, is 
unexcelled. 

Surface condensers are recommended where the cooling-water is un- 
fitted for boiler-feed and where no suitable and cheap supply of pure 
boiler-feed is available. 

_ Where a natural supply of coohng-water, as from a well, spring, lake or 
river, is not available, a water-cooling tower can be installed and the same 
coolmg- water used over and over. (Wheeler Condenser and Eng. Co.) 

Owing to their great cost as compared with jet-condensers, surface 
ccmdensers should not be used except where absolutely necessary, i.e., 
where lack of feed-water for the boiler warrants the extra cost. Of course 
there are cases, such as at sea, where surface condensers are indispensable. 



COOLING TOWERS. 1079 

On land, suitable feed-water can always be obtained at some expense, 
and that cost capitalized makes it a simple arithmetical problem to 
determine the extra investment permissible in order to be able to return 
condensed steam as feed-water to the boiler. Unfortunately there is 
another point which greatly complicates the matter, and one which makes 
it impossible to give exact figures, viz., the corrosion and deterioration of 
the condenser tubes themselves, the exact cause of which is not often 
understood. With clean, fresh water, free from acid, the tubes of a con- 
denser last indefinitely, but where the cooling-water contains sulphur, 
as in drainage from coal mines, or sea-water contaminated by sewage, 
such as harbor water, the deterioration is exceedingly rapid. 

A better vacuum may possibly be obtained from a surface condenser 
where there is plenty of cooling-water easily handled. The better vacuum 
is due to the fact that the air-pump will have much less air to handle inas- 
much as the air carried in suspension by the cooling-water does not have 
to be extracted as in the case of jet-condensers. Water in open rivers, 
the ocean, etc., is said to carry in suspension 5% by volume of air. It 
may be said that except for leakages, which should not exist, the air- 
pump will have no work to do at all inasmuch as the water will have no 
opportunity to become aerated. On the other hand, if the cooling-water 
is limited, these advantages are offset by the fact that a surface condenser 
cannot heat the cooling-water so near to the temperature of the exhaust 
steam as can a jet-condenser. (F. Hodgkinson, El. Jour., Aug., 1909.) 

A barometric condenser used in connection with a 15,000-k.w. steam- 
engine-turbine unit at the 59th St. station of the Rapid Transit Co., New 
York, contains approximately 25,000 sq. ft. of cooling surface arranged in 
the double two-pass system of water circulation, with a 30-in. centrifugal 
circulating pump having a maximum capacity of 30,000 gal. per hour. 
The dry vacuum pump is of the single-stage type, 12- and 29-in. X 24-in., 
with Coriiss valves on the air cylinder. The condensing plant is capable 
of maintaining a vacuum within "^1.1 in. of the barometer when condensing 
150,000 lb. of steam per hour when supplied wdth circulating water at 70° F. 
— (H. G. Stott, Jour. A.S.M.E., Mar., 1910.) 

Coolin!? Towers are usually made in the shape of large cylinders of 
sheet steel, filled with narrow boards or lath arranged in geometrical 
forms, or hollow tile, or wire network, so arranged that while the water, 
which is sprayed over them at the top, trickles down through the spaces it 
is met by an ascending air column. The air is furnished either by disk 
fans at the bottom or is drawn in by natural draught. In the latter case 
the tower is made very high, say 60 to 100 ft., so as to act like a chimney. 
When used in connection with steam condensers, the water produced by 
the condensation of the exhaust steam is sufficient to compensate for the 
evaporation in the tower, and none need be supplied to the system. There 
is, on the contrary, a slight overflow, which carries with it the oil from 
the engine cylinders, and tends to clean the system of oil that would 
otherwise accumulate in the hot-well. 

The cooling of water in a Dond, spray, or tower goes on in three ways — 
first, by radiation, which is practically negligible; second, by conduction 
or absorption of heat by the air, which may vary from one-fifth to one- 
third of the entire effect; and, lastly, by evaporation. The latter is the 
chief effect. Under certain conditions the water in a cooling tower can 
actually be cooled below the temperature of the atmosphere, as water is 
cooled by exposing it in porous vessels to the winds of hot and dry climates. 

The evaporation of 1 lb. of water absorbs about 1000 heat units. The 
rapidity of evaporation is determined, first, by the temperature of the 
water, and, second, by the vapor tension in the air in immediate contact 
with the water. In ordinary air the vapor present is generally in a con- 
dition corresponding to superheated steam, that is, the air is not saturated. 
If saturated air be brought into contact with colder water, the cooUng 
of the vapor will cause some of it to be precipitated out of the air; on the 
other hand, if saturated air be brought into contact with warmer water, 
some of the latter will pass into the form of vapor. This is what occurs in 
the cooling tower, so that the latter is in a large measure independent 
of cUmatic conditions; for even if the air be saturated, the rise in tem- 
perature of the atmospheric air from contact with the hot water in the 
cooUng tower will greatly increase the water-carrying capacity of the air, 
enabling a large amount of heat to be absorbed through the evaporation 



1080 



THE STEAM-ENGINE. 



of the water. The two things to be sought after in cooling-tower design 
are, therefore, first, to present a large surface of water to the air, and. 
second, to provide for bringing constantly into contact with tiiis surface 
the largest possible volume of new air at the least possible expenditure of 
energy. (Wheeler Condenser and Engineering Co.) 

The great advantage of the cooling tower lies in the fact that large 
surfaces of water can be presented to the air wliile the latter is kept in 
rapid motion. 

Calculation of the Air Supply for a Cooling Tower. — Let Ti and T2 
be the temperatures of the water entering and leaving; t\ temperature 
of the air supply; z its relative humidity; t2, temperature of the air 
leaving; m\ 1712, pounds of moisture in one pound of saturated air at 
temperatures ti, ^2; ei, €2, total heat, B.T.U., above 32° F. per pound 
of water vapor at temperatures ^1, t2', A = lb. of air supplied per lb. of 
entering water. All temperatures are in degrees F. 

Then, for each 1 lb. of water entering the tower the heat (B.T.U.) 
carried in is : by the water, Ti— 32; by the air, 0.2375 A (^1— 32) -{-Ami e\z. 
The -heat carried out is: by the water, [1 — {m2—m\z)\ X (T2— 32); by 
the air, 0.2375 A (^2—32) + A (m2 €2). Neglecting loss by radiation, the 
heat carried into the tower equals the heat leaving it. Equating these 
quantities and solving for A we have: 

A = y^-^^ . 

0.2375 (t2 - ti) + 771262 - mieiz - {rm - miz) (r2-32) 
From this equation the table on p. 1081 has been calculated. 

Water Evaporated in a Cooling Tower. — The following table 
gives the values of {m2—m\z) per pound of air in the cooling-tower formula. 
Multiplying these values by the number of pounds of air per pound of 
water for the given conditions, will give the amount of water evapo- 
rated, or make-up water required with surface condensers, per pound 
of the inflowing water. 

Pounds Water Evaporated per Pound of Air. 





h = 50° 


70° 


80° 


ri= 100° 


2=0.5 


0.7 


0.9 


0.5 


0.7 


0.9 


0.5 


0.7 


0.9 


<2 = 


r 92 
88 
84 


.02912 
.02503 
.02141 


.02761 
.02352 
.01990 


.02610 
.02201 
.01839 


.02455 
.02046 
.01684 


.02120 
.01711 
.01349 


.01786 
.01377 
.01015 


.02188 
.01779 
.01417 


.01748 
.01339 
.00977 


.01308 
.00899 
.00537 


Ti= 110° 


/i=50° 


70° 


90° 


( 102 

h=\ 98 
\ 94 


.04179 
.03626 
.03135 


.04028 
.03475 
.02984 


.03877 
.03324 
.02833 


.03722 
.03169 
.02678 


.03387 
.02834 
.02343 


.03053 
.02500 
.02009 


.03017 
.02464 
.01972 


.02402 .01785 
.01848 .01232 
.013571.00741 


Ti= 120° 


<i=50° \ 


70° 


90° 


(112 

t2= \ 108 

<104 


.05905 
.05151 
.04482 


.05754 
.05000 
.04331 


.05603 
.04845 
.04180 


.05448 .05113 .04779 
.04694 .04359 .04025 
.04025 .03690 .03356 


.04743 .04127 
.03989 .03373 
.03320 .02704 


.03511 
.02757 
.02088 



Tests of a Cooling Tower and Condenser are reported by J. H. Vail 
in Trans. A.S, M . E ., 1898. The tower was of the Barnard type, with two 
chambers, each 12 ft. 3 in. X 18 ft. X 29 ft. 6 in. high, containing gal^ 
vanized-wire mats. Four fans supplied a strong draught to the two cham- 
bers. The rated capacity of each section was to cool the circulating 
water needed to condense 12,500 lbs. of steam, from 132° to 80° F., when 
the atmosphere does not exceed 75° F. nor the humidity 85%. The fol- 
lowing is a record of some observations. 



Date, 1898. 


Jan. 
31. 


Feb. 


June 
20. 


July. 


Aug. 
26. 


Nov. 
4. 


Aug. 2. 


Max.| Min. 


Temperature atmosphere . 


30° 


36° 


78° 


96° 


85° 


59° 


103° 


83° 


Temp. condenser discharge 


110° 


110° 


120° 


130° 


118° 


129° 


128° 


106° 


Temp, water from tower.. 


65° 


84° 


84° 


93° 


88° 


92° 


98° 


9,u 


Heat extracted by tower. . 


45° 


26° 


36° 


37° 


30° 


37° 


32° 


21° 


Speed of fans, r.p.m 


36 





145 


162 


150 


148 


160 


140 


Vacuum, inches 


251/2 


26 


25 


241/2 


2512/ 


25 


26 


26 



COOLING TOWERS. 



1081 



Pounds of Air per Pound of Circulating Water. 

Outflowing air saturated. 



100°. 


h = 50° 


70° 


80° 


T2 t2 


2=0.5 


0.7 


0.9 


0.5 


0.7 


0.9 


0.5 


0.7 


0.9 


(92 

70^88 

(84 

(92 

80^88 

(84 

(92 

90s' 88 

(84 


0.732 
0.842 
0.984 

0.492 
0.565 
0.654 

0.248 
0.285 
0.329 


0.761 
0.881 
1.027 

0.511 
0.591 
0.689 

0.257 
0.298 
0.347 


0.793 
0.924 
1.085 

0.532 
0.620 
0.728 

0.268 
0.312 
0.367 


0.956 
1.152 
1.415 

0.642 
0.774 
0.951 

0.324 
0.390 
0.479 


1.076 
1.333 
1.698 

0.723 
0.895 
1.141 

0.364 
0.451 
0.575 


1.233 
1.580 
2.120 

0.828 
1.061 
1.423 

0.417 
0.534 
0.717 


1.147 
1 .442 
1.879 

0.771 
0.970 
1.264 

0.389 
0.489 
0.638 


1.395 
1.857 
2.650 

0.938 
1.249 

1.783 

0.472 
0.632 
0.899 


1.780 
2.608 
4.500 

1.196 
1.752 
3.025 

0.603 
0.883 
1.524 


Ti = 
110°. 


^1 = 50° 


70° 


90° 


( 102 

70^ 98 

( 94 

( 102 
80^ 98 

( 94 

( 102 

90s 98 

( 94 


0.702 
0.799 
0.912 

0.530 
0.603 
0.689 

0.356 
0.402 
0.463 


0.722 
0.824 
0.946 

0.545 
0.623 
0.715 

0.366 
0.418 
0.480 


0.743 
0.852 
0.983 

0.561 
0.644 
0.742 

0.377 
0.432 
0.498 


0.844 
0.988 
1.168 

0.638 
0.747 
0.883 

0.429 
0.502 
0.593 


0.911 
1.082 
1.302 

0.689 
0.818 
0.984 

0.463 
0.549 
0.661 


0.991 
1.196 
1.470 

0.749 
0.904 
1.111 

0.503 
0.607 
0.746 


1.139 
1 .419 
1.822 

0.862 
1 .074 
1.379 

0.580 
0.722 
0.928 


1.400 
1.847 
2.595 

1.059 
1 .404 
1.963 

0.712 
0.944 
1.321 


1.815 
2.646 
4.505 

1.376 
2.001 
3.405 

0.923 
1.345 
2.291 


120°. 


h = 50° 


70° 


90° 


( 112 
70^ 108 

( 104 

( 112 

80^ 108 

( 104 

( 112 

90-^^ 108 

( 104 


0.640 
0.725 
0.823 

0.516 
0.585 
0.663 

0.390 
0.442 
0.501 


0.654 
0.742 
0.845 

0.527 
0.598 
0.681 

0.398 
0.452 
0.515 


0.667 
0.760 
0.868 

0.538 
0.613 
0.699 

0.406 
0.463 
0.528 


0.730 
0.843 
0.977 

0.589 
0.680 
0.788 

0.445 
0.514 
0.596 


0.770 
0.896 
1.050 

0.621 
0.722 
0.846 

0.469 
0.546 
0.640 


0.814 
0.956 
1.133 

0.656 
0.771 
0.914 

0.496 
0.583 
0.690 


0.890 
1.063 
1.287 

0.718 
0.858 
1.038 

0.543 
0.649 
0.786 


1.007 
1.234 
1.547 

0.812 
0.996 
1.248 

0.613 
0.753 
0.944 


1.160 
1.472 
1.940 

0.936 
1.187 
1.564 

0.707 
0.898 
1.183 



Cubic Feet in 1 Pound of Air. 
Temp. deg. F. 32 50 60 70 80 90 

Cu. ft. 12.387 12.84 13.09 13.34 13.59 13.84 

Weight of Water Vapor Mixed with 1 lb. of Air at Atmospheric 

Pressure. 

Full Saturation. Values interpolated from table on page 613. 



Deg. 


Mois- 
ture, 
lb. 


Deg. 


Mois- 
ture, 
lb. 


Deg. 
F. 


Mois- 
ture, 
lb. 


Deg. 
F. 


Mois- 
ture, 
lb. 


Deg. 
F. 


Mois- 
ture, 
lb. 


32 


0.00374 


54 


0.00874 


76 


0.01917 


98 


0.04002 


120 


0.08099 


34 


.00406 


56 


.00940 


78 


.02054 


100 


.04270 


122 


.08629 


36 


.00439 


58 


.01012 


80 


.02200 


102 


.04555 


124 


.09193 


38 


.00475 


60 


.01089 


82 


.02353 


104 


.04858 


126 


.09794 


40 


.00514 


62 


.01171 


84 


.02517 


106 


.05182 


128 


.10437 


42 


.00555 


64 


.01259 


86 


.02692 


108 


.05527 


130 


.11123 


44 


.00600 


66 


.01353 


88 


.02879 


110 


.05893 


132 


.11855 


46 


.00648 


68 


.01453 


90 


.03077 


112 


.06281 


134 


.12637 


48 


.00699 


70 


.01557 


92 


.03288 


114 


.06695 


136 


.13473 


50 


.00753 


72 


.01669 


94 


.03511 


116 


.07134 


138 


.14367 


52 


.00812 


74 


.01789 


96 


.03750 


118 


.07601 


140 1 


.15324 



1082 THE STEAM-ENGINE. 

"but in the two tests on Aug. 2 the H.P. developed was 900 I.H.P. in the 
first and 400 in the second, the engine being a tandem compound, Corliss 
type, 20 and 36 X 42 in., 120 r.p.m. 

J. R. Bibbins (Trans.A.S.M.E., 1909) gives a large amount of informa- 
tion on the construction and performance of different styles of cooling 
towers. He suggests a type of combined fan and natural draft tower 
suited to most eflficient running on peak as well as light loads. 

Evaporators and Distillers are used with marine engines for the pur- 
pose of providing fresh water for the boilers or for drinking purposes. 

Weir's Evaporator consists of a small horizontal boiler, contrived so as 
to be easily taken to pieces and cleaned. The water in it is evaporated by 
the steam from the main boilers passing through a set of tubes placed in 
its bottom. The steam generated in this boiler is admitted to the low- 
pressure valve-chest, so that there is no loss of energy, and the water con- 
densed in it is returned to the main boilers. 

In Weirds Feed-heater the feed-water before entering the boiler is heated 
up very nearly to boiling-point by means of the waste water and steam 
from the low-pressure valve-chest of a compound engine. 

ROTARY STEAM-ENGINES — STEAM TURBINES. 

Rotary Steam-engines, other than steam turbines, have been invented 
by the thousands, but not one has attained a commercial success, as regards 
economy of steam. For all ordinary uses the possible advantages, such 
as saving of space, to be gained by a rotary engine are overbalanced by 
its waste of steam. Rotary engines are in use, however, for special pur- 
poses, such as steam fire-engines and steam feeds for sawmills, in which 
steam economy is not a matter of importance. 

Impulse and Reaction Turbines. — A steam turbine of the simplest 
form is a wheel similar to a water wheel, which is moved by a jet of steam 
impinging at high velocity on its blades. Such a wheel was designed 
by Branca, an Italian, in 1629. The De Laval steam turbine, w^hich is 
similar in many respects to a Pelton water wheel, is of this class. It is 
known as an impulse turbine. In a book written by Hero, of Alexan- 
dria, about 150 B.C., there is shown a revolving hollow metal ball, into 
which steam enters through a trunnion from a boiler beneath, and 
escapes tangentially from the outer rim through two arms which are 
bent backwards, so that the steam by its reaction causes the ball to 
rotate in an opposite direction to that of the escaping jets. This wheel 
is the prototype of a reaction turbine. In most modern steam turbines 
both the impulse and reaction principles are used, jets of steam striking 
blades or buckets inserted in the rim of a wheel, so as to give it a forward 
impulse, and escaping from it in a reverse direction so as to react upon 
it. The name impulse wheel, however, is now generally given to wheels 
like the De Laval, in which the pressure on the two sides of a wheel con- 
taining the blades is the same, and the name reaction wheel to one in 
which the steam decreases in pressure in passing through the blades. 
The Parsons turbine is of this class. 

The De Laval Turbine. — The distinguishing features of this turbine 
are the diverging nozzles, in which the steam expands down to the at- 
mospheric pressure in non-condensing, and to the vacuum pressure in 
condensing wheels; a single forged steel disk carrying the blades on its 
periphery; a slender, flexible shaft on which the wheel is mounted and 
which rotates about its center of gravity; and a set of reducing gears, 
usually 10 to 1 reduction, to change the very high speed of the turbine 
to a moderate speed for driving macliinery. Following are the sizes 
and speeds of some De Laval turbines: 

Horse-power 5 30 100 300 

Revolutions per minute 30,000 20,000 13,000 10,000 

Diam. to center of blades, ins. 3.94 8.86 19.68 29.92 

The number and size of nozzles vary with the size of the turbine. 
The nozzles are provided with valves, so that for light loads some of 
them may be closed, and a relatively high efficiency is obtained at light 
loads. The taper of the nozzles differs for condensing and non-condens- 
ing turbines. Some turbines are provided with two sets of nozzles, one 
for condensing and the other for non-condensing operation. 

The disk of the De Laval turbine is not mounted midway between 
the shaft bearings, but considerably nearer to the spherical bearing 



ROTARY STEAM-ENGINES — STEAM TURBINES. 1083 

at the governor end. At low speeds the shaft bends, but as the speed 
increases the gyroscopic action of the disk causes it to rotate in a plane 
at right angles to an axis through the center of gravity of the shaft 
and disk. The speed just below that at which tliis takes place, and at 
which the vibration of the shaft is greatest, is called the critical speed. 
It is about 1/5 to i/s of the normal speed of the turbine. 

The diameter of the shaft of a De Laval 100-H.P. turbine is 1 in., 
and that of a 300-H.P. about is/ie in. The teeth of the pinions of 
the reducing gear are cut in an enlarged section of the shaft. The pitch 
of the gears is very small, 0.15 in. in the smallest and 0.26 in. in the 
largest sizes. The shaft is said to be made of 0.60 to 0.80 C steel and 
the gears of 0.20 C steel. 

The Zolley or Rateau Turbine. — The Zolley or Rateau turbines 
are aevelopments of the De Laval and consist of a number of De Laval 
elements in series, each succeeding element utilizing the exhaust steam 
from the preceding. The steam is partly expanded in the first row of 
nozzles, strikes the first row of buckets and leaves them \\ith practically 
zero velocity. It is then further expanded through the second row of 
nozzles, strikes a second row of moving buckets and again leaves them 
with zero velocity. This process is repeated until the steam is com- 
pletely expanded. 

The Parsons Turbine. — In the Parsons, or reaction type of turbine, 
there are a large number of rows of blades, mounted on a rotor or revolv- 
ing drum. Between each pair of rows there is a row of stationary blades 
attached to the casing, which take the place of nozzles. A set of sta- 
tionary blades and the following set of moving blades constitute w^hat is 
known as a stage. The steam expands and loses pressure in both sets. 
The speed of rotation, the peripheral speed of the blades and the velocity 
of the steam through the blades are very much lower than in the De Laval 
turbine. The rotor, or drum, on which the moving blades are carried. 
Is usually made in three sections of different diameters, the smallest at 
the high-pressure end where steam is admitted, and the largest at the 
exhaust end. In each section the radial length of the blades and also 
their width increase from one end to the other, to correspond with the 
increased volume of steam. The Parsons turbine is built in the United 
States by the Westinghouse Machine Co. and by the Alhs-Chalmers Co. 

The Westinghouse Double-flow Turbine. — For sizes above 5000 K.W. 
a turbine is built in wliich the impulse and reaction types are combined. 
It has a set of non-expanding nozzles, an impulse wheel with tw^o velocity 
stages (that is two wheels with a set of stationary non-expanding blades 
between), one intermediate section and two low-pressure sections with 
Parsons blading. After steam has passed through the impulse wheel 
and the intermediate section it is divided into two parts, one going to 
the right and the other to the left hand low-pressure section. There is 
an exhaust pipe at each end. In tliis turbine, the end thrust, which has 
to be balanced in reaction turbines of the usual type, is almost entirely 
avoided. Other advantages are the reduction in size and w-eight, due to 
higher permissible speed; blades and casing are not exposed to high 
temperatures: reduction of size of exhaust pipes and of length of shaft; 
avoidance of large balance pistons. 

The Curtis Turbine, made by the General Electric Company, is an 
impulse wheel of several stages. Steam is expanded in nozzles and 
enters a set of three or more blades, at least one of which is stationary. 
The blades are all non-expanding, and the pressure is practically the same 
on both sides of any row of blades. In smaller sizes of turbines, only 
one set of stationary and movable blades is used, but in large sizes there 
are from tw-o to five sets, each forming a pressure stage, separated by 
diaphragms containing additional sets of nozzles. The smaller sizes have 
horizontal shafts, but the larger ones have vertical shafts supported on a 
step bearing suppUed with oil or water under a pressure sufficient to 
support the whole weight of the shaft and its attached rotating disks. 
Curtis turbines are made in sizes from 15 K.W. at 3600 to 4000 revs, per 
minute up to 9000 K.W. at 750 revs, per minute. 

The Spiro Turbine consists of two " herring-bone" helical gear wheels 
meshed together and revolving in a closely fitting casing. The steam 
enters through two non-expanding nozzles at mid-length of the gears, 
expands into the spaces between adjacent gear teeth and escapes at 



1084 THE STEAM-ENGINE. 

the outer ends of the teeth when they pass the Hne of contact between 
the two rotors. The turbine is made in small sizes, under 100 H.P., 
and is used non-condensing. Its merits are compactness and simphcity, 
but it is not economical of steam. 

Mechanical Theory of the Steam Turbine. — In the impulse turbine 
of the De Laval type, with a single disk containing blades at its rim, 
steam at high pressure enters the smaller end or throat of a tapering 
nozzle, and, as it passes through the nozzle, is expanded adiabatically 
down to the pressure in the casing of the turbine, that is to the pressure 
of the atmosphere, in a non-condensing turbine, or to the pressure of 
the vacuum, if the turbine is connected to a condenser. The steam 
thus expanded has its volume and its velocity enormously increased, 
its pressure energy being converted into energy of velocity. It then 
strikes tangentially the concave surfaces of the curved blades, and thus 
drives the wheel forward. In passing through the blades it has its direc- 
tion reversed, and the reaction of the escaping jet also helps to drive the 
wheel forward. If it were possible for the direction of the jet to be com- 
pletely reversed, or through an arc of 180°, and the velocity of the blade 
in the direction of the entering jet was one-half the velocity of the jet, 
then all the kinetic energy due to the velocity of the jet would be con- 
verted into work on the blade, and the velocity of the jet with reference 
to the earth would be zero. This complete reversal, however, is impos- 
sible, since room has to be allowed between the blades for the passage of 
the steam, and the blades, therefore, are curved through an arc consid- 
erably less than 180°, and the jet on leaving the wheel still has some 
kinetic energy, which is lost. The velocity of the entering steam jet 
also is so great that it is not practicable to give the wheel rim a velocity 
equal to one-half that of the jet, since that would be beyond a safe speed. 
The speed of the wheel being less than half that of the entering jet, also 
causes the jet to leave the wheel with some of its energy unutilized. 
The mechanical efficiency of the wheel, neglecting radiation, friction, and 
other internal losses, is expressed by the fraction (Ei — E2) -J- Ei, in 
which El is the kinetic energy of the steam jet impinging on the wheel 
and E2 that of the steam as It leaves the blades. 

In multiple-stage impulse turbines, the high velocity of the wheel is 
reduced by causing the steam, to pass through two or more rows of 
blades, which rows are separated by a row of stationary curved blades 
which direct the steam from the outlet of one row to the inlet of the 
next. The passages through all the blades, both movable and secondary, 
are parallel, or non-expanding, so that the steam does not change its 
pressure in passing through them. The wheel with two rows of movable 
blades running at half the velocity of a single-stage turbine, or one with 
three rows at one-third the velocity, causes the same total reduction in 
velocity as the single-stage wheel; and a greater reduction in the velocity 
of the wheel can be obtained by increasing the number of rows. It is, 
therefore, possible by having a sufficient number of rov/s of blades, or 
velocity stages, to run a wheel at comparatively slow speed and yet 
have the steam escape from the last set of blades at a lower absolute 
velocity than is possible with a single-stage turbine. In the reaction 
turbine the reduction of the pressure and its conversion into kinetic 
energy, or energy of velocity, takes place in the blades, wliich are made 
of such shape as to allow the steam to expand while passing through them. 
The stationary blades also allow of expansion in volume, thus taking 
the place of nozzles. 

In all turbines, whether of the impulse, reaction, or combination 
tvpe, the object is to take in steam at high pressure and to discharge it 
into the atmosphere, or into the condenser, at the lowest pressure and 
largest volume possible, and with the lowest possible absolute velocity, 
or velocity with reference to the earth, consistent with getting the steam 
away from the wheel, and to do this with the least loss of energy in the 
wheel due to friction of the steam through the passages, to shock due 
to incorrect shape, or position of the blades, to windage of frictional 
resistance of the steam in contact with the rotating wheel, or other 
causes. The minimizing of these several losses is a problem of extreme 
difflcultv which is being solved by costly experiments. 

Heat Theory of the Steam Turbine. — The steam turbine may also be 
considered as a heat engine, the object of which is to take a pound of 



ROTARY STEAM-ENGINES — STEAM TURBINES. 1085 




01--— . , 

^ ^ J 

h- 03 — ^ 

Fig. 176. 



steam containing a certain quantity of heat. Hi, transform as great a 
part of this heat as possible into work, and discharge the remaining part, 
H2, into the condenser. The thermal efficiency of the operation is 
(Hi — H2) -^ Hi, and the theoretical limit of this efficiency is (7\ — T2) 
-i- T2, in which Ti is the initial and T2 the final absolute temperature. 

Referring to temperature entropy dia- 
gram, Fig. 176, the total heat above 32° F, 
of 1 lb. of steam at the temperature Ti is 
represented by the area OACDG and its 
entropy is <t>i. Expanding adiabatically to 
T2 part of its heat energy is converted into 
work, represented by the area BCDF, 
while OABFG represents the heat dis- 
charged into the condenser. The total 
heat of 1 lb. of dry saturated steam at T2 
is greater than this by the area EFGH, the 
fraction FE -r- BE representing moisture in 
the 1 lb. of wet steam discharged. If 
Hi = heat units in 1 lb. of dry steam at the 
3tate-point D, and H2 = heat units in 1 lb. 
of dry steam at the state-point E, at the 
temperature Ti, then the energy converted 
into work =^BCDF=Hi - i?2 + (02 - 0i) T2. 
This quantity is called the available en- 
ergy Ea, of 1 lb. of steam between the 
temperatures Ti and T2' 

If the steam is initially wet, as repre- 
sented by the state-point d and entropy 
0^, then the work done in adiabatic expan- 
sion is BCdfB, which is equal to Ea = 
Hi - H2 + (02 - 0i) T2 - (01 - 0;,) LTi - To). 

The quantity <t>i- (t>x = (L/Ti) (l-x), in which L = latent heat 
of evaporation at the temperature Ti, and x = the moisture in 1 lb. of 
steam. The values of Hi, H2, 0i, 02. etc., for different temperatures, 
may be taken from steam tables or diagrams. 

If the steam is initially superheated to the temperature T^, as repre- 
sented by the state-point j, the entropy being 03, then the total heat at 
j is Hi + C {Ts — Ti) , in which C is the mean specific heat of super- 
heated steam between Ti and T^. The increase of entropy above 0i 
is 03 —01 = C loge (Ts/Ti). The energy converted into work is ^^ = 
H1-H2+ (02 - 0i) T2 + [1/2 (Ts + Ti) - T2] (03 - 0i). 

Velocity of Steam in Nozzles. — Having obtained the total available 
energy in steam expanding adiabatically between two temperatures, as 
shown above, the maximum possible flow into a vacuum is obtained 
from the common formula. Energy, in foot-pounds, = 1/2 W/g X V^, in 
which Wis the weight (in this case 1 lb.), V is the velocity in feet per 
second, and ^ = 32.2. As the energy Ea is in heat units, it is multi- 
plied by 778 to convert it into foot-pounds, and we have 

V = V 77SX 2 gEa = 223.8 V^a- 

This is the theoretically maximum possible velocity. It cannot be 
obtained in a short nozzle or orifice, but is approximated in the long 
expanding nozzles used in turbines. In the throat or narrow section of 
an orifice, the velocity and the weight of steam flowing per second may 
be found by Napier's or Rateau's formula, see page 876, or from Gras- 
hof's formula as given by Moyer, F = yloPiO-97 -=- 60, or Ao = 60 F -7- 
PO.97, in which Ao is the area of the smallest section of the nozzle, 
sq. in., F is the flow of steam (initially dry saturated) in lbs. per sec, 
and P is the absolute pressure, lbs. per sq. in. This formula is apph- 
cable in all cases where the final pressure P2 does not exceed 58 % of the 
initial pret^sure. For wet steam the formula becomes F = ^oPiO-97 -^ 
60 \/~x, Ao = 60 F \/~x -7- P1O.97, in which x is the dryness quality of the 
inflowing steam, 1 — x being the moisture. 

For superheated steam F = AoPiO.97 (i -\. 0.00065 D) -r- 60; Ao = 
60 F -7- P1O.97 (1 -t- 0.00065 D), D being the superheat in degrees F. 



1086 



THE STEAM-ENGINE. 



When the final pressure P2 is greater than 0.58 Pi, a coefficient is to 
be applied to F in the above formulae, the value of which is most con- 
veniently taken from a curve given by Rateau. The values of this co- 
efficient, c, for different ratios of P1/P2, are approximately as follows: 
P2-5-Pi= 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 
C= 1. 0.995 0.985 0.975 0.965 0.955 0.945 0.93 0.91 0.88 0.85 
Pi-r-Pi= 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 
C= 0.82 0.79 0.76 0.72 0.675 0.625 0.57 0.51 0.42 0.30 0.00 

The quality of steam after adiabatic expansion, xi, is found from the 
formula X2 = {xxLx/Tt + di - 62) T2/L2, (8) 

in which di and 62 are the entropies of the liquid, Li and L2 the latent 
heats of evaporation, and Xi and X2 the dryness quality, at the initial 
and final conditions respectively. Curves of steam quality are plotted in 
an entropy-total heat chart given in Moyer's "Steam Turbines" and 
also in Marks and Davis's "Steam Tables and Diagrams." 

The area of the smallest section or throat of the nozzle being found, 
the area of any section beyond the throat is inversely proportional to the 
velocity and directly proportional to the specific volume and to the 
dryness, or Ai/Aq= Vq/Vi X Vi/Vq X a-i/xo, in which A is in the area in 
sq. ins., V the velocity in ft. per sec, v the volume of 1 lb. of steam in 
cu. ft., and x the dryness fraction, the subscript referring to the 
smallest section and the subscript 1 to any other section. The ratio 
Ai/Ao for the largest cross section of a property designed nozzle depends 
upon the ratio of the initial to the final pressure. Moyer gives it as 
Ai/Ao = 0.172 P1/P2 + 0.70, and for P1/P2 greater than 25, Ai/Ao = 0.175 
(Pi/P2)0.94-|-0.70. 

In practice expanding nozzles are usually made so that an axial sec- 
tion shows the inner walls in straight lines. The transverse section is 
usually either a circle or a square with rounded corners. The diver- 
gence of the walls is about 6 degrees from the axis for the non-condens- 
ing and as much as 12 degrees for condensing turbines for low vacuums. 
Moyer gives an em pirical formula for the length between the throat and 

the mouth, L = Vl5 Aq inches. The De Laval turbine uses a much 
longer nozzle for mechanical reasons. The entrance to the nozzle above 
the throat should be well rounded. The efficiency of a well-made nozzle 
with smooth surfaces as measured by the velocity is about 96 to 97%, 
corresponding to an energy efficiency of 92 to 94%. 

Speed of the Blades. — If V^ = peripheral velocity of the blade, 
Vi = absolute velocity of the steam entering the blades and a the nozzle 
angle, or angle of the nozzle to the plane of the wheel, then (in impulse 
turbines with equal entrance and exit angles of the blade with the plane 
of the wheel) for maximum theoretical efficiency of the blade, Vb = 1/2 VI 
cos a. The nozzle angle is usually about 20°, cos a = 0.940, and the 
efficiency of a single row of blades is (0.94 - Vb/Vi) 4 V^/Vi. 

For Vi = 3000 ft. per sec, the efficiency for different blade speeds is 
a out as o o^s^^^ ^^^ ^^^ ^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^^^^ ^qoo 

Efficiency, % 23 44 60 72 81 87 89 87 80 71 
The highest efficiency is obtained when 
Vb = about 1/2 V2. It is difficult, for mechan- 
ical reasons, to use speeds much greater than 
500 ft. per sec, therefore the highest effi- 
ciencies are often sacrificed in commercial 
machines. The blade speeds used in practice 
vary from 500 to 1200 ft. per sec For an 
impulse wheel with more than one row of mov- 
ing blades in a single pressure stage, efficiency 
4NVb f NVb\ 

Referring to Fig. 177, if Vi is the absolute 
direction and velocity of the entering jet, Vj, 
the direction and velocity of the blade, the 
resultant, Vr, is the velocity and direction of the jet relatively to the 
blade, and the edge of the blade is made tangent to this direction. Also 




Fig. 177. 



ROTARY STEAM-ENGINES — STEAM TURBINES. 1087 

V^, the resultant of V5 and V/at the other edge of the blade, is the 
absolute velocity and direction of the steam escaping from the wheel. 
If 3 is the angle between Vj, and Vjf,, the maximum energy is abstracted 
from the steam when the angle between V^ and V5 = 90 - 1/2 0, and 
the efficiency is cos ^ -~ cos2 1/2 0. 

For details of design of blades, and of turbines in general, see Moyer 
Foster Thomas, Stodola and other works on Steam Turbines, also 
Peabody s "Thermodynamics." Calculations of stages, nozzles, etc., 
are much facihtated by the use of Peabody 's " Steam Tables" and Marks 
and Davis's "Steam Tables and Diagrams." 

Comparison of Commercial Impulse and Reaction Turbines. (Moyer ) 

Impulse. Reaction. 

1. Few stages. 1. Many stages. 

2. Expansion in nozzles. 2. No nozzles. 

3. Large drop in pressure in a 3. SmaU drop in pressure in a 
^ stage. stage. 

4. Initial steam velocities 1000 to 4. All steam velocities low. 300 to 

4000 ft. per sec. 600 ft. per sec. 

5. Blade velocities 400 to 1200 ft. 5. Blade velocities 150 to 400 ft 

per sec. per sec. 

6. Best efficiency when the blade 6. Best efficiency when the blade 

velocityisnearly half the ini- velocity is nearly equal to 

tial velocity of steam. the highest velocity of the 

steam. 
Loss due to Windage (or friction of a turbine wheel rotating in steam) 
— Moyer gives for the friction of a plain disk without blades, F^, and of 
one row of blades without the disk, i^^, in horse-power; 

F^= 0.08 d2 (w/100)2-8 w -i- (1 + 0.00065 D)2, 
F5 = 0.3 cf n-Kw/100)2-8 w-i- (1 + 0.00065 D)2, 
in which d = diam. of disk to inner edge of blade, in feet; u = peripheral 
velocity of disk, in ft. per sec: w = density of dry saturated steam at 
the pressure surrounding the disk, in lbs. per en. ft. and D = super- 
heat in degrees F. The sum of F^ and F^ is the friction of the disk and 
blades. For moist sieam the term 1 + 0.00065 D is to be omitted and 
the expression multiplied by a coefficient c, whose value is approxi- 
mately as follows: 
Per cent mois- 
ture in steam 2 4 6 8 10 12 16 20 24 
Coefficient c. . 1.01 1.05 1.10 1.16 1.25 1.37 1.65 2.00 2.44 
At high rotative speeds the rotation loss of a non-condensing turbine 
with wheels revolving in steam at atmospheric pressure is quite large, 
and in small turbines it may be as much as 20% of the total output. 
The loss decreases rapidly with increasing vacuum. In a turbine with 
more than one stage part of the friction loss of rotation is converted into 
heat which in the next stage is converted into kinetic energy, thus partly 
compensating for the loss. 

Efficiency of the 3Iachine. — The maximum possible thermodynamic 
efficiency of a steam turbine, as of any other steam engine, is expressed 
by the ratio which the available energy between two temperatures bears 
to the total heat, measured above absolute zero, of the steam at the 
liigher temperature. In the temperature-entropy diagram Fig. 176 it is 
represented by the ratio of the area BCDF to OACDG. Of this avail- 
able energy, from 50 to 75 and possibly 80 per cent is obtainable at the 
shaft of turbines of different sizes and designs. As with steam engines, 
the liighest mechanical and thermal efficiencies are reached only with 
large sizes and the most expensive designs. The several losses which 
tend to reduce the efficiency of turbines below the theoretical maximum 
are: 1, residual velocity, or the kinetic energy due to the velocity of the 
steam escaping from the turbine; 2, friction and imperfect expansion 
in the nozzles; 3, windage, or friction due to rotation of the wheel in 
steam; 4, friction of the steam traveling through the blades; 5, shocks, 
impacts, eddies, etc., due to imperfect shape or roughness of blades; 6, 
leakage around the ends of the blades or through clearance spaces; 7, shaft 
friction; 8, radiation. The sum of all these losses amounts to about 
25% of the available energy in the largest and best design ^.nd to 50% 
or more in small sizes or poor designs. 



1088 



THE STEAM-ENGINE. 



Steam Consumption of Turbines. — The steam consumption of any- 
steam turbine is so greatly influenced by the conditions of pressure, 
moisture or superheat, and vacuum, that it is necessary to know the effect 
of these conditions on anj^ turbines whose performances are to be com- 
pared with each other or with a given standard. Manufacturers usually 
furnish with their guarantees of performance under standard conditions 
of pressure, superheat and vacuum, a statement or set of curves showing 
the amount that the steam consumption per K.W.-hour will be increased 
or diminished by stated variations from these standard conditions. 
When a test of steam consumption is made under any conditions varying 
from the standard, the results should be corrected in order to compare 
them with other tests. Moyer gives the following example of applj'ing 
corrections to a pair of tests made in 1907, to reduce them both to a steam 
pressure of 179 lbs. gauge, 28.5 ins. vacuum, and 100° F. superheat. 





7500-K.W. 
Westing- 

house- 
Parsons. 


Correc- 
tions, 
per cent. 


9000-K.W. 

Curtis. 


Correc- 
tions, 
per cent. 


Average steam pressure 

Average vacuum, ins., referred 
to 30-in barometer 


177.5 

27.3 
95.7 
9830.5 
15.15 


-0.15 

-3.36 
-0.29 


179 

29.55 
116 
8070 
13.0 




+ 12 39 


Average superheat, deg. F 

Average load on generator.K.W. 
Steam cons., lbs. per K.W.-hr. . 


+ 1.28 






Net correction, per cent 


-3.80 


+ 13.67 


Corr. st. cons., lbs. per K.W.-hr. 


14.57 


14.77 











For the 7500-K.W. turbine, the following corrections given by the manu- 
facturer were used: pressure, 0.1% for each pound; vacuum, 2.8% for 
each inch; superheat. 7% for each 100° F. For the 9000-K.W. turbine, 
the following corrections were used: superheat, 8% for 100° F.; vacuum, 
8% for each inch. 

The results as corrected show that the two turbines would give practi- 
cally the same economy if tested under uniform conditions. The results 
are equivalent respectively to 9.58 and 9.72 lbs. per I.H.P.-hour, as- 
suming 97% generator efficiency and 91% mechanical efficiency of a 
steam-engine. 

The proper correction for moisture in a steam turbine test is stated to 
be a little more than twice the percentage of moisture. There is a large 
increase in the disk and blade rotation losses when wet steam is used. 

Effect of Vacuum on Steam Turbines. — M. R. Bump (Power, June 
15, 1909) gives the following as the steam consumption per K.W. hour 
of a 1000 K.W. turbine at full rated load, 175 lb. gage pressure, 100° 
superheat : 



Vacuum, in. . 
Steam per 
K.W. hr. lb. . 



29 



28 



27 



26 



25 



24 23 22 21 



15.35 16.55 17.50 18.55 19.35 20.00 20.6 21.1 21.6 



The gain in economy per inch of vacuum at different vacuums is 
given as follows in Mech. Engr., Feb. 24, 1906. 



Inches of Vacuum. 


28 


27 


26 


25 


Curtis, per cent gain per inch of vacuum. . 

Parsons, per cent gain per inch of vacuum 

Westiiighouse-Parsons, per cent gain per 

inch of vacuum 


5.1 
5.0 

3.14 
5.2 


4.8 
4.0 

3.05 
4.4 


4.6 
3.5 

2.95 
3.7 


4.2 
3.0 

2.87 


Theoretical per cent gain per inch of vac. 


3.0 



Tests of Turbines. — The following results of tests of turbines are 
selected from a series of tables in Moyer 's "Steam Turbines." 



KOTARY STEAM-ENGINES — STEAM TURBINES. 



1089 



1^ 


h 






i 

u 




-s^* 




li 


g d bib 


a 


kW o 


c3M 


6« 






^' 


5^-2 




§^ 


s^ 




^.^ 


;3«'^ 


2000 

c. 


r 555 


155 


204 


28.5 


18.09 


300 ( 
W.^P.| 


233 


145 


4.1 


28.0 


15.99 


1067 


170 


120 


28.4 


16.31 


461 


145 


4.8 


28.0 


13.99 


( 2024 


166 


207 


28.5 


15.02 


688 


140 


7.0 


27.2 


15.73 




( 5374 


182 


133 


29.4 


13.15 




383 


153 


2 


28.2 


14.15 


9000 


8070 


179 


116 


29.4 


13.00 




756 


149 


1 


27.8 


13.28 


c. 


10186 


176 


147 


29.5 


12.90 


500 


1122 


149 


5 


26.5 


14.32 




13900 


198 


140 


29.3 


13.60 


W.-P.' 


386 


148 


3 


0.8 


24.94 


1500 


530 
1071 


145 
131 


110 

124 


28.9 
28.3 


21.58 
18.24 




767 
1144 


147 
126 


3 

11 


0.8 
0.8 


22.10 
24.36 


1585 


128 


125 


27.5 


17.60 


1000 ( 
W.-P.| 


752 


151 





27.5 


14.77 


300 J 
P. 


303 
297 


158 
161 






26.6 



23.15 
34.20 


1503 
2253 


147 
145 






27.0 
25.2 


13.61 
15.29 




194 


171 


A7 


27 7 


31 97 


3000 ( 
W.-P.l 


2295 


152 


102 


26.2 


12.36 


1000 


425 


144 


21 


27.6 


24.91 


4410 


144 


87 


26.2 


11.85 


R. ' 


871 


166 


n 


23.6 


24.61 


300 ( 
D 1 


196 


198 


16 


27.4 


15.62 




1024 


164 


10 


25.0 


21.98 


298 


197 


64 


27.4 


14.35 














352 


199 


84 


27.2 


13.94 



C, Curtis; P., Parsons; W.-P., Westinghouse-Parsons; R., Rateau; 
D., De Laval. Note that the figures of steam consumption in the first 
half of the table are in lbs. per K.W.-hour; in second half, in lbs. per Brake 
H.P.-hour. 

A test of a Westinghouse double-flow turbine at the Williamsburg 
power station, Brooklyn N. Y., gave the following results (Eng. News, 
Dec. 30, 1909): Speed, 750 r.p.m.; Steam pressure at throttle, 203.4 lbs.; 
Superheat, 80.1° F.; Vacuum, 28.6 ins.: Load, 13,384 K.W.: Steam per 
K.W.-hour. 14.4 lbs.: Efficiency of generator, 98%; Windage, 2.0%; 
Eqiiivalent B. H. P., 18,620; Steam per B. H. P.-hour, 10.3 lb. 

Efficiency of the Rankine Cycle, and the Rankine Cycle Ratio. — 

An ideal engine operating on the Rankine cycle expands the steam 
adiabatically to the condenser pressure and the exhaust steam heats 
the feed water to the condenser temperature. It has no clearance nor 
loss by leakage or radiation. The eflaciency of the Rankine cycle is 
the quotient of the number of heat-units converted into work by the 
ideal engine per lb. of steam divided by the difference between the 
total heat per lb. of the entering steam and the total heat of 1 lb. of 
feed-water at the condenser temperature. 

The Rankine Cycle Ratio is the ratio between the thermal efficiency 
of an actual engine or tiu*bine and the efficiency of an ideal engine 
operating on the Rankine cycle between the same temperature and 
pressure limits as those of the actual engine. 

The available energy of 1 lb. of steam supplied = heat utilized per 
lb. in an ideal engine operating on the Rankine cycle = U = if _ —Hz + 
r2(iV2 - Ns) in which ^ 

H = heat-units per lb. of the entering steam, whether saturated or 
superheated. 

if 2 = heat units per lb. of the exhaust steam. 

Ti = absolute temperature of the exhaust. 

N and A^2 = respectively the entropy of the entering and of the 
exhaust steam. 

If the exhaust steam is superheated (as it may be in the case of the 
high-pressure cylinder of a triple expansion engine using highly super- 
heated steam) U = Hg — H2— TiiNg — N2). (These formulae may be 
derived from a study of the entropy temperature diagram, page 1085.) 

Example. — A steam turbine operating with 225 lb. absolute pres- 
sure, 150° superheat, and 28.5 in, vacuum uses 10 lb. of steam per 



1090 



THE STEAM-ENGINE. 



brake horse-power hour. Required the available energy per lb. steam, 
the Rankine cycle efficiency and the Rankine cycle ratio. 

Hs= 1285.9] il2= 1099.2; r2 = 549.6; /i = heat units per lb. of 
feed- water at the temperature r2 = 58. T^ = lb. steam per H. P. -hour = 
10. A = heat equivalent of one H.P.-hour = 1,980,000 -f- 777.54 = 
2546.5 B.T.U.; A^^ = 1.6296; A^2 = 2.0058 TF(if,; - /i) = total heat 
supply per H.P.-hour = 10 X (1285.9 - 58) = 12,279 B.T.U. Thermal 
efficiency E = 2546.5 ^ W(H - h) = 20.74%. Available energy per 
lb., U = 1285.9 - 1099.2 + 549.6 (2.0058 - 1.6296) = 393.5 B.T.U. 
Rankine cycle efficiency Eb = U ^ {Hg - h) = 393.5 ~ 1227.9 = 32.04%. 
Rankine cycle ratio R = E -r- Er ^ 20.74 -r- 32 = 64.7%. 

Factors for Reduction to Equivalent Rankine Efficiency. — When 
engines are tested with different pressures, superheat and vacuum, 
it is often desirable to reduce the results to a common standard of 
assumed conditions. The conditions stated in the above example 
correspond with good modern practice and they probably furnish as 
good a standard for comparison as any other. The Rankine cycle 
efficiency Er, for this set of conditions is 32.04% ; the thermal efficiency, 
for W= 10 lb. is 20.74 % ; and the ratio E ^Er is 64.7 %. For another 
set of conditions, pressure 150 lb., vacuum 27 in., and dry saturated 
steam Er is 27.0. The quotient 32.04 ^ 27.0 = 1.187, may be used 
as a factor to reduce the Rankine efficiency, the Rankine cycle ratio, 
and the steam consumption per H.P.-hour to the equivalent for stand- 
ard conditions; thus, equivalent E = 27 X 1.187 = 32.04, equivalent R 
(assuming W = 11.87 and E = 17.48%) = 17.48 X 1.187 = 20.74, and 
equivalent W= 11.87 ^ 1.187 = 10 lb., provided the percentage losses 
due to friction, radiation and leakage are the same for the two condi- 
tions. The factor is used as a multiplier to obtain the equivalent 
thermal efficiency and Rankine cycle ratio, and as a divisor to obtain 
the equivalent steam consumption. The factor may be found also 
32.04 {Hg- h), 



from the equation F = 



U 



in which Ho, h, and U are the 



values for the given set of conditions. The factors computed by this 
formula and the efficiency of the Rankine cycle for different conditions 
are given in the table at the top of p. 1091. 

Effect of Increase in Pressure, Vacuum and Superheat on Efficiency. — 

Selecting from the table on p. 1091 the figures for Rankine cycle efficiency 
given in the table below and comparing them by taking differences 
between consecutive figures in both the horizontal and the vertical rows, 
we find that the increase of efficiency due to increasing either the pres- 
sure, the superheat or the vacuum cannot be expressed as a constant 
percentage, but that it varies with variations in each condition. 
Effect of Varying Conditions on Ranking Cycle Efficiency. 



Pressure, 


Vacuum, 
In. 




Superheat. 






Absolute . 


0« 


Diff. 


150° 


Difif. 


300° 


Diff. 




p;.... 


27.0 


1.4 


0.5 


27.5 


1.5 


1.1 


28.6 


1.4 




150 


28.... 


28.4 


2.4 


0.6 


29.0 


2.4 


1.0 


30.0 


2.4 






( 29.... 


30.8 




0.6 


31.4 




1.0 


32.4 








(27.... 


28.5 


1.4 


0.6(1.5) 


29.1 


1.4 


1.0(1.6) 


30.1 


1.4 


(1.5) 


200 


-| 28.... 


29.9 


2.3 


0.6(1.5) 


30.5 


2.3 


1.0(1.5) 


31.5 


2.3 


(1.5) 




(29.... 


32.2 




0.6(1.4) 


32.8 




1.0(1.4) 


33.8 




(1.4) 




.27.... 


29.7 


1.3 


0.6(1.2)j 30.3 


1.3 


0.9(1.2) 


31.2 


1.4 


(I.l) 


250 


•^28.... 


31.0 




0.6 (1.1)1 31.6 




1.0(1.1) 


32.6 




(1.1) 




/ 


1 2.2 


1 


2.3 






2.8 






( 29. . . . 


33.2 1 


0.6(1.0); 33.9 




0.9(1.1)1 34.2 




(1.1) 



The figures in parentheses show the increase in efficiency due to 



ROTARY STEAM-ENGINES — STEAM TURBINES. 1091 



Eflflciency of Rankine Cycle, En (per cent) and Factor .Ffor Reduction 
to Standard Conditions, 

(225 Lb. Absolute Pressure, 150° Superheat, 28.5 In. Vacuum and 
Rankine Cycle eflBciency of 32 per cent being taken as standard.) 



Absolut. 


















Pres- 


Vacuum 




Superheat, 


Degrees 


Fahrenheit. 




sure, 


In. 
















Lb. per 


Mercury . 
















Sq. In. 







50 


100 


150 


200 


250 


300 




27 If- 


27.0 


27.1 


27.3 


27.5 


27.8 


28.2 


28.6 




1.187 


1.182 


1.174 


1.163 


1.150 


1.136 


1.122 




28 ]f« 


28.4 


28.5 


28.7 


29.0 


29.3 


29.6 


30.0 




1.127 


1.122 


1.115 


1.105 


1.094 


1.081 


1.068 


150 


28.5 1 f R 


29.4 


29.6 


29.8 


30.0 


30.3 


30.6 


31.0 




1.088 


1.083 


1.076 


1.067 


1.057 


1.046 


1.033 




29 If-' 


30.8 


31.0 


31.1 


31.4 


31.7 


32.0 


32.4 




1.040 


1.035 


1.028 


1.020 


1.011 


1.001 


0.989 




27 \f 


28.5 


28.6 


28.8 


29.1 


29.4 


29.7 


30.1 




1.124 


1.119 


1.111 


1.100 


1.090 


1.078 


1.064 




28 ]!■< 


29.9 


30.0 


30.2 


30.5 


30.8 


31.1 


31.5 




1.072 


1.067 


1.060 


1.051 


1.041 


1.030 


1.018 


200 


28.5 |f« 


30.9 


31.0 


31.2 


31.5 


31.8 


32.1 


32.4 




1.038 


1.033 


1.026 


1.018 


1.009 


0.998 


0.988 




29 If"' 


32.2 


32.3 


32.6 


32.8 


33.1 


33.4 


33.8 




0.995 


0.990 


0.984 


0.977 


0.968 


0.959 


0.949 




77 i ^R 


29.1 


29.2 


29.5 


29.7 


30.0 


30.3 


30.7 




1.101 


1.096 


1.087 


1.078 


1.068 


1.056 


1.044 




28 If- 


30.5 


30.6 


30.8 


31.1 


31.3 


31.7 


32.0 




1.052 


1.047 


1.040 


1.031 


1.022 


1.011 


1.000 


225 


28.5 If- 


31.4 


31.6 


31.8 


32.0 


32.3 


32.6 


33.0 




1.019 


1.014 


1.008 


1.000 


0.991 


0.981 


0.971 




29 If- 


32.7 


32.9 


33.1 


33.4 


33.6 


34.0 


34.3 




0.978 


0.973 


0.967 


0.960 


0.952 


0.943 


0.934 




27 ]f^ 


29.7 


29.8 


30.0 


30.3 


30.5 


30.9 


31.2 




1.079 


1.075 


1.068 


1.059 


1.049 


1.038 


1.026 




28 If- 


31.0 


31.1 


31.3 


31.6 


31.9 


32.2 


32.6 




1.033 


1.029 


1.022 


1.014 


1.005 


0.995 


0.984 


■ 250 


28.5 jf- 


32.0 


32.1 


32.3 


32.6 


32.8 


33.2 


33.5 


1 


1.002 


0.998 


0.992 


0.984 


0.975 


0.966 


0.956 


i 


29 If- 


33.2 


33.4 


33.6 


33.9 


34.1 


34.5 


34.8 


? 


0.963 


0.959 


0.953 


0.946 


0.938 


0.930 


0.920 



increase of 50 lb. in pressure, the superheat and the vacuum being 
constant. 



Constant. 



Increase of 



Pressure and vacuum] Superheat from ^^0 to 150° 



Pressure and 

Superheat 

Superheat and 

vacuum 



j Vacuum 
I Pressure 



27 

28 
150 
200 



300 

28 

29 

200 

250 



Increases 
Efficiency. 
0.5 to 0.6 av. 0.6 



0.9 
1.3 
2.2 
1.4 
1.0 



1.1 
1.5 
2.4 
1.6 
1.2 



1.0 
1.4 
2.3 
1.5 
1.1 



W. H. Wallis (Enc/'o, April 21, 1911) finds as the results of tests of 
a compound reaction turbine that the percentage reduction of steam 
consumption by increasing the vacuum from 25 in. to the figures given 
was as follows: Vacuum, 27 in.; reduction, 7 1/2%; 28 in., 12%; 28.6 in., 
16%. 

Steam Consumption and Heat Consumption of tlie Ideal Engine. — 

If the Rankine cycle efficiency is given for a stated set of conditions, 



1092 



THE STEAM-ENGINE. 



the corresponding theoretical steam consumption per H. P.-hour may be 

* ^ u ^u ^ 1 Txr 2546.5 2546.5 

found by the formula W = • — — — = ■= — ~rz — 

U Er {Hg - h) 

For the extreme cases in the table on p. 1090, we have: 



Pres- 
sure, 
Lb. 


Vac, 
In. 


Super- 
heat. 


Hs- 


h. 


^ie. 


U. 


w. 


Hs-h 


W (Hs-h). 


150 
250 


27 
29 



300° 


1193.4 
1363.5 


82.0 
44.6 


27.0 
34.8 


299.7 
459.1 


8.49 
5.60 


1114.4 
1318.9 


9461 
7376 



The figures in the last column, WiHg — h), show the B.T.U. con- 
sumed (or supplied by the boiler) per H. P. -hour. The number of 
pounds of steam supplied under the second set of conditions is 33.3 % less 
than that supplied under the first set, but the saving of heat is only 
(9461 - 7376) 4- 9461 = 22%. 

Westinghouse Turbines at the Manhattan 74th Street Station, 
New York. — Each of the 30,000 Kw. cross-compound units consists 
of two turbines, a high and a low pressure, side by side. Each half 
drives a generator, the high pressure running 1500 r.p.m. and the low 
pressure 750, the generators being tied together electrically. The tur- 
bines are reaction throughout, having no impulse wheel. The h.p. 
is a single flow machine and the l.p. a double flow. The turbines are 
to have a vacuum of 97% = 29.1 in. mercury, or 0.442 lb. per sq. in. 
absolute. The boilers will run at 215 lb. pressure, and at peak of the 
load, twice each day of 24 hours, will run at 300% of rating. Under- 
feed stokers. Superheat at throttle, 120°. (Pow;er, April 27, 1915). 

A Steam Turbine Guarantee. — A 22,500-Kw. steam turbine built 
in 1913 by C. A. Parsons Co., Newcastle, England, for the Common- 
wealth Edison Co., Chicago, was guaranteed as follows: At 750 r.p.m. 
200 lb. pressure by gage, 29 in. vacuum in the condenser 

Load, Kw 10,000 15,000 20.000 25,000 

Steam per Kw.-hour, lb ; 12.50 11.65 11.25 11.65 

Efficiency of a 5000-Kw. Steam Turbine Generator. (F. W. Ballard, 
Trans. A. S. M. E., 1914.) — A plotted diagram of a series of tests shows 
that the total steam consumption at different loads follows the Willans 
straight-line law up to the point of maximum efficiency. The turbine 
was of the Allis-Chalmers-Parsons type, rated at 5000 Kw., 1800 r.p.m., 
11,000 volts, A.C. With steam at 225 lb. gage, superheat 125° F., 
vacuum 281/2 in., 90% power factor, the steam consumption at 
different loads was as follows (figures approximate, from the chart) : 

Load, Kw 2,000 4,000 5,000 6,000 6,500 7,000 7,900 

Steam per Kw.- 
hour, lb 15.5 13.75 13.50 13.20 13.00 13.10 13.30 

Total steam per 

hour, lb 31,000 55,000 67,500 79,000 85,000 91,500 105,000 

Up to a load of 6500 Kw. the total consumption is 9000 + 12 X 
Kw. load, nearly. The efficiency ratio on the Rankine cycle was 0.6S 
at 6500 Kw. 

Comparison of Large Turbines and Reciprocating Engines. — Moyer 
gives a set of curves of the steam consumption of a standard 5000-Kw. 
turbine generator and a 4-cylinder compound reciprocating steam- 
engine generator, assuming both units, operating under the same con- 
ditions. The following figures are taken from the curves: 

Load in Kilowatts 3000 4000 5000 6000 7000 7500 

Lb. Steam per Kilowatt-hour. 
16.0 15.5 15.3 15.25 15.4 



Turbine 

Reciprocating engine: 
With equal work in cylinders. 
Unequal work in cylinders. . 



18.0 
18.4 



17.4 
17.0 



17.8 19.0 
17.2 17.5- 



20.8 
18.4 



15.5 



22.0 
19.0 



ROTARY STEAM-ENGINES — STEAM TURBINES. 1093 



Steam Consumption of Small Steam Turbines. — Small turbines, 
from 5 to 200 H.P., are extensively used for purposes where liigh speed of 
rotation is not an objection, such as for driving electric generators, cen- 
trifugal fans, etc., and where economy of fuel is not as important as 
saving of space, convenience of operation, etc. The steam consump- 
tion of these turbines varies as greatly as does that of small high-speed 
steam-engines, according to the desig;n, speed, etc. A paper by Geo. A. 
Orrok in Trans. A. S. M. E., 1909, discusses the details of several makes 
of machines. From a curve presented by R. H. Rice in discussion of 
this paper the following figures are taken showing the steam consumption 
in lbs. per B.H.P.-hour of different makes of impulse turbines. 



Type. 


Sturte- 
vant. 


Terry. 


Bliss. 


Bliss. 


Kerr. 


Curtis. 


Curtis. 


Rated H.P 

^l\rf/'^5oa^'::: 

^f^ Full load.. 
^* U 1/4 load. . . 


20 
72 
65 
61 
58 


50 
59 
49 
46 
44 


100 

58 
48 
43 
40 


200 
55 
47 
42 
39 


150 
52 
44 
41 
39 


50 
44 
36 
3? 
31 


200 
32 
30 
29 
28 



Dry steam, 150 lbs. pressure;, atmospheric exhaust. 

Mr. Orrok shows that the steam consumption of these turbines largely 
depends on their peripheral speed. From a set of curves plotted with 
speed as the base it appears that the steam consumption per B.H.P.-hour 
ranges about as follows: 
Peripheral speed, ft, 

per min 5,000 10,000 15,000 20,000 25,000 

Steam per B.H.P.-hour 45 to 70 38 to 60 31 to 52 29 to 45 29 to 40 

Low-Pressure Steam Turbines. — Turbines designed to utilize the ex- 
haust steam from reciprocating engines are used to some extent. For 
steam at or below atmospheric pressure the turbine has a great advan- 
tage over reciprocating engines in its ability to expand the steam down 
to the vacuum pressure, w'hile a reciprocating condensing engine generally 
does not expand below 8 or 10 lbs. absolute pressure. In order to ex- 
pand to lower pressures the low-pressure cylinder would have to be 
inordinately large, and therefore costly, and the increased loss from 
cylinder condensation and radiation would more than counterbalance 
the gain due to greater expansion. 

Mr. Parsons (Proc. Inst. Nav. Arch., 1908) gives the following figures 
showing that the theoretical economy of the combination of a recipro- 
cating engine and an exhaust steam turbine is about the same whether 
the turbine receives its steam at atmospheric pressure or at 7 lbs. abso- 
lute, the initial steam pressure in the engine being 200 lbs. absolute and 
the vacuum 28 ins. 

Back pressure of engines, lbs. abs. 16 131/2 8 

Initial pressure, turbine, lbs. abs 15 12V2 7 

Theoretical B.T.U. \\^tu& 142 III 100 

utilized per lb. of steam \ jStl'i^"^ :.••.:::::■.::::: 320 3I0 31° 

The following figures, by the General Electric Co., show the percentage 
over the output of a condensing reciprocating engine that may be made 
by installing a low-pressure turbine between the engine and the con- 
denser, the vacuum being 28 1/2 ins. 
Inches vacuum at admission 

valve 4 8 12 16 20 24 

Percent of work gained . .. 26.1 26.5 26.8 26.3 25.3 23.6 20 

It appears that a well-designed reciprocating compound engine work- 
ing down to about atmospheric pressure is a more efficient machine than 
a turbine with the same terminal pressure, and that between the atmos- 
phere and the condenser pressure the turbine is far more economical; 
therefore a combination of an engine and a turbine can be designed 
which will give higher economy than either an engine or a turbine work- 
ing through the whole range of pressure. 



1094 THE STEAM-ENGINE. 

When engines are run intermittently, such as rolling-mill and hoisting 
engines, their exhaust steam may be made to run low-pressure turbines 
by passing it first into a heat accumulator, or thermal storage system, 
where it gives up its heat to water, the latter furnishing steam continu- 
ously to the turbines. (See Thermal Storage, pages 927 and 1014.) 

The following results of tests of a Westinghouse low-pressure turbine 
are reported by Francis Hodgkinson. 

Steam press., 

lb. abs.... 17.4 
Vacuum, ins. 26.0 
Brake H.P. . 920 
Steam per 

B.H.P.-hr., 

lbs 27.9 37.1 29.9 37.3 64.4 28.0 30.4 38.6 54.8 

Tests of a 1000-K.W. low-pressure double-flow Westinghouse turbine 
are reported to have given results as follows. (Approximate figures, 
from a curve.) 

Load, Brake H.P 200 400 600 800 1000 1200 1500 2000 

Pressure at inlet, lbs. 

abs 4.1 5.1 6.1 7.2 8.3 9.4 11.0 13.5 



12.4 


11.8 


7.7 


5.2 


11.6 


8.7 


6.1 


4 5 


26.0 


27.0 


27.0 


27.0 


27.8 


28.0 


27.9 


28.0 


472 


592 


321 


102 


586 


458 


234 


114 



Steam per ) 271/2 in vac. 75 47.5 38 33 36 28 26.5 24.5 
^Q^jT-^^'g ) 28 in. vac. 62 42 33 29 27 25.5 24.5 22.5 

The total steam consumption per hour followed the Willans law, 
being directly proportional to the power after adding a constant fo7 
load, viz.: for 27V2-in. vacuum the total steam consumption per hour 
was 12,000 lbs. + 18 X H.P., and for 28-in. vacuum, 9000 lbs. + 18 X 
H.P. (approx.). 

The guaranteed steam consumption of a 7000- K.W. Rateau-Smoct 
low-pressure turbine generator is given in a curve by R. C. Smoot {Power, 
June 22, 1909), from which the following figures are taken. The admis- 
sion pressure is taken at 16 lbs. absolute and the vacuum 28 1/2 ins. 

K.W. output 1500 2000 3000 4000 5000 6000 7000 

Steam per K.W.-hr., lb.. .. 40 37 32.5 29.5 27.6 26.2 25.7 
Over-all efficiency, % 43 47 54 60 65 68 70 

The performance of a combined plant of several reciprocating 2000- 
K.W. engines and a 7000-K.W. low-pressure turbine is estimated as fo' 
lows, the engines expanding the steam from 215 to 16 lbs. absolute, and 
the turbines from 16 lbs. to 0.75 lb., the vacuum being 28.5 ins. with 
the barometer at 30 ins. 

Engine. Turbine. 

Theoretical steam per K.W.-hour, lbs 18 17.8 

Steam per K.W.-hr. at switchboard, lbs 27.7 26.6 

Combined efficiency of engine and dynamo, per cent.. . 65 67 

Steam per K.W.-hour for combined plant = 1 -r- (1/27.7 + 1/26.6) = 

13.6 lbs. 

The combined efficiency is 66%, representing the ratio of the energy 
at the switchboard to the available energy of the steam delivered to the 
engine and expanded down to the condenser pressure, after allowing foi 
all losses in engine, turbine, and dynamo. 

Very little difference is made in the plant efficiency if the intermediate 
pressure is taken anj^where from 3 or 4 lbs. below atmosphere to 15 or 
20 lbs. above. 

M. B. Carroll {Gen. Elec. Rev., 1909) gives an estimate of the steam 
consumption of a combined unit of a 1000-K.W. engine and a low-pres- 
sure turbine. The engine, non-condensing, will develop 1000 H.P., 
with 32,000 lbs. of steam per hour. Allowing 8% for moisture in th€ 
exhaust, 29,440 lbs. of dry steam will be available for the turbine, which 
at 33 lbs. per K.W.-hour will develop 893 K.W., making a total output of 
1893 K.W. for 32.000 lbs. steam, or 16.9 lbs. per K.W.-hour. The engine 
alone as a condensing endne will develop 1320 K.W. at 24.2 lbs. per K.W.- 
hour. The combined unit therefore develops 573 K.W., or 43.5% more 
than the condensing engine using the same amount of steam. The 
maximum capacity of the engine, non-condensing, is 1265 K.W., and 
condensing, 1470 K.W., and of the combined unit 2500 K.W. 



INTERNAL-COMBUSTION ENGINES. 1095 

Tests of a 15,000 K.W. Steam-Engine-Turbine Unit are reported 
by H. G. Stott and R. J. S. Pigott in Jour. A.S.M.E., Mar., 1910. The 
steam-engine is one of the 7500 K.W. Manhattan type engines at the 59th 
St. station of the Rapid Transit Co., New York, with two 42-in. horizontal 
h.p. and two 86-in. vertical i.p. cylinders, and the turbine, also 7500 K.W., 
is of the vertical three-stage impulse type. ^ The principal results are sum- 
marized as follows: An increase of 100% in the maxinmm capacity and 
146% in the economical capacity of tbe plant; a saving of about 85% of 
the condensed steam for return to the boilers [it was previously wasted]; 
an average improvement in economy of 13% over the best high-pressure 
turbine results, and of 2.5% (between 7500 and 15,000 K.W.) over the re- 
sults obtained bv the engine alone; an average thermal efficiency between 
6500 and 15,500 K.W. of 20.6%. [This efficiency is not quite equal to 
that reached by triple-expansion pumping engines. See page 806.] 

Reduction Gear for Steam Turbines. — Double spiral reduction gears, 
usually of a ratio of 1 to 10, are used with the DeLaval turbine to obtain 
a velocity of rotation suitable for dynamos, centrifugal pumps, etc. G. W. 
Melville and J. H. McAlpine have designed a similar gear, with the pinion 
carried in a floating frame supported at a single point between the bear- 
ings to equahze the strain on the gear teeth, for reducing the speed of 
large horizontal turbines to suitable speeds for marine propellers. A 
6000 H.P. gear with reduction from 1500 to 300 r.p.m. has given an effi- 
ciency of 98.5% {Eng'g, Sept. 17; Eng. News, Oct. 21 and Dec. 30, 1909). 

The Fottinger Transformer or Hydraulic Pinion is an apparatus for 
reducing the speed of a propeller shaft below the speed of the steam- 
turbine shaft. It consists of a turbine w^heel or water motor, moimted 
on the end of the propeller shaft, and a centrifugal pump mounted on 
the shaft of the steam turbine. The water is delivered by the pump 
to the motor and from the motor it passes to a tank and thence to the 
inlet of the pump. The ratio of reduction is determined by the design 
of the turbine and pump. The ratios hitherto applied range from 1.2:1 
to 6:1. Reversing is accomplished by means of a second turbine on 
the propeller shaft, a valve directing the water to either the ahead or 
astern turbine as required. Hydraulic pinions transmitting 10,000 
shaft horse-power have shown an over-all efficiency of about 92 per cent. 
An illustrated description will be found in Engineering of Sept. 25, 1914. 

HOT-AIR ENGINES. 

Hot-air (or Caloric) Engines. — Hot-air engines are used to some 
extent, but their bulk is enormous compared with their effective power. 
For an account of the largest hot-air engine ever built (a total failure) see 
Church's Life of Ericsson. For theoretical investigation, see Rankin's 
Steam-engine and Roentgen's Thermodynamics. For description of con- 
structions, see Appleton's Cyc. of Mechanics and Modern Mechanism, and 
Babcock on Substitutes for Steam, Trans. A, S. M. E., vii, p. 693. 

Test of a Hot-air Engine (Robinson). — A vertical double-cylinder 
(Caloric Engine Co.'s) 12 nominal H.P. engine gave 20.19 I. H.P. in the 
working cylinder and 11.38 I. H.P. in the pump, leaving 8.81 net I.H.P.; 
wliile the effective brake H.P. was 5.9, giving a mechanical efficiency of 
67%. Consumption _of coke, 3.7 lbs. per brake. H.P. per hour. Mean 
pressure on pistons 15.37 lbs. per square inch, and in pumps 15.9 lbs., the 
area of working cylinders being twice that of the pumps. The air was 
supplied about 1160° F. and rejected at end of stroke about 890° F. 

INTERNAL-COMBUSTION ENGINES. 

References.—For theory of the internal-combustion engine, see 
paper by Dugald Clerk, Proc. Inst. C. E., 1882, vol. Ixix; and Van 
Nostrand's Science Series, No. 62. See also Wood's Thermodynamics; 
Standard works on gas-engines are ** A Text-book on Gas, Air, and Oil 
Engines," by Bryan Donkin; "The Gas and Oil Engine," by Dugald 
Clerk; "Internal Combustion Engines," by Carpenter and Diederichs; 
*' Gas Engine Design," by C. E. Lucke: "Gas and Petroleum Engines," 
by W. Robinson; "The Modern Gas Engine and the Gas Producer," by 
A. M. Levin, and "The Gas Engine," by C. P. Poole. For prac- 
tical operation f gas and oil engmes, see "The Gas Engine," by 
F. R. Jones, and " The Gas Engine Handbook," by E. W, Roberts. 



1096 INTERNAL-COMBUSTION ENGINES. 

For descriptions of large gas-engines using blast furnace gas see papers 
in Proc. Iron and Steel Inst., 1906, and Trans. A. I. M. E., 1906. IVlany 
papers on gas-engines are in Trans. A.S.M.E., 1905 to 1909. 

An Internal-combustion Engine is an engine in which combustible 
gas, vapor, or oil is burned in a cylinder, generating a high temperature 
and liigh pressure in the gases of combustion, which expand behind a 
piston, driving it forward. (, Rotary gas-engines or gas turbines, are still, 
1915, in the experimental stage.) 

Four-cycle and Two-cycle Gas-Engines. — In the ordinary type of 
single-cylinder gas-engine (for example the Otto) known as a four-cycle 
engine, one ignition of gas takes place in one end of the cylinder every 
two revolutions of the fly-wheel, or every two double strokes. The fol- 
lowing sequence of operations takes place during four consecutive strokes: 
(a) inspiration of a mixture of gas and air during an entire stroke; {h) 
compression during the second (return) stroke; (c) ignition at or near the 
dead-point, and expansion during the third stroke; {d) expulsion of the 
burned gas during the fourth (return) stroke. Beau de Rochas in 1862 
laid down the law that there are four conditions necessary to reahze the 
best results from the elastic force of gas: (1) The cylinders should have 
the greatest capacity with the smallest circumferential surface; (2) the 
speed should be as high as possible; (3) the cut-off should be as early as 
possible; (4) the initial pressure should be as liigh as possible. 

(Strictly speaking four-cycle should be called four-stroke-cycle, but the 
term four-cycle is generally used in the trade.) 

The two great sources of waste in gas-engines are: 1. The high tempera- 
ture of the rejected products of combustion; 2. Loss of heat through the 
cylinder walls to the water-jacket. As the temperature of the water- 
jacket is increased the efficiency of the engine becomes higher. 

Fig. 178 is an indicator diagram of a four-cycle gas-engine. AB, the 
lower line, shows the admission of the mixture, at a pressure slightly 
below the atmosphere oh account of the re- 
sistance of the inlet valve, BC is the com- 
pression into the clearance space, ignition 
taking place at C and combustion with 
increase of pressure continuing from C to D. 
Thfe gradual termination of the combustion 
is shown by the rounded corner at D. DE 
is the expansion line, EF the line of pressure 
drop as the exhaust valve opens, and FA the 
line of expulsion of the burned gases, the 
pressure being slightly above the atmos- 
T^^_ T«Q B phere on account of the resistance of the 

^^^•■^'^- exhaust valve. 

In a two-cycle single-acting engine an explosion takes place with every 
revolution, or with each forward stroke of the piston. Referring to the 
diagram Fig. 178 and beginning at E, when the exhaust port begins to 
open to allow the burned gases to escape, the pressure drops rapidly to F. 
Before the end of the stroke is reached an inlet port opens, admitting 
a mixture of gas and air from a reservoir in which it has been compressed. 
This mixture being under pressure assists in driving the burned gases 
out through the exhaust port. The inlet port and the exhaust port close 
early in the return stroke, and during the remainder of the stroke BC 
the mixture, which may include some of the burned gas, is compressed and 
the ignition takes place at C, as in the four-cycle engine. 

In one form of the two-cycle engine only compressed air is admitted 
while the exhaust port is open, the fuel gas being admitted under pressure 
after the exhaust port is closed. By this means a greater proportion of 
the burned gases are swept out of the cylinder. Tliis operation is known 
as " scavenging." 

Theoretical Pressures and Temperatures in Gas-Engines. — Referring 
to Fig. 178, let P^ be the absolute pressure at B, the end of the suction 
stroke, P^ the pressure at C, the end of the compression stroke; P^; the 
maximum pressure at D, when the gases of combustion are at their 
highest temperature; P^ the pressure at E, when the exhaust valve begins 
to open. For the hypothetical case of a cylinder with walls incapable of 
absorbing or conducting heat, and of perfect and instantaneous combustion 




INTERNAL COMBUSTION ENGINES. 1097 

or explosion of the fuel, an ideal diagram might be constructed which 
would have the following characteristics. In a four-cycle engine receiv- 
ing a charge of air and gas at atmospheric pressure and temperature, 
the pressure at B, or P^, would be 14.7 lbs. per sq. in. absolute, and the 
temperature say 62° F., or 522° absolute. The pressure at C, or P^' would 
depend on the ratio Vi ^ V2, Vi being the original volume of the mixture 
in the cyhnder before compression, or tlie piston displacement plus the 
volume of the clearance space, and V2 the volume after compression, or 
the clearance volume, and its value would be P^ = P^ (V1/V2) . The 
absolute temperature at the end of compression would be Tf. = 522 X 
{Vi/V2)^~\ or it may be found from the formula PgVs^ ^5 = ^c^^c-^ J^c 
the subscripts s and c referring respectively to conditions at the beginning 
and end of comipression. The compression would be adiabatic, and the 
value of the exponent n would be about the value for air, or 1.406. The 
work done in compressing the mixture would be calculated by the formula 
for compressed air (see page 634). The theoretical rise of tempera- 
ture at the end of the explosion, T^, above the temperature at the end of 
the compression T^, may be found from the formula (T^ — T^) C^ = H, 
in which H is the amount of heat in British thermal units generated by 
the combustion of the fuel in 1 lb. of the mixture, and C^ the mean specihc 
heat, at constant volume, of the gases of combustion between the tem- 
peratures T^ and T^. Having obtained the temperature, the correspond- 
ing pressure P^. may be found from the formula P^; = Pc^ (T^/Tf,)^~^ , 
In like manner the pressure and temperature at the end of expansion, 
Pg and Tg, and the work done during expansion, may be calculated by 

the formula for adiabatic expansion of air. 

The ideal diagram of the adiabatic compression of air, instantaneous 
heating, and adiabatic expansion, differs greatly from the actual diagram 
of a gas-engine, and the pressures, temperatures, and amount of work 
done are different from those obtained bv the method described above. 
In the first place the mixture at the beginning of the compression stroke 
is usually below atmospheric pressure, on account of the resistance or 
the inlet valve, in a four-cycle engine, but may be above atniosphenc 
pressure in a two-cycle engine, in which the mixture is deUvered from a 
receiver under pressure. Then the temperature is much higher than 
that of the atmosphere, since it is heated by the walls of the cyhnder 
as it enters. The compression is not adiabatic, since heat is receivea 
from the walls during the first part of the stroke. If the clearance space 
is small and the pressure and temperature at the end of compression there- 
fore liigh, the gas may give up some heat to the walls during the latter 
part of the stroke. The explosion is not instantaneous, and during its 
continuance heat is absorbed by the cylinder walls, and therefore neither 
the temperature nor the pressure found by calculaUon will be actually 
reached. Poole states that the rise in temperature produced by com- 
bustion is from 0.4 to 0.7 of what it would be \dth instantaneous com- 
bustion and no heat loss to the cylinder walls. Finally the expansion 
is not adiabatic, as the gases of combustion, at least during the first part 
of the expanding stroke, are giving up heat to the cylinder. 

Calculation of the Power of Gas-Engines.— If the mean effective pres- 
sure in a gas-engine cylinder be obtained from an indicator diagram, its 
power is found by the usual formula for steam-engines, H.P. = ''^ ^ +vf 
33,000, in which P is the mean effective pressure in lbs. per sq. in., -^^ "the 
length of stroke in feet, A the area of the piston in square inches, and iV 
the number of explosion strokes per minute. , 

For purposes of design, however, the mean effective pressure either 
has to be assumed from a knowledge of that found in other engines of 
the same type and working under the same conditions as those of the 
design, or it may be calculated from the ideal air diagram and modified 
by the use of a coefficient or diagram factor depending on the kind of 
fuel used and the compression pressure. Lucke gives the following 



1098 



INTERNAL-COMBUSTION ENGINES. 



factors for four-cycle engines by which the mean effective pressure 
of a theoretical air diagram is to be multiplied to obtain the actual M.E.P. 
for the several conditions named. 



Kind of Fuel and Method of Use. 



Kerosene, when previously vaporized 

Kerosene, injected on a hot bulb, may be as low as. 
Gasoline, used in carburetor requiring a vacuum. . . 

Gasoline, with but little initial vacuum 

Producer gas 

Coal gas 

Blast-furnace gas 

Natural gas 



Compres- 
sion. 
Gauge 
Pressure. 



Lb. 
43-75 



80-130 
100-160 
Av.80 
130-180 

90-140 



Factor. 
Per Cent. 



30-40 
20 

25-40 
50-30 
56-40 
Av. 45 
48-30 
52-40 



Factors for two-cycle engines are about 0.8 those for four-cycle engines. 

Pressures and Temperatures at end of Compression and at Re- 
lease. — The following tables, greatly condensed from very full tables 
given by C. P. Poole, show approximately the pressures and tempera- 
tures that may be realized in practice under different conditions. Poole 
says that the value of n, the exponent in the formula for compression, 
ranges from 1.2 to 1.38, these being extreme cases; the values most 
commonly obtained are from 1.28 to 1.35. The tables for compression 
pressures and temperatures are based on n = 1.3 and 1.4, on compres- 
sion ratios or Vt/V2 from 3 to 8, on absolute pressures in the cylinder 
before compression from 13 to 16 lbs., and on absolute temperatures 
before compression of 620° to 780° (160° to 820° F.). The release pres- 
sures and temperatures are based on values of n of 1.29 and 1.32, abso- 
lute pressures at the end of the explosion from 240 to 360 lbs. per sq. in., 
and absolute temperatures at the end of the explosion of 1800° to 3000° F. 

Compression Pressures. 



g « 03 



3.00 
4.00 
5.00 
6.00 
7.00 
8.00 



n = 1.3. 



13 13.5 14 



54.2 
78.8 
105.4 
133.5 
163.2 
194.0 



56.3 
81.9 
109.4 
138.7 
169.4 
201.5 



58.4 
84.9 
113.5 
143.8 
175.7 
209.0 



62.6 
90.9 
121.6 
154.1 
188.3 
223.9 



16 



66.7 
97.0 
129.7 
164.3 
200.8 
238.7 



t-. 5 o 
a.o-2 

a «2 c| 



3.00 
4.00 
5.00 
6.00 
7.00 
8.00 



n = 1.34. 



P„=13 13.5 14 15 16 



56.7 
83.3 
112.3 
143.4 
176.3 
210.9 



58.9 
86.5 
116.7 
148.9 
183.1 
219.0 



61.0 
89.7 
121.0 
154.5 
189.9 
227.1 



65.4 
96.1 
129.6 
165.5 
203.5 
243.4 



69.7 
102.5 
138.3 
176.5 
217.0 
259.6 



Compression Temperatures. 



£ 1." 






n=1.3 






h i> 






n=1.34. 
















&c ° 










620° 


660" 


700° 


740° 


780° 


ft 


620° 


660° 


700° 


740° 


780° 


3.00 


862 


918 


973 


1029 


1084 


3.00 


901 


959 


1017 


1075 


1133 


4.00 


940 


1000 


1061 


1122 


1182 


4.00 


993 


1057 


1122 


1186 


1250 


5.00 


1C05 


1070 


1134 


1199 


1264 


5.00 


1072 


1141 


1210 


1279 


1348 


6.00 


1061 


1130 


1198 


1267 


1335 


6.00 


1140 


1214 


1287 


1361 


1434 


7.00 


1112 


1183 


1255 


1327 


1398 


7.00 


1201 


1279 


1357 


1434 


1512 


8.00 


1157 


1232 


1306 


1381 


1456 


8.00 


1257 


1338 


1420 


1501 


1582 



INTERNAL- COMBUSTION ENGINES. 



1099 



Absolute Pressures per Squarb Inch at Release. 
Corresponding to Explosion Pressures commonly obtained. 
Note: — The expansion ratios in the left-hand column are based on 
the volume behind the piston when the exhaust valve begins to open. 





ng=-1.29. 




n,= 1.32. 


S.2 








9 o 








&^ 




Value of P^ 




a-^ 




Value of P^ 




^^ 


240 


270 300 330 


360 


w^ 


240 


270 300 330 


360 


3.00 


58.2 


65.4 


72.7 


80.0 


87.2 


3.00 


56.3 


63.3 


70.4 


77.4 


84.4 


4.00 


40.1 


45.2 


50.2 


55.2 


60.2 


4.00 


38.5 


43.3 


48.1 


52.9 


57.8 


5.00 


30.1 


33.9 


37.6 


41.4 


45.1 


5.00 


28.7 


32.3 


35.8 


39.4 


43.0 


6.00 


23.8 


26.8 


29.7 


32.7 


35.7 


6.00 


22.5 


25.4 


28.2 


31.0 


33.8 


7.00 


19.5 


21.9 


24.4 


26.8 


29.2 


7.00 


18.4 


20.7 


23.0 


25.3 


27.6 


8.00 


16.4 


18.5 


20.5 


22.6 


24.6 


8.00 


15.4 


17.3 


19.3 


21.2 


23.1 



Absolute Temperatures at Release. 
Corresponding to Explosion Temperatures commonly obtained. 



o ^ 


n,= 1.29. 


§•2 


ng=1.32. 


n 




Value of T^ 






Value of T^ 




&^ 


1800 


2100 2400 2700 


3000 


1800 


2100 2400 2700 


3000 


3.00 


1309 


1527 


1745 


1963 


2182 


3.00 


1266 


1478 


1689 


1900 


2111 


4.00 


1204 


1405 


1606 


1806 


2007 


4.00 


1155 


1348 


1540 


1733 


1925 


5.00 


1129 


1317 


1505 


1693 


1881 


5.00 


1075 


1255 


1434 


1613 


1792 


6.00 


1070 


1249 


1427 


1606 


1784 


6.00 


1015 


1184 


1353 


1522 


1691 


7.00 


1024 


1194 


1365 


1536 


1706 


7.00 


966 


1127 


1288 


1449 


1610 


8.00 


985 


1149 


1313 


1477 


1641 


8.00 


925 


1079 


1234 


1388 


1542 



Pressures and Temperatures after Combustion. — According to 
Poole, the maximum temperature after combustion may be as high as 
3000° absolute, F., and the maximum pressure as high as 400 lbs. per 
sq. in. absolute; these are high figures, however, the more usual figures 
being about 2300° and 250 lbs. Poole gives the following figures for 
the average rise in pressure, above the pressure at the end of compres- 
sion, produced by combustion of different fuels, with different ratios of 
compression. 

Average Pressure Rise in lbs. per sq. in. Produced by 
Combustion. 



4 


•X- 

«t3 






,d 


* 


.2 




d 








6 


03 

1 


d 


OH 

"^2 


d 




d 

S 
o 


1 i 


o 


1— 1 


O 


w 


o 


12; 


o 


P4 


o 


5 


4.0 


146 


195 


168 


5.0 


192 


6.0 


225 


7.0 


211 


4.2 


156 


208 


179 


5.2 


202 


6.2 


234 


7.2 


218 


4.4 


166 


221 


190 


5.4 


211 


6.4 


243 


7.4 


225 


4.6 


175 


234 


202 


5.6 


221 


6.6 


252 


7.6 


232 


4.8 


185 


247 


213 


5.8 


230 


6.8 


261 


7.8 


239 


5.0 


195 


260 


224 


6.0 


240 


7.0 


270 


8.0 


246 



* Per cubic foot measured at 32° F. 
The following figures are given by Poole as a rough approximate 
guide to the mean effective pressures in lbs. per sq. in. obtained with 



1100 



INTERNAL-COMBUSTION ENGINES. 



different fuels and different compression pressures in a four-cycle engine. 
In a two-cycle engine the mean effective pressure of the pump diagram 
should be subtracted. The delivery pressure is usually from 4 to 8 lbs. 
per sq. in. above the atmosphere, and the corresponding mean effective 
pressure of the pump about 3.8 to 7. 

Pbobable Mean Effective Pressure. 



Suction Anthracite Producer Gas. 


MoND Producer Gas. 


Engine 
H.P. 


Compression Pressure, 
abs. lbs. per sq. in. 


Engine 
H.P. 


Compression Pressure. 




100 


115 


130 


145 


160 


100 


115 


130 


145 


160 


10 


55 


60 


65 






10 




65 


65 


65 




25 


60 


65 


70 


75 




25 


60 


65 


65 


70 


75 


50 


65 


70 


75 


80 


80 


50 


65 


70 


70 


75 


80 


100 


70 


75 


80 


85 


85 


100 


65 


70 


75 


80 


85 


250 


75 


80 


85 


90 


90 


250 


70 


75 


80 


85 


90 


500 


80 


85 


90 


90 


90 


500 


75 


80 


85 


90 


90 



Natural and Illuminating Gases. 



Engine 
H.P. 


Compression Pressure. 


Engine 
H.P. 


Compression Pressures. 


65 


75 


85 


100 


115 


75 


85 


100 


115 


130 


10 
25 
50 


60 
65 
70 


65 
70 
75 


70 
75 
80 


75 
80 
90 


'8*5' 
90 


100 
250 
500 


80 
85 


85 
90 
95 


90 
95 
100 


95 
100 
105 


100 
105 
110 



Kerosene Spray. 


Gasoline Vapor. 


Engine 
H.P. 


Compression Pressures. 


Engine 
H.P. 


Compression Pressures. 


65 


75 


85 

60 
65 
70 
75 


100 


115 


65 


75 


85 


100 

85 
90 
90 
95 




5 
10 
25 
50 


50 
55 
60 
65 


55 
60 
65 
70 


65 
70 
75 
80 


70 
75 
80 

85 


5 
10 
25 
50 


70 
75 
80 
85 


75 
80 
85 
90 


80 
85 
90 
95 


... 



Sizes of Large Gas Engines. — From a table of sizes of the Ntfrnberg 
gas engine, as built by the AlUs-Chalmers Co., the following figures are 
taken. These figures relate to two-cylinder tandem double-acting engines. 

Diam. cyl., Ins...... 18 

Stroke cyl., ins 24 

Revs, per min 150 

Piston speed, ft. per 

min 600 

Rated B.H.P 260 

Factor C 0.8 

Diam., ins 34 

Stroke, ins 42 

Revs, per min 100 

Piston speed 700 

Rated B.H.P 1105 

Factor C 0.96 

The figures "factor C" are the values of C in the equation B.H.P. = 
C X i)2, in which D = diam. of cylinder in ins. For twin-cylinder double- 
acting engines, multiply the B.H.P. and the value of C by 0.95; for twin- 



20 


21 


22 


24 


24 


26 


28 


30 


32 


24 


30 


30 


30 


36 


36 


36 


42 


43 


150 


125 


125 


125 


115 


115 


115 


100 


100 


600 


625 


625 


625 


690 


690 


690 


700 


700 


320 


370 


405 


490 


545 


630 


740 


855 


985 


0.8 


0.84 


0.84 


0.85 


0.95 


0.93 


0.94 


0.95 


0.96 


36 


38 


40 


42 


44 


46 


48 


50 


52 


48 


48 


48 


54 


64 


54 


60 


60 


62 


92 


92 


92 


86 


86 


86 


78 


78 


78 


736 


736 


736 


774 


774 


774 


780 


780 


780 


1300 


1460 


1630 


1875 


2080 


2280 


2475 


2720 


2950 


1 


1.01 


1.02 


1.06 


1.07 


1 OS 


1.07 


1.09 


1.09 



INTERNAL-COMBUSTION ENGINES. 



1101 



tandem double-acting engines, multiply by 2; for two-cylinder single- 
acting, or for single-cylinder double-acting engines, divide by 2; for 
single-acting single-cylinders, divide by 4. The figures for B.H.P. corre- 
spond to mean effective pressures of about 66, 68, and 70 lbs. per sq. in. 
for 20, 40, and 50 in. cylinders respectively if we assume 0.85 as the me- 
chanical efficiency, or the ratio B.H.P. -s- I.H.P. 

Engine Constants for Gas Engines. — The following constants for 
figuring the brake H.P. of gas engines are given in Power, Dec. 7, 1909. 
They refer to four-stroke cycle single-cylinder engines, single acting; for 
double-acting engines multiply by 2. Producer gas, 0.000056. Illumi- 
nating gas, 0.000065. Natural gas, 0.00007. Constant X diam.2 x stroke 
in ins. X revs, per min. = probable B.H.P. A deduction should be made 
for the space occupied by the piston rods, about 5% for small engines up 
to 10% for very large engines. 

Kated Capacity of Automobile Engines. — The standard formula for 
the American Licensed Automobile Manufacturers Association (called 
the A. L. A. M. formula) for approximate rating of gasoline engines 
used in automobiles is Brake H.P. = Diam.2 x jsJq. of cylinders ^ 2.5. 
It is based on an assumed piston speed of 1000 ft. per min. The following 
ratings are derived from the formula: 

Bore, ins 2V2 

Bore, mm 64 

H.P., 1 cylinder 2 1/2 

H.P., 2 cyUnders. . . 5 

H.P.. 4 " ... 10 

H.P., 6 •• ... 15 

A committee of the Institution of Automobile Engineers recommends 
the foUowing formula: B.H.P. = 0.45 {d + s) {d - 1.18)N, in which 
d = diam., in., s = stroke, in., iV = number of cylinders. The formula 
was derived from the results of tests of engines in first-class condition 
on the test bench. For ordinary engines on the road the result should 
be multiplied by 0.6. (Eng'g, Feb. 10, 1911.) 

The American Power Boat Association's formula for rating 2-cycle 
engines is H.P. = area of piston X number of cylinders X length of 
stroke X 1.5. 

Approximate Estimate of the Horse-power of a Gas Engine. — 
From the formula I.H.P. = PLAN -^ 33,000, in which P= mean effective 
pressure in lbs. per sq. in., L = length of stroke in ft., A = area of piston 
in sq. ins., A^ = No. of explosion strokes per min., we have l.B..F, = Pd^S-^ 
42,017, in which d = diam. of piston, and 5 = piston speed in ft. per min., 
for an engine in which there are two explosion strokes in each revolution, 
as in a 4-cycle double-acting, 2-cylinder engine, or a 2-cycle, 2-cylinder, 
single-acting engine. If the mechanical efficiency is taken at 0.84. then 
the brake horse power B.H.P. = Pd^S -J- 50,000. Under average con- 
ditions the product of P and S is in the neighborhood of 50,000, and in 
that case B.H.P. = d^. Generally, B.H.P. = C X d\ in which C is a 
coefficient having values as below: 



3 


31/2 


4 


41/2 


5 


51/2 


6 


76 


89 


102 


114 


127 


140 


154 


3.6 


4.9 


6.4 


8.1 


10 


12.1 


14.4 


7.2 


9.8 


12.8 


16.2 


20 


24.2 


28.8 


14.4 


19.6 


25.6 


32.4 


40 


48.4 


57.6 


21.6 


29.4 


38.4 


48.6 


60 


72.6 


86.4 



M.E.P. 


Piston Speed, Ft. per Minute. 


Lbs. per 


500 


600 700 


800 900 1000 


Sq. In. 


Value of C for Two Explosions per Revolution. 


50 


0.50 


0.60 


0.70 


0.80 


0.90 


1.00 


60 


0.60 


0.72 


0.84 


0.96 


1.08 


1.20 


70 


0.70 


0.84 


0.98 


1.12 


1.26 


1.40 


80 


0.80 


0.96 


1.12 


1.28 


1.44 


1.60 


90 


0.90 


1.08 


1.26 


1.44 


1.62 


1.80 


100 


1.00 


1.20 


1.40 


1.60 


1.80 


2.00 


110 


1.10 


1.32 


1.54 


1.76 


1.98 


2.20 



These values of C apply to 4-cylinders, 4-cycle, single-acting, to 2- 
cyl., 2-cycle, single-acting, and to 1-cyl., 2-cycle double-acting. For 
single cylinders, 4-cycle, single-acting, divide by 4; for single cylinders, 
4-cycle, double-acting, or 2-cycle, single-acting, divide by 2. 

Oil and Gasoline Engines. — The lighter distillates of petroleum, such 
as gasohne, are easily vaporized at moderate temperatures, and a gaso- 
line engine differs from a gas-engine only in having an atomizer attached 



1102 INTEEJ^AL-COMBUSTION ENGINES. 

for spraying a fine jet of the liquid into the air-admission pipe. With 
kerosene and other heavier distillates, or crude oils, it is necessary to 
provide some method of atomizing and vaporizing the oil at a high 
temperature, such as injecting it into a hot vaporizing chamber at the 
end of the cyhnder, or into a chamber heated by the exhaust gases. 

The Diesel Oil Engine. — The distinguishing features of the Diesel 
engine are: It compresses air only, to a predetermined temperature above 
the firing point of the fuel. Ttiis fuel is blown as a cloud of vapor (by 
air from a separate small compressor) into the cylinder when compres- 
sion has been completed, ignites spontaneously without explosion, 
solely by reason of the heat of the air generated by the compression, 
and burns steadily with no essential rise in pressure. The temperature 
of gases, developed and rejected, is much lower than with engines of the 
explosive type. The engine uses crude oil and residual petroleum prod- 
ucts. Guarantees of fuel consumption are made as low as 8 gallons of 
oil (not heavier than 19° Baum^) for each 100 brake H.P. hour at any 
load between half and full rated load. 

American Diesel engines are built for stationary purposes, in sizes of 
120, 170, and 225 H.P. in three cylinders, and in "double units" (six 
cylinders) of 240, 340 and 450 H.P. See catalogue of the American 
Diesel Engine Co., St. Louis, 1909. 

Much larger sizes have been built in Europe, where they are also 
built for marine purposes, including submarines in the French and other 
navies. For the theory of the Diesel engine see a lecture by Rudolph 
Diesel, in Zeit. des Ver Deutscher Ing., 1897, trans, in Progressive Age, 
Dec. 1 and 15, 1897, and paper by E. D. Meier in Jour. Frank. Inst., 
Oct. 1898. 

The De La Vergne Oil Engine is described in Eng. News, Jan. 13, 1910. 
It is a four-cycle engine. After the charge of air is compressed to about 
200 lbs. per sq. in., the charge of oil is injected, by a jet of air at about 
600 lbs. per sq. in., into a vaporizing bulb at the end of the cylinder. Ig- 
nition of the oil is caused by the high temperature in this bulb. Average 
results of tests of an engine developing 128 H.P. showed an oil consump- 
tion per B.H.P. hour of 0.408 lb. with Solar fuel oil, and 0.484 lb. with 
CaUfornia crude oil. 

Alcohol Engines. — Bulletin No. 392 of the U.S. Geol. Survey (1909,) 
on Comparisons of Gasolene and Alcohol Tests in Internal Combustion 
Engines, by R. M. Strong, contains the following conclusions: 

The "low" heat value of completely denatured alcohol will average 
10,500 B.T.U. per lb., or 71,900 B.T.U. per gallon. The low heat value 
of 0.71 to 0.73 sp. gr. gasolene will average 19,200 B.T.U. per lb., or 
115,800 B.T.U. per gallon. 

A gasolene engine having a compression pressure of 70 lbs. but other- 
wise as well suited to the economical use of denatured alcohol as gasolene, 
will, when using alcohol, deUver about 10% greater maximum power 
than when using gasolene. 

When the fuels for which they are designed are used to an equal advan- 
tage, the maximum B.H.P. of an alcohol engine having a compression 
pressure of 180 lbs. is about 30% greater than that of a gasolene engine 
of the same size and speed having a compression pressure of 70 lbs. 

Alcohol diluted with water in any proportion, from denatured alcohol, 
which contains about 10% water, to mixtures containing about as much 
water as denatured alcohol, can be used in gasolene and alcohol engines if 
the engines are properly equipped and adjusted. 

When used in an engine having constant compression, the amount of 
pure alcohol required for any given load increases and the maximum 
available horse-power of tne engine decreases with diminution in the 
percentage of pure alcohol in the diluted alcohol suppUed. The rate of 
increase and decrease, respectively, however, is such that the use of 
80% alcohol instead of 90% has but little effect upon the performance: 
so that if 80% alcohol can be had for 15% less cost than 90% alcohol and 
could be sold without tax when denatured, it would be more economical 
to use the 80% alcohol. 

Ignition. — The "hot-tube" method of igniting the compressed mixture 
of gas and air in the cylinder is practically obsolete, and electric systems 
are used instead. Of these the " make-and-break " and the "jump- 
spark " systems are in common use. In the former two insulated contact 



INTERNAL-COMBUSTION ENGINES. 1103 

pieces are located in the end of the cylinder, and through them an electric 
current passes wliile they are in contact. A spark-coil is included in the 
circuit, and when the circuit is suddenly broken at the proper time for 
ignition, by mechanism operated from the valve-gear shaft, a spark is 
made at the contacts, wliich ignites the gas. In the "jump-spark" 
system two insulated terminals separated about 0.03 in. apart are located 
In the cylinder, and the secondary or high-tension current of an induction 
coil causes a spark to jump across the space between them w^hen the 
circuit of the primary current is closed by mechanism operated by the 
engine. In some oil engines the mixture of air and oil vapor is ignited 
automatically by the temperature generated by compression of the vapor, 
in a chamber at the end of the cylinder, called the vaporizer, which is 
not water-jacketed and therefore is kept hot by the repeated ignitions. 
Before starting the engine the vaporizer is heated by a Bunsen burner 
or other means. 

Timing. — By adjusting the cam or other mechanism operated by the 
valve-gear shaft for causing ignition, the time at which the ignition takes 
place, with reference to the end of the compression stroke, can be regulated. 
The mixture is usually ignited before the end of the stroke, the advance 
depending upon the inflammability of the mixture and on the speed of 
the engine. A slow-burning mixture requires to be ignited earlier than 
a rapid-burning one and a high-speed earlier than a slow-speed engine. 

Governing. — Two methods of governing the speed of an engine are 
in common use, the " hit-and-miss " and the throttling methods. In the 
former the engine receives its usual charge of air and gas only when the 
engine is running at or below its normal speed; at liigher speeds the ad- 
mission of the charge is suspended until the engine regains its normal 
speed. One method of accomplishing this is to interpose between the 
valve-rod and its cam or other operating mechanism, a push-rod, or 
other piece, the position of which with reference to the end of the valve- 
rod is controlled by a centrifugal governor so that it hits the valve-rod if 
the speed is at or below normal and misses it if the speed is above normal. 
The liit-and-miss method is economical of fuel, but it involves irregularity 
of speed, making a large and heavy fly-wheel necessary if reasonable 
uniformity of speed is desired. The throttling method of regulating is 
similar to that used in throttUng steam engines; the quantity of mixture 
admitted at each charge being varied by varying the position of a butter- 
fly valve in the inlet pipe. Cut-off methods of governing are also used, 
such as varying the time of closing the admission valve during the suction 
stroke, or varying the time of admission of the gas alone, or " quality 
regulation." 

Gas and Oil Engine Troubles. — The gas engine is subject to a 
greater number of troubles than the steam engine on account of its greater 
mechanical complexity and of the variable quality of its operating fluid. 
Among the causes of troubles are: the variable composition of the fuel; 
too much or too little air supply; compression ratio not right for the 
kind of fuel; ignition timer set too late or too early; pre-ignition; back- 
firing; electrical and mechanical troubles with the igniting system; 
carbon deposit? in the cyUnder and on the igniting contacts. For a very 
full discussion of these and many other troubles and the remedies for 
them, see Jones on the Gas-Engine. 

Conditions of Maximum Efficiency. — The conditions which appear 
to give the highest thermal efficiency in gas and oil engines are: 1, high 
temperature of coohng water in the jackets; 2, high pressure at the end 
of compression; 3, lean mixture; 4, proper timing of the ignition; 5, 
maximum load. The higher economy of a lean mixture may be due to 
the fact that high compressions may be usf^d with such a mixture, while 
with rich mixtures high compression pressures cannot be used without 
danger of pre-ignition. The effect of different timing on economy is 
shown in a test by J. R. Bibbins, reported by Carpenter and Diederichs, of 
an engine using natural gas of a lower heating value* of 934 B.T.U. per 
cu. ft., delivering 71 H.P. at 297 revs, per min. The maximum thermal 
efficiency, 23.3%, was obtained when the timing device was set for igni- 

* By "lower heating value'* is meant the value computed after sub- 
tracting the latent heat of evaporation of 9 lbs. of water per pound of 
hydrogen contained in the gas. See page 561. 



1104 



INTERNAL-COMBUSTION ENGINES. 



tion 30° in advance of the dead center, while the efficiency with ignitioD 
at the center was 19%, and with ignition 55° in advance 17.3%. 

Other things being equal, the hotter the walls of the cylinder the less 
heat is transferred into them from the hot gases, and therefore the higher 
the efficiency. Cool walls, however, allow of iiigher compression without 
pre-ignition, and high compression is a cause of high efficiency. Cool 
walls also tend to give the engine greater capacity, since with hot walls 
the fuel mixture expands more on entering the cylinder, reducing the 
weight of charge admitted in the suction stroke. 

Heat Losses in the Gas Engine, — The difference between the thermal 
efficiency, which is the proportion of heat converted into work in the 
engine, and 100%, is the loss of heat, which includes the heat carried away 
in the jacket water, that carried away in the waste gases, and that lost 
by radiation. The relative amounts of these three losses vary greatly, 
depending on the size of the engine and on the amount of water used for 
cooUng. Thurston, in Heat as a Form of Energy, reports a test in which 
the heat distribution was as follows: Useful work, 17.3%; jacket water, 
52%: exhaust gas, 16%; radiation, 15%. Carpenter and Diederichs 
quote the following, showing that the distribution of the heat losses 
varies with the rate of compression and with the speed. 



Ratio 

of 
Com- 
pres- 
sion. 


R.p.m. 


M.E.P. 

lbs. 
per sq. 

in. 


Ratio 
Air to 
Gas. 


Heat- 
ing 
Value 

of 
Charge, 
B.T.U. 


Work 

done 

byl 

B.T.U., 

Ft.-lbs. 


Ex- 
haust 
Temp. 
Deg. F. 


Heat Distribution, 
Per Cent. 


Work. 


Jacket 
Water. 


Ex- 
haust. 


2.67 
2.67 
4.32 
4.32 


187 
247 
187 
247 


54.3 
51.5 
69.3 
65.2 


7.11 
7.35 
7.43 
7.40 


18.5 
17.4 
17.0 
16.8 


140 
141 
190 
184 


1022 
1137 
867 
992 


18.0 
18.1 

24.4 
23.7 


51.2 
45.6 
53.8 
49.5 


30.8 
36.3 
21.8 
26.8 



In the long table of results of tests reported by Carpenter and Diede- 
richs, figures of the distribution of heat show that of the total heat re- 
ceived by the engines the heat lost in the jacket water ranged from 25.0 
to 50.4%. and that lost in the exhaust gases from 55 to 23.4%. 

In small air-cooled gasoline engines, such as those used in some auto- 
mobile engines, in which the cjdinders are surrounded by thin metal 
ribs to increase the radiating surface, and air is propelled against them 
by a fan, the air takes the place of the jacket water, and the total loss 
of heat is that carried away by the air and by the exhaust gases. 

Economical Performance of Gas Engines. — The best performance 
of a gas engine using producer gas (1909) is about 30% better than the 
best recorded performance of a triple-expansion steam engine, or about 
0.71 lb. coal per I.H.P. hour, as compared with 1.06 lbs. for the steam 
engine. It is probable that the performance of the combination of a 
high-pressure reciprocating engine, using superheated steam generated in 
a well-proportioned boiler supplied with mechanical stokers and an econo- 
mizer, and a low-pressure steam turbine will ere long reduce the steam 
engine record to 0.9 lb. per I.H.P. hour. As compared vsith an ordinary 
steam engine, however, the gas engine with a good producer is far more 
economical than the steam engine. Where gas can be obtained cheaply, 
such as the waste-gas from blast furnaces, or natural gas, the gas-engine 
can furnish power much more cheaply than it can be obtained from the 
same gas burned under a boiler to furnish steam to a steam engine. 

In tests made for the U. S. Geological Survey at the St. Louis Exhibi- 
tion, 1904, of a 235-H.P. gas engine with different coals, made into gas 
In the same producer, the best result obtained was 1.12 lbs. of West 
Virginia coal per B.H.P. hour, and the poorest result 3.23 lbs. per B.H.P. 
hour, with North Dakota lignite. 

A 170-H.P. Crossley (Otto) engine tested in England in 1892, using 
producer gas, gave a consumption of 0.85 lb. coal per I.H.P. hour, or a 
thermal efficiency of engine and producer combined of 21 .3%. 

Experiments on a Taylor gas producer using anthracite coal and a 



TESTS OF GAS AND OIL ENGINES. 1105 

100-H.P. Otto gas engine showed a consumption of 0.97 lb. carbon per 
I.H.P. hour. {Iron Age, 1893.) 

In a table in Carpenter and Diederichs on Internal Combustion Engines 
the lowest recorded coal consumption per B.H.P. hour is 0.71 lb., with 
a Tangye engine and a suction gas producer, using Welsh anthracite coal. 
Other tests show figures ranging from 0.74 lb. to 1.95, the last with a 
Westinghouse 500-H.P. engine and a Taylor producer using Colorado 
bituminous coal. 

In the same book are given the following figures of the thermal efficiency 
on brake H.P. with different gas and liquid fuels. Illuminating gas, 
6 tests, 16.1 to 31.0%; natural gas, 4 tests, 16.1 to 29.0%; coke-oven gas, 
1 test, 27.5%; Mond gas, 1 test, 23.7%; blast-furnace gas, 3 tests, 20.4 to 
28.2%; gasoline, 8 tests, 10.2 to 28%; kerosene, Diesel engine, 3 tests, 
25.8 to 31.9%: kerosene, other engines, 8 tests, 9.2 to 19.7%; crude oil, 
Diesel engine, 1 test, 28.1%; alcohol, 4 tests, 21.8 to 32.7%. 

Tests of Diesel engines operating centrifugal pumps in India are 
reported in Eng. News, Nov. 25, 1909. Using Borneo petroleum residue 
of 0.934 sp. gr., and a fuel value of 18,600 B.T.U. per lb., an average of 
151 B.H.P. during a season, for a total of 6003 engine hours, was obtained 
with a consumption of 0.462 lb. of fuel per B.H.P. hour, or one B.H.P. 
for about 8600 B.T.U. per hour, equal to a thermal efficiency of 29.5%. 
The pump efficiency at maximum lift of 14 to 16 ft. was 70%, and the 
fuel consumption per water H.P. hour at the same lift was 0.7 lb. 

Utilization of Waste Heat from Gas Engines. — The exhaust gases 
from a gas engine may be used to heat air by passing them across a nest 
of tubes through which air is flowing. A design of this kind, for heating 
the Ives library building. New Haven, Conn., by Harrison Engineering 
Co., New York, is illustrated in Heat, and Vent. Mag., Jan., 1910. 

The waste heat might also be used in a boiler to generate steam at or 
below atmospheric pressure, for use in a low pressure steam turbine. On 
account of the comparatively low temperature of the exhaust gases, 
however, the boiler would require a much greater extent of heating sur- 
face for a given capacity than a boiler with an ordinary coal-fired furnace. 

RULES FOR CONDUCTING TESTS OF GAS AND OIL, 
ENGINES*. CODE OF 1902. 

(From the report of the committee of the A. S. M. E. on Engine Tests.) 
[Only a brief abstract is here given. The items, 1, Objects of the Tests; 
2, General Conditions of the Engine; 3, Dimensions; 5, CaUbration of 
Instruments, are practically the same as in the report on Steam Engine 
Tests.] 

IV. Fuel. — Decide upon the gas or oil to be used, and if the trial is 
to be made for maximum efficiency, the fuel should be the best of its 
class that can readily be obtained, or one that shows the highest calorific 
power. 

VI. Duration of Test. — The duration of a test should depend largely 
upon the objects in view, and in any case the test should be continued until 
the successive readings of the rates at which oil or gas is consumed, 
taken at say half-hourly intervals, becom.e uniform and thus verify each 
other. If the object is to determine the working economy, and the period 
of time during whirh the engine is usually in motion is some part of 
twenty-four hours, the duration of the test should be fixed for this number 
of hours. If the engine is one using coal for generating gas, the test 
should be of at least twenty-four hours' duration. 

VII. Starting a Test. — 'in a test for determining the maximum econ- 
omy of an engine, it should first be run a sufficient time to bring all 
the conditions to a normal and constant state. 

If a test is made to determine the performance under working condi- 
tions, the test should begin as soon as the regular preparations have 
been made for starting the engine in practical work, and the measurements 
should then commence and be continued until the close of the period 
covered by the day's work. 

VIII. Measurement of Fuel. — If the fuel used is coal furnished to a gas 

* Hot-air engines are not included in this code, those in the market 
being of comparatively small size, and seldom tested. 



1106 INTERNAL-COMBUSTION ENGINES. 

produceFj the same methods apply for determining the consumption as 
are usea in steam-boiler tests. 

If the fuel used be gas, the only practical method of measurement is . 
the use of a meter through which the gas is passed. The temperature 
and pressure of the gas should be measured, and the quantity of gas 
should be determined by reference to the cahbration of the meter, taking 
into account the temperature and pressure of the gas. 

If the fuel is oil, tliis can be drawn from a tank wliich is filled to the 
original level at the end of the test, the amount of oil required for so 
doing being weighed ; or, for a small engine, the oil may be drawn from a 
calibrated vertical pipe. 

IX. Measurement of Heat-Units Consumed by the Engine. — The num- 
ber of heat-units used is found by multiplying the number of pounds of 
coal or oil or the cubic feet of gas consumed, by the total heat of combus' 
tion of the fuel as determined by a calorimeter test. In determining the 
total heat of combustion no deduction is made for the latent heat of the 
water vapor in the products of combustion. 

It is sometimes desirable, also, to have a complete chemical analysis 
of the oil or gas. The total heat of combustion may be computed, if 
desired, from the results of the analysis, and should agree well with the 
calorimeter values. 

X. Measurement of Jacket Water, — The jacket water may be meas- 
ured by passing it through a water meter or allowing it to flow from a 
measuring tank before entering the jacket, or by collecting it in tanks 
on its discharge. 

XI. Indicated Horse-power, — The directions given for determining 
the indicated horse-power for steam engines apply in all respects to inter- 
nal combustion engines. 

XII. Brake Horse-power. — The determination of the brake horse- 
power is the same for internal combustion as for steam engines. 

XIII. Speed. — The same directions apply to internal combustion 
engines as to steam engines for the determination of speed. 

In an engine which is governed by varjing the number of explosions 
or working cycles, a record should be kept of the number of explosions 
per minute; or if the engine is running at nearly maximum load, by 
counting the number of times, the governor causes a miss in the ex- 
plosions. 

XIV. Recording the Data. — The pressures, temperatures, meter 
readings, speeds, and other measurements should be observed every 20 
or 30 minutes when the conditions are practically uniform, and at more 
frequent intervals if they are variable. Observations of the gas or oil 
measurements should be taken with special care at the expiration of each 
hour, so as to divide the test into hourly periods, and reveal the uniform- 
ity, or otherwise, of the conditions and results as the test goes forward. 

XV. Uniformity of Conditions. — When the object of the test is to 
"determine the maximum economy, all the conditions relating to the 
operation of the engine should be maintained as constant as possible 
during the trial. 

XVI. Indicator Diagrams. — Sample diagrams nearest to the mean 
should be selected from those taken during the trial and appended to the 
tables of the results. If there are separate compression or feed cylinders, 
the indicator diagrams from these should be taken and the power deducted 
from that of the main cylinder. 

XVII. Standards of Economy and Efficiency. — The hourly consump- 
tion of heat, divided by the indicated or the brake horse-power, is the 
standard expression of engine economy recommended. 

In making comparisons between the standard for internal combustion 
engines and that for steam engines, it must be borne in mind that the 
steam engine standard does not cover the losses due to combustion, while 
the internal combustion engine standard, in cases where a crude fuel 
such as oil is burned in the cylinder, does cover these losess. 

The thermal efficiency ratio per indicated horse-power or per brake 
horse-power for internal combustion engines is expressed by the fraction 

2545 -i- B.T.U. per H.P. per hour. 

XVIII. Heat Balance. — For purposes of scientific research, a heat 
balance should be drawn which shows the manner in which the total 



TESTS OF GAS AND OIL ENGINES. 1107 



heat of combustion is expended in the various processes concerned in 
the working of the engine. It may be divided into three parts: first, 
the heat wliich is converted into the indicated or brake work: second, the 
heat rejected in the cooUng water of the jackets; and third, the heat 
rejected in the exhaust gases, together with that lost through incomplete 
combustion and radiation. 

To determine the first item, the number of foot-pounds of work per- 
formed by, say, one pound or one cubic foot of the fuel, divided by 778, 
gives the number of heat-units desired. The second item is determined 
by measuring the amount of cooUng water passed through the jackets, 
equivalent to one pound or one cubic foot of fuel consumed, and multi- 
plying this quantity by the difference in the sensible heat of the v/ater 
leaving the jacket and that entering. The third item is obtained by 
subtracting the sum of the first two items from the total heat supphed. 
The third item can be subdivided by computing the heat rejected in the 
exhaust gases as a separate quantity. The data for this computation 
are found by analyzing the fuel and the exhaust gases, or by measuring 
the quantity of air admitted to the cylinder in addition to that of the gas 
or oil. 

XIX. Report of Test. — The data and results of a test should be re- 
ported in the manner outlined in one of the following tables, the first of 
which gives a complete summary when all the data are determined, and 
the second is a shorter form of report in which some of the minor items 
are omitted. [The short form is given below.] 

Data and Results of Standard Heat Test of Gas or Oil Engine. 

Arranged according to the Short Form advised by the Engine Test 
Committee, American Society of Mechanical Engineers. Code of 
1902. 

1- Made by of 

on engine located at 

to determine 

2. Date of trial". !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 

3. Type and class of engine 



4. Kind of fuel used 

(a) Specific gravity deg Fahr. 

(h) Burning point 

(c) Flashing point '* 

5. Dimensions of engine: 

1st Cyl. 2d Cyl. 
(a) Class of cyUnder (working or for com- 
pressing the charge) 

(6) Single or double acting 

(c) Cylinder dimensions: 

Bore in. 

Stroke * ft. 

Diameter piston rod in. 

{d) Average compression space, or clear- 
ance, in per cent 

(e) Horse-power constant for one lb. M.E.P. 
and one revolution per minute 

Total Quantities. 

6. Duration of test hours 

7. Gas or oil consumed cu. ft. or lbs. 

8. CooUng water supplied to jackets 

9. Calorific value of fuel by calorimeter test, determined 

by calorimeter B.T.U. 

Pressures and Temperatures. 

10. Pressure at meter (for gas engine) in inches of water. .. ins. 

11. Barometric pressure of atmosphere: 

(a) Reading of barometer " 

(6) Reading corrected to 32 degs. Fahr " 



1108 LOCOMOTIVES. 

12. Temperature of cooling water: 

(a) Inlet deg. Fahr. 

(&) Outlet 

13. Temperature of gas at meter (for gas engine) " 

14. Temperature of atmosphere: 

(fl) Dry bulb thermometer '* 

(b) Wet bulb thermometer '* 

(c) Degree of humidity •* 

15. Temperature of exhaust gases •* 

Data Relating to Heat Measurement. 

16. Heat miits consumed per hour (pounds of oil or cubic 

feet of gas per hour multiplied by the total heat of 
combustion) B.T.U. 

17. Heat rejected in cooUng water per hour 

Speed, etc. 

18. Revolutions per minute rev. 

19. Average number of explosions per minute 

Indicator Diagrams. 

20. Pressure in lbs. per sq. in. above atmosphere: 

1st Cyl. 2d Cyl. 

(a) Maximum pressure 

(6) Pressure just before ignition 

(c) Pressure at end of expansion ....... 

(d) Exhaust pressure 

(e) Mean effective pressure 

Power. 

21. Indicated horse-power: 

First cylinder H.P. 

Second cylinder .* 

Total 

22. Brake horse-power " 

23. Friction horse-power by friction diagrams " 

24. Percentage of indicated horse-power lost in friction. . per cent. 

Standard Efficiency, and Other Results. 

25. Heat units consumed by the engine per hour: 

(a) Per indicated horse-power B.T.U. 

(b) Per brake horse-power " 

26. Pounds of oil or cubic feet of gas consumed per hour: 

(a) Per indicated horse-power lbs. or cu. ft. 

(b) Per brake horse-power 

Additional Data. 
Add any additional data bearing on the particular objects of the test 
or relating to the special class of service for which the engine is to be 
used. Also give copies of indicator diagrams nearest the mean, and 
the corresponding scales. 

LOCOMOTIVES. 

Resistance of Trains. — Resistance due to Speed. — Various formulae 
and tables for the resistance of trains at different speeds on a straight 
level track have been given by different writers. Among these are 
the following: 

By D. L. Barnes, Eng. Mag., June, 1894: 

Speed, miles per hour 50 60 70 80 90 100 

Resistance, pounds per gross ton . . 12 12.4 13.5 15 17 20 

By Engineering News, March 8, 1894: 

Resistance in lbs. per ton of 2000 lbs. = 1/4 v + 2. 

Speed 5 10 15 20 25 30 35 40 50 60 70 80 90 100 

Resistance 3 1/4 4.5 53/4 7 8 1/4 9.5 IO3/4 12 14.5 17 19.5 22 24.5 27 



IiOCOMOTIVES. 1109 

This formula seems to be more generally accepted than the others. 
It gives results too small, however, below 10 miles an hour. At starting, 
the resistance is about 17 lbs. per ton, dropping to 4 or 5 lbs. at 5 miles 
an hour. 

By Baldwin Locomotive Works: 

Resistance in lbs. per ton of 2000 lbs. = 3 + v -*- 6. 

Speed 5 10 15 20 25 30 35 40 45 50 55 60 70 80 90 100 

Resistance. 3.8 4.7 5.5 6.3 7.2 8 8.8 9.7 10.5 11.3 12.2 13 14.7 16.3 18 19.7 

The resistance due to speed varies with the condition of the track, the 
number of cars in a train, and other conditions. 

For tables showing that the resistance varies with the area exposed to 
the resistance and friction of the air per ton of loads, see Dashiell, Trans. 
A. S. M. E., vol. xiii. p. 371. 

P. H. Dudley (Bulletin International Ry. Congress, 1900, p. 1734) 
shows that the condition of the track is an important factor of train 
resistance which has not hitherto been taken account of. The resist- 
ance of heavy trains on the N. Y. Central R. R. at 20 miles an hour is 
only about 31/2 lbs. per ton on smooth 80-lb. SVs-in. rails. The resist- 
ance of an 80-car freight train, 60,000 lbs. per 'car, as given by indicator 
cards, at speeds between 15 and 25 miles per hour, is represented by the 
formula R = 1 + VsV, in which R = resistance in lbs. per ton and 
V = miles per hour. These values are much below the average and 
should not be used in estimating the hauling power needed. 

New FormulcB for Resistance. — The Amer. Locomotive Co. (Bulletin 
No. 1001, Feb., 1910) states that the figures obtained from the old formulae 
for train resistance are much too high for modern loaded freight cars 
of 40 to 50 tons capacity, and in some instances too low for very light 
or empty cars. The best data available show that the resistance varies 
from about 2.5 to 3 lbs. per ton (of 2000 lbs.) for 72-ton cars (including 
weight of empty car) to 6 to 8 lbs. for 20-ton cars. From speeds between 
5 to 10 and 30 to 35 miles an hour, the resistance of freight cars is prac- 
tically constant. The resistance of the engine and tender is figured 
separately, and is composed of the following factors: (a) Engine friction = 
22.2 lbs. per ton, or 1.11% of the weight on drivers, (b) Head air resist- 
ance = cross-sectional area (taken at 120 sq. ft.) X 0.002 V^, V being 
the speed in miles per hour, (c) Resistance due to weight on engine 
trucks and trailing wheels, and to the tender, the same per ton as that 
due to the cars, (d) Grade resistance = 20 lbs. per ton for each per 
cent of grade, (e) Curve resistance, which varies with the wheel-base 
of the locomotive, and is taken as 0.4 + cD lbs. per ton, in which D is 
the degree of the curve and c a constant whose value is. 

For wheel-base, ft. 5 6 7 8 9 12 13 15 16 20 

Value of c 0.380 .415 .460 .485 .520 .625 .660 .730 .765 .905 

The sum of these resistances is to be deducted from the tractive force of 
the locomotive to obtain the available tractive force for overcoming the 
resistance of the cars. (See Tractive Force, below.) The maximum 
tractive force is taken for low speeds at 85% of that due to the boiler 

Eressure; for piston speeds over 250 ft. per min. this is to be multiplied 
y a speed factor to obtain the actual force. Speed factors and percent- 
ages of maximum horse-power corresponding to different piston speeds 
are given below. S = piston speed, ft. per min., F = speed factor, 
P = % of maximum H.P. 

S 250 300 350 400 450 500 550 600 650 700 750 

F 1.00 .954 .908 .863 .817 .772 .727 .680 .636 .592 .550 

P 60.4 69.1 77.2 83.7 89.0 93.5 96.8 98.7 99.7 100 100 

S 800 850 900 950 1000 1100 1200 1300 1400 1500 1600 

F 0.517 .487 .460 .435 .412 .372 .337 .307 .283 .261 .241 

P 100 100 100 100 100 99 97.8 96.8 95.7 94.7 93.5 

The resistance of freight cars, according to experiments on the Penna. 
R.R., varies wuth the weight in tons per car as follows: 

Tons per car 10 20 25 30 40 50 60 70 72 

Resistance, lbs. per ton 

13.10 7.84 6.62 5.78 4.66 3.94 3.44 3.06 3.00 



1110 LOCOMOTIVES. 

From plotted curves of resistances of trains of empty and loaded cars 
the following figures are derived. R = resistance in lbs. per ton. 

Wt. loaded, tons 75 70 65 60 55 50 

Wt. empty, tons 21 20.3 19.5 18.6 17.6 16.5 

Per cent of loaded wt 28 29 30 31 32 33 

72 loaded 2.90 3.07 3.24 3.43 3.65 3.90 

i2 empty 5.63 5.82 6.00 6.26 6.50 6.85 

Wt. loaded, tons 45 40 35 30 25 20 15 

Wt. erapiy, tons 15.3 14.0 12.6 11.1 9.5 7.8 6.0 

Per cent of loaded wt.. . . 34 35 36 37 38 39 40 

7? loaded 4.18 4.40 4.74 5.07 5.44 5.91 6.40 

72 empty 7.26 7.65 8.05 8.45 9.05 9.60 10.3 

The resistance of passenger cars is derived from the formula 72 = 5.4 + 
0.002(F - 15)2+ 100 -^ (F + 2)3. V in miles per hour, R = resistance 
in lbs. per ton (2000 lbs.) H.P. == horse-power per ton. 

F = 5 10 15 20 25 30 35 

72= 5.89 5.51 5.42 5.46 5.60 5.85 6.20 

H.P. = 0.079.147 .217 .291 .374 .469 .578 

F = 40 45 50 60 70 80 90 

72= 6.65 7.20 7.85 9.45 11.45 13.85 16.65 

H.P.= 709 .864 1.047 1.515 2.135 2.95 4.00 

Resistance of Electric Railway Cars and Trains. — W. J. Davis, Jr. 
(Street Ry. Jour., Dec. 3, 1904), gives as a result of numerous experiments 
the following formulse: 

(A) For light open platform street cars, 8 tons to 20 tons; maximum 
speed, 30 miles per hour; cross-section, 85 sq. ft. 

72 = 6 + 0.11V + 2~^'^ [1 + 0.1 (71- 1)1. 

(B) For standard interurban electric cars, 25 tons to 40 tons; maximum 
speed, 60 m.p.h.; cross section, 100 sq. ft. 

72 = 5+ 0.13F+ 0.3F2/rfl+ 0.1 (n - 1)]. 

(C) For heavy interurban electric cars, or steam passenger coaches, 
40 tons to 50 tons; maximum speed, 75 m.p.h.; crosss-ection, 110 sq. ft. 

72 = 4 + 0.13 F + 0.33 V^/T [1 + 0.1 (n - 1)]. 

(D) For heavy freight trains, cars weighing 45 tons loaded; maximum 
speed, 35 m.p.h.; average cross-section, 110 sq. ft. 

72 = 3.5 + 0.13 F+ 0.385 F2/r[l + 0.1 (n - 1)]. 

72 = resistance in lbs. per ton of 2000 lbs., F= speed in miles per hour 
T = weight of train in tons, n = number of cars in train, including lead- 
ing motor car. The cross-section includes the space bounded by the wheels 
between the top of rails and the body. 

Resistance due to Grade. — The resistance due to a grade of 1 ft. per 
mile is, per ton of 2000 lbs., 2000 X 1/5280 = 0.3788 lb, per ton, or if 
72^ = resistance in lbs. per ton due to grade and G = ft. per mile 72^ = 
0.3788 G, 

If the grade is expressed as a percentage of the length, the resistance Is 
20 lbs. per ton for each per cent of grade. 

Resistance due to Curves. — Mr. G. R. Henderson in his book entitled 
"Locomotive Operation" gives the resistance due to curvature at 0.7 
lb. per ton of 2000 lbs. per degree of the curve. (For definition of 
degrees of a railroad curve see p. 54.) For locomotives, this factor is 
sometimes doubled, making the resistance in lbs. per ton = 0.7 c for cars 
and 1.4 c for locomotives, c being the number of degrees. 

The Baldwin Locomotive Works take the approximate resistance due 
to each degree of curvature as that due to a straight grade of 1 1/2 ft. per 
mile. This corresponds to 72^ = 0.5682 c. 

The Amer. Locomotive Co. takes 0.8 lb. per ton per degree of curva^ 
ture for the resistance of cars on curves. 



LOCOMOTIVES. 



1111 



For mine cars, with short wheel-bases and wheels loose on the axles, 
experiments quoted by the Baldwin Locomotive Works, 1904, lead to the 
formula, Resistance due to curvature, in pounds, = 0.20 X wheel-base X 
weight of loaded cars in pounds. -^ radius of curve in feet. 

Resistance due to Acceleration. — This may be calculated by the ordi- 
nary formula (see page 529), or reduced to common railroad units, and 
including the rotative energy of wheels and axles, which increases the 
effect of the weight of the cars by an equivalent of about 5%, we have 

y2 V V*? — Y^ 
P = 70 -^ =95.6 -7 =70 5 , where P= the accelerating force in 

O 6 O 

pounds per ton. V = the velocity in miles per hour, S = the distance 
in feet, and t = the time in seconds in which the acceleration takes 
place. Vi and V2 = the smaller and greater velocities, respectively, 
in miles per hour, for a change of speed. 

Total Resistance. — The total resistance in lbs. per ton of 2000 lbs. due 
to speed, to grade, to curves, and to acceleration is the sum of the resist- 
ances calculated above. 

The Baldwin Locomotive Works in their ** Locomotive Data" take the 
total resistance on a straight level track at slow speeds at from 6 to 10 lbs. 
per ton, and in a communication printed in the fourth edition (189S) of 
this Pocket-book, p. 1076, say: "We know that in some cases, for in- 
stance in mine construction, the frictional resistance has been shown to 
be as much as 60 lbs. per ton at slow speed. The resistance should be 
approximated to suit the conditions of each individual case, and the 
increased resistance due to speed added thereto." 

Resistance due to Friction. — In the above formulae no account has been 
taken of the resistance due to the friction of the working parts. This is 
rather an obscure subject. Mr. Henderson estimates the percentage of 
the indicated power consumed by friction to be 0.15 7 -}- c, where 
V = speed in miles per hour and c = a constant, whose value may 
vary from 2 to 8, the latter figure being the safest to use for heavy work 
at slow speeds. Ordinarily 8% of the indicated power is consumed by 
internal resistance under these conditions^ Professor Goss gives the 
following formula, obtained from tests at the Purdue locomotive testing 
laboratory: 

Let d = diameter of cylinder: S = stroke of piston: P = diameter of 
drivers, all in inches. Then the internal friction= 3.Sd^S/D,in pounds 
at the circumference of the drivers. 

Concerning the effect of increasing speed on tractive force, Mr. Hender- 
son says (1906): 

From a number of tests and information from various roads and au- 
thorities it seems as if, for ordinary simple engines, the coefficient 0.8 

8 Pd'^s 
in the equation Actual tractive force = ^ — could be modified in ac- 
cordance with the speed in order to obtain the actual tractive force at 
various speeds about as follows: 

Revs, per min. = 20 40 60 80 100 120 140 160 

Coefficient = . 80 . 80 . 80 . 70 0.61 . 53 . 46 . 40 

Revs, per min. = 180 200 220 240 260 280 300 320 340 

Coefficient = . 35 0.31 0.28 0.26 0.24 0.23 0.21 0.20 0.19 

Eflflciency of the 3Iechanism of a T^ocomotive. — Frank C.Wagner 
(Proc. A. A. A. S., 1900, p. 140) gives an account of some dynamometer 
tests which indicate that in ordinary freight service the power used to 
drive the locomotive and tender and to overcome the friction of the 
mechanism is from 10% to 35% of the total power developed in the steam- 
cylinder. In one test the weight of the locomotive and tender was 16% 
of the total weight of the train, while the power consumed in the loco- 
motive and tender was from 30% to 33% of the indicated horse-power. 

Adhesion. — The limit of the hauling capacity of a locomotive is the 
adhesion due to the weight on the driving wheels. Holmes gives the 
adhesion, in English practice, as equal to 0.15 of the load on the driving 
wheels in ordinary dry weather, but onljr 0.07 in damp weather or when 
the rails are greasy. In American practice it is generally taken as from 
1/4 to 1/5 of the load on the drivers. 



1112 



LOCOMOTIVES. 



Tractive Force of a Locomotive. — Single Expansion. 
Let F = indicated tractive force in lbs. 

p = average effective pressure in cylinder in lbs. per sq. in. 
iS = stroke of piston in inches, 
d = diameter of cylinders in inches. 
D == diameter of driving-wheels in inches. Then 
^d2pS_ d^pS 
D ' 



F = 



4 TtD 

The average effective pressure can be obtained from an indicator, 
diagram, or by calculation, when the initial pressure and ratio of expan- 
sion are known, together with the other properties of the valve-motion. 
The subjoined table from Auchincloss gives the proportion of mean 
effective pressure to boiler-pressure above atmosphere for various pro- 
portions of cut-off. 



Stroke, 
Cut-off at - 



0.1 
.125 = 1/8 
.15 
.175 
.2 

.25 = 1/4 
.3 



M.E.P. 

(Boiler- 
pres. = 1). 



0.15 
.2 
.24 
.28 
.32 
.4 
.46 



Stroke, 
Cut-off at- 



0.333 = 1/3 
.375 = 3/g 
.4 
.45 



M.E.P. 

(Boiler- 
pres. = I). 



0.5 - V. 

.57 
.62 
.67 
.72 



Stroke, 
Cut-off at - 



0.625 = 5/8 
.666 = 2/3 

:75 =3/4 

.8 

.875 = 7/8 



M.E.P. 

(Boiler- 
pres. = 1). 



0.79 
.82 
.85 
.89 
.93 
.98 



These values were deduced from experiments with an English locomo- 
tive by Mr. Gooch. As diagrams vary so much from different causes, 
this table will only fairly represent practical cases. It is evident that 
the cut-off must be such that the boiler will be capable of supplying 
sufficient steam at the given speed. 

We can, however, allow for wire drawing to the steam chest and drop in 
pressure due to -expansion, and internal friction by writing the formula: 

Actual Tractive Force = — — j^ , d, S, and D being as before and P 

representing boiler pressure in lbs. per sq. in. 

Compound Locomotives. — The Baldwin Locomotive Works give the fol- 
lowing formulae for compound engines of the Vauclaln four-cylinder type: 
rp_ C^S X 2/3 P c^S X 1/4 P 
^ ~ D "^ D 

T= tractive force in lbs. C= diam. of high-pressure cylinder in ins. 
c= diam. of low-pressure cyUnder in ins. P= boiler-pressure in lbs. 
S= stroke of piston in ins. D= diam. of driving-wheels in ins. 

For a two-cylinder or cross-compound engine it is only necessary to con- 
sider the high-pressure cylinder, allowing a sufficient decrease in boiler 
pressure to compensate for the necessary back-pressure. The formula is 

^ C'^SXVsP 
^ D 

The above formulae are for speeds of from 5 to 10 miles an hour, or 
less; above that the capacity of the boiler limits the cut-off which can be 
used, and the available tractive force is rapidly reduced as the speed 
increases. For a full discussion of this, see page 375 of Henderson's 
*' Locomotive Operation." 

The Size of Locomotive Cylinders is usually taken to be such that 
the engine will just overcome the adhesion of its wheels to the rails under 
favorable circumstances. 

The adhesion is taken by^ a committee of the Am. Ry. Master Mechan- 
ics' Assn. as 0.25 of the weight on the drivers fo? passenger engines, 0.24 
for freiglit, and 0.22 for switching engines; and ttie mean effective pres- 
sure In the cylinder, when exerting the maximum tractive force, is taken 
at 0.85 of the boiler-pressure. 



LOCOMOTIVES. 



1113 



Let W = weight on drivers in lbs.; P = tractive force in lbs., — say 
0.25 W; vi = boiler-pressure in lbs. per sq. in.; p = mean effective 
pressure, ^ 0.85 pi; d =■ diam. of cylinder, 8 = length of stroke, and 
D = diam. of driving-wheels, all in inches. Then 



D 



D 



Whence d-O.S \^= 0.542 \^ • 

Von Borries's rule for the diameter of the low-pressure cylinder of a 
compound locomotive is d- = 2ZD -^ ph, in which d= diameter of l.p. 
cylinder in inches; D = diameter of driving-wheel in inches; p = mean 
effective pressure per sq. in., after deducting internal machine friction; 
h = stroke of piston in inches; Z = tractive force required, usually 0.14 
to 0.16 of the adhesion. 

The value of p depends on the relative volume of the two cylinders, 
and from indicator experiments may be taken as follows: 

Ratio of Cylinder p in percent of p for Boiler-pres- 
Volumes. Boiler-pressure, sure of 176 lbs. 

Large-tender eng's. 1 : 2 or 1 : 2.05 42 74 

Tank-engines 1 : 2 or 1 : 2.2 40 71 

Horse-power of a Loconiotive. — For each cylinder the horse-power 
is H.P. = pLaN -^ 33,000, in which p = mean effective pressure, L = 
stroke in feet, a = area of cylinder = 1/4 Ttd^, N ^ number of single 
.strokes per minute, LN = piston speed, ft. per min. Let M = speed of 
train in miles per hour, *S = length of stroke in inches, and D = diam- 
eter of driving-wheel in inches. Then LN =' M X SS X 2 S -r- nD. 
Whence for the two cylinders the horse-power is 

2 X P X 1/4 7rd2 X 176 ^ X M pd^SM 



Class of Engine. 



nD X 33,000 



375 D 



Revolutions per Minute for Various Diameters of Wheels 
AND Speeds. 











Miles per Hour 








Diameter 


















of Wheel. 




















10 


20 


30 


40 


50 


60 


70 


80 


50 in. 


67 


134 


201 


268 


336 


403 


470 


538 


56 in. 


60 


120 


180 


240 


300 


360 


420 


480 


60 m. 


56 


112 


168 


224 


280 


336 


392 


448 


62 in. 


54 


108 


162 


217 


271 


325 


379 


433 


66 in. 


51 


102 


153 


204 


255 


306 


357 


408 


68 in. 


49 


99 


148 


198 


247 


296 


346 


395 


72 in. 


47 


93 


140 


187 


233 


279 


326 


373 


78 in. 


43 


86 


129 


172 


215 


258 


301 


344 


80 in. 


42 


84 


126 


168 


210 


252 


294 


336 


84 in. 


40 


80 


120 


160 


200 


240 


280 


320 


90 in. 


37 


75 


112 


150 


186 


224 


261 


299 



The Size of Locomotive Boilers. (Forney's Catechism of the Loco- 
motive.) — They should be proportioned to the amount of adhesive 
weight and to the speed at which the locomotive is intended to work. 
Thus a locomotive with a great deal of weight on the driving-wheels 
could pull a heavier load, would have a greater cylinder capacity than 
one with little adhesive weight, would consume mbre steam, and there- 
fore should have a larger boiler. 

The weight and dimensions of locomotive boilers are in nearly all 
cases determined by the limits of weight and space to which they are 
necessarily confined. It may be stated generally that within these limits 
a locomotive boiler cannot he made too large. In other words, boilers for 



1114 



LOCOMOTIVES. 



locomotives should always be made as larg:e as is possible under the 
conditions that determine the weight and dimensions of the locomotives. 
(See also Holmes on the Steam-engine, pp. 371 to 377 and 383 to 389 
and the Report of the Am. Ry. M. M. Ass'n. for 1897, pp. 218 to 232.) ' 
Holmes gives the following from English practice: 

Evaporation, 9 to 12 lbs. of water from and at 212°. 

Ordinary rate of combustion, 65 lbs. per sq. ft. of grate per hour. 

Ratio of grate to heating surface, 1 : 60 to 90. 

Heating surface per lb. of coal burnt per hour. 0.9 to 1.5 sq. ft. 
Mr. Henderson states the approximate heating surface needed per 
indicated horse-power as follows: 

Compound Locomotives 2 square feet. 

Simple Locomotives (cut-off 1/2 stroke or less) 21/3 square feet. 

Simple Locomotives (cut-off 1/2 to 3/4 stroke) 22/3 square feet. 

Simple Locomotives (full stroke) 3 square feet. 

For the ratio of heating surface to grate area the Master Mechanics 
Ass'n Committee of 1902 advised as below: 



Fuel. 


Passenger. 


Freight. 


Simple. 


Com- 
pound. 


Simple. 


Com- 
pound. 


Free burning bituminous 


65 to 90 
50 to 65 
40 to 50 

35 to 40 

28 to 35 


75 to 95 
60 to 75 
35 to 60 

30 to 35 

24 to 30 


70 to 85 
45 to 70 
35 to 45 

30 to 35 

25 to 30 


65 to 85 


Average bituminous 


50 to 65 


Slow burning bituminous 


45 to 50 


Bituminous slack and free burning. . 
anthracite 


40 to 45 


Low grade bituminous, lignite and 
slow burning anthracite 


30 to 40 







A. E. Mitchell, {Eng'g News, Jan. 24, 1891) says: Square feet of boiler- 
heating surface for bituminous coal should not be less than 4 times the 
square of the diameter in inches of a cylinder 1 inch larger than the 
cyUnder to be used. One tenth of this should be in the fire-box. On 
anthracite locomotives more heating-surface is required in the fire-box, on 
account of the larger grate-area required, but the heating-surface of the 
flues should not be materiaUy decreased. 

Wootten's Locomotive. (Clark's Steam-engine; see also Jour. 
Frank. Inst. 1891, and Modern Mechanism, p. 485.) — J. E. Wootten 
designed and constructed a locomotive boiler for the combustion of an- 
thracite and lignite, though specially for the utilization as fuel of the 
waste produced in the mining and preparation of anthracite. The special 
feature of the engine is the fire-box, which is made of great length and 
breadth, extending clear over the wheels, giving a grate-area of from 
64 to 85 sq. ft. The draught diffused over these large areas is so gentle 
as not to hft the fine particles of the fuel. A number of express-engines 
having this type of boiler are engaged on the fast trains between Phila- 
delphia and jersey City. The fire-box shell is 8 ft. 8 in. wide and 10 ft. 
5 in. long: the fire-box is 8 X 91/2 ft., making 76 sq. ft. of grate-area. 
The grate is composed of bars and water-tubes alternately. The regular 
types of cast-iron shaking grates are also used. The height of the fire- 
box is only 2 ft. 5 in. above the grate. The grate is terminated by a 
bridge of fire-brick, beyond which a combustion-chamber, 27 in. long, 
leads to the flue-tubes, about 184 in number, 13/4 in. diam. The cylin- 
ders are 21 in. diam., with a stroke of 22 inches. The driving-wheels, 
four-coupled, are 5 ft. 8 in. diam. The engine weighs 44 tons, of which 
29 tons are on driving wheels. The heating-surface of the fire-box is 
135 sq. ft., that of the flue-tubes is 982 sq. ft.: together, 1117 sq. ft., or 
14.7 times the grate-area. Hauling 15 passenger-cars, weighing with 
passengers 360 tons, at an average speed of 42 miles per hour, over ruling 
gradients of 1 in 89, the engine consumes 62 lbs. of fuel per mile, oj" 
341/4 lbs. per sq. ft. of grate per hour. 



LOCOMOTIVES. 



1115 



Grate-surface, Smoke-stacks, and Exhaust-nozzles for Locomo- 
motives. — A. E. Mitchell, Supt. of Motive Power of the Erie R. R., says 
(1895) that some roads use the same size of stack, 13V2 in. diam. at 
throat, for all engines up to 20 in. diam. of cylinder. 

The area of the orifices in the exhaust-nozzles depends on the quantity 
and quality of the coal burnt, size of cylinder, construction of stack, 
and the condition of the outer atmosphere. It is therefore impossible 
to give rules for computing the exact diameter of the orifices. All that 
can be done is to give a rule by which an approximate diameter can be 
found. The exact diameter can only be found by trial. Our experi- 
ence leads us to believe that the area of each orifice in a double exhaust- 
nozzle should be equal to 1/400 part of the grate-surface, and for single 
nozzles 1/200 of the grate-surface. These ratios have been used in finding 
the diameters of the nozzles given in the following table. The same 
sizes are often used for either hard or soft coal-burners. [These sizes are 
small at the present day (1909) as locomotives have enormously in- 
creased in size.] 



Size of 


Grate-area 
for Anthra- 
cite Coal, in 
sq. in. 


Grate-area 
for Bitumin- 
ous Coal, in 
sq. in. 


Diameter 
of Stacks, 
in inches. 


Double 
Nozzles. 


Single 
Nozzles. 


Cylinders, 
in inches. 


Diam. of 

Orifices, in 

inches. 


Diam. of 

Orifices, in 

inches. 


12x20 
13x20 
14x20 
15x22 
16x24 
17x24 
18x24 
19x24 
20x24 


1591 
1873 
2179 
2742 
3415 
3856 
4321 
4810 
5337 


1217 
1432 
1666 
2097 
2611 
2948 
3304 
3678 
4081 


91/2 
101/2 
111/4 
121/2 
14 
15 

153/4 
161/2 
171/2 


2 

21/8 

25/16 

29/16 
27/8 
31/16 
31/4 
37/16 
35/8 


213/16 

31/4 

311/16 

41/16 

45/16 

45/8 

413/16 

51/16 



Exhaust-nozzles in Locomotive Boilers. — A committee of the 
Am. Ry. Master Mechanics' Ass'n. in 1890 reported that they had, after 
two 5'ears of experiment and research, come to the conclusion that, 
owing to the great diversity in the relative proportions of cylinders and 
boilers, together with the difference in the quality of fuel, any rule which 
does not recognize each and all of these factors would be worthless. 

The committee was unable to devise any plan to determine the size 
of the exhaust-nozzle in proportion to any other part of the engine or 
boiler. The conditions desirable are: That it must create draught 
enough on the fire to make steam, and at the same time impose the least 
possible amount of work on the pistons in the shape of back pressure. 
It should be large enough to produce a nearly uniform blast without 
lifting or tearing the fire, and be economical in its use of fuel. The 
Annual Report of the Association for 1896 contains interesting data on 
this subject. 

Much important information regarding stacks and exhaust nozzles is 
embodied in the tests at Purdue University, reported to the Master 
Mechanics' Ass'n. in 1896 and in the tests "^ reported in the American 
Engineer in 1902 and 1903. 

Fire-brick Arches in Locomotive Fire-boxes. — A committee of 
the Am. Ry. Master Mechanics' Ass'n. in 1890 reported strongly in favor 
of the use of brick arches in locomotive fire-boxes. They say: It is the 
unanimous opinion of all who use bituminous coal and brick arch, that 
it is most efficient in consuming the various gases composing black 
smoke, and by impeding and delating their passage through the tubes, 
and mingling and subjecting then: to the heat of the furnace, greatly 
lessens the volume ejected, and intensifies combustion, and does not in 
the least check but rather augments draught, with the consequent saving 
of fuel and increased steaming capacity that might be expected from 
such results, This in particular when used in connction with extension 
front. 



1116 IiOCOMOTIVES. 

Arches now (1909) are not quite so much in favor, largely on account 
of the difficulty and delay caused to workmen when flues must be calked, 
as occurs frequently in bad water districts, and some of their former 
advocates are now omitting them altogether. 

Economy of High Pressures. — Tests of a Schenectady locomotive 
with cylinders 16 X 24 ins., at the Purdue University locomotive testing 
plant, gave results as follows: {Eng. Digest, Mar., 1909; Bull. No. 26, Univ. 
of 111. Expt. Station). 

Boiler pressure, lbs. per sq. in. 120 140 160 180 200 220 240 
Steam per 1 H.P. hour, lbs. 29.1 27.7 26.6 26. 25.5 25.1 24.7 
Coal per 1 H.P. hour, lbs. 4 3.77 3.59 3.50 3.43 3.37 3.31 

In the same series of tests the economy of the boiler at different rates of 
driving and different pressures wa^ determined, the results leading to the 
formula E = 11.305 — 0.221 H, in which E = lbs. evaporated from and 
at 212'' per lb. of Youghiogheny coal, and H the equivalent evaporation 
per sq. ft. of heating surface per hour, with an average error for any 
pressure which does not exceed 2.1%. 

Leading American Types of Locomotive for Freight and 
Passenger Servicco 

1. The eight-wheel or '* American" passenger type, having four coupled 
driving-wheels and a four-wheeled truck in front. 

2. The "ten-wheel" type, for mixed traffic, having six coupled drivers 
and a leading four-wheel truck. 

3. The "Mogul" freight type, having six coupled dri\dng-wheels and 
a pony or two-wheel truck in front. 

4. The "ConsoUdation" type, for heavy freight service, having eight 
coupled driving-wheels and a pony truck in front. 

Besides these there is a great variety of types for special conditions of 
service, as four-wheel and six-wheel switching-engines, ^^ithout trucks; 
the Forney type used on elevated railroads, with four coupled wheels 
under the engine and a four-wheeled rear truck carrying the water-tank 
and fuel; locomotives for local and suburban service with four coupled 
driving-wheels, with a two-wheel truck front and rear, or a two-wheel 
truck front and a four-wheel truck rear, etc. "Decapod" engines for 
heavy freight service have ten coupled driving-wheels and a two-wheel 
truck in front. 

Q_Qa n n n o O E 

O O O b O O O n f 

oooo c n n n n o o 
n n r, n . nnnn o h 

Classification of Locomotives (Penna. R. R. Co., 1900). — Class A, 
two pairs of drivers and no truck. Class B, three pairs of drivers and no 
truck. Class C, four pairs of drivers and no truck. Class D, two pairs of 
drivers and four-wheel truck. Class E, two pairs of drivers, four-wheel 
truck, and trailing wheels. Class F, three pairs of driving-wheels and 
two-wheel truck. Class G, three pairs of drivers and four-wheel truck. 
Class H, four pairs of drivers and two-wheel truck. Class A is com- 
monly called a "four-wheeler"; B, a "six-wheeler"; D, an "eight- 
wheeler," or "American" type; E, "Atlantic" type; F, "Mogul"; 
G, "ten-wheeler"; H, "Consolidation." 

Modern Classification. — The classes shown above, lettered A, B, C, 
etc., are commonly represented respectively by the symbols 0-4-0; 
0-6-0; 0-8-0, 4-4-6; 4-4-2, 2-6-0; 4-6-0; 2-8-0; the first figure being 
the number of wheels in the truck, the second the driving-wheels, and the 
third the trailers. Other types are the "Pacific," 4-6-2; the 'Trairie," 2-6-2; 



I/)COMOTIVES. 



1117 



and the "Santa Fe," 2-10-2. Engines on the Mallet system, with two 
locomotive engines under one boiler, are classified 0-8-8-0, 2-6-6-2, etc. 

Forinulae for Curves. (Baldwin Locomotive Works.) 
Approximate Formula for Radius. Approximate Formula for Swing. 

R = 0.7646 IF -^ 2 P. {T - W) T -^ 2 S == R. 



O 



d) 





o 



o 



R = radius of min. curve in feet. W = rigid wheel-base. 

JP = play of driving-wheels in T = total wheel-base, 

decimals of 1 ft. R = radius of curve. 

W = rigid wheel-base in feet. S = swing on each side of centre. 

Steam-distribution for High-speed Locomotives. 

(C. H. Quereau, Eng'g News, March 8, 1894. 

Balanced Valves. — Mr. Philip Wallis, in 1886, when Engineer of Tests 
for the C, B. & Q. R. R., reported that while 6 H.P. was required to 
work unbalanced valves at 40 miles per hour, for the balanced valves 
2.2 H.P. only was necessary. 

[Later tests were reported by the Master Mechanics* Committee in 1896. 
Unbalanced valves required from 3/4 to 21/2 per cent of the I. H.P. for 
their motion, balanced valves from 1/3 to 1/2 as much, and piston valves 
about Vo or i/e. Generally in balanced valves, the area of balance == 
area of exhaust port + area of two bridges 4- area of one steam port. J 

Effect of Speed on Average Cylinder-pressure. — Assume that a locomo- 
tive has a train in motion, the reverse lever is placed in the running 
notch, and the track is level; by what is the maximum speed limited? 
The resistance of the train and the load increase, and the power of the 
locomotive decreases with increasing speed till the resistance and power 
are equal, when the speed becomes uniform. The power of the engine 
depends on the average pressure in the cylinders. Even though the 
cut-off and boiler-pressure remain the same, this pressure decreases as 
the speed increases; because of the higher piston-speed and more rapid 
valve-travel the steam has a shorter time in which to enter the cylinders 
at the higher speed. The following table, from indicator-cards taken 
from a locomotive at varying speeds, shows the decrease of average 
pressure with increasing speed: 

Miles per hour 46 51 51 53 54 57 60 66 

Speed, revolutions 224 248 248 258 263 277 292 321 

Average pressure per sq. in.: 

Actual 51.5 44.0 47.3 43.0 41.3 42.5 37.3 36.3 

Calculated 46.5 46.5 44.7 43.8 41.6 39.5 35.9 

The "average pressure calculated" was figured on the assumption that 
the mean effective pressure would decrease in the same ratio that the 
speed increased. The main difference lies in the higher steam-line at 
the lower speeds, and consequent higher expansion-line, showing that 
more steam entered the cylinder. The back pressure and compression- 
lines agree quite closely for all the cards, though they are slightly better 
for the slower speeds. That the difference is not greater may safely be 
attributed to the large exhaust-ports, passages, and exhaust tip, which 
is 5 in. diameter. These are matters of great importance for high speeds. 

Boiler-pressure. — Assuming that the train resistance increases as the 
speed after about 20 miles an hour is reached, that an average of 50 lbs. 
per sq. in. is the greatest that can be realized in the cylinders of a given 
engine at 40 miles an hour, and that this pressure furnishes just sufficient 
power to keep the train at this speed, it follows that, to increase the 
speed to 50 miles, the mean effective pressure must be increased in the 
same proportion. To increase the capacity for speed of any locomotive 
its power must be increased, and at least hy as much as the speed is to 
be increased. One way to accomplish this is to increase the boiler- 



1118 LOCOMOTIVES. 

Eressure. That this is generally realized, is shown by the increase In 
oiler-pressure in the last ten years. For twenty-three single-expansion 
locomotives described in the railway journals tliis year the steam-pres- 
sures are as follows: 3, 160 lbs.; 4, 165 lbs.; 2, 170 lbs.; 13 180 lbs.; 
1, 190 lbs. 

Valve-travel. — An increased average cylinder-pressure may also be 
obtained by increasing the valve-travel without raising the boiler- 
pressure, and better results will be obtained by increasing both. The 
longer travel gives a higher steam-pressure in the cylinders, a later 
exhaust-opening, later exhaust-closure, and a larger exhaust-opening — 
all necessary for high speeds and economy. I believe that a 20-in. 
port and 6V2-in. (or even 7-in.) travel could be successfully used for 
liigh-speed engines, and that frequently by so doing the cylinders could 
be economically reduced and the counter-balance lightened. Or, better 
still, the diameter of the drivers increased, securing lighter counterbal- 
ance and better steam-distribution. 

Size of Drivers. — Economy will increase with increasing diameter of 
drivers, provided the work at average speed does not necessitate a cut-off 
longer than one fourth the stroke. The piston-speed of a locomotive 
with 62-in. drivers at 55 miles per hour is the same as that of one with 
68-in. drivers at 61 miles per hour. 

Steam-ports. — The length of steam-ports ranges from 15 in. to 23 in., 
and has considerable influence on the power, speed, and economy of the 
locomotive. In cards from similar engines the steam-line of the card 
from the engine wdth 23-in. ports is considerably nearer boiler-pressure 
than that of the card from the engine with 17V4-in. ports. That the 
higher steam-line is due to the greater length of steam-port there is little 
room for doubt. The 23-in. port produced 531 H.P. in an 18i/2-in. 
cyUnder at a cost of 23.5 lbs. of water per I. H.P. per hour. The I71/4 
in. port, 424 H.P., at the rate of 22.9 lbs. of water, in a 19-in. cyhnder. 

Allen Valves. — There is considerable difference of opinion as to the 
advantage of the Allen ported-valve. (See Eng. Aews, July 6, 1893.) 

A Report on the advantage of Allen valves was made by the Master 
Mechanics' Committee of 1896. 

Speed of Railway Trains. — In 1834 the average speed of trains on 
the Liverpool and Manchester Railway was 20 miles an hour; in 1838 it 
was 25 miles an hour. But by 1840 there were engines on the Great 
Western Railway capable of running 50 miles an hour with a train and 
80 miles an hour without. {Trans. A. S. M. E., vol. xiii, 363.) 

The limitation to the increase of speed of heavy locomotives seems at 
present to be the difhculty of counterbalancing the reciprocating pans. 
The unbalanced vertical component of the reciprocating parts causes 
the pressure of the driver on the rail to vary with every revolution. 
Whenever the speed is high, it is of considerable magnitude, and its 
change in direction is so rapid that the resulting effect upon the rail is 
not inappropriately caUed a "hammer blow." Heavy rails have been 
kinked, and bridges have been shaken to their fall under the action of 
heavily balanced drivers revolving at high speeds. The means by 
which the evil is to be overcome has not yet been made clear. See 
paper by W. F. M. Goss, Trans. A. S. M. E., vol. xvi. 

Much can be accomplished, however, by carefully designing and 
proportioning the counter-balance in the wheels and by using light, but 
strong, reciprocating parts. Pages 41-74 of *' Locomotive Operation," 
gives complete rules and results. 

Balanced compound locomotives, with 4 cylinders, the adjacent pis- 
tons and crossheads being connected 180° apart have also done much 
to reduce the disturbance of the moving parts. 

Engine No. 999 of the New York Central Railroad ran a mile in 32 
«econds equal to 112 miles per hour. May 11, 1893. 

Speed in ) circum. of driving-wheels in in. X no. of rev. per min. X 60 
miles per ^ —■ — 



hour ) 63,360 

= diam., of driving-wheels in in. X no. of rev. per min. X.003 
(approximate, giving result s/^q of 1 per cent too great). 
Performance of a High-speed Locomotive. — The Baldwin com- 
pound locomotive No. 1027, on the Phila. & Atlantic City Ry., in 1897 
made a record as follows: 



LOCOMOTIVES. 



1119 



For the 52 days the train ran, from July 2d to August 31st, the average 
time consumed on the run of 551/2 miles from Camden to Atlantic City 
was 48 minutes, equivalent to a uniform rate of speed from start to stop 
of 69 miles per hour. On July l-ith the run from Camden to Atlantic 
City was made in 461/2 min., an average of 71.6 miles per hour for the total 
distance. On 22 days the train consisted of 5 cars and on 30 days it was 
made up of 6, the weight of cars being as follows: combination car, 57,200 
lbs.; coaches, each, 59,200 lbs.; Pullman car, 85,500 lbs. 

The general dimensions of the locomotive are as follows: cylinders, 
13 and 22 X 26 in.; height of drivers, 841/4 in.; total wheel-base, 26 ft. 
7 in.; dri\'ing- wheel base, 7 ft. 3 in.; length of tubes, 13 ft.; diameter of 
boiler, 583/4 in.; diameter of tubes, 1 3/4 in.; number of tubes, 278; length 
of fire-box, 113 7/8 in.; width of fire-box, 96 in.; heating-surface of fire- 
box, 136.4 sq. ft.; heating-surface of tubes, 1614.9 sq. ft.; total heating- 
surface, 1835.1 sq. ft.; tank capacity, 4000 gallons; boiler-pressure, 
200 lbs. per sq. in.; total weight of engine and tender, 227,000 lbs.; 
weight on drivers (about), 78,600 lbs. 

Fuel Efficiency of American Locomotives. — Prof. W. M. Goss, as 
a result of a series of tests run on the Purdue locomotive, finds the dis- 
position of the heat developed by burning coal in a locomotive fire-box 
to be on the average about as shown in the following table: 

Absorbed by steam in the boiler, 52%; by the superheater, 5 %; 
total, 57 %. Losses: In vaporizing moisture in the coal, 5 %; discharge 
of CO., 1 %; high temperature of the products of combustion, 14 %; 
unconsumed fuel in the form of front-end cinders, 3 % ; cinders or sparks 
passed out of the stack, 9 %; unconsumed fuel in the ash, 4 %; radia- 
tion, leakage of steam and water, etc., 7 %. Total losses, 43 %. 

It is probable that these losses are considerably less than the losses 
which are experienced in the average locomotive in regular railway 
service. — (Bulletin No. 402, U.S. Geol. Survey, 1909.) 

Locomotive Link 3Iotion. — Mr. F. A. Halsey, in his work on " Loco- 
motive Link Motion, ' ' 1898, shows that the location of the eccentric-rod 
pins back of the link-arc and the angular vibrations of the eccentric- 
rods introduce two errors in the motion which are corrected by the 
angular \abration of the connecting-rod and by locating the saddle-stud 
back of the link-arc. He holds that it is probable that the opinions of 
the critics of the locomotive link motion are mistaken ones, and that it 
comes little short of all that can be desired for a locomotive valve motion. 
The increase of lead from full to mid gear and the heavy compression at 
mid gear are both advantages and not defects. The cylinder problem of 
a locomotive is entirely different from that of a stationary engine. With 
the latter the problem is to determine the size of the cylinder and the dis- 
tribution of steam to drive economically a given load at a given speed. 
With locomotives the cylinder is made of a size which will start the 
heaviest train which the'^adhesion of the locomotive wiU permit, and the 
problem then is to utilize that cylinder to the best advantage at a greatly 
increased speed, but under a greatly reduced mean effective pressure. 

Negative lead at full gear has been used in the recent practice of some 
railroads. The advantages claimed are an increase in the power of the 
engine at full gear, since positive lead offers resistance to the motion of 
the piston; easier riding; reduced frequency of hot bearings; and a 
slight gain in fuel economy. Mr. Halsey gives the practice as to lead on 
several roads as follows, showing great diversity: 





Full Gear 
Forward, in. 


Full Gear 
Back, in. 


Reversing 
Gear, in. 


New York, New Haven & 
Hartford 


V16 pos. 



V32 pos. 
I/I6 neg. 

3/16 neg. 


1/4 neg. 
1/4 neg. 


1/4 pos. 


Maine Central 




Illinois Central 


abt 3/16 
S/I6 pos. 
3/16 to 9/16 
1/4 pos. 


Lake Shore 


9/64 neg. 



Chicago Great Western 

Chicago & Northwestern 







1120 



LOCOMOTIVES. 



DIMENSIONS OF SOME LARGE AMERICAN 
LOCOMOTIVES, 1893 AND 1904. 

Of the four locomotives described in the table on the next page the 
first two were exhibited at the Chicago Exposition in 1893. The dimen- 
sions are from Engineering News, Jime, 1893. The first, or Decapod 
engine, has ten-coupled driving-wheels. It is one of the heaviest and 
most powerful engines built up to that date for freight service. The 
second is a simple engine, of the standard American 8-wheel type, 4 
driving-wheels, and a 4- wheel truck in front. Tliis engine held the 
world's record for speed in 1893 for short distances, having run a mile 
in 32 seconds. 

The other two engines formed part of the exhibit of the Baldwin 
Locomotive Works at the St. Louis Exposition in 1904. The Santa Fe 
type engine has five pairs of driving-wheels, and a two- wheeled truck at 
the front and at the rear. It is equipped with Vauclain tandem com- 
pound cy finders. 

Dimensions of Some American Locomotives. 

(Baldwin Loco. Wks. 1904-8.) 





si 


Boilers. 


Tubes. 


Heating 
Surface. 


Driving 
Wheels 

Diam., 


Weight, lbs. 


o a3 


irr 


id 


No. 


§2 


W) 




i^ 


on 


Total 






2 fl 

Q""^ 


^6^ 


s-^ 






t^ 


ins. 


Drivers 


Engine 








ft. in. 












1 


150 


42 


9 


97 


2 


11 7 


41 


586 


37 


44,420 


52,720 


2 


160 


50 


14.6 


160 


2 


10 6 


75 


873 


48 


72,150 


84,650 


3 


200 


60 


25.9 


287 


2 


11 7 


133 


1733 


69 


83,680 


124,420 


4 


200 


62 


30 


272 


2 


16 1 


136 


2279 


68 


112,000 


159,000 


5 


200 


76 


37.2 


298 


21/4 


13 10 


200 


2414 


51 


164,000 


179,500 


6 


200 


68 


35 


306 


21/4 


14 6 


195 


2593 


56 


166,000 


186,000 


7 


200 


66 


49.5 


273 


21/4 


18 10 


190 


3015 


79 


101,420 


193,760 


8 


200 


70 


53.5 


318 


21/4 


19 


195 


3543 


79 


144,600 


209,210 


9 


210 


70 


55 


303 


21/4 


21 


190 


3772 


74 


151,290 


230,940 


10 


225 


78 


58.5 


463 


21/4 


19 


210 


5155 


57 


237,800 


267,800 


11 


200 


84 


68.4 


401 


21/4 


21 


232 


4941 


57 


394,150 


425,900 



Type and cylinder size: 1, Mogul, 13 X 18; 2, Mogul, 16 X 20; 3, Am- 
erican, 18 X 24; 4, 10-wheel balanced compound, 16 X 26 and 26 X 28; 
5, Consofidation, 22 X 28; 6, Consofidation, 23 and 35 X 32; 7, Atlantic, 
15 and 25 X 26; 8, Prairie, 17 and 28 X 28; 9, Pacific, 22 X 28; 10, Deca- 
pod, 19 and 32 X 32; 11, Mallet, two each 26 and 40 X 30. 

Tlie Mallet Compound Locomotive. — The Mallet articulated loco- 
motive consists principally of two sets of engines flexibly connected un- 
der one boiler; the rear, which is a high-pressure engine of two cylinders, 
fixed rigid with the boiler and receiving the steam direct from the dome. 
The front or low-pressure engine, also provided with two cylinders, is 
capable of lateral movement to adjust itself to the curvature of the road 
on the same general principle as a radial truck. The high-pressure 
engine exhausts into a receiver fiexibly connecting the cylinders of the 
two sets of engines, from which the low-pressure engine receives its 
steam supply and Is exhausted from the latter through a fiexible pipe 
to the stack. Each cylinder has its independent valve and gear con- 
nected to and operated with a common reversing rigging. By this 
means the tractive power can be doubled over that of the ordinary 
engine for a given weight of rail with a substantial saving in fuel. 
(See paper by C. J. Mellin. Trans. A. S. M. E., 1909.) 

This type of locomotive is adapted to a wider range of service than per- 
haps any other design. It was originally intended for narrow-gage roads 
of light construction, necessitating sharp curves and steep grades, in com- 
bination with light rails. The characteristics of this design are flexibihty 
and uniform distribution of weight combined with the use of two separate 
engines which would not slipat thesame time, and the total weight carried 
on the drivers, giving great tractive power. The first engine of this class 



LARGE AMERICAN LOCOMOTIVES 



1121 



Running-gear: 

Driving-wheels, diam. . 

Truck " " .. 

Journals, driving-axles 
truck- 
" tender- " 

Wheel-base: 

Driving 

Total engine 

tender 

eng. and tender. . 
Wt. in working-order: 

On drivers 

On truck-wheels 

Engine, total 

Tender *' 

Eng. and tend., loaded 
Cylinders: 

h.p.(2) 

l.p.(2) 

Piston-rod, diam 

Connecting-rod, I'gth. . 

Steam-ports 

Exhaust-ports 

Valves, out. lap, h.p. . . 
out. lap, l.p. . . . 

" in. lap, h.p 

*' in. lap, l.p 

" max. travel . . . 

lead, h.p 

lead, l.p 

Boiler.— Type 

Diam. barrel inside .... 
Thickness of plates . . . 
Height from rail to 

center line 

Length of smoke-box. . 

Working pressure 

Firebox.— type 

Length inside 

Width " 

Depth at front 

Thickness side plates. . 

back plate . . 

" crown-sheet. 

tube sheet.. . 

Grate-area 

Stay-bolts, U/sin 

Tubes— iron 

Pitch 

Diam., outside 

Length 

Heating-surface : 

Tubes, exterior 

Fire-box 

Miscellaneous: 

Exhaust-nozzle, diam . 

Stack, smal'st diam. . . 

height from 

rail to top 



Baldwin. 

N.Y., L.E. 

&W.R.R. 
Decapod 
Freight. 



50 in. 

30 " 
9 XlOin. 
5 XIO" 
41/2X 9 " 



18 ft. 
27 " 
16 " 
53 " 



10 in. 
3 " 



170,000 lbs. 
29,500 " 
192,500 " 
117,500 " 
310,000 " 

16X28 in. 
27X28 " 

4 in. 
9^ 87/16'^ 

281/2X2 in. 

281/2X8 " 

7/8 in. 

5/8 " 



6 in. 

Viein. 

5/16 " 

Straight 

6 ft. 21/2 in. 

3/4 in. 

8 ft. in. 

5 *' 77/8 - 

180 lbs. 

Woo t ten 

lO' 119/16- 

8 ft. 21/8 in. 

4 " 6 ♦* 

5/i6in. 

5/16 *' 

3/8 " 

1/2 " 

89.6 sq. ft. 

pitch, 41/4 in. 

354 

23/4 in. 

2 

11 ft. 11 in. 

2,208.8 ft. 
234.3 " 



1 ft. 6 in. 
15ft.61/2in. 



N.Y. C. & 
H.R.R. 
Empire 

State 
Express. 
No. 999. 



86 in. 
40 " 

9 X 121/2 in 
6I/4XIO " 

41/8X 8 " 

8 ft. 6 in. 
23 " 11 " 
15 "21/2 * 
47 " 81/8 " 

84,000 lbs. 

40,000 " 
124,000 " 

80,000 " 
204,000 " 

19X24 in. 



33/8 in. 
8 ft. U/2in. 

11/2Xl8in. 

23/4X18 " 
1 in. 



VlO in. 
"51/2 in. ' 



W^agon top 

4 ft. 9 in. 

9/l6in. 

7 ft. 11 1/2 in. 
4" 8 

190 lbs. 

Buchanan 

9 ft. 63/8 in. 

3 " 47/8 " 

6 " 11/4 " 

5/l6in. 

5/16 " 

3/8" 

V2 " 

30.7 sq.ft. 

4 in. 

268 



2 in. 
12 ft. in. 



1,697 sq. 
233 ' 



ft. 



31/2 in. 
1ft. 3 1/4 in. 

14ft. 10 in. 



Baldwin. 

Santa Fe 

Type 

2-10-2 

Freight. 



57 in. 

29 1/4 & 40'' 

11 X12" 

6I/9XIO" 

71/2X12" = 

19 ft. 9 in. 
35 " 11 " 



66 ft. Oin. 

234,580 lbs. 
52,660 " 
287,240 " 



450,000 " 

19X32 in. 

32X32 " 



29 3/4x1 5/8'' 

and 13/4" 

29 3/4X6 3/4'- 

7/8 in. 

3/4 " 
neg. i/4in. 
neg. 3/8 " 

6 in. 

" 

1/8 " 

Wagon to 

783/4 in. 

7/8 & 15/16'' 



225 lbs. 



108 in. 

78 " 
80 1/4 in. 
781/4 " 
3/8 " 
3/8 " 
3/8" 
9/16 " 
58.5 sq.ft. 
391 



21/4 in. 
20 ft. 

4,586 sq.ft. 2, 
210 " 



Baldwin. 

Pacific 

Type 4^-6-2 

Passenger. 



77 in. 
331/2 & 45" 
10xi2in. 

6X10 " 

8X12 " ^ 

13 ft. 4 in. 
33 " 4 " 



62' 83/4" 

141,290 

81,230 

222,520 



357,000 

22X28 in. 
22X28 " 



307/8X11/2" 

307/8X3" 

1 in. 



neg. i/ie" 



6 in. 
3/32 in. 



Straight 

70 in. 
11/10 in. 



108 in. 
66 " 
68 *' 
64 " 



3/8 " 
1/2 " 
49.5 sq. 
245 



21/4 in. 
20 ft. 

,874 sq.ft. 
179 " 



* Back truck journals. 



1122 



LOCOMOTIVES. 



was built about 1887, and in 1909 there were approximately 500 running in 
Europe. They are now extensively in use in the United States for the 
heaviest service. The largest locomotive yet built is described in Eng. 
News, April 29, 1909. It was built by the Baldwin Locomotive Works 
for use on the heavy grades of the Southern Pacific R.R. The principal 
dimensions areas follows: Cylinders, 26 and 40 X 30 ins.; valves, balanced 
piston; boiler (steel): diameter, 84 ins.; thickness, is/^g and 27/32 ins.; work- 
ing pressure, 200 lbs. per sq. in.; fuel, oil; fire-tubes, 401, 21/4 ins. dia. X 
21 ft.; firebox: length, 126 ins., width, 78V4ins.. depth, front, 751/2 ins., 
depth, back, 70 1/2 ins.; water spaces, 5 ins.; grate area, 68.4 sq. ft.; 
feed-water heater: length, 63 ins., tubes, 401, 2 1/4 ins. dia.; heating sur- 
face: firebox, 232 sq. ft., fire-tubes, 4941 sq. ft., feed-water heater tubes, 
1220 sq. ft.; smokebox superheater, 655 sq. ft.; wheels: driving (16), 
57 ins. O. dia., main journals, 11X12 ins., other journals, 10 X 12 ins. 
truck (4), 30 1/2 ins. dia., journals, 6 X 10 ins.; tender (8), 33 V2 ins. dia., 
journals, 6X11 ins.; wheelbase: driving, 39 ft. 4 ins., rigid, 15 ft., total 
engine, 56 ft. 7 ins., total engine and tender, 83 ft. 6 ins.; length over all, 
93 ft. 6I/2 ins.; weight: on drivers, 394,150 lbs., on front truck, 14,500 lbs., 
on back truck, 17,250 lbs., total engine 425,900 lbs., total engine and 
tender 596,000 lbs.; tender: water tank capy., 9000 gals., oil tank capy.. 
2850 gals. 

Indicated Water Consumption of Single and Compound Loco- 
motive Engines at Varying Speeds. 

C. H. Quereau, Eng'g News, March 8, 1894. 



Two-cylinder Compound. 


Sing 


le-expansion 




Revolutions. 


Speed, 

miles per 

hour. 


Water per 

I.H.P. per 

hour. 


Revolu- 
tions. 


Miles per 
Hour. 


Water, 


100 to 150 
150 to 200 
2D0 to 250 
250 to 275 


21 to 31 
31 to 41 
41 to 51 
51 to 56 


18.33 ibs. 
18.9 lbs. 
19.7 lbs. 
21.4 lbs. 


151 
219 
253 
307 
321 


31 
45 
52 
63 
66 


21.70 
20.91 
20.52 
20.23 
20.01 



It appears that the compound engine is the more economical at low 
speeds, the economy decreasing as the speed increases, and that the 
simple engine increases in economy with increase of speed within ordinary 
limits, becoming more economical than the compound at speeds of more 
than 50 miles per hour. 

The C, B. & Q. two-cyUnder compound, which was about 30% less 
economical than simple engines of the same class when tested in passenger 
service, has since been shown to be 15% more economical in freight 
service than the best single-expansion engine, and 29% more economical 
than the average record of 40 simple engines of the same class on the 
same division. 

The water rate is also affected by the cut-off; the following table gives 
what we should consider very good results in practice, though better 
(i.e. lower results) have occasionally been obtained. (G. R. Henderson, 
1906.) 

Cut-off per cent of stroke 10 20 30 

Lbs. water per I.H.P. hour — simple. . 26 23 22 

Lbs. water per I.H.P. hour — compound .. .. 18 

Cut-off per cent of stroke 60 70 80 

Lbs. water per I.H.P. hour — simple ... 24 26 29 

Lbs. water perl H. P. hour — compound I8V2 191/2 2OV2 



40 
^2 
18 

90 
33 

221/0 



50 
23 
18 

100 
38 
25 



Indicator-tests of a Locomotive at High Speed. (Locomotive 
Eng'g, June, 1893.) — Cards were taken by Mr. Angus Sinclair on the 
locomotive drawing the Empire State Express. 



LOCOMOTIVES. 



1123 



Results of Indicator-diagrams. 







Miles 








Miles 




Card No. 


Revs. 


per hour. 


I.H.P. 


Card No. 


Revs. 


per hour. 


I.H.P. 


1 


160 


37.1 


648 


7 


304 


70.5 


977 


2 


260 


60.8 


728 


8 


296 


68.6 


972 


3 


190 


44 


551 


9 


300 


69.6 


1,045 


4 


250 


58 


891 


10 


304 


70.5 


1,059 


5 


260 


60 


960 


11 


340 


78.9 


1,120 


6 


298 


69 


983 


12 


310 


71.9 


1,026 



The locomotive was of the eight-wheel type, built by the Schenectady 
Locomotive Works, with 19 X 24 in. cy finders, 78-in. drivers, and a 
large boiler and fire-box. Details of important dimensions are as fol- 
lows: Heating-surface of fire-box, 150.8 sq. ft.; of tubes, 1670.7 sq. ft.; 
of boiler, 1821.5 sq. ft. Grate area, 27.3 sq. ft. Fire-box: length, 
8 ft.; width, 3 ft. 4 7/8 in. Tubes, 268; outside diameter, 2 in. Ports: 
steam, 18 X 1 V4 in.; exhaust, 18X2 3/4 in. Valve-travel, 51/2 in. 
Outside lap, 1 in.; inside lap, i/64 in. Journals: driving-axle, 8 1/2 X 10 1/2 
in.; truck-axle, 6 X 10 in. 

The train consisted of four coaches, w^eighing, with estimated load, 
340,000 lbs. The locomotive and tender weighed in working order 200,- 
000 lbs., making the total weight of the train about 270 tons. During 
the time that the engine was first lifting the train into speed diagram 
No. 1 was taken. It shows a mean cylinder-pressure of 59 lbs. Accord- 
ing to this, the power exerted on the rails to move the train is 6553 lbs., 
or 24 lbs. per ton. The speed is 37 miles an hour. When a speed of 
nearly 60 miles an hour is reached the average cylinder-pressure is 
40.7 lbs., representing a total traction force of 4520 lbs., without mak- 
ing deductions for internal friction. If we deduct 10% for friction, it 
leaves 15 lbs. per ton to keep the train going at the speed named. Cards 
6. 7, and 8 represent the work of keeping the train running 70 miles an 
hour. They were taken three miles apart, when the speed was almost 
uniform. The average cylinder-pressure for the three cards is 47.6 lbs. 
Deducting 10% again for friction, this leaves 17.6 lbs. per ton as the 
power exerted in keeping the train up to a velocity of 70 miles. 
Throughout the trip 7 lbs. of water were evaporated per lb. of coal. 
The work of pulhng the train from New York to Albany was done on a 
coal consumption of about 3 i/g lbs. per H. P. per hour. The highest 
power recorded was at the rate of 1120 H.P. 

Locomotive-testing Apparatus at the Laboratory of Purdue Uni- 
versity. (W. F. M. Goss, Trans. A. S. M. E., vol. xiv, 826.)— The 
locomotive is mounted with its drivers upon supporting wheels which 
are carried by shafts turning in fixed bearings, thus allowing the engine 
to be run without changing its position as a whole. Load is supplied by 
four friction-brakes fitted to the supporting shafts and offering resistance 
to the turning of the supporting wheels. Traction is measured by a 
dynamometer attached to the draw-bar. The boiler is fired in the 
usual way, and an exhaust-blower above the engine, but not in pipe 
connection with it, carries off all that may be given out at the stack. 

A Standard Method of Conducting Locomotive-tests is given in a report by 
a Committee of the A.S.M.E. in vol. xiv of the Transactions, page 1312 

Locomotive Tests of the Peiina. R. R. Co. — Eight locomotives were 
tested in the dynamometer testing plant built by the P. R. R. Co. at 
the St. Louis Exhibition in 1903. Among the principal results obtained 
and conclusions derived are the following: 



Boiler Performance. 
rate per hour. lbs. 



Coal per sq. ft 

20 40 60 80 100 

Equiv. evap. per sq. ft. H. S. per hour 

3-5 5-7.5 7-10 8.2-12 10.4-14 
Coal per sq. ft. H. S. per hour 

0.6 0.8 1.0 1.2 

Equiv. evap. per lb. dry coal 

10-11.5 9-10.5 8.2-9.7 7.7-9.1 
Equiv. evap. per sq. ft. H. S. per hour 

4 6 8 10 

Equiv. evap. per lb. dry coal 

9.7-12.3 8.8-11.3 7.8-10.5 6.8-9.6 



120 
11.4-15.3 
1.4 



1.6 



7.1-8.5 
12 



6.6-8.1 
14 
5.8-8.8 5.5-8 



1.8 
6.2-7.7 



1124 



LOCOMOTIVESo 



The coal used in these tests was a semi-bituminous, containing 16.25% 
volatile combustible, 7.00% ash and 0.90% moisture. 

The maximum boiler capacity ranged from 81^ to more than 16 lbs. 
of water evaporated per hour per sq. ft. of heating surface. Little or no 
advantage was found in the use of Serve or ribbed tubes. 

The boiler efficiency decreases as the rate of power developed increases. 

Furnace losses due to excess air are no greater with large grates properly 
fired than with smaller ones. The boilers with small grates were inferior 
in capacity to those with large grates. 

No special advantage is derived from large fire-box heating surface; the 
tube heating surface is effective in absorbing heat not taken up by the 
fire-box. 

Engine Performance. 



Maximum I.H.P., four freight locomotives, 1041, 1050, 1098, 1258 
Maximum I.H.P., four passenger locomotives, 816, 945, 1622, 1641 




Kind of Locomotive. 




Simple 
Freight. 


Com- 
pound 
Freight. 


Com- 
pound 
Passen- 
ger. 


Minimum water per I.H.P. hour 


23.67 
23.83 
28.95 


20.26 
22.03 
25.31 


18 86 


Water per I.H.P'. hr. at maximum load 

Water per I.H.P. hr. at max. consumption. .. 


21.39 
24.41 



The steam consumption of simple locomotives operating at all speeds 
and cut-offs commonly employed on the road falls between the hmits 
of 23.4 and 28.3 lbs, per I.H.P. hour; compound locomotives between 
18.6 and 27 lbs.; and with superheating the minimum steam consumption 
was reduced to 16.6 lbs. of superheated steam. 

Comparing a simple and a compound locomotive, the simple endne 
used 40% more steam than the compound at 40 revs, per min., 27% more 
at 80 revs., and only 7% more at 160 revs, per min. 

The frictional resistance of the engines showed an extreme variation 
ranging from 6 to 38% of the indicated horse-power. The frictional 
losses increased rapidly at speeds in excess of 160 revs, per mun. It 
appears that the matter of machine friction is closely related to that of 
lubrication. With oil lubrication a stress at the draw-bar of approxi- 
mately 500 lbs. is required to overcome the friction of each coupled axle, 
while with grease the required force is from 800 to 1100 lbs. 

The lowest figures for dry coal consumed per dynamometer H.P. hour 
were approximately as follows: 
Revs, per min. 

Compound freight engine, | ^ h^ j?^ 

Compound passenger engine, | j^'jj^j? 

A complete report of the St. Louis locomotive tests is contained in a 
book of 734 pages and over 800 illustrations, pubhshed by the Penna. R.R. 
Co., Philadelphia, 1906. See also pamphlet on Locomotive Tests, pub- 
lished by Amer. Locomotive Co., New York, 1906, and Trans. A. S. M. E., 
xxvii, 610. 

Weights and Prices of Loco^itiotives, 1885 and 1905. 
(Baldwin Loco. Wks.) 



40 


80 


160 


240 


2.10 


2.25 


3.25 


. . . • 


500 


800 


800 






2.8 


2.3 


3.0 




600 


900 


1000 



Type. 



American 

Mogul 

Ten wheel . . . 
Consolidation 



W'gt 


Price 


Price 
per 
lb. 

S 0828 
.0912 
.0892 
.0854 


O 


80,857 
72,800 
85,000 
92,400 


$6,695 
6.662 
7.583 
7,888 



Type. 



American. . . . , 

Atlantic 

Pacific 

Ten wheel . . . , 
Consolidation 



W'ght 



102,000 
187,200 
227,000 
156,000 
192,460 



Price 



S9,410 
15.750 
15,830 
13,690 
14,500 



Price 
per 
lb. 



S.092 
.083 
.070 
.088 
.075 



t/)COMOTIVES. 



1125 



The price per pound is figured from the weight of the engine in working 
order, without the tender. 

Depreciation of Locomotives. — (Baldwin Loco. Wks.) — It is suggested 
that for the first five years the full second-hand value of the locomotive 
(75% of first cost) be taken; for the second five years 85% of this value; 
for the third five years, 70%; after 15 years, 50% of the second-hand value; 
and after 20 years, and as long as the engine remains in use, 25% of the 
first cost. 

The Average Train Loads of 14 railroads increased from 229 tons of 
2000 lbs. in 1895 to 385 tons in 1904. On the Chicago, Milwaukee & St. 
Paul Ry. the average load increased from 152 tons in 1895 to 281 tons in 
1903, and on the Lake Shore & Michigan Southern Ry. from 318 tons in 
1895 to 615 tons in 1903. In the same time the average cost of transpor- 
tation per ton mile on the C, M. & St, P. Ry. decreased from 0.67 to 0.58 
cent; and on the L. S. & M. S. Ry. increased from 0.39 to 0.41 cent, the 
decrease in cost due to heavier train loads being offset by higher cost for 
labor and material. 

Tractive Force of Locomotives, 1893 and 1905. 

(Baldwin Loco. Wks.) 



Passenger, 1893. 


Weight 

on 
Driver. 


Trac- 
tive 
Force. 


Passenger, 1905. 


Weight 

on 
Driver. 


Trac- 
tive 
Force. 


American, single-ex. 

American, comp 

American, single-ex.. 
American, comp .. . . 
Ten- wheel type, com. 

Average 


75,210 
83,860 
64,560 
78,480 
93,850 


17,270 
12,900 
15,550 
14,050 
16,480 

15,250 


Atlantic, comp 

Atlantic, single-ex.. . 
Pacific, single-ex. . . . 
Pacific, single-ex. . . . 
Atlantic, single-ex. . . 


101,420 
103,600 
141,290 
114,890 
80,930 


22,180 
23,800 
29,910 
25.610 
21,740 

24,648 












Freight, 1893. 






Freight, 1905. 






Consolidation, comp. 
Ten-wheel, s'gle-ex.. 

Mogul, single-ex 

Decapod, compound 

Average . 


120,600 
101,000 
91,340 
172,000 


21,190 
23,310 
21,030 
35,580 

25.277 


Sante Fe type, comp. 
Consol., 2-cyl. comp.. 

Consol., single-ex 

Consol., single-ex. . .. 
Consol., single-ex 


234,580 
166,000 
151,490 
171,560 
165,770 


62,740 
40,200 
40,150 
44,080 
45,170 

46,468 













Waste of Fuel in Locomotives. — In American practice economy 
of fuel is necessarily sacrificed to obtain greater economy due to heavy 
train-loads. D. L. Barnes, in Eng. Mag., June, 1894, gives a diagram 
showing the reduction of efficiency of boilers due to high rates of com- 
bustion, from which the following figures are taken: 

Lbs. of coal per sq. ft. of grate per hour. ..12 40 80 120 160 200 
Per cent efficiency of boiler 80 75 67 59 51 43 

A rate of 12 lbs. is given as representing stationary-boiler practice, 40 
lbs. English locomotive practice, 120 lbs. average American, and 200 
lbs. maximum American, locomotive practice. 

Pages 473 and 475 of Henderson's "Locomotive Operation" give 
diagrams of evaporation per lb. of various kinds of coal for different 
rates of combustion per sq. ft. grate area and heating surface. 

Advantages of Compounding. — Report of a Committee of the 
American Railway Master Mechanics* Association on Compound Loco- 
motives {Am. Mach., July 3, 1890) gives the following summary of the 
advantages gained by compounding: (a) It has achieved a saving in the 
fuel burnt averaging 18% at reasonable boiler-pressures, with encourag- 
ing possibilities of further improvement in pressure and in fuel and water 
economy, (5) It has lessened the amount of water (dead weight) to be 



1126 LOCOMOTIVE So 

hauled, so that (c) the tender and its load are materially reduced In 
weight, (rf) It has increased the possibilities of speed far beyond 60 
miles per hour, without unduly straining the motion, frames, axles, oi 
axle-boxes of the engine, (e) It has increased the haulage-power at 
full speed, or, in other words, has increased the continuous H.P. devel- 
oped, per given weight of engine and boiler. (/) In some classes has 
increased the starting-power, (g) It has materially lessened the slide- 
valve friction per H.P. developed, (h) It has equalized or distributed 
the turning force on the crank-pin, over a longer portion of its path, 
which, of course, tends to lengthen the repair life of the engine, (i) In 
the two-cylinder type it has decreased the oil consumption, and has even 
done so in the Woolf four-cylinder engine, (j) Its smoother and steadier 
draught on the fire is favorable to the combustion of all kinds of soft 
coal; and the sparks thrown being smaller and less in number, it lessens 
the risk to property from destruction by fire, (k) These advantages 
and economies are gained without having to improve the man handling 
the engine, less being left to his discretion (or careless indifference) than 
in the simple engineo (I) Valve-motion, of every locomotive type, can 
be used in its best w^orking and most effective position, (m) A wider 
elasticity in locomotive design is permitted; as, if desired, side-rods can 
be dispensed with or articulated engines of 100 tons w^eight, with inde- 
pendent trucks, used for sharp curves on mountain service, as suggested 
by Mallet and Brunner. 

Of 27 compound locomotives in use on the Phila. and Reading Rail- 
road (in 1892), 12 are in use on heavy mountain grades, and are designed 
to be the equivalent of 22 X 24 in. simple consolidations; 10 are in some- 
what lighter service and correspond to 20 X 24 in. consolidations; o are 
in fast passenger service. The monthly coal record shows: 

Gain in Fuel 
Class of Engine. NOo Economy. 

Mountain locomotives o 12 25% to 30% 

Heavy freight service 10 12% to 17% 

Fast passenger , . , 5 9% to 11% 

(Report of Com. A. R. M. M. Assn. 1892.) For a description of the 
various types of compound locomotive, with discussion of their relative 
merits, see paper by A. Von Borries, of Germany, the Development of 
the Compound Locomotive, Trans, A. S. M. E., 1893, vol. xiv, p. 1172. 

As a rule compounds cost considerably more for repairs, and require 
a better class of engineers and machinists to obtain satisfactory results. 
(Henderson.) 

Balanced Compound liocomotivese — There are two high-pressure 
cylinders placed between the frames and two low-pressure cylinders 
outside. The inside crank shaft has cranks 90° apart, and each outside 
crank pin is 180° from the inside crank pin on the same side, so that the 
engine on each side is perfectly balanced. The balanced piston valve is 
so made that high-pressure steam may be admitted to the low-pressure 
cylinder for starting. See circular of the Baldwin Loco. Wks., No. 62, 1907. 

Superheating in Locomotives. (R. R. Age Gazette, Nov. 20, 1908.) — 
Superheating steam in locomotives has been found to effect a saving of 
10 to 15% in the fuel consumption of a locomotive, and 8 to 12% of the 
water used, or with the same fuel to increase the horse-power and the 
tractive force. The Baldwin Locomotive Works builds a superheater in 
the smoke-box, where it utilizes part of the heat of the waste gases in 
drying the steam and superheating it 50 to 100° F. The heating surface 
of the superheater is from 12 to 22% of the heating surface in the tubes and 
fire-box of the boiler. It is recommended to use a boiler pressure of about 
160 lbs. when a superheater is used, and to have cylinders of larger dimen- 
sions than when ordinary steam of 200 lbs. pressure is used. For an illus- 
trated and historical description of the use of superheating in locomotives, 
see paper by H. H. Vaughan, read before the Am. Ry. Mast. Mechs.' Assn., 
Eng. News, June 22, 1905. 

Counterbalancing Locomotives. — Rules for counterbalancing, 
adopted by different locomotive-builders, are quoted in a paper by Prof. 
Lanza (Trans. A. S. M. E., x, 302.) See also articles on Counterbalan- 
cing Locomotives, in R. R. & Eng. Jour., March and April, 1890; Trans. 
A. S, M, E„ vol. xvi, 305; and Trans. Am. Ry. Master Mechanics' Assn., 



LOCOMOTIVES. 1127 

1897. W. E. Dalby's book on the "Balancing of Engines" (Longmans, 
Green & Co., 1902) contains a very full discussion of this subject. See 
also Henderson's "Locomotive Operation" {The Railway Age, 1904). 

Narrow-gauge Railways in Manufacturing Works. — A tramway 
of 18 inches gauge, several miles in length, is in the works of the Lan- 
cashire and Yorkshire Railway. Curves of 13 feet radius are used. 
The locomotives used have the following dimensions (Proc. Inst. M, E.. 
July, 1888): The cylinders are 5 in. in diameter with 6 in. stroke, and 
2 ft. 31/4 in. centre to centre. Wheels 16i/4in. diameter, the wheel-base 
2 ft. 9 in.; the frame 7 ft. 41/4 in. long, and the extreme width of the 
engine 3 feet. Boiler, of steel, 2 ft. 3 in. outside diam. and 2 ft. long 
between tube-plates, containing 55 tubes of I3/3 in. outside diam.: fire- 
box, of iron and cylindrical, 2 ft. 3 in. long and 17 in. inside diam. Heat- 
ing-surface 10.42 SQ. ft. in the fire-box and 36.12 in the tubes, total 46.54 
sq. ft.; grate-area, 1.78 sq. ft.; capacity of tank, 26V2 gallons; working- 
pressure, 170 lbs, per sq. in. tractive power, say, 1412 lbs., or 9.22 lbs. per 
lb. of effective pressure per sq. in., on the piston. Weight, empty, 2.80 
tons; full and in working order, 3.19 tons. 

For description of a system of narrow-gauge raihvays for manufac* 
tories, see circular of the C. W. Hunt Co., New Yorko 

Light Locomotives. — For dimensions of light locomotives used for 
mining, etc., and for much valuable information concerning them, see 
catalogue of H. K. Porter Co., Pittsburgh. 

Petroleum-burning Locomotivese (From Clark's Steam-engine.) — 
The combustion of petroleum refuse in locomotives has been success- 
fully practised by Mr. Thos. Urquhart, on the Grazi and Tsaritsin Rail- 
way, Southeast Russia. Since November, 1884, the whole stock of 143 
locomotives under his superintendence has been fired with petroleum 
refuse. The oil is injected from a nozzle through a tubular opening in 
the back of the fire-box, by means of a jet of steam, with an induced 
current of air. 

A brickwork cavity or "regenerative or accumulative combustions- 
chamber" is formed m the fire-box, into which the combined current 
breaks as spray against the rugged brickwork slope. In this arrange- 
ment the brickwork is maintained at a white heat, and combustion is 
complete and smokeless. The form, mass, and dimensions of the brick- 
work are the most important elements in such a combination. 

Compressed air was tried instead of steam for injection, but no appre- 
ciable reduction in consumption of fuel was noticed. 

The heating-power of petroleum refuse is given as 19,832 heat-units, 
equivalent to the evaporation of 20.53 lbs. of w^ater from and at 212° F., 
or to 17.1 lbs. at 8 1/2 atmospheres, or 125 lbs. per sq. in., effective pres- 
sure. The highest evaporative duty was 14 lbs. of water under 8 1/2 
atmospheres per lb. of the fuel, or nearly 82% efficiency. 

There is no probability of any extensive use of petroleum as fuel for 
locomotives in the United States, on account of the unlimited supply of 
coal and the comparatively limited supply of petroleum. Texas and 
California oils are now (1902) used in locomotives of the Southern Pacific 
Railway and the Santa Fe System. 

Self-propelled Railway Cars. — The use of single railway cars con- 
taining a steam or gasolene motor has become quite common in Europe. 
For a description of different svstems see a paper on European Railway 
Motor Cars by B. D. Gray in Trans A. S. M. E., 1907. 

Fireless Locomotive. — The principle of the Francq locomotive is 
that it depends for the supply of steam on its spontaneous generation 
from a body of heated water in a reservoir. As steam is generated and 
drawn off the pressure falls; but by providing a sufficiently large volume 
of water heated to a high temperature, at a pressure correspondingly 
high, a margin of surplus pressure may be secured, and means may thus; 
be provided for supplying the required quantity of steam for the trip. 

The fireless locomotive designed for the service of the Metropohtan 
Railway of Paris has a cylindrical reservoir having segmental ends, 
about 5 ft. 7 in. in diameter, 261/4 ft. in length, with a capacity of about 
620 cubic feet. Four-fifths of the capacity is occupied by water, which 
Is heated by the aid of a powerful jet of steam supplied from stationary 
boilers. The water is heated until equilibrium is established between 
the boilers and the reservoir. The temperature is raised to about 390° F., 
corresponding to 225 lbs. per sq. in. The steam from the reservoir is 



1128 



IsOCOMOTIVES. 



passed through a reducing-valve, by which the steam is reduced to the 
required pressure. It is then passed through a tubular superheater 
situated within the receiver at the upper part, and thence through the 
ordinary regulator to the cylinders. The exhaust-steam is expanded to 
a low pressure, in order to obviate noise of escape. In certain cases the 
exhaust-steam is condensed in closed vessels, which are only in part 
filled with water. 

In working off the steam from a pressure of 225 lbs. to 67 lbs., 530 
cubic feet of water at 390° F. is sufficient for the traction of the trains, 
for working the circulating-pump for the condensers, for the brakes, 
and for electric-lighting of the train. At the stations the locomotive 
takes from 2200 to 3300 lbs. of steam — nearly the same as the weight 
of steam consumed during the run betv/een two consecutive charging 
stations. There is 210 cubic feet of condensing water. Taking the 
initial temperature at 60° F., the temperature rises to about 180° F. 
after the longest runs underground. 

The locomotive has ten wheels, on a base 24 ft long, of which six are 
coupled, 41/2 ft. in diameter. The extreme wheels are on radial axles. 
The cylinders are 231/2 in. in diameter, with a stroke of 231/2 in. 

The engine weighs, in working order, 53 tons, of which 36 tons are on 
the coupled wheels. The speed varies from 15 miles to 25 miles per hour. 
The trains weigh about 140 tons. 

Compressed-air Locomotives. — A compressed-air locomotive con- 
sists essentially of a storage tank mounted upon driving v/heels, with two 
engines similar to those of a steam locomotive. One or more reservoirs or 
storage tanks are located on the line, from which the locomotive tank is 
charged. These reservoirs are usually riveted steel cylinders, designed 
for about 1000 lbs. working pressure; but sometimes seamless steel cylinders 
of small diameter, designed for a working pressure of 2000 lbs. or upwards, 
are used. The customary maximum pressure in the locomotive tank is 
800 lbs. gauge, and the working pressure in the cylinders is from 130 to 
140 lbs. The following table is condensed from one in a circular of the 
Baldwin Locomotive Works, No. 46, 1904. 

See account of the Mekarski compressed-air locomotives, page 652 ante. 

Dimensions and Tractive Power of Four Coupled Compressed- Am 
Locomotives Having Two Storage Tanks. 



Class. . 



Cylinders, inches 

Diam. of drivers, c . 

Wheel base 

Approx. weight, lbs.. 

Inside dia. of tanks. . 

Aggregate tank vol., 
cu. ft 

App. height 

App. width over 
tanks 

App. width over cyl- 
inders 

App. length over 
bumpers 

gt^Full stroke. 

•^ I 3/4 Stroke cut-off 

rt o V2 Stroke cut-off 

^^ 1/4 Stroke cut-off 



4-4-C 


4-6^ 


4-8-C 


4-10-C 


4-12-C 


4-16-C 


5X10 

2r 

4' 0^' 

10,000 

26'' 


6X10 

zr 

4' 3" 

14,000 

28^' 


7X12 

24" 

4' 5" 

18,000 

30" 


8X14 
26" 

5, y, 

23,000 
32" 


9X14 

28" 
5, Y 

27,000 

34" 


11X14 

28" 
5' 6" 
37,000 

38" 


73 

4/ y 


100 
4' 10" 


130 
5' 0" 


170 
5' 4" 


200 
5' 8" 


280 
6' 0" 


4' lO** 
Gauge 

+2r 


Gauge 
+ 26" 


y 6" 

Gauge 
+ 27" 


5' 10'' 


6' Y 

Gauge 
+30" 


7 0'' 


12' 0'' 
1350 
1290 
940 
510 


14' 0" 
1785 
1700 
1240 
670 


15' 0" 

2915 
2780 
2025 
1100 


17' 0" 

4100 
3900 
2840 
1540 


18' 0" 
4820 
4580 
3345 
1815 


20' 0" 
7200 
6860 
4995 
2710 



12X16 

30" 

6' 0" 

44,000 

40" 

320 
6' A" 

7 4* 

Gauge 

+33' 

20' b" 
9140 
8705 
6340 
3440 



Draw-bar pull on any grade = tractive power - (.0075 + % of grade) 
X weight of engine. 



COMPEESSED-AIR LOCOMOTIVES. 



1129 



Cubic Feet of Air, at Different Storage Pressures, Required to 
Haul One Ton One Mile at Half Stroke Cut-off, with 20, 30 
AND 40 LBS. Frictional RESISTANCE PER ToN. (Baldwin Loco. Wks.) 



Storage pressure 

Cylinder working 

pressure 



Grade. 



Level 

1/2% 

1% 

2% 

3% 

4% 

5% 



R 



20.0 
31.2 

42.4 
64.8 
87.2 
109.6 
132.0 



600 
130 



1.16 
1.81 
2.47 
3.78 
5.08 
6.39 
7.69 



700 800 

135 140 



V V 



0.99 
1.56 
2.12 
3.24 
4.35 
5.48 
6.60 



0.87 
1.36 
1.85 
2.83 
3.81 
4.79 
5.77 



30.0 
41.2 
52.4 
74.8 
97.2 
119.6 
142.0 



800 
140 



V V V 



1.74 
2.40 
3.05 
4.35 
5.67 
6.97 
8.27 



1.50 
2.05 
2.61 
3.73 
4.86 
5.97 
7.09 



1.31 
1 79 

2.28 
3.26 
4.25 
5.22 
6.20 



600 
130 



700 
135 



800 
140 



40.0 
51.2 
62.4 
84.8 
107.2 
129.6 
152.0 



V V V 



2.33 

2.98 
3.64 
4.94 
6.25 
7.56 
8.86 



1.99 

2.56 
3.11 
4.24 
5.35 
6.47 
7.60 



1.74 

2.23 
2.73 
3.70 
4.69 
5.67 
6.64 



R= resistance per ton of 2240 lbs. in pounds. V = cubic feet of air. 

Air Locomotives with Compound Cylinders and Atmospheric Interheaters 
are built by H. K. Porter Co. The air enters the high-pressure cylinder 
at 250 lbs. gauge pressure and is expanded down to 50 lbs., overcoming 
resistance, while the temperature drops about 140° F. This loss of heat 
is practically all restored in the atmospheric interheater, which is a 
cylindrical reservoir filled with brass tubes located in the passage-way 
from the high- to the low-pressure cylinder. The air enters the low- 
pressure cylinder at 50 lbs. gauge and a temperature within 10 or 20° of 
that of the surrounding atmosphere. The exhaust is used to induce a 
draught of atmospheric air through the tubes of the interheater. This 
combination permits of expanding the air from 250 lbs. down to atmos- 
phere without unmanageable refrigeration. 

The following calculation shows the relative economy of a single- cylinder 
locomotive using air at 150 lbs. and of a compound using air at 250 lbs. 
in the high-pressure and 50 lbs. in the low-pressure cylinder, non-expan- 
sive working being assumed in both cases. 

11.2 cu. ft. of free air at 150 lbs. gauge and atmospheric temperature 
would till a cylinder of 1 cu. ft. capacity, and in moving a piston of 1 sq. 
ft. area one foot would develop 144 X 150 = 21,600 ft. lbs. of energy. 

11.2 cu. ft. of free air at 250 lbs. gauge if used in a cylinder 0.623 sq. ft. 
area and 1 it. stroke would develop 0.623 X 144 X 250= 22,425 ft lbs. 

If expanded in two cylinders with a ratio of 4 to 1 the energy developed 
would be 0.623 X 144 X 200 plus 4 X 0.623 X 144 X 50 = 35,880 ft. lbs., if 
the heat is restored between the two cylinders. Gain by compounding 
with interheating, over simple cylinders with 150 lbs. initial pressure, 
35,880 -r- 21,600 = 1.66. 

^ These results are about the best that can be obtained with either 
simple or compound locomotives, as any improvement due to expansive 
working just about balances the losses due to clearance and initial refrig- 
eration. The work done per cubic foot of free air in the two svstems is: 
with simple cylinders, 21,600^ 11.2 = 1840 ft. lbs.; with compound 
cylinders and atmospheric interheater, 35,880 -^ 11.2 = 3205 ft. lbs. 

The above calculations have been practically confirmed by actual 
tests, which show 1900 ft. lbs. of work per cubic foot of free air with the 
simple locomotive and 3000 ft. lbs. with the compound, the gain due to 
expansive working and the losses due to internal friction being some- 
what greater in the compound than in the simple machine. 

In the operation of compressed-air locomotives the air compressor is 
generally delivering compressed air at a pressure fluctuating between 
800 and 1000 lbs. per sq. in. into the storage reservoir, and it requires an 
average of about 12,000 ft. lbs. per cubic foot of free air to compress and 
deliver it at these pressures. The efficiency of the two systems then is: 
1900 H- 12000 = 16% for the simple locomotive, and 3000 ■*• 12000 =» 
^5% for the compound with atmospheric interheater. 



1130 SHAFTING. 



SHAFTING. 

(See also Torsional Strength; also Shafts of Steam Engines.) 
For shafts subjected to torsion only, let d = diam. of the shaft in ins., 
P = a force in lbs. appUed on a lever arm at a distance = a ins. from 
the axis, *S = shearing resistance at the outer fiber, in lbs. per sq. in., then 



Pa==-^ = — = 0.1963 d^S; d= y/ — ^ = y/ 



Pa 
K' 



It R = revolutions per minute, then the horse-power transmitted 
Pa 2 TtR Tid^S X2 7:R RSd^ . 



H.P. = 



33,000X12 16X33,000X12 321,000' 



,^^32M»0H^^^ 



CXH.P. 



R 



In practice, empirical values are ^ven to S and to the coefficients 
K = 5.1/5 and C = 321,000/*S, according to the factor of safety assumed, 
depending on the material, on whether the shaft is subjected to steady, 
fluctuating, bending, or reversed strains, on the distance between bear- 
ings, etc. Kimball and Barr (Macliine Design) state that the following 
factors of safety are indicated by successful practice: For head shafts, 
15; for line shafts carrying pulleys, 10; for small short shafts, counter- 
shafts, etc., 7. For steel shafting the allowable stress, *S, for the above 
factors would be about 4000, 6000 and 8500 lbs. respectively, whence 



for head shafts d= J ^^ ^'^' ; for line shafts c?= y ^^"^' ; for short 



shafts d 



7 38 H.P. 

V R 



Jones & Laughlin Steel Co. gives the following for steel shafts: 

Turned. Cold-rolled. 

For simply transmitting power) 

and short countershafts, bear- [ H.P. = d^R -^ 50 H.P = d^R -^ 40 

ings not more than 8 ft. apart ) 

As second movers, or line shafts, ) TT -p wsp • on u t> wsp • ^n 

bearings 8 ft. apart '}H.P. = d3i2^ 90 U.F. = dm -^ 70 

As prime movers or head shafts! 

carrying mairi driving puUey 1 p p =#/?.- 125 H P = d^ -- 100 
or gear, well supported byf^-^* a /t . i jo t±.f.-ati . luu 
bearings J 

Jones & Laughlins give the following notes: Receiving and transmit- 
ting pulleys should always be placed as close to bearings as possible; 
and it is good practice to frame short "headers" between the main tie- 
beams of a mill so as to support the maiii receivers, carried by the head 
shafts, with a bearing close to each side as is contemplated in the for- 
mulae. But if it is preferred, or necessary, for the shaft to span the full 
width of the "bay" without intermediate bearings, or for the pullcv to 
be placed away from the bearings towards or at the middle of the bay, 
the size of the shaft must be largely increased to secure the stiffness 
necessary to support the load without undue deflection. 

Diameter of shaft D to carry load at center of bays from 2 to 12 ft. 

span, D = W- d\ in which d is the diameter derived from the formula 

for head shafts, c = length of bay in inches, and Ci = distance in inches 
between centers of bearings in accordance with the formula for horse- 



SHAFTING. 



1131 



power of head shafts. (Jones & Laughlin Steel Co.) 
different diameters d are as follows: 



Values of Ci for 



d Ci 


d c, 


d c. 


d 


Ci 


d c 


d c 


ltd 3/8 15 


213/16 25 


315/16 & 4 37 


5 1/4 & 5 3/8 


55 


63/8 71 


73/8 88 


UVl6& 13/4 16 


27/8 to 3 26 


43/16 40 


51/2 


57 


61/2 73 


71/2 91 


113/16 & 17/8 17 


31/8 to 31/4 28 


41/4 41 


55/8 


59 


65/8 75 


75/8 93 


115/16 to 21/8 18 


33/8 30 


47/16 & 41/2 44 


53/4 


61 


63/4 77 


73/4 96 


23/16 & 21/4 19 


3 7/16 & 31/2 31 


43/4 47 


57/8 


63 


67/8 79 


77/8 99 


25/16 to 27/16 20 


39/16 & 35/8 33 


413/16 49 


6 


65 


7 81 


8 101 


21/2 to 25/8 24 


311/16 & 33/4 34 


5 51 


61/8 


67 


71/8 84 


81/2 112 


211/16 & 23/4 22 


37/8 36 


51/8 52 


61/4 


69 


71/4 86 


9 123 



Should the load be applied near one end of the span or bay instead of 
at the center, multiply the fourth power of the diameter of the shaft 
required to carry the load at the center of the span or bay by the prod- 
uct of the two parts of the shaft when the load is near one end, and 
divide this product by the product of the two parts of the shaft when 
the load is carried at the center. The fourth root of this quotient will 
be the diameter required. 

The shaft in a hue which carries a receiving-puUey, or which carries a 
transmitting-puUey to drive another Une, should always be considered a 
head-shaft, and should be of the size given by the rules for shafts carrying 
main pulleys or gears. 

The greatest admissible distance between bearings of shafts subject to 
no tran sverse strain e xcept from their own weight is f or cold-rolled shafts, 

L = ^330,608 X £>^ and for turned shafts, L = -sj/ 319,586 X D^. D = 
diam. and L = length of shaft, in inches. These formulae are based on 
an allowable deflection at the center of Vso in. per foot of length, weight 
of steel 490 lbs. per cu. ft., and modulus of elasticity = 29,000,000 for 
turned and 30,000,000 for cold-rolled shafting. [In deriving these formulae 
the weight of the shaft has been taken as a concentrated instead of a dis- 
tributed load, giving additional safety.] 

Kimball and Barr say that the lateral deflection of a shaft should not 
exceed 0.01 in. per foot of length, to insure proper contact at the bear- 
ings. For ordinary small shafting they give_the following as the allow- 
able distance between the hangers: L = 7 ^d^, for shaft without pulleys; 
L = 5 ^1 d^, for shaft carrjing pulleys. (L in ft., d in ins.) 

Deflection of Shafting. (Pencoyd Iron Works.) — For continuous 
line-shafting it is considered good practice to hmit the deflection to a 
maximum of i/ioo of an inch per foot of length. The weight of bare shaft- 
ing in pounds = 2.6 d'^L = W , or when as fully loaded with pulleys as is 
customary in practice, and allowing 40 lbs. per inch of width for the 
vertical pull of the belts, experience shows the load in pounds to be about 
13 d^L = W. Taking the modulus of transverse elasticity at 26,000,000 
lbs., we derive from authoritative formulae the following: 



L = -^873 d2, d = ^L3/873, for bare shafting; 

L = -N^ 175 d^, d = VL3/175, for shafting carrying pulleys, etc., 

L being the maximum distance in feet between bearings for continuous 
shafting subjected to bending stress alone, d = diam. in inches. 

The torsional stress is inversely proportional to the velocity of rota- 
tion, while the bending stress will not be reduced in the same ratio. It 
is therefore impossible to write a formula covering the whole problem 
and sufficiently simple for practical application, but the following rules 
are correct within the range of velocities usual in practice. 

For continuous shafting so proportioned as to deflect not more than 



1132 



SHAFTING. 



Vioo of an inch per foot of length, allowance being made for the weaken- 
ing effect of key-seats, 

d = -^50 H.P. -7- R, L = ^720l^, for bare shafts; 

d = ^70 H.P. -i- R, L = 'Nyi40 d^, for shafts carrying pulleys, etc. 

d = diam. in inches, L = length in feet, R = revs, per min. 

The following are given by J. B. Francis as the greatest admissible dis- 
tances between the bearings of continuous steel shafts subject to no trans- 
verse strain except from their own weight, as would be the case were the 
power given off from the shaft equal on all sides, and at an equal distance 
from the hanger-bearings. 

Diam. of shaft, in. ... 23456789 
Dist. bet. bearings, ft. 15.9 18.2 20.0 21.6 22.9 24.1 25.2 26.2 

These conditions, however, do not usually obtain in the transmission of 
power by belts and pulleys, and the' varying circumstances of each case 
render it impracticable to give any rule which would be of value for 
universal appUcation. 

For example, the theoretical requirements would demand that the 
bearings be nearer together on those sections of shafting where most 
power is delivered from the shaft, while considerations as to the location 
and desired contiguity of the driven machines may render it impracti- 
cable to separate the driving-pulleys by the intervention of a hanger at 
the theoretically required location. (Joshua Rose.) 

Horse-Power Transmitted by Cold-rolled Steel Shafting at Different 
Speeds as Prime Movers or Head Shafts Carrying 3Iain Driving 
Pulley or Gear, vv^ell Supported by Bearings. 

Formula H.P. = d^R -^ 100. 



Revolutions per minute. 


Revolutions per minute. 


Diam. 


100 


200 


300 


400 


500 


Diam. 


100 


200 


300 


400 


500 


IV2 


3.4 


6.7 


10.1 


13.5 


16.9 


27/8 


24 


48 


72 


95 


119 


19/16 


3.8 


7.6 


11.4 


15.2 


19.0 


215/16 


25 


51 


76 


101 


127 


»5/8 


4.3 


8.6 


12.8 


17.1 


21 


3 


27 


54 


81 


108 


135 


1 11/16 


4.8 


9.6 


14.4 


19.2 


24 


31/8 


31 


61 


91 


122 


152 


13/4 


5.4 


10.7 


16.1 


21 


27 


33/16 


32 


65 


97 


129 


162 


1 13/16 


5.9 


11.9 


17.8 


24 


30 


31/4 


34 


69 


103 


137 


172 


17/8 


6.6 


13.1 


19.7 


26 


33 


33/8 


38 


77 


115 


154 


192 


1 15/16 


7.3 


14.5 


22 


29 


36 


37/16 


41 


81 


122 


162 


203 


2 


8.0 


16.0 


24 


32 


40 


31/2 


43 


86 


128 


171 


214 


2Vl6 


8.8 


17.6 


26 


35 


44 


39/16 


45 


90 


136 


180 


226 


21/8 


9.6 


19.2 


29 


38 


48 


35/8 


48 


95 


143 


190 


238 


23/16 


10.5 


21 


31 


42 


52 


311/16 


50 


100 


150 


200 


251 


21/4 


11.4 


23 


34 


45 


57 


33/4 


55 


105 


158 


211 


264 


25/16 


12.4 


25 


37 


49 


62 


37/8 


58 


116 


174 


233 


291 


23/8 


13.4 


27 


40 


54 


67 


315/16 


61 


122 


183 


244 


305 


27/16 


14.5 


29 


43 


58 


72 


4 


64 


128 


192 


256 


320 


21/2 


15.6 


31 


47 


62 


78 


43/16 


74 


147 


221 


294 


367 


29/16 


16.8 


34 


50 


67 


84 


41/4 


77 


154 


230 


307 


383 


25/8 


18.1 


36 


54 


72 


90 


47/16 


88 


175 


263 


350 


438 


211/16 


19.4 


39 


58 


77 


97 


41/2 


91 


182 


273 


365 


456 


23/4 


21 


41 


62 


83 


104 


43/4 


107 


214 


322 


429 


537 


213/16 


22 


44 


67 


89 


111 


5 


125 


250 


375 


500 


625 



For H.P. transmitted by turned steel shafts, as prime movers, etc., 
multiply the figures by 0.8. 

For shafts, as second movers or line shafts, ) 
bearings 8 ft. apart, multiply by ) 

For simply transmitting power, short counter- 
shafts, etc., bearings not over 8 ft. apart, multi- 
ply by 2 2.50 



Cold-rolled Turned 
1.43 1.11 



SHAFTING. 



1133 



The horse-power is directly proportional to the number of revolutions 
per minute. 

Speed of Shafting. — Machine shops 120 to 240 

Wood-working 250 to 300 

Cotton and woollen mills . . 300 to 400 

Flange Couplings. — The bolts should be designed so that theii 
combined resistance to a torsional moment around the axis of the shaft 
is at least as great as the torsional strength of the shaft itself; and the 
bolts should be accurately fitted so as to distribute the load evenly 
among them. Let D = diam. of the shaft, d = diam. of the bolts, 
r = radius of bolt circle, in inches, n = number of bolts, S = allowab le shear - 
ing stress per sq. in., then 7rd3^-r-16 = i/4 Tzd^rS, whence d= 0.5 '^D^/inr)- 
Kimball and Barr give n = 3 +D/2, but this number may be modified for 
convenience in spacing, etc. 

Effect of Cold Rolling. — Experiments by Prof. R. H. Thurston in 
1902 on hot-rolled and cold-rolled steel bars (Catalogue of Jones & 
LaughUn Steel Co.) showed that the cold-rolled steel in tension had its 
elastic limit increased 15 to 97%; tensile strength increased 20 to 45%; 
ductility decreased 40 to 69%. In transverse tests the resistance in- 
creased 11 to 30% at the elastic Hmit and 13 to 69 7o at the yield point. 
In torsion the resistance at the yield point increased 31 to 64%, and at 
the point of fracture it decreased 4 to 10%. The angle of torsion at 
the, elastic Umit increased 59 to 103%, while the ultimate angle de- 
creased 19 to 28%. Bars turned from 13/4 in. diam. to various sizes 
down to 0.35 in. showed that the change in quality produced by cold 
roUing extended to the center of the bar. The maximum strength of 
the cold-rolled bar of full size was 82,200 lbs. per sq. in., and that of the 
smallest bar 73,600 lbs. In the hot-rolled steel bars the maximum 
strength of the full-sized bar was 62,900 lbs. and that of the smallest bar 
58,600 lbs. per sq. in. 

Hollow Shafts. — Let d be the diameter of a solid shaft, and dxd2 the 
external and internal diameters of a hollow shaft of the same material. 

Then the shafts will be of equal torsional strength when d^ = -^—-z • 

A 10-inch hollow shaft with internal diameter of 4 inches will weigh 16% 
less than a soUd 10-inch shaft, but its strength will be only 2.56% less. 
If the hole were increased to 5 inches diameter the weight would be 
25% less than that of the solid shaft, and the strength 6.25% less. 

Table for Laying Out Shafting, — The table on the next page 
(from the Stevens Indicator, April, 1892) is used by Wm. Sellers & Co. to 
facilitate the laying out of shafting. 

The wood-cuts at the head of this table show the position of the hangers 
and position of couplings, either for the case of extension in both direc- 
tions from a central head-shaft or extension in one direction from that 
head -shaft. 

Sizes of Collars for Shafting, Wm. Sellers & Co., Am. Mach. Jan. 28, 
1897. — D, diam. of collar; T, thickness; d, diam. of set screw; I, length. 
All in inches. 

Loose Collars. 



Shaft 


D 


T 


d 


I 


Shaft 


D 


T 


d 


I 


Shaft 


D 


t 

17/8 


d 

3/4 


I 


1 


13/4 


3/4 


7/16 


5/16 


21/4 


33/8 


13/16 


5/8 


5/8 


4 


513/16 




11/4 


17/8 


13/16 


7/16 


3/8 


21/2 


3 3/4 


11/4 


5/8 


11/16 


41/2 


67/16 


17/8 


3/4 




IV-;! 


21/4 


iVifi 


7/16 


7/16 


23/4 


4 


15/16 


5/8 


11/16 


5 


615/16 


17/8 


3/4 




15/8 


25/8 




7/16 


7/16 


3 


41/:^ 


17/16 


5/8 


13/16 


i'l/2 


^1/2 


2 


3/4 




13/4 


23/4 


11/16 


1/2 


9/1 6 


31/4 


47/8 


15/8 


3/4 


13/16 


6 


8 


2 


3/4 




2 


3 


11/8 


5/8 


9/16 


31/2 


!>3/l6 


13/4 


3/4 


15/16 












Fast Collars. 


Shaft 


D 


T 


Shaft 


D 


T 


Shaft 


D 


T 


Shaft 


D 


T 


u/?, 


2 


1/2 


21/2 


31/4 


9/16 


31/2 


45/8 


7/8 


51/2 


75/8 


13/16 


13/4 


21/4 


^h. 


23/4 


35/8 


5/8 


4 


!>3/8 


IW16 


6 


81/4 


11/4 


2 


25/8 


1/?, 


3 


4 • 


11/16 


41/2 


6 


1 


61/2 


9 


13/8 


21/4 


3 


i)/l6 


31/4 


41/4 


11/16 


5 7 1 1 1/8 1 


7 93/4 


11/2 



1134 



SHAFTING. 



sui 'xog JO 'Sui 




•ja^ainBiQ 1$: '" ^ ^ - 



H ^ »H CO ■> 



N M 00 00^^ 



saqoui 



1 »f3 ■r-l tH ^ CC CO 

'—*—'— — — '— — — CMCN r<i (Nj fs 



8 6.^^;:? 

c .5 u c rt '^ 



1 (U.S 



s":;; 



TOO ,C * 

"1 (U ♦^ I/) ■ * 



o c^ 



bj: - S ^ '^^ 

DC . c-a 
^ t„ D c a> 






D-o <U 43 s i«!«i 
'-'^ N ii 5 c a 






— — — — — — (N«Sfsi 



iM M c^ es 



t<^f<N"^"^mvOt^oo 



c^ e^ e^ M c<i 






o\o — — r^ 



aoovov 






rt 1; P =:v- ; 
= -5 c (« rt 






?5 a-^ «2 






^ ^ ^ '^-^-5!-5?ira~ 00^^ 00 N {vj •* 



h — breadth of arm at hub. 



PULLEYS. 1135 

PULLEYS. 

Proportions of Pulleys. (See also Fly-wheels, page 1049.) — Let 
n = number of arms, D = diameter of pulley, *S = thickness of belt, 
t = thickness of rim at edge, 2' = thickness in middle, B = width of rim, 
fi = width of belt, h = breadth of arm at hub, hi = breadth of. arm at 
rim, e = thickness of arm at hub, ei = thickness of arm at rim, c = 
amount of crowning; dimensions in inches. 

Unwin. Reuleaux. 

B = width of rim 9/8 (/? + .4) 9/8 /5 to 5/4 ^ 

t = thickness at edge of rim .7 S + .005 D | ^yfhto^iUh^'^ 

T «= thickness at middle of rim ... 2t-\- c 

For single . /bd 

belts = 0.6337V IT ^ r. 

For double , VbD ^^^^' "^ 4 "^ 20 n 
belts = 0.798 V "^ 

hi = breadth of arm at rim Vsh .Sh 

e = tliickness of arm at hub Ah 0.5/i 

ci =» thickness of arm at rim OAhi 0.5 /ii 

n = number of arms, for a single set 3 + ^tq 1/2(5+ ^-^ j 

{B for sin.-arm 
pulleys. 
2 B for double- 
arm pulleys. 

M — thickness of metal in hub hio^Uh 

c = crowning of pulley V24 B 

The number of arms is really arbitrary, and may be altered if necessary, 
(Unwin.) 

Pulleys with two or three sets of arms may be considered as two or three 
separate pulleys combined in one, except that the proportions of the arms 
should be .8 or .7 that of single-arm pulleys. (Reuleaux.) 

Example. — Dimensions of a pulley 60 in. diam., 16 in. face, for double 
belt 1/2 in. thick. 

Solution by n h hi e ei t T L M c 

Unwin 9 3.79 2.53 1.52 1.01 0.65 1.97 10.7 3.8 0.67 

Reuleaux 4 5.0 4.0 2.5 2.0 1.25 16 5 

The following proportions are given in an article in the Amer. Machinist 
authority not stated: 

/i = .0625 D + .5 in., ?m - .04 D + .3125 in., e = .025 D + .2 
In., ei = .016 D + .125 in. 

These give for the above example: h = 4.25 in., hi =» 2.71 in., c = 
1 .7 in., ei = 1 .09 in. The section of the arms in all cases is taken as 
elliptical. 

The following solution for breadth of arm is proposed by the author: 
Assume a belt pull of 45 lbs. per inch of width of a single belt, that the 
whole strain is taken in equal proportions on one-half of the arms, and that 
the arm is a beam loaded at one end and fixed at the other. We have 
the formula for a beam of elliptical section /P = .0982 Rbd"^ ^l, in which 
P = the load, R = the modulus of rupture of the cast iron, b = breadth, 
d — depth, and I = lene:th of the beam, and / = factor of safety. Assume 
a modulus of rupture of 36,000 lbs., a factor of safety of 10, and an addi- 
tional allowance for safety in taking I = 1/2 the diameter of the pulley 
instead of 1/2 D less the radius of the hub. 

Take d = h, the breadth of the arm at the hub, and h = e ^ Ah 
the thickness. We then have/P - 10 X -^^^ = 900 - = 3535X0.4/^3 ^ 
'' 71 H- 2 n 1/2 Z> 

^/ 900 BD ^1 BD 
whence ^ = i/ ~oF^ — = 0.6331/ , which is practically the same as 

the value reached by Unwin from a different set of assumptions. 



1136 



PULLEYS. 



Relation of Belt Width to Pulley Face. (Am. Mach., Feb. 11, 
1915.) — Carl G. Barth recommends that the relation between the face 
of the pulley and the belt be expressed by the formula F = 1 s/ig B + 3/8 
in., in which F and B are the widths respectively of the pulley face 
and belt, both in inches. If the limits of design make it impractical 
to use the dimension given by the equation, the following equation 
may be substituted: F = \ 3/32 B + 3/i6 in. 

Convexity of Pulleys. — Authorities differ. Morin gives a rise equal 
to 1/10 of the face; IMolesworth, 1/24; others from i/g to i/ge- Scott A. 
Smith says the crown should not be over i/g inch for a 24-inch face. 
Pulleys for shifting belts should be " straight," that is, without crowning. 
Mr. Barth uses the formula H = 0.03125 F ^1^, in which H is the height 
of crown and F the width of face in inches. 

CONE OR STEP PULLEYS. 

To find the diameters for the several steps of a pair of cone-pulleys: 

1. Crossed Belts. — Let D and d be the diameters of two pulleys 
connected by a crossed belt, L = the distance between their centers, 
and ^ = the angle either half of the belt makes with a line joining the 

centers of the pulleys: then total length of belt ={D+d) ~ -h {D + d) ^. 

2, lo u 

+ 2 L cos /?. /? =^ angle whose sine is ■ . L Cos /?= J V- - f — ^ — ) • 

The length of the belt is constant when D + c? is constant; that is, in a 
pair of step-pulleys the belt tension will be uniform when the sum of the 
diameters of each opposite pair of steps is constant. Crossed belts are 
seldom used for cone-pulleys, on account of the friction between the 
rubbing parts of the belt. 

To design a pair of tapering speed-cones, so that the belt may fit 
equally tight in all positions: When the belt is crossed, use a pair of equal 
and similar cones tapering opposite ways. 

2. Open Belts. — When the belt is uncrossed, use a pair of equal 
and similar conoids tapering opposite ways, and bulging in the middle, 
according to the following formula: Let L denote the distance between 
the axes of the conoids; R the radius of the larger end of each; r the radius 
of the smaller end; then the radius in the middle, ro, is found as follows: 

ro == —^r- + ^ og r • (Rankme.) 



2 ' 6.28Z/ 

If Do = the diameter of equal steps of a pair of cone-pulleys 
d = the diameters of unequal opposite steps, and L 

D+ d , (D - d)'^ 
the axes, Do = -^ + 1^5^67/ 

If a series of differences of radii of the steps, R 

lor each pair of step^— 7; — = ro , and the radii of each may 

be computed from their half sum and half difference, as follows: 



D and 
distance betv/een 



r, be assumed, then 



R = 



R + 



R - r 



• ; ^ 



R+ r _ R - r 
2 2 



2 

A. J. Frith (Trans. A. S. M. E., x, 298) shows the following application 
of Rankine's method: If we had a set of cones to design, the extreme 
diameters of which, including thickness of belt, were 40 ins. and 10 ins., 
and the ratio desired 4, 3, 2, and 1, we would make a table as follows, 
L being 100 ins.: 



Trial 
Sum of 


Ratio. 


Trial Diams. 


Values of 

(D-dy^ 


Amount 
to be 
Added. 


Corrected Values. 


D 


d 




D+ d 


12.56 L 


D 1 d 


50 
50 
50 
50 


4 
3 

2 

1 


40 
37.5 
33.333 
25 


10 

12.5 
16.666 
25 


0.7165 

.4975 
.2212 
.0000 


0.0000 
.2190 
.4953 
.7165 


40 

37.7190 
33.8286 
25.7165 


10 

12.7190 
17.1619 
25.7165 



The above formulae are approximate, and they do not give satisfactory 



CONE AND STEP PULLEYS. 1137 

i^esults when the difference of diameters of opposite steps is large and 
when the axes of the pulleys are near together, giving a large belt-angle. 
Two more accurate solutions of the problem, one by a graphical method, 
and another by a trigonometrical method derived from it, are given by 
C. A; Smith (Trans. A. S. M. E. x, 269). These were copied in earlier 
editions of this Pocket-book, but are now replaced by formulae derived 
from a graphical solution by Burmester {'' Lehrbuch der Kinematic"; 
Mach'y Reference Series, No. 14, 1908), which give results far more 
accurate than are required in practice. 

In all cases 0.8 of the thickness of the belt should be subtracted from 
the calculated diameter to obtain the actual diameter of the pulley. 
This should be done because the belt drawn tight around the pulleys is 
not the same length as a tape-line measure around them. — (C. A. Smith.) 

Using Burmester 's diagram the author has devised an algebraic solu- 
tion of the problem (Indust. Eng., June, 1910) Avhich leads to the follow- 
ing equations: 

Let L = distance between the centers. 

ro = radius of the steps of equal diameter on the two cones, 
rj, r2 = radii of any pair of steps. 
a = 0.79057 L - ro. 

If ri is given, r2 = Vi.25 L^ - (0.79057 L -ro+ ri)^ - 0.79057 L + Tq. 
If the ratio r2 h- rt is given, let r2/ri = c: r2 = cri. 

We then have a + cri = ^R^— (a + ri)2, which reduces to 

(1 -f c2) ri2 -f 2 a (1 + c) n = 1.25 L2 - 2 a"^, a quadratic equation, in 
which a = 0.79057 L - Tq. Substituting the value of a we have 

(l + c2)ri2+ (1.58114 L - 2ro) (1+ c)ri = 3.16228 Xro- 2ro2, 
in which L, ro and c are given and n is to be found. 

Let L = 100, c = 4, ro = 12.858 as in Mr. Frith's example, page 11.S6. 

Then 17ri2+ 10ari, = 12,500 -8764.62, from which r, =5.001, r2=20.004. 

If c = 3, r, = 6.304, r2 = 18.912. If c = 2, n = 8.496, ro = 16.992. 

Checking the results by the approximate formula for length of belt, 
page 1148, viz, Length = 2 L+ 7tlri-\- ro) + (r2 - Vx)- -^ L, we have 
fore = 1, 200+ 80.79+ = 280.79 

2, 200+80.07 + 0.72 = 280.79 

3, 200+79.22+ 1.59 = 280.81 

4, 200+78.56 + 2.25 = 280.81 
The maximum difference being only 1 part in 14,000. 

J.J. Clark (^Indust. Eng., Aug., 1910) gives the following solution: 
Using the same notation as above, 

^^~^^% i2 + r(c+l)ri=27rro (1) 

.(c+l)n + Xa;(|^^)=2.ro (2) 

a:= (r2 - r,)2 -- L2 (3) 

The quadratic equation (1) gives the value of n with an approximation 
to accuracy sufficient for all practical purposes. If greater accuracy is for 
any reason desired it may be obtained by (2) and (3), using in (3) the values 
of rt and r2, = cri, already found from (1). Taking n = 3.1415927, the re* 
suit will be correct to the seventh figure. 

Speeds of Shaft with Cone Pulleys. — If 5 = speed (revs, per min.) 
of the driving shaft, 

Si, S2, 52, 5^2, = speeds of the driven shaft, 
Di, Z>2, I>3, 2)^= diameters of the pulleys on the driving cone, 

di, cf2, dz, d^=diams. of corresponding pulleys on the driven cone, 
SDi-=Sidi', SD2=S2d2, etc. 
sJS = Di/di = ri; s^/S = D^/d^, = r^. 
The speed of the driving shaft being constant, the several speeds of 



1138 BELTING. 

the driven shaft are proportional to the ratio of the diameter of the 
dri\ing pulley to that of tlie driven, or to D/d. 

Speeds in Geometrical Progression. — If it is desired that the speed 
ratios shall increase by a constant percentage, or in geometrical progres- 
sion, thenr2/ri = n/r^ = r^/r^_^ = c, a constant. 

r)_l ""^z 

Example. If the speed ratio of the driven shaft at its lowest speed, 
to the driving shaft be 0.76923, and at its highest speed 2.197, the speeds 
being in geometrical progression, what is the constant multiplier if n=5? 

Log 2.197 = 0.341830 

Log 0.76923 = 1.886056 

0.455774 

Divide by n- 1,= 4, 0.113943 = log of 1.30. 

If Z)2/rf2 = 1, then Dx/dx = l -- 1.3 = 0.769; Dzdz= 1.30; Di/d^^ 
1.69; D^/d^ -= 2.197. * 

BELTING. 

Theory of Belts and Bands. — A pulley is driven by a belt by means 
of the friction between the surfaces in contact. Let Ti be the tension on 
the driving side of the belt, T2 the tension on the loose side; then S,= 2\ 
— Ti, is the total friction between the band and the pulley, which is 
equal to the tractive or driving force. Let / = the coefficient of friction, 
e the ratio of the length of the arc of contact to the length of the radius, 
o = the angle of the arc of contact in degrees, e = the base of the Nape- 
rian logarithms = 2.71828, m= the modulus of the common logarithms = 
0.434295. The following formulae are derived by calculus (Rankine'a 
Mach'y and Millwork, p. 351; Carpenter's Exper. Eng'g, p. 173): 

|l= e/^; T2= -^ ; Ti- 2^2 = Ti - ^ = Ti (1 - e'f^). 
Ti- T2== Tx (1 - e-/^) = Tx (1 - 10 -/^^) = Ti (1 -10~^-^^^V^); 

Tx _ iq0.00758> Ti=^T2X 100-00758/^;r2 = Jj.^, ' 

If the arc of contact between the band and the pulley expressed in 
turns and fractions of a turn = n, = 27rn; e/^= lo^-'^^ss/^. that is, ef^ is 
the natural number corresponding to the common logarithm 2.7288/n, 

The value of the coefficient of friction /depends on the state and mate- 
rial of the rubbing surfaces. For leather belts on iron pulleys, Morin 
found / = .56 when dry, .36 when wet, .23 when greasy, and .15 
when oily. In calculating the proper mean tension for a belt, the smallest 
value, / = .15, is to be taken if there is a probability of the belt becom- 
ing wet with oil. The experiments of Henry R. Towne and Robert 
Briggs, however (Jour, Frank. Inst., 1868), show that such a state of 
lubrication is not of ordinary occurrence; and that in designing macliinery 
we may in most cases safely take / = .42. Reuleaux takes / = .25. 
Later writers have shown that the coefficient is not a constant quantity, 
but is extremely variable, depending on the velocity of sUp, the condition 
of the surfaces, and even on the weather. 

The following table shows the values of the coefficient 2.7288 /, by 
which n is multiplied in the last equation, corresponding to different 
values of /; also the corresponding values of various ratios among the 
forces, when the arc of contact is half a circumference: 



/= 0.15 


0.25 


0.42 


0.56 


2.7288/= 0.41 


0.68 


1.15 


1.53 


Let = TT and n = 1/2, then 








Ti ^ T2 = 1.603 


2.188 


3.758 


5.821 


Ti -^ S == 2.66 


1.84 


1.36 


1.21 


2^1 + ^2 ■&■ 2>S= 2.16 


1.34 


0.86 


0.71 



BELTING. 1139 

Tn ordinary practice it is usual to assume T2= S; Ti= 2 S; Ti + T2 -r 
2S == 1.5. Tills corresponds to / = 0.22 nearly. 

For a wire rope on cast iron / may be taken as .15 nearly; and if the 
groove of the p'Ucy is bottomed with p:iitta-percha, .25. (Rankine.) 

Centrifugal Tension of Belts. — When a belt or band runs at a high 
velocity, centrifugal force produces a tension in addition to that existing 
when the belt is at rest or moving at a low velocity. This centrifugal 
tension diminishes the effective driving force. 

Ranlune says: If an endless band, of any figure whatsoever, runs at a 
given speed, the centrifugal force produces a uniform tension at each 
cross-section of the band, equal to the weight of a piece of the band whose 
length is twice the height from which a heavy body must fall in oraer 
to acquire the velocity of the band. (See Cooper on Belting, p. 101.) 
If T^= centrifugal tension; 

V= velocity in feet per second; 
g= acceleration due to gravity = 32.2; 
W= weight of a piece of the belt 1 ft. long and 1 sq. in. sectional 
area, — 
Leather weighing 56 lbs. per cubic foot gives TT = 56 -•- 144 = 0.388. 
T^ = WV^ -^ g =^ 0.388 V^ -f- 32.2 = .012F2. 

Belting Practice. Handy Formulae for Belting. — Since in the 
practical appUcation of the above formulae the value of the coethcient of 
friction must be assumed, its actual value varying within wide limits 
(15% to 135%), and since the values of Ti and 2^2 also are fixed arbi- 
trarily, it is customary in practice to substitute for these theoretical 
formulae more simple empirical formulae and rules, some of which are 
given below. 

Let d = diam. of pulley in inches; 7rd = circumference; 

F = velocity of belt in ft. per second; 7; = vei. in ft. per minute; 

= angle of the arc of contact: 

L = length of arc of contact in feet = nda -^ (12 X 360); 

F = tractive force per square inch of sectional area of belt; 

iy = width in inches; t = thickness; 

5== tractive force per inch of width = F X t; 
r.p.m. = revs. per minute; r.p.s. = revs, per second = r.p.m. ~ 60. 

. = |xr.p.s.=f^X^=0.004363.Xr.p.m. = l|^; 
v= ^ X r.p.m.; = .2618 d X r.p.m. 

Horse-power, H.P. = 330^0 = -550 = 126050 

If F = working tension per square inch =275 lbs., and t= 7/32 inch, 
5 = 60 lbs. nearly, then 

H.P. = 1^ = .109 Vw = .000476 wd X r.p.m. = ^^^^^j^^' • (1) 

If F = 180 lbs. per square inch, and t = Ve inch, S = 30 lbs., then 

H.P. = ~~ =0.055 Vw =0.000238 wd X r.p.m. = ^^^202'"^ ' ' ^^^ 

If the working strain is 60 lbs. per inch of width, a belt 1 inch wide 

travehng 550 ft. per minute will transmit 1 horse-power. If the working 

strain is 30 lbs. per inch of width, a belt 1 inch wide travehng 1100 ft. 

per minute will transmit 1 horse-power. Numerous rules are given by 

different writers on belting which vary between these extremes. A rule 

commonly used is: 1 inch wide travehng 1000 ft. per min. = IH.P. 

^•^- = 1^ =^ -^^ ^^=^ -000262 wd X r.p.m. = ^^ ^/^g'"^ ' . (3) 

This corresponds to a working strain of 33 lbs. per inch of width. 

Many writers give as safe practice for single belts in good condition a 
workmg tension of 45 lbs. per inch of width. This gives 

H.P.= ^ = .0818 Vw==0 .000357 wd X r.p.m. =: '^'^ 28Qq'"" - ' <4) 



1140 



BELTING. 



For double belts of average thickness, some writers say that the trans- 
mitting efficiency is to that of single belts as 10 to 7, which would give 

^"^ 0.1169 Vw = 0.00051 wd X r.p.m. = ^'^ ^J^^'^' (5) 



H.P. = 



Other authorities, however, make the transmitting power of double belts 
twice that of single belts, on the assumption that the thickness of a double 
belt is twice that of a single belt. 

Rules for horse-power of belts are sometimes based on the number of 
square feet of surface of the belt which pass over the pulley in a minute. 
Sq. ft. per min. = wv -^ 12. The above formulae translated into this 
form give: 

(1) For aS = 60 lbs. per inch wide; H.P. = 46 sq. ft. per minute. 

(2) " S = SO •' " " H.P. = 92 " 

(3) •• 5 = 33 " " *• H.P. = 83 

(4) - ^ = 45 " •* " H.P. = 61 • 

(5) •• 5 = 64.3** •' " H.P. = 43 " " (double belt). 
The above formulas are all based on the supposition that the arc of con- 

tact is 180°. For other arcs, the transmitting power is approximately 
proportional to the ratio of the degrees of arc to 180°. 

Some rules base the horse-power on the length of the arc of contact in 

feet. Smce L=^^^3^3g5aadH.P.= 33^ = g3^j^X;f2X r.p.m. Xj^. 



we obtain by substitution H.P. = 



Sw 



X 1/ X r.p.m., and the five for- 



16500 
mulse then take the following form for the several values of Sx 

wL X r.p.m. ^^^ wLX r.p.m. ^^, wLX r.p.m . ,^, wL X r.p.m . ^^^ 
^•^- = 275 ^^^' 550 ^2^' 500 ^^^' 367 ^^^' 



H.P. (double belt) = 



wL X r.p .m. 
257 



(5), 



None of the handy formulae take into consideration the centrifugal 
tension of belts at high velocities. When the velocity is over 3000 ft. 
per minute the effect of this tension becomes appreciable, and it should 
be taken account of, as in Mr. Nagle's formula, which is given below. 

Horse-power of a Leather Belt One Inch wide. (Nagle.) 

Formula: H.P. = CVtw {S - 0.012 V'-) -^ 550. 

For/ = 0.40, a = 180°, C = 0.715, w = 1. 



i 


Laced Belts, S = 275. 


§1 


Riveted Belts, S = 400. 


li, 


Thickness in inches = t. 


Thickness in inches = t. 


5^ 


1/7 


1/6 


3/16 


7/32 


1/4 


5/16 


1/3 


7/32 


1/4 


5/16 


1/3 


3/8 


7/16 


1/2 


10 


0.51 


0.59 


0.63 


0.73 


0.84 


1.05 


1.18 


15 


1.69 


1.94 


2.42 


2.58 


2.91 


3.39 


3.87 


15 


0.75 


0.88 


1.00 


1.16 


1.32 


1.66 


1.77 


20 


2.24 


2 57 


3.21 


3.42 


3.85 


4.49 


5.13 


20 


1.00 


1.17 


1.32 


1.54 


1.75 


2.19 


2.34 


25 


2.79 


3,19 


3.98 


4.25 


4.78 


5.57 


6.37 


25 


1.23 


1.43 


1.61 


1.88 


2.16 


2.69 


2.86 


30 


3.31 


3,79 


4.74 


5.05 


5.67 


6.62 


7.58 


30 


1.47 


1.72 


1.93 


2.25 


2.58 


3.22 


3.44 


35 


3.82 


4 37 


5.46 


5.83 


6.56 


7.65 


8.75 


35 


1.69 


1.97 


2.22 


2.59 


2.96 


3.70 


3.94 


40 


4.33 


4.95 


6.19 


6.60 


7.42 


8.66 


9.90 


40 


1.90 


2.22 


2.49 


2.90 


3.32 


4.15 


4.44 


45 


4.85 


5,49 


6.86 


7.32 


8.43 


9.70 


10.98 


45 


2.09 


2.45 


2.75 


3.21 


3.67 


4.58 


4.89 


5(1 


5.26 


6 01 


7.51 


8.02 


9.02 


10.52 


12.03 


50 


2.27 


2.65 


2.98 


3.48 


3.98 


4.97 


5.30 


55 


5.68 


6.50 


8.12 


8.66 


9.74 


11.36 


13.00 


55 


2.44 


2.84 


3.19 


3.72 


4.26 


5.32 


5.69 


60 


6.09 


6,96 


8.70 


9.28 


10.43 


12.17 


13.91 


60 


2.58 


3.01 


3.38 


3.95 


4.51 


5.64 


6,02 


65 


6.45 


7 37 


9.22 


9,83 


11.06 


12.90 


14.75 


65 


2.71 


3.16 


3.55 


4.14 


4.74 


5.92 


6.32 


70 


6.78 


7.75 


9.69 


10.33 


11.62 


13.56 


15.50 


70 


2.81 


3.27 


3.68 


4.29 


4.91 


6.14 


6.54 


75 


7.09 


8 11 


10 13 


10.84 


12.16 


14.18 


16.21 


75 


2.89 


3.37 


3.79 


4.42 


5.05 


6.31 


6.73 


80 


7 36 


8 41 


10 51 


11.21 


12.61 


14.71 


16.81 


80 


2.94 


3.43 


3.86 


4.50 


5.15 


6.44 


6.86 


85 


7,58 


8,66 


10.82 


11.55 


13.00 


15.16 


17.32 


85 


2.97 


3.47 


3.90 


4.55 


5.20 


6.50 


6.93 


90 


7.74 


8.85 


11,06 


11.80 


13.27 


15.48 


17.69 


90 


2.97 


3.47 


3.90 


4.55 


5.20 


6.50 


6.93 


100 


7.96 


9.10 


11.37 


12.13 


13.65 


15.92 


18.20 


The H.P. becomes a maximum 


The H.P. becomes a maximum at 


at 87.41 ft. per sec. = 5245 ft. p. min. 


105.4 ft. per sec. = 6324 ft. per min. 



BELTING. 



1141 



In the above table the angle of subtension, a, is taken at 180°. 



Should it be 

Multiply above 
values by .... 



90° 


100° 


110° 


120° 


130° 


140° 


150° 


160° 


170° 


180° 


.65 


.70 


.75 


.79 


.83 


.87 


-.91 


.94 


,.97 


1 



1.05 
1881, p. 91. 



A. F. Nagle's Formula (Trans. A. S. M. E., vo 

Tables published in 1882). 

H.P.= cr..(^^^f-> 

C = 1 - IO-0-0O75S fa: ^_ thickness in inches; 

a = degrees of belt contact; v= velocity in feet per second; 
/ = coefficient of friction; S= stress upon belt per square Inch. 

w = width in inches: 

Taking S at 275 lbs. per sq. in. for ictced belts and 400 lbs. per sq. ia 
for lapped and riveted belts, the formula becomes 

H.P.= CVtw (0.50 - 0.0000218 F2) for laced belts; 
H.P. = CVtw (0 .727 - .0000218 V^) for riveted belts. 
Values of C= 1 - 10-ooo758 fa. (Nagle.) 











Degrees of coni 


act = 


a. 








/ = coefficient 
of friction. 




90° 


100° 


110° 
0.250 


120° 
0.270 


130° 
0.288 


140° 
0.307 


150° 
0.325 


160° 
0.342 


170° 
0.359 


180° 
0.376 


200° 


0.15 


0.210 


0.230 


0.408 


.20 


.270 


.295 


.319 


.342 


.364 


.386 


.408 


.428 


.448 


.467 


.503 


.25 


.325 


.354 


.381 


.407 


.432 


.457 


.480 


.503 


.524 


.544 


.582 


.30 


.376 


.408 


.438 


.467 


.494 


.520 


.544 


.567 


.590 


.610 


.649 


.35 


,423 


.457 


.489 


.520 


.548 


.575 


.600 


.624 


.646 


.667 


.705 


.40 


.467 


.502 


.536 


.567 


.597 


.624 


.649 


.673 


.695 


.715 


.753 


.45 


.507 


.544 


.579 


.610 


.640 


.667 


.692 


.715 


.737 


.757 


.792 


.50 


.543 


.582 


.617 


.649 


.679 


.705 


.730 


.753 


.772 


.792 


.826 


.55 


.578 


.617 


.652 


.684 


.713 


.739 


.763 


.785 


.805 


.822 


.853 


.60 


.610 


.649 


.684 


.715 


.744 


.769 


.792 


.813 


.832 


.848 


.877 


1.00 


.792 


.825 


.853 


.877 


.897 


.913 


.927 


.937 


.947 


.956 


.969 



The following table gives a comparison of the formulae already given 
for the case of a belt one inch wide, with arc of contact 180°. 



Horse-power 


of a Belt One Inch wide. Arc of Contact 180°« 




Comparison of Different Formula. 






.2 o 


^d 




Form. 1 


Form .2 


Form. 3 


Form. 4 


Form. 5 
double 


Nagle's 


Form. 




*5 d 




H.P. = 

wv 


H.P. = 

wv 


H.P. = 

wv 


H.P. = 

wv 


belt 
H.P.= 


v32-m. smgie 
belt. 


o ^ 


o 


^ 


550 


1100 


1000 


733 


wv 
513 


Laced. 


Riv't'd 


10 


600 


50 


1.09 


0.55 


0.60 


0.82 


1.17 


0.73 


1.14 


20 


1200 


100 


2.18 


1.09 


1.20 


1.64 


2.34 


1.54 


2.24 


30 


1800 


150 


3.27 


1.64 


1.80 


2.46 


3.51 


2.25 


3.31 


40 


2400 


200 


4.36 


2.18 


2.40 


3.27 


4.68 


2.90 


4.33 


50 


3000 


250 


5.45 


2.73 


3.00 


4.09 


5.85 


3.48 


5.26 


60 


3600 


300 


6.55 


3.27 


3.60 


4.91 


7.02 


3.95 


6.09 


70 


4200 


350 


7.63 


3.82 


4.20 


5.73 


8.19 


4.29 


6.78 


80 


4800 


400 


8.73 


4.36 


4.80 


6.55 


9.36 


4.50 


7.36 


90 


5400 


450 


9.82 


4.91 


5.40 


7.37 


10.53 


4.55 


7.74 


100 


6000 


500 


10.91 


5.45 


6.00 


8.18 


11.70 


4.41 


7.96 


110 


6600 
7200 


550 
600 












4.05 
3.49 


7.97 


120 












7.75 

















Width of Belt for a Given Horse-power. — The width of belt 
required for any given horse-power may be obtained by transposing the 



1142 



BELTING. 



formulae for horse-power so as to give the value of w. Thus: 

, ,,, 550 H.P. 9.17 H.P. 2101 H.P. 275 H.P. 

From formula (1), w^ — — — 



From formula (2), w = 
From formula (3) , w = 
From formula (4), w = 
From formula (5),*iy = 



V V d X r.p.m. L Xr.p.m. 

1100 H.P. 18. 33 H.P. 4202 H.P. 530 H.P. 



1000 H.P . 

V 

733 H.P. 

V 

513 H.P. 



V 
^ 16.67 H.P. 

V 
12 .22 H.P. ^ 

V 
8.56 H.P. 



d X r.p.m. 

3820 H.P. 

d X r.p.m. 
2800 H.P. _ 
dXr.p.iD. 
1960 H.P. 



L Xr.p.m. 
500 H.P. . 
L Xr.p.m. 
_ 360 H.P 
" L Xr.p.m/ 
257 H.P. 



V V d X r.p.m. L Xr.p.m. 

Many authorities use formula (1) for double belts and formula (2) or 
(3) for single belts. 

To obtain the width by Nagle's formula, '^ = cvt{f-0^m.2 V^Y ^^ 

divide the given horse-power by the figure in the table corresponding to 
the given thickness of belt and velocity in feet per second. 

The formula to be used in any particular case is largely a matter of judg- 
ment. A single belt proportioned according to formula (1), if tightly 
stretched, and if the surface is in good condition, will transmit the horse- 
power calculated by the formula, but one so proportioned is objectionable, 
first, because it requires so great an initial tension that it is apt to stretch, 
slip, and require frequent restretcliing and relacing; and second, because 
tills tension will cause an undue pressure on the pulley-shaft, and therefore 
an undue loss of power by friction. To avoid these difficulties, formula 
(2), (3), or (4), or Mr. Nagle's table, should be used; the latter especially 
in cases in which the velocity exceeds 4000 ft. per min. 

The following are from the notes of the late Samuel Webber. (Am. 
Mach. May 11, 1909.) 

Good oak-tanned leather from the back of the hide weighs almost 
exactly one avoirdupois ounce for each one-hundredth of an inch in thick- 
ness, in a piece of leather one foot square, so that 





Lbs. 
per Sq. 

Ft. 


Approx. 
Thick- 
ness. 


Actual 
Thick- 
ness. 


Vel. per 

Inch for 

1 H.P. 


Safe Strain 
per Inch 
Width. 


bmgie belt. . . « « 


16 oz. 
24 " 

28 ''•' 
33 " 
45 " 


1/6 in. 
1/4" 

5/16 ;; 

1/3" 
9/tB " 


0.16 in. 
0.24 " 
0.28 " 
0.33 " 
0.45 " 


625 ft. 
417 " 
357 " 
303 " 
222 " 


52 8 Ib^;. 


Light double. . • 


78.1 •• 


Medium 


92.5 •• 


Standard*. 


109 


3-d1 v 


148 •• 



The rule for velocity per inch width for 1 H.P. is: 

Multiply the denominator of the fraction expressing the thickness of 
the belt in inches by 100, and divide it by the numerator; 

Good, well-calendered rubber belting made with 30-ounce duck and 
new (i. e.. not reclaimed vulcanized) rubber will be as follows: 



Nomenclature. 


Approximate 
Thickness. 


Safe Working 

Strain for 1 Inch 

Width. 


Velocity per Inch for 
for 1 H.P. 


3.ply 

5 •• 

6 " 

7 " 

8 *• 


0.18in. 
0.24 " 
0.30 •• 
0.35 ♦• 
0.40 •• 
45 •♦ 


45 pou 
65 ' 
85 * 
105 • 
125 * 
145 • 


nds 


735 ft. per min. 
508 '* " •* 
388 •* " " 
314" *• *• 
264 •* " " 
218 ♦* " " 



The thickness of rubber belt does not necessarily govern the strength, , 
but the weight of duck does, and with 30-ounce duck, the safe working ■ 
strains are as above. 

Belt Factors. W. W. Bird (Jour. Worcester Polyt. Inst., Jan. 1910.) 1 

— The factors given in the table below, for use in the formula H.P. =3 

vw -i- F,ia which F is an empirical factor, are based on the following 

assumptions: A belt of single thickness will stand a str e ss on the tight 

* For double belts. 



BELTING. 



1143 



side, Tu of 60 lbs. per inch of width, a double belt 105 lbs., and a 
triple belt 150 lbs., and have a fairly long life, requiring only occasional 
taking up; the ratio of tensions Tv T- should not exceed 2 on small, 
2. 5 on medium and 3 on large pulleys; the creep (travel of the belt 
relative to the surface of the pulley due to the elasticity of the belt 
and not to slip) should not exceed 1 % — this requires that the differ- 
ence in tensions Ti - T2 should not be greater than 40 lbs. oer inch ot 
width for single, 70 for double and 100 for triple belts 



Pulley diam, 


Under 
Sin. 


8 to 
36 in. 


Over 
3 ft. 


Under 
14 in. 


14 to 
60 in. 


Over 
5 ft. 


Under 
21 in. 


21 to 

84 in. 


Over 

7 ft. 


Belt thick- 
ness. 


Single. 


S'gle. 


S'gle. 


Dbl. 


Dbl. 


Dbl. 


Triple. 


Triple. 


Triple. 


Factor 

Ti-T2 

Creep, %.... 

Ti-^ T2 

Ti 


1100 

30 
0.74 
2 

60 


920 
36 

0.89 

2.5 
60 


830 
40 

0.99 

3 
60 


630 
52.5 
0.74 
2 
105 


520 
63 
0.89 
2.5 
105 


470 
70 
0.99 
3 
105 


440 
75 
0.74 
2 
150 


370 
90 
0.89 
2.5 
150 


330 

100 

0.99 

3 

150 









These factors are for an arc of contact of 180°. For other arcs they 
are to be multiplied by the figures given below. 

Arc 220° 210° 200° 190° 170° 160° 150° 140° 130° 120° 

Multiply by.. . 0.89 0.92 0.95 0.97 1.04 1.07 1.11 1.16 1.21 1 27 

Taylor's Rules for Belting. — F. W. Taylor {Trans. A. S. M.' E., 
XV, 204) describes a nine years' experiment on belting in a machine shop, 
giving results of tests of 42 belts running night and day. Some of these 
belts were run on cone pulleys and others on sliifting, or fast-and-loose, 
pulleys. The average net working load on the shifting belts was only 
0.4 of that of the cone belts. 

The shifting belts varied in dimensions from 39 ft. 7 in. long, 3.5 in. 
wide, .25 in. thick, to 51 ft. 5 in. long, 6 .5 in. wide, .37 in. thick. The 
cone belts varied in dimensions from 24 ft. 7 in. long, 2 in. wide, .25 in. 
thick, to 31 ft. 10 in. long. 4 in. wide, .37 in. thick. 

Belt-clamps were used having spring-balances between the two pairs 
of damns, so that the exact tension to which the belt was subjected was 
accurately weighed when the belt was first put on, and each time it was 
tightened. The tension imder which each belt was spliced was care- 
fully figured so as to place it under an initial strain — while the belt 
was at rest immediately after tightening — of 71 lbs. per inch of width 
of double belts. This is equivalent, in the case of 

Oak tanned and fulled belts, to 192 lbs. per sq. in. section; 
Oak tanned, not fulled belts, to 229 " " " " 
Semi-raw-hide belts, to 253 " " " " 

Raw-hide belts to 284 " " " " 

From the nine years experiment Mr. Taylor draws a number of con- 
clusions, some of which are given in an abridged form below. 

In using belting so as to obtain the greatest economy and the most 
satisfactory results, the following rules should be observed: 



A double belt, having an arc of contact of 
180°, will give an effective pull on the face 
of a pulley per inch of width of belt of . . . 

Or, a different form of same rule: 

The number of sq. ft. of double belt passing 
around a pulley per minute required to 

transmit one horse-power is 

Or: The number of lineal feet of double 
belting 1 in. wide passing around a pulley 
per minute required to transmit one horse- 
power is 

Or: A double belt 6 in. wide, running 4000 to 
5000 ft. per min., will transmit 



Oak Tanned 

and Fulled 

Leather Belts 



35 lbs. 

80 sq. ft, 

950 ft. 
30 H.P. 



Other Types 

of Leather 

Belts and 

6- to 7-ply 

Rubber Belts. 



30 lbs. 
90 sq. ft. 

1100 ft. 

25 H.P. 



1144 BELTING. 

The terms "initial tension," "effective pull," etc., are thus explained 
by Mr. Taylor: When pulleys upon which belts are tightened are at rest 
both strands of the belt (the upper and lower) are under the same stress 
per in. of width. By "tension," "initial tension," or "tension while at 
rest," we mean the stress per in. of width, or sq. in. of section, to which 
one of the strands of the belt is tightened, when at rest. After the belts 
are in motion and transmitting power, tlie stress on the slack side, or 
strand, of the belt becomes less, while that on the tight side — or the side 
which does the pulhng — becomes greater than when the belt was at rest. 
By the term "total load" we mean the total stress per in. of width, or 
sq. in. of section, on the tight side of belt while in motion. 

The difference between the stress on the tight side of the belt and its 
slack side, wliile in motion, represents the effective force or pull which is 
transmitted from one pulley to another. By the terms "working load," 
"net working load," or "effective pull," we mean the difference in the 
tension of the tight and slack sides of the belt per in. of width, or sq. in. 
section, while in motion, or the net effective force that is transmitted from 
one pulley to another per in. of width or sq. in. of section. 

The discovery of Messrs. Lewis and Bancroft (Trans. A. S. M. E., 
vii, 549) that the "sum of the tension on both sides of the belt does not 
remain constant," upsets all previous theoretical belting formulae. 

The belt speed for maximum economy should be from 4000 to 4500 ft. 
per minute. 

The best distance from center to center of shafts is from 20 to 25 ft. 

Idler pulleys work most satisfactorily when located on the slack side 
of the belt about one-quarter way from the driving-pulley. 

Belts are more durable and work more satisfactorily made narrow and 
thick, rather than wide and tliin. 

It is safe and advisable to use: a double belt on a pulley 12 in. diameter 
or larger; a triple belt on a pulley 20 in. diameter or larger; a quadruple 
belt on a pulley 30 in. diameter or larger. 

As belts increase in width they should also be made tliicker. 

The ends of the belt should be fastened together by splicing and cement- 
ing, instead of lacing, wiring, or using hooks or clamps of any kind. 

A V-splice should be used on triple and quadruple belts and when 
idlers are used. Stepped splice, coated with rubber and vulcanized in 
place, is best for rubber belts. 

For double belting the rule works well of making the splice for all belts 
up to 10 in. wide, 10 in. long; from 10 in. to 18 in. wide the spUce should 
be the same width as the belt, 18 in. being the greatest length of sphce 
required for double belting. 

Belts should be cleaned and greased every five to six months. 

Double leather belts will last well when repeatedly tightened under 
a strain (when at rest) of 71 lbs. T>eT in. of width, or 240 lbs. per sq. in. 
section, but they will not maintain this tension for any length of time. 

Belt-clamps having spring-balances between the pairs of clamps should 
be used for weighing the tension of the belt each time it is tightened. 

The stretch, durability, cost of maintenance, etc., of belts proportioned 

(A) according to the ordinary rules of a total load of 111 lbs. per inch of 
width, corresponding to an effective pull of 65 lbs. per inch of width, and 

(B) according to a more economical rule of a total load of 54 lbs., corre- 
sponding to an effective pull of 26 lbs. per inch of width, are found to be 
as follows: 

When it is impracticable to accurately weigh the tension of a belt in 
tightening it, it is safe to shorten a double belt one-half inch for every 
10 ft. of length for (A) and one inch for every 10 ft. for (B), if it requires 
tightening. 

Double leather belts, when treated with great care and run night and 
day at moderate speed, should last for 7 years (A): 18 years (B). 

The cost of aU labor and materials used in the maintenance and repairs 
of double belts, added to the cost of renewals as they give out, through a 
term of years, will amount on an average per year to 37% of the original 
cost of the belts (A) ; 14% or less (B). 

In figuring the total expense of belting, and the manufacturing cost 
chargeable to this account, by far the largest item is the time lost on the 
machines while belts are being relaced and repaired. 

The total stretch of leather belting exceeds 6% of the original length. 



• BELTING. 1145 



The stretch during the first six months of the life of belts is 36% o( 
their entire stretch (A); 15 7o (B). 

A double belt will stretch 0.47% of its length before requiring to be 
tightened (A); 0.81% (B). 

The most important consideration in making up tables and rules for the 
use and care ot belting is how to secure the minimum of interruptions to 
manufacture from tliis source. 

The average double belt (A), when running night and day in a machine- 
shop, will cause at least 26 interruptions to manufacture during its life, 
or 5 interruptions per year, but with (B) interruptions to manufacture 
will not average oftener for each belt than one in sixteen months. 

The oak-tanned and fulled belts showed themselves to be superior in 
all respects except the coefficient of friction to either the oak-tanned 
not fulled, the semi-raw-liide, or raw-hide with tanned face. 

Belts of any width can be successfuUy sliifted backward and forward 
on tight and loose puUeys. Belts running between 5000 and 6000 ft. 
per min. and driving 300 H.P. are now being daily sliifted on tight and 
loose puUeys, to throw lines of shafting in and out of use. 

The best form of belt-sliifter for wide belts is a pair of rollers twice the 
width of belt, either ot wliich can be pressed onto the flat surface of the 
belt on its slack side close to the driven pulley, the axis of the roller 
making an angle of 75° with the center line of the belt. 

Remarks on Mr. Taylor's Kules. (W. Kent, Trans. A. S. M. E., xv, 
242.) — ^The most notable feature in Mr. Taylor's paper is the great dif- 
ference between liis rules for proper proportioning of belts and those 
given by earlier writers. A very commoniy used rule is, one horse-power 
may be transmitted by a single belt 1 in. wide running x ft. per min., sub- 
stituting for X various values, according to the ideas of different engineers, 
ranging usually from 550 to 1100. 

The practical mechanic of the old school is apt to swear by the figure 
600 as being thoroughly reUable, while the modern engineer is more apt 
to use the figure 1000. Mr. Taylor, however, instead of using a figure 
from 550 to 1100 for a single belt, uses 950 to 1100 for double belts. It 
we assume that a double belt is twice as strong, or will carry twice as much 
power, as a single belt, then he uses a figure at least twice as large as that 
used in modern practice, and would make the cost of belting for a given 
shop twice as large as if the belting were proportioned according to the 
most liberal of the customary rules. 

This great difference is to some extent explained by the fact that the 
problem which Mr. Taylor undertakes to solve is quite a different one 
from that which is solved by the ordinary rules with their variations. The 
pro"blem of the latter generally is, " How wide a belt must be used, or how 
narrow a belt may be used, to transmit a given horse-power?" Mr, 
Taylor's problem is: ■* How wide a belt must be used so that a given horse- 

f)ower may be transmitted with the minimum cost for belt repairs, the 
ongest life to the belt, and the smallest loss and inconvenience from stop- 
ping the machine wliile the belt is being tightened or repaired?" 

The difference between the old practical mechanic's rule of a 1-in.- 
wide single belt, 600 ft. per min., transmits one horse-power, and the rule 
commonly used by engineers, in wliich 1000 is substituted for 600, is due 
to the behef of the engineers, not that a horse-power could not be trans- 
mitted by the belt proportioned by the older rule, but that such a pro- 
portion involved undue strain from overtightening to prevent slipping, 
which strain entailed too much journal friction, necessitated frequent 
tightening; and decreased the length of the life of the belt. 

Mr, Taylor's rule substituting 1100 ft. per min. and doubling the belt. 
Is a further step, and a long one, in the same direction. Whether it will 
be taken in any case by engineers will depend upon whether they appre- 
ciate the extent of the losses due to shppage of belts slackened by use 
under overstrain, and the loss of time in tightening and repairing belts, 
to such a degree as to induce them to allow the first cost of the belts to 
be doubled in order to avoid these losses. 

It should be noted that Mr. Taylor's experiments were made on rather 
narrow belts, used for transmitting power from shafting to machinery, 
and his conclusions may not be appUcable to heavy and wide belts, such 
as engine fly-wheel belts. 



1146 BELTING. 



Barth^s Studies on Belting. (Trans. A. S. M. E., 1909.) — Mr. 

Carl G. Barth has made an extensive study of the work of earlier writers 
on the subject of belting, and has derived several new formulae and dia- 
grams showing the relation of the several variables that enter into the 
belt problem. He has also devised a sUde rule by which calculations of 
belts may easily be made. He finds that the coefficient of friction de- 
pends on the velocity of the belt, and may be expressed by the formula 

/ = 0.54 - ^QQ_|_^ , in which V is the velocity in feet per minute. 

Taking Mr. Taylor's data as a starting point, Mr Barth has adopted 
the rule, as a basis for use of belts on belt-driven macliines, that for the 
driving belt of a machine the minimum initial tension must be such 
that when the belt is doing the maximum amount of work intended, the 
sum of the tension in the tight side of the belt and one-half the tension in 
the slack side will equal 240 lbs. per square inch of a^oss-section for all 
belt speeds; and that for a belt driving a countershaft, or any other belt 
inconvenient to get at for retightening or more readily made of liberal 
dimensions, this sum will equal 160 lbs. Further, the maximum initial 
tension, that is, the initial tension under which a belt is to be put up in 
the first place, and to which it is to be retightened as often as it drops 
to the minimum, must be such that the sum defined above is 320 lbs. 
for a machine belt, and 240 lbs. for a counter-shaft belt or a belt simi- 
lariy circumstanced. 

From a set of curves plotted by Mr. Barth from his formula the follow- 
ing tables are derived. The figures are based upon the conditions named 
in the above rule, and on an arc of contact = 180°. 

Belts on Machines. Tension in tight side -+- 1/2 tension in slack side 
s= 240 lbs. 

Velocity, ft. per min... 500 1000 2000 3000 4000 5000 6000 

Initial tension, io 124 120 121 128 136 144 152 

Centrifugal tension i^ . + 3 13 31 56 86 124 

Difference, fo - ^c 123 117 108 97 80 58 28 

Tension on tight side, «i 210 212 211 207 198 187 173 
Tension on slack side, fe 60 • 54 57 68 84 107 134 
EffecUvepuU, ii - ^2.. 150 158 154 139 114 80 39 
Sum of tensions ti + ^2 270 268 269 274 282 294 307 
H.P. per sq. in. of sec- 
tion 2.27 4.79 9.33 12.64 13.82 12.12 7.09 

H.P. per in. width, 5/ig 

in.thick 0.71 1.50 2.82 3.95 4.32 3.71 2.22 

Belts driving countershafts, ti + V2 ^2 = 160 lbs. 

Velocity of belt, ft. per min 500 1000 2000 3000 4000 5000 

Initial tension, to 82 81 83 89 96 102 

Tension on tight side, ii 140 141 140 134 125 114 

Tension on slack side, t2 40 38 41 53 69 92 

Effecrive pull, ti - t2 100 103 99 81 56 22 

Sum of tensions 180 179 181 187 194 206 

H.P. per sq. in. of section 1.51 3.12 6.04 7.36 6.79 3.33 

H.P. per in. width, 5/16 in. thick 0.47 0.97 1.87 2.30 2.12 1.04 

MISCELLANEOUS NOTES ON BELTING. 

Formulae are useful for proportioning belts and pulleys, but they fur- 
nish no means of estimating how much power a particular belt may be 
transmitting at any given time, any more than the size of the engine is a 
measure of the load it is actually drawing, or the known strength of a 
horse is a measure of the load on the wagon. The only reliable means of 
determining the power actually transmitted is some form of dynamometer. 
(See Trans. A. S. M. E., vol. xii, p. 707.) 

If we increase the thickness, the power transmitted ought to increase 
in proportion; and for double belts we should have half the width required 
for a single belt under the same conditions. With large pulleys and 
moderate velocities of belt it is probable that this holds good. With 
small pulleys, however, when a double belt is used, there is not such per- 



MISCELLANEOUS NOTES ON BELTING. 1147 

feet contact between the pulley-face and the belt, due to the rigidity of 
the latter, and more work is necessary to bend the belt-fibers than when a 
thinner and more pliable belt is used. Tiie centriiugal lorce tending to 
throw the belt irom the puUey also increases with the tiiickness, and for 
these reasons the width of a double belt required to transmit a given 
horse-power when used with small pulleys is generally assumed not less 
than seven-tentlis the width of a single belt to transmit the same power, 
(Flather on "Dynamometers and Measurement of Power.") 

F. W. Taylor, however, finds that great phability is objectionable, and 
favors thick belts even for small pulleys. The power consumed in bending 
the belt around the pulley he considers inappreciable. According to 
Rankine's formula for centrifugal tension, tliis tension is proportional to 
the sectional area of the belt, and hence it does not increase with increase 
of tliickness when the width is decreased in the same proportion, the 
sectional area remaining constant. 

Scott A. Smith (Trans. A.S,M. E., x, 765) says: The best belts are made 
from all oak-tanned leather, and curried with the use of cod oil and 
taUow, all to be of superior quaUty. Such belts have continued in use 
tliirty to forty years when used as simple driving-belts, driving a proper 
amount of power, and having had suitable care. The flesh side should 
not be run to the pulley-face, for the reason that the wear from contact 
with the pulley should" come on the grain side, as that surface of the belt 
is much weaker in its tensile strength than the flesh side; also as the grain 
is hard it is more enduring for the wear of attrition; further, if the grain is 
actually worn off, then the belt may not suffer in its integrity from a 
ready tendency of the hard grain side to crack. 

The most intimate contact of a belt with a pulley comes, first, in the 
smoothness of a pulley-face, including freedom from ridges and hollows 
left by turning-tools; second, in the smoothness of the surface and even- 
ness in the texture or body of a belt ; third, in having the crown of the driv- 
ing and receiving pulleys exactly alike, — as nearly so as is practicable 
in a commercial sense; fourth, in having the crown of pullej^s not over 
1/8 in. for a 24-in. face, that is to say, that the pulley is not to be over 
1/4 in. larger in diameter in its center; fifth, in having the crown other 
than two planes meeting at the center; sixth, the use of any material 
on or in a belt, in addition to those necessarily used in the currying 
process, to keep them pliable or increase their tractive quality, should 
wholly depend upon the exigencies arising in the use of belts; non-use is 
safer than over-use; seventh, with reference to the lacing of belts, it 
seems to be a good practice to cut the ends to a convex shape by using a 
former, so that there may be a nearly uniform stress on the lacing through 
the center as compared with the edges. For a belt 10 ins. wide, the center 
of each end should recede i/io in. 

Lacing of Belts. — In punching a belt for lacing, use an oval punch, 
the longer diameter of the punch being parallel with the sides of the belt. 
Punch two rows of holes in each end, placed zigzag. In a 3-in, belt there 
should be four holes in each end — two in each row. In a 6-in. belt, 
seven holes — four in the row nearest the end. A 10-in„ belt should have 
nine holes. The edge of the holes should not come nearer than 3/4 in. 
from the sides, nor 7/g in. from the ends of the belt. The second row 
should be at least 13/4 ins. from the end. On wide belts these distances 
should be even a little greater. 

Begin to lace in the center of the belt and take care to keep the ends 
exactly in line, and to lace both sides with equal tightness. The lacing 
should not be crossed on the side of the belt that runs next the pulley. 
In taking up belts, observe the same rules as in putting on new ones. 

Setting a Belt on Quarter-twist. — A belt must run squarely on to 
the pulley. To connect with a belt two horizontal shafts at right angles 
with each other, say an engine-shaft near the floor with a line attached to 
the ceiling, will require a quarter-turn. First, ascertain the central point 
on the face of each pulley at the extremity of the horizontal diameter 
where the belt will leave the pulley, and then set that point on the driven 
pulley plumb over the corresponding point on the driver. This will cause 
the belt to run squarely on to each pulley, and it mil leave at an angle 
greater or less, according to the size of the pulleys and their distance from 
each other. 

In quarter-twist belts, in order that the belt may remain on the pulleys. 



1148 BELTING. 

the central plane on each pulley must pass through the point of delivery 
of the other pulley. This arrangement does not admit of reversed 
motioUc 
To find the Length of Belt required for two given Pulleys. — 

When the length cannot be measured directly by a tape-line, the follow- 
ing approximate rule may be used: Add the diameter of the two pulleys 
together, divide the sura by 2, and multiply the quotient by 31/4, and 
add the product to twice the distance between the centers of the shafts. 
(See accurate formula below.) 

To find the Angle of the Arc of Contact of a Belt. — Divide the 
difference between the radii of the two puUeys in inches by the distance 
between their centers, also in inches, and in a table of natural sines find 
the angle most nearly corresponding with the quotient. Multiply this 
angle by 2, and add the product to 180° for the angle of contact with the 
larger pulley, or subtract it from 180° for the smaller pulley. 
Or, let R = radius of larger pulley, r = radius of smaller; 
L = distance between centers of the pulleys; 
a = angle whose sine is (R — r) -i- L. 

Arc of contact with smaller pulley = 180° — 2 a; 
Arc of contact with larger puUey = 180° + 2 a. 

To find the Length of Belt in Contact with the Pulley. — For the 

larger pulley, multiply the angle a, found as above, by .0349, to the 
product add 3.1416, and multiply the sum by the radius of the pulley. 
Or length of belt in contact with the pulley 

= radius X (^r + .0349 a) = radius X 7r(l + a/90). 
For the smaller pulley, length = radius X (tt — O .0349 a) 
= radius X ^(1 — a)-i-90. 

The above rules refer to Open Belts. The accurate formula for length 
of an open belt is, 

Length = 7rR(l-h a/90) + 7rr(l --a/90) + 2 L cos a. 

= i2(7r+ 0.0349 a) + r (tt -0.0349 a) + 2 L cos a, 

in which R = radius of larger pulley, r = radius of smaller pulley, 

L = distance between centers of pulleys, and a = angle whose 
sine is 
(R - r) -i- L; cos a = Vl^ - (i2 - r)2 ^ L, 
An approximate formula is 
Length == 2 L +1: (R +r) + (R - r)^/L 

For I/ = 4, 72 = 2, r = l, this formula gives length = 17.6748, the 
accurate formula gi\ing 17.6761 

For Crossed Belts the formula is 

Length of belt = n R{1 +/3/90) + Trr (1 + i3/90) + 2 Z cos /5 
=■• (R + r) X (tt + 0.0349 /3) + 2 L cos jS, 

In which /3 = angle whose sine is (R+ r)-^ L; cos /3 = \^L^ — {R+ r)^ -?- L. 

To find the Length of Belt when Closely Rolled. — The sum of the 

diameter of the roll, and of the eye in inches, X the number of turns made 
by the belt and by 0.1309, = length of the belt in feet. 

To find the Approximate Weight of Belts. — Multiply the length 
of belt, in feet, by the width in inches, and divide the product by 13 for 
single and 8 for double belt. 

Good oak- tanned leather from the back of the hide weighs almost 
exactly 1 oz. per sq. ft. per 0.01 in. thickness. The thickness of single 
belts is 0.16 in. ; of hght double belts, 0.24 in. ; of medium weight double 
belt, 0.28 in.; of standard double belt, 0.33 in.; of 3-ply bolts. 0.45 in. 
(W. O. Webber, in Trans. Natl. Assoc. Cotton Mfrs., 1908, p. 345.) 

Relations of the Size aid Speeds of Driving and Driven Pulleys. 
— The driving pulley is called the driver, D, and the driven pulley the 
driven, d. If the number 01 teeth in gears is used instead of diameter, 
in these calculations, number of teeth must be substituted wherever 
diameter occurs. R = revs, per min. of driver, r = revs, per min. of 
driven. 



MISCELLANEOUS NOTES ON BELTING. 



1149 



Diam. of driver = diam. of driven X revs, of driven -r- revs, of driver. 

d = DR^r; 
Diam. of driven = diam. of driver X revs, of driver ~- revs, of driven. 

R = dr -^ D; 
Revs, of driver = revs, of driven X diam. of driven -r- diam. of driver, 

r = DR -r- d; 
Revs, of driven == revs, of driver X diam. of driver ~ diam. of driven. 

Evils of Tight Belts. (Jones and Laughlins.) — Clamps with power- 
ful screws are often used to put on belts with extreme tigntness, and with 
most injurious strain upon the leather. They should be very judiciously 
used for horizontal belts, which should be allowed sufficient slackness 
to move with a loose undulating vibration on the returning side, as a test 
that they have no more strain imposed than is necessary simply to trans- 
mit the power. 

On tills subject a New England cotton-mill engineer of large experience 
says: I beheve that three-quarters of the trouble experienced in broken 
puUeys, hot boxes, etc., can be traced to the fault of tight belts. The 
enormous and useless pressure thus put upon pulleys must in time break 
them, if they are made in any reasonable proportions, besides wearing 
out the whole outfit, and causing heating and consequent destruction of 
the bearings. Below are figures showing the power taken, in average 
modern mills with first-class shafting, to drive the shafting alone: 



Mill 
No. 


Whole 
Load, 
H.P. 


Shafting Alone. 


Mill 

No. 


Whole 
Load, 
H.P. 


Shafting Alone. 


Horse- 
power. 


Per cent 
of whole. 


Horse- 
power. 


Per cent 
of whole. 


1 

2 
3 
4 


199 
472 
486 
677 


51 

111.5 
134 
190 


25.6 
23.6 
27.5 
28.1 


5 
6 
7 
8 


759 
235 
670 
677 


172.6 

84.8 
262.9 
182 


22.7 
36.1 
39.2 
26.8 



These may be taken as a fair showing of the power that is required in 
many of our best mills to drive shafting. It is unreasonable to think that 
all that power is consumed by a legitimate amount of friction of bearings 
and belts. I know of no cause for such a loss of power but tight belts. 
These, when there are hundreds or thousands in a mill, easily multiply 
the friction on the bearings, and would account for the figures. 

Sag of Belts. Distance between Pulleys. — In the location of shafts 
that are to be connected with each other by belts, care should be taken 
to secure a proper distance one from the other. This distance should be 
such as to allow of a gentle sag to the belt when in motion. 

A general rule may be stated thus: Where narrow belts are to be run 
over small pulleys 15 feet is a good average, the belt having a sag of 
1 1/2 to 2 inches. 

For larger belts, working on larger pulleys, a distance of 20 to 25 feet 
does well, with a sag of 21/2 to 4 inches. 

For main belts working on very large pulleys, the distance should be 25 
to 30 feet, the belts working well with a sag of 4 to 5 inches. 

If too great a distance is attempted, the belt will have an unsteady 
flapping motion, which will destroy both the belt and machinery. 

Arrangement of Belts and Pulleys. — If possible to avoid it, con- 
nected shafts should never be placed one directlv over the other, as in 
such case the belt must be kept verv tight to do the work. For this 
purpose belts should be carefully selected of well-stretched leather. 

It is desirable that the angle of the belt with the floor should not exceed 
45°. It is also desirable to locate the shafting and machinery so that 
belts should run off from each shaft in opposite directions, as this arrange- 
ment will relieve the bearings from the friction that would result when 
the belts all pull one way on the shaft. 

In arrandng the belts leading from the main line of shafting to the 
counters, those pulling in an opposite direction should be placed as near 
each other as practicable, while those pulling in the same direction 
should be separated. This can often be accomplished by changing the 
relative positions of the pulleys on the counters. By this procedure 
much of the friction on the journals may be avoided. 

If possible, machinery should be so placed that the direction of the belt 



1150 BELTING. 

motion shall be from the top of the driving to the top of the driven pulley, 
when the sag will increase the arc of contact. 

The pulley should be a little wider than the belt required for the work. 

The motion of driving should run with the laps of the belts. 

Tightening or guide pulleys should be applied to the slack side of belts 
and near the smaller pulley. 

Jones and LaughUns, in their Useful Information, say: The diameter of 
the pulleys should be as large as can be admitted, provided they will not 
produce a speed of more than 4750 feet of belt motion per minute. 

They also say: It is better to, gear a mill with small pulleys and run 
them at a high velocity, than with large pulleys and to run them slower. 
A mill thus geared costs less and has a much neater appearance than with 
large heavy pulleys. 

M. Arthur Achard {Proc. Inst. M. E., Jan., 1881, p. 62) says: When the 
belt is wide a partial vacuum is formed between the belt and the pulley 
at a high velocity. The pressure is then greater than that computed from 
the tensions in the belt, and the resistance to slipping is greater. This 
has the advantage of permitting a gicater power to be transmitted by a 
given belt, and of diminishing the strain on the shafting. 

On the other hand, some writers claim that the belt entraps air between 
Itself and the pulley, which tends to diminish the friction, and reduce 
the tractive force. On this theory some manufacturers perforate the 
belt with numerous holes to let the air escape. 

Care of Belts. — Leather belts should be well protected against water, 
loose steam, and all other moisture, with which they should not come in 
contact. But where such conditions prevail fairly good results are 
obtained by using a special dressing prepared for the purpose of water- 
proofing leather, though a positive water-proofing material has not yet 
been discovered. 

Belts made of coarse, loose-fibered leather will do better service in dry 
and warm places, but if damp or moist conditions exist then the very, 
finest and firmest leather should be used. (Fayerweather & Ladew.) 

Do not allow oil to drip upon the belts. It destroys the life of the leather. 

Leather belting cannot safely stand above 130° of heat. 

"Duxbak" waterproof belt, is advertised to withstand any amoimt 
of moisture, and temperatures up to 200 degrees. 

Strength of Belting. — The ultimate tensile strength of belting does 
not generally enter as a factor in calculations of power transmission. 

The strength of the soUd leather in belts is from 2000 to 5000 lbs. per 
square inch; at the lacings, even if well put together, only about 1000 to 
1500. If riveted, the joint should have half the strength of the solid 
belt. The working strain on the driving side is generally taken at not 
over one-third of the strength of the lacing, or from one-eighth to one- 
sixteenth of the strength of the soUd belt. Dr. Hartig found that the 
tension in practice varied from 30 to 532 lbs. per sq. in. , averaging 273 lbs. 

Effect of Humidity Upon a Leather Belt. (W. W. Bird and F. W. 
Roys, Trans. A. S. M. E., 1915.) — Tests with a 4-in. oak-tanned single 
belt, with constant horse-power transmitted, and with the center dis- 
tance and humidity varying, showed increase of the sum of the tensions 
as the humidity decreased, figures taken from curves of the results 
being as follows: 

Center distance: 9 ft. 6 in., 9 ft. 61 /2 in., 9 ft. 7 in., 9 ft. 71/2 in. 
Relative Humidity. Sum of the Tensions, pounds. 

90 95 210 325 445 

65 125 260 400 550 

20 150 310 465 620 

Increase of temperature as well as increase of humidity tends to 
lengthen the belt and decrease the tension. The most important con- 
clusions are: 

1. If a belt be set up at a medium relative hmnidity, the tensions will 
not be excessive at lower relative humidities, nor will there be any 
great danger of slipping at high relative humidities unless there are 
excessive temperature changes. 

2. If a belt be set up at any relative humidity with a spring or 
gravity tightener, a load 50 per cent greater than the standard can 
be transmitted at either high or low humidity without danger of stretch- 
ing the belt, slipping, or excessive pressure on the bearings. 



MISCELLANEOUS NOTES ON BELTING. 1151 

Adhesion Independent of Diameter. (Schultz Belting Co.) — 

1. The adhesion of the belt to the pulley is the same — the arc or number 
of degrees of contact, aggregate tension or weight being the same — 
without reference to width of belt or diameter of pulley. 

2. A belt will slip just as readily on a pulley four feet in diameter as It 
will on a pulley two feet in diameter, provided the conditions of the faces 
of the pulleys, the arc of contact, the tension, and the number of feet 
the belt travels per minute are the same in both cases. 

3. To obtain a greater amount of power from belts the pulleys may be 
covered with leather; this will allow the belts to run very slack and give 
25% more durability. 

Endless Belts. — If the belts are to be endless, they should be put on 
and drawn together by "belt clamps" made for the puVpose. If the belt 
is made endless at the belt factory, it should never be ru.n on to the pulleys, 
lest the irregular strain spring the belt. Lift out one shaft, place the 
belt on the pullej^s, and force the shaft back into place. 

Belt Data. — A fly-wheel at the Amoskeag Mfg. Co., Manchester, N.H., 
30 feet diameter, 110 inches face, running 61 revs, per min., carried two 
heavy double-leather belts 40 Inches wide each, and one 24 inches wide. 
The engine indicated 1950 H.P., of which probably 1850 H.P. was trans- 
mitted by the belts. The belts w^ere heavily loaded, but not overtaxed, 
the speed being 323 ft. per min. for 1 H.P. per inch of width. 

Samue' Weboer {Am. Mach., Feb. 22, 1894) reports a case of a belt 30 
ins. wide, 3/8 in. tliick, running for six years at a velocity of 3900 ft, per 
rain., on to a pulley 5 ft. diameter, and transmitting 556 H.P. This gives 
a velocity of 210 ft. per min. for 1 H.P. per in. of width. By Mr. Nagle's 
table of riveted belts this belt would be designed for 332 H.P, By Mr. 
Taylor's rule it would be used to transmit only 123 H.P. 

The above may be taken as examples of what a belt may be made to 
do, but they should not be used as precedents' in designing. It is not 
stated how much power was lost by the journal friction due to over- 
tightening of these belts. 

The United States Navy Department Specifications for Leather 
Belting.^ Belting to be cut from No. 1 native packer steer hides or 
their equal. All hides to be tanned with white or chestnut oak by 
slow process (six to eight months) and chemical processes must not be 
used. The leather is to be thoroughly cured by hand and must not 
be stuffed or loaded for artificial weight. Leather must not crack 
open on grain side when doubled strongly by hand with grain side 
out. Belting is to be cut from central part of the hide no further 
than 15 in. from backbone or more than 48 in. from tail toward shoulder. 

Belts 8 in. and over must be cut to include backbone. All leather 
is to be stretched 6 in. in lengthwise direction of the butt and is 
not to exceed 54 in. after stretching. Centers and sides are to be 
stretched 6 in. separately. That is, all side leathers from which widths 
under 8 in. are to be cut, must be stretched after the belting is removed 
from the backbone center section. Center sections are to be stretched 
in exactly the same size for which they are to be used. 

For single belts up to 6 in., laps must not exceed 6 in. nor be less 
than 3 1/2 in. long. For single belts over 6 in. laps must not be more 
than 1 in. wider than belt. 

For double belts, laps must not exceed 5 1/2 in. nor to be less than 
3 1/2 in. No filling straps wall be permitted. All laps must be held 
securely at every part with the best quality of belt cement, and wdien 
pulled apart shall show no resinous, vitreous, oily or w^atered condition. 
Belting is to be stretched again after manufacture. 

Belting is to weigh for all sizes of single belts 16 oz. per sq. ft. and 
for double belts per sq. ft. as follows: 1 to 2 in., 26 oz.; 21/2 to 4 in., 
28 oz.; 41/2 to 5 in., 30 oz.; 6 in. and over, 32 oz. 

Only hand cut, green slaughter hides of the best quality are to be 
used for lacing. Raw hide laces to be cut 1/4, s/ie, 3/g, 7/16, 1/2, s/g, 
and 3/4-in. sizes. They must be cut lengthwise from the hide and 
have an ultimate tensile strength of not less than 

Width, in 1/4 5/16 3/8 7/16 I/2 S/g 8/4 

Tensile strength, lb. .. . 95 125 155 165 180 205 230 

Belt Dressings. — We advise that no belt dressing ' should be used 
except when the belt becomes dry and husky, and in such Instances we 



1152 BELTING. 

recommend the use of a dressing. Where this is not used beef tallow at 
blood-warm temperature should be applied and then dried in, either by 
artificial heat or the sun. The addition of beeswax to the tallow will be 
of some service if the belts are used in wet or damp places. Resin 
should never be used on leather belting. (Fayerweather & Ladew.) 

Belts should not be soaked in water before oiling, and penetrating oils 
should only be used when a belt gets very dry and husky from neglect. 
It may then be moistened a little, and neatsfoot oil applied. Frequent 
applications of such oils to a new belt render the leather soft and flabby, 
thus causing it to stretch, and making it liable to run out of line. A 
composition of tallow and oil, with a httle resin or beeswax, is better to 
use. Prepared castor-oil dressing is good, and may be apphed with a 
brush or rag while the belt is running. (Alexander Bros.) 

Some forms of belt aressing, the compositions of which have not been 
pubUshed, appear to have the property of increasing the coefficient of 
friction between the belt and the pulley, enabUng a given power to be 
transmitted with a lower belt tension than with undressed belts. C. W. 
Evans {Power, Dec, 1905), gives a diagram, plotted from tests, which 
shows that three of these compositions gave increased transmission for 
a given tension, ranging from about 10% for 90 lbs. tension per inch of 
width to 100% increase with 20 lbs. tension. 

Cement for CJoth or Leather. (Molesworth.) — 16 parts gutta- 
percha, 4 india-rubber, 2 pitch, 1 sheUac, 2 linseed-oil, cut small, melted 
together and well mixed. 

Rubber Belting. — The advantages claimed for rubber belting are 
perfect uniformity in width and tliickness; it will endure a great degree of 
heat and cold without injury; it is also specially adapted for use in damp 
or wet places, or where exposed to the action of steam; it is very durable, 
and has great tensile strength, and when adjusted for service it has the 
most perfect hold on the nullevs. hence is less Uable to sUd than leather. 

Never use animal oil or grease on rubber belts, as it will soon destroy] 
them. 

Rubber belts will be improved, and their durability increased, by 
putting on with a painter's brush, and letting it dry, a composition made 
of equal parts of red lead, black lead, French yellow, and litharge, mixed 
with boiled linseed-oil and japan enough to make it dry quickly. The 
effect of this will be to produce a finely polished surface. If, from dust 
or other cause, the belt should slip, it should be lightly moistened on the 
pulley side with boiled linseed-oil. (From manufacturers' circulars.) 

The best conditions are large pulleys and high speeds, low tension and 
reduced width of belt. 4000 ft. per min. Is not an excessive speed oa 
proper sized pulleys. 

H.P. of a 4-plv rubber belt = (length of arc of contact on smaller pulley 
in ft. X width of belt in ins. X revs, per min.) -5- 325. For a 5-ply belt 
multiply by 1 1/3, for a 6-ply by I2/3, for a 7-ply by 2, for an 8-ply by 21/3. 
When the proper weight of duck is used a 3- or 4-ply rubber belt is equal 
to a single leather belt and a 5- or 6-Dly rubber to a double leather belt. 
When the arc of contact is 180°, H.P. of a 4-ply belt = width m ins. X 
velocity in ft. per min. -^ 650. (Boston Belting Co.) 

Steel Belts. — The Eloesser-Kraftband-Gesellschaft, of Berhn, has 
introduced a steel belt for heavy power transmission at high speeds 
{Am. Mach., Dec. 24, 1908). It is a thin flat band of tempered steel. 
The ends are soldered and then clamped by a special device consisting of 
two steel plates, tapered to thin edges, which are curved to the radius 
of the smallest pulley to be used, and joined together by small screws 
which pass through holes in the ends of the belt. It is stated that the 
slip of these belts is less than 0.1%; they are about one-fifth the width 
of a leather belt for the same power, and they are run at a speed of 10,000 
ft. per minute or upwards. The following figures give a comparison of 
a rope drive with six ropes 1.9 ins. diam., a leather belt 9.6 ins. wide and 
a steel belt 4 ins. wide, for transmitting 100 H.P. on pulleys 3 ft. diam, 
30 ft. apart at 200 r.p.m. 

Rope Leather Steel 
Drive. Belt. Belt. 

Weight of pulley, lbs 2200 1120 460 

Weight of rope or belt, lbs 530 240 30 

Total cost of drive $335 $425 $260 

Power lost, per cent of 100 H.P 13 6 OtP 



ROLLER CHAIN AND SPROCKET DRIVES. 1153 

ROLLER CHAIN AND SPROCKET DRIVES. 

The following is abstracted from an article by A. E. Michel, in 
Mach'y, Feb., 1905. (Revised, March, 1915.) 

Steel chain of accurate pitch, high tensile strength, and good wearing 
quaUties, possesses, when used within proper limitations, advantages 
enjoyed by no other form of transmission. It is compact, affords a posi- 
tive speed ratio, and at slow speeds is capable of transmitting heavy 
strains. On short transmissions it is more efficient than belting and will 
operate more satisfactorily in damp or oily places. There is no loss of 
power from stretch, and as it aUows of a low tension, journal friction is 
minimized. 

Roller chain has been known to stand up at a speed of 4,000 ft. per 
min., and transmit 25 H.P. at 1,250 ft. per min.; but speeds of 1,000 ft. 
per min. and under give better satisfaction. Block chain is adapted to 
slower speeds, say 700 ft. per min. and under, and is extensively used on 
bicycles, small motor cars and machine tools. Where speed and pull are 
not fixed quantities, it is advisable to keep the speed high, and chain 
pull low, yet it should be borne in mind that high speeds are more de- 
structive to chains of large than to those of small pitch. 

The following table of tensile strengths, based on tests of " Diamond" 
chains taken from stock, may be considered a fair standard: 

Roller Chain. 

Pitch, in 1/2 5/8 3/4 1 11/4 11/2 13/4 2 

Tens, strength, 

lbs 2,500 3,900 5,600 10,000 15,600 18,500 30,500 40,000 

Block Cham.. . 1 inch, 1,200 to 2,500; II/2 inch, 5,000. 

The safe working load of a chain is dependent on the amount of rivet 
bearing surface, and varies from i/e to 1/30 of the tensile strength, ac- 
cording to the speed, size of sprockets, and other conditions peculiar to 
each case. The tendency now is to use the widest possible chain in 
order to secure maximum rivet bearing surface, thus insuring minimum 
wear from friction. Manufacturers are making heavier chains than 
heretofore for the same duty. As short pitch is always desirable, 
special double and even triple width chains are now made to conform 
to the requirements when a heavy single width chain of greater pitch 
is not practical. A double chain has a Uttle more than twice the rivet 
bearing surface and half again as much tensile strength as the corre- 
sponding single one. 

The length of chain for a given drive may be found by the following 
formula : 

All dimensions in inches. D = Distance between centers of shafts. 
A = Distance between limiting points of contact. R = Pitch radius of 
large sprocket, r = Pitch radius of small sprocket. N = Number of 
teeth of large sprocket, n = Number of teeth of small sprocket. P = 
Pitch of chain and sprockets. (180° + 2 a) = angle of contact on large 
sprocket. (180° — 2 a) = angle of contact on small sprocket, o. s= 
angle whose sine is (R — r)/D. A = D cos a. 

Length of chain required : 

^ 180 +2a__„ ,180 -2a _, _^_ 

^ = 360 ^^ + 360 riP -^2 cos a. 

For block chain, the total length specified in ordering should be in 
multiples of the pitch. For roller chain, the length should be in multi- 
ples of twice the pitch, as a union of the ends can be effected only with 
an outside and an inside link. 

Wherever possible, the distance between centers of shafts should per- 
mit of adjustment in order to regulate the sag of the chain. A chain should 
be adjusted, in proportion to its length, to show slack when running, care 
being taken to have it neither too tight nor too loose, as either condition 
is destructive. If a fixed center distance must be used, and results in 
too much sag, the looseness should be taken up by an idler, and when 
there is any considerable tension on the slack side, this idler must be 
a sprocket. Where an idler is not practical, another combination of 
sprockets giving approximately the same speed ratio may be tried, and 
in this manner a combination giving the proper sag may always be 
obtained. The Diamond Chain and Mfg. Co. says that the center 



1154 BELTING. 

line distance between sprockets should not be less than II/2 times the 
diameter of the larger sprocket nor more than 10 or 12 ft. 

In automobile drives, too much sag or too great a distance between 
shafts causes the chain to whip up and down — a condition detrimental 
to smooth running and very destructive to the chain. In this class 
of work a center distance of over 4 ft. has been used, but greater eflS- 
ciency and longer life are secured from the chain on shorter lengths, 
say 3 ft. and under. 

Sprocket Wheels. Properly proportioned and machined sprockets are 
essential to successful chain gearmg. The important dimensions of a 
sprocket are the pitch diameter and the bottom and outside diameters. 
For block chain these are obtained as follows: 

N = No. of teeth, b = Diameter of round part of chain block. B = 
Center to center of holes in chain block. A = Center to center of holes 
in side links, a = 180°/iV. Tan 3 = sin a 4- (B/A -{- cos a). 

Pitch diameter = A /sin 3, 

Bottom diam. = pitch diam. — 6. Outside diam. = pitch diam. + &. 

For roller chain: N = Number of teeth. P = Pitch of chain. D = 
Diameter of roller, a = 180°/iV. Pitch diameter = P/sin a. 

Bottom diam. = pitch diam. — D. 

For sprockets of 17 teeth and over, outside diam. = pitch diam. + D. 

The outside diameters of small sprockets are cut down so that the 
teeth will clear the roller perfectly at high speeds. 





Outside diam. 


= pitch diam. 


■\-D -E. 






Pitch. 




Values of E. 




8 to 12 
Teeth. 


13 to 16 
Teeth. 


1/2 in. to 3/4 in . . . 


0.062 in. 
0.125 in. 


0.031 in. 


1 in. to 2 in 


0.062 in. 



Sprocket diameters should be very accurate, particularly the base 
diameter, which should not vary more than 0.002 in. from the calculated 
values. Sprockets should be gauged to discover thick teeth and inaccur- 
ate diameters. A poor chain may operate on a good sprocket, but a bad 
sprocket will ruin a good chain. Sprockets of 12 to 60 teeth give best 
results. Fewer may oe used, but cause undue elongation m the cnain, 
wear the sprockets and consume too much power. Eight-tooth sprockets 
ruin almost every roller chain applied to them, and ten and eleven teeth 
are fitted only for medium and slow speeds with other conditions unusu- 
ally favorable. 

Sprocket teeth seldom break from insufficient strength, but the tooth 
must be properly shaped. A chain will not run well unless the sprockets 
have sidewise clearance and teeth narrowed at the ends by curves begin- 
ning at the pitch line. 

Calling W the width cf the chain between the links, 

^ = 1/2 If = width of tooth at top. B = uniform width below pitch line. 
B = W — 1/64 in. when W = 1/4 in. or less. 

= W — 1/32 in. when W = s/ie to s/g in. inclusive. 

= W — 1/16 in. when W = 3/4 in. or over. 

If the sprocket is flanged the chain must seat itself properly without the 
side bars coming into contact with the flange. 

The principal cause of trouble within the chain is elongation. It is 
the result of stretch of material or natural wear of rivets and their bearings. . 
To guard against the former, chain makers use special materials of high 
tensile strength, but a chain subjected to jars and jolts beyond the limit > 
of elasticity of the material may be put in worse condition in an instant 
than in months of natural wear. If for any reason a link elongates 
unduly it should be replaced at once, as one elongated link will eventually 
ruin the entire chain. Such elongation frequently results from all the 
load being thrown on at once. 

To minimize natural wear, chains should be well greased inside and 
out protected from mud and heavy grit, cleaned often and replaced to 



ROLLEK CHAIN AND SPROCKET DRIVES. 1155 

run in the same direction and same side up. A new chain should never 

be applied to a much-worn sprocket. 

Importance of pitch line clearances: In a sprocket with no clearances 
a new chain fits perfectly, but after natural wear the pitch of chain and 
sprocket become unlike. The chain is then elongated and climbs the 
teeth, which act as wedges, producing enormous strain, and it quickly 
wrecks itself. With the same chain on a driven sprocket, cut with 
clearances, all rollers seat against their teeth. After long and useful life, 
the working roller shifts to the top, and the other rollers still seat with 
the same ease as when new. Theoretically, all the rollers share the load. 
This never occurs in practice, for infinitesimal wear within the chain 
causes one, and only one, roller to bear perfectly seated against the 
working face of the sprocket tooth at any one time. Clearance alone on 
the driver will not provide for elongation. To operate properly the 
pitch of the driver must be lengthened, w^hich is done by increasing the 
pitch diameter by an amount dependent upon the clearance allowed. 
For theoretical reasoning' on this subject see "Roller Chain Gear," a 
treatise on English practice, by Hans Renold. 

When the load reverses, each sprocket becomes alternately driver and 
driven. This happens in a motor car during positive and negative accel- 
eration, or in ascending or descending a hill. In this event, the above 
construction is not applicable, for a driven sprocket of longer pitch than 
the chain will stretch it. No perfect method of equalizing the pitch of a 
roller chain and its sprockets under reversible load and at all periods of 
chain elongation has been found. This fault is eliminated in the " silent " 
type of chain: hence it runs smooth at a very much greater speed than 
roller chain will stand. 

In practice there are comparatively few roller chain drives with chain 
pull always in the same direction, so manufacturers generally cut the 
driver sprockets for these with normal pitch diameter, same as the 
driven. Recent experiments have proven that the difficulties are greatly 
lessened by cutting both driver and driven with liberal pitch line clear- 
ance. Accordingly, chain makers now advise the following pitch line 
clearance for standard rollers: 



Pitch, in., 


1/2 


3/4 


1 


11/4 


11/2 


13/4 2 


Clearance, in.. 


1/32 


1/16 


3/32 


3/16 


7/32 


1/8 5/32 



Cutters may be obtained from Brown & Sharpe Mfg. Co. with this 
clearance. 

Belting versus Chain Drives. — Chains are suitable for positive 
transmissions of very heavy powers at slow speed. They are properly 
used for conveying ashes, sand, chemicals and Uquids wliich would cor- 
rode or destroy belting. Chains of this kind are generally made of 
malleable iron. For conveyers for clean substances, flour, wheat an^ 
other grains, belts are preferable, and in the best installations leather is 
preferred to cotton or rubber, being more durable. Transmission 
chains have to be carefully made. If the chain is to run smoothly, 
noiselessly, and without considerable friction, both the links and the 
sprockets must be mathematically correct. This perfection of design 
is found only in the highest and best makes of steel chain. 

Deterioration of chains starts in with the beginning of service. Even 
in such light and flexible duty as bicycle transmission, a chain is sub- 
jected to sudden severe strains, which either stretch the chain or distort 
the bearing surfaces. Either mishap is fatal to smooth, frictionless 
running. If the transmission is positive, as from motor or shaft to a 
machine tool, sudden variations in strain become sledge-hammer blows, 
and the chain must either break or the parts yield. To avoid the evils 
arising from the stretching of the chain, self-adjusting forms of teeth 
have been invented, and the Renold and the Morse silent-chain gears 
are examples. 

Chain drives are recommended for use under the following conditions: 
(1) Where room is lacking for the proper size pulleys for belts. (2) 
Where the centers between shafts are too short for belts. (3) W^here a 
positive speed ratio is desired. (4) W^here there is moisture, heat or 
dust that would prevent a belt working properly. (5) W^here a maxi- 
mum power per inch of width is desired. 

The Renold and the IVIorse chain gears use springs in the sprocket 



1156 



BELTING. 



wheel to absorb the shock when a reversal of strain takes place, which 
is infrequent in ordinary power transmission, but is found in reciprocat- 
ing air-compressors and pumps, in gas-engine drives where an insufficient 
balance wheel is suppUed, and where a heavy shock load occiu's and it is 
desirable to cushion the effect by mounting the wheel on springs. 

Nickel steel is generally used for the chains. The joint pins are 
made from 31/2% nickel chrome steel, heat-treated. The ends of the 
joint pins are softened by an electric arc to facihtate riveting to the 
chain Unks. 

Data Used in the Preliminary Design of Morse Silent Cliain Drives 



Pitch, in 


1/2 


5/8 


3/4 


9/10 


12/10 


1 1/2 


2 


3 


Minimum no. of teeth : 
Small sprocket driver.. 
Small sprocket driven . 


13 
17 


13 
17 


13 
21 


15 
25 


15 
29 


17 
29 


17 
31 


17 
35 


Desirable no. of teeth 
in small sprockets 


15-17 


17-21 


17-21 


17-23 


17-23 


17-27 


17-31 


19-31 


Maximum no. of teeth in 
large sprockets. (See 
Note 3.J 


99 


109 


115 


125 


129 


129 


129 


131 


Desirable no. of teeth in 
large sprockets 


55-75 


55-75 


55-85 


55-95 


55-105 


55-115 


55-115 


55-115 


Pitch diam. of wheel = 
no. of teeth X 


0.159 


0.199 


0.239 


0.2865 


0.382 


0.477 


0.636 


0.955 


Addendum for outside 
diam.. of sprockets 20 to 
130 T. (See Note 1.), in. 


0.10 


0.12 


0.15 


0.18 


0.24 


0.30 


0.40 


0.60 


Maximum r.p.ra 


2400 1800 


1200 


1100 


850 


600 


400 


250 


Tension per in. width of 
chain, lb. : 
Small sprocket driver. . 
Small sprocket driven . 


80 100 
65 , 80 


120 
95 


150 
120 


200 
160 


270 
210 


450 
350 


750 
600 


Radial clearance beyond 
tooth required for 
chain, in 


0.50 0.62 


0.75 


0.90 


1.2 


1.5 


2.0 


3.0 


Approx. weight of chain 
per in. wide, I ft. long. 


1.00 1.20 


1.50 


1.80 


2.50 


3.00 


4.00 


6.00 


C for solid pinions 


0.0045.0.0063 


0.009 


0.013 


0.023 


0.035 


0.058 
2.0 


0.145 


C for armed sprockets . . 


0.16 0.25 


0.35 


0.45 


0.7 


1.0 


4.0 



Approximate Weights for Solid and Armed Sprockets. 
T = Number of teeth. F = Face in inches. 

C = Constant in lb. per in. in face per tooth as per table. 
Weight of armed sprocket = T X F X C. 
Add 25 % for split and 50 % for spring and spht sprockets. 
. Weight of sohd pmion = r2 x (F + 1) X C. 

Notes. 
1. — Number of teeth = T. 

Exact outside diameter = D. 
For T less than 20 teeth. D = pitch diameter. 
For T more than 20 teeth, D = pitch diameter + addendum. 
2. — Use sprockets having an odd number of teeth whenever possible. 
3. — When specially authorized, a larger number of teeth than shown 1 

may be cut in large sprocket. 
4. — Thickness of sprocket rim, including teeth, should be at least 

1.2 times the chain pitch. 
5. — The number of grooves in the sprocket, their width and distance 
apart, varies according to pitch and ^vidth of chain. Leave the 
designing and turning of grooves to the manufacturer. 
6. — The width of the sprocket should be i/s to 1/4 in. greater on small 
drives, and 1/4 to 1/2 in. greater on large drives than the nominal 
width of the chain. 



GEARING. 



1157 



7. — An even number of links in the chain and an odd number of teeth 

in the wheels are desirable. 
8. — Horizontal drives preferred; tight chain on top necessary for 
short drives without center adjustment, and desirable for long 
drives with or without center adjustment. 
9. — Adjustable wheel centers desirable for horizontal drives and 

necessary for vertical drives. 
10. — Avoid vertical drives. 
11. — Allow a side clearance for chain (parallel to axis of sprockets and 

measured from nominal width of chain) equal to the pitch. 
12. — Maximum linear velocity for commercial service, 1200 to 1600 
ft. per min. 

Comparison of Rope and Chain Drives. — ^Horse-power, 1200; 240 
to 80 r.p.m. 

Rope. Chain. 

Distance between centers 42 ft. 8 ft. 4 in. 

Diameter driving sheave or sprocket 6 ft. 4 1/2 in. 30.21 in. 

Diameter driven sheave or sprocket 20 ft. 89.42 in. 

The rope drive has 30 ropes, each I3/4 in. diameter. The chain drive 
has a Morse silent chain, length, 33.5 ft.; width, 27 in.; pitch, 3 in. 



Data of Some Chain Drives that Have Given Good Service 

Sprockets, Center Rev. H.P. 
No of Distance, per Trans- 
Teeth. In. Min. mitted. 
17 & 75 25.5 1750 & 397 7.5 
95 & 95 85 97 & 97 200 
59 & 95 169 97 & 60 200 

29 & 57 68 418 & 290 85 
61 «& 77 135 95 & 75 500 
61 & 83 103 95 & 70 1000 

30 & 89 100 240 & 80 1200 
26 & 120 144 300 & 65 350 

A chain transmission gear of 5000 H.P. has been built, with the 
total width of chain 168 in. The efficiency of the best chain drives 
when in good condition is claimed to be from 98 to 99 % . 







Speed, 


Pitch, 


Width. 


Ft. per 


In. 


In. 


Min. 


5/8 


2 1/2 


1550 


11/2 


12 


1150 


11/2 


18 


715 


2 


5 


1400 


3 


12 


1450 


3 


24 


1450 


3 


27 


1870 


2 


24 


780 



GEARING. 

TOOTHED-WHEEL GEARING. 

Pitch, Pitch-circle, etc. — If two cyUnders with parallel axes are 
pressed together and one of them is rotated on its axis, it will drive the 
other by means of the friction between the surfaces. The cylinders may 
be considered as a pair of spur-wheels with an infinite number of very small 
teeth. If actual teeth are formed upon the cyUnders, making alternate 
elevations and depressions in the cylindrical surfaces, the distance between 
the axes remaining the same, we have a pair of gear-wheels which will 
drive one another by pressure upon the faces of the teeth, if the teeth are 
properly shaped. In making the teeth the cylindrical surface may 
entirely disappear, but the position it occupied may still be considered as 
a cylindrical surface, wliich is called the "pitch-surface," and its trace 
on the end of the wheel, or on a plane cutting the wheel at right angles to 
its axis, is called the "pitch-circle" or "pitch-hne. " The diameter of 
this circle is called the pitch-diameter, and the distance from the face 
of one tooth to the corresponding face of the next tooth on the same 
wheel, measured on an arc of the pitch-circle, is called the "pitch of the 
tooth," or the circular pitch. 

If two wheels having teeth of the same pitch are geared together so 
that their pitch-circles touch, it is a property of the pitch-circles that 
their diameters are proportional to the number of teeth in the wheels, 
and vice versa; thus, if one wheel is twice the diameter (measured on the 
pitch-circle) of the other, it has twice as many teeth. If the teeth are 
properly shaped the hnear velocities of the two wheels are equal, and the 
angular velocities, or speeds of rotation, are inversely proportional to the 



1158 



GEARING. 



Thus the wheel that has twice as 



number of teeth and to the diameter. 

many teeth as the other will revolve 
just half as many times in a minute. 

The "pitch," or distance meas- 
ured on an arc of the pitch-circle 
from the face of one tooth to the 
face of the next, consists of two 
parts — the "tliickness" of the 
tooth and the "space" between it 
and the next tooth. The space is 
larger than the thickness by a small 
amount called the "backlash," 
which is allowed for imperfections 
of workmanship. In finely cut 
gears the backlash may be almost 
nothing. 

The length of a tooth in the 
direction of the radius of the w^heel 
is called the "depth," and tliis is divided into two parts: First, the 
"addendum," the height of the tooth above the pitch line; second, the 
"dedendum," the depth below the pitch4ine, which is an amount equal to 
the addendum of the mating gear. The depth of the space is usually 
given a Httle "clearance" to allow for inaccuracies of workmanship, 
especiallv in cast gears. 

Referring to Fig. 178, vh pl are the pitch-Unes, al the addendum-hne, 
rl the root-line or dedendum-line, cl the clearance-line, and b the back- 
lash. The addendum and dedendum are usually made equal to each 
other. (Some writers make the dedendum include the clearance.) 
, , ., ^ No of teeth 3.1416 . 

Diametral pitch = ~ 




Fig. 178 



Circular pitch = 



diam. of pitch-circle in inches ~" circular pitch* 
diam.X 3.1416 _ 3.1416 

No. of teeth diametral pitch' 



Some writers use the term diametral pitch to mean - 



diam. 



No. of teeth 

— o ^ ^J^ — f but the first definition is the more common and the more 

3-1413 

convenient. A wheel of 12 in. diam. at the pitch-circle, with 48 teeth, is 

48/12 = 4 diametral pitch, or simply 4 pitch. The circular pitch of the 

same wheel is 12 X 3.1416 ^ 48 = 0.7854, or 3.1416 -^^4 = 0.7854 in. 

Relation of Diametral to Circular Pitch. 



Diame- 




Diame- 






Diame- 




Diame- 


tral 


Circular 


tral 


Circular 


Circular 


tral 


Circular 


tral 


Pitch. 


Pitch. 


Pitch. 


Pitch. 


Pitch. 


Pitch. 


Pitch. 


Pitch. 


1 


3. 142 in. 


11 


0.286 in. 


3 


1.047 


15/16 


3.351 


1 1/2 


2.094 


12 


.262 


2 1/2 


1.257 


7/8 


3.590 


2 


1.571 


14 


.224 


2 


1.571 


13/16 


3.867 


21/4 


1.396 


16 


.196 


17/8 


1.676 


3/4 


4.189 


21/2 


1.257 


18 


.175 


I 3/4 


1.795 


11/16 


4.570 


2 3/4 


1.142 


20 


.157 


15/8 


1.933 


5/8 


5.027 


3 


1.047 


22 


.143 


1 1/2 


2.094 


9/16 


5.585 


31/2 


0.898 


24 


.131 


I 7/i6 


2.185 


1/2 


6.283. 


4 


.785 


26 


.121 


1 3/8 


2.285 


7/16 


7.181 


5 


.628 


28 


.112 


1 5/16 


2.394 


3/8 


8.378 


6 


.524 


30 


.105 


1 1/4 


2.513 


5/16 


10.053 


7 


.449 


32 


.098 


1 3/16 


2.646 


1/4 


12.566 


8 


.393 


36 


.087 


1 1/8 


2.793 


3/16 


16.755 


9 


.349 


40 


.079 


1 1/16 


2.957 


1/8 


25.133 


10 


.314 


48 


.065 


1 


3.142 


1/16 


50.266 



Since circ. pitch 



diam. X 3.1416 
No. of teeth 



diam. 



circ. pitch X No. of teeth 
3.1416 



which always brings out the diameter as a number with an inconvenient 
fraction if the pitch is in even inches or simple fractions of an inch. By 



TOOTHED-WHEEL GEARING. 



1159 



the diametral-pitch system this inconvenience is avoided. The diameter 
may be in even inches or convenient fractions, and the number of teeth 
is usually an even multiple of the number of inches in the diameter. 

Diameter of Pitch-line of Wlieels from 10 to 100 Teeth of 1 in. 
Circular Pitch. 



























^1 


ii 




U 


|1 


is 




§ fl 


6% 


i.s 




U 


H 


5 


H 


5 


rn 


5 


H 


s 


H 


Q 


H 


5 


10 


3.183 


26 


8.276 


41 


13.051 


56 


17.825 


71 


22.600 


86 


27.375 


11 


3.501 


27 


8.594 


42 


13.369 


57 


18.144 


72 


22.918 


87 


27.693 


12 


3.820 


28 


8.913 


43 


13.687 


58 


18.462 


73 


23.236 


88 


28.011 


13 


4.138 


29 


9.231 


44 


14.006 


59 


18.781 


74 


23.555 


89 


28.329 


14 


4.456 


30 


9.549 


45 


14.324 


60 


19.099 


75 


23.873 


90 


28.648 


15 


4.775 


31 


9.868 


46 


14.642 


61 


19.417 


76 


24.192 


91 


28.966 


16 


5.093 


32 


10.186 


47 


14.961 


62 


19.735 


77 


24.510 


92 


29.285 


17 


5.411 


33 


10.504 


48 


15.279 


63 


20.054 


78 


24.878 


93 


29.603 


18 


5.730 


34 


10.823 


49 


15.597 


64 


20.372 


79 


25.146 


94 


29.921 


19 


6.048 


35 


11.141 


50 


15.915 


65 


20.690 


80 


25.465 


95 


30.239 


20 


6.366 


36 


11.459 


51 


16.234 


66 


21.008 


81 


25.783 


96 


30.558 


21 


6.685 


37 


11.777 


52 


16.552 


67 


21.327 


82 


26.101 


97 


30.876 


22 


7.003 


38 


12.096 


53 


16.870 


68 


21.645 


83 


26.419 


98 


31.194 


23 


7.321 


39 


12.414 


54 


17.189 


69 


21.963 


84 


26.738 


99 


31.512 


24 


7.639 


40 


12.732 


55 


17.507 


70 


22.282 


85 


27.056 


100 


31.831 


25 


7.958 























For diameter of wheels of any other pitch than 1 in., multiply the figures 
in the table by the pitch. Given the diameter and the pitch, to find the 
number of teeth. Divide the diameter by the pitch, look in the table 
under diameter for the figure nearest to the quotient, and the number 
of teeth will be found opposite. 

Proportions of Teeth. Circular Pitch = 1. 





1 


1. 


2. 


3. 


4. 


5. 


6. 


Depth ot tooth above pitch-line 

Depth of tooth below pitch-line 

Working depth of tooth 


0.35 

.40 
.70 
.75 
.05 

.45 
.54 
.09 


0.30 
.40 
.60 
.70 
.10 
.45 
.55 
.10 


0.37 
.43 
J3 

.80 
.07 
.47 
.53 
.06 
47 


0.33 

■*;66" 

.75 


0.30 
.40 


0.30 
.35 


Total depth of tooth 


.70 


65 


Clearance at root 




Thickness of tooth 


.45 
.55 
.10 

45 


'!475 
.525 
.05 
70 


485 


Width of space 


515 


Backlash 


03 


Thif^kne«s of rim 


65 




7. 


8. 




?. 


10.* 


Depth of tooth above pitch- 
line 

Depth of tooth below pitch- 
line 


0.25 to 0.33 
.35 to .42 


0.30 
.35+. 08'' 


0.318 

.369 
.637 
.687 
.04 to .05 

.48 to .5 1 
52 tn ^ / 


I-P 

1 157-i.p 


Working depth of tooth. . . 


2^P 


Total depth of tooth 

Clearance at root 


.6 to .75 


.65+. 08'' 


2.157^P 
157-^p 


Thickness of tooth 

Width of space 


A8 to .485 

.52 to .515 
.04 to .03 


.48-. 03'' 
52+ 03" 


1.51 -Pto 

1.57 -rP 

1.57 -^Pto 


Backlash . . . 


.04H 


-.06" 


.0 t( 


..04^ 


1.63 - 
.Oto 


- P 

06- P 



* In terms of diametral pitch. 

Authorities. — 1. Sir Wm. Fairbairn. 2, 3. Clark, R. T. D.; "used 
by engineers in good practice. " 4. Molesworth. 5,6. Coleman Sellers: 
5 for cast, 6 for cut wheels. 7, 8. Unwin. 9, 10. Leading American 
manufacturers of cut gears. 

The Chordal Pitch (erroneously called "true pitch" by some authors) 
is the length of a straight line or chord drawn from center to center of two 
adjacent teeth. The term is now but little used, except in connection 
with chain and sprocket gearing. 



1160 



GEARING. 



Chordal pitch = diam. of pitch-circle X sine of 



180° 



Chordal 



No. of teeth 

pitch of a wheel of 10 in. pitch diameter and 10 teeth, 10 X sin 18° =« 
3.0902 in. Circular pitch of same wheel = 3.1416. Chordal pitch is 
used with chain or sprocket wheels, to conform to the pitch of the chain. 

Gears with Short Teeth. — There is a tendency in recent years to 
depart widely from the proportions of teeth given in the above and to 
use much shorter teeth, especially for heavy machinery. C. W. Hunt 
gives addendum and dedendum each = 0.25, and the clearance 0.05 of 
the circular pitch, making the total depth of tooth 0.55 of the circular 
pitch. The face of the tooth is involute in form, and the angle of action 
is 141/2°, C. H. Logue uses a 20° involute with the following proportions: 
Addendum 0.25P' = 0.7854 -^P; dedendum 0.30 P' = 0.9424 -i- P; 
clearance, 0.05P' = 0.157P: whole depth 0.55P' = 1.7278 -^ P. P' = 
circular pitch, P = diametral pitch. See papers by R. E. Flanders and 
Norman Litchfield in Trans. A. S. M. E., 1908. 

John Walker (Am. Mach., Mar. 11, 1897) says: For special purposes of 
slow-running gearing with great tooth stress I should prefer a length of 
tooth of 0.4 of the pitch, but for general work a length of 0.6 of the pitch. 
In 1895 Mr. Walker made two pairs of cut steel gears for the Chicago 
cable railway with 6-in. circular pitch, length = 0.4 pitch. The pinions 
had 42 teeth and the gears 62, each 20-in. face. The two pairs were 
set side by side on their shafts, so as to stagger the teeth, making the 
total face 40 ins. The gears transmitted 1500 H.P. at 60 r.p.ra. replac- 
ing cast-iron gears of 71/2 in. pitch which had broken in service. 
Formulae for Determining the Dimensions of Small Gears. 
(Brown & Sharpe Mfg. Co.) 

P = diametral pitch or the number of teeth to one inch of diameter of 
pitch-circle ; 



D'= diameter ot pitch- circle.. 

D = whole diameter 

N = number of teeth 

V = velocity 



d' = diameter of pitch-circle. . 

d = whole diameter. 

n = number of teeth 

V = velocity , 



Larger 
Wheel. 



Smaller 
Wheel. 



These 
wheels run 
together. 



a = distance between the centers of the two wheels; 

b = number of teeth in both wheels; 

t = thickness of tooth or cutter on pitch-circle; 

5 = adaendum; 
D" = working depth of tooth; 

/ = amount added to depth of tooth for rounding the corners and for 
clearance; 
£)''+/= whole depth of tooth; 

TT = 3.1416. 
P' = circular pitch, or the distance from the center of one tooth to th« 
center of the next measured on the pitch-circle. 

Formulae for a single wheel: ^^ 



P = 



iV+2 






D' = 
D = 



DXN 

N +2' 
N_ 
P' 
N + 2 



D''= J=25; 5=-i=— = 0.3183 P'; 
P P n * 



P-^ 



D = D 

Formulae for a pair of wheels 
6 = 2aP: n = 



N = PD-2; 
N^PD'; 

'^ 10' 

1.57 



D' 



A^+2 ' 



+ |; t- ^ 



s + /=^(l+^)=0.3685P. 
1/2 P'. 






PD'V 

V ' 

PD'V 



2a(N+2) 

b ' 

2 a (n+2) 



TOOTHED-WHEEL GEARING. 



1161 



n =- 



iV= 



n— 



NV, 

V * 

bv 
v + V' 

bV 



NV 






D' = 



2 ai; 



b 

2 ' 
2aV 



v + F 



Width of Teeth. — The width of the faces of teeth is generally made 
from 2 to 3 times the circular pitch, that is from 6.28 to 9.42 divided by 
the diametral pitch. There is no standard rule for width. 

The following sizes are given in a stock list of cut gears in "Grant's 
Gears:" 

Diametral pitch. . 34 6 8 12 16 

Face, inches 3 and 4 21/2 island 2 1 1/4 and II/2 3/4 and 1 1/2 and s/g 

The Walker Company gives: 
Circular pitch, in.. 1/2 s/g 3/4 7/3 1 1 1/2 2 21/2 3 4 5 6 
Face, in II/4 IV2 13/4 2 21/2 41/2 6 71/2 9 12 16 20 

The following proportions of gear-wheels are recommended by Prof. 
Coleman Sellers. (Stevens Indicator, April, 1892.) 





Proportions of Gear-wheels. 








Circular 

Pitch. 

P 


Outside of 
Pitch-line. 
P X0.3. 


Inside of Pitch-line . 


Width of Space. 


Diametral 
Pitch. 


For Cast 

or Cut 

Bevels or 

for Cast 


For Cut 
Spurs. 
PX0.35. 


For Cast 
Spurs or 
Bevels. 


For Cut 

Bevels or 

Spurs. 








Spurs. 


PX0.525. 


PX0.51. 








PX0.4. 






^ 




V4 


0.075 


O.IOO 


0.088 


0.131 


0.128 


12 


0.2618 


.079 


.105 


.092 


.137 


.134 


10 


0.31416 


.094 


.126 


.11 


.165 


.16 




3/8 


.113 


.150 


.131 


.197 


.191 


8 


0.3927 


.118 


.157 


.137 


.206 


.2 


7 


0.4477 


.134 


.179 


.157 


.235 


.228 




1/2 


.15 


.20 


.175 


.263 


.255 


6 


0.5236 


.157 


.209 


.183 


.275 


.267 




9/16 


.169 


.225 


.197 


.295 


.287 




5/8 


.188 


.25 


.219 


.328 


.319 


5 


0.62832 


.188 


.251 


.22 


.33 


.32 




3/4 


.225 


.3 


.263 


.394 


.383 


4 


0.7854 


.236 


.314 


.275 


.412 


.401 




7/8 


.263 


.35 


.307 


.459 


.446 




1 


.3 


.4 


.35 


.525 


.51 


3 


1.0472 


.314 


.419 


.364 


.55 


.534 




11/8 


.338 


.45 


.394 


.591 


.574 


2 3/4 


1.1424 


.343 


.457 


.40 


.6 


.583 




11/4 


.375 


.5 


.438 


.656 


.638 


21/2 


1.25664 


.377 


.503 


.44 


.66 


.641 




13/8 


.413 


.55 


.481 


.722 


.701 




11/2 


.45 


.6 


.525 


.788 


.765 


2 


1.5708 


.471 


.628 


.55 


.825 


.801 




13/4 


.525 


.7 


.613 


.919 


.893 




2 


.6 


.8 


.7 


1.05 


1.02 


11/2 


2.0944 


.628 


.838 


.733 


1.1 


1.068 




21/4 


.675 


.9 


.788 


1.181 


1.148 




21/2 


.75 


1.0 


.875 


1.313 


1.275 




23/4 


.825 


1.1 


.963 


1.444 


1.403 




3 


.9 


1.2 


1.05 


1.575 


1.53 




3.1416 


.942 


1.257 


1.1 


1.649 


1.602 




31/4 


.975 


1.3 


1.138 


1.706 


1.657 




31/2 


1.05 


1.4 


1 225 


1.838 


1.785 



Thickness of rim below root = depth of tooth. 



1162 GEARING. 

Rules for Calculating the Speed of Gears and PulleySo — The 

relations of the size and speed of driving and driven gear-wheels are the 
same as those of belt pulleys. In calculating for gears, multiply or 
divide by the diameter of the pitch-circle or by the number of teeth, as 
may be requiied. In calculating for pulleys, multiply or divide by their 
diameter in inches. 

If D = diam. of driving wheel, d = diam. of driven, R — revolutions 
per minute of driver, r = revs, per min. of driven, RD = rd; 
R = rd ^ D; r = RD -r- d; D = dr -^ R; d = DR -rr r. 

If iV == No. of teeth of driver and n = No. of teeth of driven, NR = nr; 
N = nr -r- R; n = NR -^ r; R = rn -^ N; r= RN -5- n. 

To find the number of revolutions of the last wheel at the end of a 
train of spur-wheels, all of which are in a line and mesh into one another, 
when the revolutions of the first wheel and the number of teeth or the 
diameter or tne first and last are given: Multiply the revolutions of the 
first wheel by its number of teeth or its diameter, and divide the product 
by the number of teeth or the diameter of the last wheel. 

To find the number of teeth in each wheel for a train of spur-wheels, 
each to have a given velocity: Multiply the number of revolutions of 
the driving-wheel by its number of teeth, and divide the product by the 
number of revolutions each wheel is to make. 

To find the number of revolutions of the last wheel in a train of wheels 
and pinions, when the revolutions of the first or driver, and the diameter, 
the teeth, or the circumference of all the drivers and pinions are given; 
Multiply the diameter, the circumference, or the number of teeth of all 
the driving-w^heels together, and this continued product by the number 
of revolutions of the first wheel, and divide this product by the contin- 
ued product of the diameter, the circumference, or the number of teeth 
of aU the driven wheels, and the quotient will be the number of revolutions 
of the last wheel. 

Example. — 1. A train of wheels consists of four wheels each 12 in. 
diameter of pitch-circle, and three pinions 4, 4, and 3 in. diameter. The 
large wheels are the drivers, and the first makes 36 revs, per min. Re- 
quired the speed of the last wheel. 

2. What is the speed of the first large wheel if the pinions are the 
drivers, the 3-in. pinion being the first driver and making 36 revs, per min.? 

12 X 12 X 12 ^ 

Milling Cutters for Interchangeable Gears. — The Pratt & Whit- 
ney Co. makes a series of cutters for cutting epicycloidal teeth. The 
number of cutters to cut from a pinion of 12 teeth to a rack is 24 for 
each pitch coarser than 10. The Brown & Sharpe Mfg. Co. makes a 
similar series, and also a series for involute teeth, in which eight cutters 
are made for each pitch, as follows: 

No 1 2 3 4 5 6 7 8 

Will cut from . 135 55 35 26 21 17 14 12 

to Rack 134 54 34 25 20 16 13 

FORMS OF THE TEETH. 

In order that the teeth of wheels and pinions may run together smoothly 
and with a constant relative velocity, it is necessary that their working 
faces shall be formed of certain curves called odontoids. The essential 
property of these curves is that when two teeth are in contact the com- 
mon normal to the tooth curves at their point of contact must pass through 
the pitch-point, or point of contact of the two pitch-circles. Two such . 
curves are in common use — the cycloid and the involute. 

The Cycloidal Tooth. — In Fig. 179 let PL and pi be the pitch- 
circles of two gear-wheels: GC and gc are two equal generating-circies, 
whose radii should be taken as not greater than one-half of the radius 
of the smaller pitch-circle. If the circle oc be rolled to the left on tne ^ 
larger pitch-circle PL, the point will describe an epicycloid, Oefgh. li 
the other ceneratins'-rirrle OC be rolled to the rierht on PL. the point • 
win describe a hypocycloid abed. These two curves, which are tangent i 



FORMS OF THE TEETH. 



1163 



at 0, form the two parts of a tooth curve for a gear whose pitch-circle is 

PL The upper part Oh is called the face and the lower part Odis called 
the flank. If the same circles be rolled on the other pitch-circle pi, they 
will describe the curve for a tooth of the gear pi, which will work properly 
with the tooth on PL. 

The cvcloidal curves may be drawn without actually rolhne: the gren- 
eratin^-circle, as follows: On the line PL, from 0, step off and mark equal 
distances, as 1. 2, 3, 4, etc. From 1, 2, 3, etc., draw radial Unes toward 
the center of PL, and from 6, 7, 8, etc.. draw radial lines from the same 
center, but beyond PL. With the radius of the generating-circle, ana 
with centers successively placed on these radial Unes, draw arcs of circles 
tangent to PL at 1, 2, 3, 6, 7, 8, etc. With the dividers set to one ot the 
equal divisions, as 01, step off on the generating circle gc the points a 0, 
c\ d', then take successively the chordal distances Oa, 06, Oc, Oct, 
and lay them off on the several arcs 6e, If, Sg, 9/i, and la, 2o, 6c, 4a; 
through the points efgh and abed draw the tooth curves- 




Fig. 179. 



The curves for the mating tooth on the other wheel may be found in 
like manner by drawing arcs of the generating-circle tangent at equidistant 
points on the pitch-circle pi. 

The tooth curve of the face Oh is limited by the addendum-line r or ri, 
and that of the flank OH by the root curve R or Ri. R and r represent 
the root and addendum curves for a large number of small teeth, and Rir 
the Uke curves for a small number of large teeth. The form or appearance 
of the tooth therefore varies according to the number of teeth, while the 
pitch-circle and the generating-circle may remain the same. 

In the cycloidal system, in order that a set of wheels of different diam- 
eters but equal pitches shall all correctly work together, it is necessary 
that the generating-circle used for the teeth of all the wheels shall be 
the same, and it should have a diameter not greater than half the diam- 
eter of the pitch-line of the smallest wheel of the set. The customary 
standard size of the generating-circle of the cycloidal system is one having 
a diameter equal to the radius of the pitch-circle of a wheel having 12 
teeth., (Some srear-makers adopt 15 teeth.) This circle gives a radial 
flank to the teeth of a wheel having 12 teeth. A pinion of 10 or even a 
smaller number of teeth can be made, but in that case the flanks will be 



1164 



GEARING. 



undercut, and the tooth will not be as strong as a tooth with radial 
flanks. If in any case the describing circle be half the size of the pitch- 
circle, the flanks will be radial ; if it be less, they will spread out toward 
the root of the tooth, giving a stronger form; but if greater, the flanks 
will curve in toward each other, whereby the teeth become weaker and 
difficult to make. 

In some cases cycloid al teeth for a pair of gears are made with the 
generating-circle of each gear having a radius equal to half the radius 
of its pitch-circle. In this case each of the gears will have radial flanks. 
This method makes a smooth working gear, but a disadvantage is that 
the wheels are not interchangeable with other wheels of the same pitch 
but different numbers of teeth. 

The rack in the cycloidal system is equivalent to a wheel with an 
infinite number of teeth. The pitch is equal to the circular pitch of 
the mating gear. Both faces and flanks are cycloids formed by rolling 
the generating-circle of the mating gear-wheel on each side of the 
straight pitch-line of the rack. 

Another method of drawing the cycloidal curves is shown in Fig. 180. 
It is known as the method of tangent arcs. The generating-circles, as 
before, are drawn with equal radii, the length of the radius being less 
than half the radius of pi, the smaller pitch-circle. Equal divisions 1, 2, 




Fig. 180. 

3, 4, etc., are marked off on the pitch-circles and divisions of the same 
length stepped off on one of the generating-circles, as 0, a, b, c. From the 
points 1, 2, 3, 4, 5 on the line pO, with radii successively equal to the chord 
distances a, 0&, Oc, Od,Oe, draw the five small arcs F. A line drawn 
through the outer edges of these small arcs, tangent to them all, will be 
the hypocycloidal curve for the flank of a tooth below the pitch-line pL 
From the points 1, 2, 3, etc., on the line 01, with radii as before, draw the 
small arcs G. A line tangent to these arcs will be the epicycloid for the 
face of the same tooth for which the flank curve has already been drawn. 
In the same way, from centers on the fine PO, and OL, with the same 
radii, the tangent arcs H and K may be drawn,, which will give the tooth 
for the gear whose pitch-circle is PL» 



FORMS OP THE TEETH. 



1165 



If the generating-circle had a radius just one-half of the radius of pU 

the hypocycloid F would be a straight line, and the flank of the tooth 
would have been radial. 

The Involute Tooth. — In drawing the involute-tooth curve, Fig. 181, 
the angle of obUquity, or the angle which a common tangent to the teeth, 
when they are in contact at the pitch-point, makes with a hne joining 
the centers of the wheels, is first arbitrarily determined. It is customary 
to take it at 15°. The pitch-Unes pi and PL being drawn in contact at O, 
the line of obUquity AB is drawn through O normal to a common tangent 
to the tooth curves, or at the given angle of obliquity to a common tan- 
gent to the pitch-circles. In the cut the angle is 20°. F,rom the centers 
of the pitch-circles draw circles c and d tangent to the hne AB, These 
circles are called base-lines or base-circles, from which the involutes F 
and K are drawn. By laying off convenient distances, 0, 1, 2, 3, which 
should each be less than Vio of the diameter of the base-circle, small arcs 
can be drawn with successively increasing radii, which will form the 
involute. The involute extends from the points F and K down to their 




Fig. 181. 

respective base-circles, where a tangent to the involute becomes a radius 
of the circle, and the remainders of the tooth curves, as G and H, are 
radial straight lines. 

To draw the teeth of a rack Mvhich is to gear with an involute wheel (Fig. 
182). — Let AB be the pitch-line of the rack and A/= //'= the pitch. 
Through the pitch-point / draw EF at the given angle of obliquity, 

E. G G^ 




Fig. 182. 



Draw AE and I'F perpendicular to EF. Through E and F draw lines 
EGG' and FH parallel to the pitch-Une. EGG' will be the addendum- 
line and HF the flank-Une. From / draw IK perpendicular to AB equal 
to the greatest addendum in the set of wheels of the given pitch and 
obliquity plus an allowance for clearance equal to l/s of the addendum. 
Through K, parallel to AB, draw the clearance-Une. The fronts of the 
teeth are planes perpendicular to EF, and the backs are planes inclined 
at the same angle to AB in the contrary direction. The outer half of the 
working face AE may be sUghtly curved. Mr. Grant makes it a circular 
arc drawn from a center on the pitch-line' with a radius = 2.1 inches 
divided by the diametral pitch, or 0.67 in. X circular pitch. 

In the involute system the customary standard form of tooth is one 
having an angle of obliquity of 15° (Brown and Sharpe use 141/2°). an 




1166 GEARING. 

addendum of about one-third the circular pitch, and a clearance of about 

one-eighth of the addendum. In this system the smallest gear oi a set 
has 12 teeth, this being the smallest num.ber of teeth that will gear together 
when made with this angle of obliquity. In gears with less than 30 teeth 
the points of the teeth must be slightly rounded over to avoid interference 
(see Grant's Teeth of Gears). All involute teeth of the same pitch and 
with the same angle of obUquitv work smoothly together. The rack to 
gear ^^-ith an involute-toothed wheel has straight faces on its teeth, w'hich 
make an angle with the middle hne of the tooth equal to the angle of 
obhquity, or in the standard form the faces are inchned at an angle ot 
30° with each other. . ^ ^ xv. 

To Draw an Angle of lS° without using a Protractor. — From C, on the 
line AC, with radius AC, draw an arc AB, and from A, with the same 

radius, cut the arc at B. Bisect 
the arc BA by drawing small arcs 
at D from, A and B as centers, 
with the same radius, which must 
be greater than one-half of AB, 
Join DC, cutting BA at E. The 
angle EC A is 30°. Bisect the arc 
AE in hke manner, and the angle 
FCA will be 15°. 

A property of involute-toothed 
wheels is that the distance between 
the axes of a pair of gears may be 
altered to a considerable extent 
without interfering with their ac- 
tion. The backlash is therefore 
variable at will, and may be ad- 
justed by mo\1ng the wheels farther 
from or nearer to each other, and 
may thus be adjusted so as to be no greater than is necessary to prevent 
jamming of the teeth. 

. The relative merits of cycloidal and involute-shaped teeth are a 
subject of dispute, but there is an increasing tendency to adopt the 
involute tooth for all purposes. 

Clark (R. T. D., p. 734) says: Involute teeth have the disadvantage of 
being too much inchned to the radial hne, by wliich an undue pressure is 
exerted on the bearings. 

Unwin (Elements of Machine Design, 8th ed., p. 265) says: The obhquity 
of action is ordinarily aheged as a serious objection to involute wheels. 
Its importance has perhaps been overrated. 

George B. Grant {Am. Mach., Dec. 26, 1885) says: 

1. The work done by the friction of an involute tooth is always less 
than the same work for any possible epicycloidal tooth. 

2. With respect to work done by friction, a change of the base from a 
gear of 12 teeth to one of 15 teeth makes an improvement for the epicycloid 
of less than one-half of one per cent. 

3. For the 12-tooth system the involute has an advantage of IVs per 
cent, and for the 15-tooth system an advantage of 3/4 per cent. 

4. That a maximum improvement of about one per cent can be accom- 
plished by the adoption of any possible non-interchangeable radial flank 
tooth in preference to the 12-tooth interchangeable system. 

5. That for gears of very few teeth the involute has a decided advan- 
tage. 

6. That the common opinion among millwTights and the mechanical 
public in general in favor of the epicycloid is a prejudice that is founded 
on long-continued custom, and not on an intimate knowledge of -the 
properties of that curve. 

Wilfred Lewis (Proc. Engrs. Club of Phila., vol. x, 1893) says a strong 
reaction in favor of the involute system is in progress, and he believes 
that an involute tooth of 22 1/2° obhquity wlU finally supplant aU other 
forms. 

A-Pproximation by Circular Arcs. — Having found the form of the 
actual tooth-curve on the drawing-board, circular arcs may be found by 
trial which will give approximations to the true curves, and these may be 
used in completing the drawing and the pattern of the gear-wheels. The 



FORMS OF THE TEETH. 



1167 



root of the curve is connected to the clearance by a fillet, which should 
be as large as possible to give increased strength to the tooth, provided 
it is not large enough to cause interference. 

Molesworth gives a method of construction by circular arcs as follows: 
From the radial line at the edge of the tooth on the pitch-line, lay off the 
line HK at an angle of 75° with the radial line; on this hnewill be the 
centers of the root AB and the point EF. The lines struck from these 
centers are shown in thick Unes. Circles drawn through centers thus 
found will give the hnes in wliich the remaining centers will be. The 
radius DA for striking the root AB is the pitch 4- the thickness of the 
tooth. The radius CE for striking the point of the tooth EF = the pitch. 







Fig. 184. 

George B. Grant says: It is sometimes attempted to construct the curve 
by some handy method or empirical rule, but such methods are generally 
worthless. 

Stub Gear Teeth. — The stub gear tooth developed by the Fellows 
Gear Shaper Co. has been largely adopted for automobile drives. The 
stub gear tooth has a shorter addendum and dedendum than the 
ordinary involute tooth. The pressure angle is 20° and the teeth are 
based on two diametral pitches, one of which is used to obtain the 
dimensions of the addendum and dedendum, while the other is used 
for the dimensions of the tooth thickness, the number of teeth and 
pitch diameter. Stub tooth gears are designated by a fraction as 
4/5 pitch, 10/12 pitch, etc. The numerator designates the pitch deter- 
mining the thickness of the tooth and number of teeth. The denomi- 
nator designates the pitch determining depth of the tooth. The 
clearance is (0.25 -7- diametral pitch). The advantages of this form 
of tooth compared to the ordinary involute gear tooth are: greater 
strength; same arc of rolling contact as in 141/2° involute tooth; avoid- 
ance of extreme sliding contact; more even wearing contact. Dimen- 
sions of the Fellows system of stub gear teeth are given in the table 
below: 

Fellows Stub Gear Tooth System (Dimensions in Inches). 











Depth of 






Diametral 
Pitch. 


Thick- 
ness of 
Tooth. 


Adden- 
dum. 


Working 
Depth. 


Space 
Below 
Pitch 
Line. 


Clear- 
an e. 


Whole 
Depth of 
Tooth. 


4/5 


0.3927 


0.2000 


0.4000 


0.2500 


0.0500 


0.4500 


5/7 


.3142 


.1429 


.2858 


.1786 


.0357 


.3214 


6/8 


.2618 


.1250 


.2500 


.1562 


.0312 


.2812 


7/9 


.2244 


.1111 


.2222 


.1389 


.0278 


.2500 


8/10 


.1963 


.1000 


.2000 


.1250 


-.0250 


.2250 


9/11 


.1745 


.0909 


.1818 


.1136 


.0227 


.2045 


10/12 


.1571 


.0833 


.1667 


.1041 


.0208 


.1875 


12/14 


.1309 


.0714 


.1429 


.0993 


.0179 


.1607 



Another system of stub gear teeth is also in use, in which the tooth 
dimensions are based upon circular pitch. The addendum is 0.250 X 
circular pitch, and the dedendum is 0.300 X circular pitch. The former 
system is the one in more general use. 



1168 



GEAEING. 




Stepped Gears. — Two gears of the same pitch and diameter mounted 
side by side on the same shaft will act as a single gear. If one gear is 
keyed on the shaft so that the teeth of the two wheels are not in Une, 
but the teeth of one wheel sUghtly in advance of the other, the two gears 
form a stepped gear. If mated with a similar stepped gear on a parallel 
shaft the number of teeth in contact will be twice as 
great as in an ordinary gear, which will increase the 
strength of the gear and its smoothness of action. 

Twisted Teeth. — If a great number of very thin 
gears were placed together, one slightly in advance of 
the other, they would still act as a stepped gear. Con- 
tinuing the subdivision until the thickness of each 
separate gear is infinitesimal, the faces of the teeth 
instead of being in steps take the form of a spiral or 
twisted surface, and we have a twisted gear. The twist 
may take any shape, and if it is in one direction for half 
the width of the gear and in the opposite direction for 
the other half, we have what is known as the herring- 
bone or double helical tooth. The obliquity of the 
twisted tooth if twisted in one direction causes an end 
thrust on the shaft, but if the herring-bone twist is Fig. 185. 
used, the opposite obliquities neutrahze each other. This form of tooth 
is much used in heavy rolling-mill practice, where great strength and 
resistance to shocks are necessary. They are frequently made of steel 
castings (Fig. 185). The angle of the tooth with a line parallel to the 
axis of the gear is usually 30°. 

Spiral or Helical Gears. — If a twisted gear has a uniform twist it 
becomes what is commonly called a spiral gear (properly a helical gear). 
The line in which the pitch-surface intersects the face of the tooth is part 
of a heUx drawn on the pitch-surface. A spiral wheel may be made with 
only one helical tooth wrapped around the cyUnder several times, in 
which it becomes a screw or worm. If it has two or three teeth so 
wrapped, it is a double- or triple-threaded screw or worm. A spiral-gear 
meshing into a rack is used to drive the table of some forms of planing- 
machine. For methods of laying out and producing spiral gears see 
Brown and Sharpe's treatise on Gearing and Halsey's Worm and Spiral 
Gearing, also Machy., May 1906 and Machy's Reference Series No. 20. 

Worm-gearing. — When the axes of two spiral gears are at right 
angles, and a wheel of one, two, or three threads works with a larger wheel 
of many threads, it becomes a worm-gear, or endless screw, the smaller 
wheel or driver being called the worm, and the larger, or driven wheel, 
the worm-wheel. With this arrangement a high velocity ratio may be 
obtained with a single pair of wheels. For a one-threaded wheel the veloc- 
ity ratio is the number of teeth in the worm-wheel. The worm and wheel 
are commonly so constructed that the worm will drive the wheel, but the 
wheel will not drive the worm. 

To find the diameter of a worm-wheel at the throat, number of teeth and 
pitch of the worm being given: Add 2 to the number of teeth, multiply 

the sum by 0.3183, and 
by the pitch of the worm 
in inches. 

To find the number of 
teeth, diameter at throat 
and pitch of worm being 
given: Divide 3.1416 
times the diameter by the 
pitch, and subtract 2 
from the quotient. 

In Fig. 186 ah is the 
diara. of the pitch-circle, 
cd is the diam. at the 
throat. 

Example. — Pitch of 
worm 1/4 in., number of teeth 70; required the diam. at the throat. (70 
4- 2) X .3183 X .25 = 5 .73 in. 

For design of worm gearing see Kimball and Barr's Machine Design. 
For efficiency of worm-gears see page 117 X. 




Fig. 186. 



FORMS OF THE TEETH. 1169 

The Hindley Worm. — In the Hindley worm-?ear the worm, in- 
stead of being cyhndrical in outhne, is of an hour-glass shape, the pitch 
line of the worm being a curved line corresponding to the pitch line of the 
gear. It is claimed that there is surface contact between the faces of 
the teeth of the worm and gear, instead of only line contact as in the case 
of the ordinary worm gear, but this is denied by some writers For 
discussion of the Hindley worm see Am. Mach., April 1, 1897 and 
Machy., Dec. 1908. The Hindley gear is made by the Albro-Clem 
Elevator Co., Philadelpliia. 

Teeth of Bevel-wheels. (Rankine*s Machinery and Millwork.) — 
The teeth of a bevel-wheel have acting surfaces of the conical kind, gen- 
erated by the motion of a line traversing the apex of the conical pitch- 
surface, while a point in it is carried round the traces of the teeth upon 
a spherical surface described about that apex. 

The operations of drawing the traces of the teeth of bevel-wheels exactly, 
whether by involutes or by rolUng curves, are in every respect analogous 
to those for drawing the traces of the teeth of spur-wheels; except that in 
the case of bevel-wheels all those operations are to be performed on the 
surface of a sphere described about the apex, instead of on a plane, sub- 
stituting poles for centers and great circles for straight lines. 

In consideration of the practical difficulty, especially in the case of 
large wheels, of obtaining an accurate spherical surface, and of drawing 
upon it when obtained, the follow- ^ 

ing approximate method, proposed 
originally by Tredgold, is generally 
used: / 

Let 0, Fig. 187, be the common / 

apex of the pitch-cones, OBI, OB'I, / 

of a pair of bevel-wheels; OC, OC , / 

the axes of those cones; 01 their M0/I/lMi 

line of contact. Perpendicular to ./.^^^MvvvJ 
01 draw AIA' , cutting the axes in ^'^^^^^S^ 
A, A'-, make the outer rims of the ^^^ 

patterns and of the wheels portions XT 

of the cones ABI, A'B'I, of which >v 

the narrow zones occupied by the \ 

teeth will be sufficiently near for 

practical purposes to a spherical A' - — xj 

surface described about 0. As the p^r 1S7 

cones ABl, A'B'l cut the pitch- "'• '* 

cones at right angles in the outer pitch-circles IB, IB', they may be called 

the normal cones. To find the traces of the teeth upon the normal cones, 

draw on a flat surface circular arcs, ID, ID' , with the radii AI, A'I\ those 

arcs will be the developments of arcs of the pitch-circles IB, IB' when the 

conical surfaces ABI, A'B'l are spread out flat. Describe the traces of 

teeth for the developed arcs as for a pair of spur-wheels, then wrap the 

developed arcs on the normal cones, so as to make them coincide with 

the pitch-circles, and trace the teeth on the conical surfaces. 

For formulae and instructions tor designing bevel-gears, and for much 
other valuable information on the subject of gearing, see "Practical 
Treatise on Gearing," and "Formulas in Gearing," published by Brown 
& Sharpe Mfg. Co.; and "Teeth cl Gears, " by George B. Grant, Lexington, 
Mass. The student may also consult Kankine's Machinery and Millwork, 
Reuleaux's Constructor, and Unwinds Elements of Macliine Design. See 
also article on Gearing, by C. W. MacCord in App. Cyc. Mech., vol. ii. 

Annular and Differential Gearing. (S. W. Balch, Am, Mach.-, 
Aug. 24, 1893.) — In internal gears the sum of the diameters of the describ- 
ing circles for faces and flanks should not exceed the difference in the 
pitch diameters of the pinion and its internal gear. The sum may be 
equal to tliis difference or it may be less; if it is equal, the faces of the 
teeth of each wheel will drive the faces as well as the flanks of the teeth of 
the other wheel. The teeth wiU therefore make contact with each other 
at two points at the same time. 

Cycloidal tooth-curves for interchangeable gears are formed with de- 
scribing circles of about ^/s the pitch diameter of the smaUest gear ot the 
series. To admit two such circles between the pitch-circles of the pinion 
and internal gear the number of teeth in the internal gear should exceed 



1170 



GEARING. 



the number in the pmion by 12 or more, if the teeth are of the customary 

proportions and curvature used in interchangeable gearing. 

Very often a less difference is desirable, and the teeth may be modified 
in several ways to make this possible. 

First. The tooth curves resulting from smaller describing circles may 
be employed. These will give teeth which are more rounding and nar- 
rower at their tops, and therefore not as desirable as the regular forms. 

Second. The tips of the teeth may be rounded until they clear. This 
is a cut-and-try method wliich aims at modifying the teeth to such out- 
lines as smaller describing circles would give. 

Third. One of the describing circles may be omitted and one only 
used, which may be equal to the difference between the pitch-circles. 
This will permit the mesliing of gears differing by six teeth. It will usu- 
aUy prove inexpedient to put wheels in inside gears that differ by much < 
less than 12 teeth. 

If a regular diametral pitch and standard tooth forms are determined 
on, the diameter to which the internal gear-blank is to be bored is calcu- 
lated by subtracting 2 from the number of teeth, and dividing the re- 
mainder by the diametral pitch. 

The tooth outlines are the match of a spur-gear of the same number 
of teeth and diametral pitch, so that the spur-gear will fit the internal 
gear as a punch fits its die, except that the teeth of each should fail to 
bottom in the tooth spaces of the other by the customary clearance of one- 
tenth the thickness of the tooth. 

Internal gearing is particularly valuable when employed in differential 
action. This is a mechanical movement in which one of the wheels is 
mounted on a crank so that its center can move in a circle about the center 
of the other wheel. Means are added which restrain the wheel on the 
crank from turning over and confine it to the revolution of the crank. 

The ratio of the number of teeth in the revolving wheel compared with 
the difference between the two ^-ill represent the ratio between the revolv- 
ing wheel and the crank-shaft by which the other is carried. The advan- 
tage in accomplishing the change of speed with such an arrangement, as 
compared with ordinary spur-gearing, hes in the almost entire absence of 
friction and consequent wear of the teeth. 

But for the limitation that the difference between the wheels must not 
be too small, the possible ratio of speed might be increased almost indefi- 
nitely, and one pair of differential gears made to do the service of a whole 
train of wheels. If the problem is properiy worked out with bevel-gears 
this limitation may be completely set aside, and external and internal 
bevel-gears, differing by but a single tooth if need be, made to mesh per- 
fectly with each other. 

EFFICIENCY OF GEAEEVG. 

An extensive series of experiments on the efficiency of gearing, chiefly 
worm and spiral gearing, is described by Wilfred Lewis in Trans. A. S. 
M. E., vii, 273. The average results are shown m a diagram, from 
which the following approximate average figures are taken: 

Efficiency of Spur, Spiral, and Worm-Gearing. 



Gearing. 


Pitch. 


Velocity at pitch-line in feet per min. 


3 


10 


40 


100 


200 


Spur pinion 




0.90 
.81 
.75 
.67 
.61 
.51 
.43 
.34 


0.935 
.87 
.815 
.75 
.70 
.615 
.53 
.43 


0.97 
.93 
.89 
.845 
.805 
.74 
.72 
.60 


0.98 
.955 
.93 
.90 
.87 
.82 
.765 
.70 


0.985 


Spiral pinion 


45° 

30 

20 

15 

10 

7 

5 


.965 




.945 


ft ft 


.92 


ft ft 


.90 


Spiral pinion or worm 


.86 

.815 

.765 



The experiments showed the advantage of spur-gearing over all other 
kinds in both durability and efficiency. The variation from the mean 
results rarely exceeded 5% in either direction, so long as no cutting 
occurred, but the variation became much greater and very irregular as 
soon as cutting began. The loss of power varies with the speed, the 



EFFICIENCY OF GEARING. 



1171 



pressure, the temperature, and the condition of the surfaces. The high 
friction of worm- and spiral-gearing is largely due to end thrust on the 
collars of the shaft, and may be considerably reduced by roller-bearings 
for the collars. 

When two worms with opposite spirals run in two spiral worm-gears 
that also work with each other, and the pressure on one gear is opposite 
that on the other, there is no thrust on the shaft. Even with light loads 
a worm will be^in to heat and cut if run at too high a speed, the limit for 
safe working being a velocity of the rubbing surfaces of 200 to 300 ft. 
per minute, the former being preferable where the gearing has to work 
continuously. The wheel teeth will keep cool, as they form part of a 
casting having a large radiating surface; but the worm itself is so small 
that its heat is dissipated slowly. Whenever the heat generated increases 
faster than it can be conducted and radiated away, the cutting of the 
worm may be expected to begin. A low efficiency for a worm-gear means 
more than the loss of power, since the power which is lost reappears as 
heat and may cause the rapid destruction of the worm. 

Unwin (Elements of Machine Design, p. 294) says: The efficiency is 
greater the less the radius of -the worm. Generally the radius of the 
worm = 1 .5 to 3 times the pitch of the thread of the worm or the circular 
pitch of the worm-wheel. For a one-threaded worm the efficiency, is 
only 2/5 to 1/4: for a two-threaded worm, 4/7 to 2/5 ; for a +hree-threaded 
worm, 2/3 to 1/2 . As so much work is wasted in friction it is natural that 
the wear is excessive. The table below gives the calculated efficiencies 
of worm-wheels of 1, 2, 3, and 4 threads and ratios of radius of worm to 
pitch of teeth of from 1 to 6, with a coefiacient of friction of 0.15. 



No. of 


Radius of Worm -^ Pitch. 


Threads. 


1 


1 1/4 


1 1/2 


13/4 


2 


21/2 


3 


4 


6 


1 


0.50 


0.44 


0.40 


0.36 


0.33 


0.28 


0.25 


0.20 


0.14 


2 


.67 


.62 


.57 


.53 


.50 


.44 


.40 


.33 


.25 


3 


.75 


.70 


.67 


.63 


.60 


.55 


.50 


.43 


.33 


4 


.80 


.76 


.73 


.70 


.67 


.62 


.57 


.50 


.40 



Efficiency of TVorm Gearing. — Worm gearing as a means of trans- 
mitting power has generally been looked upon with suspicion, its efficiency 
being considered necessarily low and its life short. When properly pro- 
portioned, however, it is both durable and reasonably efficient. Mr. F. 
A. Halsey discusses the subject in Am. Machinist, Jan. 13 and 20, 1898. 
He quotes two formulas for the efficiency of worm gearing: 



E 



tana (1 -/tana) 
tan a + / 



(1) ^- 



tana (1 — /tan a) 



approx., 



(2) 



tan a+ 2/ 

In which E = efficiency; a = angle of thread, being angle between thread 

and a line perpendicular to the axis of the worm: / = coefficient of friction. 

Eq. (1) applies to the worm thread only, while (2) applies to the worm 

and step combined, on the assumption that the mean friction ra dius o f the 

two is equal. Eq. (1) gives a maximum for E w^h en tan a = ^/l + P — f 
. . . (3) and eq. (2) a maximum when tan a = V2 4- 4/2 — 2/ . . . , (4) 
Using 0.05 for /gives a in (3) = 43° 34' and in (4) = 52° 49'. 

On plotting equations (1) and (2) the curves show the striking influence 
of the pitch-angle upon the efficiency, and since the lost work is expended 
in friction and wear, it is plain why worms of low angle should be short- 
lived and those of high angle long-lived. The following table is taken 
from Mr. Halsey 's plotted curves: 
Relation or Thread-angle, Speed and Efficiency of Worm-Gears. 



Velocity of 

Pitch-line, 

Feet per 

Minute. 


Angle of Thread. 


5 


10 


20 1 30 


40 


45 


Efficiency. 


3 


35 


52 


66 


73 


76 


77 


5 


40 


56 


69 


76 


79 


80 


10 


47 


62 


74 


79 


82 


82 


20 


52 


67 


78 


83 


85 


86 


40 


60 


74 


83 


87 


88 


88 


100 


70 


82 


88 


91 


91 


91 


200 


76 


85 


91 


92 


92 


92 



1172 



GEARING, 



The experiments of Mr. Wilfred Lewis on worms show a very satisfac- 
tory correspondence with the theory. Mr. Halsey gives a collection of 
data comprising 16 worms doing heavy duty and having pitch-angles 
ranging between 4° 30' and 45°, which show that every worm having an 
angle above 12° 30' was successful in regard to durability, and every worm 
below 9° was unsuccessful, the overlapping region being occupied oy 
worms some of which were successful and some unsuccessful. In several 
cases worms of one pitch-angle had been replaced by worms of a different 
angle, an increase in the angle leading in every case to better results and a 
decrease to poorer results. He concludes with the following table from 
experiments by Mr. James Christie, of the Pencoyd Iron Works, and gives 
data connecting the load upon the teeth with the pitch-hne velocity of 
the worm. 

Limiting Speeds and Pressures of Worm Gearing. 





Single-thread 
Worm 1" Pitch, 
27/8 Pitch Diam. 


Double- 
thread 
Worm r 
Pitch, 27/8 
Pitch Diam. 


Double- 
thread 
Worm 21/2" 

Pitch, 41/2 
Pitch Diam. 


Revolutions per minute 

Velocity at pitch-line, feet per 
minute 


128 

96 
1700 


201 

150 
1300 


272 

205 
1100 


425 
320 


128 
96 


201 

150 
1100 


272 

205 
1100 


201 

235 
1100 


272 

319 
700 


425 
498 


Limiting pressure, pounds 


700|1100 


400 



Efficiency of Automobile Gears. (G. E. Quick, Horseless Age, Feb. 12, 
1908.) — A set of slide gears was tested by an electric-driven absorption 
dynamometer. The following approximate results are taken from a 
series of plotted curves: 



Horse-power input 




2 1 4 1 6 1 8 1 10 1 14 1 18 




r.p.m. 


Efficiency, per cent. 


Direct driven, third speed , . 


.800 


89 


95 


97 


97 5 


97 5 


97 5 


96 


Direct driven, third speed 


1,500 


80 


89 


93 


95 


96 5 


97 


97 


Second speed, ratio 1 .76 to 1 . . . 


800 


87 


92 5 


94 


95 


94 


93 




Second speed, ratio 1 .76 to 1 ... 


1,500 


79 


88 


92,5 


94 


95 


95 


94 


First speed, ratio 3.36 to 1 


800 


75 


87.5 


93 


94 


94 


93 5 


9?, «> 


First speed, ratio 3.36 to 1 


1,500 


70 


84 


89 


92 


93 


97 




Reverse speed, ratio 4.32 to 1.. . 


800 


75 


84 


87 


87 


86 


H2 5 




Reverse speed, ratio 4.32 to 1... 


1,500 




70 


79 


83 


86 


87 


85 


Worm-gear axle, ratio 6.83 to h. 


400 


85 


S7 


86 5 


85.5 


84 


80 


75 


Worm-gear axle, ratio 6.83 to 1 .. 


800 


83 


87 


88.5 


89 


89 


88 


87 


Worm-gear axle, ratio 6.83 to 1 .. 


1.500 


80 


85 


87.5 


88.5 


89 


89 


89 



Two bevel-wheel axles were tested, one a floating type, ratio 15 to 32, 
141/2° involute; the other a sohd wheel and axle type, ratio 13 to 54, 20^^ 
involute. Both gave efficiencies of 95 to 96 % at 800 to 1500 r.p.m., 
and 10 to 26 H.P., with lower efficiencies at lower power and at lower 
speed. The friction losses include those of the journals and thrust ball 
bearings. 

The worm was 6-threaded, lead, 4.69 in.: pitch diam., 2.08 in.; the 
gear had 41 teeth; pitch diam., 10.2 in. The worm was of hardened 
steel and the gear of phosphor-bronze. A test of a steel gear and steel 
worm gave somewhat lower efficiencies. In both tests the heating was 
excessive both in the gears and in the thrust bearings, the balls in which 
were 7/iq in. diam. 

STRENGTH OF GEAR-TEETH. 

The strength of gear-teeth and the horse-power that may be transmitted 
by them depend upon so many variable and uncertain factors that it is 
not surprising that the formulas and rules given by different writers 
show a wide variation. In 1879 John H. Cooper (Jour. Frank. Inst., 
July, 1879) found that there were then in existence about 48 well-estab- 
lished rules for horse-power and working strength, differing from each 
other in extreme cases about 500%. In 1886 Prof. Wm. Harkness 
(Proc. A. A. A. S., 1886), from an examination of the bibUogrraphy of the 
subject, begiiming in 1796. found that according to the constants and 



STRENGTH OF GEAR-TEETH. 1173 

^fonnulse used by various authors there were differences of 15 to 1 in the 

power which could be transmitted by a given pair of geared wheels. 
The various elements which enter into the constitution of a formula to 
represent the working strength of a toothed wheel are the following: 
1. The strength of the metal, usually cast iron, which is an extremely 
variable quantity. 2. The shape of the tooth, and especially the relation 
of its thickness at the root or point of least strength to the pitch and to 
the length. 3. The point at which the load is taken to be applied, 
assumed by some authors to be at the pitch-line, by others at the extreme 
end, along the whole face, and by still others at a single outer corner. 
4. The consideration of whether the total load is at any time received 
by a single tooth or whether it is di\ided between two teeth. 5. The 
influence of velocity in causing a tendency to break the teeth by shock. 
6. The factor of safety assumed to cover all the uncertainties of the 
other elements of the problem. 

Prof. Harkness, as a result of his investigation, found that all the 
formulse on the subject might be expressed in one of three forms, viz.; 
Horse-power = CVpf, or CFp^ or CVp^f; 

in which C is a coefficient, V = velocity of pitch-line in feet per second, 
p = pitch in inches, and / = face of tooth in inches. 

Jb'rom an examination of precedents he proposed the following formula 
for cast-iron wheels: 

jj p^ _ 0.910 Vpf ^ 

Vl + 0.65 V 

He found that the teeth of chronometer and watch movements were 
subject to stresses four times as great as those wliich any engineer would 
dare to use in like proportion upon cast-iron wheels of large size. 

It appears that all of the earher rules for the strength ot teeth neglected 
the consideration of the variations in their form; the breaking strength, as 
said by Mr. Cooper, being based upon the tliickness of the teeth at the 
pitch-hne or circle, as if the tliickness at the root of the tooth were the 
same in all cases as it is at the pitch-line. 

Wilfred Lewis (Proc. Eng'rs Club, Phila., Jan., 1893; Am. Much., 
June 22, 1893) seems to have been the first to use the form of the tooth 
in the construction of a working formula and table. He assumes that 
in well-constructed machinery the load can be more properly taken as 
well distributed across the tooth than as concentrated in one corner, but 
that it cannot be safely taken as concentrated at a maximum distance 
from the root less than the extreme end of the tooth. He assumes that 
the whole load is taken upon one tooth, and considers the tooth as a 
beam loaded at one end, and from a series of drawings of teeth of the 
involute, cycloidal, and radial flank systems, determines the point of 
weakest cross-section of each, and the ratio of the thickness at that section 
to the pitch. He thereby obtains the general formula, 

W = spfy\ 

In which W is the load transmitted by the teeth, in pounds; 5 Is the safe 
working stress of the material, taken at 8000 lbs. for cast iron, when the 
working speed is 100 ft. or less per minute; p = pitch; / = face, in 
inches; ]/ = a factor depending on the form of the tooth, whose value for 
different cases is given in the table on page 1174. 

The values of s in the above table are given by Mr. Lewis tentatively, 
in the absence of sufficient data upon which to base more definite values, 
but they have been found to give satisfactory results in practice. 

Example. Required to find the working strength of a 12-toothed pin- 
ion, 1-inch pitch, 2 i^-inch face, driving a wheel of 60 teeth at 100 feet or 
less per minute, and let the teeth be of the 20-degree involute form. In 
the formula W = spfy we have for a cast-iron pinion s = 8000, pf = 2.5, 
and y = 0.078: and multiplying these values together, we have W = 
1560 pounds. For the wheel we have y = 0.134 and W = 2680 pounds. 

The cast-iron pinion is, therefore, the measure of strength; but if a 
steel pinion be substituted we have 5 = 20,000 and W = 3900 pounds, in 
which combination the wheel is the weaker, and it therefore becomes the 
measure of strength. 

For bevel- wheels Mr. Lewis gives the following, referring to Fig. 188: 



1174 



GEARING. 



D = large diameter of bevel; d = small diameter of bevel; p = pitch 
at large diameter; n = actual number of teeth; / = face of bevel; 
N = formative number of teeth = n X secant a, or 
■ the number corresponding to radius R; y = factor de- 
] pending upon shape of teeth and formative number iY; 
I w = working load on teeth, assumed to be apphed at 
' the large end of the bevel gear on the pitch line. 




W = spfu 



D^-d^ 



; or, more simply, W = spfy ■ 



/^ x' I which gives almost identical results when d is not less 
\ I than 2/3 D, as is the case in good practice. 

M jj^ ^^^ Mach., June 22, 1893, Mr. Lewis gives the 

following formulae for the working strength of the three 

188 systems of gearing, which agree very closely with those 

obtained by use of the table: 



For involute, 20° obliquity, 



For involute 15°, and cycloidal, 
For radial flank system, 



W= spf /o.l54-5:^); 

TF = sp/ (0.124 -^-fi); 



0.27 6> 
n 

in which the factor within the parenthesis corresponds to y in the general 
formula. For the horse-power transmitted, Mr. Lewis's general formula 

- 33,000 H.p. * 1 ^v, * XT -D ^pfy^ 

spfy = . may take the form H.P. 



W ■■ 



in which 



V - 33,000 

V = velocity in feet per minute; or since v = dir X r.p.m. -^ 12 
.2618 d X r.p.m., in wliich d = diameter in inches, 
Wv _ spfy X dX r.p.m. 
"" 126,050 



H.P. 



.000007933 dspfy X r.p.m. 



33,000 

It must be borne in mind, however, that in the case of machines which 
consume power intermittently, such as punching and shearing machines, 
the gearing should be designed with reference to the maximum load W, 
wliich can be brought upon the teeth at any time, and not upon the 
average horse-power transmitted. 

Values of y in Lewis's Formula. 



No. of 

Teeth. 



Factor for Strength y. 



Involute 
20° Ob- 
liquity. 



Involute 

15° and 

Cycloidal 



Radial 
Flanks. 



No. of 
Teeth. 



Factor for Strength, y. 



Involute 
20° Ob- 
liquity. 



Involute 

15° and 

Cycloidal 



Radial 
Flanks. 



12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
23 
25 



0.078 
.083 
.088 
.092 
.094 
.096 
.098 
.100 
.102 
.104 
.106 
.108 



0.067 
.070 
.072 
.075 
.077 
.080 
.083 
.087 
.090 
.092 
.094 
.097 



0.052 
.053 
.054 
.055 
.056 
.057 
.058 
.059 
.060 
.061 
.062 
.063 



27 

30 

34 

38 

43 

50 

60 

75 

100 

150 

300 

Rack. 



0.111 

.114 
.118 
.122 
.126 
.130 
.134 
.138 
.142 
.146 
.150 
.154 



0.100 
.102 
.104 
.107 
.110 
.112 
.114 
.116 
.118 
.120 
.122 
.124 



0.064 
.065 
.066 
.067 
.068 
.069 
.070 
.071 
.072 
.073 
.074 
.075 



Safe Working Stress, s, for Different Speeds. 


Speed of Teeth in 
. Ft. per Minute. 


100 or 

less. 


200 


300 


600 


900 


1200 


1800 


2400 


Cast iron 


8000 


6000 


4800 


4000 3000 1 2400 


2000 
5000 


1700 


Steel 


20000 


15000 


12000 


10000 


7500 


6000 


4300 



Comparison of the Harkncss and Lewis Formulae. — Take an 
average case in which the safe working strength of the material, s = 6000, 



STBENGTH OF GEAR-TEETH. 



1175 



v= 200 ft. per min., and y = 0.100, the value in Mr. Lewis's table for an 

involute tooth of 15° obhquity, or a cycloidal tooth, the number of teeth 
in the wheel being 27. 

Pfv 
■ 55 



H.P. = 



spfijv _ 6000 pfv X 0.100 



33,000 33,000 

if V is taken in feet per second. 



1.091 pfV, 



Prof. Harkness gives H.P. = 



0.910 Vpf 



If the V in the denominator 



Vi -f- 0.65 V 

be taken at 200 -^ 60 = 31/3 ft. per sec, H.P. = 0.571 pfV, or about 
52% of the result given by Mr. Lewis's formula. This is probably as 
close an agreement as can be expected, since Prof. Harkness derived his 
formula from an investigation of ancient precedents and rule-of-thumb 
practice, largely with common cast gears, while Mr. Lewis's formula was 
derived from considerations of modern practice witn machine-molded 
and cut gears. 

Mr. Lewis takes into consideration the reduction in working strength 
of a tooth due to increase in velocity by the figures in his table of the 
values of the safe working stress s for different speeds. Prof. Harkness 
gives expressio n to the sam e reduction by means of the denominator of 

his formula, '^l 4- 0.65 V. The decrease in strength as computed by 
this formula is somewhat less than that given in Mr. Lewis's table, and as 
the figures given in the table are not based on accurate data, a mean 
between the values given by the formula and the table is probably as 
near to the true value as may be obtained from our present knowledge. 
The following table gives the values for different speeds according to Mr. 
Lewis's table and Prof. Harkness's formula, taking for a basis a working 
stress s, for cast-iron 8000, and for steel 20,000 lbs. at speeds of 100 ft. 
per minute and less: 



V = speed of teeth, ft. per min. . 
V = speed of teeth, ft. per sec . . 



Safe stress s, cast iron, Lewis . 
Relative do., s 4- 8000 



1 -^ V) + 0.65 V 

Relative val. c -^ 0.693 

§1 = 8000 X (c -r 0.693).. 

Mean of s and si, cast-iron = S2. 
Mean of s and Si, for steel = S3.. 
Safe stress for steel, Lewis 



100 

1 2/3 



8000 

1 
,6930 

1 

8000 

8000 

20000 

20000 



200 
31/3 



6000 
0.75 

5621 
0.811 
6488 
6200 
15500 
15000 



300 
5 



4800 
0.6 

4850 
0.700 

5600 

5200 
13000 
12000 



600 
10 



4000 
0.5 

3650 
0.526 
4208 
4100 
10300 
10000 



900 
15 



3000 
0.375 
3050 
0.439 
3512 
3300 
8100 
7500 



1200 
20 



2400 
0.3 

.2672 
0.385 
3080 
2700 
6800 
6000 



1800 
JO 

2000 
0.25 
2208 
0.318 
2544 
2300 
5700 
5000 



2400 
40 



1700 
0.2125 

.1924 
0.277 
2216 
2000 
4900 
4300 



In Am. Mack., Jan. 30, 1902, Mr. Lewis says that 8,000 lbs. was given 
as safe for cast-iron teeth, either cut or cast, and that 20,000 lbs. was 
intended for any steel suitable for gearing whether cast or forged. 
These were the unit stresses for static loads. 

The iron should be of good quahty capable of sustaining about a ton 
on a test bar 1 in. square between supports 12 in. apart, and the steel 
should be sohd and of good quahty. The value given for steel was in- 
tended to include the lower grades, but when the quahty is known to be 
high, correspondingly higher values may be assigned. 

Comparing the two formulae for the case of s = 8000, corresponding to 
a speed of 100 ft. per min., we have 

Harkness: H.P. = 1 -^ Vl + 0.65 VX 0.9107p/= 1 .053 p/, 
spfyv _ spfyV ^ 8000 X 1 2/3 pfy 
550 



Lewis: H.P. = 



33,000 



550 



= 24.24 p/y, 



in which y varies according to the shape and number of the teeth. 
For radial-flank gear with 12 teeth y = 0.052; 24.24 p/v = 1.260p/; 

For20°inv.,19teeth, orl5°inv.,27teeth?/ = 0.100; 24.24 //v = 2.424p/; 
For 20° involute, 300 teeth y = 0.150; 24.24 p/?/ = 3.636p/. 

Thus the weakest-shaped tooth, according to Mr. Lewis, will transmit 
20 per cent more horse-power than is given by Prof. Harkness's formula, 
in which the shape of the tooth is not considered, and the average-shaped 



1176 GEARING. 

tooth, according to Mr. Lewis, will transmit more than double the 
horse-power given by Prof. Harkness's formula. 
Comparison of Other Formuiae.— Mr, Cooper, in summing up hia 

examination, selected an old English rule, which Mr. Lewis considers as 
a passably correct expression of good general averages, viz.: X = 2000 vf* 
X — breaking load of tooth in pounds, p = pitch, / = face. If a factor 
o^ safety of 10 be taken, this would give for safe working load W =200 vf- 

George B. Grant, in his Teeth of Gears, page 33, takes the breaking 
load at 3500 pf, and, with a factor of safety of 10, gives W = 350 pf. 

Nystrom's Pocket-Book, 20th ed., 1891, says: "The strength and dura- 
bility of cast-iron teeth require that they shall transhiit a force of 80 lbs. 
per inch of pitch and per inch breadth of face. " This is equivalent to 
W = 80 pf, or only 40% of that given by the English rule. 

F. A. Halsey (Clark's Pocket-Book) gives a table calculated from the 
formula H.P. = pfd X r.p.m. -r- 850. 

Jones & Laughlins give H.P. = pfdX r.p.m. -h 550. 

These formulae transformed give W = 128 pf and W = 218 p/, respec- 
tively. 

Unwin, on the assumption that the load acts on the corners of the 
teeth, derives a formula p = K ^W^ in which K is a coefficient derived 
from existing wheels, its values being: for slowly moving gearing not sub- 
ject to much vibration or shock K = 0.04; in ordinary mill-gearing, 
running at greater speed and subject to considerable vibration, K = .05; 
and in wheels subjected to excessive vibration and shock, and in mortise 
gearing, K = 0.06. Reduced to the form W = Cpf, assuming that/ = 
2 p, these values of K give W = 262 pf, 200 pf. and 139 pf, respectively. 

Unwin also give the following, based on the assumption that th e pres- 
sure is distributed along the edge of the tooth: p = Ki ^p/f^W, where 
Ki = about .0707 for iron wheels and .0848 for mortise wheels when 
the breadth of face is not less than twice the pitch. For the case of /= 
2 p and the given values of Ki tliis reduces to W = 200 p/and W = 139 pf, 
respectively. 

Box, in his Treatise on Mill Gearing, gives H.P. = 12 p^f \^dn -i- 1000, 
in which n = number of revolutions per minute. This formula differs 
from the more modern formulae in making the H.P. vary as j^f, instead 
of as pf, and in this respect itjs no doubt incorrect. 

Making the H.P. vary as ^dn or as ^v, instead of directly as v, makes 
the velocity a factor of the working strength as in the Harkness and 
Lewis formulae, the relative strength varying as 1/^v, which for different 
velocities is as follows: 

Speed of teeth in £t. per I jQQ 200 300 600 900 1200 1800 2400 

Relative strength = 1 0.707 0.574 0.408 0.333 0.289 0.236 0.20 

showing a somewhat more rapid reduction than is given by Mr. Lewis. 

For the purpose of comparing different formulae tliey may in general 
be reduced to either of the following forms: 

H.P. = Cpfv, H.P. = CipfdX r.p.m., W = cpf, 

in which p = pitch, / = face, d = diameter, all in inches; v = velocity 
in feet per minute, r.p.m. revolutions per minute, and C, Cx and c coeffi- 
cients. The formulae for transformation are as follows: 

H.P. = Wv -^ 33,000 = WXdX r.p.m. -^ 126,050; 

^ 33,000 H.P. 126,050 H.P. ^o nnn ^ r r ^ -^^ H-P- "^ 

Tr==- — ■ =— ft; = 33,000 Cpf; p/=-Tr- =77-77^ = — 

V d X r.p.m. ' ^j ^ t-j ^^ CidX r.p.m. c 

C, = 0.2618 C',c== 33,000 C; C = 3.82 C,, = 33^; c = 126,050 Ci. 

In the Lewis formula C varies with the form of the tooth and with the 
speed, and is equal to sy -^ 33,000, in which y and s are the values taken 
from the table, and c = sy. 

In the Harkness formula C varies with the speed and is eaual to 



STRENGTH OF GEAR-TEETH. 1177 

--—==- (F being in feet per second), = 0.01517 h- Vl + 0.011 v. 
VI + 0.65 V 

In the Box for mula C vari es with the pitch and also with the velocit3r. 

and equals ^^ ^ ^qq^ J'^'""' = .02345 -^ . c = 33,000 C = 774 A- , 

For V = 100 ft. per min. C = 77.4 p: for v = 600 ft. per mi n., c = 31.6 p. 
In the other formulae considered C, Ci, and c are constants. Reducing 
the several formulae to the form W = cpf, we have the following: 

COMPARISION OF DIFFERENT FORMULA FOR STRENGTH OF GeAR-TeETH. 

Safe working pressure per inch pitch and per inch of face, or value ol 
c in formula IF = cpf: 

?; = ft. per min. 100 600 

Lewis: Weak form of tooth, radial flank, 12 teeth c = 416 208 

Medium tooth, inv. 15°, or cycloid, 27 teeth. c = 800 400 

Strong form of tooth, inv. 20°, 300 teeth, .c = 1200 600 

Harkness: Average tooth c = 347 184 

Box: Tooth of 1 inch pitch c= 77 A 31.6 

Box: Tooth of 3 inches pitch c = 232 95 

The Gleason Works gives for ft. per min. 500 1000 1500 2000 2500 

working stress in pounds = p.f. X 480 400 340 290 240 

These are for cut gears, 18 teeth or more, rigidly supported, for average 
steady loads. Hammering loads, as in rolling mills and saw mills, require 
heavier gears. 

C. W. Hunt, Trans. A.S.M.E., 1908, gives a table of working loads of 
cut cast gears with a strong short form of tooth, which is practically 
equivalent to W = 700 pf . 

Various, in which c is independent of form and speed: Old English 
rule, c = 200; Grant, c = 350; Nystrom, c = 80; Halsey, c = 128; Jones 
& LaughUns, c = 218; Unwin, c = 262, 200, or 139, according to speed, 
shock, and vibration. 

The value given by Nystrom and those given by Box for teeth of small 
pitch are so much smaller than those given by the other authorities that 
they may be rejected as having an entirely unnecessary surplus of strength. 
The values given by Mr. Lewis seem to rest on the most logical basis, the 
form of the teeth as well as the velocity being considered; and since they 
are said to have proven satisfactory in an extended machine practice, 
they may be considered reliable for gears that are so well made that 
the pressure bears along the face of the teeth instead of upon the coimers. 
For rough ordinary work the old Enghsh rule W = 200 pf is probably 
as good as any, except that the figure 200 may be too high for weak forms 
of tooth and for high speeds. 

The formula 17= 200 p/ is equivalent to H .'P . = pfd X r.p.m.-^630'= pfv 
-M65 or, H. P. =0.0015873 p/d X r.p.m. = .006063 p/t-. 

Raw-hide Pinions. — Hnions of raw-hide are in common use for 
gearing shafts driven by electric motors to other shafts which carry 
machine-cut cast-iron or steel gears, in order to reduce vibration, noise 
and wear. A formula for the maximum horse-power to be transmitted 
by such gears, given by the New Process Raw-Hide Co., Syracuse, N. Y., 
is H.P. = pitch diam. X circ. pitch X face X r.p.m. -^ 850, or pfd X 
r.p.m. ^ 850. This is about 3/4 of the H.P. for cast-iron teeth by the old 
Enghsh rule. The formula is to be used only when the circular pitch 
does not exceed 1.65 ins. 

Composite gears also are made, consisting of alternate sheets of raw- 
hide or fibre and steel or bronze, so that a high degree of strength is 
combined with the smooth-running quality of the fibre. 

Maximum Speed of Gearing. — A. Towler, Eng'g, April 19, 1889, 
p. 388, gives the maximum speeds at which it was possible under favor- 
able conditions to run toothed gearing safely as follows, in ft. per min.: 
Ordinary cast-iron wheels, 1800; Helical, 2400; Mortise, 2400; Ordinary 
cast-steel wheels, 2600; HeUcal, 3000: special cast-iron machine-cut 
wheels, 3000. 

Prof. Coleman Sellers (Stevens Indicator, April, 1892) recommends that 
gearing be not run over 1200 ft. per minute, to avoid great noise. The 



1178 GEARING. 

Walker Company, Cleveland, Ohio, say that 2200 ft. per min. for iron 

gears and 3000 ft. for wood and iron (mortise gears) are excessive, and 
should be avoided if possible. The Coriiss engine at the Philadelphia 
Exhibition (1876) had a fly-wheel 30 ft. in diameter running 35 r.p.m. 
geared into a pinion 12 ft. diam. The speed of the pitch-line was 3300 ft. 
per min. 

A Heavy Machine-cut Spur-gear was made in 1891 by the Walker 
Company, Cleveland, Ohio, for a diamond mine in South Africa, with 
dimensions as follows: Number of teeth, 192; pitch diameter, 30 ft. 
6.66 ins.: face, 30 ins.: pitch, 6 ins.: bore, 27 ins.: diameter of hub, 9 ft. 
2 ins.: weight of hub, 15 tons: and total weight of gear, 663/4 tons. The 
rim was made in 12 segments, the joints of the segments being fastened 
witn two bolts each. Tne spokes were bolted to the middle of the seg- 
ments and to the hub with four bolts in each end. 

Frictional Gearing. — In frictional gearing the wheels are toothless, 
a.nd one wheel drives the other by means of the friction between the two 
Burfaces which are pressed together. They may be used where the power 
to be transmitted is not very great; when the speed is so high that toothed 
wheels would be noisy; when the shafts require to be frequently put into 
and out of gear or to have their relative direction of motion reversed; 
or when it is desired to change the velocity-ratio while the machinery 
is in motion, as in the case of disk friction-wheels for changing the feed 
In machine tools. 

Let P = the normal pressure in pounds at the Une of contact by which 
two wheels are pressed together, T = tangential resistance of the driven 
wheel at the Une of contact, / = the coefficient of friction, V the veloc- 
ity of the pitch-surface in feet per second, and H.P. = horse-power; then 
T may be equal to or less than/P; H.P. = TV -^ 550. The value off 
for metal on metal may be taken at 0.15 to 0.20; for wood on metal, 
0.25 to 0.30; and for wood on compressed paper, 0.20. The tangential 
driving force T may be as high as 80 lbs. per inch wddth of face of the 
driving surface, but this is accompanied by great pressure and friction on 
the journal-bearings. 

In frictional grooved gearing circumferential wedge-shaped grooves are 
cut in the faces of two wheels in contact. If P = the force pressing the 
wheels together, and ^V = the normal pressure on all the grooves, P = N 
(sin a + /cos a), in which 2 a = the incUnation of the sides of the grooves, 
and the maximum tangential available force T = fN. The incUnation 
of the sides of the grooves to a plane at right angles to the axis is usually 
30°. 

Frictional Grooved Gearing. — A set of friction-gears for trans- 
mitting 150 H.P. is on a steam-dredge described in Proc. Inst. M. E., 
July, 1888. Two grooved pinions of 54 in. diam., with 9 grooves of 13/4in. 
pitch and angle of 40° cut on their face, are geared into two wheels of 
1271/2 in. diam. similarly grooved. The wheels can be thrown in and out 
of gear by levers operating eccentric bushes on the large wheel-shaft. 
The circumferential speed of the wheels is about 500 ft. per min. AUow- 
ing for engine friction, if half the power is transmitted through each set 
of gears the tangential force at the rims is about 3960 lbs., requiring, if 
the angle is 40° and the coefficient of fricrion 0.18, a pressure of 7524 lbs. 
between the wheels and pinion to prevent sUpping. 

The wear of the wheels proving excessive, the gears were replaced by 
spur-gear wheels and brake-wheels with steel brake-bands, which arrange- 
ment has proven more durable than the grooved wheels. Mr. Daniel 
Adamson states that if the frictional wheels had been run at a higher 
speed the results would have been better, and says they should run at 
least 30 ft. per second. 

Power Transmitted by Friction Drives. (W. F. M. Goss, Trans. 
A. S. M. E., 1907.) — A friction drive consists of a fibrous or somewhat 
gelding driving wheel working in rolling contact with a metallic driven i 
wheel. Such a drive may consist of a pair of plain cvUnder wheels 
mounted upon parallel shafts, or a pair of beveled wheels, or of any 
other arrangement which wiU serve in the transmission of motion by 
rolhng contact. 

Driving wheels of each of the materials named in the table below wer«^ 
tested in peripheral contact with driving wheels of iron, aluminum and 
type metal. All the wheels were 16 in. diam. ; the face of the driving 



FRICTION CLUTCHES. 



1179 



wheels was 13/4 in., and that of the driven wheels 1/2 in. Records were 
made of the pressure of contact, of the coefficient of friction developed, 

and of the percentage of slip resulting from the development of the said 
coefficient of friction. Curves were plotted showing the relation of the 
coefficient and the slip for pressures of 150 and 400 lbs. per inch width 
of face in contact. Another series of tests was made in which the slip 
was maintained constant at 2% and the pressures were varied. In most 
of the combinations it was found that with constant slip the coefficient 
ot friction diminished very shghtlv as the pressure of contact was in- 
creased, so that it may be considered practically constant for all pres- 
sures between 150 and 400 lbs. per sq. in. 

The crushing strength of each material under the conditions of the 
test was determined by running each combination with increasing loads 
until a load was found under which the wheel failed before 15,000 revo- 
lutions had been ma.de. The results showed the failure of the several 
fiber wheels under loads per inch of width as follows: Straw fiber 
750 lbs.; leather fiber, 1,200 lbs.; tarred fiber, 1,200 lbs.; leather, 750 lbs.; 
sulphite fiber, 700 lbs. One-fifth of these pressures is taken as a safe 
working load. The coefficient of iriction approaches its maximum 
value when the shp between driver and driven wheel is 2%. The safe 
working horse-power of the drive is calculated on the basis of 60% the 
coefficient developed at a pressure of 150 lbs. per inch of width, a re- 
duction of 40% being made to cover possible decrease of the co^.^cient 
in actual service and to cover also loss due to friction of the journals. 
From these data the following table is constructed showing the H.P. 
that may be transmitted by driving wheels of the several materials 
named when in frictional contact with iron, aluminum and type metal. 

The formula for horse-power is H.P.= || X ^^^^^qqq'^^ = KdWN, in 

which d = diam. in inches, TF = width of face in inches, P = safe work- 
ing pressure in lbs. per in. of v/idth, N = revs, per min., / = coefficient 
of friction, 0.6 a factor for the decrease of the coefficient in service and 
for the loss in journal friction, K a coefficient including P, / and the 
numerical constants. 

Coefficients of Friction and Horse-power of Friction Drives. 





On Iron. 


On Aluminum. 


On Type Metal. 




/ 


k 


/ 


k 


/ 


k 


Straw fiber 


0.255 
0.309 
0.150 
0.330 
0.135 


0.00030 
0.00059 
0.00029 
0.00037 
0.00016 


0.273 
0.297 
0.183 
0.318 
0.216 


0.00033 
0.00057 
0.00035 
0.00035 
0.00026 


0.186 
0.183 
0.165 
0.309 
0.246 


0.00022 


Leather fiber 


00035 


Tarred fiber 


0.00031 


Sulphite fiber 

Leather 


0.00034 
0.00029 



Horse-power = K x d WN, 

Friction Clutches. — Much valuable information on different forms of 
friction clutches is given in a paper by Henry Souther in Trans. A. S. M. 
E., 1908, and in the discussion on the paper. All friction clutches contain 
two surfaces that rub on each other when the clutch is thrown into gear, 
and until the friction between them is increased, by the pressure with 
which they are forced together, to such an extent that the surfaces bind 
and enable one surface to drive the other. The surfaces may be metal 
on metal, metal on wood, cork, leather or other substance, leather on 
leather or other substance, etc. The surfaces may be disks, at right 
angles to the shaft, blocks sliding on the outer or inner surface, or both, 
of a pulley rim, or two cones, internal and external, one fitting in the 
other, or a band or ribbon around a pulley. The driving force which is 
just sufficient to cause one part of the clutch to drive the other is the 
product of the total pressure, exerted at right angles to the direction of 
sliding, and the coefficient of friction. The latter is an axceedingly 
variable quantity, depending on the nature and condition of the sliding 
surfaces and on their lubrication. The surfaces must have sufficient 
area so that the pressure per square inch on that area will not be suffi- 
cient to cause undue heating and wear. The total pressure on the parts 
of the mechanism that forces the surfaces together also must not cause 
undue wear of these parts. 



llgO 



GEAHING. 



For cone clutches, Reuleaux states that the angle of the cone should 
not be less than 10°, in order that the parts may not become wedged 
together. He gives the coefficient of cast iron on cast iron, for such 
clutches, at 0.15. 

For clutches with maple blocks on cast iron Mr. Souther gives a coeffi- 
cient of 0.37, and for a speed of 100 r.p.m. he gives the following table of 
capacity of such clutches, made by the Dodge Mfg. Co. 



Horse- 
power. 


Block 
Area, Ins. 


Diam. at 
Block, Ins. 


Circumferen- 
tial Pull at 
Block Center, 
Lbs. 


Total 
Pressure. 


Total Pres- 
sure per 
Sq. In. 


25 
32 
50 
98 


120 
141 
208 
280 


16 
18 

21.5 
27.5 


1.960 
2.240 
2.900 
4.500 


5.300 
6.000 
7.800 
12.000 


44 

44.5 
37.5 
43.5 



Prof. I. N. Hollis has found the coefficient of cork on cast iron to be 
from 0.33 to 0.37, or about double that of cast iron on cast iron or on 
bronze. A set of cork blocks outlasted a set of maple blocks in the ratio 
of five to one. Prof. C. M. Alien has found the torque for cork inserts 
to be nearly double that of a leather-faced clutch for a given dimension. 

Disk clutches for automobiles are made with frictional surfaces of 
leather, bronze, or copper against iron or steel. The Cadillac Motor Car 
Co. give the following: Mean radius of leather frictional surface 45/i6ins; 
area of do., 36V2sq.ins.; axial pressure, 1000 to 1200 lbs.; H.P. capacity 
at 400 r.p.m., 51/2 H.P.: at 1400 r.p.m., 10 H.P. 

C. H. Schlesinger (Horseless Age, Oct. 2, 1907) gives the following 
formula for the ordinary cone clutch: 

H.P. = PfrR -f- 63,000 sin. d, 

in which P = assumed pressure of engaging spring in lbs., / = coeff. of 
friction, which in ordinary practice is about 0.25; r = mean radius of 
the cone, ins.; R = T.p.m. of the motor; 6 = aiigle of the cone with the 
axis. Mr. Souther says the value of / = 0.25 is probably near enough 
for a properly lubricated leather-iron clutch. 

The Hele-Shaw clutch, with V-shaped rings struck up in the surfaces 
of disks, is described in Proc. Inst. M. E., 1903. A clutch of this form 
18 ins. diam. between theV's transmitted 1000 H.P. at 700 or 800 r.p.m. 

Coil Friction Clutches. (H. L. Nachman, Am. Much., April 1, 1909.) 
— Friction clutches are now in use which will transmit 1000, and even 
more, horse-power. A type of clutch which is satisfactory for the trans- 
mission of large powers is the coil friction clutch. It consists of a steel 
coil wound on a chilled cast-iron drum. At each end of the coil a head 
is formed. The head at one end is attached to the pulley or shaft that is 
to be set in motion, wliile that at the other end of the coil serves as a 
point of application of a force which pulls on the coil to wind it on the 
drum, thus gripping it firmly. 

The friction of the coil on the drum is the same as that of a rope or 
belt on a pulley. That is, the relation of the tensions at the two ends of 
the coil may be found from the equation P/Q = e^^ where P = pull at fixed 
end of coil; Q = pull at free end of coil; e= base of natural logarithms = 
2.718; n = coefficient of friction between coils and drum; and a= Angle 
subtended by coil in radian measure, = 6.283 for each turn of coil. 

Values of P/Q for different numbers of turns are as follows, assuming 
N = 0.05 for steel on cast iron, lubricated: 
No. of turns 1234567 8 

P/Q = 1.37 1.87 2.57 3.51 4.81 6.58 8.60 12.33 



If D = diam. of drum in ins., N = 
(12 X 33.000) = 0.00000793 Z>iVP. 



revs., per min., then H.P. =;rZ)iVP-j- 



HOISTING AND CONVEYING. 



1181 



HOISTING AND CONVEYING. 

strength of Ropes and Chains. — For the weight and strength of rope 
for hoisting see notes and tables on pages 410 to 416. For strength of 
chains see page 264. 

Working Strength of Blocks. 

(Boston and Lockport Block Co., 1908.) 

REGULAR BLOCKS WITH LOOSE HOOKS— LOADS IN POUNDS 



Size, Inches. 


5 


6 


8 


10 


12 


14 


Rope diameter, inches .... 
2 single blocks 


9/16 

150 
250 
400 


3/4 
250 
400 
650 


7/8 
700 
1200 
1900 


1 
2000 
4000 
6000 


1 1/8 
4000 
8000 
12000 


7000 


2 double blocks 


12000 


2 triple blocks 


19000 







LOADS IN TONS. 












Wide Mortise with 
Loose Hooks. 


Extra Heavy with 
Shackles. 


Size, inches 

Rope, diam., in. . . . 
2 single blocks. . 


8 
1 

1/2 
1 

2 


10 

11/4 

2 
3 

4 


12 

15/16 
4 
6 
8 


14 

15/8 
6 
8 
10 


16 

13/4 
10 
12 
14 


18 
2 


20 

21/4 


22 

2 1/2 


24 
3 


2 double blocks. . . . 

2 triple blocks 

2 fourfold blocks . . 


25 
30 
40 


30 
35 

45 


35 
40 
55 


40 
50 
70 

















WORKING LOADS FOR A PAIR OF WIRE-ROPE BLOCKS-TONS 


Loose Hooks. 


Shackles. 


Sheave 


Two 


Two 


Two 


Two 


Two 


Two 


Diam., In. 


Singles. 


Doubles. 


Triples. 


Singles. 


Doubles. 


Triples. 


8 


3 


4 


5 


4 


5 


6 


10 


4 


5 


6 


6 


8 


10 


12 


5 


6 


7 


8 


10 


12 


14 


6 


7 


8 


10 


12 


15 


16 


7 


8 


10 


12 


15 


20 


18 


8 


10 


12 


15 


20 


25 



Chain Blocks. — Referring to the table on the next page, the speed 
of a chain block is governed by the pull required on the hand chain 
and the distance the hand chain must travel to lift the load the re- 
quired distance. The speeds are given for short lifts with men ac- 
customed to the work; for continuous easy lifting two-thirds of these 
speeds are attainable. The triplex block lifts rapidly, and the speed 
increases for light loads because the length of hand chain to be overhauled 
is small. This fact also enables the operator to lower the load very 
quickly with the triplex block. The 12- to 20-ton triplex blocks are 
provided with two separate hand wheels, thus permitting two men to 
hoist simultaneously, thereby securing double speed. In the triplex 
block the power is transmitted to the hoisting-chain wheel by means of a 
train of spur gearing operated by the hand chain. In the duplex block 
the power is transmitted through a worm wheel and screw. In the dif- 
ferential block the power is applied by pulling on the slack part of the 
load chain and the force is multipUed by means of a differential sheave. 
(See page 539.) The relative efficiency and durability of the three types 
are as follows: 





Differen- 
tial. 


Duplex. 


Triplex. 


Relative efficiency 


35 
20 
40 


50 
80 
80 


100 


Relative durability 


100 


Relative cost 


too 



1182 



HOISTING AND CONVEYING* 



Chain Block Hoisting Speeds* 

(Yale & Towne Mfg. Co., 1908.) 





Pull 


Feet of Hand- 


Hoisting Speeds. Feet per Minute 




in Pounds re- 
quired on 
Hand-Chain 

to Lift 
Full Loads. 


Chain to be 


Attainable and No. of Men re- 




PuUea by 


quired for Hoisting Full Loads 


s 


Operator to 

Lift Load 

One Foot 

High. 


without Pulling over 80 Lb. 




Triplex. 


Duplex. 


Differ- 
ential. 










1 








rt 


























•"0 




u 


i 


i 


^ 13 


X 
o 


>< 




3 


^i 




• 6 


h3 




03 


^d 






& 


ia'-^ 


a 


13 




3 


M^ 


B^ 




=3 


o o 


"3 






H 


Q 


Q- 


H 


Q 


Q 


i^ 




a 




t^ 


-i— 


6. 
6 


-J— 


V4 






72 
122 






18 
24 










1 


1/2 


62 


68 


21 


40 


8. 


16. 


24. 


1 


4. 


.... 


2 


1 


82 


87 


216 


31 


59 


30 


4. 


8. 


12. 


1 


2 


1 


^ 70 


^ 


11/2 


110 


94 


246 


35 


80 


36 


4.8 


9.6 


14.4 


2 


2,40 


2 


?, 50 


^ 


2 


120 


115 


308 


42 


93 


42 


3.6 


7.2 


10.8 


2 


1 80 


?, 


? 30 


4 


3 


114 


132 


557 


69 


126 


38 


2.3 


4.6 


6.9 


2 


I 10 


?, 


? 30 


7 


4 


124 

no 

130 

135 

140 

130* 

135* 

140* 


142 
145 
145 
160 
160 




84 
126 
126 
168 
210 
126* 
168* 
210* 


155 
195 
252 
310 
390 




1.7 
1.3 
1.1 
0.8 
0.6 
1.1 
0.8 
0.6 


3.5 
2.6 
2.2 
1.6 
1.2 
2.2 
1.6 
1.2 


5.2 
3.9 
3.3 
2.4 
1.8 
3.3 
2.4 
1.8 


2 
2 
2 
2 
2 
4 
4 
4 


0.80 
0.65 
0.50 
0.35 
0.30 


2 
2 
2 
2 
2 






5 






6 






8 






10 






12 






16 


















20 


















♦ On eac 


h of 


the 


two 


hanc 


i-cha 


ins. 



















t The number of men is based on each man pulling not over 80 lb. 
One man pulling 160 lb. or less, as given in the first two columns, can lift 
the full capacity of any Triplex or Duplex Block. 



Efficiency of Hoisting Tackle. 

11, 1903. 



• (S. L. Wonson, Eng. News, June 



1 1/4 to 2-in. Manila rope. 


Parts of line. 


2 


3 


4 


5 


6 


7 


8 


9 












Ratio of load to pull 

Efficiency, per cent 


1.91 
96 


2.64 
88 


3.30 3.84 
83 77 


4.33 4.72 
72 67 


5.08 
64 


5.37 
60 






3/4-in. Wire rope. 


Parts of line. 


3 


4 


5 

4.11 
82 


6 


7 


8 

5.68 
71 


9 

6.08 
68 


10 

6.46 
65 


11 

6.78 
62 


12 13 


Tlatio load to pull 


2.73 3.47 


4.70 5.20 


7 08 7 34 


Efficiency, per cent 


91 


87 


78 


74 


59 56 



Proportions of Hooks. — The following formulae are given by Henry 
R. Towne, in his Treatise on Cranes, as a result of an extensive experi- 
mental and mathematical investigation. They apply to hooks of 
capacities from 250 lb. to 20,000 lb. Each size of hook is made from 
some commercial size of round iron. The basis in each case is, there- 
fore, the size of iron of which the hook is to be made, indicated by A 
in the diagram. The dimension D is arbitrarily assumed. The other 
dimensions, as given by the formulae, are those which, while preserving 
a proper bearing-face on the interior of the hook for the ropes or chains 
which may be passed through it, give the greatest resistance to spread- 
mg and to ultimate rupture, which the amount of material in the original 
bar admits of. The symbol A is used to indicate the nominal capacity 
of the hook in tons of 2000 lb. The formulae which determine the lines 



HOOKS. 



1183 



the 




Fig. 189. 



6 



8 10 tons 



2 21/4 21/2 2 7/8 31/4 in. 



of the other parts of the hooks of the several sizes are as follows, 
measurements being all expressed in 
inches : 

£) = 0.5 A + 1.25; 

E = 0.64 A+ 1.60; 

F= 0.33 A + 0.85; 

G = 0.75 D; 

H= 1.08 A; 

f = 1.33 A; 

J= 1.20 A; 

K= LISA; 

L = 1.05 A; 

M= 0.50 A; 

N= 0.85 B- 0.16; 

= 0.363 A + 0.66; 

Q= 0.64 A+ 1.60; 

U= 0.866 A. 
The dimensions A are necessarily- 
based upon the ordinary merchant sizes 
of round iron. The sizes which it has 
been found best to select are the follow- 
ing: 
Capacity of hook : 

1/8 1/4 1/2 111/2 2 3 

Dimension A: 

5/8 11/16 3/4 11/16 11/4 1 S/g 1 8/4 

Experiment has shown that hooks made according to the above formulae 
will give way first by opening of the jaw, which, however, will not 
occur except with a load much in excess of the nominal capacity of the 
hook. This yielding of the hook when overloaded becomes a source of 
safety, as it constitutes a signal of danger which cannot easily be over- 
looked, and which must proceed to a considerable length before rupture 
will occur and the load be dropped. 

Heavy Crane Hooks. — A. E. Holcomb, vice-pres. of the Earth Mov- 
ing Machinery Co., contributes the following (1908). Seven years ago, 
while engaged in the design of a 100-ton crane, I made a study of the 
variations in strength with the different sectional forms for hooks in most 
common use. As a result certain values which gave the best results were 
substituted in "Gordon's" formula and a formula was thereby obtained 
which was good for hooks of any size desired, provided the proper allowable 
fiber stress per square inch was made use of when designing. From this 
formula the enclosed table was made up and was published in the American 
Machinist of Oct. 31, 1901. Smce that time hundreds of hooks of cast 
or hammered steel have been designed and made according to my formula, 
and not one of them, so far as I know, has ever failed. 

The Industrial Works, Bay City, Michigan, manufacturers of heavy 
cranes, in December, 1904, made the following test under actual working 
conditions: 

A hook was made of hammered steel having an elastic limit or yield 
point at approximately 36,000 lbs. per sq. in. liber stress and having the 
following important dimensions: c/ = 75/8in.; r = 4i/2in.; D = 20T/iQm. 

When the applied load reached 150,000 lbs. the hook straightened out 
until the opening at the mouth of the hook was 21/2 in. larger than 
formerly, and the distance from center of action line of load to center of 
gravity of section was found to have decreased 1/2 in., at which point the 
hook held the load. Upon increasing the load still further, the hook 
opened still more. From the dimensions of the hook as originally formed, 
we find from the formula or table that the fiber stress with a load of 
150,000 lbs. was 37,900 lbs. per sq. in., or in excess of the yield point, 
whereas making use of the dimensions obtained from the hook when it 
held we find that the fiber stress per square inch was reduced to 35,940 lbs., 
or under the yield point. 

The desierner must use his own judgment as to the selection of a proper 
allowable fiber stress, bemg governed therein by the nature of the material 



1184 



HOISTING AND CONVEYING. 



to be used and the probability of the hookJbeing overloaded at some time. 

Cinder average condiiions I have made use of the following values for (/): 





Values of (/) in pounds for a load of — 




1,000 to 
5000 
lbs. 


5,000 to 
15,000 

lbs. 


15,000 

to 

30.000 

lbs. 


30,000 

to 
60,000 

lbs. 


60,000 

to 
100,000 

lbs. 


100,000 

lbs. 
and up. 


Cast iron 


.2,000 
6,000 
12,000 


2,500 
8,000 
16,000 










$tcel casting 


10,000 
20,000 


11,250 
22,500 


12,500 
25,000 




Hammered steel 


*2*7,566 



Mr. Holcomb's formula is given below, and his table in condensed 
form is given on page 1185. 

Directions. -— P and / being known, assume r to suit the requirements 
for which the hook is to be designed. Divide P by / and find the quotient 
in the column headed by the required r. At the side of the Table, in the 
same row, will be found the necessary depth of section, d. 

Notation. —P = load. S = area of section. R^ = square of the radius 
of gyration. / = allowable fiber stress in lbs. per sq. in., 20,000 lbs. for 
hammered steel. For other letters see Fig. 190. 

P S 



f^d^. 



General formula. 




Assuming b = 0.66d; c = 0.22a, 



7.44 cZ-h 12.393 r 
dx=0.bd. 

Fig. 190. D = 2r+1.5d. 

For values of K and r intermediate to those given in the taoie approx- 
imate values of d may be found by interpolation. Thus, for K = 3.700» 
r = 2.75. 

r = 2.5 3.0 Int. for 2.75 

K = 3.462 3.213 3.338 

K = 4.128 3.842 3.985 

;.700 -3.338) ) ^ ,7 ^ A ^^ _ A 7S 
:3:338)} X (7.0 - 6.5) - 6.78. 



Tabular values, 

d = 6.50 
d = 7.00 



Whence: 



3.5 + 



|(3/ 

I r3.< 



(3.985- 

In like manner, if d and r are given the value of K and the corresponding 
safe load may be found. 

Strength of Hooks and Shackles. (Boston and Lockport Block Co., 
1908.) — Tests made at the Watertown arsenal on the strength of hooks 
and shackles showed that they failed at the loads given in the table on 
page 1 185. In service they should be subjected to only 50 % of the figures 
in the table. Ordinarily the hook of a block gives way first, and where 
heavy weights are to be handled shackles are superior to hooks and 
should be used wherever possible. 

Horse-power Required to Raise a Load at a Given Speed. — H.P. = 
Gross^ weight m lb. ^ ^^^^^ .^ ^^ p^^ ^^ ^^ ^^^ ^^^ 25% to 50% for 

The gross weight includes the weight of 



33,000 
friction, contingencies, etc. 



HOOKS. 



1185 



Values of K. 



d. 


r. 


0.50 1 0.75 1 1.00 1 1.50 


2.00 


2.50 1 3.00 1 3.50 | 4.00 1 5.00 | 6.00 


2.00 


0.379 

.496 

.629 

.778 

.944 

1.143 

1.342 

1.558 

1.790 

2.038 

2.304 

2.586 

2.884 

3.214 

3.532 


0.331 

.437 
.559 
.697 
.852 
1.039 
1.226 
1.429 
1.649 
1.886 
2.138 
2.408 
2.694 
3.008 
3.315 
3.651 
4.003 
4.757 
5.578 


0.292 

.391 

.504 

.632 

.776 

.953 

1.129 

1.321 

1.530 

1.754 

1.995 

2.253 

2.527 

2.828 

3.124 

3.447 

3.787 

4.516 

5.311 

6.173 

7.102 

8.096 

9.158 


0.240 

.329 

.420 

.532 

.659 

.801 

.957 

1.148 

1.336 

1.544 

1.760 

1.996 

2.248 

2.525 

2.801 

3.101 

3.418 

4.100 

4.848 

5.661 

6.540 

7.485 

8.496 

9.574 

10.788 

12.098 

13.374 

14.717 

16.126 

17.601 


0.203 

.275 

.360 

.460 

.572 

.700 

.841 

.998 

1.187 

1.373 

1.575 

1.793 

2.072 

2.281 

2.538 

2.818 

3.115 

3.754 

4.459 

5.227 

6.061 

6.960 

7.924 

8.954 

10.220 

11.381 

12.608 

13.901 

15.261 

16.686 

18.178 

19.735 

21.359 

23.050 

24.807 

26.630 

28.520 


0.176 0.155 
. 239 7-1 2 










2 25 










2 50 


.316 

.404 

.506 

.621 

.750 

.893 

1.067 

1.239 

1.426 

1.627 

1.843 

2.081 

2.321 

2.583 

2.861 

3.463 

4.128 

4.855 

5.648 

6.504 

7.424 

8.409 

9.460 

10.746 

11.922 

13.173 

14.485 

15.862 

17.305 

18.814 

20.389 

22.031 

23.738 

25.511 

27.351 


.281 

.360 

.454 

.559 

.677 

.808 

.953 

1.129 

1.321 

1.490 

1.691 

1.913 

2.140 

2.385 

2.646 

3.213 

3.842 

4.533 

5.287 

6.104 

6.984 

7.928 

8.932 

10.008 

11.316 

12.518 

13.785 

15.117 

16.514 

17.976 

19.504 

21.098 

22 758 










2 75 










3 00 


0.411 

.508 

.617 

.738 

.873 

1.038 

1.214 

1.374 

1.563 

1.770 

1.983 

2.215 

2.461 

2.998 

3.594 

4.252 

4.970 

5.750 

6.593 

7.498 

8.467 

9.499 

10.766 

11.926 

13.150 

14.442 

15.792 

17.210 

18.694 

20.242 

7\ PAf^ 








3 25 








3 50 








3 75 








4 00 


0.805 

0.943 

1.124 

1.275 

1.453 

1.647 

1.849 

2.067 

2.300 

2.809 

3.377 

4.003 

4.689 

5.436 

6.243 

7.113 

8.044 

9.039 

10.267 

11.388 

12.572 

13.820 

15.132 

16.508 

17.948 

19.453 

21.023 

22.658 

24.358 






4 25 






4 50 






4 75 






5 00 






5 25 






5.50 
5.75 
6.00 
6.50 
7.00 
7 50 


1.628 

1.825 

2.035 

2.496 

3.012 

3.584 

4.213 

4.900 

5.645 

6.450 

7.316 

8.241 

9.228 

10.448 

11.558 

12.730 

13.965 

15.263 

16.624 

18.049 

19.536 

21.088 

22.704 


2.246 
2.719 
3.244 


8 00 






3 825 


8.50 
9 00 






4.460 
5.152 


9.50 






5.901 


10 00 








6.708 


10 50 








7.573 


11 00 








8 498 


11 50 








9.482 


12 00 








10.697 


12.50 








11.802 


13 00 








12.967 


13 50 










14.195 


14 00 










15 484 


14 50 










16.835 


15 00 










18 248 


15.50 










24.483 23.535 


19.724 


16.00 










26.274 


25.388 


21.262 



Strength of Hooks and Shackles. 



Hooks.* | Shackles. 


c 

C 


f2 


i. 


Description of 
Fracture. 


1 

c 
1— 1 


i 

a 


to 
a . 

|£ 


Description of 
Fracture. 


l/o 


1,890 
2.560 
3,020 
4,470 
6.280 
12,600 
13,520 

16,800 






13/8 
11/2 

1^/8 

21/2 


17,310 
20,940 
23,670 
27.420 

36,120 
38,100 

55.380 


103,750 
119,800 
125,900 
146,804 

162,700 
196,600 

210,400 


Eye of shackle. 


9/16 






Eye of shackle. 


5/8 






Eye of shackle. 


3/4 

11/8 
11/4 


20,700 
38,100 
51,900 
62,900 

75,200 


Eye of shackle. 
Eye of shackle. 
Eye of shackle. 
Sheared shackle 

pin. 
Eye of shackle. 


Sheared shackle 

pin. 
Eye of shackle. 
Shackle at neck 

of eye. 
Eye of shackle. 



* All the hooks failed by straightening the hook. 



1186 HOISTING AND CONVEYING. 

cage, rope, etc. In a shaft with two cages balancing each other use the 
net load + weight of one rope, instead of the gross weight. 

To find the load which a given pair of engines will start. — Let A = area 
of cyUnder in square inches, or total area of both cylinders, if there are 
two; P = mean effective pressure in cyhnder in lb. per sq. in.\ S = stroke 
of cylinder, inches; C = circumference of hoisting-drum, inches; L = 
load lifted by hoisting-rope, lb.; i^ = friction, expressed as a diminution 
of the load. Then L = ^ X -^ X ^^ _ p 

An example in ColVy Engr., July, 1891, is a pair of hoisting-engines 
24" X 40'', drum 12 ft. diam., average steam-pressure in cylinder = 
59.5 lb.; A = 904.8; P = 59.5; >S = 40; C = 452.4. Theoretical load, 
not allowing for friction, AXPX2S-^C = 9589 lb. The actual load 
that could just be lifted on trial was 7988 lb., making friction loss F == 
1601 lb., or 20 4- per cent of the actual load lifted, or 162/3% of the theo- 
retical load. 

The above rule takes no account of the resistance due to inertia of 
the load, but for all ordinary cases in which the acceleration of speed of 
the cage is moderate, it is covered by the allowance for friction, etc. The 
resistance due to inertia is equal to the force required to give the load the 
velocity acquired in a given time, or, as shown in Mechanics, equal to the 

product of the mass by the acceleration, ot R = —^ » in which R — 

resistance in lb. due to inertia; W = weight of load in lb.; F = maximum 
velocity in ft. per second; T = time in seconds taken to acquire the 
velocity V;p = 32.16. 

Safe Loads for Ropes and Chains. — The table on p. 1187 was pre- 
pared by the National Founder's Association and published in Indust, 
Eng., Sept., 1914. It shows the safe loads that can be carried by wire 
rope, crane chain and manila rope of the sizes given when used in the 
positions and combinations shown. The loads in the table are lower 
than those usually specified, in order to insure absolute safety. When 
handling molten metal, the ropes and chains should be 25 per cent 
stronger than the figures in the table. 

Effect of Slack Rope upon Strain in Hoisting:. — A series of tests 
with a dynamometer are published by the Trenton Iron Co., which show 
that a dangerous extra strain may be caused by a few inches of slack rope. 
In one case the cage and full tubs weighed 11,300 lb.; the strain when the 
load was lifted gently was 11,525 lb.; with 3 in. of slack chain it w^as 
19,025 lb.; with 6 in. slack 25,750 lb., and with 9 in. slack 27,950 lb. 

Limit of Depth for Hoisting. — Taking the weight of a cast-steel 
hoisting-rope of IVsin. diameter at 2 lb. per running foot, and its break- 
ing strength at 84,000 lb., it should, theoretically, sustain itself until 
42,000 feet long before breaking from its own weight. But taking the 
usual factor of safety 01 7, then the safe working length of such a rope 
would be only 6000 ft. If a weight of 3 tons is now hung to the rope, 
which is equivalent to that of a cage of moderate capacity vvith its loaded 
cars, the maximum length at which such a rope could be used, v/ith the 
factor of safety of 7, is 3000 ft., or 

2x+ 6000 = 84,000 ~ 7; .'. x == 3000 feet. 

This limit may be greatly increased by using special steel rope of higher 
strength, by using a smaller factor of safety, and by using taper ropes. 
(See paper by H. A. Wheeler, Trans. A. I. M. E., xix. 107.) 

Large Hoisting Records. — At a colliery in North Derbyshire during 
the first week in June, 1890, 6309 tons were raised from a depth of 509 
yards, the time of winding being from 7 a.m. to 3.30 p.m. 

At two other Derbyshire pits, 170 and 140 yards in depth, the speed of 
winding and changing has been brought to such perfection that tubs are^ 
drawn and changed three times in one minute. (Proc. Inst. M. E., 1890.) 

At the Nottingham Colliery near Wilkesbarre, Pa., in Oct., 1891, 70,152 
tons were shipped in 24.15 days, the average hoist per day being 1318 mine 
cars. The depth of hoist was 470 ft., and all coal came from one openii^?. 
The engines were fast motion, 22 X 48 in., conical drums 4 ft. 1 m. long, 7 It. 
diameter at small end and 9 ft. at large end. (Eng'g News, Nov. 1891.) 

Large Engines. — Two 34 X 60 in. four-cylinder engines built by 
Nordberg Mfg. Co. for tlie Taniarack copper mine at Caliunet, Mich., are 



PNEUMATIC HOISTING. 



1187 



Safe Loads for Ropes and Chains. 






When Used 


When Used 


When Used 


When Used 


Note. The safe loads in 


Straight. 


at 60° 


at 45° 


at 30° 


table are for each Single 




Angle. 


Angle. 


Angle. 


rope or chain. When used 






A 






double or in other multiples 






/\ 






the loads may be increased 






/ \ 


yV 




proportionately. 






/ \ 


/\ 


,/^ 














Dia. 
In. 


Lb. 


Lb. 


Lb. 


Lb. 


Plow Steel Wire 


3/8 


1,500 


1,275 


1,050 


750 


Rope. 


1/2 


2,400 


2,050 


1,700 


1,200 




V8 


4,000 


3,400 


2,800 


2,000 


[6 strands of 1 9 or 


3/4 


6,000 


5,100 


4,200 


3,000 


37 wires.] 


7/8 


8,000 


6,800 


5,600 


4,000 




1 


10,000 


8,500 


7,000 


5,000 


If crucible steel rope 


1 1/8 


13,000 


11,000 


9,000 


6,500 


is used reduce loads 


11/4 


16,000 


13,500 


11,000 


8,000 


one-fifth. 


1V8 


19,000 


16,000 


13,000 


9,500 




11/2 


22,000 


19,000 


16.000 


11,000 





A V4 


600 


500 


425 


300 


Crane Chain. 


S 3/8 


1,200 


1,025 


850 


600 




a 1/2 


2,400 


2,050 


1,700 


1,200 


[Best grade of 


o 5/8 


4,000 


3,400 


2,800 


2,000 


wrought iron, hand- 


^ 3/4 


5,500 


4,700. 


3,900 


2,750 


made, tested, short- 


-3 7/8 


7,500 


6,400 


5,200 


3,700 


link chain.] 


.1 


9,500 


8,000 


6,600 


4,700 




SU/8 


12,000 


10,200 


8,400 


6,000 




;^|l/4 


15,000 


12,750 


10,500 


7,500 




Q|3/8 


22,000 


19,000 


16,000 


11,000 




Dia. 


Cir. 












In. 


In. 












3/8 


1 


120 


100 


85 


60 


Manila Rope. 


1/2 


11/2 


250 


210 


175 


125 




5/8 


2 


360 


300 


250 


180 




3/4 


21/4 


520 


440 


360 


260 


[Best long fibre 


7/8 


23/4 


620 


520 


420 


300 


grade.] 


1 


3 


750 


625 


525 


375 




11/8 


3 1/2 


1,000 


850 


700 


500 




11/4 


3 3/4 


1,200 


1,025 


850 


600 




11/2 


4 1/2 


1,600 


1,350 


1,100 


800 




13/4 


51/2 


2,100 


1,800 


1,500 


1,050 




2 


6 


2,800 


2,400 


2,000 


1,400 




21/2 


71/2 


4,000 


3,400 


2,800 


2,000 




3 


9 


6,000 


5,100 


4,200 


3,000 



designed to lift a load from a depth of 6,000 ft. at an average hoisting 
speed of 5,000 ft. per min. The load is made up of ore, 12,000 lbs. ; cage 
and cars, 8,500 lbs.; 6,500 ft. of l^^-in. rope, 21,200 lbs.; total, 41,700 
lbs. The center lines of the cylinders are placed 90° apart and the cranks 
135° apart. By this arrangement three of the four cylinders are al- 
ways available for starting the hoist. 

Pneumatic Hoisting. (H. A. Wheeler, Trans. A. I. M. E. xix, 107.) — 
A pneumatic hoist was installed in 1876 at Epinac, France, consisting 
of two continuous air-tight iron cylinders extending from the bottom to 
the top of the shaft. Within the cylinder moved a piston from which 
was hung the cage. It was operated by exhausting the air from above 
the piston, the lower side being open to the atmosphere. Its use was 
discontinued on account of the failure of the mine. Mr. Wheeler gives 
a description of the system, but criticizes it as not being equal on the 
whole to hoisting by steel ropes. 

Pneumatic hoisting-cylinders using compressed air have been used at 
blast-furnaces, the weighted piston counterbalancing the weight of the 



1188 HOISTING AND CONVEYING. 

cage, and the two being connected by a wire rope passing over a pulley- 
sheave above the top of the cylinder. In the more modern furnaces 
steam-engine or electric hoists are generally used. 

Electric Mine-Hoists. — An important paper on this subject, 'by D. 
B. Rushmore and K. A. Pauly, will be found in Trans. A. I. M, £., 
1910. See also Electrical Hoisting, page 1464. 

Counterbalancing of Winding-engines, (H. W. Hughes, Columbia 
Coll. Qly.) — Engines running unbalanced are subject to enormous 
variations in the load; for let W = weight of cage and empty tubs, say 
6270 lb.; c = weight of coal, say 4480 lb.; r = weight of hoisting rope, 
say 6000 lb.; r' = weight of counterbalance rope hanging down pit, say 
6000 lb. The weight to be hfted will be: 

If weight of rope is unbalanced. If weight of rope is balanced. 
At beginning of lift: -^ 

W+c+r-^WoT 10,480 lb. TF + c + r - (PT + r'). 

At middle of lift: or 

Tr+c+^-(TF + 0or448Olb. TF + C + ^ +^- (tF + ^+ ^), M480 

At end of lift: 

PF + c - (TF + r) or minus 1520 lb. TF + c + r' - (TF + r), J 
That counterbalancing materially affects the size of winding-engines is 
shown by a formula given by Mr. Robert Wilson, which is based on the 
fact that the greatest work a winding-engine has to do is to get a given 
mass into a certain velocity uniformly accelerated from rest, and to raise 
a load the distance passed over during the time this velocity is being 
obtained. 

Let W == the weight to be set in motion: one cage, coal, number of empty 
tubs on cage, one winding rope from pit head-gear to bottom, 
and one rope from banking level to bottom. 
V = greatest velocity attained, uniformly accelerated from rest; 
g = gravity = 32.2; 

t = time in seconds during which v is obtained; 
L = unbalanced load on engine; 
R = ratio of diameter of drum and crank circles; 
P = average pressure of steam in cyhnders; 
N = number of cylinders; 

S = space passed over by crank-pin during time t; 

C = 2/3, constant to reduce angular space passed through by crank to 

the distance passed through by the piston during the time t; 

A = area of one cylinder, without margin for friction. To this an 

addition for friction, etc., of engine is to be made, varying 

from 10 to 30% of A. 



1st. Where load is balanced. 

A = 



{(^V(-1)}« 



PNSC 



2d. Where load is unbalanced: 

The formula is the same, with the addition of another term to allow for 
the variation in the lengths of the ascending and descending ropes. IQ 
this case 

/ij = reducea length of rope in t attached to ascending cage; 
^2 = increased length of rope in t attached to descending cage; 
fjD ca weight of rope per foot in pounds. Then 






^ " PM3C 

Applying the above formula when designing new engines, Mr. Wilson 

found that 30 in. diameter of cylinders would produce equal results, when 

balanced, to those of the 36-in. cyUnder in use, the latter being unbalanced. 

Counterbalancing may be employed in the following methods: 

(a) Tapering Rope. — At the initial stage the tapering rope enables U8 

to wind from greater depths than is possible with ropes of uniform section. 



CRANES. 1189 

The thickness of such a rope at any point should only be such as to safely 
bear the load on it at that point. 

With tapering ropes we obtain a smaller difference between the initial 
and final load, but the difference is still considerable, and for perfect 
equalization of the load we must rely on some other resource. The theory 
of taper ropes is to obtain a rope of uniform strength, thinner at the cage 
end where the weight is least, and thicker at the drum end where it is 
greatest. 

(b) The Counterpoise System consists of a heavy chain working up and 
down a staple pit, the motion being obtained by means of a special small 
drum placed on the same axis as the winding drum. It is so arranged 
that the chain hangs in full length down the staple pit at the commence- 
ment of the winding; in the center of the run the whole of the chain rests 
on the bottom of the pit, and, finally, at the end of the winding the counter- 
pofse has been rewound upon the small drum, and is in the same con- 
dition as it was at the commencement. 

(c) Loaded-wagon System. — A plan, formerly much employed, was to 
have a loaded wagon running on a short incline in place of this heavy 
chain; the rope actuating this wagon being connected in the same manner 
as the above to a subsidiary drum. The incline was constructed steep 
at the commencement, the inclination gradually decreasing to nothing. 
At the beginning of a wind the wagon was at the top of the incline, and 
during a portion of the run gradually passed down it till, at the meet of 
cages, no pull was exerted on the engine — the wagon by this time being 
at the bottom. In the latter part of the wind the resistance was all 
^against the engine, owing to its having to pull the wagon up the incline, 
and this resistance increased from nothing at the meet of cages to its 
greatest quantity at the conclusion of the hft. 

(d) The Endless-rope System is preferable to aH others, if there is suffi- 
cient sump room and the shaft is free from tubes, cross timbers, and other 
impediments. It consists in placing beneath the cages a tail rope, similar 
in diameter to the winding rope. And, after conveying this down the pit, 
it is attached beneath the other cage. 

(e) Flat Ropes Coiling on Reels. — This means of winding allows of a 
certain equalization, for the radius of the coil of ascending rope continues to 
increase, while that of the descending one continues to diminish. Conse- 
quently, as the resistance decreases in the ascending load the leverage 
increases, and as the power increases in the other, the leverage diminishes. 
The variation in the leverage is a constant quantity, and is equal to the 
thickness of the rope where it is wound on the drum. 

By the above means a remarkable uniformity in the load may be ob- 
tained, the only objection being the use of flat ropes, which weigh heavier 
and only last about two-thirds the time of round ones. 

'(/) Conical Drums. — Results analogous to the preceding may be 
obtained by using round ropes coiling on conical drums, which may either 
be smooth, with the successive coils lying side by side, or they may be 
provided with a spiral groove. The objection to these forms is, that 
perfect equalization is not obtained with the conical drums unless the sides 
are very steep, and consequently there is great risk of the rope slipping:; 
to obviate this, scroll drums were proposed. They are, however, expen- 
sive, and the lateral displacement of the winding rope from the center 
line of pulley becomes very great, owing to their necessary large width. 
(g) The Koepe System of Winding. — An iron pulley with a single cir- 
cular groove takes the place of the ordinary drum. The winding rope 
passes from one cage, over its head-gear pulley, round the drum, and, 
after passing over the other head-gear pulley, is connected with the second 
cage. The winding rope thus encircles about half the periphery of the 
drum in the same manner as a driving-belt on an ordinary pulley. There 
is a balance rope beneath the cages, passing round a pulley in the sump; 
the arrangement is like an endless rope, with the cages as points of 
attachment. 

CEANES. 

Classification of Cranes. (Henry R. Towne, Trans. A. S. M. E. iv., 

288. Revised in Hoisting, published by The Yale & Towne Mfg. Co.) 
A Hoist is a machine for raising and lowering weights. A Crane is ^ 
hoist with the added capacity of moving the load in a horizontal or 
lateral direction. 



1190 HOISTING AND CONVEYING. 

Cranes are divided into two classes, as to their motions, viz. Rotary and 
Rectilinear, and into four groups, as to their source of motive power, viz. : 

Hand, — When operated by manual power. 

Power. — When driven by power derived from line shafting. 

Steam, Electric, Hydraulic, or Pneumatic. — When driven by an engine 
or motor attached to the crane, and operated by steam, electricity, water, 
or air transmitted to the crane from a fixed source of supply. 

Locomotive. — When the crane is provided with its own boiler or other 
generator of power, and is self-propeUing; usually being capable of both 
rotary and rectilinear motions. 

Rotary and Rectilinear Cranes are thus subdivided. 

RoTAEY Cranes. 

(1) String-cranes. — Having rotation, but no trolley motion. 

(2) Jib-cranes. — Having rotation, and a trolley traveling on the jib. 

(3) Column-cranes. — Identical with the jib-cranes, but rotating around 
a fixed column (which usually supports a floor above). 

(4) Pillar-cranes. — Having rotation only; the pillar or column being 
supported entirely from the foundation. 

(5) Pillar Jib-cranes. — Identical with the last, except in having a jib 
and trolley motion. 

(6) Derrick-cranes. — Identical with jib-cranes, except that the head of 
the mast is held in position by guy-rods, instead of by attachment to a 
roof or ceiling. 

(7) Walking-cranes. — Consisting of a pillar or jib-crane mounted on 
wheels and arranged to travel longitudinally upon one or more rails. 

(8) Locomotive-cranes. — Consisting of a pillar-crane mounted on a 
truck, and provided with a steam-engine capable of propelling and rotat- 
ing the crane, and of hoisting and lowering the load. 

Rectilinear Cranes. 

(9) Bridge-cranes. — Having a fixed bridge spanning an opening, and a 
trolley moving across the bridge. 

(10) Tram-cranes. — Consisting of a truck, or short bridge, traveling 
longitudinally on overhead rails, and without trolley motion. 

(11) Traveling-cranes. — Consisting of a bridge moving longitudinally 
on overhead tracks, and a trolley moving transversely on the bridge. 

(12) Gantries. — Consisting of an overhead bridge, carried at each end 
by a trestle traveling on longitudinal tracks on the ground, and having 
a trolley moving transversely on the bridge. 

(13) Rotary Bridge-cranes. — Combining rotary and rectilinear move- 
ments and consisting of a bridge pivoted at one end to a central pier or 
post, and supported at the other end on a circular track; provided with a 
trolley moving transversely on the bridge. 

For descriptions of these several forms of cranes see Towne's " Treatise 
on Cranes." 

Stresses in Cranes. — See Stresses in Framed Structures, p. 541, ante. 

Position of the Inclined Brace in a Jib-crane. — The most econom- 
ical arrangement is that in which the inclined brace intersects the jib at 
a distance from the mast equal to four-fifths the effective radius of the 
crane. (Hoisting.) 

Electric Overhead Traveling Cranes. (From data supphed by 
Alliance Machine Co., Alliance, O., and Pawling & Harnischfeger, Mil- 
waukee.) — Electric overhead traveling cranes usually have 3 motors, for 
hoisting, traversing the hoist trolley on the bridge and for moving the 
bridge, respectively. The usual range of motor sizes is as follows: Hoist, 
15-50 H.P.; trolley, 3-15 H.P.; bridge, 15-50 H.P. The speeds at which 
the various motions are made range as follows, the figures being feet per 
minute: Hoist, 8-60; trolley traverse, 75-200; bridge travel, 200-600. 
These speeds are varied in the same capacity of crane to suit each par- 
ticular installation. In general, the speed of the bridge in feet per minute 
should not exceed (length of runway + 100). If the runway is long and 
covered by more than one crane, the speed mav be made equal to the 
average distance between cranes 4- 100. Usually 300 ft. per min. is a 
good speed. For small cranes in special cases, the speeds may be increased, 
but for cranes of over 50 tons capacity the speed should be below 300 ft. 
per min. unless the building is made especially strong to stand the strains 
incident to starting and stopping heavy cranes geared for high speeds. 



CRANES. 



1191 



Cranes of over 15 tons capacity usually have an auxiliary hoist of 1/5 the 

capacity 01 tne mam hoist, and usually operated by the same motor. 
Wire rope is now almost exclusivelv used for hoisting with cranes. The 
diameter of the drums and sheaves should be not less than 30 times 
the diameter of the hoisting rope, and should have a factor of safety of 5. 
Cranes are equipped with automatic load brakes to sustain the load when 
lifted and to regulate the speed when lowering, it being necessary for the 
hoist to drive the load down. 

The voltage now standard for crane service is 220 volts at the crane 
motor, although 110 volts for small cranes is not objectionable. Voltages 
of 500-600 are inadvisable, especially in foundries and steel works, where 
dust and metallic oxides cover many parts of the crane and necessitate 
frequent cleaning to avoid grounds. On account of the danger from the 
higher voltages, the operators are apt to neglect this part of their work. 

Power Required to Drive Cranes. (Morgan Engineering Co., 
Alhance, O., 1909.) — The power required to drive the different parts of 
cranes is determined by allowing a certain friction percentage over the 
power required to move the dead load. On hoist motions 331/3% is 
allowed for friction of the moving parts, thus giving a motor of 1/3 greater 
capacity than if friction were neglected. For bridge and. trolley motions, 
a journal friction of the track wheel axles of 10% of the total weight of 
the crane and load is allowed. There is then added an allowance of 331/3% 
of the horse-power required to drive the crane and load plus the track wheel 
axle friction, to cover friction of the gearing. In selecting motors, the 
most important consideration is the maximum starting torque which 
the motor can exert. With alternating-current motors, this is less than 
with direct-current motors, requiring a larger motor, particularly on the 
bridge and trolley motions wlilch require the greatest starting torque. 

Walter G. Stephan says {Iron Trade Rev., Jan. 7, 1909) that the bridge 
girders should be made of two plates latticed, or box girders, their depth 
varying from i/io to 1/20 of the span. Ihe important feature of crane 
girder design is ample strength and stiffness, both vertically and laterally. 
Especial attention should be given to the transverse strain on the bridge 
due to suddea stopping or starting of heavy loads. The wheel base on 
the end trucks should have a ratio to the crane span of 1 to 6, although 
for long spans this ratio must necessarily be reduced to 1 to 8. Quick- 
traveling cranes should have as long a wheel base as possible, since the 
tendency to twist increases with the speed. Where several wheels are 
necessary at each end to support the crane, equalizing means should be 
used. 

A recent development in cranes is the four- or six-girder crane for han- 
dling ladles of molten metal in steel works. The main trolley runs on the 
outer girders, with the hoist ropes depending between the outer and inner 
girders. The auxiliary trolley runs on the inner girders, thus being able 
to pass between the main ropes, and tilt the ladle in either direction. 



Dimensions and Wheel Loads of Electric Traveling Cranes. 

Based on 60-ft. span and 25-ft. lift; wire rope hoist. 
(Alliance Machine Co., 1908.) 



Capacity, 

Tons (2000 

Lb.). 



5 

10 
25 
40 
50 



Distance Run- 
way Rail to 
Highest Point. 



Ft. 
6 
6 
7 



In. 

6 
4 

9 



Distance 

Center of 

Rail to Ends 

of Crane. 



In. 
9 
10 
12 
12 
12 



Wheel Base of 
End Truck. 



Ft. In. 
9 



10 
11 
12 
12 



Maximum 
Load per 
Wheel; Trol- 
ley at End of 
Bridge. 



Pounds. 
20,000 
27,000 
51.000 
82,000 
48,000* 



* Has 8 track wheels on bridge. 

Standard cranes are built in intermediate sizes, varying by 5 tons, up 
to 40 tons. 



1192 



HOISTING AND CONVEYING. 



Standard Hoisting and Traveling Speeds of Electric Cranes* 

(Pawling & Harnischfeger, 1908.) 



Capacity, 


Hoisting 


Bridge Travel 


Capacity 


Speed Aux. 


Tons (2000 


Speed, Ft. per 


Speed, Ft. per 


Aux. Hoist, 


Hoist, Ft. per 


Lb.). 


Min. 


Min. 


Tons. 


Min. 


) 


25-100 
20-75 


300-450 
300-450 






10 


3 


30-75 


25 


10-40 


250-350 


{.0 


50-125) 
25-60 


40 


9-30 


250-350 


Wo 


40-100 { 
25-60 f 


50 


8-30 


200-300 


w 


40-100) 
25-60 } 


75 


6-25 


200-250 


15 


20-50 


!25 


5-15 


200-250 


25 


20-50 


150 


5-15 


200-250 


25 


20-50 



TroUey' travel speed from 100-150 ft. per min. in aU cases. 
Notable Crane Installations. (1909.) 



m 






^ 


H.P.of 


>> 


?u 


tT 


is 

eg? 


ey Trav- 
e Speed, 
per Min. 


d 






1 




1 




Hoist 
Motor. 




bJD 

o o 


1^ 


e3 
"1 


1 

l-H • 




.f 






»H* 


e8 


a 


o 
d 


^■M 




3 c3 


r-s 


i^ 


CO ^ 






r 




e3 


6 


m 


^ 


6 


1^ 


<1d 


ffi 


w 


W 


« 


H 


Q 


^ 


1^ 




Ft. In. 




















Ft.In. 




150 


65 


1 


25 


75t 


{in} 


30 


75 


8-24 


150-200 


100-150 


7 


4 


1 


150 


55 


1 


30 


120 


^50 


35 


50 


8 


150-200 


75-100 




5 




150 


65 


2 


15 


75t 


30t 


18t 


75 


10-25 


150-200 


100-150 


7 6 


4 




125* 




2 




110 


{^^} 
18 


ll^} 


loot 


10 


200 


{.^} 

100-150 


5 10 


6 




120 


56 7 


2 


10 


50t 


lot 


52t 


10-25 


150-300 


5 5 


7 




100 


65 


2 


10 


50t 


18 


10- 


50 


10-25 


200-250 


100-150 


5 5 


8 


80 


74 


2 


10 


40t 


18t 


10- 


40 


10-25 


200-250 


100-150 


5 101/2 


9 


50 


129 111/4 


1 


15 


50 


25 


71/2 


50 


10 


100-150 


80-100 


8 6 


10 




50 


125 10 


1 


15 


50 


25 


71/7 


50 


10 


100-150 


80-100 


8 6 


11 




50 


121 2 


1 


5 


75 


15 


15 


75 


ni/2 


225 


125 


8 4 


12 


2 



* Four-girder ladle crane, f On each trolley. 

t Divided equally between 2 motors for series-parallel control. 

1. Pawling & Harnischfeger; 2. Alliance Mach. Co.; 3. Morgan Ea- 
glneering Co.; 4. Midvale Steel Co., Phila.; 5. Homestead Steel Works, 
Munhall, Pa.; 6. Indiana Steel Co., Gary, Ind.; 7. Oregon Ry. & Nav. 
Co., Portland, Ore.; 8. El Paso & S. W. Ry., El Paso, Tex.; 9. C. & E. I. 
Ry., Danville, 111.; 10. 3d Ave. Ry., N. Y. City; 11. United Rys. Co.. 
Baltimore; 12. Carnegie Steel Co., Youngstown, Ohio. 

A 150-ton Pillar-crane was erected in 1893 on Finnieston Quay, 
Glasgow. The jib is formed of two steel tubes, each 39 in. diam. and 90 
ft. long. The radius of sweep for heavy hfts is 65 ft. The jib and its load 
are counterbalanced by a balance-box weighted with 100 tons of iron and 
steel punchings. In a test a 130-ton load was lifted at the rate of 4 ft. per 
minute, and a complete revolution made with this load in 5 minutes. 
Eng'g News, July 20, 1893. 

Compressed-air Tra velin g-cranes. — Compressed-air overhead travel- 
ing-cranes have been built by the Lane & Bodley Co., of Cincinnati. 
They are of 20 tons nominal capacity, each about 50 ft. span and 400 ft. 
length of travel, and are of the triple-motor type, a pair of simple reversing- 
engines being used for each of the necessary operations, the pair of engines 
for the bridge and the pair for the trolley travel being each 5-inch bore by 
7-inch stroke, while the pair for hoisting is 7-inch bore by 9-inch stroke. 



LIFTING MAGNETS. 1193 

The air-pressure when required is somewhat over 100 pounds. The air- 
compressor IS allowed to run continuously without a governor, the speea 
being regulated by the resistance of the air in a receiver. An auxihary 
receiver is placed on each traveler, whose object is to provide a supply 
of air near the engines for immediate demands and independent of the 
hose connection. Some of the advantages said to be possessed by this 
type of crane are: simplicity; absence of all moving parts, excepting 
those required for a particular motion when that motion is in use; no 
danger from fire, leakage, electric shocks, or freezing; ease of repair; 
variable speeds and reversal without gearing; almost entire absence of 
noise; and moderate cost. 

, Quay-cranes. — An illustrated description of several varieties of sta- 
tionary and traveling cranes, with results of experiments, is given in a 
paper on Quay-cranes in the Port of Hamburg by Chas. Nehls, Trane, 
A. S. C, E., 1893. 

Hydraulic Cranes, Accumulators, etc. — See Hydraulic Pressure 
Transmission, page 812, ante. 

Electric versus Hydraulic Cranes for Docks. — A paper by V. L. 
Raven, in Trans. A. S. M. E., 1904. describes some tests of capacity and 
efficiency of electric and hydraulic power plants for dock purposes at Mid- 
dlesbrough, Eng, In loading two cargoes of rails, weighing respectively 
1210 and 1225 tons, the first was done with a hydraulic crane, in 7 hours, 
with 3584 lbs. of coal burned in the power station, and the second with 
an electric crane in 5 1/4 hours, with 2912 lbs. of coal. The total cost in- 
cluding labor, per 100 tons, was 327 pence with the hydraulic and 245 
pence for the electric crane, a saving by the latter of 25 %. 

Loading and Unloading and Storage 3Iachinery for coal, ore, etc., 
is described by G. E. Titcomb in Trans. A. S. M. E., 1908. The paper 
illustrates automatic ore unloaders for unloading ore from the hold of a 
vessel and loading it onto cars, and car-dumping machinery, by which 
a 50-ton car of coal is lifted, turned over and its contents discharged 
through a chute into a vessel. Methods of storage of coal and of re- 
loading it on cars are also described. 

Power Required for Traveling-Cranes and Hoists. — Ulrich Peters, 
in Machij, Nov. 1907, develops a series of formulae for the power re- 
quired to hoist and to move trolleys on cranes. The following is a brief 
abstract. Resistance to be overcome in moving a trolley or crane- 
bridge. Pi = rolling friction of trolley w^heels, P2 = journal friction 
of wheels or axles, Pz = inertia of trolley and load. P = sum of these 

resistances = Pi+P2+P3 = (?'+L) (^^^^ + -t|^) in which r = weight 

of trolley, L = load, /i = coeff. of rolling friction, about 0.002, (0.001 to 
0.003 for cast iron on steel); /2= coeff. of journal friction, = 0.1 for start- 
ing and 0.01 for running, assuming a load on brasses of 1000 to 3000 lb. 
per sq. in.; [/2 is more apt to be 0.05 unless the lubrication is perfect. See 
Friction and Lubrication, W. K.] d = diam. of journal; D = diam. of 
wheels; v = trolley speed in ft. per min.; t = time in seconds in which 
the trolley under full load is required to come to the maximum speed. 
Horse-power = sum of the resistances X speed, ft. per min. ^ 33,000. 

Force required for hoisting and lowering: Fh = actual hoisting force, 
Fo = theoretical force or pull, L = load, v = speed in ft. per min. of 
the rope or chain, c = hoisting speed of the load L, c/v = transmission 
ratio of the hoist, e = efficiency = Fo/Fh,. The actual work to raise 
the load per minute = Fhv = Lc = Fqv -h e. The efficiency e is the 
product of the efficiencies of all the several parts of the hoisting mech- 
anism, such as sheaves, windlass, gearing, etc. Methods of calculating 
these efficiencies, with examples, are given at length in the original paper 
by Mr. Peters. 

Lifting 3Iagnets. — (From data furnished by the Electric Controller 
and Mfg. Co., Cleveland, and the Cutler-Hammer Clutch Co., Milwaukee). 
Lifting magnets first came into use about 1898. They have had wide 
application for handling pig iron, scrap, castings, etc. A lifting magnet 
comprises essentially a maynet winding, a pole-piece, a shoe and a pro- 
tecting case, which is ribbed to afford ample radiating surface to dissi- 
pate the heat generated in operation. The winding usually consists of 
coils, each wound with copper ribbon and insulated with asbestos. The 
insulation must be designed to withstand a higher voltage than the line 



1194 



HOISTING AND CONVEYING. 



voltage, due to the inductive kick when the circuit is opened. The weaiv 

ing plate, which takes the shocks incident to picking up the load, is usually 
made of manganese steel. The shape of the pole piece or lifting surface of 
the magnet must be varied, as the same shape is not usually applicable 
to all classes of materials. For handling pig iron, scrap, etc., a concave 
pole surface is usually superior to a flat one, which is adapted to hand- 
ling plates or flat material of similar character, and which bear equally 
on the piece to be lifted at both the edge and center. A test of a lift- 
ing magnet made at the works of the Youngstown Sheet and Tube Co., 
in 1907, showed the following results: 

Total pig iron unloaded, 109,350 pounds; weight of average lift, 785 
pounds; time required, 2 hours. 15 minutes; current on magnet, 1 hour 
15 minutes; current required, 30 amperes. 

The No. 3 and No. 4 magnets are particularly fitted for use on steam- 
driven locomotive cranes, and when so used are usually supplied with 
current from a small steam-driven generator set mounted on the crane, 
steam being drawn from the boiler of the crane. Nos. 5 and 6 are adapted 
for use with overhead electric traveling cranes in cases where large lifts 
and high speed of handling are essential. 

Sizes and Capacities of the Electric Controller & Mfg. Co.'s 
Type S-A Lifting Magnets (1909). 



Size. 


Diam. 


Weight. 


Average 
Current at 
220 Volts. 


Lifts in Machine Cast 
Pig Iron. 


Maximum 
Lift. 


Average 
Lift. 


3 

4 

5 
6 


In. 
36 
43 
52 
61 


Lb. 
2.100 
3.200 
4.800 
6.600 


Amp. 
11 
27 
35 
45 


Lb. 
1.405 
2.180 
3.087 
4.589 


Lb. 
750 
1.250 
1.800 
2.600 


Sizes and Capacities of Lifting Magnets (Cutler-Hammer), 1908. 


Size, 
In. 


Weight 
Lb. 


Maximum* 

Lifting 

Capacity, 

Lb. 


Average 

Lifting 

Capacity, 


Current 

Required 

at 220 Volts, 

Amperes. 


Head-room 

Required, 

Ft. 


10 


75 
1.650 
5.000 


800 

5.000 

20.000 


100-300 

500-1.000 

1.000-2.000 


1 
15-18 
30-35 




35 
50 


4 
6 



*This capacity can be obtainea only under the most favorable con- 
ditions, with complete magnetic contact between the magnet and the 
piece to be lifted. 

The capacity of a lifting magnet in service depends on many other 
factors than the design of the magnet. Most important is the character 
of the material handled. Much more can be handled at a single lift 
with material like billets, ingots, etc., than with scrap, wire, pig iron, 
etc. The speed of the crane, from which the magnet is suspended, and 
the distance it must transport the material are also important factors to 
be considered in calculating the capacity of a given magnet under given 
conditions. The following results have been selected from a great num- 
ber of tests of the Electric Controller and Mfg. Co.'s No. 2 Type S magnets 
in commercial service, and represent what is probably average practice. 
It should be borne in mind that the average lift is determined from a large 
number of lifts, including lifts made from a full car of, say, pig iron, 
where the magnetic conditions are very favorable, and also the " lean " 
lifts where the car is nearly empty, and magnetic conditions unfavorable; 
the magnet can reach only a few pigs at one time on the lean lifts, with a 
consequent heavy decrease in the size of the load. The average lift is 
therefore less than the maximum lift in handling a given lot of material. 
•■ When operated from an ordinary electric overhead traveling crane a 
magnet of the type used in these trials will handle from 20 to 30 tons 
per hour of the scrap used by open-hearth furnaces. If operated from 
a special fast crane, the amount may be somewhat increased. Average 
lifts in pounds for various materials are as follows: 



LIFTING MAGNETS. 



1195 



Skull cracker balls up to 20,000; ingot (or If ground man places 

magnet, two), each. 6,000: billet slabs, 900-6,000. 

The above weights depend on dimensions and whether in pile or 
stacked evenly. 

Machine cast pig iron, 1,250; sand cast pig iron, 1,150. 

These are values obtained in unloading railway cars, including lean 
lifts in cleaning up. 

Machine cast pig iron, 1.350; sand cast pig iron, 1,200. 

The above are average lifts from stockpile. 

Heavy melting stock (billets, crop ends of billets, rails or structural 
shapes, 1,250; boiler plate scrap, 1,100; farmers' scrap (harvesting 
machinery parts, plow points, etc.), 900; small risers from steel castings, 
1,600; fine wire scrap, scrap tubing not over 3 ft. long, loose even or 
lamination scrap, 500; bundled scrap, 1,200; miscellaneous junk deal- 
ers' scrap, 400-800. 



Commercial Results with a 52-inch, 5,000 pound Magnet. 
(Electric Controller & Mfg. Co., 1908.) 



Hoist 


Crane. 


Distance 
moved. 


^1^ 


m 

ft: 




• 

.as 


•2? 


speed, 

ft. per 

min. 


Trolley 


Bridge 




s? 


o 


speed, 


speed, 


«3 . 


o 


to 


i?g§ 


*S 


H 


•rt.S 


11 


ft. per 


ft. per 


'S£ 


¥ 


^^H 


d 


0^ 




min. 


min. 


M* 


H 


^ 


< 


H 


6 


60 


80 


315 


5 


6 


3 


60 


73 


1,650 


75 


1* 


60 


80 


315 


3 


6 


6 


35 


55 


1,275 


60 


2 


60 


80 


315 


10 


36 


15 


39.3 


60 


1,328 


60 


3 


60 


80 


315 


10 


20 


40 


33.9 


55 


1,234 


55 


4 


50 


200 


550 


3 


6 


3 


78. 


132 


1,182 


135 


5 


50 


200 


550 


4 


7 


8 


78 


168 


929 


190 


6 


50 


200 


550 


5 


8 





26 


30 


173 


45 


7 


50 


200 


550 


4 


6 


3 


80 


300 


534 


300 


8 


240 


171 


160 


12 


30 


12 


25 


25 


2.000 


80 


9 


240 


171 


160 


15 


10 


150 


112 


56 


4,000 


120 


10 


240 


171 


160 


7 


12 


5 


7 


8 


1,740 


15 


11 


240 


171 


160 


5 


13 





5 


4 


2,660 


10 


12 



* 1, Machine cast pig handled from stock pile to charging boxes. 2. 
Bull heads, ditto. 3. Sand cast pig unloaded from car to stock pile. 
4. Baled tin and wire unloaded from car to stock pile. 5. Boiler pZate 
scrap handled from stock pile to charging boxes. 6. Farmers' scrap, com- 
prising knotters and butters from threshing and binding machines, sections 
of cutter bars from mowers, broken steel teeth from hay rakes, plow points, 
etc., from stock pile to charging boxes. 7. Small risers from steel castings, 
handled from stock pile to charging boxes. 8. Laminated plates from 
armatures and transformers, mixed sizes, from stock pile to charging 
boxes. 9. Cast iron sewer pipe, 3 feet diameter, weighing 2,000 pounds 
each, lifted from cars to flat boat. Each nipe had to be blocked and 
lashed to prevent washing overboard. 10. Pennsylvania Railrocid East- 
River tunnel section castings, convex on one side, concave on other, 
weighing 4,000 pounds each. Handled from local float to barge for ship- 
ment. 11. Steel plate 1/2-inch X 10 inches X 6 feet inches handled 
from car to float. 12. Steel rails, 40 pounds per yard, 25 feet long. 
Handled from car to lighter, about 8 rails per lift. 

The above results of tests relate to the Electric Controller & Mfg. 
Co.'s No. 2 Type " S " magnet, 52 in. diameter and weighing 5200 lbs. 
and are the average of a large number of tests made at various plants 
between the years 1905 and 1908. This type of magnet is being super- 
seded by the No. 4 Type S-A magnet which is 43 in. diameter, weighs 
3200 lbs, and gives substantially the same average lift. 



1196 HOISTING AND CONVEYING. 

TELPHERAGE. 

Telpherage is a name given to a system of transporting materials in 
which the load is suspended from a trolley or small truck running on a 
cable or overhead rail, and in which the propelling force is obtained 
from an electric motor carried on the trolley. The trolley, with its 
motor, is called a *' telpher." A historical and iUustrated description 
Of the system is given in a paper by C. M. Clark, in Trans. A. I. E. E., 
1902. A series of circulars of the Link Belt Co., Philadelpliia. show 
numerous illustrations of the system in operation for handling different 
classes of materials. Telpherage is especially applicable for moving 
packages in warehouses, on wharfs, etc. The moving machinery 
consists of the telpher or the conveying power, vath accompanying 
trailers; the portable electric hoist or the vertical elevating power, and 
the carriers containing the load. Among the accessories are brakes, 
switches and controlling devices of many kinds. 

An automatic line is controlled by terminal and intermediate switches 
which are operated by the men who do the loading and unloading, no 
additional labor being required. A non-automatic line necessitates a 
boy to accompany the telpher. The advisability of using the, non- 
automatic rather than the automatic line is usually determined by the 
distance between stations. 

COAL-HANDLING MACHINERY. 

The following notes and tables are supplied by the Link-Belt ©0. 

In large boiler-houses coal is usually deUvered from hopper-cars into 
a track-hopper, about 10 feet wide and 12 to 16 feet long. A feeder set 
under the track-hopper feeds the coal at a regular rate to a crusher, which 
^reduces it to a size suitable for stokers. 

After crushing, the coal is elevated or conveyed to overhead storage- 
bins. Overhead storage is preferred for several reasons: 

1. To avoid expensive v/heeiing of coal in case of a breakdown of the 
coal-handling machinery. 

2. To avoid running the coal-handling machinery continuously. 

3. Coal kept under cover indoors will not freeze in winter and clog the 
supply-spouts to the boilers. 

4. It is often cheaper to store overhead than to use valuable ground- 
space adjacent to the boiler-house. 

5. As distinguished from vault or outside hopper storage, it is cheaper 
to build steel bins and supports than masonry pits. 

Weight of Overhead Bins. — Steel bins of approximately rectangular 
cross-section, say 10 X 10 feet, will weigh, exclusive of supports, about 
one-sixth as much as the contained coal. Larger bins, with sloping 
bottoms, may weigh one-eighth as much as the contained coal. Bag 
bottom bins of the Berquist type will weigh about one-twelfth as much as 
the contained coal, not including posts, and about one-ninth as much, 
including posts. 

Supply-pipes from Bins. — The supply-pipes from overhead bins to 
the boiler-room floor, or to the stoker-hoppers, should not be less than 12 
inches in diameter. They should be fitted at the top with a flanged cast- 
ing and a cut-off gate, to permit removal of the pipe when the boilers are 
to be cleaned or repaired. 

Types of Coal Elevators. — Coal elevators consist of buckets of 
various shapes attached to one or more strands of link-belting or chain, or 
to rubber belting. The buckets may either be attached continuously or 
at intervals. The various types are as follows: 

Continuous bucket elevators consist usually of one strand of chain and 
two sprocket-wheels with buckets attached continuously to the chain. 
Each bucket after passing the head wheel acts as a chute to direct the 
flow from the next bucket. This type of elevator will handle the larger 
sizes of coal. It runs at slow speeds, usually from 90 to 175 feet per min- 
ute, and has a maximum capacity of about 120 tons per hour. 

Centrifugal discharge elevators consist usually of a single strand of chain, 
v/ith the buckets attached thereto at intervals. They are used to handle 
the smaller sizes of coal in small quantities. They run at high speeds, 
nsuallv 34 to 40 revolutions of the head wheel per minute, and have a 
capacity up to 40 tons per hour. 



COAL-HANDLING MACHINERY. 1197 

Perfect discharge elevators consist of two strands of chain, with buckets 

at Intervals between them. A pair of idlers set under the head wheels 
cause the buckets to be completely inverted, and to make a clean delivery 
into the chutes at the elevator head. This type of elevator is useful in 
handhng material which tends to chng to the buckets. It runs at slow 
speeds, usually less than 150 feet per minute. The capacity depends on 
the size of the buckets. 

Combined Elevators and Conveyors are of the following types: 

Gravity discharge elevators, consisting of two strands of chain, with 
spaced V-shaped buckets fastened between them. After passing the head 
wheels the buckets act as conveyor-flights and convey the coal in a trough 
to any desired point. This is the cheapest type of combined elevator and 
conveyor, and is economical of power. A machine carrying 100 tons of 
coal per hour, in buckets 20 inches wide, 10 inches deep, and 24 inches long, 
spaced 3 feet apart, reauires 5 H.P. when loaded and 1 1/2 H.P. when empty 
for each 100 feet of horizontal run, and 1/9 H.P. for each foot of vertical lift. 

Rigid bucket-carriers consist of two strands of chain with a special 
bucket rigidly fastened between them. The buckets overlap and are so 
shaped that they wiU carry coal around three sides of a rectangle. The 
coal is carried to any desired point and is discharged by completely 
inverting the bucket over a turn-wheel. 

Pivoted bucket-carriers consist of two strands of long pitch steel chain to 
which are attached, in a pivotal manner, large malleable iron or steel 
buckets so arranged that their adjacent lips are close together or overlap. 
Overlapping buckets require special devices for changing the lap at the 
corner turns. Carriers in which the buckets do not overlap should be 
fitted with auxiliary pans or buckets, arranged in such a manner as to 
catch the spill which falls between the lips at the loading point, and so 
shaped as to return the spill to the buckets at the corner turns. Pivoted 
bucket-carriers will carry coal around four sides of a rectangle, the buckets 
being dumped on the horizontal run by striking a cam suitablj^ placed. 
Buckets for these carriers are usually of 2 ft. pitch, and range in width 
from 18 in. to 48 in. They run at low speeds, usually not over 50 ft. per 
minute, 40 ft. per minute being most usual. At the latter speed, the 
capacities when handling coal vary from 40 tons per hour for the 18 in. 
width to 120 tons for the 48 in. width. On account of the superior con- 
struction of these carriers and the slow speed at which they run, they are 
economical of power and durable. -The rollers mounted on the chain 
joints are usually 6 in. diameter, but for severe duty 8-in. rollers are often 
used. It is usual to make these hollow to carry a quantity of oil for 
internal lubrication. 

Coal Conveyors. — Coal conveyors are of four general types, viz., 
scraper or flight, bucket, screw, and belt conveyors. 

The flight conveyor consists of a trough of any desired cross-section and 
a single or double strand of chain carrying scrapers or flights of approxi- 
mately the same shape as the trough. The flights push the coal ahead of 
them in the trough to any desired point, where it is discharged through 
openings in the bottom of the trough. 

For short, low-capacity conveyors, malleable link hook-joint chains 
are used. For heavier service, malleable pin-joint chains, steel link chains, 
or monobar, are required. For the heaviest service, two strands of steel 
link chain, usuaUy with rollers, are used. 

Flight conveyors are of three types: plain scraper, suspended flight, and 
roller flight. 

In the plain scraper conveyor, the flight is suspended from the chain 
and drags along the bottom of the trough. It is of low first cost and is 
useful where noise of operation is not objectionable. It has a maximum 
capacity of about 30 tons per hour, and requires more power than either 
of the other two types of flight conveyors. 

Suspeiided flight conveyors use one or two strands of chain. The flights 
are attached to cross-bars having wearing-shoes at each end. These wear- 
ing-shoes slide on angle-iron tracks on each side of the conveyor trough. 
The flights do not touch the trough at any point. This type of conveyor 
is used where quietness of operation is a consideration. It is of higher 
first cost than the plain scraper conveyor, but requires one-fourth less 
power for operation. It is economical up to a capacity of about 80 tons 
per hour. 



1198 



HOISTING AND CONVEYING. 



The roller flight conveyor is similar to the suspended flight, except 
that the wearing-shoes are replaced by rollers. It is highest in first 
cost of all the flight conveyors, but has the advantages of low power 
consumption (one-half that of the scraper), low stress in chain, long 
life of chain, trough, and flights, and noiseless operation. It has an 
economical maximum capacity of about 120 tons per hour. 

The following formula gives approximately the horse-power at the 
head wheel required to operate flight conveyors: 

H.P. = (ATL + BWS) 4- 1000. 

T = tons of coal per hour; L = length of conveyor in feet, center to 
center; W = weight of chain, flights, and shoes (both runs) in pounds; 
»S = speed in feet per minute; A and B constants depending on angle 
of incline from horizontal. See example below. 

Example. — Required the H.P. for a monobar conveyor 200 ft. 
center to center carrying 100 tons of coal per hour, up a 10° incline at 
a speed of 100 feet per minute. Conveyor has No. 818 chain and 8 X19 
suspended flights, spaced 18 inches apart. 

„ ^ 0.5 X 100 X 200 + 0.008 (400 X 5.7 -f 267 X 15.55) X 100 , ^ , ^ 
H.P. = ^^^ = 15.15. 

The following table shows the conveying capacities of various sizes 
of flights at 100 feet per minute in tons, of 2000 lb., per hour. The 
values are true for continuous feed only. 





Horizontal Conveyors, Tons. 


Inclined Conveyors, Tons. 


Size of 
Flight. 


Flight 

Every 

16". 


Flight 

Every 

18". 


Flight 

Every 

24". 


Pounds 
Coal per 
Flight. 


10° 

Flights 

Every 

24". 


20° 
Flights 
Every 

24". 


30° 
Flights 
Every 

24". 


6X14 
8X19 


69.75 


62 
130 


46.5 
97.5 

172.5 

220 

268 

315 


31 
65 
115 
147 
179 
210 


40.5 

78 
150 
184 
225 
264 


31.5 

62 
120 
146 
177 
210 


22.5 
52 


10X24 




90 


10X30 






116 


10X36 






142 


10X42 






167 



Bucket Conveyors. — Rigid bucket-carriers are used to convey large 
quantities of coal over a considerable distance when there is no inter- 
mediate point of discharge. These conveyors are made with two strands 
of steel roller chain. They are built to carry as much as 10 tons of coal 
per minute. 

Screw Conveyors. — Screw conveyors consist of a hehcal steel flight, 
either in one piece or in sections, mounted on a pipe or shaft, and running 
in a steel or wooden trough. These conveyors are made from 4 to 18 
inches in diameter, and in sections 8 to 12 feet long. The speed ranges 
from 20 to 60 revolutions per minute and the capacity from 10 to 30 tons 
of coal per hour. It is not advisable to use this type of conveyor for coal, 
as it will only handle the smaller sizes and the flights are very easily dam- 
aged by any foreign substance of unusual size or shape. 

Belt Conveyors. — Rubber and cotton belt conveyors are used for 
handling coal, ore, sand, gravel etc., in all sizes. They combine a high 
carrying capacity with low power consumption. 

In some cases the belt is fiat, the material being fed to the belt at Its 
center in a narrow stream. In the majority of cases, however, the belt 
is troughed by means of idler pulleys set at an angle from the horizontal 
and placed at intervals along the length of the belt. Rubber belts are 
often made more flexible for deep troughing by removing some of the 
layers of cotton from the belt and substituting therefor an extra thickness 
of rubber. 

Belt conveyors may be used for elevating materials up to about 23° 
Incline. On greater inclines the material slides back on the belt and spills. 
With many substances it is important to feed the belt steadily if the con- 
veyor stands at or near the limiting angle. If the flow is interrupted 
the material may slide back on the belt. 

Belt conveyors are run at any speed from 200 to 800 feet per minute, 
and are made in widths varying from 12 inches to 60 inches. 



CONVEYORS. 



1199 



Values of A and B, 



Angle, 
Deg. 


A 


B 


Angle, 
Deg. 


A 


B 


Angle, 
Deg. 


A 


B 





0.343 


0.01 


10 


0.50 


0.01 


30 


0.79 


0.009 


2 


0.378 


0.01 


14 


0.57 


0.01 


34 


0.84 


0.008 


4 


0.40 


0.01 


18 


0.63 


0.009 


38 


0.88 


0.008 


6 


0.44 


O.Ol 


22 


0.69 


0.009 


42 


0.92 


0.007 


8 


0.47 


0.01 


26 


0.74 


0.009 


46 


0.95 


0.007 



For suspended flight conveyors take B as 0.8 and for roller flights as 
0.6, of the values given in the table. 

Weight of Chain in Pounds per Foot. 



Link-belting. 


MONOBAR. 


Chain 


Pitch of Flights, Inches. 


Chain 
No.* 


Pitch of Flights, Inches. 


No. 


12 


18 


24 


36 


12 


18 


24 


36 


48 


54 


72 


78 


2.4 
2.8 


2.3 
2.7 


2.26 
2.6 


2.2 
2.5 


612 
618 


3 P 




3.6 


3.5 

2.8 








88 






3 







2.7 




85 


3.1 


2.8 


2.7 


2.6 


818 






5 


7 




5.5 




5.3 




103 


4.6 


4.4 


4.3 


4.2 


824 










4.9 




4.7 




4.6 


108 


4.9 


4.7 


4.4 


4.1 


1018 






11 


5 




10.7 




10.4 




110 


5.6 


5.2 


4.9 


4.7 


1024 










9.6 




9.07 




8.8 


114 


6.3 


6.0 


5.9 


5.7 


1224 










14.7 




14.04 




13.8 


122 


8.1 


7.7 


7.4 


7.2 


1236 












11.8 






11.34 


124 


8.9 


8.4 


8.2 


7.9 


1424 










20.^ 




19.7 




19.4 



* In monobar the first one or two figures in the number of the chain 
denote the diameter of the chain in eighths of an inch. The last two 
figures denote the pitch in inches. 



Pin Chains. 


Roller Chains. 


No. 


Pitch of Flights, Inches. 


No. 


Pitch of Flights, Inches. 


12 


18 


24 


36 


12 18 1 24 


36 








720 
730 
825 


5.9 
6.9 
9.6 


5.6 
6.6 
9.3 


5.4 
6.4 
9.1 


5.3 
6.3 
8.9 


1112 
1113 
1130 


7.7 6.9| 6.2 
9.5i 8.8 8.0 
10.51 9.5! 9.0 


5.7 
7.5 

7.8 









Weight of Flights with Wearing-shoes and Bolts. 



Size, Inches. 


Steel. 


Malleable Iron. 


Suspended Flights. 


Size. 


Weight, Lb. 


4X10 


3.5 


4.3 


6X14 


12.37 


4X12 


3.9 


4.7 


8X19 


15.55 


5X10 


4.1 


5.2 


10X24 


25.57 


5X12 


4.6 


5.7 


10X30 


%'^ 


5X15 


5.8 


5.9 


10X36 


6X18 


8.1 


9.2 


10X42 


34.97 


8X18 


10.1 


12.7 






8X20 


11.0 


13.4 






8X24 


12.6 


14.4 






10X24 


15.2 


17.4 







Capacity of Belt Conveyors in Tons of Coal per Hour. 



Width 

of 
Belt, 


Velocity, Feet per 
Minute. 


Width 

of 
Belt, 
Ins. 


Velocity, Feet per Minute. 


Ins. 


300 


350 


400 


300 


350 


400 


450 


500 


12 
14 
16 
18 


34 
47 
62 
78 


72 
91 


82 
104 


20 
24 
30 
36 


96 
139 
218 
315 


112 
162 
254 
368 


128 
186 
290 
420 


210 
326 

472 


520 



1200 



HOISTING AND CONVEYING. 



For materials other than coal, the figures in the above table shoiild be 
multiplied by the coeflQcients given in the table below: 



Material. 


Coefficient. 


Material. 


Coefficient. 


Ashfs rdaniD) ... 


0.86 
1.76 
1.26 
0.60 


Earth 


1.4 


Cement 


Sand 


1.8 


Clay 


Stone (crushed) 


2.0 


Coke 





Belt Convej'or Construction, (C. K. Baldwin, Trans. A. S. M. E,l 
1908.) — The troughing idlers should be spaced as follows, depending 
on the weight of the material carried: 

Belt width 12-16 in. 18-22 in. 24-30 in. 32-36 in. 

Spacmg, ft. 43^-5 4-43^ 3 3^-4 3-33^ 

The stress in the belt should not exceed 18 to 20 lb. per inch of width 
per ply with rubber belts. This may be increased about 20% with 
belts in which 28 oz. duck is used. Where the power required is small 
the stiffness of the belt fixes the number of plies. The minimum num- 
ber of pUes is as foUows: 

Belt width, in. 12-14 16-20 22-28 30-36 

Minimum phes 3 4 5 6 

Pulleys of small diameter should be avoided on heavy belts, or the con- 
stant bending of the belt under heavy stress will cause the friction to 
lose its hold and destroy the belt. In many cases it is advisable to 
cover the driving pulley with a rubber lagging to increase the tractive 
power, particularly in dusty places. The minimum size of driving 
pulleys to be used is shown in the table below. 

Smallest Diameter of Driving Pulleys for Belt Conveyors. 



Width of 
Belt. 


Diameter 
of Pulley. 


Width of 
Belt. 


Diameter of 
Pulley. 


Width of 
Belt. 


Diameter of 
Pulley. 


In. 
12 
14 
16 
IS 


In. 

16-18 

16-18 

20-24 

20-24 

20-24 


In. 
22 
24 
26 
28 
30 


In. 

20-30 

24-30 

24-30 

24-30 

30-36 


In. 
32 
34 
36 


In. 
30-36 
30-42 
30-48 


20 







Horse-power to Drive Belt Conveyors. (C. K. Baldwin, Trans. 
A. S. M. E., 190S.) — The power required to drive a belt conveyor de- 
pends on a great variety of conditions, as the spacing of idlers, type of 
drive, thickness of belt, etc. In figuring the power required, the belt 
should run no faster than is necessary to carry the desired load.e* If it 
should be necessary to increase the speed, the load should be increased 
In proportion and the power figured accordingly. 

For level conveyors U.F. = C X T X L -^ 1000. 

For inclined conveyors 

H.P. = (C X T XL ^ 1000) -\- {T XH -^ 1000). 

C = power constant from table below; T = load, tons per hour; L = 
length of conveyor, center to center, ft.; H = vertical height material is 
lifted, ft.; S = belt speed, ft, per minute; B = width of belt, in. 

For each movable or fixed tripper add horse-power in coliunn 3 of 
table. Add 20% to horse-power for each conveyor under 50 ft. long. 
Add 10% to horse-power for each conveyor between 50 ft. and 100 ft. 
long. The formulae above do not include gear friction, should the 
conveyor be gear-driven. 

When horse-power and speed are known the stress in the Delt in pounds 
per inch of width is 

stress = »P,><^|-QO» • I 

From this the number of plies can be found, using 20 lb. per ply per 
inch of width as a maximum for rubber belts. 

Relative Wearing Power of Conveyor Belts. (T. A. Bennett, 
Trans, A. S. M. E,, 1908.) — Different materials used in the construction 



PNEUMATIC CONVEYING. 



1201 





Constants for Formulae for Belt Conveyors. 






1 


2 


3 


4 


5 




C for Mate- 


C for Mate- 


H.P. Re- 
quired for 
Each Mov- 






Width of 


rial Weigh- 


rial Weigh- 


Minimum 


Maximum 


Belt 


ing from 25 


ing from 75 




Plies of 


Plies of 


In. 


Lb. to 75 Lb. 


Lb. to 125 Lb. 


Fixed 


Belt. 


Belt. 




per Cu. Ft. 


per Cu. Ft. 


Tripper. 






12 


0.234 


0.147 


1/2 


3 


4 


14 


0.226 


0.143 


1/2 


3 


4 


16 


0.220 


0.140 


3/4 


4 


5 


18 


0.209 


0.138 


1 


4 


5 


20 


0.205 


0.136 


1 1/4 


4 


6 


22 


0.199 


0.133 


1 1/0 


5 


6 


24 


0.195 


0.131 


1 3/4 


5 


7 


26 


0.187 


0.127 


2 


5 


7 


28 


0.175 


0.121 


2 1/4 


5 


8 


30 


0.167 


0.117 


2 1/2 


6 


8 


32 


0.163 


0.115 


2 3/4 


6 


9 


34 


0.161 


0.114 


3 


6 


10 


36 


0.157 


0.112 


3 1/4 


6 


10 



of conveyors were subjected to the uniform action of a sand blast for 45 
minutes, and the relative abrasive resisting qualities were found to be as 
follows, taking the volume of rubber belt worn away as 1.0: 

Rubber belt 1.0 Woven cotton belt, high grade 6 . 5 

Rolled steel bar 1.5 Stitched duck, high grade 8.0 

Cast iron 3.5 Woven cotton belt, low grade, 9.0 to 

Balata belt , including gum cover 5 . 15.0 

A Symposium on Hoisting and Conveying was presented at the Detroit 
meeting of the A. S. M. E, 1908 (Trans., vol. xxx.), in papers by G. E. 
Titcomb, S. B. Peck, C. K. Baldwin, C. J. Tomlinson and E. J. Haddock. 
Among the subjects discussed are the loading and unloading of cargo 
steamers; car unloaders; storing of ore and coal; continuous conveying of 
merchandise; conveying in a Portland cement plant, and suspension 
cableways. 

PNEUMATIC CONVEYING 

Pneumatic Conveying. — A pneumatic conveying system consists of 
a pipe line, a feeding hopper, a blower or exhauster, and a receiver. It 
is used for conveying grain, slack coal, sawdust, shavings, and other 
light material. Grain has been carried over 2,000 ft. horizontally and 
raised to any desired height. The pressure system is simpler and 
requires less pipe than the vacuum system, but the latter is more com- 
mon and is adapted to a greater variety of conditions. The principal 
advantages of the pneumatic system, as against aU types of mechanical 
conveyors, are simplicity, adaptability to peculiar conditions, the little 
attention required, few repairs, and shut-downs. (For details of 
apparatus, etc., see bulletins of the ConnersviUe Blower Co.) 

Pneumatic Postal Transmission. — A paper by A. Falkenau (Eng'rs 
Club of Philadelphia, April, 1894), entitled the "First United States 
Pneumatic Postal System," gives a description of the system used in 
London and Paris, and that recently introduced in Philadelphia between 
the main post-office and a substation. In London the tubes are 2 }4 and 
3-incli lead pipes laid in cast-iron pipes for protection. The carriers 
used in 2 ^-inch tubes are but 1 }4 inches diameter, the remaining space 
being taken up by packing. Carriers are despatched singly. First, 
vacuum alone was used; later, vacuum and compressed air. The tubes 
used in the Continental cities in Europe are wrought iron, the Paris tubes 
being 2}4 inches diameter. There the carriers are despatched in trains 
of six to ten, propelled by a piston. In Philadelphia the size of tube 
adopted is 6 K inches, the tubes being of cast iron bored to size. The 
lengths of the outgoing and return tubes are 2928 feet each. The pressure 



1202 HOISTING AND CONVEYING. 

at the main station is 7 lb., at the substation 4 lb., and at the end of the 
return pipe atmospheric pressure. The compressor has two air-cylinders 
18 X 24 in. Each carrier holds about 200 letters, but 100 to 150 are 
taken as an average. Eight carriers may be despatched in a minute, 
giving a dehvery of 48,000 to 72,000 letters per hour.* The time 
required in transmission is about 57 seconds, 

Pneumatic postal transmission tubes were laid in 1898 by the Batcheller 
Pneumatic Tube Co. between the general post-offices in New York and 
Brooklyn, crossing the East River on the Brooklyn bridge. The tubes 
are cast iron, 12-ft. lengths, bored to 8V8 in. diameter. The joints are 
bells, calked with lead and yarn. There are .two tubes, one operating 
in each direction. Both lines are operated by air-pressure above the 
atmospheric pressure. One tube is operated by an air-compressor in the 
New York office and the other by one located in the Brooklyn office. 

The carriers are 24 in. long, in the form of a cylinder 7 in. diameter, 
and are made of steel, with fibrous bearing-rings which fit the tube. Each 
carrier will contain about 600 ordinary letters, and they are despatched 
at intervals of 10 seconds in each direction, the time of transit between 
the two offices being 3 V2 minutes, the carriers travelling at a speed of 
from 30 to 35 miles per hour. 

One of the air-compressors is of the duplex type and has two steam- 
cylinders 10 X 20 in. and two air-cylinders 24 X 20 in., delivering 
1570 cu. ft. of free air per minute, at 75 r.p.m. The power is about 50 H.P. 
Two other duplex air-compressors have steam-cylinders 14 X 18 in, 
and air-cyhnders 26 1/4 X18 in. They are designed for 80 to 90 r.p.m, 
and to compress to 20 lb. per sq. in. 

Another double line of i^neumatic tubes has been laid between the 
main office and Postal Station H, Lexington Ave. and 44th St., in New 
York City. This hne is about 31/2 miles in length. There are three 
intermediate stations. The carriers can be so adjusted when they are 
put into the tube that thev %vill traverse the line and be discharged auto- 
matically from the tube at the station for which they are intended. The 
tubes are of the same size as those of the Brooklyn line and are operated 
in a similar manner. The initial air-pressure is about 12 to 15 lb. On 
the Brooklyn line it is about 7 lb'. 

There is also a tube system between the New York Post-office and the 
Produce Exchange. For a very complete description of the system and 
its machinery see "The Pneumatic Despatch Tube System," by B. C. 
Batcheller, J. B. Lippincott Co., Philadelphia, 1897. 

WniE-ROFE HAULAGE. 

Methods for transporting coal and other products by means of wire rope, 
though varying from each other in detail, may be grouped in five classes: 
I. The Self-acting or Gravity Inclined Plane. 
TI. The Simple Engine-plane. 

III. The Tail-rope System. 

IV. The Endless-rope System. 
V. The Cable Tramway. 

The following brief description of these systems is abridged from a 

Eamphlet on Wire-rope Haulage, by Wm. Hildenbrand, C.E., published 
y John A. Roebhng's Sons Co., Trenton, N. J. 

I. The Self-acting Inclined Plane. — The motive power for the 
eelf-acting incUned plane is gravity: consequently this mode of transport- 
ing coal finds appHcation only in places where the coal is conveyed from a 
hierher to a lower point and where the plane has sufficient grade for the 
loaded descending cars to raise the empty cars to an upper level. 

At the head of the plane there is a drum, which is generally constructed 
of wood, having a diameter of seven to ten feet. It is placed high enough 
to allow men and cars to pass under it. Loaded cars coming from the pit 
are either singly or in sets of two or three switched on the track of the 
plane, and their speed in descending is regulated by a brake on the drum. 
Supporting rollers, to prevent the rope dragging on the ground, are 

* A report of a U. S. Postal Commission states that up to the piosent 
time (1910), the sending and receiving apparatus does not permit the 
successful operation of carrier service with an interval of less than 
13 to 15 seconds between carriers, for 6- and 8-in. tubes. 



WIRE-ROPE HAULAGE. 1203 

generally of wood, 5 to 6 in. in diameter and 18 to 24 in. long, with 

3/4 to 7/8 in. iron axles. The distance between the rollers varies from 15 to 
30 ft., steeper planes requiring less rollers than those with easy grades. 
Considering only the reduction of friction and what is best for the preserva- 
tion of rope, a general rule may be given to use rollers of the greatest 
possible diameter, and to place them as close as economy will permit 

The smallest angle of inclination at wliich a plane can be made self- 
acting will be when the motive and resisting forces balance each other. 
The motive forces are the w^eights of the loaded car and of the descending 
rope. The resisting forces consist of the weight of the empty car and 
ascending rope, of the rolling and axle friction of the cars, and of the axle 
friction of the supporting rollers. The friction of the drum, stiffness of 
rope, and ressistance of air may be neglected. A general rule cannot be 
given, because a change in the length of the plane or in the weight of the 
cars changes the proportion of the forces; also, because the coefficient of 
friction, depending on the condition of the road, construction of the cars, 
etc., is a very uncertain factor. 

For working a plane ^Ith a Vs-in. steel rope and lowering from one to 
four pit cars weighing empty 1400 lb. and loaded 4000 lb., the rise in 100 ft. 
necessary to make the plane self-acting will be from about 5 to 10 ft., 
decreasing as the number of cars increase, and increasing as the length of 
plane increases. 

A gravity inclined plane should be slightly concave, steeper at the top 
than at the bottom. The maximum deflection of the curve should be at 
an inclination of 45 degrees, and diminish for smaller as well as for steeper 
inclinations. 

II. The Simple Engine-plane. — The name ** Engine-plane" is given 
to a plane on which a load is raised or low^ered by means of a single wire 
rope and stationary steam-engine. It is a cheap and simple method of 
conveying coal underground, and therefore is applied wherever circum- 
stances permit it. Under ordinary conditions such as prevail in the 
Pennsylvania mine region, a train of twenty-five to thirty loaded cars will 
descend, with reasonable velocity, a straight plane 5000 ft. long on a 
grade of l^U ft. in 100, while it would appear that 21/4 ft. in 100 is neces- 
sary for the same number of emptj^ cars. For roads longer than 5000 ft. 
or containing sharp curves, the grade should be correspondingly larger. 

III. The Tail-rope System. — Of all methods for conveying coal 
underground by wire rope, the tail-rope system has found the most appli- 
cation. It can be applied under almost any condition. The road may be 
straight or curved, level or undulating, in one continuous line or with side 
branches. In general principle a tail-rope plane is the same as an engine- 
plane worked in both directions with two ropes. One rope, called the 
*' main rope," serves for dramng the set of full cars outward; the other, 
called the " tail-rope,'* is necessary to take back the empty set, which on 
a level or undulating road cannot return by gravity. The two drums may 
be located at the opposite ends of the road, and driven by separate eixgines, 
but more frequently they are on the same shaft at one end of the plane. 
In the first case each rope would require the length of the plane, but in the 
second case the tail rope must be twice as long, being led from the drum 
around a sheave at the other end of the plane and back again to its starting- 
point. When the main rope drawls a set of full cars out, the tail-rope drum 
runs loose on the shaft, and the rope, being attached to the rear car, un- 
winds itself steadily. Going in, the reverse takes place. Each drum is 
provided with a brake to check the speed of the train on a down grade and 
prevent its overrunning the forward rope. As a rule, the tail rope is 
strained less than the main rope, but in cases of heavy grades dipping out- 
ward it is possible that the strain in the former may become as large, or 
even larger, than in the latter, and in the selection of the sizes reference 
should be had to this circumstance. 

IV. The Endless-rope System. — The principal features of this 
system are as follows: 

1. The rope, as the name indicates, is endless. 2. Motion is given to 
the rope by a single w^heel or drum, and friction is obtained either by a 
grip-wheel or by passing the rope several times around the wheel. 3. The 
rope must be kept constantly tight, the tension to be produced by artificial 
means. It is done in placing either the return-wheel or an extra tension 
wheel on a carriage and connecting it with a weight hanging over a 
pulley, or attaching it to a fixed post by a screw which occasionally can be 



1204 



HOISTING AND CONVEYING. 



shortened. 4. The cars are attached to the rope by a grip or clutch, 

which can take hold at any place and let go again, starting and stopping 
the train at will, without stopping the engine or the motion of the rope. 
5. On a single-track road the rope works forward and backward, but on a 
double track it is possible to thu it always in the same direction, the full 
cars going on one track and the empty cars on the other. 

This method of conveying coal, as a rule, has not found as general an in- 
troduction as the tail-rope system, probably because its efficacy is not so 
apparent and the opposing difficulties require greater mechanical skill and 
more complicated apphances. Its advantages are, first, that it requires 
one-third less rope than the tail-rope system. This advantage, however, 
is partially counterbalanced by the circumstance that the extra tension in 
the rope requires a heavier size to move the same load than when a main 
and tail rope are used. The second and principal advantage is that it is 
possible to start and stop trains at will without signaling to the engineer. 
On the other hand, it is more difficult to work curves with the endless sys- 
tem, and still more so to work different branches, and the constant stretch 
of the rope under tension or its elongation under changes of temperature 
frequently causes the rope to slip on the wheel, in spite of every attention, 
causing delay in the transportation and injury to the rope. 

Stress in Hoisting-ropes on Inclined Planes. 

(Trenton Iron Co., 1906.) 





1 

1 . 

M a 
■S-2 






■J: 



•S-2 






•s-2 


hi 




d 
< 


5 




^ 

< 




^0 


"^ 

< 


m ^^ 


Ft. 






Ft. 






Ft. 






5 


2° 52' 


140 


55 


28° 49' 


1003 


110 


47° 44' 


1516 


10 


50 43/ 


240 


60 


30° 58' 


1067 


120 


50° 12' 


1573 


15 


8<^ 32' 


336 


65 


33° 02' 


1128 


130 


52° 26' 


1620 


20 


11° 18' 


432 


70 


35° 00' 


1185 


140 


54° 28' 


1663 


25 


14° 03' 


527 


75 


36° 53' 


1238 


150 


56° 19' 


1699 


30 


16° 42' 


613 


80 


38° 40' 


1287 


160 


58° 00' 


1730 


35 


19° 18' 


700 


85 


40° 22' 


1332 


170 


59° 33' 


1758 


40 


21° 49' 


782 


90 


42° 00' 


1375 


180 


60° 57' 


1782 


45 


24° 14' 


860 


95 


43° 32' 


1415 


190 


62° 15' 


1804 


50 


26° 34' 


933 


100 


45° 00' 


1454 


200 


63° 27' 


1822 



The above table is based on an allowance of 40 lb. per ton for rolling 
friction, but an additional allowance must be made for stress due to the 
weight of the rope proportional to the length of the plane. A factor of 
safety of 5 to 7 should be taken. 

In hoisting the slack-rope should be taken up gently before beginning 
the lift, otherwise a severe extra strain will be brought on the rope. 

V. Wire-rope Tramways. — The methods of conveying products on 
a suspended rope tramway find especial application in places where a mine 
is located on one side of a river or deep ravine and the loading station on 
the other. A wire rope suspended between the two stations forms the 
track on which material in properly constructed " carriages " or " buggies" 
is transported. It saves the construction of a bridge or trestlework and is 
practical for a distance of 2000 feet without an intermediate support. 

There are two distinct classes of rope tramways: 

1. The rope is stationary, forming the track on which a bucket holding 
the material moves forward and backward, pulled by a smaller endless 
wire rope. 2. The rope is movable, forming itself an endless line, which 
serves at the same time as supporting track and as pulling rope. 

Of these two the first method has found more general application, and 
is especially adapted for long spans, steep inclinations, and heavy loads. 



WIRE-ROPE HAULAGE. 1205 

The second method is used for long distances, divided into short spans, 
and is only applicable for light loads dehvered at regular intervals. 

For detailed descriptions ot ilie several systems of wire-rope transporta- 
tion, see circulars of John A. Roebiing's Sons Co., The Trenton Iron Co., 
A. Leschen & Sons Rope Co. See also paper on Two-rope Haulage Sys- 
tems, by R. Van A. Norris, Trans. A.. S. M. E., xii. 626. 

In the Bleichert System of wire-rope tramways, in which the track rope 
is stationary, loads up to 2000 lb. are carried at a speed of 3 to 4 miles pet 
hour. While the average spans on a level are from 150 to 200 ft., in cross- 
ing rivers, ravines, etc., spans up to 1500 ft. are frequently adopted. In a 
tramway on this system at Bingham, Utah, the total length of the line is 
12,700 ft. with a fall of 1120 ft. The line operates by gravity and carries 
35 tons per hour. The cost of convejdng on this carrier is 73/4 cents per 
ton of 2000 lb. for labor and repairs, without any apparent deterioration 
in the condition of track cables and traction rope. 

The Aerial Wire-rope Tramway of A. Leschen & Sons Co. is of the 
double-rope type, in which the buckets travel upon stationary track 
cables and are propelled by an endless traction rope. The buckets are 
attached to the traction rope by means of clips — spaced according to 
the desired tonnage. The hold on the rope is positive, but the clip is 
easily removable. The bucket is held in its normal position in the frame 
by two malleable iron latches — one on each side. A tripping bar 
engages these latches at the unloading terminal when the bucket dis- 
charges its material. This operation is automatic and takes place while 
the carriers are moving. At the loading term.inal, the bucket is auto- 
matically^ returned to its normal position and latched. Special carriers 
are provided for the accommodation of any class of material. At each 
of the terminal stations is a 10-ft. sheave wheel around which the trac- 
tion rope passes, these wheels being provided with steel grids for the 
control of the traction rope. When the loaded carriers travel down 
grade and the difference in elevation is sufficient, this tramw^ay will 
operate by the force due to gravity, otherwise the power is applied to 
the sheaves through bevel gearing. Numerous modifications of the 
system are in use to suit different conditions. 

An Aerial Tramway 21.5 miles long, with an elevation of the loading 
end above the discharging end of 11,500 ft., built by A. Bleichert & Co. 
for the government of the Argentine Republic, connecting the mines of 
La Mejicana with the town of Chilecito, is described by Wm. Hewitt in 
Indust. Eng., Aug. 15, 1909. Some of the inclinations are as much as 
45 deg., there are some spans nearly 3000 ft. long, and there is a tunnel 
nearly 500 ft. long. The line is divided into eight sections, each with 
an independent traction rope. The gravity of the descending loaded 
carriers is sufficient to make the line self-operating when it is once set 
in motion, but in order to ensure full control, and to provide for carrying 
four tons upward while the descending carriers are empty, four steam 
engines are installed, one for each two sections. The carriers hold 10 cu. 
ft., or about 1100 lbs. of ore. The speed is 500 ft. per minute, and the 
interval between carriers 45 seconds. The stress in the traction rope is 
as high as 11,000 lbs. in some sections. 

Suspension Cableways or Cable Hoist-con?eyors* 

(Trenton Iron Co.) 

In quarrying, rock-cutting, stripping, piling, dam-building, and many 
other operations where it is necessary to hoist and convey large individual 
loads economically, it frequently happens that the application of a system 
of derricks is impracticable, by reason of the limited area of their effi- 
ciency and the room which they occupy. To meet such conditions cable 
hoist-conveyors are adopted, as they can be operated in clear spans up to 
1500 ft., and in lifting individual loads up to 15 tons. Two types are 
made — one in which the hoisting and conveying are done by separate 
running ropes, and the other applicable only to inchnes in which the 
carriage descends by gravity, and but one running rope is required. The 
moving of the carriage in the former is effected by means of an endless 
rope, and these are commonly known as " endless-rope " hoist-convevors 
to distinguish them from the latter, which are termed "inclined" hoist- 
conveyors. 



1206 HOISTING AND CONVEYING. 

The general arrangement of the endless-rope hoist-conveyors consists 
of a main cable passing over towers, A-frames or masts, as may be most 
convenient, and anchored firmly to the ground at each end, the requisite 
tension in the cable being maintained by a turnbuckle at one anchorage. 

Upon this cable travels the carriage, which is moved back and forth 
over the line by means of the endless rope. The hoisting is done by a 
separate rope, both ropes being operated by an engine specially designed 
for the purpose, which may be located at either end of the line, and is 
constructed in such a way that the hoisting-rope is coiled up or paid out 
automatically as the carriage is moved in and out. Loads may_ be picked 
up or discharged at any point along the hue. Where sufficient inchnation 
can be obtained in the main cable for the carriage to descend by gravity, 
and the loading and unloading are done at fixed points, the endless rope can 
be dispensed with. The carriage, which is similar in construction to the 
carriage used in the endless-rope cableways, is arrested in its descent by a 
stop-block, which may be clamped to the main cable at any desired point, 
the speed of the descending carriage being under control of a brake on the 
engine-drum. 

A Double-suspension Cahleway, carrying loads of 15 tons, erected near 
Williamsport, Pa., by the Trenton Iron Co., is described by E. G. Spilsbury 
in Trans. A. I. M. E., xx. 766. The span is 733 ft., crossing the Susque- 
hanna River. Two steel cables, each 2 in. diam., are used. On these 
cables runs a carriage supported on four wheels and moved by an endless 
cable 1 inch in diam. The load consists of a cage carrying a railroad-car 
loaded with lumber, the latter weighing about 12 tons. The power is 
furnished by a 50-H.P. engine, and the trip across the river is made in 
about three minutes. 

A hoisting cableway on the endless-rope system, erected by the Lidger- 
wood Mfg. Co., at the Austin Dam, Texas, had a single span 1350 ft. in 
length, with main cable 21/2 in. diam., and hoisting-rope 13/4 in. diam. 
Loads of 7 to 8 tons were handled at a speed of 600 to 800 ft. per minute. 

Another, of still longer span, 1650 ft., was erected by the same company 
at Holyoke, Mass., for use in the construction of a dam. The main cable 
is the EUiott or locked-wire cable, having a smooth exterior. In the con- 
struction of the Chicago Drainage Canal twenty cableways, of 700 ft. span 
and 8 tons capacity, were used, the towers traveling on rails, 

Tension required to Prevent Slipping of Rope on Drum. (Trenton 
Iron Co., 1906.) — The amount of artificial tension to be applied in an 
endless rope to prevent sUpping on the driving-drum depends on the char- 
acter of the drum, the condition of the rope and number of laps which it 
makes. If T and S represent respectively the tensions in the taut and 
slack lines of the rope; W, the necessary weight to be applied to the tail- 
sheave; R, the resistance of the cars and rope, allowing for friction; n, the 
number of half-laps of the rope on the driving-drum; and /, the coefficient 
of friction, the following relations must exist to prevent slipping: 

T = Se^^"", W = T+ S, Sind R = T - S; 

from which we obtain W = -^ R, 

in which e = 2.71828, the base of the Naperian system of logarithms. 
The following are some of the values of /: 

Dry. Wet. Greasy. 
Wire-rope on a grooved iron drum. .. . 0.120 0.085 0.070 

Wire-rope on wood-filled sheaves 0. 235 0. 170 0. 140 

Wire-rope on rubber and leather fiUing 0.495 0.400 0.205 
The importance of keeping the rope dry is evident from these figures. 

ofmr _^ -^ 
The values of the coefficient -^ . corresponding to the above values 

of/, for one up to six half-laps of the rope on the driving-drum or sheaves. 
are given in the table at the top of p. 1207. 

When the rope is at rest the tension is distributed equally on the two 
lines of the rope, but when running there will be a difference in the 
tensions of the taut and slack lines equal to the resistance, and the 
values of T and 5 may be readily computed from the foregoing formulae. 



WIRE-EOPE HAULAGE. 



1207 





Values of Coefficient (ef^^ + l) n 


. (efn^ - l) 


/ 


n = Number of HalWaps on Driving-wheel. 


1 


2 1 3 1 4 


5 


6 


0.070 


9.130 


4.623 


3. 141 


2.418 


1 .999 


1.729 


0.085 


7.536 


3.833 


2.629 


2.047 


1.714 


1.505 


0.120 


5.345 


2.777 


1.953 


1.570 


1.358 


1.232 


0.140 


4.623 


2.418 


1.729 


1.416 


1.249 


1.154 


0.170 


3.833 


2.047 


1.505 


1.268 


1.149 


1.085 


0.205 


3.212 


1.762 


1.338 


1.165 


1.083 


1.043 


0.235 


2.831 


1.592 


1.245 


1.110 


1.051 


1.024 


0.400 


1.795 


1.176 


1.047 


1.013 


1.004 


1.001 


0.495 


1.538 


1.093 


1.019 


1.004 


1.001 





The increase in tension in the endless rope, compared with the main 
rope. of the tail-rope system, where the stress in the rope is equal to 
the resistance, is about as follows: 

n= 123456 

Increase in tension in endless rope, 

compared with direct stress %... . 40 9 21/3 2/3 1/5 i/jo 
These figures are useful in determining the size of rope. For instance, 
if the rope makes two half-laps on the driving drum, the strength of the 
rope should be 9 % greater than a main rope in the tail-rope system. 

General Formulae for Estimating the Deflection of a Wire Cable 
Corresponding to a Given Tension. 

(Trenton Iron Co., 1906.) 

Let s =■ distance between supports or spanrA.S; m and n = arms into 
which the span is divided by a vertical through the required point of 
deflection x, m representing the arm corresponding to the loaded side; 
y = horizontal distance from load to point of support corresponding with 
m;w = wt. of rope per ft.; g' = load; t = tension; h = required deflection 
at any point x\ all measures being in feet and pounds. 
A B 

__ S 




Fig. 191. 



, mnw . ws^ ^ X r 

h = - , at X, or -3-7 at center of span. 



h = Y^ ^t X, or Yf. s-t center of span. 



For deflection due to rope alone, 
For deflection due to load alone, 

If y =^ 1/2S, h = ~ at X, or j-, at center of span. 

If y = m, h =^ ^-j— at x, or j-, at center of span. 
For total deflection, 

, wmns + 2 gny , ws"^ + 4 g'?/ ^ 

^= 75-7 — ^— ^ at X, or at center of span. 

Jits 06 

T* < , T, wmn + gn ^ ws^ -h 2 gs . . . 

If 2/ = 1/2 s,h=^ -.. at X, or 3-7 — — at center of span. 

Zt o t 

T* 1, wmns + 2 gmn ^ ws^ + 2 gs . ^ , 

If y = m, h = — — - — at x, or —. at center of span. 

If the tension is required for a given deflection, transpose t and h in 
above formulae. 



1208 TRANSMISSION OF POWER BY WIRE ROPE. 

Taper Ropes of Uniform Tensile Strength. — The true form of rope 
is not a regular taper but follows a logarithmic curve, the girth rapidly 
increasing toward the upper end. Mr. Chas. D. West gives the following 
formula, based on a breaking strain of 80,000 lb. per sq. in. of the rope, 
core included, and a factor of safety of 10: log G = F-^3680+ logs', in 
which F = length in fathoms, and G and g the girth in inches at any two 
sections F fathoms apart. The girth g is first calculated for a safe strain 
of 8000 lb. per sq. in., and then G is obtained by the formula. For a 
mathematical investigation see The Engineer, April, 1880, p. 267. 



TRANSMISSION OP POWER BY 
WIRE ROPE. 



The following notes have been furnished to the author by Mr. Wm. 
Hev/itt, Vice-President of the Trenton Iron Co. (See also circulars of the 
Trenton Iron Co. and of the John A. Roebling's Sons Co., Trenton, N. J.; 
*' Transmission of Power by Wire Ropes," by A. W. Stahl, Van Nostrand's 
Science Series, No. 28; and Reuleaux's Constructor.) 

The load stress or working tension should not exceed the difference 
between the safe stress and the bending stress as determined by the table 
on page 1209. 

The approximate strength of iron-wire rope composed of wires hav- 
ing a tensile strength of 75,000 to 90,000 lbs. per sq. in. is half that of 
cast-steel rope composed of wires of a tensile strength of 150,000 to 
190,000 lbs. per sq. in. Extra strong steel wires have a tensile strength 
of 190,000 to 225,000 and plow-steel wires 225,000 to 275,000 lbs. per 
sq. in. 

The 19-wire rope is more flexible than the 7- wire, and for the same 
load stress may be run around smaller sheaves^ but it is not as well 
adapted to withstand abrasion or surface wear. 

The working tension may be greater, therefore, as the bending stress 
is less; but since the tension in the slack portion of the rope cannot be 
less than a certain proportion of the tension in the taut portion, to avoid 
slipping, a ratio exists between the diameter of sheave and the wires 
composing the rope corresponding to a maximum safe working tension. 
This ratio depends upon the number of laps that the rope makes about 

the sheaves, and tlie kind of filling in 
the rims or the character of the ma- 
terial upon which the rope tracks. 

For ordinary purposes the maximum 

safe stress should be about one-third 

the ultimate, and for shafts and eleva- 

i^ij^i^ Kjcvwv^ii yy6&\ ^^^^ about one-fourth the ultimate. 

4 W^r^ of Arm. ^M ^^ estimating the stress due to the load 

T mi M'i^ ' ^P ^^^ shafts and elevators, allowance 

• ^^^m0 should be made for the additional 

f x^^r stress due to acceleration in starting. 

s 1 I For short inclined planes not used for 

passengers a factor of safety as low as 

2 3^^ is sometimes used, and for derricks, 

'►; j-i>' in which large sheaves cannot be used, 

7 Li^ and long life of the rope is not expected, 

I the factor of safety may be as low as 2. 

Fig. 192. The Scale wire rope is made of six 

strands of 19 wires, laid 9 around 9 

around 1, the intermediate layer being smaller than the others. It is 

intermediate in flexibility between the 7-wire and the ordinary 19-wire 

rope. (In the Scale cable d = diam. of larger wires.) All ropes 6 

strands each. Extra flexible rope has 8 strands. 

The sheaves (Fig. 192), are usually of cast iron, and are made as light 
as possible consistent with the requisite strength. Various materials 
have been used for filling the bottom of the groove, such as tarred oakum, 
jute yarn, hard wood. India-rubber, and leather. The filling which 
gives the best satisfaction, however, in ordinary transmissions consists of 




Section 
of Rim. 



TRANSMISSION OF POWER BY WIRE ROPE. 1209 
Approximate Breaking Strength of Steel-Wire Ropes. 



6 Strands of 19 Wires Each. 


6 Strands of 7 Wires Each. 




wt. 

per 
Ft. 
Lbs. 


Approximate Breaking 
Stress, Lbs. 




Wt. 

F^t!: 

Lbs. 


Approximate Breaking 
Stress, Lbs. 


Cast 
Steel. 


Extra 
Strong 
Steel. 


Plow 
Steel. 


Cast 
Steel. 


Extra 
Strong 
Steel. 


Plow 
SteeL 


13/4 
15/8 
11/2 
13/8 
11/4 
11/8 

7/8 
3/4 

9/16 

1/2 

7/16 

3/8 

•Vl6 

1/4 


8.00 
6.30 
4.85 
4.15 
3.55 
3.00 
2.45 
2.00 
1.58 
1.20 
0.89 
0.62 
0.50 
0.39 
0.30 
0.22 
0.15 
0.10 


312,000 

248,000 

192,000 

168,000 

144,000 

124,000 

100,000 

84,000 

68,000 

52,000 

38,800 

27,200 

22,000 

17,600 

13,600 

10,000 

6,800 

4,800 


364,000 

288,000 

224,000 

194,000 

168,000 

144,000 

116,000 

98,000 

78,000 

60,000 

44,000 

31,600 

25,400 

20,200 

15,600 

11,500 

8,100 

5,400 


416,000 

330,000 

256,000 

222,000 

192,000 

164,000 

134,000 

112,000 

88,000 

68,000 

50,000 

36,000 

29,000 

22,800 

17,700 

13,100 


11/2 
13/8 
11/4 
11/8 

3/4 
11/16 

5/8 
9/16 

1/2 
7/16 

3/8 
5/16 
9/32 


3.55 
3.00 
2.45 
2.00 
1.58 
1.20 
0.89 
0.75 
0.62 
0.50 
0.39 
0.30 
0.22 
0.15 
0.125 


136,000 

116,000 

96,000 

80,000 

64,000 

48,000 

37.200 

31,600 

26,400 

21,200 

16,800 

13,200 

9,600 

6,800 

5,600 


158.000 

136,000 

112,000 

92,000 

74,000 

56,000 

42,000 

36,800 

30,200 

24,600 

19,400 

15,000 

11,160 

7,760 

6,440 


182,000 

156,000 

128,000 

106,000 

84,000 

64,000 

48,000 

42,000 

34,000 

28,000 

22,000 

17,100 

12,700 





























segments of leather and blocks of India-rubber soaked in tar and 
packed alternately in the groove. Where the working tension is very- 
great, however, the wood filling is to be preferred, as in the case of long- 
distance transmissions where the rope makes several laps about the 
sheaves, and is run at a comparatively slow speed. 
The Bending Stress is determined by the formula 

Eg 

^ ~ 2.06 {R^ d) + C 

k = bending stress in lbs.; E = modulus of elasticity = 28,500,000; 
a = aggregate area of wires, sq. ins. ; i^ = radius of bend; d = diam. of 
wires, ins. 

For 7-wire rope d = 1/9 diam. of rope; C = 9.27. 
" 19- wire " d = 1/15 " " " C = 15.45. 
" the Scale cable d = 1/12 " " " C = 12.36. 
From this formula the tables below and on p. 1210 have been cal- 
culated. 





Bending Stresses, 


7-wire Rope 










Diam. bend. 


24 1 36 


48 


60 


1 72 


84 


96 1 108 


120 1 132 


Diam. Rope. 






















1/4 


826 


553 


412 


333 


277 


238 


208 


185 


166 


151 


8/32 


1,120 


750 


563 


451 


376 


323 


282 


251 


226 


20d 


5/16 


1,609 


1,078 


810 


649 


541 


464 


406 


361 


325 


296 


3/8 


2,774 


1,859 


1,398 


1,120 


934 


801 


702 


624 


562 


511 


7/16 


4,383 


2,982 


2,217 


1,777 


1,482 


1,272 


1,113 


990 


892 


811 


1/2 


6,200 


4,161 


3,131 


2,510 


2,095 


1,797 


1,574 


1,400 


1,260 


1,146 


9/16 


9,072 


6,095 


4,589 


3,679 


3,071 


2,635 


2,308 


2,053 


1,848 


1,681 


5/8 




8,547 


6,438 


5,164 


4,310 


3,699 


3,240 


2,882 


2,595 


2,360 


11/16 





10,922 


8,230 


6,603 


5,513 


4,731 


4,144 


3,687 


3,320 


3,020 


3/4 




14,202 


10,706 


8,591 


7,174 


6,158 


5,394 


4,799 


4,322 


3,931 


//8 




22,592 


17,045 


13,685 


11,431 


9,815 


8,599 


7,651 


6,892 


6,269 


1 






25,476 


20,464 


17,100 


14 686 


12 869 


11 452 


10317 


9 386 


11/8 






36,289 


29,165 


24,416 


20,942 


18.355 


16 336 


14 718 


13 391 


11/4 








40,020 


33,464 


28,754 


25 206 


22 437 


20 216 


18,396 
24.510 


13/8 










44,551 


38,290 


33,571 


29.888 


26.933 


IV2 








57,8351 49,718[43,599138,821 [34,9871 31,842 



1210 TRANSMISSION OF POWER BY WIRE ROPE. 



Bending Stresses, 19-wire Rope. 



Diam.Bend. 12 



24 



36 



48 



60 



72 



84 



96 



108 



120 



Diam.Rope. 

1/4 

5/16 

3/8 

7/16 

1/2 

9/16 

5/8 

11/16 

3/4 

,7/s 

3/8 

11/2 

5/8 

3/4 

17/8 
2 

21/4 
21/2 



993 
1,863 
2,771 
4,859 
7,125 



502 

944 

1,406 

2,473 

3,635 

5,319 

7,452 

9,767 

12,512 

19,436 

29,799 



336 
632 
942 
658 
;,440 
,573 
Oil 
572 
427 
111 
136 
153 
034 
,609 
065 



252 

475 

708 

1,247 

1,836 

2,690 

3,774 

4,953 

6,352 

9,891 

15,205 

21,276 

28,766 

39,067 

50,049 

62,895 

79,749 

97,018 



202 

380 

567 

1,000 

1,472 

2,157 

3,027 

3,973 

5,098 

7,941 

12,214 

17,099 

23,130 

31,430 

40,284 

50,647 

64,252 

78,202 

94,016 

134,319 



168 

317 

473 

834 

1,228 

1,800 

2,526 

3,317 

4,257 

6,633 

10,206 

14,293 

19,340 

26,290 

33,707 

42,391 

53,798 

65,500 

78,769 

112,611 

154,870 



144 

272 

406 

716 

1,054 

1,545 

2,169 

2,847 

3,654 

5,696 

8,766 

12,278 

16,618 

22,594 

28,976 

36,450 

46,270 

56,347 

67,778 

96,943 

133,386 



126 

238 

355 

627 

923 

1,353 

1,900 

2,494 

3,201 

4,990 

7,681 

10,761 

14,567 

19,811 

25,410 

31,969 

40,590 

49,438 

59,478 

85,103 

117.137 



112 

212 

316 

557 

821 

1,203 

1,690 

2,219 

2,848 

4,440 

6,836 

9,578 

12,967 

17,637 

22,625 

28,470 

36,152 

44,039 

52,989 

75,840 

104,417 



101 
191 

285 

502 

739 

1,084 

1,522 

1,998 

2,565 

3,999 

6,158 

8,689 

11,683 

15,893 

20,390 

25,661 

32,589 

39,701 

47,777 

68,396 

94.189 



Horse-Power Transmitted. — The general formula for the amount 
of power capable of being transmitted is as follows: 

H.P. = [cd^ - 0.000006 {w-\-gi-{-g2)\v', 

in which d = diameter of the rope in inches, v = velocity of the rope In 
feet per second, w = weight of the rope, gi = weight of the terminal 
sheaves and shafts, g2 = weight of the intermediate sheaves and shafts 
(all in lbs.), and c = a constant depending on the material of the rope, 
the filling in the grooves of the sheaves, and the number of laps about 
the sheaves or drums, a single lap meaning a half-lap at each end. The 
values of c for one up to six laps for steel rope are given in the following 
table: 



c = for steel rope on 


Number of laps about sheaves or drums 


1 


2 


3 


4 


5 


6 


Iron 


5.61 
6.70 
9.29 


8.81 
9.93 
11.95 


10.62 
11.51 
12.70 


11.65 
12.26 
12.91 


12.16 
12.66 
12.97 


12.56 


Wood 


12.83 


Rubber and leather 


13.00 



The values of c for iron rope are one half the above. 

When more than three laps are made, the character of the surface in 
contact is immaterial as far as slippage is concerned. 

From the above formula we have the general rule, that the actual 
horse-power capable of being transmitted by any wire rope approximately 
equals c times the square of the diameter of the rope in inches, less six mil' 
lionths the entire weight of all the moving parts, multiplied by the speed of 
the rope, in feet per second. 

Instead of grooved drums or a number of sheaves, about which the 
rope makes two or more laps, it is sometimes found more desirable, 
especially where space is limited, to use grip-pulleys. The rim is fitted 
with a continuous series of steel jaws, which bite the rope in contact by 
reason of the pressure of the same against them, but as soon as relieved 
of this pressure they open readily, offering no resistance to the egress of 
the rope. 

In the ordinary or " flying " transmission of power, where the rope 
makes a single lap about sheaves lined with rubber and leather or wood, 
the ratio between the diameter of the sheaves and the wires of the rope, 
'Corresponding to a maximum safe working tension, is.: For 7-wire rope. 



TRANSMISSION OF POWER BY WIRE ROPE. 1211 



steel, 79.6; iron, 160.5. For 12-wire rope, steel, 59.3; iron, 120. For 
19- wire rope, steel, 47.2; iron, 95.8. 

Diameters of Minimum Siieaves in Inches, Corresponding to a Maxi- 
mum Safe Working Tension. 



Diameter 




Steel. 






Iron. 




of Rope, 
In. 














7-Wire. 


12-Wire. 


19- Wire. 


7-Wire. 


12-Wire. 


19-Wire. 


1/4 


20 


15 


12 


40 


30 


24 


5/16 


25 


19 


15 


50 


38 


30 


3/8 


30 


22 


18 


60 


45 


36 


7/16 


35 


26 


21 


70 


53 


42 


1/2 


40 


30 


24 


80 


60 


48 


9/16 


45 


33 


27 


90 


68 


54 


5/8 


50 


37 


30 


100 


75 


60 


11/16 


55 


41 


32 


110 


83 


66 


3/4 


60 


44 


35 


120 


90 


72 


7/8 


70 


52 


41 


140 


105 


84 


1 


80 


59 


47 


160 


120 


96 



Assuming the sheaves to be of equal diameter, and of the sizes in the 
above table, the horse-power that may he transmitted by a steel rope making 
a single lap on wood-filled sheaves is given in the table below. 

- u 1,1^^^^"^"^^^^^°^ ^^ greater horse-powers than 250 is impracticable 
with filled sheaves, as the tension would be so great that the filling would 
quickly cut out, and the adhesion on a metallic surface would be insuffi- 
cient where the rope makes but a single lap. In this case it becomes 
necessary to use the Reuleaux method, in which the rope is given more 
than one lap, as referred to below, under the caption " Long-distance 
Transmissions." 
Horse-power Transmitted by a Steel Rope on Wood-filled Sheaves. 



Diameter 

of Rope, 

In. 


Velocity of Rope in Feet per Second. 


10 


20 


30 


40 


1 50 


! 60 


70 


80 


90 


100 


1/4 

^/16 
3/8 
7/16 

S/16 
5/8 


4 
7 

10 
13 
17 

22 
27 
32 
38 
52 
68 


8 
13 
19 
26 
34 
43 
53 
63 
76 
104 
135 


13 

20 
28 
38 
51 
65 
79 
95 
103 
156 
202 


17 

26 
38 
51 
67 
86 
104 
126 
150 
206 


21 
33 
47 
63 
83 
106 
130 
157 
186 


25 
40 
56 
75 
99 
128 
155 
186 
223 


28 
44 
64 
88 
115 
147 
179 
217 


32 
51 
73 

99 
130 
167 
203 
245 


37 
57 
80 
109 
144 
184 
225 


40 
62 
89 
121 
139 
203 
247 









































The horse-power thoZ may oe transmitted by iron ropes is one-half of the 
above. 

This table gives the amount of horse-power transmitted by wire ropes 
under maximum safe w^orking tensions? In using wood-lined sheaves, 
therefore, it is well to make some allowance for the stretching of the 
rope, and to advocate somewhat heavier equipments than the above table 
would give; that is, if it is desired to transmit 20 horse-power, for in- 
stance, to put in a plant that would transmit 25 to 30 horse-power, avoid- 
ing the necessity of having to take up a comparatively small amount of 
stretch. On rubber and leather filling, however, the amount of power 
capable of being transmitted is 40 per cent greater than for wood, so that 
this filling is generally used, and in this case no allowance need be made 
for stretch, as such sheaves will likely transmit the power given by the 
table, under all possible deflections of the rope. 

Under ordinary conditions, ropes of seven wires to the strand, laid 
about a hemp core, are best adapted to the transmission of power, but 
conditions often occur where 12- or 19-wire rope is to be preferred, as 
stated below, under " Limits of Span." 

Deflections of the Rope. — The tension of the rope is measured by 
the amount of sag or deflection at the center at the span, and the defleo- 



1212 TRANSMISSION OF POWER BY WIRE ROPE. 

tion corresponding to the maximum safe working tension is detertiiined 

by the following formulae, in which S represents the span in feet: 

^ Steel Rope. Iron Rope. 

Def. of still rope at center, in feet , .h = .00004 *S2 /i = .00008 *S2 

driving " " ♦' ...hi =.000025^2 /ij = .00005 *S2 

" slack " " *• ,..h2 = .0000875 aS2 /i2 = .00017 5/S2 

Limits of Span. — On spans of less than sixty feet, it is impossible to 
splice the rope to such a degree of nicety as to give exactly the required 
deflection, and as the rope is further subject to a certain amount of 
stretch, it becomes necessary in such cases to apply mechanical means 
for producing the proper tension in order to avoid frequent splicing, 
which is very objectionable; but care should always be exercised in using 
such tightening devices that they do not become the means, in unskilled 
hands, of overstraining the rope. The rope also is more sensitive to 
every irregularity in the sheaves and the fluctuations in the amount of 
power transmitted, and is apt to sway to such an extent beyond the 
narrow limits of the required deflections as to cause a jerking motion, 
which is very injurious. For this reason on very short spans it is found 
desirable to use a considerably heavier rope than that actually required 
to transmit the power; or in other words, instead of a 7-wire rope cor- 
responding to the conditions of maximum tension, it is better to use a 
19-wire rope of the same size wires, and to run this under a tension con- 
siderably below the maximum. In this way are obtained the advantages of 
increased weight and less stretch, without having to use larger sheaves, 
while the wear will be greater in proportion to the increased surface. 

In determining the maximum limit of span, the contour of the ground 
and the available height of the terminal sheaves must be taken into con* 
sideration. It is customary to transmit the power through the lower 
portion of the rope, as in this case the greatest deflection in this portion 
occurs w^hen the rope is at rest. When running, the lower portion rises 
and the upper portion sinks, thus enabling obstructions to be avoided 
which otherwise would have to be removed, or make it necessary to erect 
very high towers. The maximuni limit of span in this case is determined 
by the maximum deflection that may be given to the upper portion of 
the rope when running, which for sheaves of 10 ft. diameter is about 
600 feet. 

Much greater spans than this, however, are practicable where the con- 
tour of the ground is such that the upper portion of the rope may be the 
driver, and there is nothing to interfere with the proper deflection of the 
under portion. Some very long transmissions of power have been 
effected in this way without an intervening support, one at Lockport, 
N.y., having a clear span of 1700 feet. 

Long-distance Transmissions. — When the distance exceeds the 
limit for a clear span, intermediate supporting sheaves are used, with 
plain grooves (not filled), the spacing and size of which will be governed 
by the contour of the ground and the special conditions involved. The 
size of these sheaves will depend on the angle of the bend, gauged by the 
tangents to the curves of the rope at the points of inflection. If the cur- 
vature due to this angle and the working tension, regardless of the size of 
the sheaves, as determined by the table on the next page, is less than 
that of the minimum sheave (see table p. 1211), the intermediate sheaves 
should not be smaUer than such minimum sheave, but if the curvature is 
greater, smaUer intermediate sheaves may be used. 

In very long transmissions of power, requiring numerous intermediate 
supports, it is found impracticable to run the rope at the high speeds 
maintained in " flying transmissions." The rope therefore is run under 
a higher working tension, made practicable by wrapping it several times 
about grooved terminal drums, with a lap about a sheave on a take-up or 
counter- weighted carriage, which preserves a constant tension in the slack 
portion. 

Inclined Transmissions. — When the terminal sheaves are not on 
the same elevation, the tension at the upper sheave will be greater than 
that at the lower, but this difference is so slight, in most cases, that it 
may be ignored. The span to be considered is the horizontal distance 
between the sheaves, and the principles governing the limits of span will 



TRANSMISSION OF POWER BY WIRE ROPE. 1213 



hold good in this case, so that for every steep inclinations it becomes 
necessary to resort to tightening devices for maintaining the requisite 
tension m the rope. The hmiting case of inchned transmissions occurs 
when one wheel is directly above the other. The rope in this case pro- 
duces no tension whatever on the lower wheel, while the upper is sub- 
ject only to the weight of the rope, which is usually so insienihcant that 
It may be neglected altogether, and on vertical transmissions, therefore, 
mechanical tension is an absolute necessity. 

Bending Curvature of Wire Ropes. — The curvature due to any 
bend in a wire rope is dependent on the tension, and is not always the 
same as the sheave in contact, but may be greater, which explains how 
It is that large ropes are frequently run around comparatively small 
sheaves without detriment, since it is possible to place these so close that 
the bending angle on each will be such that the resulting curvature will 
not overstrain the wires. This curvature may be ascertained from 
the formula and table below, which give the theoretical radii of 
curvature in inches for various sizes of ropes and different angles for one 
pound tension in the rope. Dividing these figures by the square root 
of the actual tension in pounds, gives the radius of curvature of the rope 
when" this exceeds the curvature of the sheave. The rigidity of the rope 
or internal friction of the wires and core has not been taken into account 
in these figures, but the effect of this is insignificant, and it is on the safe 
side to ignore it. By the "angle of bend" is meant the angle between 
the tangents to the curves of the rope at the points of inflection.- When 
the rope Is straight the angle is 180°. For angles less than 160° the 
radius of curvature in most cases will be less than that corresponding to 
the safe working tension, and the proper size of sheave to use in such 
cases will be governed by the table headed "Diameters of Minimum 
Sheaves Corresponding to a Maximum Safe Working Tension" on p. 1211. 

Radius of Curvature of Wire Ropes in Inches lor 1-lb. Ten- 
sion. Formula: R- = Ed^n^ 20t (1 — sin 3^ 6); in which R = radius of 
curvature; E = modulus of elasticity = 28,500,000; d = diameter of wires; 
n = no. of wires in the rope; 6 = angle of bend; i = working stress (lbs. and 
ins.). Divide by square root of stress in pounds to obtain radius in inches. 



Diam. of Rope. 


120° 


140° 


160° 


165° 


170° 


174° 


176° 


178° 


179° 




r 1^ 


38 
61 
87 
116 
155 
195 
238 

66 
103 
145 
198 
259 
328 
406 


56 
91 
129 
174 
232 
290 
355 

98 
153 
216 
295 
386 
489 
605 


112 
181 
257 

346 
461 
578 
708 

196 
306 
430 
587 
769 
975 
1205 


149 

242 
342 
461 
615 
770 
943 

261 

407 
572 
782 
1024 
1298 
1606 


223 
362 
513 
690 
921 
1154 
1414 

391 
610 
858 
1172 
1535 
1946 
2407 


373 
604 
856 
1151 
1536 
1925 
2358 

651 
1018 
1431 
1954 
2559 
3246 
4013 


559 
905 
1282 
1725 
2302 
2885 
3533 

976 
1525 

2145 
2929 
3835 
4864 
6015 


1126 
1824 
2586 
3479 
4643 
5818 
7125 

1969 
3076 
4325 
5907 
7735 
9809 
12129 


2181 


»■ 


y^ 


3533 


rt 


M .::...: 


5007 


u 


6737 




1 .... 


8991 


^ 


xii 


11266 


\% 


13797 


I 




3812 
5957 


ri 


H . 


8375 


vs' /:::/' 


11438 


2 * 


1 ..;::::.:: 


14978 


^ 


\i4 


18994 


\}4 


23487 









The 7-wire rope has 6 strands of 7 wires each, the i9-wire rope has 
6 strands of 19 wires each. 



1214 ROPE-DRIVING. 



ROPE-DRIVING. 

The transmission of power by cotton or manila ropes is a competitor 
with gearing and leather belting when the amount of power is large, or 
the distance between the power and the work is comparatively great. 
The following is condensed from a paper by C. W. Hunt, Trans, A. S, 
M. E., xii, 230: 

But few accurate data are available, on account of the long period 
required in each experiment, a rope lasting from three to six years. 
Installations which have been successful, as well as those in which the 
wear of the rope was destructive, indicate that 200 lbs. on a rope one 
inch in diameter is a safe and economical working strain. When the 
strain is materially increased, the wear is rapid. 

Ir. the following equations 

C = circumference of rope, inches; g == gravity; 

D = sag of the rope in inches; H = horse-power; 

F = centrifugal force in pounds; L = distance between pulleys, ft.; 

P = pounds per foot of rope; w = working strain in pounds; 

R = force in pounds doing useful work; 
S = strain in pounds on the rope at the pulley; 
T = tension in pounds of driving side of the rope; 
t = tension in pounds on slack side of the rope; 
V = velocity of the rope in feet per second; 
W = ultimate breaking strain in pounds. 
W = 720 C2; P = 0.032 C^; w =^ 20 CK 

This makes the normal working strain equal to Vse of the breaking 
strength, and about V25 of the strength at the splice. The actual strains 
are ordinarily much greater, owing to the vibrations in running, as well 
as from im.perfectly adjusted tension mechanism. 

For this investigation we assume that the strain on the driving side 
of a rope is equal to 200 lbs, on a rope one inch in diameter, and an 
equivalent strain for other sizes, and that the rope is in motion at vari- 
ous velocities of from 10 to 140 ft. per second. 

The centrifugal force of the rope in running over the pulley will reduce 
the amount of force available for the transmission of power. The cen- 
trifugal force F = Pv'^ -r- g. 

At a speed of about 80 ft. per second, the centrifugal force increases 
faster than the power from increased velocity of the rope, and at about 
140 ft. per second equals the assumed allowable tension of the rope. 
Computing this force at various speeds and then subtracting it from the 
assumed maximum tension, we have the force available for the trans- 
mission of power. The whole of this force cannot be used, because a 
certain amount of tension on the slack side of the rope is needed to give 
adhesion to the pulley. What tension should be given to the rope for 
this purpose is uncertain, as there are no experiments which give accurate 
data. It is knov/n from considerable experience that when the rope runs in 
a groove w^hose sides are inclined toward each other at an angle of 45° 
there is sufficient adhesion when the ratio of the tensions T -i- t = 2. 

For the present purpose T can be divided into three parts: 1. Tension 
doing useful work; 2. Tension from centrifugal force; 3. Tension to 
balance the strain for adhesion. 

The tension t can be divided into two parts: 1. Tension for adhesion; 
2. Tension from centrifugal force. 

It is evident, however, that the tension required to do a given work 
should not be materially exceeded during the life of the rope. 

There are two methods of putting ropes on the pulleys; one in which 
the ropes are single and spliced on, being made very taut at first, and 
less so as the rope lengthens, stretching until it slips, when it is re- 
spliced. The other method is to wind a single rope over the pulleys 
as many turns as needed to obtain the necessary horse-power and put a 
tension pulley to give the necessary adhesion and also take up the wear. 
The tension t on one of the ropes required to transmit the normal horse- 
power for the ordinary speeds and sizes of rope is computed by formula 
(1), below. The total tension T on the driving side of the rope is 
assumed to be the same at all speeds. The centrifugal force, as well as 
an amotint equal to the tension for adhesion on the slack side of the 



ROPE-DRIVING. 



1215 



la 


























1 


^ 




i=i. 


r^ 


r 


1 




















36 


ROPE DRIVING 

Horse Power of manila 
rope at various speeds 








^ 










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s 
























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N 


















34 

32 
SO 

28 
u26 
1 2i 




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S 
















/ 






















V 






























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/ 














—J 












N 




























^ 


,/ 








^ 


^ 










N 










s 
























^/ 






o^> 


















s 






\ 
























/ 


/ 




\N 


r>' 


























1 


V 




















-V 




•s^X 
























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oe 


















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y 










'also 
.218 

^t 

12 

10 

8 

6 

i 


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l^ 














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s 




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f/ 




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y\ 


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s, 




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h 


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L 



rope, must be taken from the total tension T to ascertain the amount of 

force available for the transmission of power. 

It is assumed that the tension on the slack side necessary for giving 
adhesion is equal to one hall the force doing usefulwork on the driving 

42 
40 
38 
36 
34 
32 
30 
28 
26 
24 
22 
20 
18 
16 
14 
12 
10 
8 
6 
4 
2 

5D 10 20 ;30 40 50 60 70 80 90 100 110 120 130 IIQ 

Velocity of Drrving Rope in feet per second 

Fig. 193. 

side of the rope: hence the force for useful work is i? = 2/3 (T' — F); and 

the tension on the slack side to give the required adhesion is Vs (7" — F). 

Hence t = {T - F)/3 + F (1) 

The sum of the tensions T and t is not the same at different speeds, as 
the equation (1) indicates. As F varies as the square of the velocity, 
there is, with an increasing speed of the rope, a decreasing useful force, 
and an increasing total tension, i, on the slack side. 

With these assumptions of allowable strains the horse-power will be 
if = 22; (r-F) -^(3X550) (2) 

Transmission ropes are usually from 1 to 2 Inches in diameter. A 
computation of the horse-power for four sizes at various speeds and 
under ordinary conditions, based on a maximum strain equivalent to 
200 lbs. for a rope one inch in diameter, is given in Fig. 193. The 
horse-power of other sizes is readily obtained from these. The maxi- 
m.um power is transmitted, under the assumed conditions, at a speed of 
about 80 feet per second. 

The w^ar of the rope is both internal and external; the internal is 
caused by the movement of the fibers on each other, under pressure in 
bending over the sheaves, and the external is caused by the slipping and 
the wedging in the grooves of the pulley. Both of these causes of wear 

Horse-power of Transmission Rope at Various Speeds. 

Computed from formula (2) given above. 



"OoJ 


Speed of the Rope in feet per minute. 


M m 2J 


5^ 


1500 


2000 


2500 


3000 


3500 


4000 


4500 


5000 


6000 


7000 


8000 


























mQPh.S 


l/o 


1.45 


1.9 


2.3 


2.7 


3 


3.2 


3.4 


3.4 


3.1 


2.2 





20 


5/8 


2.3 


3.2 


3.6 


4.2 


4.6 


5.0 


5.3 


5.3 


4.9 


3.4 





24 


3" 


3.3 


4.3 


5.2 


5.8 


6.7 


7.2 


7.7 


7.7 


7.1 


4.9 





30 


7/8 


4.5 


5.9 


7.0 


8.2 


9.1 


9.8 


10.8 


10.8 


9.3 


6.9 





36 


1 


5.8 


7.7 


9.2 


10.7 


11.9 


12.8 


13.6 


13.7 


12.5 


8.8 





42 


IV4 


9.2 


12.1 


14.3 


16.8 


18.6 


20.0 


21.2 


21.4 


19.5 


13.8 





54 


IV? 


13.1 


17.4 


20.7 


23.1 


26.8 


28.8 


30.6 


30.8 


28.2 


19.8 





60 


13 i 


18 


23.7 


28.2 


32.8 


36.4 


39.2 


41.5 


41.8 


37.4 


27.6 





72 


2 


23.2 


30.8 


36.8 


42.8 


47.6 


51.2 


54.4 


54.8 


50 


35.2 





84 



1216 



ROPE-DRIVING, 



are, within the limits of ordinary practice, assumed to be directly pro- 
portional to the speed. 

The rope is supposed to have the strain T constant at all speeds on 
the driving side, and in direct proportion to the area of the cross-section; 
hence the catenary of the driving side is not affected by the speed or by 
the diameter of the rope. 

The deflection of the rope between the pulleys on the slack side varies 
with each change of the load or change of the speed, as the tension equa- 
tion (1) indicates. 

The deflection of the rope is computed for the assumed value of T and 

pf 2 

t by the parabolic formula S = ^-^ + PD, S being the assumed strain 

T on the driving side, and t, calculated by equation (1), on the slack 
side. The tension t varies with the speed. 

The following notes are from the circular of the C. W. Hunt Co.: 

For a temporary installation, it might be advisable to increase the work 
to double that given in the table. 

For convenience in estimating the necessarjr clearance on the driving 
and on the slack sides, we insert a table showing the sag of the rope at 
different speeds when transmitting the horse-power given in the pre- 
ceding table. When at rest the sag is not the same as when running, 
being greater on the driving and less on the slack sides of the rope. The 
sag of the driving side when transmitting the normal horse-power is the 
same no matter what size of rope is used or what the speed driven at, 
because the assumption is that the strain on the rope shall be the same 
at all speeds when transmitting the assumed horse-power, but on the 
slack side the strains, and consequently the sag, vary with the speed of 
the rope and also with the horse-pov/er. The table gives the sag for 
three speeds. If the actual sag is less than given in the table, the rope 
is strained more than the work requires. 

This table is only approximate, and is exact only when the rope is 
running at its normal speed, transmitting its full load and strained to the 
assumed amount. All of these conditions are varying in actual work. 

Sag op the Rope Between Pulleys. 



Distance 
between 


Driving Side. 


Slack Side of Rope. 


Pulleys 
in feet. 


All Speeds. 


80 ft. per sec. 


60 ft. per sec. 


40 ft. per sec. 


40 

60 

80 

100 . 
120 
140 
160 


feet 4 inches 

" 10 " 

1 " 5 ** 

2 " '* 

2 " 11 " 

3 " 10 ** 
5 *♦ 1 " 


feet 7 inches 

1 " 5 " 

2 " 4 " 

3 " 8 ** 
3 .. 3 «« 

7 " 2 " 
9 " 3 " 


feet 9 inches 

1 ♦♦ 8 " 

2 *♦ 10 ** 
4 " 5 " 
6 *♦ 3 *• 
8 " 9 *• 

11 ♦• 3 " 


feet 1 1 inches 

1 '' n *' 

3 ** 3 " 

5 '* 2 " 

7-4 « 

9 '• 9 " 
14 •• 



The size of the pulleys has an important effect on the wear of the rope — 
the larger the sheaves, the less the fibers of the rope slide on each other, 
and consequently there is less internal wear of the rope. The pulleys 
should not be less than forty times the diameter of the rope for economical 
wear, and as much larger as it is possible to make them. This rule applies 
also to the idle and tension pulleys as well as to the main driving-pulley. 

Tension on the Slack Part of the Rope. 



Speed of 
Rope, in feet 


Diameter of the Rope and Pounds Tension on the Slack Rope 










per second. 


1/2 


5/8 


3/4 


7/8 


1 


11/4 


11/2 


13/4 


2 


20 


10 


27 


40 


54 


71 


no 


162 


216 


283 


30 


14 


29 


42 


56 


74 


115 


170 


226 


296 


40 


15 


31 


45 


60 


79 


123 


181 


240 


315 


50 


16 


33 


49 


65 


85 


132 


195 


259 


339 


60 


18 


36 


53 


71 


93 


145 


214 


285 


373 


70 


19 


39 


59 


78 


101 


158 


236 


310 


406 


80 


21 


43 


64 


85 


111 


173 


255 


340 


445 


90 


24 


48 


70 


93 


122 


190 


279 


372 


487 



ROPE-DRIVING. 



1217 



The angle of the sides of the grooves in which the rope runs varies, 
with difterent engineers, trora 45° to 60". It is very important that the 
sides of these grooves should be carefully polished, as the fibers of the 
rope rubbing on the metal as it comes from the lathe tools will gradually 
break fiber by fiber, and so give the rope a short life. It is also neces- 
sary to carefully avoid all sand or blow holes, as they will cut the rope 
out with surprising rapidity. 

Much depends also upon the arrangement of the rope on the pulleys. 
especially where a tension weight is used. Experience shows that ihe 
increased wear on the rope from bending the rope first in one direction 
and then in the other is similar to that of wire rope. At mines where 
two cages are used, one being hoisted and one lowered by the same 
engine doing the same work, the wire ropes, cut from the same coil, are 
usually arranged so that one rope is bent continuously in one direction 
and the other rope is bent first in one direction and then in the other, in 
winding on the drum of the engine. The rope having the opposite bends 
wears much more rapidly than the other, lasting about three quarters 
as long as its mate. This difference in wear shows in manila rope, both 
in transmission of power and in coal-hoisting. The pulleys should be 
arranged, as far as possible, to bend the rope in one direction. 
Diameter of Pulleys and Weight of Rope. 



Diameter of 


Smallest Diameter 


Length of Rope to 


Approximate 


Rope, 


of Pulleys, in 


allow for Splicing, 


Weight, in Ibg. per 


In inches. 


inches. 


in feet. 


foot of rope. 


1/2 


20 


6 


0.12 


5/8 


24 


6 


0.18 


3/4 


30 


7 


0.24 


7/8 


36 


a 


0.32 


1 


42 


9 


0.49 


11/4 


54 


10 


0.60 


11/2 


60 


12 


0.83 


13/4 


72 


13 


1.10 


2 


84 


14 


1.40 



For large amounts of power it is common to use a number of repes 
lying side by side in grooves, each spliced separately. For lighter drives 
some engineers use one rope wrapped as many times around the pulleys 
as is necessary to get the horse-power required, with a tension pulley to 
take up the slack as the rope wears when first put in use. The weight 
put upon this tension puUey should be carefully adjusted, as the over- 
straining of the rope from this cause is one of the most common errors 
in rope-driving. We therefore give a table showing the proper strain on 
the rope for the various sizes, from which the tension weight to transmit 
the horse-power in the tables is easily deduced. This strain can be still 
further reduced if the horse-power transmitted is usually less than the 
nominal work which the rope was proportioned to do, or if the angle of 
groove in the pulleys is acute. 

With a given velocity of the driving-rope, the weight of rope required 
for transmitting a given horse-power is tUe same, no matter what size 
rope is adopted. The smaller rope will require more parts, but XhQ 
weight will be the same. 

Miscellaneous Notes on Rope-Driving. — Reuleaux gives formulae 
for calculating sources of loss in hemp-rope transmission due to (1) journal 
friction, (2) stiffness of ropes, and (3) creep of ropes. The constants in 
these formluae are, however, uncertain from lack of experiniental data. 
He calculates an average case giving loss of power due to journal friction 
= 4%, to stiffness 7.8%, and to creep 5%, or 16.8% in all, and says this 
is not to be considered higher than the actual loss. 

Spencer Miller, in a paper entitled "A Problem in Continuous Rope- 
driving " (Trans. A. S. C. E., 1897), reviews the difficulties which occur in 
rope-drivjng, with a continuous rope from a large to a small pulley. He 
adopts the angle of 45° as a minimum angle to use on the smaller pulley, 
and recommends that the larger pulley be grooved with a wider angle to a 
degree such that the resistance to sUpping is equal in both wheels. 

Mr. Miller refers to a 250-H.P. drive which has been running ten years; 
the large pulley being grooved 60° and the smaller 45^. This drive was 
designed to use a 1 M-in. manila rope, but the grooves were made deep 



1218 



ROPE-DRIVING. 



Data of Manila Transmission Rope. 

From the " Blue Book " of The American Mfg. Co., New York. 





e3 


^ 






Length of 


xh 




s. 


. 






Sp 


ice. Ft. 


s5 








a 


.5 -p 

If 


III 

C ^ OT 


1 


1 


4 
1 

so 


5| 

1*^ 




3/4 


0.5625 


0.20 


3,950 


112 


6 


8 




28 


760 


7/8 


0. 7656 


0.26 


5,400 


153 


6 


8 


. • • . 


32 


650 


1 


] 


0.34 


7,000 


200 


7 


10 


14 


36 


570 


iVs 


i;2656 


0.43 


8.900 


253 


7 


10 


16 


40 


510 


11/4 


1.5625 


0.53 


10,900 


312 


7 


10 


16 


46 


460 


13/8 


1.8906 


0.65 


13,200 


378 


8 


12 


16 


50 


415 


IV2 


2.25 


0.77 


15,700 


450 


8 


12 


18 


54 


380 


15/8 


2.6406 


0.90 


18,500 


528 


8 


12 


18 


60 


344 


13/4 


3.0625 


1.04 


21,400 


612 


8 


12 


18 


64 


330 


2 


4. 


1.36 


28,000 


800 


9 


14 


20 


72 


290 


21/4 


5.0625 


1.73 


35,400 


1,012 


9 


14 


20 


82 


255 


21/2 


6.25 


2.13 


43,700 


1,250 


10 


16 


22 


90 


230 



Weight of transmission rope 
Breaking strength 
Maximum allowable tension 
Diam. smallest practicable 

sheave, 
Velocity of rope (assumed) 



= 0.34 X diam.2 
= 7,000 X diam.2 
= 200 X diam.2 

= 36 X diam. 
= 5.400 ft. per min. 



enough so that a 7/8-in. rope would not bottom. In order to determine the 
value of the drive a common 7/8-in. rope was put in at first, and lasted six 
years, working under a factor of safety of only 14. He recommends, how- 
ever, for continuous rope-driving a factor of safety of not less than 20. 

A heavy rope-drive on the separate, or English, rope system is described 
and illustrated in Power, April, 1892, It is in use at ths India Mill at Dar- 
wen, England, and is driven by a 2000-H.P. engine at 54 revs, per min. 
The fly-wheel is 30 ft. diameter, weighs 65 tons, and is arranged with 30 
grooves for 13/4-in. ropes. These ropes lead off to receiving-pulleys upon 
the several floors, so that each floor receives its power direct from the fly- 
wheel. The speed of the ropes is 5089 ft. per min., and five 7-ft. receivers 
are used. Lambeth cotton ropes are used. (For much other information 
on this subject see " Rope-Driving," by J. J. Flather, John Wiley &, Sons.) 

Cotton Ropes are advantageously used as bands or cords on the 
smaller machine appliances; the fiber, being softer and more flexible 
than manila hemp, gives good results for small sheaves; but for large 
drives, where power transmitted is in considerable amounts, cotton rope, 
as compared with manila, is hardly to be considered, on account of 
the following disadvantages: It is less durable; it is injuriously affected 
by the weather, so that for exposed drives, paper-mill work, or use in 
water-wheel pits, it is absokitely unsatisfactory; it is difficult, if not 
impossible, to splice uniformly; even the best quality cotton rope is 
much inferior to manila in strength, the breaking strain of the highest 
grade being but 4000 X diam.2 as against 7000 X diam.2 for manila; while, 
for the transmission of equal powers, the cost of a cotton rope varies 
from one-third to one-half more than manila. — ('* Blue Book " of the 
Amer. Mfg. Co.) 

A different opinion is found in a paper by E. Kenyon in Proc. Inst. 
Engrs. and Shipbuilders of Scotland, 1904. He says: Evidences of the 
progress of cotton in the manufacture of driving-ropes are so far-reaching 
that its superiority may be considered as much an accepted principle in 
rope transmission as the law of gravitation is in science. As to tne longevity 
of cotton ropes, 24 cotton ropes 13/4-in. diam. are transmitting 820 H .P. at a 
peripheral speed of 4396 ft. per min., from a driving pulley 28 ft. diam. 
All the card-room ropes in this drive have been running since 1878, a 
period of 26 years, without any attention whatever. 



FRICTION AND LUBRICATION. 



1219 



FRICTION AND LUBRICATION. 

Friction is defined by Rankine as that force which acts between two 
bodies at their surface of contact so as to resist their sliding on each 
other, and which depends on the force with which the bodies are pressed 
together. 

Coefficient of Friction, — The ratio of the force required to shde a 
body along a horizontal plane surface to the weight of the body is called 
the coefficient of friction. It is equivalent to the tangent of the angle of 
repose, which is the angle of inclination to the horizontal of an inclined 
plane on which the body will just overcome its tendency to slide. The 
angle is usually denoted by 6, and the coefficient by /. / = tan 0. 

Friction of Rest and of Motion. — The force required to start a 
body sliding is called the friction of rest, and the force required to con- 
tinue its sliding after having started is called the friction of motion. 

Rolling Friction is the force required to roll a cyhndrical or spheri- 
cal body on a plane or on a curved surface. It depends on the nature of 
the surfaces and on the force with which they are pressed together, but 
is essentially different from ordinary, or sliding, friction. 

Friction of Solids. — Rennie's experiments (1829) on friction of solids, 
usually unlubricated and dry, led to the following conclusions: 

1. The laws of sliding friction differ with the character of the bodies 
rubbing together. 

2. The friction of fibrous material is increased by increased extent of 
surface and by time of contact, and is diminished by pressure and speed. 

3. With wood, metal, and stones, within the limit of abrasion, friction 
varies only with the pressure, and is independent of the extent of surface, 
time of contact, and velocity. 

4. The limit of abrasion is determined by the hardness of the softer of 
the two rubbing parts. 

5. Friction is greatest with soft and least with hard materials. 

6. The friction of lubricated surfaces is determined by the nature of 
the lubricant rather than by that of the solids themselves. 

Friction of Rest. (Rennie.) 



Pressure, 

Lbs. 
per Square 


Values of/. 


Wrought Iron on 


Wrought on 


Steel on 


Brass on 


Inch. 


Wrought Iron. 


Cast Iron. 


Cast Iron. 


Cast Iron. 


187 


0.25 


0.28 


0.30 


0.23 


224 


.27 


.29 


.33 


.22 


336 


.31 


.33 


.35 


.21 


448 


.38 


.37 


.35 


.21 


560 


.41 


.37 


.36 


.23 


672 


Abraded 


.38 


.40 


.23 


784 


" 


Abraded 


Abraded 


.23 



Law of Unlubricated Friction. — A. M. Wellington, Eng'g News, 
April 7, 1888, states that the most important and the best determined of 
all the laws of unlubricated friction may be thus expressed : 

The coeflScient of unlubricated friction decreases materially with 
velocity, is very much greater at minute velocities of 4-, falls very 
rapidly with minute increases of such velocities, and continues to fall 
much less rapidly with higher velocities up to a certain varying point, 
following closely the laws which obtain with lubricated friction. 

Friction of Steel Tires Sliding on Steel Rails. (Westmghouse & 
Galton.) 

Speed, miles per hour 10 15 25 38 45 50 

Coefficient of friction 0.110 .087 .080 .051 .047 .040 

Adhesion, lbs. per gross ton 246 195 179 128 114 90 

Rolling Friction is a consequence of the irregularities of form and 
the roughness of surface of bodies rolling one over the other. Its laws 
are not yet definitely established in consequence of the uncertainty 
which exists in experiment as to how much of the resistance is due to 
roughness of surface, how much to original and permanent irregularity 
of form, and how much to distortion under the load. (Thurston.) 



1220 



FRICTION AND LUBRICATION. 



Coefficients of Rolling Friction. — If R = resistance applied at the 
circumference of the wheel, W = total weight, r = radius of the wheel, 
and/ « a coefficient, R = fW -j- r. /is very variable. Coulomb gives 
0.06 for wood, 0.006 for metal, where T^is in pounds and r in feet. Tred- 
gold made the value of / for iron on iron 0.002. For wagons on soft soil 
Morin found / = 0.065, and on hard smooth roads 0.002. 

A Committee of the Society of Arts (Clark, R. T. D.) reported a 
loaded omnibus to exhibit a resistance on various loads as below: 
Pavement. Speed per hour. Coefficient. Resistance. 

Granite 2.87 miles. 0.007 17 .41 per ton. 

Asphalt 3.56 " 0.0121 27.14 

Wood 3.34 " 0.0185 41.60 

Macadam, graveled 3.45 " 0.0199 44.48 " 

Macadam, granite, new 3.51 " 0.0451 101.09 " 

Thurston gives the value of / for ordinary railroads, 0.003; well-laia 
railroad track, 0.002; best possible railroad track, 0.001. 

The few experiments that have been made upon the coefficients ol 
rolling friction, apart from axle friction, are too incomplete to serve as a 
basis for practical rules. (Trautwine.) 

Laws of Fluid Friction. — For all fluids, whether liquid or gaseous, 
the resistance is (1) independent of the pressure between the masses in 
contact; (2) directly proportional to the area of rubbing-surface; (3) pro- 
portional to the square of the relative velocity at moderate and high 
gpeeds, and to the velocity nearly at low speeds; (4) independent of the 
nature of the surfaces of the solid against which the stream may flow, but 
dependent to some extent upon their degree of roughness; (5) proportional 
to the density of the fluid, and related in some way to its viscosity, 
(Thurston.) 

The Friction of Lubricated Surfaces approximates that of solid friction 

as the journal is run dry, and that of fluid friction as it is flooded with oil. 

Angles of Repose and Coefficients of Friction of Building Materials. 

(From Rankine's Applied Mechanics.) 



e. 



31° to 35° 

361/2° 

22° 

35° to 162/3° 

26 1/2° to 11 1/3° 

31° to 111/3° 

14° to 81/2° 

27° 

181/4° 

14° to 45° 



I / = tan 0. I 1 ^ tan < 



0.6 to 0.7 

0.74 
about 0.4 
0.7 to 0.3 
0.5 to 0.2 
0.6 to 0.2 
0.25 to 0.15 

0.51 

0.33 
0.25 to 1.0 

0.38 to 0.75 
I.O 
0.31 

0.81 



1.67 to 1.4 

1.35 

2.5 
1.43 to 3.3 

2 to 5 
1.67 to 5 
4 to 6.67 

1.96 

3. 
4 to I 

2.63 to 1.33 
1 
3.23 

1.23 toO. 9 



Dry masonry and brickwork. . * 
Masonry and brickwork With 

damp mortar 

Timber on stone , 

Iron on stone 

Timber on timber 

Timber on metals 

Metal3 on metals 

Masonry on dry clay 

Masonry on moist clay 

Earth on earth 

Earth on earth, dry sand, clay, 

and mixed earth. . « 

Earth on earth, damp clay 

Earth on earth, wet clay 

Earth on earth, shingle and 

gravel 



2r 



to 37° 

45° 

17° 



39° to 48° 



Coefficients of Friction of Journals. (Morin.) 



Material. 


Unguent. 


Lubrication. 


Intermittent.! Continuous. 


Oa,it Iron on cast Iron | 

Cast Iron on bronze 

Cast iron on lignum vitae. . . 
Wrought iron on cast iron . ) 
Wrought iron on bronze. . ) 

Iron on lignum vitse | 

Bronie on bronze | 


Oil, lard, tallow. 
Unctuous and wet 
Oil, lard, tallow. 
Unctuous and wet 
Oil, lard. 

Oil, lard, tallow. 

Oil, lard. 
Unctuous. 
Olive oil. 
Lard. 


0.07 to 0.08 

0.14 
0.07 to 0.08 

0.16 


0.03 to 0.054 

0.03 to 0.054 

0.09 


0.07 to 0.08 

0.11 
0.19 
0.10 
0.09 


0.03 to 0.054 



I*RICT10N AND LUBRICATION. 



1221 



Prof. Thurston says concerning the foregoing figures that much better 
results are probably obtained in good practice witli ordinary machinery. 
Those here given are so modified by variations of speed, pressure, and 
temperature, that they cannot be taken as correct for general purposes. 

Friction of Motion. — The following is a table of the angle of repose 
0, the coefficient of friction / = tan d, and its reciprocal, 1 -r- /, for the 
materials of mechanism — condensed from the tables of General Morin 
(1831) and other sources, as given by Rankine: 



No. 



Surfaces. 



/. 



1 -/- 



Wood on wood, dry 

" " " soaped 

Metals on oak, dry 

•* ** '• wet 

•* " •• soapy 

** ** elm, dry 

Hemp on oak, dry 

" " *' wet 

Leather on oak 

*' ** metals, dry 

** " metals, wet 

** *' " greasy.. 

oily 

Metals on metals, dry 

" *' " wet 

Smooth surfaces, occasion- 
ally greased 

Smooth surfaces, continu- 
ously greased 

Smooth surfaces, best results 
Bronze on lignum vitse, con- 
stantly wet 



14° to 261/2° 
1 1 1/2° to 2° 
261/2° to 31° 
131/2° to 14° 

111/2° 

lU/2° to 14° 

28° 

181/2° 
15° to 191/2° 
291/2° 

20° 

13° 

81/2° 
81/2° to 11° 

161/2° 

4° to 41/2° 



1 3/4° to 2° 

3°? 



0.25 to 0.5 
0.2 to 0.04 
0.5 to 0.6 
0.24 to 0.26 

0.2 
0.2 to 0.25 

0.53 

0.33 
0.27 to 0.38 

0.56 

0.36 

0.23 

0.15 
0.15 to 0.2 

0.3 

0.07 to 0.08 

0.05 
0.03 to 0.036 

0.05? 



4 to 2 

5 to 25 
2 to 1.67 

4.17 to 3.85 

5 

5 to 4 

1.89 

3 

3.7 to 2.86 

1.79 

2.78 

4.35 

6.67 

6.67 to 5 

3.33 

14.3 to 12.5 

20 



Average Coefficients of Friction. — Journal of cast iron in bronze 
bearing; velocity 720 feet per minute; temperature 70° F.; intermittent 
feed through an oil-hole. (Thurston on Friction and Lost Work.) 


Oils. 


Pressures, Pounds per Square Inch. 


8 


16 


32 


48 


Sperm, lard, neatsfoot, etc. . 
Olive, cotton-seed, rape, etc. 
Cod and menhaden 


.159 to .250 
.160 to .283 
.248 to .278 


.138 to .192 
.107 to .245 
.124 to .167 
.145 to .233 


.086 to .141 
.101 to .168 
.097 to .102 
.086 to .178 


.077 to .144 
.079 to .131 
.081 to .122 


Mineral lubricating-oils .... 


.154 to .261 


.094 to .222 



With fine steel journals running in bronze bearings and continuous 
lubrication, coefficients far below those above given are obtained. 
Thus with sperm-oil the coefficient with 50 lbs. per square inch pres- 
sure was 0.0034; with 200 lbs., 0.0051; with 300 lbs.. 0.0057. 

For very low pressures, as in spindles, the coefficients are much 
higher. Thus Mr. Woodbury found, at a temperature of 100° and a 
velocity of 600 feet per minute. 

Pressures, lbs. per sq. in. . . 1 2 3 4 5 

Coefficient 0.38 0.27 22 0.18 0.17 

These high coefficients, however, and the great decrease in the co- 
efficient at increased pressures are limited as a practical matter only to 
the smaller pressures which exist especially in spinning machinery, 
where the pressure is so light and the film of oil so thick that the viscos- 
ity of the oil is an important part of the total frictional resistance. 

Experiments on Friction of a Journal Lubricated by an Oil- 
batli (reported by the Committee on Friction, Proc. Inst. M. E., 
Nov., 1883) show that the absolute friction, that is, the absolute tan- 
gential force per square inch of bearing, required to resist the tendency 
of the brass to go round with the journal, is nearly a constant under all 
loads, within ordinary working limits. Most certainly it does not in- 



1222 TRICTION AND LUBRICATION 

crease in direct proportion to the load, as it should do accordiflg to the 
ordinary theory of soUd friction. The results of these experiments 
seem to show that the friction of a perfectly lubricated journal follows 
the laws of liquid friction much more closely than those of solid friction. 
They show that under these circumstances the friction is nearly inde- 
pendent of the pressure per square inch, and that it increases with the 
velocity, though at a rate not nearly so rapid as the square of the velocity. 

The experiments on friction at different temperatures indicate a great 
diminution in the friction as the temperature rises. Thus in the case of 
lard-oil, taking a speed of 450 r.p.m., the coefficient of friction at a tem- 
perature of 120° is only one-third of what it was at a temperature of 60°. 

The journal was of steel, 4 ins. diameter and 6 ins. long, and a gun- 
metal brass, embracing somewhat less than half the circumference of the 
journal, rested on its upper side, on which the load was appUed. When 
the bottom of the journal was immersed in oil, and the oil therefore carried 
under the brass by rotation of the journal, the greatest load carried with 
rape-oil was 573 lbs. per sq. in., and with mineral oil 625 lbs. 

In experiments with ordinary lubrication, the oil being fed in at the 
center of the top of the brass, and a distributing groove being cut in the 
brass parallel to the axis of the journal, the bearing would not run cool 
with only 100 lbs. per sq. in., the oil being pressed out from the bearing- 
surface and through the oil-hole, instead of being carried in by it. On 
Introducing the oil at the sides through two parallel grooves, the lubrica- 
tion appeared to be satisfactory, but the bearing seized with 380 lbs. 
per sq. in. 

When the oil was introduced through two oil-holes, one near each end 
of the brass, and each connected with a curved groove, the brass refused 
to take its oil or run cool, and seized with a load of only 200 lbs. per sq. in. 

With an oil-pad under the journal feeding rape-oil, the bearing fairiy 
carried 551 lbs. Mr. Tower's conclusion from these experiments is that 
the friction depends on the quantity and uniformity of distribution of the 
oil, and may be anything between the oil-bath results and seizing, accord- 
ing to the perfection or imperfection of the lubrication. The lubrication 
may be very small, giving a coefficient of Vioo; but it appeared as though 
it could not be diminished and the friction increased much beyond this 
point without imminent risk of heating and seizing. The oil-bath prob- 
ably represents the most perfect lubrication possible, and the limit 
beyond which friction cannot be reduced by lubrication; and the experi- 
ments show that with speeds of from 100 to 200 feet per minute, by 
property proportioning the bearing-surface to the load, it is possible to 
reduce the coefficient of friction to as low as Viooo. A coefficient of Visoo 
is easily attainable, and probably is frequently attained, in ordinary 
engine-bearings in which the direction of the force is rapidly alternating 
and the oil given an opportunity to get between the surfaces, while the 
duration of the force in one direction is not sufficient to allow time for 
the oil film to be squeezed out. 

Observations on the behavior of the apparatus gave reason to believe 
that with perfect lubrication the speed of minimum friction was from 
100 to 150 feet per minute, and that this speed of minimum friction tends 
to be higher with an increase of load, and also with less perfect lubrica- 
tion. By the speed of minimum friction is meant that speed in approach- 
ing which from rest the friction diminishes, and above which the friction 
increases. 

Coefficients of Friction of Motion and of Rest of a Journal. — 
A cast-iron journal in steel boxes, tested by Prof. Thurston at a sneed of 
rubbing of 150 feet per minute, with lard and with sperm oil, gave the 
following : 

Press, per sq. in., lbs . 50 100 250 500 750 1000 

CoefT., with sperm ...0.013 . 008 . 005 . 004 . 0043 . 009 
Coeff., with lard 0.02 0.0137 0.0085 0.0053 0.0066 0.125 

The coefficients at starting were: 

Withsperm 0.07 0.135 0.14 0.15 0.185 0.18 

Withlard 0.07 0.11 0.11 0.10 0.12 0.12 

The coefficient at a speed of 150 feet per minute decreases with in- 
crease of pressure until 500 lbs. per sq. in. is reached; above this it in- 
creases. The coefficient at rest or at starting increases with the pressure 
throughout the range of the tests. 



FEICTION AND LUBRICATION. 



1223 



Coefficients of Friction of Journal with Oil-bath. — Abstract of 

results of Tower's experiments on friction (Proc. Inst. M. E., Nov., 
1883). Journal, 4 in. diam., 6 in. long; temperature, 90° F. 



i 


Nominal Load, in Lbs. per Sq. In. 


Lubricant in Bath. 


625 ( 520 1 415 ] 310 | 205 I 153 | 100 


Coefficient of Friction. 


Lard oil* 157 ft. per min 




.0009 
.0017 
.0014 
.0022 
seiz'd 


.0012 
.0021 
.0016 
.0027 
.0015 
007,1 


.0014 

.0029 

.0022 

.004 

.0011 

.0019 

.0008 
.0016 
.0014 
.0024 

0056 


.0020 
.0042 
.0034 
.0066 
.0016 
.0027 

.0014 
.0024 
.0021 
.0035 

.0098 
.0077 

.0105 
.0078 


.0027 
.0052 
.0038 
.0083 
.0019 
.0037 

.002 
.004 


0042 


" "471 " '* 

Mineral grease: 157 ft. per mm.. . . 

Sperm-oil* 157 ft. per min 


■".66i* 

.002 


.009 
.0076 
.0151 
.003 


" 471 " " 




0064 


TRane-oil* 157 ft. Der min 


(5731b. 
.001 


.001 
.0015 
.0012 
.0018 


.0009 
.0016 
.0012 
.002 


004 


•' "471 " " 


007 


Mineral-oil: 157 ft. per min 

"471 " " 


.66i3 


.004 
.007 


Rape-oil fed by 
. , 1 u • 4. ( 157 ft. per min. 




OW.'i 


siphon lubricator:|3j4 .»^ .. 

Rape-oil, pad 

J • 1 (157ft. per min. 








.0068 


.0152 








0099 


.0099 


under journal: ^^^^ a^ ♦* 








.0099 


.0133 



Comparative friction of different lubricants under same circumstances, 
temperature 90°, oil-bath: sperra-oil, 100; rape-oil, 106; mineral oil, 129; 
lard, 135; olive oil, 135; mineral grease, 217. 

Value of Anti-friction Metals. (Denton.) — The various white 
metals available for lining brasses do not afford coefficients of friction 
lower than can be obtained vdth bare brass, but they are less liable to 
"overheating," because of the superiority of such material over bronze 
in ability to permit of abrasion or crusliing, without excessive increase of 
friction. 

Thurston (Friction and Lost Work) says that gun-bronze. Babbitt, 
and other soft white alloys have substantially the same friction; in other 
words, the friction is detertpined by the nature of the unguent and not 
by that of the rubbing-surfaces, when the latter are in good order. The 
soft metals run at higher temperatures than the bronze. This, however, 
does not necessarily indicate a serious defect, but simply deficient con- 
ductivity. The value of the white alloys for bearings lies mainly in their 
ready reduction to a smooth surface after any local or general injury by 
alteration of either surface or form. 

Cast Iron for Bearings. (Joshua Rose.) — Cast iron appears to be an 
exception to the general rule, that the harder the metal the greater the 
resistance to wear, because cast iron is softer in its texture and easier to 
cut with steel tools than steel or wrought iron, but in some situations it 
is far more durable than hardened steel; thus when surrounded by steam 
it will wear better than will any other metal. Thus, for instance, ex- 
perience has demonstrated that piston-rings of cast iron will wear smoother, 
better, and equally as long as those of steel, and longer than those of 
either wrought iron or brass, whether the cylinder in wliich it works be 
composed of brass, steel, wrought iron, or cast iron; the latter being the 
more noteworthy, since two surfaces of the same metal do not, as a rule, 
wear or work well together. So also slide-valves of brass are not found 
to wear so long or so smoothly as those of cast iron, let the metal of which 
the seating is composed be whatever it may; while, on the other hand, a 
cast-iron slide-valve will wear longer of itself and cause less wear to 
its seat, if the latter is of cast iron, than if of steel, wrought iron, or 
brass. 

Friction of Metals under Steam-pressure. — The friction of brass 
upon iron under steam-pressure is double that of iron upon iron. (G. H. 
Babcock, Trans, A, S, M, E., i, 151.) 

Morin's "Laws of Friction." — 1. The friction between two bodies 
is directly proportioned to the pressure; i.e., the coefficient is constant 
for all pressures. 



1224 FRICTION AND LUBRICATION, 

2. The coeflScient and amount of friction, pressure being the'same, are 
independent of the areas in contact. 

3. The coefficient of friction is independent of velocity, although static 
friction (friction of rest) is greater than the friction of motion. 

Eng'g News, April 7, 1888, comments on these "laws" as follows: 
From 1831 till about 1876 there was no attempt worth speaking of to 
enlarge our knowledge of the laws of friction, wliich during all that period 
was assumed to be complete, although it was reaUy worse than notliing, 
since it was for the most part wholly false. In the year first mentioned 
Morin began a series of experiments wiiich extended over two or three 
years, and which resulted in the enunciation of these three "funda- 
mental laws of friction," no one of wliich is even approximately true. 

For fifty years these laws were accepted as axiomatic, and were quoted 
as such without question jn every scientific work pubhshed during that 
whole period. Now that they are so thoroughly discredited it has been 
attempted to explain away their defects on the ground that they cover 
only a very limited range of pressures, areas, velocities, etc., and that 
Morin himself only announced them as true within the range of his con- 
ditions. It is now clearly established that there are no limits or con- 
ditions within which any one of them even approximates to exactitude, 
and that there are many conditions under which they lead to the wildest 
kind of error, while many of the constants were as inaccurate as the laws. 
For example, in Morin's "Table of Coefficients of Moving Friction of 
Smooth Plane Surfaces, perfectly lubricated," which may be found in 
hundreds of text-books now in use, the coefficient of wrought iron on 
brass is given as 0.075 to 0.103, which would make the rolhng friction of 
railway trains 15 to 20 lbs. per ton instead of the 3 to 6 lbs. which it 
actuaUy is. 

General Morin, in a letter to the Secretary of the Institution of Mechan- 
ical Engineers, dated March 15, 1879, writes as follows concerning his 
experiments on friction made more than forty years before: "The results 
furnished by my experiments as to the relations between pressure, surface, 
and speed on the one hand, and sliding friction on the other, have always 
been regarded by myself, not as ihathematical laws, but as close approxi- 
mations to the truth, within the limits of the data of the experiments 
themseb^es. The same holds, in my opinion, for many other laws of 
practical mechanics, such as those of rolUng resistance, fluid resistance, 
etc. " 

Prof. J. E. Denton (Stevens Indicator, July, 1890) says: It has been 
generally assumed that friction between lubricated surfaces follows the 
simple law that the amount of the friction is some fixed fraction of 
the pressure between the surfaces, such fraction being independent of the 
intensity of the pressure per square inch and the velocity of rubbing, 
between certain limits of practice, and that the fixed fraction referred to 
is represented by the coefficients of friction given by the experiments of 
Morin or obtained from experimental data which represent conditions of 
practical lubrication, such as those given in Webber's Manual of Power. 

By the experiments of Thurston, Woodbury, Tower, etc., however, it 
appears that the friction between lubricated metallic surfaces, such as 
machine bearings, is not directly proportional to the pressure, is not 
independent of the speed, and that the coefficients of Morin and Webber 
are about tenfold too great for modern journals. 

Prof. Denton offers an explanation of this apparent contradiction of 
authorities by showing, with laboratory testing-machine data, that 
Morin's laws hold for bearings lubricated by a restricted feed of lubricant, 
such as is afforded by the oil-cups common to machinery; whereas the 
modern experiments have been made with a surplus feed or superabun* 
aance or lubricant, such as is provided only in railroad-car journals, and 
a few special cases of practice. 

That the low coefficients of friction obtained under the latter conditions 
are realized in the case of car-journals, is proved by the fact that the 
temperature of car-boxes remains at 100° at liigh velocities; and experi- 
ment shows that this temperature is consistent only with a coefficient of 
friction of a fraction of one per cent. Deductions from experiments on 
train resistance also indicate the same low degree of friction. But these 
low coefficients do not account for the internal friction of steam-engines 
as well as do the coefficients of Morin and Webber. 



FRICTION AND LtJBRICATION. 1225 

m American Machinist Oct. 23, 1890, Prof. Denton says: Morin's 

tneasurements of Irictioii of Iul)ricated journals did not extend to light 
pressures. Tiiey apply only to the conditions of general shafting and 
engine work. 

He clearly understood that there was a frictional resistance, due solely 
to the viscosity of the oil, and that therefore, for very light pressures, 
the laws which he enunciated did not prevail. 

He applied his dynamometers to ordinary shaft-journals without 
special preparation of the rubbing-surfaces, and without resorting to 
artificial methods of supplying the oil. 

Later experimenters have with few exceptions devoted themselves 
exclusively to the measurement of resistance practically due to viscosity 
alone. They have eliminated the resistance to which Morin conhned his 
measurements, namely, the friction due to such contacts of the rubbing- 
surfaces as prevail with a very thin film of lubricant between compara- 
tively rough surfaces. 

Prof. Denton also says {Trans. A. S. M. E., x, 518): "I do not believe 
there is a particle of proof in any investigation of friction ever made, 
that Morin's laws do not hold for ordinary practical oil-cups or restricted 
rates of feed." 

Laws of Friction of Well-lubricated Journals. — John Goodman 
(Trans. Inst. C. E., 1886, Eng'g News, April 7 and 14, 1888), reviewing 
the results obtained from the testing-machines of Thurston, Tower, and 
Stroudley, arrives at the following laws: 

Laws of Friction: Well-lubricated Surfaces. 
(Oil-bath.) 

1. The coefficient of friction with the surfaces efficiently lubricated fs 
from Ve to i/io that for dry or scantily lubricated surfaces. 

2. The coefficient of friction for moderate pressures and speeds varies 
approximately inversely as the normal pressure; the frictional resistance 
varies as the area in contact, the normal pressure remaining constant. 

3. At very low journal speeds the coefficient of friction is abnormally 
high; but as the speed of sliding increases from about 10 to 100 ft. per 
min.j the friction diminishes, and again rises when that speed is exceeded, 
varying approximately as the square root of the speed. 

4. The coefficient of friction varies approximately inversely as the 
temperature, within certain limits, namely, just before abrasion takes 
place. 

The evidence upon which these laws are based is taken from various 
modern experiments. That relating to Law 1 is derived from the "First 
Report on Friction Experiments," by Mr. Beauchamp Tower. 



Method of Lubrication. 



Oil-bath ,...- 

Siphon lubricator.. 
Pad under journal . 



Coefficient of 
Friction. 



0.00139 

0.0098 

0.0090 



Comparative 
Friction. 



1.00 
7.06 
6.48 



With a load of 293 lbs. per sq. in. and a journal speed of 314 ft. per 
min. Mr. Tower found the coefficient of friction to be .0016 with an oil- 
bath, and 0.0097, or six times as much, with a pad. The very low co- 
efficients obtained by Mr. Tower wiU be accounted for by Law 2, as he 
found that the frictional resistance per square inch under varying loads 
is nearly constant, as below: 
Load in lbs. per sq. in. 529 468 415 363 310 258 205 153 100 

^sq^^iif^^ ^^^^^^* ^^^ } 0.416 0.514 0.498 0.472 0.464 0.438 0.43 0.458 0.45 

The frictional resistance per square inch is the product of the coefficient 
of friction into the load per square inch on horizontal sections of the brass. 
Hence, if this product be a constant, the one factor must vary inversely 
as the other, or a liigh load will give a low coefficient, and vice versa. 

For ordinary lubrication, the coefficient is more constant under varying 
loads* the frictional resistance then varies directlv as the load, as shown 
by Mr, Tower in Table VIII of his repcwt {Proc, Inst. M. E,] 1883). 



1226 



FRICTION AND LUBRICATION. 



With respect to Law 3, A. M. Wellington {Trans. A. S. C. E., 1884), 
in experiments on journals revolving at very low velocities, found that 
the friction was then very great, and nearly constant under varying 
conditions of the lubrication, load, and temperature. But as the speed 
increased the friction fell slowly and regularly, and again returned to 
the original amount when the velocity was reduced to the same rate. 
This is shown in the following table: 
Speed, feet per minute: 

0+ 2.16 3.33 4.86 8.82 21.42 35.37 53.01 89.28 106.02 
CoeflQcient of friction : 
0.118 0.094 0.070 0.069 0.055 0.047 0.040 0.035 0.030 0.026 

It was also found by Prof. Kimball that when the journal velocity 
was increased from 6 to 110 ft. per min., the friction was reduced 
70%; in another case the friction was reduced 67% when the velocity 
was increased from 1 to 100 ft. per min. ; but after that point was reached 
the coefficient varied approximately with the square root of the velocity. 

The following results were obtained by Mr. Tower: 



Feet per minute 


209 


262 


314 


366 


419 


471 


Nominal Load 
per Sq. In. 


Coeflf. of friction 


O.OOIO 
.0013 
.0014 


0.0012 
.0014 
.0015 


0.0013 
.0015 
.0017 


0.0014 
.0017 
.0019 


0.0015 
.0018 
.0021 


0.0017 
.002 
.0024 


520 lbs. 
468 lbs. 
415 lbs. 



The variation of friction with temperature is approximately in the 
inverse ratio. Law 4. Take, for example, Mr. Tower's results, at 
262 ft. per minute: 



Temp. F. 


110° 


100° 


90° 


80° 70° 


60° 


Observed 


0.0044 
0.00451 


0.0051 
0.00518 


0.006 
0.00608 


0.0073 0.0092 
0.00733 0.00964 


0.0119 


Calculated 


0.01252 











This law does not hold good for pad or siphon lubrication, as then the 
coefficient of friction diminishes more rapidly for given increments of 
temperature, but on a gradually decreasing scale, until the normal 
temperature has been reached; this normal temperature increases 
directly as the load per sq. in. ' This is shown in the following table 
taken from Mr. Stroudley's experiments with a pad of rape-oil: 



Temp. F. 



Coefficient 

Decrease of coeff. 



105^ 



0.022 



110° 



115° 



0.01800.0160 
0.004010.0020 



120° 



125° 



130° I 135° I 140° 1 145° 



0.0140 0.0125 0.0115 0.0110 0.0106 0.0102 
O.OO20I0. 001510. 001010. 0005|0. 000410. 0002 



In the Galton-Westinghouse experiments it was found that with 
velocities below 100 ft. per min., and with low pressures, the frictional 
resistance varied directly as the normal pressure ; but when a velocity of 
100 ft.per min. was exceeded, the coeflBcient of friction greatly diminished ; 
from tne same experiments Trol. Kennedy found that the coefiicient of 
friction for high pressures was sensibly less than for low. 

Allowable Pressures on Bearing-surfaces. {Proc. InsL M. E.. 
May, 1888.) — The Committee on l-'riction experimented with a steel 
ring of rectangular section, pressed between two cast-iron disks, the 
annular bearing-surfaces of which were covered with gun-metal, and were 
12 in. inside diameter and 14 in. outside. The two disks were rotated 
together, and the steel ring was prevented from rotating by means of a 
lever, the holding force of wliich was measured. When oiled through 
grooves cut in each face of the ring and tested at from 50 to 130 revs, 
per min., it was found that a pressure of 75 lbs. per sq. in. of bearing- 
surface was as much as it would bear safely at the highest speed without 
seizing, although it carried 90 lbs. per sq. in. at the lowest speed. The 
coefficient of friction is also much higher than for a cylindrical bearing, 
and the friction follows the law of the friction of soUds much more nearly 
than that of hquids. Tliis is doubtless due to the much less perfect 
lubrication appUcabie to this form of bearing compared with a cylindrical 
one. The coefficient of friction appears to be about the same with the 
same load at all speeds, or, in other words, to be independent of the 
speed; but it seems to diminish somewhat as the load is increased, and 
may be stated approximately as V20 at 15 lbs. per sq. in., diminisliing to 
1/30 at 75 lbs. per sq. in. 

The high coefficients of friction ai;e explained by the difficulty of lubri- 
cating a collar-bearing. It is similar to the slide-block of an engine: 



FEICTION AND LUBRICATION. 1227 

which can carry only about one- tenth the load per sq. in. that can be 

earned by the crank-pins. 

In experiments on cylindrical journals it has been shown that when a 
cylindrical journal was lubricated from the side on which the pressure 
bore, 100 lbs. per sq. in. was the Umit of pressure that it would carry; 
but when it came to be lubricated on the lower side and was allowed to 
drag the oil in with it, 600 lbs. per sq. in. was reached with impunity; 
and if the 600 lbs. per sq. in., which was reckoned upon the full diameter 
of the bearing, came to be reckoned on the sixth part of the circle that was 
taking the greater proportion of the load, it followed that the pressure 
upon that part of the circle amounted to about 1200 lbs. per sq. in. 

In connection with these experiments Mr. Wicksteed states that in 
drilUng-machines the pressure on the collars is frequently as high as 336 
lbs. per sq. in., but the speed of rubbing in this case is lower than it was 
in any of the experiments of the Research Committee. In machines 
working. very slowly and intermittently, as in testing-machines, very 
much higher pressures are admissible. Prof. Thurston (Friction and 
Lost Work, p. 240) says 7000 to 9000 lbs. pressure per square inch 
is reached on the slow working and rarely moved pivots of swing 
bridges. 

Mr. Adamson mentions the case of a heavy upright shaft carried upon 
a small footstep-bearing, where a weight of at least 20 tons was carried 
on a shaft of 5 in. diameter, or, say, 20 sq. in. area, giving a pressure of 
1 ton per sq. in. The speed was 190 to 200 revs, per min. It was neces- 
sary to force the oil under the bearing by means of a pump. For heavy 
horizontal shafts, such as a fly-wheel shaft, carrying 100 tons on two jour- 
nals, his practice for getting oil into the bearings was to flatten the journal 
along one side throughout its whole length to the extent of about an 
eighth of an inch in width for each inch in diameter up to 8 in. diameter; 
above that size rather less flat in proportion to the diameter. At first 
sight it appeared alarming to get a continuous fiat place coming round 
in every revolution of a heavily loaded shaft; yet it carried fhe oil effec- 
tually into the bearing, which ran much better in consequence than a 
truly cylindrical journal without a flat side. 

In thrust-bearings on torpedo-boats Mr. Thornycroft allows a pressure 
of never more than 50 lbs. per sq. in. 

Mr. Tower says (Proc. Inst. M. E., Jan., 1884) : In eccentric-pins of punch- 
ing and shearing machines very high pressures are sometimes used with- 
out seizing. In addition to the alternation in the direction, the pressure 
is applied for only a very short space of time in these machines, so that 
the oil has no time to be squeezed out. 

In the discussion on Mr. Tower's paper (Proc. Inst. M. E., 1885) it was 
stated that it is well known from practical experience that with a con- 
stant load on an ordinary journal it is difficult and almost impossible 
to have more than 200 lbs. per square inch, otherwise the bearing would 
get hot and the oil go out of it; but when the motion was reciprocating, 
so that the load was alternately reUeved from the journal, as with crank- 
pins and similar journals, much higher loads might be applied than even 
700 or 800 lbs. per square inch. 

Mr. Goodman {Proc. Inst. C. E., 1886) found that the total frictional 
resistance is materially reduced by diminishing the width of the brass. 

The lubrication is most efficient in reducing the friction when the brass 
subtends an angle of from 120° to 60°. The film is probably at its best 
between the angles 80° and 110°. 

In the case of a brass of a railway axle-bearing where an oil-groove is 
cut along its crown and an oil-hole is drilled through the top of the brass 
into it, the wear is invariably on the off side, which is probably due to 
the oil escaping as soon as it reaches the crown of the brass, and so leaving 
the off side almost dry, where the wear consequently ensues. 

In railway axles the brass wears always on the forward side. The 
same observation has been made in marine-engine journals, which always 
wear in exactly the reverse way to what might be expected. Mr. Stroud- 
ley thinks tliis pecuharity is due to a film of lubricant being drawn in 
from the under side of the journal to the aft part of the brass, wliich 
effectually lubricates and prevents wear on that side; and that when the 
lubricant reaches the forward side of the brass it is so attenuated down 
to a wedge shape that there is insufficient lubrication, and greater wear 
consequently follows. 



1228 FRICTION AND LUBRICATION. 

C. J, Field (power, Feb., 1893) says: One of the most vital points of an 
engine for electrical service is that of main bearings. They should have 
a surface velocity of not exceeding 350 feet per minute, with a mean 
bearing-pressure per square inch of projected area of journal of not more 
than 80 lbs. Tliis is considerably witliin the safe limit of cool perform- 
ance and easy operation. If the bearings are designed in this way, it 
would admit the use of grease on all the main wearing-surface, which in 
a large type of engines for tlus class of work we think advisable. 

Oil-pressure in a Bearing. — Mr. Beauchamp Tower (Proc, Inst, 
M. E., Jan., 1885) made experiments with a brass bearing 4 ins. diameter 
by 6 ins. long, to determine the pressure of the oil between the brass and 
the journal. The bearing was half immersed in oil, and had a total 
load of 8008 lbs. upon it. The journal rotated 150 r.p.m. The pressure 
of the oil was determined by drilUng smaU holes in the bearing at different 
points and connecting them by tubes to a Bourdon gauge. It was found 
that the pressure varied from 310 to 625 lbs. per sq. in., the greatest 
pressure being a little to the "off" side of the center line of the top of the 
bearing, in the direction of motion of the journal. The sum of the up- 
ward force exerted by these pressures for the whole lubricated area was 
nearly equal to the total pressure on the bearing. The speed was re- 
duced from 150 to 20 r.p.m., but the oil-pressure remained the same, 
showing that the brass was as completely oil-borne at the lower speed aa 
at the higher. The following was the observed friction at the lower speed; 

Nominal load, lbs. per sq. in... . 443 333 211 89 

Coefficient of friction .00132 .00168 .00247 .0044 

The nominal load per square inch is the total load divided by the 
product of the diameter and length of the journal. At the low speed 
of 20 r.p.m. it was increased to 676 lbs. per sq. in. without any signs of 
heating or seizing. 

Friction of Car- journal Brasses. (J. E. Denton, Trans, A. 8. M. E.^ 
xii, 405.) — A new brass dressed with an emery-wheel, loaded with 5000 
lbs., may have an actual bearing-surface on the journal, as shown by the 
polish of a portion of the surface, of only 1 square inch. With this pressure 
of 5000 lbs. per sq. in., the coefficient of friction may be 6%, and the 
brass may be overheated, scarred and cut, but, on the contrary, it may 
wear down evenly to a smooth bearing, giving a highly polished area of 
contact of 3 sq. ins., or more, inside of two hours of running, gradually 
decreasing the pressure per square inch of contact, and a coefficient of 
friction of less than 0.5%. A reciprocating motion in the direction of the 
axis is of importance in reducing the friction. With such polished sur- 
faces any oil will lubricate, and the coefficient of friction then depends 
on the viscosity of the oil. With a pressure of 1000 lbs, per sq. in,, revo- 
lutions from 170 to 320 per min., and temperatures of 75° to 113° F., with 
both sperm and paraffine oils, a coefficient of as low as 0.11% has been 
obtained, the oil being fed continuously by a pad. 

Experiments on O verheating of Bearings. — Hot Boxes. (Denton.) 
— Tests with car brasses loaded from 1100 to 4500 lbs. per sq. in. gave 
7 cases of overheating out of 32 trials. The tests show how purely a 
matter of chance is the overheating, as a brass wliich ran hot at 5000 lbs, 
load on one day would run cool on a later date at the same or higher 
pressure. The explanation of tliis apparently arbitrary difference of 
behavior is that the accidental variations of the smoothness of the sur- 
faces, almost infinitesimal in their magnitude, cause variations of friction 
which are always tending to produce overheating, and it is solely a matter 
of chance when these tendencies preponderate over the lubricating 
influence of the oil. There is no appreciable advantage shown by sperra- 
oil, when there is no tendency to overheat — that is, paraffine can lubri- 
cate under the highest pressures which occur, as well as sperm, when the 
surfaces are within the conditions affording the minimum coefficients of 
friction. 

Sperm and other oils of high heat-resisting qualities, like vegetable oil 
and petroleum cylinder stocks, differ from the more volatile lubricants, 
like parafhne, only in their ability to reduce the chances of the continual 
accideiUal intiaitesimal abrasion producing overheating. 

The effect of emery or other gritty substance in reducing overheating 
of a bearing is thus explained: 



FRICTION AND LUBRICATION, 1229 

The effect of the emery upon the surfaces of the bearings is to cover the 
latter with a series of parallel grooves, and apparently after such grooves 
are made the presence of the emery does not practically increase the 
friction over its amount when pure oil only is between the surfaces* 

The inijiiite number of grooves constitute a very perfect means of insunng 
a uniform oil supply at every point of the bearings. As long as grooves 
in the journal match with those in the brasses the friction appears to 
amount to only about 10% to 15% of the pressure. But if a smooth 
journal is placed between a set of brasses which are grooved, and pres- 
sure be apphed, the journal crushes the grooves and becomes brazed 
or coated with brass, and then the coefficient of friction becomes upward 
• of 40%. If then emery is apphed, the friction is made very much less by 
its presence, because the grooves are made to match each other, and a 
uniform oil supply prevails at every point of the bearings, whereas before 
the application of the emery many spots of the bearing receive no oil 
between them. 

Moment of Friction and Work of Friction of Sliding-surfaces, etc. 

Moment of Friction, Energy lost by Fric- 
inch-lbs. tion in ft .-lbs. 

per min. 

Flat surfaces fWS 

Shafts and journals V%fWd 0.2618 /TFrfn 

Flat pivots VzfWr 0.349 fWm 

Collar-bearing 2/3 /TF ^4^ 0.349 /TFn ^4^ 

Conical pivot 2/3/TFr cosec a 0.349 /TFrn cosec a 

Conical journal ysfWr sec a 0.349 fWrn sec a 

Truncated-cone pivot 2/3 fW ^^^ 7^^^ - 0.349 /TTn ^^^T^ ' 

r2 sm a '' r^ sin a 

Hemispherical pivot fWr 0.5236 fWrn 

Tractrix, or Schiele's "anti- 
friction" pivot fWr 0.5236 /TFrn 

In the above/ = coefficient of friction; 

W = weight on journal or pivot in pounds; 
r = radius, d = diameter, in inches; 
S = space in feet through which shding takes place; 
r2 = outer radius, ri = inner radius; 
n = number of revolutions per minute; 
o =5 the half-angle of the cone, i.e., the angle of the slope 
with the axis. 
To obtain the horse-power, divide the quantities in the last column 

fWdn 
by 33,000. Horse-power absorbed by friction of a shaft = /q^ qcq • 

The formula for energy lost by shafts and journals is approximately 
true for loosely fitted bearings. Prof. Thurston shows that the correct 
formula varies according to the character of fit of the bearing; thus for 
loosely fitted journals, if t/ = the energy lost, 

^, 2fnr „, . , . 0.2618 /T7dn . . ,. 

U = , Wn mch-pounds = . foot-lbs. 

V1+/2 VI+/3 

For perfectly fitted journals V = 2.54: firrWn inch-lbs. = 0.3325 fWdn 
ft.-lbs. 

For a bearing in which the journal is so grasped as to give a uniform 
pressure throughout, U = fn^rWn inch-lbs. = 0.4112/irdn ft.-lbs. 

Resistance of railway trains and wagons due to friction of trains: 
Pull on draw-bar = /X 2240 -i- R pounds per gross ton, 
in which R is the ratio of the radius of the wheel to the radius of journal. 

A cylindrical journal, perfectly fitted into a bearing, and carrying a 
total load, distributes the pressure due to this load unequally on the 
bearing, the maximum pressure being at the extremity of the vertical 
radius, while at the extremities of the horizontal diameter the pressure 
is zero. At any point of the bearing-surface at the extremity of a radius 
which makes an angle 6 with the vertical radius the normal pressure is 
proportional to cos d. If p = normal pressure on a unit of surface. 



1230 FRICTION AND LUBRICATION. 

w = total load on a unit of length of the journal, and r = radius of joiunal, 
w cos & = 1.57 rp, p = w cos (f -5- 1.57 r. 
Tests of Large Shaft Bearings are reported by Albert Kingsbury 
in Trans. A. S. M. E., 1905. A horizontal shaft was supported in two 
bearings 9 X 30 Ins., and a third bearing 15 X 40 ins., midway between the 
other two, was pressed upwards against the shaft by a weighed lever, so 
that it was subjected to a pressure of 25 to 50 tons. The journals were 
flooded with oil from a supply tank. The shaft was driven by an electric 
motor, and the friction H.P. was determined by measuring the current 
supplied. Following are the principal results: 

Load, tons* 

25 25 25 25 25 33.6 42.3 47 47 50.5 

Load per sq. in.* 

83 83 83 83 83 112 141 157 157 168 

Speed, r.p.m. 

309 506 180 179 301 454 480 946 1243 1286 
Speed, ft. per min.* 

1215 1990 708 704 1180 1785 1890 3720 4900 5050 
Friction H.P.f 

12.6 21.7 6.43 5.12 10.1 16 17.9 41.9 47.8 52.3 
Coeff. of frictiont 

.0045 .0048 .0040 .0037 .0037 .0029 .0024 .0025 .0022 .0022 
* On the large bearing. t Three bearings. 

The last three tests were with paraffin oil; the others with heavy machine 
oil. 

Clearance between Journal and Bearing. — John W. Upp, in 
Trans. A. S. M. E., 1905 gives a table showing the diameter of bore 
of horizontal and vertical bearings according to the practice of one of the 
leading builders of electrical machinery. The maximum diameter of the 
journal is the same as its nominal diameter, with an allowable variation 
below maximum of 0.0005 in. up to 3 in. diam., 0.001 in. from 31/2 to 9 in., 
and 0.0015 in. from 10 to 24 in. The maximum bore of a horizontal bear- 
ing is larger than the diam. of the journal by from 0.002 in. for a V2-in. 
journal to 0.009 for 6 in., for journals 7 to 15 in. it is 0.004 + 0.001 X 
diam., and for 16 to 24 in. it is uniformly 0.02 in. For vertical journals the 
clearance is less by from 0.001 to 0.004 in. according to the diameter. The 
allowable variation above the minimum bore is from 0.001 to 0.005. 

Allowable Pressures on Bearings. — J. T. Nicholson, in a paper 
read before the Manchester Assoc, of Engrs. CAm, Mach., Jan. 16. 1908. 
Eng. Digest, Feb., 1908), as a result of a theoretical study of the lubrication 
of bearings and of their emission of heat, obtains the formula p = P/ld = 
40 (dN) '4, in which p = allowable* pressure per sq. in. of projected area, 
P = total pressure, I = length and d = diam. of journal, N = revs, per 
min. It appears from this formula that the greater the speed the greater 
the allowable pressure per sq. in., so that for a 1-in. journal the allowable 
pressure per sq. in. is 126 lbs. at 100 r.p.m. and 189 lbs. at 500 r.p.m., and 
for a 5-in. journal 189 lbs. at 100 and 283 lbs. at 500 r.p.m. W. H. Scott. 
{Eng. Digest, Feb., 1908) says this is contrary to the teaching of practical 
experience, and therefore the formula is inaccurate. Mr. Scott, from a 
study of the experiments of Tower, Lasche, and Stribeck, derives the 
following formulae for the several conditions named: 

For main bearings of double-acting vertical engines, p = 750 D^^N^!^ 

" horizontal " . p = 660 D^iVNy^ 
" " " " single-acting four-cycle gas en- ^. , ., 

gines p = 1350 ■^Vi2/ivV4 

For crank pins of vert, and hor. double-acting engines . p = 1560 D^^/N^^ 
" " " " single-acting four-cycle gas engines, p = 3000 i)V4/ivV4 

For dead loads with ordinary lubrication p = 400 N f^ 

*• forced " p = 1600 A^~V4 

p = allowable pressure in lbs. per sq. in. of projected area: D = diam« 

in ins. ; N = revs. per. min. 



FRICTION AND LUBRICATION. 1231 

F. W. Taylor {Trans. A. S. M. E., 1905). as the result of an investigation 
of line shatt and mill bearings that were running near the limit of dura- 
bility and heating yet not dangerously heating, gives the formula PV = 
400. P = pressure in lbs. per sq. in. of projected area, V = velocity of 
circumference of bearing in ft. per sec. 

The formula is applicable to bearings in ordinary shop or mill use on 
shafting which is intended to run with the care and attention which such 
bearings usually receive, and gives the maximum or most severe duty to 
which it is safe to subject ordinary chain or oiled ball and socket bearmgs 
which are babbitted. It is not safe for ordinary shafting to use cast-iron 
boxes, with either sight feed, wick feed, or grease-cup oiling, under as severe 
conditions as P X F = 200. 

Arcbbutt and Deeley's *' Lubrication and Lubricants *' gives the follow- 
ing allowable pressures in lbs. per sq. in. of projected area of bearmgs. 
Crank-pin of shearing and punching machine, hard steel, inter- 
mittent load bearing 3000 

Bronze crosshead neck journals 1200 

Crank pins, large slow engine 800-900 

Crank pins, marine engines 400-500 

Main crankshaft bearing, fast marine 400 

Same, slow marine 600 

Railway coach journals 300-400 

Flywheel shaft journals 150-200 

Small engine crank pin 150-200 

Small slide block, marine engine 100 

Stationary engine slide blocks 25-125 

Same, usual case 30- 60 

Propeller thrust bearings 50- 70 

Shafts in cast-iron steps, high speed . 15 

Bearing Pressures for Heavy Intermittent Loads. (Oberlin Smith, 
Trans. A. S. M. E., 1905.) — In a punching press of about 84 tons capa- 
city, the pressure upon the front journal of the main shaft is about 
2400 lbs. per sq. in. of projected area. Upon the eccentric the pressure 
against the pitman driving the ram is some 7000 lbs. per sq. in. — both 
surfaces being of cast iron, and sometimes running at a surface speed of 
140 feet per minute. Such machines run year in and year out with but 
little trouble in the way of heating or " cutting." An instance of excessive 
pressure may be cited in the case of a Ferracute toggle press, where the 
whole ram pressure of 400 tons is brought to bear upon hardened steel 
toggle-pins, running in cast iron or bronze bearings, 3 in. in diam. by nearly 

14 in. long. These run habitually, for maximum work, under a load of 
20,000 lbs. per sq. in. 

Bearings for Very High Rotative Speeds. (Proa. Inst M. E., 
Oct., 1888, p. 482.) — In the Parsons steam-turbine, which has a speed as 
high as 18,000 rev. per min., as it is impossible to secure absolute accuracy 
of balance, the bearings are of special construction so as to allow of a 
certain very small amount of lateral freedom. For this purpose the 
bearing is surrounded by two sets of steel washers Vi6 in. thick and of 
different diameters, the larger fitting close in the casing and about V32 in. 
clear of the bearing, and the smaller fitting close on the bearing and about 
1/32 in. clear of the casing. These are arranged alternately, and are 
pressed together by a spiral spring. Consequently any lateral movement 
of the bearing causes them to slide mutually against one another, and by 
their friction to check or damp any vibrations that may be set up in the 
spindle. The tendency of the spindle is then to rotate about its axis of 
mass, and the bearings are thereby relieved from excessive pressure, and 
the machine from undue vibration. The allowing of the turbine itself 
to find its own center of gyration is a well-known device in other branches 
of mechanics: as in the instance of the centrifugal hydro-extractor, where 
a mass very much out of balance is allowed to find its own center of 
gyration; the faster it runs the more steadily does it revolve and the less 

15 the vibration Another illustration is to be found in the spindles of 
spinning machinery which run at about 10,000 or 11,000 revs, per min.: 
although of very small dimensions, the outside diameter of ^he largest 
portion or driving whorl being perhaps not more than IV4 in., it is found 
impracticable to run them at that speed in what might be called a hard- 
and-fast bearing. They are therefore run with some elastic substance 



1232 FKICTION AND LTFBRiCAtlON". 

surrounding the bearing, such as steel springs, hemp, or cork. Any 
elastic substance is suflQcient to absorb the vibration, and permit of 
absolutely steady running. 

Bearing Pressures in Shafts of Parsons Turbines. — The product of 
the bearing pressure in lb. per sq. in. and the peripheral velocity in ft. 
per sec. is generally about 2500 {Proc, Inst. Elect. Engrs., June, 1905). 

Thfust Bearings in 3Iarine Practice. (G. W. Dickie, Trans. A. S- 
M. E., 1905.) — The approximate pressure on a thrust bearing of a propeller 
Shaft assuming two thirds of the indicated horse-power to be effective 

*u 11 • r. T TT T, ,,2X60X33000 I.H.P. ^, ^,^, . 

on the propeller is P = I.H.P. X g x 3 X 6080 = -^- ^ ^^^'^' ^^ 
which S = speed of ship in knots per hour, P = total thrust in lbs. The 
following are data of water-cooled bearings which have given satisfactory 
Service: 

Speed in knots , . . . 22 221/2 28 21 

Thrust^ring surface, horse-shoe type^ 

. sq. iris. 1188 891 581 2268 

Horse-power, one engine, I.H.P 11,500 6,800 4,200 15,000 

indicated pressure on bearing, lbs,.. . 112,700 89,000 33,600 154,000 
Pressure per sq. in. of surface, lbs. .... 95 100 58 68.1 

Mean speed of bearing surfaces, ft. per 

itiin. 642 610 '827 504 

BeaHngs for Locomotives. (G. M. Basfbrd, Trans., A. S. M. E., 
1905,) — Bearing areas for locomotive journals are determined chiefi^ 
by the possibilities of lubrication. On driving journals the following 
figures of pressure in lbs. per sq. in. of projected area give good service: 
passenger, 190; freight, 200; switching, 220 lbs. Crank pins may be 
loaded from 1500 to 1700 lbs.; wrist pins to 4000 lbs. per sq. in. Car and 
tender bearings are usually loaded from 300 to 325 lbs. per sq. in. 

Bearings of Corliss Engines. (P. H. Been, Trans- A. S. M. E., 
1905.) — In the practice of one of the largest builders the greatest pressure 
allowed per sq. in. of projected area for all shafts is 140 lbs. On most 
engines the pressure per sq. in. multiplied by the velocity of the bearing 
surface in ft. per sec. lies between 1000 and 1300. 

Edwin Reynolds says that a main engine bearing to be safe against 
undue heating should be of such a size that the product of the square root 
of the speed of rubbing-surface in feet per second multiplied by the pounds 
per square inch of projected area, should not exceed 375 for a horizontal 
engine, or 500 for a vertical engine when the shaft is lifted at every revo- 
lution. Locomotive driving boxes in some cases give the product as hi^h 
as 585, but this is accounted for by the cooling action of the air. {Am. 
Mach., Sept. 17, 1903.) 

Temperature of Engine Bearings. (A. M. Mattice, Trans. A. S. M. 
E., 1905.)— An examination of the temperature of bearings of a large num- 
ber of engines of various makes showed more above 135° F. than below 
that figure. Many bearings were running with a temperature over 150°, 
and in one case at 180°, and in all of these cases the bearings were giving 
no trouble. 

PIVOT-BEARINGS. 

The Schiele Curte. — W. H. Harrison (Am. Mach., 1891) says the 
Schiele curve is not as good a form for a bearing as the segment of a 
sphere. He says: A mill-stone weighing a ton frequently bears its whol : 
weight upon the flat end of a hard-steel pivot 1 Vs in. diam., or 1 sq. in. 
area of bearing; but to carry a weight of 3000 lbs. he advises an end 
bearing about 4 ins. diam., made in the form of a segment of a sphere 
about 1/2 in. in height. The die or fixed bearing should be dished to fit 
the pivot. This form gives a chance for the bearing to adjust itself, 
which it does not have when made flat, or when made with the Schiele 
curve. If a side bearing is necessary it can be arranged farther up the 
shaft. The pivot and die should be of steel, hardened; cross-gutters 
should be in the die to allow oil to flow, and a central oil-hole should be 
made in the shaft. 

The advantage claimed for the Schiele bearing is that the pressure is 
uniformly distributed over its surface, and that it therefore wears uni^ 
formly. Wilfred Lewis (Am. Mack., April 19, 1894) says that its merits 



BALL-BEAEINGS, ROLLER-BEARINGS, ETC. 



1233 



as a thrust-bearing have been vastly overestimated; that the term 
"anti-friction" applied to it is a misnomer, since its friction is greater 
than that of a flat step or collar of the same diameter. He advises that 
flat thrust-bearings should always be annular in form, having an inside 
diameter one-half of the external diameter. 

Friction of a Flat Pivot-bearing. — The Research Committee on 
Friction (Proc. Inst. M. E., 1891) experimented on a step-bearing, flat- 
tended, 3 in. diam., the oil being forced into the bearing through a hole 
in its center and distributed through two radial grooves, insuring thorough 
lubrication. The step was of steel and the bearing of manganese-bronze. 
At revolutions per min. 50 128 194 290 353 

The coefficient of friction \ 0.0181 0.0053 0.0051 0.0044 0.0053 

varied between / and 0.0221 0.0113 0.0102 0.0178 0.0167 

With a white-metal bearing at 128 revs, the coefficient of friction was 
a little larger than with the manganese-bronze. At the higher speeds 
the coefficient of friction was less, owing to the more perfect lubrication, 
as shown by the more rapid circulation of the oil. At 128 revs, the 
bronze-bearing heated and seized on one occasion with a load of 260 lbs., 
and on another occasion with 300 lbs. per sq. in. The white-metal bear- 
ing under similar conditions heated and seized with a load of 240 lbs. 
per sq. in. The steel footstep on manganese-bronze was afterwards 
tried, lubricating with three and vnih. four radial grooves: but the friction 
was from one and a half times to twice as great as with only the two 
grooves. 

Mercury-bath Pivot. — A nearly frictionless step-bearing may be 
obtained by floating the bearing with its superincumbent weight upon 
mercury. Such an apparatus is used in the hghthouses of La Heve, 
Havre. It is thus described in Eng'g, July 14, 1893. p. 41: 

The optical apparatus, weighing about 1 ton, rests on a circular cast- 
iron table, which is supported by a vertical shaft of wTought iron 2.36 in. 
diameter. This is kept in position at the top by a bronze ring and outer 
iron support, and at the bottom in the same wav. w^hile it rotates on a 
removable steel pivot resting in a steel socket, which is fitted to the base 
of the support. To the vertical shaft there is rioidly fixed a floating cast- 
iron nng 17.^1 in. diameter and 11.8 in. in depth, which is plunged into 
and rotates in a mercury bath contained in a fixed outer drum or tank, 
the clearance between the vertical surfaces of the drum and ring being 
only 0.2 in., so as to reduce as much as possible the volume of mercury 
(about 220 lbs.), while the horizontal clearance at the bottom is 0.4 in. 
BALL-BEARINGS, ROLLER-BEARINGS, ETC. 

Friction-rollers. — If a journal instead of revolving on ordinary 
bearings be supported on friction-rollers the force required to make the 
journal revolve wiU be reduced in nearly the same proportion that the 
diameter of the axles of the rollers is less than the diameter of the rollers 
themselves. In experiments by A. M. Wellington with a journal 31/2 in. 
diam. supported on rollers 8 in. diam., whose axles were I3/4 in. dw.m., the 
friction in starting from rest was 1/4 the friction of an ordinary 3V2-in, 
bearing, but at a car speed of 10 miles per hour it was 1/2 that of the ordi- 
nary bearing. The ratio of the diam. of the axle to diam. of roller was 
13/4: 8, or as 1 to 4.6. 

Coefficients of Friction of Roller Bearings. C. H. Benjamin, Machy. 
Oct., 1905. — Comparative tests of plain babbitted, McKeel plain roller, 
and Hyatt roller bearings gave the following values of the coefficient of 
friction at a speed of 560 r.p.m.: 



Diameter 


Hyatt Bearing. 


McKeel Bearing. 


Babbitt Beating. 


of Journal. 


Max. 


Min. 


Ave. 


Max. 


Min. 


Ave. 


Max. 


Min. 


Ave . 


1 15/16 

2 3/16 


.032 
.019 
.042 
.029 


.012 

.on 

.025 
.022 


.018 
.014 
.032 
.025 


.033 


.017 


.022 


.074 
.088 
.114 
.125 


.029 
.078 
.083 
.089 


.043 
.082 


2 7/16 
2 15/16 


.028 
.039 


.015 
.019 


.021 
.027 


.096 
.107 



The friction of the roller-bearing is from one-fifth to one-third that of 
a plain bearing at moderate loads and speeds. It is noticeable that as 
the load on a roller-bearing increases the coefficient of friction decreases. 

A slight change in the pressure dUe to the adjusting nuts was sufficient 
to increase the friction considerably. In the McKeel bearing the rolls 



1234 



FRICTION AND LUBRICATION. 



t)ore on a cast-iron sleeve and in the Hyatt on a soft-steel one. If roller 
bearings are properly adjusted and not overloaded a saving of from 2-3 
to 3-4 of the friction maj^ be reasonably expected. 

McKeel bearings contained rolls turned from solid steel and guided by 
spherical ends fitting recesses in cage rings at each end. The cage rings 
were joined to each other by steel rods parallel to the rolls. 

Lubrication is absolutely necessary with ball and roller bearings, 
although the contrary claim is often advanced. Under favorable con- 
ditions an almost imperceptible film is sufficient; a sufficient quantity 
to immerse half the lowest ball should always be provided as a rust 
preventive. Rust and grit must be kept out of ball and roller bearings. 
Acid or rancid lubricants are as destructive as rust. (Henry Hess.) 

Both ball and roller bearings, to give the best satisfaction, should be 
made of steel, hardened and ground; accurately fitted, and in proper 
alignment with the shaft and load; cleaned and oiled regularly, and fitted 
with as large-size balls or rollers as possible, depending upon the revolutions 

Eer minute and load to be carried. Oil is absolutely necessary on both 
all and roller bearings, to prevent rust. (S. S. Eveland.) 
Roller Bearings. — The Mossberg roller bearings for journals are made 
in the sizes given in the table below. D = diam. of journal; d = diam. of 
roll; N = number of rolls; P = safe load on journals, in lbs. The rolls 
are enclosed in a bronze supporting cage. (Trans. A. S. M. E., 1905.) 



D 


d 

1/4 


N 
20 


P 


D 


d 


N 


P 


D 


d 


N 


' P 


2 


3,500 


6 


11/16 


24 


50,000 


15 


13/8 


28 


255,000 


21/?, 


5/16 


22 


7,000 


7 


13/16 


22 


70, COO 


1« 


13/8 


32 


325,000 


3 


3/8 


22 


13,000 


8 


7/8 


22 


90,000 


20 


11/? 


34 


400.000 


4 


7/l« 


24 


24,000 


9 


1 


24 


115,000 


24 


u/? 


38 


576,000 


5 


9/16 


24 


37.000 


12 


11/4 


26 


175,000 











{Surface speed of journal to 50 ft. per min. Length of journal II/2 
diameters. The rolls are made of tool steel not too high in carbon, and of 
spring temper. The journal or shaft should be made not above a medium 
spring temper. The box should be made of high carbon steel and tem- 
pered as hard as possible. 

Conical Roller Thrust Bearings. — The Mossberg thrust bearing is 
made of conical rollers contained in a cage, and two collars, one being 
stationary and the other fixed to the shaft and revolving with it. One 
side of each collar is made conical to correspond v/ith the rollers which 
bear on it. The apex of the cones is at the center of the shaft. The 
angle of the cones is 6 to 7 degrees. Larger angles are objectionable, 
giving excessive end thrust. The following sizes are made; 



Diameter 

of Shaft. 

Ins. 


Outside 

Diameter 

of Ring. 

Ins. 


No. of 
Rolls. 


Safe Pressure on Bearing. 


Area of 

Pressure 

Plate. 

Sq. ins. 


Speed 

75 Rev. 

Lbs. 


Speed 
150 Rev. 
Lbs. 


21/16-21/4 
31/16-31/4 
41/18-41/4 
51/16-51/4 
6 1/16-6 1/2 
81/16-81/2 
9 1/16-9 1/2 


59/16 

105/16 
123/8 
147/8 
183/4 
201/2 


30 
30 
30 
30 
30 
32 
32 


10 
20 
35 
54 
78 
132 
162 


19,000 
40,000 
70,000 
108,000 
125,000 
200,000 
300,000 


9,500 
20,000 
35,000 
56,000 
62,000 
100,000 
150.000 



Plain Roller Thrust Bearings. — S. 8. Eveland, of the Standard 
Roller Bearing Co., contributes the following data of plain roller thrust 
bearings in use in 1903. The bearing consists of a large number of short 
cylindrical rollers enclosed in openings in a disk placed between two 
hardened steel plates. He says *' our plain roller bearing is theoretically 
wrong, but in practice it works perfectly, and has replaced many thou- 
sand ball-bearings which have proven unsatisfactory." 



BALL-BEARINGS, ROLLER-BEARINGS, ETC. 1235 



Size of 


Number and 




Wt. on 


Lineal 
Inches. 


Weight 


Weight 


Bearing, 


Size of Rollers, 


R.p.m. 


Bearings, 


per lin. 


on each 


Ins. 


Ins. 




Lbs. 


in., Lbs. 


Roll,Lb. 


4 3/4 X 6 11/16 


36 5/8 X5/16 


500 


6.000 


11 1/4 


546 


167 


4 3/4X 7 1/4 


32 3/4X5/8 


470 


10.000 


12 


833 


312 


5 1/2 X 8 1/2 


54 3/4 X 5/8 


420 


15,000 


201/4 


750 


279 


7 X 10 3/8 


48 1 XI/2 


370 


20.000 


24 


833 


417 


71/2x11 5/16 


54 l XI/2 


325 


25.000 


27 


988 


463 


8 X 15 1/2 


70 1 1/4 X5/8 


300 


60,000 


45 


1334 


833 



The Hyatt Roller Bearing. (A. L. Williston, Trans. A. S. M. E., 
1905.) — The distinctive feature of the Hyatt roller bearing is a flexible 
roller, made of a strip of steel wound into a coil or spring of uniform diam- 
eter. A roller of this construction insures a uniform distribution of the 
load along the line of contact of the roller and the surfaces on which it 
operates. It also permits any slight irregularities in either journal or box 
without causing excessive pressure. The roller is hollow and serves as 
an oil reservoir. For a heavy load, a roller of heavy stock can be made- 
while for a high-speed bearing under light pressure a roller of light weight, 
made from thin stock, can be used. Following are the results of some tests 
of the Hyatt bearing in comparison with other bearings: 

A shaft 152 ft. long, 2i5/i6 in. diam. supported by 20 bearings, belt- 
driven from one end, gave a friction load of 2.28 H.P. with babbitted 
bearings, and 0.80 H.P. with Hyatt bearings. With 88 countershafts 
running in babbitted bearings, the H.P. required was 8.85 when the main 
shaft was in babbitted bearings and 6.36 H.P. when it was in Hyatt bearings. 

Comparative tests of solid rollers and of Hyatt rollers were made in 
1898 at the Franklin Institute by placing two sets of rollers between three 
flat plates, putting the plates under load in a testing machine and measur- 
ing the force required to move the middle plate. All the rollers were 
3/4 in. diam., 10 ins. long. The Hyatt rollers were made of 1/2 X Vs in. 
steel strip. With 2000 lbs. load and plain rollers it took 26 lbs. to move 
the plate, and with the Hyatt rollers 9 lbs. With 3000 lbs. load and 
plain rollers the resistance was 34 lbs., with Hyatt rollers 17 lbs. 

In tests with a pendulum friction testing machine at the Case Scientific 
School, with a bearing Ii5/i6 in. diam. the coefficient of friction with the 
Hyatt bearing was from 0.0362 down to 0.0196, the loads increasing from 
64 to 264 lbs.; with cast-iron bearings and the same loads the coefficient 
was from 0.165 to 0.098. 

In tests at Purdue University with bearings 4 X IV2 ins. and loads 
from 1900 to 8300 lbs., the average coefficients with different bearings and 
different speeds were as follows: 

Hyatt bearing 130 r.p.m. 0.0114 302 r.p.m. 0.0099 585 r.p.m. 0.0147 
Cast-iron bearing 128 " 0.0548 302 " 0.0592 410 " 0.0683 
Bronze bearing 130 " 0.0576 320 *' 0.0661 582 '* 0.140 

The cast-iron bearing at 128 r.p.m. seized with 8300 lbs., and at 410 
r.p.m. with 5900 lbs. The bronze bearing seized at 130 r.p.m. with 3500 lbs., 
at 320 r.p.m. with 5100 lbs., and at 582 r.p.m. with 2700 lbs. 

The makers have found that the advantages of roller bearings of the 
type described are especially great with either high speeds or heavy loads. 
Generally, the best results are obtained for line-shaft work up to speeds of 
600 rev. per min., when a load of 30 lbs. per square inch of projected area 
is allowed. For heavy load at slow speed, such as in crane and truck 
wheels, a load of 500 lbs. gives the best results. 

The Friction Coefficient of a well-made annular ball-bearing Is 0.001 
and 002 of the load referred to the shaft diameter and is Independent 
of the speed and load. The friction coefficient of a good roller bearing 
is from 0.0035 to 0.014; it rises very much if the load is light. It in- 
creases also when the speeds are very low, though not so much as with 
plain bearings. (Henry Hess.) 

Notes on Ball Bearings. — The following notes are contributed by 
Mr. Henry Hess, 1910. Ball bearings in modern use date from the bi- 
cycle. That brought in the adjustable cup and cone and three-point 
contact type. Under the demands for greater load resistance and relia- 
bility the two-point contact type, without adjustability, was evolved; 
that is now used under loads from a few pounds to many tons. Such a 



1236 FRICTION AND LUBRICATION. 

bearing consists of an inner race, an outer race and the series of balls 

that roll in tracks of curved cross section. Various designs are used, 
dlfTering chiefly in the devices for separating the balls and in the arrange- 
ment for introducing the balls between the races. The most widely 
used type has races that are of the same cross section throughout, un- 
broken by any openings for the introduction of balls. To introduce 
the balls the two races are first eccentrically placed; the balls will fill 
slightly more than a half circumference; elastic separators or solid cages 
are used to space the balls. 

Another type has a filling opening of sufficient depth cut into one race; 
the race continuity is restored by a small piece that is let in. This type 
is usually filled with balls, without cages or separators. The filling 
opening is always placed at the unloaded side of the bearing, where the 
weakening of the race is not important. This type has been almost en- 
tirely discarded in favor of the one above described. 

A third type has a filling opening cut into each race not quite deep 
enough to tangent the bottom of the ball track. As this weakened 
section necessarily^ comes under the load during each revolution, the 
carrying capacity is reduced. After slight wear there develops an inter- 
ference of the balls with the edges of these openings, which seriously 
reduces the speeds and load capacity. This interference precludes the 
use of this type to take end thrust. 

The carrying capacity of a ball-bearing is directly proportional to the 
number of balls and to the square of the ball diameter. 

It may be written as: 

L = Knd^, in which L = load capacity in pounds; n — number of 
balls; d = ball diameter in eighths of an inch. K varies with the condition 
and type of bearing, as also with the material and speed. 

For a certain special steel that hardens throughout and is also unusu» 
ally tough, employed by " DWF" or " HB" (the originators of the modern 
two-point type), the following values apply. For other steels lesser values 
must be used. 

I. For Radial Bearings : 

K =* 9 for uninterrupted racG track, cross-section curvature == 0.52 

and 9/16 in. ball diameter respectively for inner and outer races, 

separated balls, uniform load, and steady speed up to 3000 

revs, per min. 
iC = 5 for full ball type, filling opening in one race at the unloaded 

side, otherwise as above. 
K = 2.5 for both ball tracks interrupted by filling openings, inelastic 

cage separators for balls, or full ball, speeds not above 2000 

revs, per min., uniform load. 
K = 0.9 for thrust on a radial bearing of the first type, as above. The 

larger the balls the smaller K. The type with filling openings 

in each race is not suitable for end thrust. 
The radial load bearing is, up to high speeds, practically unaffected 
by speed, as to carrying capacity. 

II. Thrust Bearings: 

With the thrust type, consisting of one flat plate and one seat plate 
with grooved ball races, the load capacity decreases with speed or 

T^K^nd^ 

Ki= constant for material and race cross-section, etc., R = revolu- 
tions per minute. R ranges from about 3000 revs, per min. down to 1 rev. 
per min. as for crane hooks and similar elements. 

Ki= 25 to 40 for material used by the DWF or HB, and race cross- 
section radius = approx. 1.66 ball radius. 

Ki= 0.5 for unhardened steel, occasionally used for very large races; 
a steel that is fairly hard without tempering must be used, and then only 
when there is no hammering or sharp load variation. 

Balls must be carefully selected to make sure that all that are used 
in the same bearing do not vary among one another by more than O.OOOl 
inch. A ball that is more than that larger than its fellows will sustain 
more than its proportion of the load, and may therefore be overloaded 
and will in turn overload the races. 



BALL-BEAEINGS, ROLLER-BEARINGS, ETC. 1237 



The usual test of ball quality, which consists in compressing a ball 
between flat plates and noting the load at rupture, gives the quality of 
the plates, but not of the balls. It is the abihty of the ball to resist 
permanent deformation that is of importance. 'As the deformations 
involved are very small the test is a difficult one to carry out. Of even 
greater importance than a small deformation under load is uniformity of 
such deformation between the balls employed; a hard ball will deform 
less than its softer mate and so will carry more than its share of the 
load, and will therefore be overloaded and in turn overload the races. 

Coned bearings for balls are objectionable. The defect in all these 
forms of bearings is their adjustable feature. A bearing properly propor- 
tioned with reference to a certain load may be enormously overloaded by 
a little extra effort applied to the wrench, or on the other hand the bear- 
ing may be adjusted with too little pressure, so that the balls will rattle, 
and the results consequently be unsatisfactory. The prevalent idea that 
coned ball-bearings can be adjusted to compensate for wear is erroneous. 

Mr. Hess's paper, in Trans. A. S. M. E., 1907, contains a great deal of 
useful information on the practical design of ball-bearings, including 
different forms of raceways. He prefers a two-point bearing, in which 
the ball races have a curved section, with sustaining surfaces at right 
angles with the direction of the load. 

Formulae for Number of Balls in a Bearing. (H. Rolfe, Am. Mach., 
Dec. 3, 1896.) — Let D = diam. of ball circle (the circle passing through 
the centers of the balls); d = diam. of balls; n = number of balls; s = 
average clearance space between the balls. Then D = (rf + s) -i- sin 
(180° /n); d = D sin (180°/n) - s; s = D sin (180°/n) - d; n =180° 4- 
angle w^hose sine is {d + s) ^D, The clearance s should be about 0003 in. 
Values of ISOVn and of sin 180°/^. 



1 


^ 






?! 






g 






^ 






^ 






~\ 






< 






> 


n. 


4 

o 




n. 


,4 


1 


n. 


St 


1 


n. 


si 


1 




? 


•S 




g 


fl 




8 


a 




§ 


.3 






'ot 






'53 






*S 






S 




60 


0.86603 


~J5 


12 


0.20791 


27 


6.667 


0.11609 


39 


4.615 


0.08047 




45 


.70711 


16 


11.250 


.19509 


28 


6.429 


.11197 


40 


4.500 


.07846 




36 


.58799 


17 


10.588 


.18375 


29 


6.207 


.10812 


41 


4.390 


.07655 




30 


.50000 


18 


10 


.17365 


30 


6 


.10453 


42 


4.286 


.07473 




25.714 


.43388 


19 


9.474 


. 16454 


31 


5.806 


.10117 


43 


4.186 


.07300 


8 


22.500 


.38268 


20 


9. 


.15643 


32 


5.625 


.09801 


44 


4.091 


.07134 


9 


20 


.34202 


21 


8.571 


.14904 


33 


5.455 


.09506 


45 


4 


.06976 


10 


18 


.30902 


22 


8.182 


.14233 


34 


5.294 


.09227 


46 


3.913 


.06825 


11 


16.364 


.28173 


23 


7.826 


.13616 


35 


5.143 


.08963 


47 


3.830 


.06679 


12 


15 


.25882 


24 


7.500 


. 13053 


36 


5 


.08716 


48 


3.750 


.06540 


13 


13.846 


.23931 


25 


7.200 


. 12533 


37 


4.865 


.08510 


49 


3.673 


.06407 


14 


12.857 


.22252 


26 


6.923 


.12055 


38 


4.737 


.08258 


50 


3.600 


.06279 



Grades of Balls for Bearings. (S. S. Eveland, Trans. A. S. M. E., 
1905.) — *'A" grade baUs vary about 0.0025 in. in diameter; "B" grade, 
0.001 to 0.002 in.; while " high-duty" or special balls are furnished varying 
not over 0.0001 in. The crushing strength of balls is of little importance 
as to the load a bearing will carry, the revolutions per minute bemg quite 
as important as the load. 

Saving of Power by Use of Bali-Bearings. — Henry Hess (Trans. 
A. S. M. E., 1909) describes a series of tests made by Dodge and Day on a 
215/16 in. line shaft 72 ft. long, alternately equipped with plain ring-oiling 
babbitted boxes and with Hess-Bnght ball-bearings. Eight countershafts 
were driven from pulleys on the line shaft. The countershaft pulleys had 
plain bearings. The conclusions from the tests made under normal belt 
conditions of 44 and 57 lbs. per inch width of angle of single belt are a3 
follows: 

a. Savings due to the substitution of ball-bearings for plain bearings on 
line shafts may be safely calculated by using 0.0015 as the coefficient of 
ball-bearing friction, 0.03 as the coefficient of line shaft friction, and 0.08 
as the coefficient of countershaft friction. 

b. When the belts from line shaft to countershaft pull all in one direc- 
tion and nearly horizontally the saving due to the substitution of ball- 



1238 FRICTION AND LUBRICATION. 

bearings for plain bearings on the line shaft may be safely taken as 35 % 

of the hearui^ iriction. 

c. When baU-bearings are used also on the countershafts the savings 
will be correspondingly greater and may amount to 70% or more of the 
bearing friction. 

d. These percentages of savings are percentages of the friction work 
lost in the plain bearings; they are not percentages of the total power 
transmitted. The latter will depend upon the ratio of the total power 
transmitted to that absorbed in the line and countershafts. 

e. The power consumed in the plain line and countershafts varies, as 
is weh known, from 10 to 60% in different industries and shops. The 
substitution of ball-bearings for plain bearings on the line shaft only, under 
conditions of paragraph "a," will thus result in saving of total power of 
35 X 0.10 = 3.5% to 35 X 0.60 = 21%. By using ball-bearings on the 
countershafts also, the saving of total power will be from 70 X 0.10 = 7% 
to 70 X 0.60 = 42%. 

KNIFE-EDGE BEARINGS. 
Allowable loads on knife-edges vary with the manner in which the 
pivots or knife-edges are held in the lever and the pivot supports or 
seats secured to the base of weighing machines. The extension of the 
pivot beyond the solid support is practically w^orthless. A high-grade imi- 
lorra tool steel with carbon 0.90% to 1.00% should be used. The temper 
of the seats should be drawn to a very light straw color; that of the pivots 
should be slightly darker. The angle of 90° for the knife-edge has given 
good results for heavy loads. For ordinary weighing machinery and most 
testing machinery 5000 lbs. per inch of length is ample. Loads of 10,000 
lbs. per inch of length are permissible, but the pivot must be flat at its 
upper portion, normal to the load and supported its whole length, with a 
minimum deflection of parts to secure reasonable accuracy. The edge may 
be made perfectly sharp, for loads up to 1000 lbs. per inch of length. For 
greater loads the sharp edge is rubbed with an oilstone, so that a smooth- 
ness is just visible. A pronounced radius of knife-edge will decrease the 
sensibility of the apparatus. (Jos. W. BramweU, Eng. News, June 14, 
1906.) 

FRICTION OF STEA3I-ENGINES. 
Distribution of the Friction of Engines. — Prof. Thurston, in his 
"Friction and Lost Work," gives the following: 

1. 2. 3 

Main bearings 47. 35 .4 35 .0 

Piston and rod 32.9 25.0 21.0 

Crank-pin 6.8 5.1) ,o ^ 

Cross-head and wrist-pin 5.4 4.1) ^^ '^ 

Valve and rod 2.5 26.4) c,o n 

Eccentric strap 5.3 4.0) -^-"^ 

Link and eccentric .... 9.0 

Total 100.0 100.0 100.0 

No. 1, Straight-hne, 6 x 12 in., balanced valve; No. 2, Straight-Une, 
6 X 12 in., unbalanced valve; No. 3, 7 x 10 in., Lansing traction, locomo- 
tive valve-gear. 

Prof. Thurston's tests on a number of different styles of engines indicate 
that the friction of any engine is practicaUy constant under aU loads. 
{Trans. A. S. M. E., vih, 86; ix, 74.) 

In a straight-hne engine, 8 x 14 in., I.H.P. from 7.41 to 57.54, the 
friction H.P. varied irregularly between 1.97 and 4.02, the variation 
being independent of the load. With 50 H.P. on the brake the I.H.P. 
was only 52.6, the friction being only 2.6 H.P., or about 5%. 

A compound condensing-engine, tested from to 102.6 brake H.P., gave 
I.H.P. from 14.92 to 117.8 H.P., the friction H.P. varying only from 
14.92 to 17.42. At the maximum load the friction was 15.2 H.P., or 
12.9%. 

The friction increases with increase of the boiler-pressure from 30 to 70 
lbs., and then becomes constant. The friction generally increases with 
increase of speed, but there arc exceptions to this rule. 

Prof. Denton {Stevens Indicator , .July, 1890), comparing the calculated 
fHction on a number of engines with the friction as determined by measure- 



FRICTION BRAKES AND FRICTION CLUTCHES. 1239 

ment, finds that in one case, a 75- ton ammonia ice-machine, the friction of 
the compressor, 17 1/2 H.P., is accounted for by a coefficient of friction 
of 71/2% on all the external bearings, allowing 6% of the entire friction 
of the machine for the friction of pistons, stuffing-boxes, and valves. In 
the case of the Pawtucket pumping-engine, estimating the friction of the 
external bearings with a coefficient of friction of 6% and that of the 
pistons, valves, and stuffing-boxes as in the case of the ice-machine, we 
have the total friction distributed as follows: 

Horse- Per cenx 
^ , . J ^ . ^ . . , power, of whole. 

Crank-pms and effect of piston-thrust on main shaft .71 114 

Weight of fly-wheel and main shaft 1 95 32 "4 

Steam-valves 23 3 7 

Eccentric [[[[ ^07 12 

Pistons .43 7 2 

Stuffing-boxes, six altogether 72 113 

Air-pump .' 2^10 32.8 

Total friction of engine with load 6 .21 100 

Total friction per cent of indicated power. 4.27 
The friction of this engine, though very low in proportion to the indi- 
cated power, is satisfactorily accounted for by Morin's law used with a 
^ coefficient of friction of 5%. In both cases the main items of friction are 
' those due to the weight of the fly-wheel and main shaft and to the piston- 
thrust on crank-pins and main-shaft bearings. In the ice-machine the 
latter items are the larger owing to the extra crank-pin to work the pumps, 
while in the Pawtucket engine the former preponderates, as the crank- 
thrusts are partly absorbed by the pump-pistons, and only the surplus 
effect acts on the crank-shaft. 

Prof. Denton describes in Trans. A. S, M, £*., x. 392, an apparatus by 
which he measured the friction of the piston packing-ring. When the 
parts of the piston were thoroughty devoid of lubricant, the coefficient 
of friction was found to be about 71/2%; with an oil-feed of one drop in 
two minutes the coefficient was about 5%; with one drop per minute it 
was about 3%. These rates of feed gave unsatisfactory lubrication, the 
piston groaning at the ends of the stroke when run slowly, and the flow of 
oil left upon the surfaces was found by analysis to contain about 50% of 
iron. A feed of tw^o drops per minute reduced the coefficient of friction 
to about 1%, and gave practically perfect lubrication, the oil retaining its 
natural color and purity. 

FRICTION BRAKES AND FRICTION CLUTCHES. 

I Friction Brakes are used for slowing down or stopping a moving 

I machine by converting its energy of motion into heat, or for controlling 

I the speed of a descending load. The simplest form is the block brake, 

i commonly used for railway car wheels, which resists the motion of the 

wheel not only with the force due to ordinary sliding friction, but with 

that due to cutting or grinding awav the surface of the metals in contact. 

If P = total pressure acting normal to the sliding surface, / = coefficient 

of friction, and v = velocity in feet per minute, then the energy absorbed, 

in foot-pounds per minute, is Pfv. If the surface is lubricated and the 

pressure per square inch not great enough to squeeze out the lubricant, 

then the value of / for different materials may be taken from Morin's 

tables for friction of motion, page 1221, but if the pressure is great enough 

to force out the lubricant, then the coefficient becomes much greater 

1 and the surfaces will cut and wear, with a rapid rise of temperature. 

I Other forms of brakes are disk brakes and cone brakes, in which a 

i disk or cone i3 carried by the rotating shaft and a mating disk or cone 

I is pressed against it by a lever or other means: and band brakes, also 

! called strap or ribbon brakes, in which a flexible band encircles the 

I cylindrical surface of a rotating drum or wheel, and tension applied 

to one end of the barid brings it in contact with that surface. For band 

' brakes the theory of friction of belts applies. Seepage 1138. For much 

; information on the theory and practice of friction brakes see articles by 

, C. F. Blake in Mach*y, Jan., 1901, Mar., 1905, and Aug., 1906, and by 

I E. R. Douglas, Am. Mach., Dec. 26. 1901, and R. B. Brown, Mach'y, 

April, 1909. For friction brake dynamometers see Dynamometers. 



1240 FRICTION AND LUBRICATION. 

Friction Clutclies are used for putting shafts in motion gradually^ 
without shock. If two shafts, in line with each other, one in motion and 
the other at rest, each having a disli l^eyed to the end, and the disks 
almost touching, are moved toward each other so that the disks are 
brought in contact with some pressure, the shaft at rest will be put in 
motion gradually, while the disks rub on each other, until it acquires the 
velocity of the driving shaft, when the friction ceases and the disks may 
then be locked together. This is an elementary form of friction clutch. 
A great variety of styles are made in which the sliding surfaces may be 
disks, cones, and gripping blocks of various forms. The work done by a 
clutch while the surfaces are in sliding contact, and before they are locked 
together, is the overcoming of the inertia of the driven shaft and of all 
the mechanism driven by it, and giving it the velocity of the driving 
shaft. The principles of friction brakes apply to friction clutches. The 
sliding surfaces must be of sufficient area to keep the normal pressure 
below that at which they will overheat, cut and wear, and to dissipate 
the heat generated by friction. The following values of the coefficient 
of friction to be used in designing clutches are given by C. W. Hunt; 
cork on iron, 0.35; leather on iron, 0.3; wood on iron. 0.2; iron on iron, 
0.25 to 0.3. Lower values than these should be assumed for veiocities 
exceeding 400 ft. per minute. The pressure per square inch in disk 
clutches should not exceed 25 or 30 lbs., and wooden surfaces should 
not be loaded beyond 20 to 25 lbs. per sq. in. See Kimball and Barr on 
Machine Design, also Trans. A. S. M. E., 1903 and 1908. 

Eiectrically Operated Brakes are discussed by H. A Steen in a 
paper read before the Engrs. Socy. of W. Penna., reprinted in Iron Trade 
Rev., Dec. 24, 1908. Formulge are given for the time required for stop- 
ping, for the heat generated and the temperature rise, for different types 
of brakes. 

Magnetic and Electric Brakes. — For braking the load on electric 
cranes a band brake is used which is held off the drum by the action of 
a magnet or solenoid, and is put on by the action of a spring or weight. 
The solenoid usually consists of a coil of wire connected in series with the 
motor, and a plunger working inside of the coil. It should be so pro- 
portioned that its action is not delayed by residual magnetism when the 
current is cut off. Too rapid action is prevented by making the end of 
the solenoid an air dash-pot. 

For electric-driven machinery an electric motor makes a most efficient 
brake by reversing the direction of the electric current, causing the motor 
to become a generator supplying current to a rheostat in which it is con- 
verted into heat and dissipated. In some cases the electric current 
generated, instead of being absorbed in a rheostat, is fed into the main 
electric circuit. In this case the energy of the rotating mass, instead of 
being wasted in friction or in electrical heating, is converted into electric 
energy and thus conserved for further use. 

Design of Band Brakes. (R. A. Greene, Am. Mach., Oct. 8, 1908.) — 
In the practice of the Browning Engineering Co., Cleveland, O., in 
regard to the design of band brakes the equations are: 

T= PX, t= T -P, S = -^-^, ^== SX DX 0.262 X revolutions per 

minute, in which T = the greater tension on the band, t = the lesser 
tension on the band, P = equivalent load on the brake drum, X = factor 

from the accompanying table, X = ^_ in which log. N = 102*"2ss/c, 

where / = the coefficient of friction and c the length of arc of contact in 
degrees divided by 360. D = diam. of brake drum, F = width of face 
of brake drum, S = sl checking factor which has a maximum limit of 65, , 
t? = a checking factor which has a limit of 54,000 (Yale & Towne practice) i 
or 60,000 (Brown hoist practice). 

Example. — A band brake is to be designed having an arc of contact - 
of 260°, coefficient of friction = 0.2, drum diameter 30 ins., face 4 ins., 
speed 100 r.p.m., and a load of 3000 lbs. acting on a diameter of 20 ins. 

Then 

P= 3000 X 20-4-30 = 2000 pounds, X = 1.68 (from table), T = 2000 X 
. 1.68 = 3360 pounds, t = 3360 - 2000 = 1360 pounds, S = 2 X3360^ 
(30X4) = 56 (within the Umit), i^ = 56x30 X 0.262 X 100 = 44,000 (within 
the limit). 



FRICTION OF HYDRAULIC PLUNGER PACKING. 1241 



Degrees. 


Values of X. 


Degrees. 


Values of X. 


f =0.2. 


/ =0.3. 


/ =0.4. 


f =0.2. 
1.68 


/ =0.3. 
1.35 


/ =0.4. 


180 


2.14 


1.64 


1.40 


260 


1.19 


195 


2.03 


1.56 


1.35 


270 


1,64 


1.32 


1.18 


210 


1.93 


1.50 


1.30 


280 


1.60 


1.30 


1.17 


240 


1.76 


1.40 


1.23 


290 


1.57 


1.28 


1.15 


250 


1.72 


1.37 


1.21 


300 


1.54 


1.26 


1.14 



FRICTION OF HYDRAULIC PLUNGER PACKING, 

The "Taschenbuch der Hutte" (15th edition, vol. 1. p. 202) says: "For 
stuffing-boxes with hemp, cotton or leather packing, with water pressures 
between 1 and 50 atmospheres, the frictional loss is dependent upon the 
water pressure, the circumference of the packed surface, and a coefficient 
u, which is constant tor this range of pressure. The loss is independent 
of the depth of stuffing-box or leather ring, and is given by the formula 
F = Kpd, in which F = total frictional loss in pounds, p = pressure in pounds 
per sq. in., rf = diameter of plunger in inches. 

K is Si coefficient, which depends on the kind and condition of the pack- 
ing, and is given as follows for various cases. 

For cotton or hemp, loose or braided, dipped in hot tallow; plungers 
smooth, glands not pulled down too tight, packing therefore retaining 
its elasticity; dimensions such as usually occur, iiC = 0.072. 

Same conditions, after packing is some months old, /v =0.132. 

Materials the same, but with hard packing, unfavorable conditions, 
etc., iC = as much as 0.299. 

Leather packing; soft leather, well made, etc., K = 0.036 to 0.084. 

Hard, stiffly tanned leather, K = 0.12 to 0.156. 

Unfavorable conditions; rough plungers, gritty water, etc., X = as much 
as 0.239. 

Weisbach-Hermann, " Mechanics of Hoisting Machinery," gives a 
formula which when translated into the same notation as the one in 
*' Hutte " is 

F = 0.0312 pd to 0.0767 pd. 

Since the total pressure on a plunger is Vizd'^p, the ratio of the loss of 
pressure to the total pressure is Kpd-^ViTid^p, or, using the extreme values 
of K, 0.0312 and 0.299, the ratio ranges from 0.04: ^d to 0.38 -^d, or from 
4 to 38 per cent divided by the diameter in inches. 

Walter Ferris (Am. Mach., Feb, 3, 1898) derives from the formula 
given above the following formula for the pressure produced by a hemp- 
packed hydraulic intensifier made with two plungers of different diameters: 

A-KD 

in which p2 = pressure per sq. in. produced by the intensifier, px= initial 
pressure, ^=area and Z) = diam. of the larger plunger, a = area and d = 
diam. of the smaller plunger, and K an experimental coefficient. He gives 
the following results of tests of an intensifier with a small plunger 8 ins. 
diam. and two large plungers, 14 V4 and 173/4 ins., either oije of which could 
be used as desired. 
Diam. of large plunger, in. ^ 14V4 14V4 173/4 173/4 



per sq. m. 
, lbs. per sq. in. 



285 


475 


335 


350 


750 


1450 


1450 


1510 


905 


1505 


1650 


1725 


806 


1433 


1572 


1643 


0.83 


0.965 


0.88 


0.875 



Initial pressure, lbs. 

Intensified pressure, 

Intensified if there were no friction 

Intensified calculated by formula* 

Efficiency of machine 

LUBRICATION. 

Measurement of the Durability of Lubricants. — (J. E. Denton, 
Trans. A. S. M. E., xi, 1013.) — Practical differences of durability of 
lubricants depend not on any differences of inherent ability to resist 
being "worn out" by rubbing, but upon the rate at which they flow 
through and away from the bearing-surfaces. The conditions which 



* Assuming K = 0.2. 
each case was 0.953. 



The efficiency calculated by the formula in 



1242 FRICTION AND LUBRICATION. 

control this flow are so delicate in their influence that all attempts thus 
far made to measure durability of lubricants may be said to have failed 
to make distinctions of lubricating value having any practical significance. 
In some kinds of service the limit to the consumption of oil depends upon 
the extent to which dust or other refuse becomes mixed with it, as in 
railroad-car lubrication and in the case of agricultural machinery. The 
economy of one oil over another, so far as the quality used is concerned — 
that is, so far as durabihty is concerned — is simply proportional to the 
rate at which it can insinuate itself into and flow out of minute orifices or 
cracks. Oils will differ in their ability to do this, first, in proportion to 
their viscosity, and, second, in proportion to the capillary properties which 
they may possess by virtue of the particular ingredients used in their 
composition. Where the thickness of film between rubbing-surfaces 
must be so great that large amounts of oil pass through bearings in a given 
time, and the surroundings are such as to permit oil to be fed at high 
temperatures or applied by a method not requiring a perfect fluidity, it is 
probable that the least amount of oil will be used when the viscosity is as 
great as in the petroleum cylinder stocks. When, however, the oil must 
flow freely at ordinary temperatures and the feed of oil is restricted, as in 
the case of crank-pin bearings, it is not practicable to feed such heavy 
oils in a satisfactory manner. Oils of less viscosity or of a fluidity 
approximating to lard-oil must then be used. 

Relative Value of Lubricants, (J. E. Denton, Am. Mack., Oct. 30, 
1890.) — The three elements which determine the value of a lubricant 
are the cost due to consumption of lubricants, the cost spent for coal to 
overcome the frictional resistance caused by use of the lubricant, and the 
cost due to the metallic wear on the journal and the brasses. 

The Qualifications of a Good Lubricant, as laid down by W. H. 
Bailey, in Proc. Ijist. C. E., vol. xlv, p. 372, are: 1. Sufficient body to 
keep the surfaces free from contact under maximum pressure. 2. The 
greatest possible fluidity consistent \\1th the foregoing condition. 3. The 
lowest possible coefficient of friction, which in bath lubrication would be 
for fluid friction approximately. 4. The greatest capacity for storing 
and carrying away heat. 5. A high temperature of decomposition. 
6. Power to resist oxidation or the action of the atmosphere. 7. Freedom 
from corrosive action on the metals upon which the lubricant is used. 

The Examination of Lubricating Oils. (Prof. Thos. B. Stillman, 
Stevens Indicator, July, 1890.) — The generally accepted conditions of 
a good lubricant are as follows: 

1. "Body" enough to prevent the surfaces to which it is applied from 
coming in contact with each other. (Viscosit3\) 

2. Freedom from corrosive acid, of either mineral or animal origin. 

3. As fluid as possible consistent with "body." 

4. A minimum coefficient of friction. 

5. High "flash" and burniner points. 

6. Freedom from materials liable to produce oxidation or "giunming." 
The examinations to be made to verify the above are both chemical and 

mechanical, and are usually arranged in the following order: 

1. Identification of the oil, whether a simple mineral oil, or animal oil, 
or a mixture. 2. Density. 3. Viscosity. 4. Flash-point. 5. Burning- 
point. 6. Acidity. 7. Coefficient of friction. 8. Cold test. 

Detailed directions for making all of the above tests are given in Prof. 
Stillman's article. See also Stillman's Engineering Chemistry, p. 366. 

Notes on Specifications for Petroleum Lubricants. (C. M. Everest, 
Vice-Pres. Vacuum Oil Co., Proc. Engineering Congress, Chicago World's 
Fair, 1893.) — The specific gravity was the first standard established for 
determining quality of lubricating oils, but it has long since been dis- 
carded as a conclusive test of lubricating quality. However, as the 
specific gravity of a particular petroleum oil increases the viscosity also 
increases. 

The object of the fire test of a lubricant, as well as its flash test, is the 
prevention of danger from fire through the use of an oil that will evolve 
inflammable vapors. The lowest fire test permissible is 300°, which gives 
a liberal factor of safety under ordinary conditions. 

The cold test of an oil, i.e., the temperature at which the oil will congeal, 
should^ be well below the temperature at which it is used; otherwise the 
coefiQcient of friction would be correspondingly increased.' 



LUBRICATION. 1243 

Viscosity, or fluidity, of an oil is usually expressed in seconds of time in 
which a given quantity of oil will flow through a certain orifice at the tem- 
perature stated, comparison sometimes being made with water, sometimes 
with sperm-oil, and again with rape-seed oil. It seems evident that 
within limits the lower the \isco.sity of an oil (without a too near approach 
to metallic contact of the rubbing surfaces) the lower will be the coefficient 
of friction. But we consider that each bearing in a mill or factory would 
probably require an oil of different viscosity from any other bearingin the 
mill, in order to give its lowest coefficient of friction, and that slight 
variations in the condition of a particular bearing would change the re- 
quirements of that bearing: and further, that when nearing the "danger 
point" the question of viscosity alone probably does not govern. 

The requirement of the New England Manufacturers' Association, that 
an oil shall not lose over 5% of its volume when heated to 140° Fahr. for 
12 hours, is to prevent losses by evaporation, with the resultant effects. 

The precipitation test gives no indication of the quaUty of the oil itself, 
as the free carbon in improperly manufactured oils can be easily removed. 

It is doubtful whether oil buyers who require certain given standards 
of laboratory tests are better served than those who do not. Some of 
the standards are so faulty that to pass them an oil manufacturer must 
supply oil he knows to be faulty; and the requirements of the best stand- 
ards can generally be met by products that will give inferior results in 
actual serivce. 

Penna. R. R. Specifications for Petroleum Products, 1900. — 
Five different grades of petroleum products will be used. 

The materials desired under this specification are the products of the 
distillation and refining of petroleum unmixed with any other substances. 

150° Fire-test Oil. — This grade of oil will not be accepted if sample 
(1) is not "water-white" in color; (2) flashes below 130° Fahrenheit; 
(3) burns below 151° Fahrenheit; (4) is cloudy or shipment has cloudy 
barrels when received, from the presence of glue or suspended matter; 
(5) becomes opaque or shows cloud when the sample has been 10 minutes 
at a temperature of 0° Fahrenheit. 

300° Fire-test Oil. — This grade of oil will not be accepted if sample 
(1) is not "water-white" in color; (2) flashes below 249° Fahrenheit; 
(3) burns below 298° Fahrenheit; (4) is cloudy or shipment has cloudy 
barrels when received, from the presence of glue or suspended matter; 
(5) becomes opaque or shows cloud when the sample has been 10 minutes 
at a temperature of 32° Fahrenheit; (6) shows precipitation when some 
of the sample is heated to 450° F. The precipitation test is made by 
having about two fluid ounces of the oil in a six-ounce beaker, with a 
thermometer suspended in the oil, and then heating slowly until the 
thermometer shows the required temperature. The oil changes color, 
but must show no precipitation. 

Paraffine and Neutral Oils. — These grades of oil will not be accepted 
if the sample from shipment (1) is so dark in color that printing with 
long-primer type cannot be read with ordinarv davlight through a layer of 
the oil 1/2 inch thick; (2) flashes below 298° F.: (3) has a gravity at 
60° F., below 24° or above 35° Baum^; (4) from October 1st to May 1st 
has a cold test above 10° F., and from May 1st to October 1st has a cold 
test above 32° F. 

The color test is made by having a layer of the oil of the prescribed 
thickness in a proper glass vessel, and then putting the printing on one 
side of the vessel and reading it through the layer of oil with the back 
of the observer toward the source of light. 

Well Oil. — This grade of oil will not be accepted if the sample from 
shipment (1) flashes, from May 1st to October 1st, below 298° F., or 
from October 1st to May 1st, below 249° F.; (2) has a gravity at 60° F., 
below 28° or above 31° Baum^; (3) from October 1st to May 1st has 
a cold test above 10° F., and from May 1st to October 1st has a cold test 
above 32° F.; (4) shows any precipitation when 5 cubic centimeters are 
mixed with 95 c.c. of gasoline. The precipitation test is to exclude tarry 
and suspended matter. It is made by putting 95 c.c. of 88° B. gasoline, 
which must not be above 80° F. in temperature, into a 100 c.c. graduate, 
then adding the prescribed amount of oil and shaking thoroughly. Allow 
to stand ten minutes. With satisfactory oil no separated or precipitated 
material can be seen. 



1244 



FEICTION AND LUBRICATION. 



500° Fire-test Oil, — This grade of oil will not be accepted if sample 
from shipment (1) flashes below 494° F.; (2) shows precipitation with 
gasoline when tested as described for well oil. 

Printed directions for determining flashing and burning tests and for 
making cold tests and taking gravity are furnished by the railroad company. 

Penna. R. R. Specifications for Lubricating Oils (1894). (In 
force in 1902.) 



Constituent Oils. 


Parts by volume. 


Extra lard-oil 


















1 


Extra No. 1 lard-oil 






1 
1 
4 


1 
1 
2 


1 

2 

1 


1 
1 


1 
1 


I 
2 




500° fire-test oil 




1 


4 


ParaflSne oil 






Well oil 


1 




4 


2 


1 
















Used for 


4 


B 


Ci 


C2 


Cs 


2)i 


D2 


Dz 


F 









A, freight cars; engine oil on shifting-engines.; miscellaneous greasing 
in foundries, etc. B, cylinder lubricant on marine equipment and on 
stationary engines. C, engine oil; all engine machinery; engine and 
tender truck boxes; shafting and machine tools; bolt cutting; general 
lubrication except cars. D, passenger-car lubrication. E, cylinder 
lubricant for locomotives. Ci, Di, for use in Dec, Jan., and Feb.; Cj, 
Z)2, in March, April, May, Sept., Oct., and Nov.; Cs, Dz, in June, July, 
and August. Weights per gallon. A, 7.4 lbs.; B, C, D, E, 7.5 lbs. 

Grease Lubricants. — Tests made on an Olsen lubricant testing machine 
at Cornell University are reported in Power, Nov. 9, 1909. It was found 
that some of the commercial greases stood much higher pressures than 
the oils tested, and that the coefRcients of friction at moderate loads were 
often as low as those of the oils. The journal of the testing machine 
was 3 3/4 in. diam . , 3 V2 in. long, and the babbitt bearing shoe had a projected 
area of 5.8 sq. in. The speed v/as 240 r.p.m. and each test lasted one 
hour, except when the bearing showed overheating. The following are 
the coefficients of friction obtained in the tests: 



Lbs. 

per 

sq.iii. 


Min- 1 Ani- 

eral mal 

Grease, IQrease. 


Graph- 
ite 
Grease. 


Min- 
eral 
Grease. 


Engine 


Engine 
Oil. 


Grease. 


Grease. 


86.2 
172.4 
258.6 
344 8 


0.024 
0.021 
0.021 
0.025 
0.050 


0.023 0.04 . 0.023 
0.023 0.05 0.018 

0.023 , 0.018 

0.025 1 0.019 


0.019 

0.04 

0.06 


0.015 
0.022 
0.037 


0.020 
0.015 
0.014 
0.017 
0.026 


0.025 
0.022 
0.020 
0.020 


431.0 


0.035 




0.028 






0.019 



Testing Oil for Steam Turbines. (Robert Job, Trans. Am. Soc. for 
Testing Matls., 1909.) — 

In some types of steam-turbines, the bearings are very closely adjusted 
and, if the oil is not clear and free from waxy substances, clogging and 
heating quickly results. A number of red engine and turbine oils some 
of which had given good service and others bad service were tested and 
it was found that clearness and freedom from turbidity were of importance, 
but mere color, or lack of color, seemed to have little influence, and good 
service results were obtained with oils which were of a red color, as well 
as with those which were filtered to an amber color. 

Heating Test. — It was found that on heating the oils to 450° F. all 
which had given bad service showed a marked darkening of color, while 
those which had proved satisfactory showed little change. With oils 
that had been filtered or else had been chemically treated in such manner 
that the so-called " amorphous waxes " had been completely removed, 
on applying the heating test only a slight darkening of color resulted. 
It is of advantage in addition to other requirements to specify that an 
Oil for steam turbines on being heated to 450° F. for five rninutes shall 
show not more than a slight darkening of color. The test is that com- 
monly used in test of 300° oil for burning purposes. 

Separating Test. — It is known that elimination of the waxes causes an 
increase in the ease \\1th which the oil separates from hot water when 
thoroughly shaken with it. This condition can be taken advantage 9f 
by prescribing that when one ounce of the oil is placed in a 4-oz. bottie 



LtTBKlCATION. 1245 

with two ounces of boiling water, the bottle corked and shaken hard for 
one minute and let stand, the oil must separate from the water within a 
specified time, depending upon the nature of the oil, and that there must 
be no appearance of waxy substances at the line of demarcation between 
the oil and the water. 

Quantity of Oil needed to Rim an Engine. — The Vacuum Oil Co. in 
1892, in response to an inquiry as to cost of oil to run a 1000-H.P. Corliss 
engine, wrote: The cost of running two engines of equal size of the same 
make is not always the same. Therefore, while we could furnish figures 
showing what it is costing some of our customers having Corliss engines 
of 1000 H.P., we could only give a general idea, which in itself might be 
considerably out of the way as to the probable cost of cylinder- and 
engine-oils per year for a particular engine. Such an engine ought to 
run readily on less than 8 drops of 600 W oil per minute. If 3000 drops 
are figured to the quart, and 8 drops used per minute, it would take about 
two and one half barrels (52.5 gallons) of 600 W cyUnder-oil, at 65 cents 
per gallon, or about $85 for cyUnder-oil per year, running 6 days a week 
and 10 hours a day. Engine-oil would be even more difficult to guess at 
what the cost would be, because it would depend upon the number of 
cups required on the engine, which varies somewhat according to the 
style of the engine. It would doubtless be safe, however, to calculate 
at the outside that not more than twice as much engine-oil would be 
required as of cvlinder-oil. 

The Vacuum Oil Co. in 1892 published the following results of practice 
with "600 W" cylinder-oil: 

Corliss compound engine. { 20 and 33 x 48; 83 revs, per min.; 1 drop of 

^ ° ' I oil per min. to 1 drop in two minutes. 

triple exp. *• 20, 33, and 46 x 48; 1 drop every 2 minutes. 

(20 and 36 x 36; 143 revs, per min.; 2 drops 

Porter- Allen " < of oil per min„, reduced afterwards to 1 drop 

( per min. 
T>-n M ns and 25 x 16; 240 revs, per min.; 1 dfop 

( every 4 minutes. 

Results of tests on ocean-steamers communicated to the author by 
Prof. Denton in 1892 gave: for 1200-H.P. marine engine, 5 to 6 EngHsh 
gallons (6 to 7.2 U. S. gals.) of engine-oil per 24 hours for external lubri- 
cation; and for a 1600-H.P. marine engine, triple expansion, running 
75 revs, per min., 6 to 7 EngUsh gals, per 24 hours. The cylinder-oil 
consumption is exceedingly variable, — from 1 to 4 gals, per day on 
different engines, including cyUnder-oil used to swab the piston-rodd. 

Cylinder Lubrication. — J. H. Spoor, in Power, Jan. 4. 1910, has made 
a study of a great number of records of the amount of oil used for lubri- 
cating icylinders of different engines, and has reduced them to a svs- 
tematic basis of the equivalent number of pints of oil used in a lO-hour 
day for different areas of surface lubricated. The surface is determined 
in square inches by multiplying the circumference of the cylinder by the 
length of stroke. The results are plotted in a series of curves for different 
types of engines, and approximate average figures taken from these curves 
are given below: 

Compound Engines. 

Sq. ins. lubricated 2,000 4,000 6,000 8,000 10,000 12,000 18,000 

Pints of oil used in 10 hrs. 2 3.5 4.3 5 5.5 6 6.5 
Corliss Engines. 

Sq. ins. lubricated 1,000 2,000 3,000 4,000 

Pints of oil in 10 hrs. Avge 0.9 1.65 2.25 3.75 

Max 1.2 2.25 

Min 1.00 

Automatic high-speed engines, about 2 pints per 1.000 sq. in. 

Simple slide-valve engines, about 0.5 pint per 1,000 sq. in. 

As shown in the figures under 2,000 Corliss, a certain engine may take 
21/4 times as much oil as another engine of the .same size. The difference 
may be due to smoothness of cylinder surface, kind and pressure of piston 
rings, quality of oil, method of Introducing the lubricant, etc. Variations 
in speed of a given type of engine and in steam pressure do not appear to 
make much difference, but the small automatic high-speed engine takes 
more oil than any other type. Vertical marine engines are commonly run 



1246 FRICTION AND LUBRICATION. 

without any cylinder oil, except that used occasionally to swab the piston 
rods. 

Quantity of Oil used on a Locomotive Crank-pin. — Prof. Denton, 
Trans. A. S. M, E., xi, 1020, says: A very economical case of practical 
oil-consumption is when a locomotive main crank-pin consumes about 
six cubic inches of oil in a thousand miles of service. This is equivalent 
to a consumption of one milUgram to seventy square inches of surface 
nibbed over. 

Soda Mixture for Machine Tools* (Penna. R. R. 1894.) — Dissolve 
6 lbs. of common sal-soda in 40 gallons of water and stir thoroughly. 
When needed for use mix a gallon of this solution with about a pint of 
engine oil. Used for the cutting parts of machine tools instead of oil. 

Water as a Lubricant. (C. W. Naylor, Trans. A. S. M. E., 1905.) — 
Two steel jack-shafts 18 ft. long with bearings 5 X 14 ins. each receiving 
175 H.P. from engines and driving 5 electric generators, with six belts all 
pulling horizontally on the same side of the shaft, gave trouble by heating 
when lubricated with oil or grease. Water was substituted, and the snafts 
ran for 1 1 years, 10 hours a day, without serious interruption. Oil was fed 
to the shaft before closing down for the night, to prevent rusting. The 
wear of the babbitted bearings in 11 years was about V4 in., and of the shaft 
nil. 

Acheson's " Deflocculated " Graphite. {Trans. A. I. E. E., 1907; 
Eng. News, Aug. 1, 1907.) — In 1906, Mr. E. G. Acheson discovered a 
process of producing a fine, pure, unctuous graphite in the electric fur- 
nace. He calls it deflocculated graphite. By treating this graphite 
in the disintegrated form with a water solution of tannin, the amount 
of tannin being from 3% to 6% of the weight of the graphite treated, 
he found that it would be retained in suspension in water, and that it 
was in such a fine state of subdivision that a large part of it would run 
through the finest filter paper, the filtrate being an intensely black liquid 
in which the graphite would remain suspended for months. The addition 
of a minute quantity of hydrochloric acid causes the graphite to floccu- 
late and group together so that it will no longer flow through filter paper. 
The same effect has been obtained with alumina, clay, lampblack and 
siloxicon, by treatment with tannin. The graphite thus suspended in 
water, known as ''aquedag," has been successfully used as a lubricant 
for journals with sight-feed and with chain-feed oilers. It also prevents 
rust in iron and steel. The deflocculated graphite has also been sus- 
pended in oil, in a dehydrated condition, making an excellent lubricant 
known as "oildag.** Tests by Prof. C. H. Benjamin of oil with 0.5% 
of graphite showed that it had a lower coefiBcient of friction than the oil 
alone. 

SOLID LUBRICANTS. 

Graphite in a condition of powder and used as a solid lubricant, so 
called, to distinguish it from a liquid lubricant, has been found to do well 
where the latter has failed. 

Rennie, in 1829, says: "Graphite lessened friction in all cases where it 
was used." General Morin, at a later date, concluded from experiments 
that it could be used with advantage under heavy pressures: and Prof. 
Thurston found it well adapted for use under both hght and heavy pres- 
sures when mixed with certain oils. It is especially valuable to prevent 
abrasion and cutting under heavy loads and at low velocities. 

For comparative tests of various oils with and without graphite, see 
paper on lubrication and lubricants, by C. F. Mabery, Jour. A.S.M.E., 
Feb.. 1910. 

Soapstone, also called talc and steatite, in the form of powder and 
mixed with oil or fat, is sometimes used as a lubricant. Graphite or 
soapstone, mixed with soap, is used on surfaces of wood working against 
either iron or wood. 

Metaline is a solid compound, usually containing graphite, made in the 
form of small cylinders which are fitted permanently into holes drilled 
in the surface of the bearing. The bearing thus fitted runs without any 
other lubrication. j r. xi« 

Bushings fitted with graphite packed into grooves are made by tne 
Graphite Lubricating Co., Bound Brook, N. J. 



THE FOUNDRY. 



1247 



THE FOUNDRY. 

(See also Cast-iron, pp. 437 to 445, and Fans and Blowers, pp. 653 to 673.) 

Cupola Practice. 

The following table and the notes accompanying it are condensed from 
an article by Simpson Bolland in Am. Mach., June 30, 1892: 



Diam. of lining, in 

Height to char'g door, It. .. 

Fuel used in bed, lbs 

First charge of iron, lbs. . . . 

Other fuel charges, lbs 

Other iron charges, lbs 

Diam. blast pipe, in 

No. of 6-in. round tuyeres. . 

Equiv. No. flat tuyeres 

Width of flat tuyeres, in — 
Height of flat tuyeres, in. . . 

Blast pressure, oz 

Size of Root blower, No 

Revs, per min 

Engine for blower, H.P 

Sturtevant blower. No 

Engine for blower, H.P 

Melting cap., lbs. per hr 



36 


48 


54 


60 


66 


72 


12 


13 


14 


15 


15 


16 


840 


1380 


1650 


1920 


2190 


2460 


2520 


4140 


4950 


5760 


6570 


7380 


302 


554 


680 


806 


932 


1058 


2718 


4986 


6120 


7254 


8388 


9522 


14 


18 


20 


22 


22 


24 


3.7 


6.8 


10.7 


13.7 


15.4 


19 


4 


6 


» 


8 


8 


10 


2 


2.5 


2.5 


3 


3 


3 


13.5 


13.5 


15.5 


16.5 


18.5 


18.5 


8 


12 


14 


14 


14 


16 


2 


4 


4 


5 


5 


6 


241 


212 


277 


192 


240 


163 


2.5 


10 


14 


181/2 


23 


33 


4 


6 


7 


8 


8 


9 


3 


93/4 


16 


22 


22 


35 


4820 


10,760 


13,850 


16,940 


21,200 


26,070 



84 
16 
3000 
9000 
1310 
11,790 
26 
31 
16 
3.5 
16 
16 
7 
160 
47 
10 
48 
37,530 



Mr. Bolland says that the melting capacities in the table are not sup-; 
posed to be all that can be melted in the hour by some of the best cupolas, 
but are simply the amounts which a common cupola under ordinary 
circumstances may be expected to melt in the time specified. 

By height of cupola is meant the distance from the base to the bottom 
side of the charging door. The distance from the sand-bed, after it has 
been formed at the bottom of the cupola, up to the under side of the 
tuyeres is taken at 10 ins. in all cases. 

All the amounts for fuel are based upon a bottom of 10 ins. deep. The 
quantity of fuel used on the bed is more in proportion as the depth is 
increased, and less when it is made shallower. 

The amount of fuel required on the bed is based on the supposition that 
the cupola is a straight one all through, and that the bottom is 10 ins. 
deep. If the bottom be more, as in those of the Colliau type, then addi- 
tional fuel will be needed. 

First Charge of Iron. — The amounts given are safe figures to work upon 
in every insiance, yet it will always be in order, after proving the ability 
of the bed to carry the load quoted, to make a slow and gradual increase 
of the load until it is fully demonstrated just how much burden the bed 
will carry. 

Succeeding Charges of Fuel and Iron. — The highest proportions are 
not favored, for the simple reason that successful melting with any greater 
proportion of iron to fuel is not the rule, but, rather, the exception. 

Diameter of Main Blast-pipe. — The sizes given are of sufficient area 
for all lengths up to 100 feet. 

Tuyeres. — Any arrangement or disposition of tuyeres may be made, 
which shall answer in their totality to the areas given in the table. On no 
consideration must the tuyere area be reduced; thus, an 84-inch cupola 
must have tuyere area equal to 31 pipes 6 ins. diam., or 16 flat tuyeres 
16 X 31/2 ins. The tuyeres should be arranged in such a manner as will 
concentrate the fire at the melting-point into the smallest possible com- 
pass, so that the metal in fusion will have less space to traverse while 
exposed to the oxidizing influence of the blast. 

To accomplish this, recourse has been had to the placing of additional 
rows of tuyeres in some instances — the "Stewart rapid cupola" having 
three rows, and the "Colliau cupola furnace" having two rows, of tuyeres. 



1248 TSE FOUNDI^Y. 

[Cupolas as large as 84 inches in diameter are now (1906) built without 
boshes. The most recent development with this size cupola is to place a 
center tuyere in the bottoin discharging air vertically upwards.] 

Blast-pressure. — About 30,000 cu. ft. of air are consumed in melting a 
ton of iron, which would weigh about 2400 pounds, or more than both 
iron and fuel. When the proper quantity of air is supplied, the com« 
bustion of the fuel is perfect, and carbonic-acid gas is the result. When 
the supply of air is insufficient, the combustion is imperfect, and car- 
bonic-oxide gas is the result. The amount of heat evolved in these two 
cases is as 15 to 4V2, showing a loss of over two-thirds of the heat by 
imperfect combustion. [Combustion is never perfect in the cupola except 
near the tuyeres. The CO2 formed by complete combustion is largely 
reduced to CO in passing through the hot coke above the fusion zone.] 

It is not always true that we obtain the most rapid melting when we are 
forcing into the cupola the largest quantity of air. Too much air absorbs 
heat, reduces the temperature, and retards combustion, and the fire in the 
cupola may be extinguished with too much blast. 

Slag in Cupolas. — A certain amount of slag is necessary to protect the 
molten iron which has fallen to the bottom from the action of the blast; if 
it was not there, the iron would suffer from decarbonization. 

When slag from any cause forms in too great abundance, it should be 
led away by inserting a hole a little below the tuyeres, through which it 
will find its way as the iron rises in the bottom. 

With clean iron and fuel, slag seldom forms to any appreciable extent 
in small heats: but when the cupola is to be taxed to its utmost capacity 
it is then incumbent on the melter to flux the charges all through the heat, 
carrying it away in the manner directed. 

The best flux for this purpose is the chips from a white-marble yard. 
About 6 pounds to the ton of iron will give good results when all is clean. 
[Fluor-spar is now largely used as a flux.] 

When fuel is bad, or iron is dirty, or both together, it becomes imperative 
that the slag be kept running all the time. 

Fuel for Cupolas. — The best fuel for melting iron is coke, because it 
requires less blast, makes hotter iron, and melts faster than coal. When 
coal must be used, care should be exercised in its selection. All anthra- 
cites which are bright, black, hard, and free from slate, will melt iron 
admirably. For the best results, small cupolas should be charged with 
the size called ''tgg," a still larger grade for medium-sized cupolas, and 
what is called "lump" will answer for all large cupolas, when care is taken 
to pack it carefully on the charges. 

Melting Capacity of Different Cupolas. — The following figures 
are given by W. B. Snow, in The Foundry, Aug., 1908, showing the 
records of capacity and the blast pressure of several cupolas: 
Diam. of lining, 

ins 44 44 47 49 54 54 54 60 60 60 74 

Tons per hour.. 6.7 7.3 8.4 9.1 7.7 8.8 10.2 12.4 14.8 13.8 13.0 
Pressure, oz. per 

sq. in 12.9 16.4 17.5 11.8 13.6 11.0 20.8 15.5 16.8 12.6 8.7 

From plotted diagrams of records of 46 tests of different cupolas the 
following figures are obtained: 

Diam. of lining, ins 30 36 42 48 54 60 66 72 

Max. tons per hour 3 5 7.3 9.5 12 15 18 21 

Avge. " " " 2.5 4 5.5 7.5 9 11 13 16 

Max. pressure, oz 11 12 13.5 14 14.6 15.2 15.7 16 

For a given cupola and blower the melting rate increases as the square 
root of the pressure. A cupola melting 9 tons per hour with 10 ounces 
pressure will melt about 10 tons with 12.5 ounces, and 11 tons with 15 
ounces. The power required varies as the cube of the melting rate, so 
that it would require (11/9)3 = 1.82 times as much power for 11 tons as 
for 9 tons. Hence the advantage of large cupolas and blowers with light 
pressures 

Charging a Cupola, — Chas. A, Smith (Am. Mach., Feb. 12, 1891) 
gives the following: A 28-in. cupola should have from 300 to 400 lbs. of 
coke on bottom bed; a 36-in. cupola, 700 to 800 lbs.; a 48-in. cupola, 
1600 lbs.; and a 60-in. cupola should have one ton of fuel on bottom bed. 



THE FOUNDRY. 



1249 



To every pound of fuel on the bed, three, and sometimes four pounds of 
metal can be added with safety, if the cupola has proper blast; in after- 
charges, to every pound of fuel add 8 to 10 pounds of metal; any well- 
constructed cupola will stand ten. 

F. P. Wolcott (Am. Mack., Mar. 5, 1891) gives the following as the 
practice of the Colwell Iron-works, Carteret, N. J.: "We melt daily from 
twenty to forty tons of iron, with an average of 11.2 pounds of iron to 
one of fuel. In a 36-in. cupola seven to nine pounds is good melting, 
but in a cupola that lines up 48 to 60 inches, anything less than nine 
pounds shows a defect in arrangement of tuyeres or strength of blast, 
or in charging up." 

"The Holder's Text-book," by Thos. D. West, gives forty-six reports 
in tabular form of cupola practice in thirty States, reaching from Maine 
to Oregon. 

Improvement of Cupola Practice. — The following records are given 
by J. R. Fortune and H. S. Wells {Proc. A. S. M. E., Mar., 1908) showing 
how ordinary cupola practice may be improved by making a few changes. 
The cupola is 13 ft. 4 in. in height from the top of the sand bottom to 
the charging door, and of three diameters, 50 in. for the first 3 ft. 6 in., 
then 54 in. for the next 2 ft. 4 in., then 60 in. to the top. When driven 
with a No. 8 Sturtevant blower, the maximum melting rate, from iron 
down to blast off, was 8.5 tons per hour. A No. 11 high-pressure blower 
was then installed. Test No. 1 in the table below gives the result with 
cupola charges as follows in pounds: Bed, 590 coke, followed by 826 coke, 
2000 iron; 400 coke, 2000 iron; 300 coke, 2000 iron; and thereafter all 
charges were 200 coke, 2000 iron. The time between starting fire and start- 
ing blast was 2 hr. 30 min., and the time from blast on to iron down, 
11 min. The melting rate, tons per hour, is figured for the time from 
iron down to blast off. The tuyeres were eight rectangular openings 
111/4 in. high and of a total area of 1/9.02 of the area of the 54-in. circle. 



No. of Test. 



Total tons. .. 
Tons per hr.. 
Lbs. permin* 
Iron -r- cokef 
Blast, oz 



1 



22.7 
9.45 

19.81 
7.54 

11.60 



24. 

8.88 
18.61 

7.40 
10.63 



22.15 
8.86 

18.55 
7.28 

10.00 



24.25 
9.15 

19.17 
8.58 
9.47 



24.25 
9.66 

20.25 
8.94 
9. 



22.65 

10.24 

21.44 

8.71 

9.86 



24. 
10.43 
21.82 
9.02 
10.00 



8 


9 


10 


20.30 


23.85 


22.35 


10.91 


11.35 


11.17 


22,95 


23.77 


23.39 


9.02 


10.02 


9.49 


10.13 


10.55 


10.55 



* Per sq. ft. cupola area at 54 in. diam. from iron down to blast ofif. 
t Including bed. 

The tuyeres were then enlarged, making their area 1/5.98 of the cupola 
(54 in.) area, and the results are shown in tests No. 2 and 3 of the table. 
The iron was too hot, and the coke charge was decreased to a ratio of 
1/13.33 Instead of 1/10, the bed of coke being increased. The result, 
test No. 4, was an increased rate of melting, a decrease in the amount of 
coke, and a decrease in the blast pressure. Tests 5, 6, 7, 8 and 9 were 
then made, the coke being decreased, while the blast pressure was in- 
creased, resulting in a decided increase in the melting speed. In tests 
5, 6 and 7 the iron layer was 13.33 times the weight of the coke layer; 
in test 8, 14.28 times; and in test 9, 15.38 times. In test 9 it was noticed 
that the iron was not at the proper temperature, and in test 10 the coke 
layer was increased to a ratio of 1 to 14.28 without altering the blast 
pressure; this resulted in a decreased melt per hour. It has been found 
that a coke charge of 150 lbs. to 2000 lbs. of iron, with a blast pressure 
of 10.5 ounces, results in a melt of 11.5 tons per hour, the iron coming 
down at the proper temperature. 

An excess of coke decreases the melting rate. Iron in the cupola is 
melted in a fixed zone, the first charge of iron above the bed being melted 
by burning coke in the bed. As this iron is melted, the charge of coke 
above it descends and "restores to the bed the amount which has been 
burned away. If there is too much coke in the charge, the iron is held 
above the melting zone, and the excess coke must be burned away before 
it can be melted, and this of course decreases the economy and the melting 
speed. 



1250 



THE FOUNDRY. 



Cupola Charges in Stove-foundries. {Iron Age, April 14, 1892.) — 
No two cupolas are charged exactly the same. The amount of fuel on 
the bed or between the charges differs, while varying amounts of iron are 
used in the charges. Below will be found charging-lists from some of the 
prominent stove-foundries in the country: 



lbs 

A— Bed of fuel, coke 1,500 

First charge of iron 5,000 

All other charges of iron 1 ,000 

First and second charges of 
coke, each 200 



lbs. 
Four next charges of coke, 

each 150 

Six next charges of coke, each 120 
Nineteen next charges of coke, 

each 100 



Thus for a melt of 18 tons there would be 5120 lbs. of coke used, giving 
a ratio of 7 to 1. Increase the amount of iron melted to 24 tons, and a 
ratio of 8 pounds of iron to 1 of coal is obtained. 



lbs. 



Second and third charges of 
fuel 

All other charges of fuel, 
each 



lbs 



B— Bed of fuel, coke 1,600 

First charge of iron 1,800 

First charge of fuel . 150 

All other charges of iron, 

each 1,000 

For an 18-ton melt 5060 lbs. of coke would be necessary, giving a ratio 
of 7.1 lbs. of iron to 1 pound of coke. 

lbs. 

C— Bed of fuel, coke 1,600 

First charge of iron 4,000 

First and second charges of 

coke 200 

In a melt of 18 tons 4100 lbs. of coke would be used, or a ratio of 8.5 to 1. 



130 
100 



lbs. 



All other charges of iron 2,000 

All other charges of coke 150 



lbs. 

D— Bed of fuel, coke 1 ,800 

First charge of iron 5,600 



lbs 

All charges of coke, each 200 

All other charges of iron 2,900 

In a melt of 18 tons, 3900 lbs. of fuel would be used, giving a ratio of 
9.4 pounds of iron to 1 of coke. Very high, indeed, for stove-plate. 

lbs. 



All other charges of iron, each 2,000 
All other charges of coal, each 175 



lbs. 

E— Bed of fuel, coal 1,900 

First charge of iron 5,000 

First charge of coal 200 

In a melt of 18 tons 4700 lbs. of coal would be used, giving a ratio of 
7.7 lbs. of iron to 1 lb. of coal. 

These are sufficient to demonstrate the varying practices existing 
among different stove-foundries. In all these places the iron was proper 
for stove-plate purposes, and apparently there was little or no difference 
in the kind of work in the sand at the different foundries. 

Foundry Blower Practice. (W. B. Snow, Trans. A. S. M. E„ 
1907.) — The v elocity of air produced by a blower is expressed by the 
formula V = V^2 gp/d. If p, the pressure, is taken in ounces per sq. in., 
and d, the density, in pounds per cu. ft. of dry air at 50° and atmospheric 
pressure o f 14.69 lbs, or 235 oun ces. = 0.77884 lb., the formula reduces 
to y = v^l, 746,700 p/(235 + p), no allowance being made for change of 
temperature during discharge. From this formula the following figures 
are obtained. Q = volume discharged per min. through an orifice of 
1 sq. ft. effective area, H.P. = horse-power required to move the given 
volume under the given conditions, p = pressure in ounces per sq. in. 



p 


Q 


H.P. 


P 


Q 


H.P. 


P 


Q 


H.P. 


P 


Q 


H.P. 


I 


35.85 


0.00978 


6 


86.89 


0.1422 


11 


116.45 


0.3493 


16 


139.03 


0.6067 


2 


50.59 


0.02759 


7 


93.66 


0.1788 


12 


121.38 


0.3972 


17 


143.03 


0.6631 


3 


61.83 


0.05058 


8 


99.92 


0.2180 


13 


126.06 


0.4470 


18 


146.88 


0.7211 


4 


71.24 


0.07771 


9 


105.76 


0.2596 


14 


130.57 


0.4986 


19 


150.61 


0.7804 


5 


79.48 


0.1084 


10 


111.25 


0.3034 


15 


134.89 


0.5518 


20 


154.22 


0.8412 



The greatest effective area over which a fan will maintain the maximum 
velocity of discharge is known as the "capacity area" or "square inches 
of blast." As originally established by Sturtevant it is represented by 
(>W/3, D = diam. of wheel in ins., W = width of wheel at circumference. 



THE FOUNDRY. 



1251 



in inches. For the ordinary type of fan at constant speed maximum 
efficiency and power are secured at or near the capacity area; the powet 
per unit of volume and the pressure decrease as the discharge area and 
volume increase; with closed outlet the power is approximately one-third 
of that at capacity area. 

The following table is calculated on these bases: Capacity area per inch 
of width at periphery of wheel = 1/3 of diam. Air, 50° F. Velocity 
of discharge = circumferentiar speed of the wheel. Power = double the 
theoretical. In rotary positive blowers, as well as in fans, the velocity 
and the volume vary as the number of revolutions, the pressure varies 
as the square, and the power as the cube of the number of revolutions. 
In the fan, however, increase of pressure can be had only by increasing 
the revolutions, while in the rotary blower a great range of pressure is 
obtainable with constant speed by merely varying the resistance. With a 
rotary blower at constant speed, theoretically, and disregarding the effect 
of changes in temperature and density, the volume is constant: the velocity 
varies inversely as the effective outlet area; the pressure varies inversely 
as the square of the outlet area, hence as the square of the velocity; 
and the power varies directly as the pressure. The maximum power is 
required when a fan discharges against the least, and when a rotary 
blower discharges against the greatest resistance. 



Performance 


OF Cupola Fan Blowers at Capacity Area 
OF Peripheral Width. 


PER 


Inch 


in 

0-; 




Total Pressure in Ounces per Square loch. 


S^ 


Item. 




















1 






6 


7 


8 


9 


10 


11 


12 


13 


14 


15 16 


18 


r.p.m. 
cu. ft. 
h.p. 


2660.0 

520.0 

1.7 


2860.0 

560.0 

2.1 


3050.0 

600.0 

2.6 


3230.0 

640.0 

3.1 


3400.0 

670.0 

3.6 


3560.0 

700.0 

4.2 


3710.03850.0 

730.0! 760.0 

4.8 5.4 


3990.0 

780.0 

6.0 


4120.0 

810.0 

6.6 


4250.0 

830.0 

7.3 


24 1 


r.p.m. 
cu. ft. 
h.p. 


2000.0 

700.0 

2.3 


2150.0 

750.0 

2.9 


2290.0 

800.0 

3.5 


2420.0 

850.0 

4.2 


2550.0 

890.0 

4.9 


2670.0 

930.0 

5.6 


2780.0 

970.0 

6.4 


2890.0 

1010.0 

7.1 


2990.0 

1040.0 

8.0 


^090.0 

1080.0 

8.8 


3190.0 

1110.0 

9.7 


"l 


r.p.m. 
cu. ft. 
h.p. 


1590.0 
870.0 

2.8 


1720.0 

940.0 

3.6 


1830.0 

1000.0 

4.4 


1940.0 

1060.0 

5.2 


2040.0 

1110.0 

6.1 


2140.0 

1160.0 

7.0 


2230.0 

1210.0 

7.9 


2310.0 

1260.0 

8.9 


2390.0 

1310.0 

10.0 


2470.0 

1350.0 

11.0 


2550.0 

1390.0 

12.1 


"I 


r.p.m. 
cu. ft. 
h.p. 


1330.0 

1040.0 

3.4 


1430.0 

1120.0 

4.3 


1530.0 

1200.0 

5.2 


1620.0 

1270.0 

6.2 


1700.0 

1340.0 

7.3 


1780.0 

1400.0 

8.4 


1850.0 

1460.0 

9.5 


1930.0 

1510.0 

10.7 


2000.0 

1570.0 

11.9 


2060.0 

1620.0 

13.2 


2120.0 

1670.0 

14.5 


«j 


r.p.m. 
cu. ft. 
h.p. 


1140.0 

1220.0 

3.9 


1230.0 

1310.0 

5.0 


1310.0 

1400.0 

6.1 


1380.0 

1480.0 

7.3 


1460.0 
1560.0 

8.5 


1530.0 

1630.0 

9.8 


1590.0 

1700.0 

11.1 


1650.0 

1770.0 

12.5 


1710.0 

1830.0 

13.9 


1770.0 

1890.0 

15.4 


1820.0 

1950.0 

17.0 


48 J 


r.p.m. 
cu. ft. 
h.p. 


1000.0 

1390.0 

4.5 


1070.0 

1500.0 

5.7 


1150.0 

1600.0 

7.0 


1210.0 

1690.0 

8.3 


1270.0 

1780.0 

9.7 


1330.0 

1860.0 

11.2. 


1390.0 

1940.0 

12.7, 


1450.0 

2020.0 

14.3 


1500.0 

2090.0 

15.9, 


1550.0 

2160.0 

17.7 


1590.0 

2230.0 

21.0 



The air supply required by a cupola varies with the melting ratio, the 
density of the charges, and the incidental leakage. Average practice is 
represented by the following: 

Lbs. iron per lb. coke 6 7 8 9 10 

Cu. ft. air per ton of iron 33,000 31,000 29,000 27,000 25,000 

It is customary to provide blower capacity on a basis of 30,000 cu. ft., 
which corresponds to 75 to 80% of the chemical requirements for complete 
combustion with average coke, and a melting ratio of 7.5 to 1. 

In comparative tests with a 54-inch lining cupola under identical con- 
ditions as to contents, alternately run with a No. 10 Sturtevant fan and 
a 33 cu. ft. Connersville rotary, with the fan the pressure varied between 
I2V2 and 141/8 ounces in the wind box, the net power from 25 to 38.5 H.P., 
while with the rotary blower the pressure varied between 10 1/2 and 25 
ounces, and the power between 19 and 45 H.P. With the fan 28.84 tons 



1252 



THE FOUNDRY. 



were melted in 3.77 hours, or 7.65 tons per hour, while with the rotary- 
blower 2.82 hours were required to melt 31.5 tons, an hourly rate of 10.6 
tons, an increase of nearly 40 per cent in output. This reduces to a net 
input of 4.09 H.P. per ton melted per hour with the fan, and 2.98 H.P. 
with the rotary blower; an apparent advantage of 27% in favor of the 
rotary. Had the rotary been of smaller capacity such excessive pressures 
would not have been necessary, the power would have been decreased, 
and the duration of the heat prolonged, *with probable decrease in the 
H.P. hours per ton. Had the fan been run at higher speed the H.P. 
would have increased, the time decreased and the power per ton per hour 
would have more closely approached that required by the rotary blower. 
Theoretically, for otherwise constant conditions, the following relations 
hold for cupolas and melting rates within the range of practical operation: 

For a given_cupolaj For a given melting rate: For a given volume: 

Af X F,Vp. or yiTp. Focl--Z)2 M cc D 

" -- Pqc d 

H.P. X POTl -f- 2)4 



Foe M 

Poo V^ _ 

H.P. oc ikf3 or Vps 



Ecx,M,P, oil -^ D* 



For a given cupola 
E oc M2, or P 

Duration of h^at 
oc 1 -=- Vp 

M = melting rate; F = volume; P = pressure; H.P. = horse-power; 
D = diam. of lining; E = operating efficiency = power per ton per hour; 
d = depth of the charge; oc, varies as. 

These relations might be the source of formulae for practical use were 
it possible to establish accurate coefficients. But the variety in cupolas, 
tuyere proportions, character of fuel and iron, and difference in charging 
practice are bewildering and discouraging. Maximum efficiency in a 
given case can only be assured after direct experiment. Something short 
of the maximum is usually accepted in ignorance of the ultimate possi- 
bilities. 

The actual melting range of a cupola is ordinarily between 0.6 and 
0.75 ton per hour per sq. ft. of cross section. The limits of air supply 
per minute per sq. ft. are roughly 2500 and 4000 cu. ft. The possible 
power rec^ired varies even more widely, ranging from 1.5 to 3.75 H.P. 
per sq. ft., corresponding to 2.5 and 5 H.P. per ton per hour for the melting 
rates specified. The power may be roughly calculated, from the theoreti- 
cal requirement of 0.27 H.P. to deliver 1000 cu. ft. per minute against 
1 oz. pressure. The j)ower increases directly with the pressure, and de- 
pends also on the efficiency of the blower. Current practice can only be 
expressed between limits as in the following table. 

Range of Performance of Cupola Blowers. 



Diameter inside 
Lining, in. 


Capacity per 
Hour, tons. 


Pressure 

persq. 

in., oz. 


Volume of Air 
permin., cu. ft. 


Horse- 
power. 


18 


0.25- 0.5 
1.00- 1.5 
2.00- 3.5 
4.00- 5.0 
5.00- 7.0 
8.00-10.0 
9.00-12.0 
12.00-15.0 
14.00-18.0 
17.00-21.0 
19.00-24.0 
21.00-27.0 


5- 7 
7-9 

8-11 
8-12 
8-13 
8-13 
9-14 
9-14 
9-15 
10-15 
10-16 
10-16 


150- 300 
600- 900 
1,200- 2,000 
2,200- 2,800 
2,700- 3.700 
4,000- 5,000 
4,500- 6,000 
6,000- 7,500 
7,000- 9,000 
8,500-10,500 
9,500-12,000 
10,500-13,500 


0.5- 1.5 


24 


2 0- 6.0 


30 


5.0- 15.0 


36 


10.0- 23.0 


42 


12.0- 32.0 


48 


18.0- 45 


54 


22.0- 60.0 


60 


30.0- 75.0 


66 


35.0- 90.0 


72 


45.0-110.0 


78 


52.0-130.0 


84 


60.0-150.0 



Results of Increased Driving. (Erie City Iron-works, 1891.) — 
May-Dec, 1890: 60-in. cupola, 100 tons clean castings a week, melting 
8 tons per hour; iron per pound of fuel, 71/2 lbs.; per cent weight of good 
castings to iron charged, 75^/4. Jan.-May, 1891: Increased rate of melt- 
ing to 111/2 tons per hour; iron per lb. fuel, 91/2; per cent weight of good 
castings, 75: one week, 131/4 tons per hour, 10.3 lbs. iron per lb. fuel; 
per cent weight of good castings, 75.3. The increase was made by putting 
m an additional row of tuyeres and using stronger blast, 14 ounces. Coke 
was used as fuel. (W. O. Webber, Trans. A. S. M, E„ xii, 1045.) 



THE FOUNDRY. 1253 

Power Required for a Cupola Fan. (Thos. D. West, The Foundry, 
April, 1904.) — The power required when a fan is connected with a cupola 
depends on the length and diameter of the piping, the number of bends, 
valves, etc., and on the resistance to the passage of blast through the 
cupola. The approximate power required in everyday practice is the 
difference between the power required to run the fan with ttie outlet open 
and with it closed. Another rule is to take 75% of the maximum power 
or that with the outlet open. A fan driving a cupola 66 ins. diam., 
1800 r.p.m., driven by an electric motor required horse-power and gave 
pressures as follows : Outlet open, 146.6; outlet closed, 37.2, pressure 
15 oz.; attached to cupola, with no fuel in it, 120.5, 5 oz.; after kindling 
and coke had been fired, 101.0, 10 oz.; during the run 70.8 to 76.7, 11 to 
13 oz., the variations being due to changes in the resistances to the passage 
of the blast. 

Utilization of Cupola Gases. — Jules De Clercy, in a paper read 
before the Amer. Foundrymen's Assn., advises the return of a portion of 
the gases from the upper part of the charge to the tuyeres, and thus 
utilizing the carbon monoxide they contain. He says that A. Baillot 
has thereby succeeded in melting 15 lbs. of iron per lb. of coke, and at the 
same time obtained a greater melting speed and a superior quality of 
castings. 

Loss in Melting Iron in Cupolas. — G. O. Vair, Am. Mach,^ March 
5, 1891, gives a record of a 45-in. Colliau cupola as follows: 
Ratio of fuel to iron, 1 to 7.42. 

Good castings 21 ,314 lbs. 

New scrap 3,005 ** 

Millings 200 " 

Loss of metal 1,481 **' 

Amount melted 26,000 lbs. 

Loss of metal, 5.69%. Ratio of loss, 1 to 17.55. 

Use of Softeners in Foundry Practice. (W. Graham, Iron Age, 
June 27, 1889.) — In the foundry the problem is to have the right pro- 
portions of combined and graphitic carbon in the resulting casting; this 
is done by getting the proper proportion of silicon. The variations in 
the pr9portions of silicon afford a reliable and inexpensive means of 
producing a cast iron of any required mechanical charaeter which is 
possible with the material employed. In this w^ay, by mixing suitable 
irons in the right proportions, a required grade of casting can be made 
more cheaply than by using irons in v/hich the necessary proportions are 
already found. 

Hard irons, mottled and white irons, and even steel scrap, all containing 
low percentages of silicon and high percentages of combined carbon, 
could be employed if an iron having a large amount of silicon were mixed 
with them in sufficient amount. This would bring the silicon to the 
proper proportion and would cause the combined carbon to be forced into 
the graphitic state, and the resulting casting would be soft. High-silicon 
irons used in this way are called "softeners." 

Mr. Keep found that more silicon is lost during the remelting of pig of 
over 10% silicon than in remelting pig iron of lower percentages of silicon. 
He also points out the possible disadvantage of using ferro-silicons con- 
taining as high a percentage of combined carbon as 0.70% to overcome 
the bad effects of combined carbon in other irons. 

The Scotch irons generally contain much more phosphorus than is 
desired in irons to be employed in making the strongest castings. It is a 
mistake to mix with strong low-phosphorus irons an iron that would 
increase the amount of phosphorus for the sake of adding softening 
qualities, when softness can be produced by mixing irons of the same low 
phosphorus. 

(For further discussion of the influence of silicon, see pages 438 and 447.) 

Weakness of Large Castings. (W. A. Bole, Trans. A. S. M, E., 
1907.) — Thin castings, by virtue of their more rapid cooling, are almost 
ceiiai.i to be stronger per unit section than would be the case if the same 
metal were poured into larger and heavier shapes. Many large iron castings 
are of questionable strength, because of internal strains and lack of har- 
mony between their elements, even though the casting is poured out of iron 
of the best quality. This may be due to lack of experience on the part of 



1254 THE FOUNDRY. 



the designer, especially in the cooling and shrinking of the various parts 
of a large casting after being poured. 

Castings are often designed with a useless multiplicity of ribs, walls, 
gussets, brackets, etc., which, by their asynchronous cooling and their 
inharmonious shrinkage and contraction, may entirely defeat the intention 
of the designer. 

There are some castings which, by virtue of their shapes, can be specially 
treated by the foundryman, and artificial cooling of certain critical parts 
may be effected in order to compel such parts to cool more rapidly than 
they would naturally do, and the strength of the casting may by such 
means be beneficially affected. As for instance in the case of a fly-wheel 
with heavy rim but comparatively light arms and hub; it may be bene- 
ficial to- remove the flask and expose the rim to the air so as to hasten its 
natural rate of cooling, while the arms and hub are still kept muffled up 
in the sand of the mold and their cooling retarded as much as possible. 

Large fillets are often highly detrimental to good results. Where two 
walls meet and intersect, as in the shape of a T, if a large fillet is swept 
at the juncture, there will be a pool of liquid metal at this point which will 
remain liquid for a longer time than either wall, the result being a void, 
or "draw," at the juncture point. 

Risers and sink heads should often be employed on iron castings. In 
large iron-foundry work interior cavities may exist without detection, 
and some of these may be avoided by the use of suitable feeding devices, 
risers and sink heads. 

Specimens from a casting having at one point a tensile strength as high 
as 30,250 lbs. per sq. in. have shown as low as 20,500 in another and 
heavier section. Large sections cannot be cast to yield the high strength 
of specimen test pieces cast in smaller sections. 

The paper describes a successful method of artificial cooling, by means of 
a coil of pipe with flowing water, of portions of molds containing cylinder 
heads with ports cast in them. Before adopting this method the internal 
ribs in these castings always cracked by contraction. 

Shrinkage of Castings. — The allowance necessary for shrinkage 
varies for different kinds of metal, and the different conditions under 
which they are cast. For castings where the thickness runs about one 
inch, cast under ordinary conditions, the following allowance can be made; 

For cast iron, Vs inch per foot. For zinc, s/^g inch per foot. 

** brass, ^iq " *' *' " tin, 1/12 " 

'* steel, 1/4 '* " ** " aluminum, ^iq " *' " 

" mal. iron, 1/8 " '* '* ** britannia, 1/32 " 

Thicker castings, under the same conditions, will shrink less, and thinner 
ones more, than this standard. The quality of the material and the man- 
ner of molding and cooling will also make a difference. (See also 
Shrinkage of Cast Iron, page 447.) 

Mr. Keep (Trans. A. S. M. E., vol. xvi) gives the following "approxi- 
mate key for regulating foundry mixtures" so as to produce a shrinkage 
of Vs in. per ft. in castings of different sections; 

Size of casting 1/2 1 2 3 4 in. sq. 

Silicon required, per cent 3.25 2.75 2.25 1.75 1.25 per cent. 

Shrinkage of a V2-in. test-bar.. 0.125 .135 .145 .155 .165 in per. ft. 

Growth of Cast Iron by Heating. (Proc. I. and S. Inst., 1909.) — 
Investigations by Profs. Rugan and Carpenter confirm Mr. Outerbridge's 
experiments. (See page 449 ) They found: 1. Heating white iron causes 
it to become gray, and it expands more than sufficient to overcome the 
original shrinkage. 2. Iron when heated increases in weight, probably 
due to absorption of oxygen. 3. The change in size due to heating is 
not only a molecular change, but also a chemical one. 4. The growth of 
one bar was shown to be due to penetration of gases. When heated in 
vacuo it contracted. 

Hard Iron due to Excessive Silicon. — W. J. Keep in Jour. Am. 
Foundrymen's Assn., Feb., 1898, reports a case of hard iron containing 
graphite, 3.04; combined C, 0.10; Si, 3.97; P, 0.61; S, 0.05; Mn, 0.56. He 
says: For stove plate and hght hardware castings it is an advantage to 
have Si as high as 3.50. When it is much above that the surface of the 
castings often become very hard, though the center will be very soft. 



THE FOUNDRY. 



1255 



The surface of heavier parts of a casting having 3.97 Si will be harder than 
the surface of thinner parts. Ordinarily if a casting is hard an increase 
of silicon softens it, but after reaching 3.00 or 3.50 per cent, silicon hardens 
a casting. 

Ferro- Alloys for Foundry Use. E. Houghton {Iron Tr. Rev., 
Oct. 24, 1907.) — The objects of the use of ferro-alloys in the foundry are: 
1, to act as deoxidizers and desulphurizers, the added element remaining 
only in small quantities in the ftnished casting; 2, to alter the composition 
of the casting and so to control its mechanical properties. Some of these 
alloys are made in the blast furnace, but the purest grades are made in 
the electric furnace. The following table shows the range of composition 
of blast furnace alloys made by the Darwen & Mostyn Iron Co. All of 
these alloys may be made of purer quality in the electric furnace. 



Mn.... 

Si 

P 

C 

s 



Ferro- 
Mn. 



41.5- 87.9 

0.10- 0.63 

0.09- 0.20 

5.62- 7.00 

nil 



Spiegel- 
eisen. 



9.25-29.75 
0.42- 0.95 
0.06- 0.09 
3.94- 5.20 
nil-trace 



Silicon 
Spiegel. 



17.50-20.87 

9.45-14.23 

0.07- O.IO 

1.05- 1.89 

nil 



Ferro- 
sil. 



1.17- 2.20 
8.10-17.00 
0.06- 0.08 
0.90- 1.75 
0.02- 0.05 



Ferro- 
phos. 



3.00- 5.90 
0.50- 0.84 
15.71-20.50 
0.27- 0.30 
0.16- 0.33 



Ferro- 
Chrome. 



1 .55- 2.30 
0.13-0.36 
0.04- 0.07 
5.34- 7.12 
Cr, 13.50-41.39 



The following are typical analyses of other alloys 
furnace: 


made in the electric 




Si 


Fe 


Mn 


Al 


Ca 


Mg 

nil' 
0.26 


C 

3.28 
0.55 
1.14 


S 

0.03 
O.Ol 
0.01 


P 

0.02 
0.03 
0.04 


TI 


Ferro-titanium 

Ferro-aluminum-silicide 

FeiTo-calcium-silicide 


1.21 
45.65 
69.80 


44! i5 
11.15 


tr. 
0.22 


0.30 
9.45 
2.55 


"nil" 
15.05 


53.0 



Ferro-aluminum, Al, 5, 10 and 20%. Metallic manganese, Mn, 95 to 
98; Fe, 2 to 4; C, under 5. Do. refined. Mn, 99; Fe, 1; C, 0. 

Dangerous Ferro-silicon. — Phosphoretted and arseniuretted hydro- 
gen, highly poisonous gases, are said to be disengaged in a humid atmos- 
phere from ferro-silicon containing between 30 and 40% and between 47 
and 65% of Si, and there is therefore danger in transporting it in passenger 
steamships. A French commission has recommended the abandonment 
of the manufacture of FeSi of these critical percentages. (La Lumiere 
Electrique, Dec. 11, 1909. Elep. Rev., Feb. 26, 1910.) 

Quality of Foundry Coke. (R. Moldenke, Trans. A. S. M. E., 
1907.) — Usually the sulphur, ash and fixed carbon are sufficient to give 
a fair idea of the value of coke, apart from its physical structure, specific 
gravity, etc. The advent of by-product coke will necessitate closer 
attention to moisture Beehive coke, when shipped in open cars, may, 
through inattention, cause the purchase of from 6 to 10 per cent of water 
at coke prices. 

Concerning sulphur, very hot running of the cupola results in less sulphur 
in the iron. In good coke, the amount of S should not exceed 1.2 per 
cent; but, unfortunately, the percentage often runs as high as 2.00. If 
the coke has a good structure, an average specific gravity, not over 11 per 
cent of ash and over 86 per cent of fixed carbon, it does not matter much 
whether it be of the "72 hour" or '*24 hour" variety. Departure from 
the normal composition of a coke of any particular region should place the 
foundryman on his guard at once, and sometimes the plentiful use of 
limestone at the right moment may save many castings. 

Castings made in Permanent Cast-iron Molds. — E. A. Custer, in 
a paper before the Am. Foundrymen's Assn. {Eng. News, May 27, 1909), 
describes the method of making castings in iron molds, and the quality 
of these castings. Very heavy molds are used, no provision is made 
against shrinkage, and the casting is removed from the mold as soon as 
it has set, giving it no time to chill or to shrink by cooling. Over 6000 
pieces have been cast in a single mold without its showing any signs of 



1256 



THE FOUNDRY. 



failure. The mold should be so heavy that it will not become highly 
heated in use. Casting a 4-in. pipe weighing 65 lbs. every seven min- 
utes in a mold weighing 6500 lbs. did not raise the temperature above 
300° F. In using permanent molds the iron as it comes from the cupola 
should be very hot. The best results in casting pipe are had with iron 
containing over 3% carbon and about 2% silicon. Iron when cast in 
an iron mold and removed as soon as it sets, possesses some unusual prop- 
erties. It will take a temper, and when tempered will retain magnetism. 
If the casting be taken from the mold at a bright heat and suddenly 
quenched in cold water, it has the cutting power of a good high-carbon 
steel, whether the iron be high or low in silicon, phosphorus, sulphur or 
manganese. There is no evidence of "chill"; no white crystals are shown. 

Chilling molten iron swiftly to the point of setting, and then allowing 
it to cool gradually, produces a metal that is entirely new to the art. It 
has the chemical characteristics of cast iron, with the exception of com- 
bined carbon, and it also possesses some of the properties of high-carbon 
steel. A piece of cast iron that has 0.44% combined, and over 2% free 
carbon, has been tempered repeatedly and will do better service in a lathe 
than a good non-alloy steel. Once this peculiar property is imparted to 
the casting, it is impossible to eliminate it except by remelting. A bar of 
iron so treated can be held in a flame until the metal drips from the end, 
and yet quenching will restore it to its original hardness. 

The character of the iron before being quenched is very fine, close- 
grained, and yet it is easily machined. If permanent molds can be used 
with success in the foundry, and a system of continuous pouring be 
inaugurated which in duplicate work would obviate the necessity of having 
molders, why is it necessary to melt pig iron in the cupola? What could 
be more ideal than a series of permanent molds supplied with molten iron 

f)ractically direct from the blast furnace? The interposition of a reheating 
adle such as is used by the steel makers makes possible the treatment of 
the molten iron. 

The molten iron from the blast furnace is much hotter than that ob- 
tained from the cupola, so that there is every reason to believe that the 
castings obtanied from a blast furnace would be of a better quality than 
when the pig is remelted in the cupola. 

It is immaterial whether an iron contains 1,75 or 3% silicon, so long as 
the molten mass is at the proper temperature, so that the high tempera- 
tures obtained from .he blast furnace would go far toward offsetting the 
variations in the impurities. 

R. H. Probert {Castings, July, 1909) gives the following analysis of 
molds which gave the best results: Si, 2.02; S, 0.07; P, 0.89: Mn, 0.29: 
C.C., 0.84: G.C., 2.76. Molds made from iron with the following analysis 
were worthless: Si, 3.30; S, 0.06; P, 0.67j Mn, 0.12; C.C, 0.19; G.C., 2.98. 

Weight of Castings determined from Weight of Pattern. 

(Rose's Pattern-makers' Assistant.) 



A Pattern weighing One 
Pound, made of — 


Will weigh when cast in 


Cast 
Iron. 


Zinc. 


Copper. 


Yellow 
Brass. 


Gun 
metal. 


Mahogany — Nassau 


lbs. 
10.7 
12.9 
8.5 
12.5 
16.7 
14.1 


lbs. 
10.4 
12.7 
8.2 
12.1 
16.1 
13.6 


lbs. 
12.8 
15.3 
10.1 
14.9 
19.8 
16.7 


lbs. 
12.2 
14.6 
9.7 
14.2 
19.0 
16.0 


lbs. 
12 5 


" Honduras 

** Spanish 


15. 
9 9 


Pine red 


14.6 


*' white 


19.5 


** yellow . . - 


16.5 







Molding Sand. (Walter Bagshaw, Proc. Inst. M. E., 1891.)— The 
chemical composition of sand will affect the nature of the casting, no 
matter what treatment it undergoes. Stated generally, good sand is 
composed of 94 parts silica, 5 parts alumina, and traces of magnesia and 
oxide of iron. Sand containing much of the metallic oxides, and especially 



THE FOUNDBY. 



1267 



lime, is to be avoided. Geographical position is the chief factor governing 
the selection of sand; and whether weak or strong?, its deficiencies are made 
up for by the skill of the niolder. For this reason the same sand is often 
used for both heavy and light castings, the proportion of coal varying 
according to the nature of the casting. A common mixture of facing- 
sand consists of six parts by weight of old sand, four of new sand, and one 
of coal-dust. Floor-sand requires only half the above proportions of new 
sand and coal-dust to renew it. German founders adopt one part by 
measure of new sand to two of old sand: to which is added coal-dust in 
the proportion of one-tenth of the bulk for large castings, and one-twen- 
tieth for small castings. A few founders mix street-sweepings with the 
coal in order to get porosity when the metal in the mold is likely to be 
a long time in setting. Plumbago is effective in preventing destruction 
of the sand; but owing to its refractory nature, it must not be dusted 
on in such quantities as to close the pores and prevent free exit of the 
gases. Powdered French chalk, soapstone, and other substances are 
sometimes used for facing the mold; but next to plumbago, oak charcoal 
takes the best place, notwithstanding its liability to float occasionally and 
give a rough casting. 

For the treatment of sand in the molding-shop the most primitive 
method is that of hand-riddling and treading. Here the materials are 
roughly proportioned by volume, and riddled over an iron plate in a flat 
heap, where the mixture is trodden into a cake by stamping with the feet; 
it is turned over with the shovel, and the process repeated. Tough 
sand can be obtained in this manner, its toughness being usually tested 
by s<iueezing a handful into a ball and then breaking it; but the process 
is slow and tedious. Other things being equal, the chief characteristics 
of a good molding-sand are toughness and porosity, qualities that depend 
on the manner of mixing as well as on uniform ramming. 

Toughness of Sand. — In order to test the relative toughness, sand 
mixed in various ways was pressed under a uniform load into bars 1 in. sq. 
and about 12 in, long, and each bar was made to project further and 
further over the edge of a table until its end broke off by its own welgjut. 
Old sand from the shop floor had very irregular cohesion, breaking at all 
lengths of projections from 1/2 in. to 1 1/2 in. New sand in its natural state 
held together until an overhang of 23/4 in. was reached. A mixture of old 
sand, new sand, and coal-dust 

Mixed under rollers broke at 2 to 2 V4 in- of overhang. 

in the centrifugal machine .. . *' "2 "21/4" " 

through a riddle " *• 1 3/4 •' 21/8 " " 

showing as a mean of the tests only slight differences between the last 
three methods, but in favor of machine-work. In many instances the 
fractures were so uneven that minute measurements were not taken. 

Heinrich Ries (Castings, July, 1908) says tliat chemical analysis gives 
little or no information regarding the bonding power, texture, permea- 
bility or use of sand, the only case in which it is of value being in the 
selection of a highly silicious sand for certain work such as steel casting. 

Dimensions of Foundry L.adles. — The following table gives the 
dimensiars, inside the lining, of ladles from 25 lbs. to 16 tons capacity. 
All the ladles are supposed to have straight sides. {Am. Mach., Aug. 4, 
1892.) 



Cap'y. 


Diam. 


Depth. 


Cap'y. 


Diam. 


Depth. 


Cap'y. 


Diam. 


Depth, 




in. 


in. 




in. 


in. 




in. 


in. 


16 tons 


54 


56 


3 tons 


31 


32 


306 lbs. 


HI/2 


Ill/, 


14 " 


52 


53 


2 •• 


27 


28 


250 •• 


103/4 


11 


12 " 


49 


50 


11/2" 


241/2 


25 


200 " 


10 


101/2 


10 •• 


46 


48 


1 ton 


22 


22 


150 •• 


9 


91/ J 


8 ** 


43 


44 


8/4- 


20 


20 


100 •• 


8 


81/i 


6 ♦• 


39 


40 


1/2" 


17 


17 


75 •• 


7 


71/2 


4 •• 


34 


35 


1/4'* . 


131/2 


13 V2 


50 •• 


61/2 


61/2 



1258 



THE MACHINE-SHOP. 



THE MACHINE-SHOP. 



SPEED OF CUTTING-TOOLS IX LATHES, MILLING 
MACHINES, ETC. 

Relation of diameter of rotating tool or piece, number of revolutions 
and cutting-speed: 

Let d = diam. of rotating piece in inches, n = No. of revs, per min.; 
S = speed of circumference in feet per minute; 



S = 



ndn 



--0,2618 dn: 



d = 



3.82 5 



_ _ 3.82 5 

12 --—'-'•'' "' o.2618d d 

Approximate rule: Number 9f revolutions per minute = 4 X speed in 



feet per minute -r- diameter in inches. 

Table of Cutting-speeds 



^ 










Feet 


per minute. 












10 


20 


30 


40 


50 


" 


100 


150 


200 1 


250 1 300 


5 


Revolutions per minute. 


V4 


152.8 


305.6 


458.4 


611.2 


764.0 


1145.9 


1527.9 


2291.8 


3055.8 


3819.7 


4583.7 


3/8 


101.9 


203.7 


305.6 


407.4 


509.3 


763.7 


1018.6 


1527.5 


2036.7 


2545.8 


3055.0 


1/2 


76.4 


152.8 


229.2 


305.6 


382.0 


572.9 


763.9 


1145.9 


1527.9 


1909.9 


2291.8 


5/8 


61.1 


122.2 


183.4 


244.5 


305.6 


458.4 


611.2 


916.7 


1222.3 


1527.9 


1833.5 


3/4 


50.9 


101.8 


152.8 


203.7 


254.6 


382.0 


509.3 


763.9 


1018.6 


1273.2 


1527.9 


7/8 


43.7 


87.3 


130.9 


174.6 


218.3 


327.4 


436.6 


654.9 


873.3 


1091.5 


1309.8 


1 


38.2 


76.4 


114.6 


152.8 


191.0 


286.5 


382.0 


573.0 


763.9 


954.9 


1145.9 


n/s 


34.0 


67.9 


101.8 


135.8 


169.7 


254.4 


339.5 


508.8 


678.4 


848.0 


1017.6 


1 1/4 


30.6 


61.1 


91.7 


122.2 


152.8 


229.2 


305.6 


458.4 


611.2 


763.9 


916.7 


13/8 


27.8 


55.6 


83.3 


111.1 


138.9 


208.3 


277.7 


416.5 


555.4 


694.2 


833.1 


11/2 


25.5 


50.9 


76.4 


101.8 


127.2 


190.8 


254.4 


381.6 


508.8 


636.0 


763.2 


13/4 


21.8 


43.7 


65.5 


87.3 


109.2 


163.6 


218.1 


327.2 


436.2 


545.3 


654.3 


2 


19.1 


38.2 


57.3 


76.4 


95.5 


143.2 


191.0 


286.5 


382.0 


477.5 


573 


21/4 


17.0 


34.0 


50.9 


67.9 


84.9 


127.2 


169.6 


254.4 


339.2 


424.0 


508.8 


21/2 


15.3 


30.6 


45.8 


61.1 


76.4 


114.6 


152.8 


229.2 


305.6 


382.0 


458.4 


23/4 


13.9 


27.8 


41.7 


55.6 


69.5 


104.0 


138.7 


208.0 


277.3 


346.6 


416.0 


3 


12.7 


25.5 


38.2 


50.9 


63.7 


95.4 


127.2 


190.8 


254.4 


318.0 


381.6 


31/2 


10.9 


21.8 


32.7 


43.7 


54.6 


81.6 


108.9 


163.3 


217.7 


272.2 


326.6 


4 


9.6 


19.1 


28.7 


38.2 


47'. 8 


71.6 


95.5 


143.2 


191.0 


238.7 


286.5 


41/2 


8.5 


17.0 


25.5 


34.0 


42.5 


63.6 


84.8 


127.2 


169.6 


212.0 


254.4 


5 


7.6 


15.3 


22.9 


30.6 


33.1 


57.3 


76.4 


114.6 


152.8 


191.0 


229.2 


51/2 


6.9 


13.9 


20.8 


27.8 


34.7 


52.1 


69.4 


104.2 


138.9 


173.6 


208.3 


6 


6.4 


12.7 


19.1 


25.5 


31.8 


47.6 


63.4 


95.1 


126.8 


158.5 


190.2 


7 


5.5 


10.9 


16.4 


21.8 


27.3 


41.0 


54.6 


81.9 


109.2 


136.6 


163.9 


8 


4.8 


9.6 


14.3 


19.1 


23.9 


35.8 


47.7 


71.6 


95.5 


119.4 


143.2 


9 


4.2 


8.5 


12.7 


17.0 


21.2 


31.8 


42.4 


63.6 


84.8 


106.0 


127 2 


10 


3.8 


7.6 


11.5 


15.3 


19.1 


28.6 


38.2 


57.3 


76.4 


95.5 


114.6 


11 


3.5 


6.9 


10.4 


13.9 


17.4 


26.0 


34.7 


52.1 


69.4 


86.8 


104 2 


12 


3.2 


6.4 


9.5 


12.7 


15.9 


23.8 


31.7 


47.6 


63.4 


79.3 


95.1 


13 


2.9 


5.9 


8.8 


11.8 


14.7 


22.1 


29.4 


44.1 


58.8 


73.5 


88.2 


14 


2.7 


5.5 


8.2 


10.9 


13.6 


20.5 


27.3 


40.9 


54.6 


68.3 


81 9 


15 


2.5 


5.1 


7.6 


10.2 


12.7 


19.1 


25.4 


38 2 


50.9 


63.6 


76 3 


16 


2.4 


4.8 


7.2 


9.5 


11.9 


17.9 


23.9 


35.8 


47.8 


59.7 


71 6 


18 


2.1 


4.2 


6.4 


8.5 


10.6 


15.9 


21.2 


31.8 


42.4 


53 


63 6 


20 


1.9 


3.8 


5.7 


7.6 


9.6 


14.3 


19.1 


28.6 


38.2 


47.8 


57 3 


22 


1.7 


3.5 


5.2 


6.9 


8.7 


12.9 


17.2 


25.8 


34.4 


43.0 


51 6 


24 


1.6 


3.2 


4.8 


6.4 


8.0 


11.9 


15.9 


23.8 


31.7 


40.1 


47 6 


26 


1.5 


2.9 


4.4 


5.9 


7.3 


10.9 


14.5 


21.8 


29.0 


36.3 


435 


28 


1.4 


2.7 


4.1 


5.5 


6.8 


10.3 


13.7 


20.5 


27.3 


34.2 


41 


30 


1.3 


2.5 


3.8 


5.1 


6.4 


9.5 


12.7 


19.1 


25.4 


31.8 


38 2 


36 


1.1 


2.1 


3.2 


4.2 


5 3 


7.9 


10.6 


15.9 


21.2 


26.5 


31.8 


42 


0.9 


1.8 


2 7 


3.6 


4.5 


6.8 


9.1 


13.6 


18.2 


22.8 


27 3 


48 


0.8 


1.6 


2.4 


3.2 


4.0 


6.0 


7.9 


12.0 


15.9 


19 9 


23 9 


54 


0.7 


1.4 


2.1 


2.8 


3.5 


5.3 


7.0 


10.6 


14.1 


17.6 


21.1 


60 


0.6 


1.3 


19 


2.5 


3.2 


4.8 


6.3 


9.5 


12.7 


15.8 


19.0 



GEARING OF LATHES. 1259 

The Speed of Counter-shaft of the lathe is determined by an 
assumption of a slow speed with the back gear, say 6 feet per minute, 
on the largest diameter that the lathe will swing. 

Example. — A 30-inch lathe will swing 30 inches =, say, 90 inches 
circumference = 7 feet 6 inches; the lowest triple gear should give a 
speed of 5 or 6 feet per minute. 

Spindle Speeds of Lathes. — The spindle speeds of lathes are usu- 
ally in geometric progression, being obtained eitlier by a combination of 
cone-pulley and back gears, or by a single pulley in connection with a 
gear train. Either of these systems may be used with a variable speed 
motor, giving a wide range of available speeds. 

It is desirable to keep w^ork rotating at a rate that will give the most 
economical cutting speed, necessitating, sometimes, frequent changes in 
spindle speed. A variable speed motor arranged for 20 speeds in geometric 
progression, any one of which can be used with any speed due to the 
mechanical combination of belts and back gears, gives a fine gradation of 
cutting speeds. The spindle speeds obtained with the higher speeds of 
the motor in connection with a certain mechanical arrangement of belt 
and back gears may overlap those obtained with the lower speeds avail- 
able in the motor in connection with the next higher speed arrangement 
of belt and gears, but about 200 useful speeds are possible. E. R. Douglas 
{Elec. Rev., Feb. 10, 1906) presents an arrangement of variable speed 
motor and geared head lathe, with 22 speed variations in the motor and 3 in 
the head. The. speed range of the spindle is from 4.1 to 500 r.p.m. By 
the use of this arrangement, and taking advantage of the speed changes 
possible for different diameters of the work, a saving of 35.4 per cent was 
obtained in the time pf turning a piece ordinarily requiring 289 minutes. 
Rule for Gearing Lathes for Screw-cutting. (Garvin Machine 
Co.) — Read from the lathe index the number of threads per inch cut 
by equal gears, and multiply it by any number that will give for a pro- 
duct a gear on the index; put this gear upon the stud, then multiply the 
number of threads per inch to be cut by the same number, and put the 
resulting gear upon the screw. 

Example. — To cut 11^ threads per inch. We find on the index 
that 48 into 48 cuts 6 threads per inch, then 6 X 4 = 24, gear on stud, 
and 113^ X 4 = 46, gear on screw. Any multiplier may be used so long 
as the products include gears that belong with the lathe. For instance, 
instead of 4 as a multiplier w^e may use 6. Thus, 6 X 6 = 36, gear upon 
stud, and 11 J^ X 6 = 69, gear upon screw. 

Rules for Calculating Simple and Compound Gearing where 
there is no Index. {Am. Mach.) — If the lathe is simple-geared, 
and the stud runs at the same speed as the spindle, select some 
gear for the screw, and multiply its number of teeth by the number 
of threads per inch in the lead-screw, and divide this result by the num- 
ber of threads per inch to be cut. Tliis will give the number of teeth in 
the gear for the stud. If this result is a fractional number, or a number 
which is not among the gears on hand, then try some other gear for the 
screw. Or, select the gear for the stud first, then multiply its number of 
teeth by the number of threads per inch to be out, and divide by the 
number of threads per inch on the lead-screw. This will give the num- 
ber of teeth for the gear on the screw\ If the lathe is compound, select 
at random all the driving-gears, multiply the numbers of their teeth 
together, and this product by the number of threads to be cut. Then 
select at random all the driven gears except one; multiply the numbers 
of their teeth together, and this product by the number of threads per 
inch in the lead-screw. Now divide the first result by the second, to 
obtain the number of teeth in the remaining driven gear. Or, select 
at random all the driven gears. Multiply the numbers of their teeth 
together, and this product by the number of threads per inch in the 
lead-screw. Then select at random all the driving-gears except one. 
Multiply the numbers of their teeth together, and this result by the num- 
ber of threads per inch of the screw to be cut. Divide the first result by 
the last, to obtain the number of teeth in the remaining driver. When 
the gears on the compounding stud are fast together, and cannot be 
changed, then the driven one has usually twice as many teeth as the 
other, or driver, in which case in the calculations consider the lead-screw 
to have twice as many threads per inch as it actuaUy has, and then ignore 



1260 



THE MACHINE-SHOP. 



the compounding entirely. Some lathes are so constructed that the stud 
on which the first driver is placed revolves onlv half as last as the spindle. 
This can be ignored in the calculations by doubling the number of threads 
of the lead-screw. If both the last conditions are present ignore them 
in the calculations by multiplying the number of threads per inch in the 
lead-screw by four. If the thread to be cut is a fractional one, or if the 
pitch of the lead-screw is fractional, or if both are fractional, then reduce 
the fractions to a common denominator, and use the numerators of these 
fractions as if they equaled the pitch of the screw to be cut, and of the 
lead-screw, respectively. Then use that part of the rule given above 
which applies to the lathe in question. For instance, suppose it is desired 
to cut a thread of 25/32-inch pitch, and the lead-screw has 4 threads per 
inch. Then the pitch of the iead-screw will be 1/4 inch, which is equal to 
8/32 inch. We now have two fractions, 25/32 and 8/32, and the two screws 
will be in the proportion of 25 to 8, and the gears can be figured by the 
above rule, assuming the number of threads to be cut to be 8 per inch, 
and those on the lead-screw to be 25 per inch. But this latter number 
may be further modified by conditions named above, such as a reduced 
speed of the stud, or fixeci compound gears. In the instance given, if 
the lead-screw had been 21/2 threads per inch, then its pitch being 4/io 
inch, we have the fractions ^lio and 20/32, which, reduced to a common 
denominator, are ^^l\m and 125/160, and the gears will be the same as if the 
lead-screw had 125 threads per inch, and the screw to be cut 64 threads 
per inch. 

On this subject consult also "Formulas in Gearing," published by 
Brown & Sharpe Mfg. Co., and Jamieson's AppUed Mechanics. 

Change-gears for Screw-cutting Lathes. — There is a lack of 
uniformity among lathe-builders as to the change-gears provided for 
screw-cutting. W. R. Macdonald, in Am. Mack., April 7, 1892, pro- 
posed the following series, by which 33 whole threads (not fractional) 
may be cut by changes of only nine gears: 







Spindle. 








fcj 










Whole Threads. 


s 

^ 


20 


30 


40 


50 


60 


70 , 


no 


120 


130 




20 




8 


6 


44/5 


4 


33/7 


22/11 


2 


1 lVl3 


2 


11 


22 


44 


30 


18 




9 


71/5 


6 


51/7 


33/11 


3 


2 10/13 


3 


12 


24 


48 


40 


24 


16 


12 


93/5 


8 


66/7 


44/11 


4 


3 9/13 


4 


13 


26 


52 


50 


30 


20 


T5 




10 


8 4/7 


55/11 


5 


4 8/13 


5 


14 


28 


66 


60 


36 


24 


18 


14 2/5 




10 2/7 


66/11 


6 


5 7/13 


6 


15 


30 


72 


70 


42 


28 


21 


16% 


14 




77/11 


7 


6 8/13 


7 


16 


33 


78 


no 


66 


44 


33 


26 2/5 


22 


18 6/7 




11 


10 2/13 


8 


18 


36 




T20 


72 


48 


36 


28 4/5 


24 


20 4/7 


13X/11 




1 I Vl3 


9 


20 


39 




130 


78 


52 


39 


31 1/5 


26 


22 3/7 


14 2/11 


13 




10 


21 


42 





Ten gears are sufficient to cut all the usual threads, with the exception 
of perhaps 11 1/2, the standard pipe-thread; in ordinary practice any 
fractional thread between 11 and 12 will be near enough for the custom- 
ary short pipe-thread; if not, the addition of a single gear will give it. 

In this table the pitch of the lead-screw is 12, and it may be objected 
to as too fine for the purpose. This may be rectified by making the real 

gitch 6 or any other desirable pitch, and establishing the proper ratio 
etween the lathe spindle and the gear-stud. 

"Quick Change Gears." — About 1905, lathe manufacturers began 
building "quick change" lathes in which gear changing for screw 
cutting is eliminated. The lead-screw carries a cone of gears, one of which 
is in mesh with a movable gear in a nest of gears driven from the spindle. 
By changing the position of this movable gear, in relation to the cone of 
gears, the proper ratio of speeds between the spindle and lead-screws is 
obtained for cutting any desired thread usual in the range of the machine. 
About 16 different nurnbers of threads per inch can usually be cut by 
means of the "quick change" gear train. Different threads from those 
usually available can be cut by means of cliange gears between the spindle 



Taylor's experiments. 



1261 



and "quick change" gear train. The threads per inch usually available 
range from 2 to 46 in a 12-in. lathe to 1 to 24 in a 30-in. lathe. Catalogs 
of lathe manufacturers should be consulted for constructional details. 

Shapes of Tools. For illustrations and descriptions of various forms 
of cutting-tools, see Taylor's Experiments, below; also see Standard 
Planer Tools, p. 1271, and articles on Lathe Tools in Appleton's Cyc. 
Mech., vol. ii, and in Modern Mechanism. 

Cold Chisels. — Angle ot cutting-faces (Joshua Rose): For cast steel, 
about 65 degrees; for gun-metal or brass, about 50 degrees; for copper 
and soft metals, about 30 to 35 degrees. 

Metric Screw-threads may be cut on lathes with inch-divided lead- 
ing-screws, by the use of change-wheels with 50 and 127 teeth; since 127 
centimeters = 50 inches (127 X 0.3937 = 49.9999 in.). 

Rule for Setting the Taper in a Lathe. iA?7i. Mach.) — No rule 
can be given which will produce exact results, owing to the fact that 
the centers enter the work an indehnite distance. If it were not for 
this circumstance the following would be an exact rule, and it is an approx- 
imation as it is. To find the distance to set the center over: Divide the 
difference in the diameters of the large and small ends of the taper by 2, 
and multiply this quotient by the ratio which the total length of the shaft 
bears to the length of the tapered portion. Example: Suppose a shaft 
three feet long is to have a taper turned on the end one foot long, the large 
end of the taper being two inches and the small end one inch diameter. 



2 - 1 



X 



1 }/2 inches. 



r Lubricants for Lathe Centers. — Machinery recommends as lubri- 
cants for lathe centers to prevent cutting or abrasion: 1. Dry or 
powdered red lead mixed with a good mineral oil to the consistency of 
cream. 2. White lead mixed with sperm oil, together with enough 
graphite to give the mixture a dark red color. 3. One part graphite, 
four parts tallow, thoroughly mixed. 

TAYLOR'S EXPERIMENTS. 

Fred W. Taylor directed a series of experiments, extending over 26 
years, on feeds, speeds, shape of tool, composition of tool steel, and 
heat treatment. His results are given in Trans. A. S, M. E., xxviii, 
"The Art of Cutting IMetals." The notes below apply mainly to tools 
of high speed steel and to heavy work requiring tools not less than 
1/2 by 3/4 inch in cross-section. 

Proper Shape of Lathe TooL — Mr. Taylor discovered the best 
shape for lathe tools to be as shown in Fig. 194 with the angles given 
in the following table, when used on materials of the class shown. 
The exact outline of the nose of the tool is shown in Fig. 195. The 
actual dimensions of a 1-inch roughing tool are shown in Fig. 196. 
Let R = radius of point of tool, A = width of tool, L = length of shank, 
and H = height of shank, all in inches. Then L = 14 A 4-4: // = 1.5A; 
R = 0.5A — 0.3125 for cutting hard steel and cast iron; R = 0.5A — 
0.1875 for soft steel. The meaning of the terms back slope, etc., is 
shown in Fig. 194. 

Angles for Tools. 



* Material cut. 


a = clearance. 


b = back slope. 


c = side slope. 


Cast iron; Hard steel. 


6 degrees. 


8 degrees. 


14 degrees. 


Medium or Soft steel. 


6 degrees. 


8 degrees. 


22 degrees. 


Tire steel. 


6 degrees. 


5 degrees. 


9 degrees. 



* As far as the shape of the tool is concerned, Taylor divided metals 
to be cut into general classes: (a) cast iron and hard steel, steel of 
0.45-0.50 per cent carbon, 100,000 pounds tensile strength, and 18 per 
cent stretch, being a low limit of hardness; (&) soft steel, softer than 
above; (c) chilled iron; (d) tire steel; (e) extremely soft steel of carbon, 
say, 0.10-0.15 per cent. 

The table presupposes the use of an automatic tool grinder. If tools 
are ground by hand the clearance angle should be 9 degrees. The lip 
angles for tools cutting hard steel and cast iron should be 68 degrees; 




FiQ. 195. 



1262 



Taylor's experiments. 



1263 



for soft steel, 61 degrees; for chilled iron, 86 to 90 degrees; for tire steel, 
74 degrees; for extremely soft steel, keener than 61 degrees. A tool 
should be given more side than back slope; it can then be ground more 
times without weakening, the chip does not strike the tool post or clamps, 




^45*-^ ^ 




Fig. 196. 

and it is also easier to feed. The nose of the tool should be set to one 
side, as in Fig. 196 above, to avoid any tendency to upset. To use 
a tool of this shape, lathe tool posts should be set lower below the 
center of the work than is now (1907) customary. 

Forging and Grinding Tools. — The best method of dressing a tool 
is to turn one end up nearly at right angles to the shank, so that the 
nose will be high above the top of the body of the tool. Dressing can 
be thus done in two heats. Tools should leave the smith shop with 
a clearance angle of 20 degrees. Detailed directions for dressing a tool 
are given in Mr. Taylor's paper. To avoid overheating the tool in grind 
ing, a stream of water, of at least five gallons a minute, should be thrown 
at low velocity on the nose of the tool where it is in contact with the 
emery wheel. In hand grinding, tools should not be held firmly against 
the wheel, but should be moved over its surface. It is of the utmost 
importance that high speed steel tools should not be heated above 1200° F. 
in grinding. Automatic tool grinders are economical, even in a small 
shop. Grinding machines should have some means for automatically 
adjusting the pressure of the tool against the grinding wheel. Each size 
of tool should have adapted to it a pressure, automatically adjusted, and 
which is just sufficient to grind rapidly without overheating the tool. 
Standard shapes should be adopted, to which all tools should be ground, 
there being no economy in automatic grinding without standard shapes, 

Best Grinding Wheel. — The best grinding wheel was found to bQ 
a corundum wheel, of a mixture of 24 and 30 grit. 



1264 THE MACHINE-SHOP. 

Pressure of Tool, etc. — Mr. Taylor found that there is no definite 
relation between the cutting speed of tools and the pressure with which 
the chip bears on the Up surface of the tool. He found, however, that 
the pressure per square inch of sectional area of the chip increases 
sHghtly as the thickness of the chip decreases. The feeding pressure of 
the tool is sometimes equal to the entire driving pressure of the chip against 
the lip surface of the tool, and the feed gears should be designed to deliver 
a pressure of this magnitude at the nose of the tool. 

Chatter. — Chatter is caused by: too small lathe dogs; imperfect 
bearing at the points where the face plate drives the dogs; badly made or 
badly fitted gears; shafts in the machine of too small diameter, or of too 
great length; loose fits in bearings. A tool which chatters must be run 
at a cutting speed about 15 per cent slower than can be used if the tool 
does not chatter, irrespective of the use or non-use of water on the tool. 
A higher cutting speed can be used with an intermittent cut, as occurs 
on a planer, or shaper, or in turning, say, the periphery of a gear, than 
with a steady cut. To avoid chatter, tools should have curved cutting 
edges, or two or more tools should be used at the same time in the same 
machine. The body of the tool should be greater in height than width, 
and should have a true, solid bearing on the tool support, which latter 
should extend to almost beneath the cutting edge of the tool. Machines 
should be made massive beyond the metal needed for strength alone, 
and steady rests should be used on long work. It is advisable to use a 
steady rest, when turning any cyhndrical piece of diameter Z), when the 
length exceeds 12 D. 

Use of Water on Tool. — With the best high speed steel tools, a 
gain of 14 per cent in cutting speed can be made in cutting cast-iron 
and hard steel to 35 per cent on very hard steel by throwing a heavy 
stream of water directly on the chip at the point where it is being re- 
moved from the forging by the tool. Not less than three gallons a 
minute should be used for a 2 X 2 1/2-in. tool. The gain is practically 
the same for all qualities of steel, regardless of hardness and whether 
thick or thin chips are being cut. 

Interval between Grindings. — Mr. Taylor derived a table showing 
how long various sizes of tools should run without regrinding to give the 
maximum work for the lowest all-around cost. Time a tool should run 
continuously without regrinding equals 7 X (time to change tool + 
proper portion of time for redressing + time for grinding -f- time equi- 
valent to cost of the tool steel ground off). 

Interval Between Grindings, at Maximum Economical 
Cutting Speeds. 

Size of tool. 

Inches. 1/2 X3/4 Ws X 1 3/4X1 Vs Vs X 1 3/8 1X1 V2 

Hours. 1.25 1.25 1.25 1.5 1.5 

Size of tool. 

Inches. 1 I/4X 1 7/8 11/2X2 1/4 13/4X2 3/4 2X3 

Hours. 1.75 2.0 2.5 2.75 

If the proper cutting spee<f (A) is known for a cut of given duration, 
the speed for a cut (B) of different duration can be obtained by multiply- 
ing {A) by the factor given in the following table: 

Duration of cut in minutes: 

At known speed (A) 20 40 20 40 80 80 

At derived speed (B) 40 SO 80 20 40 20 

Factor 0.92 0.92 0.84 1.09 1.09 1.19 

For cutting speeds of high-speed lathe tools to last II/2 hours, see 
tables on pages 1266 and 1267. 

Effect of Feed and Depth of Cut on Cutting Speed. — ^With a given 
depth of cut, metal can be removed faster with a coarse feed and slow 
speed, than with fine feed and high speed. With a given depth of ciit. 

a cutting speed of S, and a feed of F, 5 varies approximately as lj\/F. 
With tools of the best high speed steel, varying the feed and depth of 
cut varies the cutting speed in the same ratio when cutting hard steel 
as when cutting soft steel. 



i 



TAYLOR^S EXPERIMENTS. 1265 

Best High Speed Tool Steel — Composition — Heat Treatment. 

— Mr. Taylor and Maunsel White developed a number of hi^h speed 
steels, the one showing the best all-around qualities having the following 
chemical composition: Vanadium, 0.29; tungsten, 18.19; chromium, 
5.47; carbon, 0.674; manganese, 0.11; silicon, 0.043. The use of 
vanadium materially improves high speed steel. The following method 
of treatment is described as the best for this or any other composition of 
high speed steel. The tool should be forged at a light yellow heat, and, 
after forging slowly and uniformly heatenl to a bright cherry red, allowing 
plenty of time for the heat to penetrate to the center of the tool, in order 
to avoid danger of cracking due to too rapid heating. The tool should 
then be heated from a bright cherry red to practically its melting-point as 
rapidly as possible in an intensely hot fire; if the extreme nose of the tool 
is slightly fused no harm is done. Time should be allowed for the tool 
to become uniformly hot from the heel to the lip surface. 

After the high heat has been given the tools, as above described, they 
Bhould be cooled rapidly until they are below the "breaking-down point, 
or. say. down to or below 1550° F. The quality of the tool will be but 
little affected whether it is cooled rapidly or slowly from this point down 
to the temperature of the air. Therefore, after all parts of a tool from 
the outside to the center have reached a uniform temperature below the 
breaking-down point, it is the practice sometimes to lay it down in any 
part of the room or shop which is free from moisture, and let it cool in 
the air, and sometimes to cool it in an air blast to the temperature of the 
air. 

The best method of cooling from the high heat to below the breaking- 
down point is to plunge the tools into a bath of red-hot molten lead below 
the temperature of 1550° F. They should then be plunged into a lead 
bath maintained at a uniform temperature of 1150° F., because the same 
bath is afterward used for reheating the tools to give them their second 
treatment. This bath should contain a sufficiently large body of the lead 
so that its temperature can be maintained uniform; and for this purpose 
should be used preferably a lead bath containing about 3600 lb. of lead. 

Too much stress cannot be laid upon the importance of never allowing 
the tool to have its temperature even slightly raised for a very short 
time during the process of cooling down. The temperature must either 
remain absolutely stationary or continue to fall after the operation of 
cooling has once started, or the tool will be injured. Any temj^orary rise 
of temperature during cooling, how^ever smaU, will injure the tool. This, 
however, applies only to cooling the tool to the temperature of about 
1240° F. Between the limits of 1240 degrees and the temperature of 
the air, the tool can be raised or lowered in temperature time after time 
and for any length of time without injury. And it should also be noted 
that during the tirst operation of heating the tool from its cold state to 
the melting-point, no injury results from allowing it to cool slightly and 
then reheating. It is from reheating during the operation of cooling 
from the high heat to 1240° F. that the tool is injured. 

The above-described operation is commonly known as the first or high- 
heat treatment. 

To briefly recapitulate, the first or high-heat treatment consists of 
heating the tool — 

(a) slowly to 1500° F.; 

(b) rapidly from that temperature to just below the melting-point. 

(c) cooling fast to below the breaking-down point, i.e., 1550''F. 

(d) cooling either fast or slowly from 1550° F. to temperature of the air. 

Second Treatment, Reheatine the Cooled Tool. — After air- 
temperature has been reached the tool should be reheated to a temperature 
of from 700 to 1240° F., preferably by plunging it in the before-mentioned 
lead bath at 1150° F. and kept at that temperature at least five minutes. 
To avoid danger of fire cracks, the tool should be heated slowly before 
immersing in the bath. The above tool heated in this fashion possesses 
a high degree of "red hardness" (ability to cut steel with the nose of the 
tool at red heat), while it is not extraordinarily hard at ordinary tem- 
peratures. It is difficult to injure it by overheating on the grindstone or 
m the lathe. It will operate at 90 per cent of its maximum cutting speed, 
even without the second or low-heat treatment. A coke fire is prefer- 
able for giving the first heat, and it should be made as deep as possible. 



1266 



THE MACHINE-SHOP. 



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1267 



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1268 THE MACHINE-SHOP. 

Cooling the tool by plunging it in oil or water, renders it liable to fire 
cracks and to brittleness in the body. Next to the lead bath an air blast 
is preferable for cooUng. 

Best Method of Treating Tools in Small Shops. — For small 
shops, in treating high-speed tools, Mr. Taylor considers the best method 
to be as follows for the blacksmith who is equipped only with the 
apparatus ordinarily found in a smith-shop. 

After the tools have been forged and before starting to give them their 
heat, fuel should be added to the smith's fire so as to give a good deep 
bed either of coke about the size of a walnut or of first-class blacksmiths' 
soft coal. A number of tools should then be laid with their noses at a 
slight distance from the hotter portion of the fire, so that they may all 
be pre-heating while the fire is being blown up to its proper intensity. 
After reaching its proper intensity, the tools should be heated one at a time 
over the hottest part of the fire as rapidly as practicable up to just below 
their melting-point. During this operation they should be repeatedly 
turned over and over so as to insure a uniform high heat throughout the 
whole end of the tool. As soon as each tool reaches its high heat, it 
should be placed with its nose under a heavy air blast and allowed to 
cool to the temperature of the air before being removed from the blast. 

Unfortunately,' however, the blacksmith's fire is so shallow that it is 
incapable of maintaining its most intense heat for more than a com- 
paratively few minutes, and, therefore, it is only through these few min- 
utes that first-class high-speed tools can be properly heated in the smith's 
fire. Great numbers of high-speed tools are daily turned out from 
smiths' fires which are not sufficiently intense in their heat, and they are 
therefore inferior in red hardness and produce irregular cutting tools. 

On the whole, a blacksmith's fire made from coke mayl3e regarded as 
better for giving the high heat to tools than a soft-coal fire, merely 
because a coke fire can be more easily made by the smith which will 
remain capable for a longer period of heating the tools quickly to their 
melting-points. 

Quality of Different Tool Steels. — Mr. Taylor in a letter to the 
author, Dec. 30, 1907, says : 

First. Any of a half dozen makes of high speed tools now on the market 
are amply good, and but little attention need be paid to the special direc- 
tions for heating and cooling hi^h speed tools given by the makers of the 
tool steel. The most important matter is that an intensely hot fire should 
be used for giving the tools their high heat, and that they should not be 
allowed to soak a long time in this fire. They should be heated as fast 
as possible and then cooled in an air blast. 

Second. The greatest number of tools are ruined on the emery wheel 
through overheating, either because a wheel whose surface is glazed is 
used, or because too small a stream of water is run upon the nose of the 
tool. The emery wheel should be kept sharp through frequent dress- 
ings with a diamond tool. 

Third. Uniformity is the most important quality in high speed tools. 
For this reason, only one make of high speed tool steel should be used 
in each shop. 

Economical Cutting Speeds. — Tools shaped as in Fig. 196, and 
of the chemical composition and heat treatment given in the precexi- 
ing paragraphs, should be run at the cutting speeds given in the tables 
on pages 1266 and 1267 in order to last one hour and 30 minutes with- 
out re-grinding. 

Cutting Speed of Parting and Thread Tools. — To find the economical 
cutting speed of a parting tool of the best high-speed steel, first ascer- 
tain the thickness of chip which is to be cut by the tool. Then from 
the tables on pages 1266 and 1267, under the standard 7/8-in. tool and 
3/16 in. depth of cut, and opposite the feed which most nearly corre- 
sponds to the thickness of chip to be taken by the parting tool, find 
the speed. Divide the figure so found by 2.7 to ascertain the speed for 
the parting tool. For thread tools, the process is the same, except 
that the divisor is 4. The thickness of chip in the latter case is the ad- 
vance in inches per revolution of the tool toward the center of the work. 

Durability of Cutting Tools. — E. G. Herbert {Am. Mach., June 24, 
1909) shows that the durability of a tool depends mainly on the tem- 
perature to which its extreme edge is raised, and that the rate of evolu- 
tion of heat and consequently the durability is proportional to the thick- 



STELLITE. 



1269 



ness and to the area of the chip and to the cube of the cutting speed. 
Or if ti = thickness or feed, Ci = depth of cut, Gi = area of the cut and 
Si = cutting speed, for any given set of working conditions, and tiC>a2 and 
S2 values for another set of conditions, then the durability of the tool 
will be the same w hen tiaiSi^ = ^0282^, or for constant durability 52 = 

Other High-Speed Steels.— Am. Mach. April 8, May 20 and 27, 
1909, describes the operations of some new varieties of high-spoed ^teol 
made by Sheffield manufacturers, which show resiilts superior to those 
of the earlier high-speed steels in endurance of tool, ability to cut very 
hard metals, and higher speeds. The following are the results of some 
of the tests in lathe-work : 



Tool 

size. 

in. 



Material Cut. 



Diam. 
in. 



Depth, 
cut in. 



Feed 



Speed 
ft. per 



Length of 
Cut. 



11/4 

11/4 

n/4 

7/8 
7/8 
7/8 
U/4 
IV2 
H/4 
1x2 
1x2 
H/4 

n/4 



Steel, 2.00 c 

Steel, 0.70 C 

Steel, 0.70C 

Steel, 0.40 C 

Steel. 0.40C 

Cast iron 

Cast iron 

Cast iron 

Steel, 0.40C 

Steel 

Nickel steel 

Steel casting, 0.45 C. 
Steel. 0.60C 



4 
4 

5 ft. 
5 ft. 
5 ft. 
53/8 in. 
93/4 in. 
3 1/2 in. 
20 in. 
71/2 in. 



3/8 

1/4 
3/16 
1/8 
1/8 
V8to3/i6 

5/16 
1/8 

3/8 

3/8 
9/64 



V16 
1/16 
1/16 
I/16 
1/32 
1/10 
1/32 
1/8 
1/10 
1/8 
0.072 
V8 
1/26 



36 
48 
65 
65 

120 
56 

107 
55 
90 
64 
52 
50 

U5 



43/4 in.* 
13 in.t 

87/8 in. 
28 ins., t 
28 ins., § 

41/2 ins. 

6 ins. 

Sing. 

54 ins. 

72 ins. 

124 ins. 

15 to 20 min. R 

18 in. 



* Then I3/4 in. at 50 ft. per min. t Then 1 Vs in. at 65 ft. per min. 
t Then 28 ins. at 98 ft. § Then 22 ins. at 160 ft. || Required 28 H. P. 
Chilled rolls, too hard for ordinary high-speed steel, were cut at a speed 
of 80 ft. per min., with s/ie in. depth of cut and 1/8 in. feed. 
The following results were obtained in drilling: 



Drill 
size. 


Material. 


Rev. 

per 
min. 


Feed 

per 

rev. 


Speed 
per 
min. 


Drilled without Re- 
grinding. 


3/4 in. 

3/4 
3/4 
13/16 


Close cast iron 

Steel, 0.25 C 


466 
247 
526 
400 


0.018 
0.011 


8 1/2 in. 

6 in. 
31/2 


70 holes, 3 ins. deep. 
60 holes, 23/4 ins. deep. 
12 holes, 21/2 ins. deep. 
14 in. at one opera-tion. 


Hard steel 


Steel 





A milling cutter 5 in. diam,, with 54 teeth, milling teeth in saw-blanks, 
at a cutting speed of 56 ft. per min. and a feed of 1 in. per min,, cuts 
80 blanks (three or more together), each 32 in. diam., 3/9 in. thick, 240 
teeth, before re-grinding. 

Sfellite. — An alloy of 25% chromium, 65% cobalt and 10% molyb- 
denum, to which the name '"stellite" has been given, is described in 
Ir. Tr. Review, Mar. 5, 1914. This alloy is extremely hard, and retain? 
its hardness even when red hot, thus making it useful as a substitute 
for tool steel. Tests made with stellite as a cutting tool on various 
materials showed the following cutting speeds, the speed attained by 
high-speed steel in the same tests being given for comparison : 



Material Cut. 



Cutting Speed, 
Ft. per IMin. 



Stellite, Steel. 
Phosphor-bronze... 900 125 
Tool steel 133 80 



Material Cut. 



Cutting Speed, 
Ft. per Min. 



Stellite. Steel. 
Seamless tubing. . . 4(X) 100 
Cast iron 200 100 



A circular issued by the Midvale Steel Co. gives the following direc- 
tions for the use of stellite, with a 1/2-in. square lathe tool: For cutting 
steel of 0.30 carbon or under, the limits will be: Depth of cut, i/s in.; 
feed, V16 in. per revolution; speed, 100 to 300 ft. per min., depending 
on the other conditions. For steel of 0.35 to 1.00 carbon, with the 
same depth of cut and feed as above the speed should }^ from 50 to 



1270 



THE MACHINE-SHOP. 



loO ft. per min. In cutting cast iron it is recommended that ligiit 
cuts, and heavy feeds, say up to 1/4 in., be used. The depth of cut 
can run to 1/4 or s/g in. under moderate feeds. SteUite cannot be 
forged, but is cast and ground to shape. It is extremely brittle, and 
its use is restricted to such tools as can be supported close to the cutting 
edge. It should not be used when the cut is one that will subject the 
fcool to heavy shocks. The fields for which it is recommended are: 
For turning steel, where turning represents a large proportion of the 
work to be done, and where the capacity of the lathe has not been 
reached with the steel tool; for turning cast iron that is not so hard 
that a slow speed with a steel tool is necessary, and where the capacity 
of the machine has not been reached with a steel tool ; for inserted teeth 
in milling cutters and reamers in a limited field where speed is important. 
For other data on the heat treatment, forging, etc., of tool steels, see 
also pages 491 to 497. 

PLANER WORK. 

Work that Should be Planed. — The planer is adapted for finishing 
flat surfaces where great accuracy is required. The Cincinnati Planer 
Co. gives (1912) in "A Treatise on Planing" the following fist of work 
which should be planed: Locomotive frames, cylinders, shoes, wedges, 
and driving-boxes; printing-press tables, frames, bearings, bases; 
laimdry frames, mangle chests; engine steam chests, valves, frames, 
pillow blocks, connecting-rods; rolling-mill guides, frames, bearings, 
key ways, tables; woodworking saw tables, frames, knife arbors, knives, 
bases; textile machinery frames, guides, bearing stands, legs; electric 
motor and generator bases and frame segments; forging machinery 
dies, guides, arches, header frames, bases; machine tool beds, tables, 
carriages, rails, slides, knees, columns. 

Cutting and Return Speeds. — A cutting speed of about 55 ft. per 
minute is about as high as it is practical to use on the planer, and this 
should be decreased for most materials. The table below shows the 
speeds recommended by the Cincinnati Planer Co. The lower cutting 
speed of the planer tool, as compared with the lathe, is probably due to 
the absence of a cooling lubricant on long cuts. If the cut is inter- 
mittent, as in planing a series of castings with gaps in between, the 
cutting speed can be higher than with a continuous cut of equal total 
length, probably due to the partial cooling of the tool during the inter- 
vals of cutting. Return speeds of 75 to 100 ft. per minute are as high 
as are recommended, although the author has seen planers operating 
at a return speed as high as 135 ft. per minute. An increase in the 
cutting speed is much more effective in increasing the capacity of the 
machine than an increase in the return speed, and it is better to increase 
the cutting speed by 25 % than to double the return speed. 

Planer Cutting Speeds, Feet per Minute. 



Iron, cast, roughing 40 to 50 

Iron, cast, finishing 20 to 25 

Iron, wrought, roughing. . 30 to 45 
Iron wrought, finishing . . 20 



Steel, cast, roughing .... 30 to 35 

Steel, cast, finishing 20 

Steel machinery 30 to 35 

Bronze and Brass 50 to 60 



Planer Feeds. — For rough planing cast-iron feeds range from i/s 
to 3/16 in.; for steel i/ie to i/s in. For finisliing cast iron with a broad 
nose tool the feed may range from 1/2 to 3/4 in. per stroke. The feed 
should be as heavy as possible, in order to decrease the time required, 
although when planing to a finished edge, a feed of as low as i/ie in. 
must be used to avoid breaking the edge at the end of the stroke. 

Power Requirements for Planing. — The principal power requirement 
in planing is^that required for reversing at the end of the stroke. The 
largest portion is used in reversing the planer pulleys, which, running 
at high speeds, store up considerable energy. The substitution of 
aluminum alloy pulleys by some planer builders for the cast-iron ones 
usually employed has reduced the power requirements for reversal and 
has increased the capacity of the machine by increasing the number of 
strokes which can be made per hour. The Cincinnati Planer Co. (1912) 
reports that with a 35-ft. cutting speed and an 85-ft. return speed, on a 
4-ft. cut, 165 strokes were made in 30 minutes with cast-iron pulleys 



PLANER WORK. 



1271 



and 189 m the same time with aluminum pulleys. In another test 
cast-iron pulleys required 39 horse-power at the reverse while aluminum 
pulleys required 30 horse-power. For other data on power required, 
see pages 1296, 1302 and 1303. 

Time Required for Planing.— The Cincinnati Planer Co. has devised 
a shde rule, shown in Fig. 197, for determining the time reciuired to 
machine work in a variable speed planer. It is adapted for u.se with 
cutting speeds of 20 to 60 ft. per min., return speeds of 50 to 130 ft 
per min. and a feed range of from i/ie to 1 in. per stroke. The feed 
which is to be used (scale B) is set opposite the intersection of the 




T~T"xnrr 

200 30a. 400 600 600 7008009001000 !♦«• 2000 3000 

S 4 66784 to 16 20 3o|40M iHr. 



iH;."i'-"i"r 



Fig. 197. Planer Time Slide Rule. 

cutting-speed curve with the retiuTi speed line (Scale A). The time 
is read on scale D underneath the figure representing the area in square 
inches to be planed (width X length) on scale C. To the time so deter- 
mined must be added the time required for setting up the work in the 
machine. 

The following tables have also been prepared by the Cincinnati 
Planer Co. for determining times for planer operation. 

Planer Table Travel, Feet per Hour. 

(Divide by length of stroke in feet for number of strokes per hotir.) 



Speed 
of Cut, 


Return Speed, Feet per Minute. 


Ft. per 


















Min. 


50 


60 


70 


80 


90 


100 


120 


150 


20 


857.1 


900.0 


933.3 


960.0 


981.8 


1000.0 


1028.6 


1058.8 


25 


1000.0 


1058.8 


1105.3 


1142.9 


1173.9 


1200.0 


1241.4 


1285.7 


30 


1125.0 


1200.0 


1260.0 


1309.1 


1350.0 


1384.6 


1440.0 


1500.0 


35 


1235.3 


1321.3 


1400.0 


1460.9 


1512.0 


1555.6 


1625.8 


1702.7 


40 


1333.3 


1440.0 


1527.3 


1600.0 


1661.5 


1714.3 


1800.0 


1894.7 


45 


1421.0 


1542.8 


1643.5 


1728.0 


1800.0 


1862.1 


1863.6 


2076.9 


50 


1500.0 


1636.4 


1750.0 


1846.2 


1928.6 


2000.0 


2117.6 


2250.0 



Time of Planer Travel per Foot. 



2£^ 


CO 

M 




03 










^ 0) 

los- 
ses 




H 




E-i 


w 


H 


OQ 


e 


m 


H 


m 


10 


6.0 


45 


1.33 


80 


0.75 


120 


0.5 


190 


0.316 


15 


4.0 


50 


1.2 


85 


.705 


130 


.461 


200 


.30 


20 


3.0 


55 


1.09 


90 


.666 


140 


.428 


220 


.273 


25 


2.4 


60 


1.0 


95 


.631 


150 


.40 


240 


.25 


30 


2.0 


65 


0.923 


100 


.60 


160 


.375 


260 


.23 


35 


1.72 


70 


.857 


105 


.571 


170 


.353 


280 


.214 


40 


1.5 


75 


.80 


110 


.545 


180 


.333 


300 


.20 



Standard Planer Tools. — Carl G. Barth designed for the use of 

the Watertown Arsenal a full line of planer tools, as shown in the 
drawings. Figs. 198 to 213, and in the tables below. These tools were 
developed according to the principles discovered by Taylor and Barth 
in the investigation into the "Art of Cutting Metals" (see p. 1261), 



1272 



THE MACHIlSrE-SHOP. 



and may be regarded as forming a standard line of tools of the best 
shape for their respective purposes. They are described in Am. Mach., 
Jan. 21 and 28, 1915. 

Round Nose Roughing Tools (Dimensions in Inches). 




Fig. 198. 



Fig. 199. 



A 
1 
1 

11/4 

11/4 

11/2 
11/2 
13/4 



Right or Left Hand (Figs, 198 and 199). 



B 
1 

11/2 
11/4 
17/8 
11/2 
2 1/4 
2 5/8 



c 

17/8 
2 5/8 
2 1/2 
2 7/s 

2 1/2 

3 1/4 
3 3/4 



D 
2 
2 

2 1/4 
21/4 
2 5/8 

2 5/8 

3 1/8 



E 

1/2 
5/8 
5/8 
1/2 
5/4 
5/8 
3/4 



3/8 
3/8 
1/2 
1/2 
5/8 
5/8 
3/4 



Parting Tools* (Dimei^kms in In<»hes). 

r 




Fig. 200. 



Flush Nose, Central 
(Fig. 200). 



' A 
5/8 
3/4 

1 

11/4 



A 

5/8 
3/4 

1 

11/4 

11/4 

11/2 



B 

1 

11/8 
11/2 
17/8 



c 

11/4 

11/2 

2 

2 1/2 



D 

13/4 
2 

2 1/4 
2 



E 

1/4 
3/8 
1/2 
5/8 



Fig. 201. 



High Nose, Right Hand, 
Straight (Fig. 201). 



A 

1/2 
5/8 
3/4 

1 

11/4 



B 

3/4 
1 

11/8 
11/2 

1 7/8 



c 

11/8 

13/8 
11/2 
2 
2 1/« 



D 

11/2 
15/8 
13/4 
2 
2 1/2 



Set Back Nose, Cent^ial, Straight (Fig. 



B 
1 

11/8 
1 

11/2 
17/8 
11/4 
11/2 



c 

13/4 

2 

18/4 

2 3/4 

21/8 
2 5/8 



* See not>e at foot of page 1273. 



D 

11/4 
11/2 
11/2 

2 

2 1/2 
17/8 
2 1/4 



E 

1/4 

5/16 

1/4 

5/8 

1/2 

5/8 

172 



202). 

F 
3 

3 1/2 
3 

4 3/4 
6 

35/4 
5 



E 

1/4 

5/16 

5/16 

8/8 

1/2 

H 
1 

11/8 

1 

11/2 

17/8 

11/4 

11/2 



STANDABD PLANER TOOLS. 



1273 



a 






^ 



ffS, 




Fig. 204. 



Fig. 205. 



Finishing Tools (Dimensions in Inches). 

Shearing Cut (Fig. 203). 

A B C D E F 

1/2 3/4 3/4 3/4 ?/§ 7/i6 

5/8 1 1 1 13/16 9/16 

3/4 11/8 11/8 11/8 11/2 5/8 

1 11/2 1 1/2 1 1/2 2 7/8 

Square, High Nose, Bent 45 Deg. (Fig. 204). 

A B C D E F 

1 11/2 2 1/8 2 1 3/8 3/4 

11/4 17/8 2 7/8 2 1/2 13/8 7/8 



External Keyway Tools (Dimensions in In.) 

Set Back Nose (Fig. 205). 

B C D E F K 

3/4 1 1/4 11/2 1/2 Width 

1 11/4 5/16 13/4 5/8 of 

11/8 11/2 3/8 2 1/4 3/4 Keyway 



-J- 



A 

1/2 
5/8 
3/4 



t^E-^ 



A 

3/4 
1 
11/4 

11/2 



Set Back Nose* 

C 

1 

11/4 

15/8 
2 



B 

11/8 
11/2 

17/8 

2 1/4 



D 
1 

13/8 
13/4 

2 



(Fig. 
E 

11/4 
11/2 

2 

2 1/2 



206). 

F 

2 5/8 

3 1/2 

4 1/2 

5 1/2 




* The sides of the nose of parting tools and external keyway tools 
with set back nose (Fig. 206) have a taper back from the cutting edge of 
1 deg. That is, in the plan each upper edge of the nose tapers inward 
1 deg. from a plane parallel to the side of the tool. Each side also 
tapers downwards from the upper edge 2 degs. from a plane parallel 
to the side of the tool. 



1274 



THE MACHINE-SHOP. 



T ^ ^-t-^- 

i — ' — ^-i— f 



I 



r-M 



r— c--| 



Fig. 207. 



if° 



Fig. 208. 






1 W 



Outline of % 
and j ^ 'tools 






Fig. 210. 



S.T 



ail 

J. 

T 






SP-T 









triSi 



Fig. 209. 



Outline of J^" f " " ''^ 
and i«" tools "^ - 



R. 



3^ 



;tTC:^_.i 






"T 

CO 



^i» 



Pig. 211. 



k E--!- 



II\ 




T 

Q 

1 



1 LU ■ 

LJ_i 



J 



Fig. 212. 



-i- 



-Hl>' 



< 

\ L 




T 



Ui. 



-E-H 



T 



it 



Fig. 213. 



MILLING MACHINE PRACTICE. 1275 

Fillet Forming Tools (Dimensions in Inches). 
180-Degree (Fig. 207). 180-Degree (Fig. 208). 

A B C D E R A B C D R 

5/8 1 1 1/4 0.04 0.02 5/8 1 1 0.2 0.1 
5/8 1 1 3/8 0.10 0.05 5/8 1 1 0.4 0.2 
3/4 11/8 11/4 1 0.80 0.40 1 

Various Radii (Fig. 209). 

Rad. A B C D E F G 

5/8 3/4 11/8 1 1/4 5/16 3/i6 T/g S/g 

0.8 3/4 11/8 1.6 3/8 1/4 7/8 S/g 

1 1/4 1 1/2 2 1/4 2 1/2 7/16 5/16 1 Vs 1 

1 3/4 _ 1 1/2 2 1/4 3 1/2 1/2 3/8 1 1/8 1 

Radius Forming Tools (Dimensions in Inches). 



H 


J 


K 


L 


1/4 


1/4 


3/8 


1/2 


1/4 


1/4 


3/8 


1/2 


1/4 


3/8 


1/2 


5/8 


1/4 


3/8 


1/2 


5/8 



180-Degree 
(Fig. 210). 

K(rad.) A B C D 

1/16 5/8 1 3/8 1 

1/8 5/8 1 1/2 1 

1/4 5/8 11 1 

1/2 5/8 1 11/4 1 



90-Degree, Right and Leit 

Hand (Fig. 211). 
7?(rad.^ A B C D 

1/32 5/8 1 1 5/16 

1/16 5/8 1 1 3/8 

1/8 5/8 1 1 1/2 

1/4 5/8 1 1 1 

1/2 5/8 1 1 11/4 

90-Degree, Right Hand or Left Hand (Figs. 212 and 213). 
R (rad.) A B C D E F 

3/4 3/4 11/8 5/16 11/8 1 I'S 1 Vs 

1 3/4 11/8 3/8 11/4 13/8 1 I/4 
11/2 1 11/2 5/8 2 21/4 2 

2 11/22 1/4 3/4 2 1/2 3 2 5/8 

MILLING MACHINE PRACTICE. 

Forms of Milling Cutters. — Milling cutters are made from either 
high speed or carbon steel. The former can be subjected to the more 
severe service and are especiaUy adapted to the removal of large 
amounts of metal, thus dictating their use as roughing cutters. The 
varieties of cutters in common use and the work to which they are 
adapted are as follows: 

The Plain Milling Cutter is a cylinder with teeth on the periphery 
only, and is used for producing a flat surface parallel to the axis of the 
cutter. Plain miUing cutters are made in a wide variety of diameters 
and widths for the various requirements of slab milling, keyway cut- 
ting, sawing, etc. Cutters less than 3/4 in. wide are usually made with 
straight teeth, while wider cutters have teeth that are a portion of a 
spiral. The spiral form enables each tooth to take a shearing cut, 
reduces the stress on the teeth, and prevents shock as each tooth 
engages the work, thus producing smoother surfaces on wide work. 
The spiral cutter requires less power to operate, and as it is under 
less strain, the tendency to chatter is reduced. Cutters for milling 
wide surfaces, whether of the spiral or straight type sometimes have 
nicks cut in the teeth, the nicks being staggered in the consecutive 
teeth. It is claimed that such cutters can be run with coarser feeds 
than plain cutters, as the nicks break up the chips and prevent jamming 
of the teeth. Nicked cutters are condemned by many authorities, 
however, for the reason that that portion of a following tooth opposite 
a nick is required to do double the usual amount of work with a re- 
sulting tendency to breakage. 

The Side Milling Cutter is a plain milling cutter with the addition 
of teeth on both sides. Side milling cutters are used in a large variety 
of work. Two or more are often placed on the same arbor with a space 
between them, in which case they are known as straddle mills. Straddle 
mills are advantageously used where the work has to be milled on 
two parallel sides, as in bolt heads, tongues, etc. Side milling cutters 
are often made with interlocking side teeth for milling slots to a stand- 
ard width, the width of the slot being maintained by means of packing 
washers between the two parts of the cutter. 



1276 THE MACHINE-SHOP. 

Face Milling Cutters have teeth cut on the periphery and on one face 
of a disk. The face mill is fastened to the end of the machine spindle 
and the teeth on the face come in full contact with the work, only a 
small portion of the peripheral teeth being in action. Some face 
mills have no teeth at all on the periphery. 

The End Mill, like the face mill, has teeth on the periphery and 
on one end. It is used for light milUng operations, such as the milling 
of slots, facing narrow surfaces, and for making cuts on the periphery 
of pieces. End mills are of four general types: The solid end mill, the 
end mill with center cut, the slotting end mill with two lips, and the 
shell end mill. The first and the last have either straight or spiral 
teeth. In the solid end mill the teeth are cut in the same piece that 
forms the shank. The shell end mill has a hole through its center so 
that it can be mounted on an arbor, and it should be used in preference 
to the solid mill whenever possible, as it is cheaper to replace when 
worn out or broken. The teeth of end mills with center cut are de- 
signed to cut at the inner end, whereas the teeth of solid mills have 
no cutting edge at this point. Center cut end mills are used for mill- 
ing shallow recesses in surfaces where there has been no hole bored 
previously for starting the cut, for milling^squares on the ends of shafts 
and for similar work. They have fewer teeth and can take heavier 
cuts than solid end mills or shell end mills. Slotting end mills are 
adapted to the rapid milling of deep slots from the solid where there 
has been no hole bored for starting the cut. A depth of cut equal 
to one-half the diameter of the mill can usually be taken from solid 
stock. 

The T-Slot cutter has teeth on its periphery and alternating teeth 
on its sides, the teeth being cut on the same piece that forms the shank. 
In making a T-slot, a groove is first cut with an ordinary side milling 
cutter or a two-lipped end mill, after which the wide groove at the 
bottom is cut with the T-slot cutter. 

Angular Cutters have teeth that are at some oblique angle to the 
axis. The cutter may have more than one angle. They are used for 
milling the edge of a piece to a required angle, or for cutting teeth in 
cutters or reamers. In work such as dovetailing where the cutter 
cannot be fastened to the arbor with a nut, it is made with a threaded 
hole or with the cutter in one piece with the shank. 

Form Cutters are of irregular outline for exactly duplicating pieces. 
In one style of form cutter the teeth are sharpened by grinding on the 
tops of the teeth, which necessarily changes the contour of the teeth 
and therefore the outline produced. The usual style is so made that 
it may be sharpened by grinding the face of the tooth, without alter- 
ing the contour. This permits the cutter to be used for duplicate 
interchangeable work until it has been ground to a point where the 
teeth are too slender to stand the strain of the work. 

Fly Cutters consist of a single cutter similar in shape to a planer 
tool, held in and rotated by an arbor. As they have but a single 
cutting edge, they are used but rarely outside of the experiment room 
or tool-room. The fly cutter can be formed exactly to any desired 
shape and will reproduce this shape exactly. Its field is those opera- 
tions that would not bear the expense of special shaped commercial 
cutters, as where but one or two teeth are to be made of a special form. 

Inserted Tooth Cutters. — When it is required to use plain milling cutters 
of a greater diameter than about 8 in., or side milling cutters of greater 
than 6 in. diameter, it is preferable to insert the teeth in a disk or head, 
so as to avoid the expense of making solid cutters and the difficulty 
of hardening them, not merely because of the risk of breakage in hard- 
ening them, but also on account of the difficulty in obtaining a uni- 
form degree of hardness or temper. The face of the inserted tooth 
should be undercut a few degrees from the radial line, thereby giving 
a smoother cut and consuming less power than would be the case were 
the face of the tooth flush with the radial line. Drawings of inserted 
tooth cutters furnished the author by the Cincinnati Milling Machine 
Co., show a rake of the teeth of from 10 to 15 degrees. 

Number of Teeth. — There is no standard rule for the number of 
teeth in milling cutters. The sizes offered commercially by cutter 
manufacturers ha\e been found as a rule satisfactory for most purposes. 



MILLING MACHINE PRACTICE. 



1277 



but in roughing out work where as much metal is to be removed as 
possible in a given time, cutters with a smaller number of te^^ah than 
the standard mills are advisable. Furthermore, a short lead spiral 
on coarse tooth cutters adapts them to a large range of Vvork that is 
not in the heavier class. Such cutters show a considerable saving of 
power over cutters with a larger number of tc^et h. The number of t(X3th 
in cutters of various types is given in Alachincnj, April, 1907, as follows: 
Plain milling cutters are usually manufactured in sizes from 2 to 5 
in. diameter, and up to 6-in. face. The use of solid plain milling 
cutters of over 5-in. face is not advised, and cutters over 5-in. face 
should be made in two or more interlocking sections. 

Number of Teeth and Amount of Spiral of Plain Milling Cutters 



No. of teeth = — ■ ; Length of Spiral = 



9 X diam. + 4. 



Diameter of cutter, 

2 2 1/4 21/2 2 3/4 3 31/2 4 41/2 5 5 1/2 6 6 I/2 7 7 1/2 8 
Number of teeth, 

16 18 18 18 20 20 22 24 24 26 26 28 30 30 32 
Length of one turn of spiral, inches, 
22 241/4 261/2 28 3/4 31 351/2 40 441/2 49 53 1/2 58 62 1/2 67 711/2 76 

A cutter with an included angle of 60° (12° on one side and 48° on the 
other) is recommended for fluting plain milling cutters, although cutters 
of 52° (12° and 40°) are commonly furnished by manufacturers. The 
angle of relief of milling cutters should be between 5° and 7°. 

The teeth of side milling cutters should have the same general form 
as those of plain milling cutters, excepting that the cutter used to 
form them should have an included angle of about 75°. 

Number of Teeth in Side Milling Cutters. 
Number of teeth = 3.1 diam. 4-11- 
Diameter of cutter, 

221/4 2 1/2 2 3/4 3 3 1/2 441/2551/266 1/2 7 
Number of teeth, 
18 18 18 20 20 22 24 24 26 28 30 32 32 

Keyways in Milling Cutters. — A number of manufacturers have 
adopted the keyways shown below, as standards. The dimensions in 
inches are given in the tables. 



71/289 
34 36 38 



MW- 



>^ 




Fig. 214. — Square Keywat. 



Fig. 215. — Half-round Keyway. 



Square Keyw^ays. 



Diam. 
Hole, 


3/8-«/l6 


5/8-7/8 


15/16-1 VS 


13/16-13/8 


17/16-13/4 


1 13/16-2 


21/16-21/2 


29/16-3 


Width 
W 


3/32 


1/8 


5/32 


3/16 


1/4 


5/16 


3/8 


7/16 


Depth, 
D 


3/64 


V16 


5/64 


3/32 


Vs 


5/32 


3/16 


3/16 


Radius. 
R 


0.020 


0.030 


0.035 


0.040 


0.050 


0.060 


0.060 


0.060 



Half-round Keyways. 



Diam. 

Hole, H 
Width 

W 
Depth, 

D 



3/8-5/8 
1/8 
I/16 



11/16-13/16 
3/16 
3/32 



7/8-1 3/16 
1/4 
1/8 



1 1/4-1 7/16 
5/lG 
5/32 



11/2-2 



3/lG 



21/16-2 7/16 
7/16 

7/32 



1278 



THE MACHINE-SHOP. 



Diameter of Cutters. — It is advisable to use cutters of as small a 
diameter as the strength will admit. The smaller the cutter, the 
shorter the distance it will have to travel in milling a given length. 
With small mills also there is less liability to chatter than with large 
ones. In addition they require less power and are not as expensive 
as large ones. The Brown & Sharpe IMfg. Co. states that a difference 
of 1/2 in. in the diameter of the mills made a difference of 10% in the 
cost of their work. In surface milling the cutter should, if possible, be 
wider than the work. 

Clearance and Rake of Cutters. — The clearance of milling cutters, 
or the amount of material removed from the top of the teeth back of 
the cutting edge to permit it to clear the surface of the work instead of 
scraping over it, depends on the diameter of the cutters. It must be 
greater for small cutters than for large ones. For plain cutters over 
3 in. diameter, the clearance angle should be 4 degrees, and for cutters 
of less than 3 in. it should be 6 degrees. For end mills it should be about 
2 degrees. It is considered advisable to have the teeth of end mills from 
0.001 to 0.002 in. lower at the center than at the outside. The Cin- 
cinnati Milling Machine Co. has furnished the author with drawings 
of cutters of various types. In these the teeth have a front rake of 
10 descrees 

Power 'Required for Milling. {Mech. Engr., Oct. 26, 1907.) — 
Mr. S. Strieff made a series of experiments to determine the power 
required to drive milling cutters of high-speed steel. The results are 
shown in the table below. A proportionately higher amount of poWer 
is required for light than heavy milling, as the power to drive the machine 
is the same at all loads. The table also shows that the depth of cut does 
not increase the power required in the same proportion as the width, and 
that work with a quick feed and a deep but comparatively narrow cut 
requires less power than a wide cut of moderate depth with slow feed, 
the amount of metal removed being the same in both cases. 

Power Required for Milling. 



§a 


Feed. 


1^0; 


3 


s 


a; 





feag 


**-< n . 






Cutting Sp 
of Cutter, 
per Minul 














Number 
Revoluti 
of Cuttei 
Minute. 


1 . 

•Si 


> C M 


24 


2.46 


0.10 


37 


0.26 


23.6 


25 


245 


0.102 


24 


3.50 


0.15 


37 


0.26 


10.2 


17 


150 


0.113 


24 


4.35 


0.18 


37 


0.14 


9.8 


17 


97 


0.175 


24 


3.50 


0.15 


37 


0.49 


9.8 


27 


490 


0.055 


19 


4.33 


0.23 


29.5 


0.28 


9.3 


17 


331 


0.051 


23 


4.17 


0.18 


36 


0.28 


20.5 


27 


386 


0.070 


23 


4.17 


0.18 


36 


0.28 


9.8 


20 


183 


0.109 


40 


1.89 


0.05 


64 


0.24 


10.2 


17 


74 


0.230 


40 


3.94 


0.10 


64 


0.37 


13.8 


21 


331 


0.063 


40 


5.79 


0.14 


64 


0.16 


16.5 


17 


123 


0.138 



P. V. Vernon reports (En'gr, Mar. 9, 1909) some milling machine 
tests made by Alfred Herbert. Ltd., showing the horse-power required 
to slab mild steel and cast iron. The tests reported include 44 on 
steel and 38 on cast iron. The horse-power was determined from the 
current readings and Includes the motor losses and also a constant 
loss of 1.8 H.P. in the jack shaft and countershaft of the machine. 

^ Horse-power per Cu. In. per Minute required for slabbing. 

Maximum. Minimum. Average. 

Steel 3.02 1.95 2.52 

Cast iron 1.25 0.89 1.10 

Later tests reported to the Manchester Assoc, of Engrs., Nov. 23, 
1912, by Mr. Vernon, embodied the following conclusions: (1) A 5-in. 
double belt, driving a 16-in. pulley at 400 r.p.m. (100,531 sq. in. of 



MILLING MACHINE PRACTICE. 



1279 



belt per niin.) geared to drive 4 1/2-in. high-speed cutter at 70 ft. per 
min. is able to remove as much as 48.1 cu. in. of cast iron or 24.31 cu. 
in- of mild steel per minute. (2) 2090 sq. in. of double belt passing 
over a pulley per minute will remove 1 cu. in. of cast iron in a milling 
machine. To remove 1 cu. in. of steel the belt surface passing should 
be 4135 sq. in. (3) A 4 i/2-in. high-speed cutter on a 2-in. arbor, run- 
ning at 70 ft. per min. is capable of removing at least 3.G3 cu. in. of 
cast iron, and possibly as much as 6.01 cu. in., and at least 2.125 cu. 
in. of mild steel, and possibly as much as 3.03 cu. in. per min. for each 
inch of width of belt, up to 8 in. From the earlier tests noted above 
the conclusion was reached that 1 H.P. would remove as much as 1.84 
cu. in. of cast iron per min., and 0.74 cu. in. of mild steel. In these 
tests the feed in cast iron ranged between 1 27/32 and IO^Iiq in. per min., 
the depth of cut from 0.14 to 1.10 in., while in steel the feeds ranged 
from 5/8 to 10 3/8 in. per min. and the depth of cut from 0.10 to 1.10 
in. per min. 

A. L. De Leeuw gives in Am. Mach., Aug. 8, 1912, the results of a 
large number of tests to determine the horse-power consumed in cutting 
machinery steel in the milling machine. From the tests there reported 
the following table has been compiled, the figures given showing the 
test in each class in which the maximum amount of metal per horse- 
power per minute was removed. The figures for horse-power are net, 
the motor losses having been deducted. 





Power Required for Milling Machinery Steel (A 


. L. De Leeuw). 




g 








^ 




















M 










1—1 












1^ 


P 







c 


1. 


i 







(N 


3 


*: 


a. 







s 




.c? 


"o 


. oJ 


^ 3 


Pk 


. oT 




2-S 


s 


. oJ 


w 3 


PU 


. . 




Iz <u 


0) 




1^ 







1 

:3 















3 


U 


Q 


P^ 


& 


w 








^ 


Q 


« 


fe 


w 


u 


S>\^ 


1/8 


20.5 


12.31 


10.96 


0.702 




B 


5/16 


20.0 


4.57 


11.959 


0.712 


1 


A 




25.0 


15.4 


13.473 


0.714 




A 




20.0 


4.56 


7.34 


0.972 




A 


** 


20.0 


11.81 


7.555 


0.977 




A 


** 


21.5 


4.89 


7.14 


1.07 


1 


C 


** 


20.0 


11.83 


7.34 


1.007 




A 


" 


16.0 


7.70 


11.0 


1.092 


2 1 D 


<* 


22.0 


12.96 


6.85 


1.183 




C 


3/8 


20.0 


3.48 


10.96 


0.596 


I 


B 


3y;6 


20.0 


7.34 


10.70 


0.643 




B 




20.0 


3.49 


7.07 


0.925 


1 


A 




20.0 


7.29 


9.749 


0.701 




A 


" 


40.5 


6.22 


12.35 


0.944 


3 


D 


** 


20.0 


7.29 


7.07 


0.967 




A 


** 


40. 


7.8 


14.55 


1.001 


3 


D 


<« 


21.5 


7.96 


6.85 


1.09 




C 


*' 


22. 


3.86 


6.85 


1.056 


1 


C 


1/4 


20.0 


5.9 


12.62 


0.584 




B 


** 


15.75 


7.66 


12.64 


1.137 


2 


D 




20.0 


5.84 


11.41 


0.64 




A 


V2 


15.5 


4.61 


12.64 


0.912 


2 


D 


tt 


19.0 


5.58 


7.62 


0.915 




A 




40.0 


6.09 


15.93 


0.955 


3 


D 


<* 


21.5 


6.26 


7.14 


1.096 




C 


5/8 


40.0 


4.71 


17.07 


0.863 


3 


D 


5/16 


20.5 


4.68 


13.20 


0.554 




B 


3/4 


39.5 


3.63 


17.38 


0.782 


3 


D 



• Note 1. — Cutter No. 1 is an 8-in., 12-blade face mill; No. 2 is a 
10-in., 16-blade high-power face mill; No. 3 is a 41/2 in., 10-tooth 
spiral nicked cutter. 

Note 2. — Material A, Elastic Limit 36,400 lb. per sq. in., elongation 
36%, reduction of area 66 7©; material B, E. L. 36,200 lb. per sq. in., 
elong. 36.5%, red. of area 59.6 9^; material C, E. L. 37,400 lb. per sq. in., 
elong. 36.5%, red. of area 60%; material D, E. L. 55,000 lb. per sq. in., 
elong. and red. of area not given; 0.26 carbon, 0.5 S^ manganese. 

Modern Milling Practice (1914).— The limit of milHng operations is 
determined by the strength and durability of the cutter. A rigid 
frame on the machine and powerful feed mechanism increase these. 
The chief causes of low output are: Improperly constructed cutters; 
insufficient rigidity in the machine; and timidity, due to lack of ex- 
perience, of both builders and operators. The principal cause of 
cutter failures is insufficient space for chips between the cutter teeth. 
Fixed rules cannot be laid down for proper feeds and speeds of milling 
cutters, these depending on the character and hardness of the metal 



128Q THE MACHINE-SHOP, 

being cut. On roughing cuts it is desirable to run the cutter at a speed 
well within its limit, and use as heavy a feed as the machine can pull. 
The size of chip taken by each tooth of the cutter with the heaviest 
feeds is comparatively light, and with properly sharpened cutters 
there is little danger of breaking the cutter by giving too great a feed. 
It is considered better practice, however, to break an occasional cutter 
than to run machines at a low rate. It is not considered desirable to 
run even high speed steel cutters at excessive speeds. The great value 
of these cutters is their long life and ability to hold a cutting edge as 
compared with carbon steel cutters. It is important to keep the 
cutters sharp, as accurate or fast work is impossible with dulled teeth, 
and a dull cutter will wear away faster than a sharp one. Cutter 
grinders should always be used for sharpening cutters. 

The following speeds in feet per minute are a good basis for roughing 
the materials indicated: 
Carbon steel cutters, 

Cast Iron. Machinery Steel. Tool Steel. Brass and Bronze. 
40 to 60 30 to 40 20 to 30 80 to 100 

High speed steel cutters, 

80 to 100 80 to 100 60 to 80 150 to 200 

On cast-iron work a Jet of air delivered to the cutter with sufficient 
force to blow the chips away as fast as made permits faster feeds and 
prolongs the cutter's life. A stream of oil fed under heavy pressure to 
wash the chips away has the same effect when cutting steel. On finish- 
ing cuts the rate of feed used determines the grade of the finish. If a 
spiral mill is used the feed should range from 0.036 in. to 0.05 in. per 
revolution of a 3-in. diameter cutter. As such cuts are light the speed 
of cutting can be much higher than that used for roughing cuts. The 
nature of the cut is a factor in determining speeds ; a saw can run twice 
as fast as a surface mill. (See paragraph. p. 1282, on high-speed milling.) 
Keyseating and similar work can be best done with a plain cutter 
rather than a side mill. 

Castings should be pickled in a solution of sulphuric acid, diluted 
with water to a specific gravity of 25 deg. (Baume), before milling, to 
remove the hard skin and sand which are destructive to cutters. If the 
castings are later to be painted, they should not be immersed in the 
pickling bath. It is better to pour the solution over them, allowing 
it to dry before making another application. This should be repeated 
4 or 5 times. Forgings should be pickled in a solution of sulphuric acid 
and water of a specific gravity of 30 deg. (Baume), for from 3 to 12 
hours. After pickling, forgings and castings should be washed with 
hot water to remove the sand and acid. 

Milling **with" or "against*' the Feed. — Tests made with the 
Brown & Sharpe No. 5 miUing-machine (described by H. L. Arnold, 
in Am. Mach., Oct. 18, 1884) to determine the relative advantage of 
running the milling cutter with or against the feed — "with the feed" 
meaning that the teeth of the cutter strike on the top surface or 
" scale " of cast-iron work in process of being milled, and "against the 
feed '* meaning that the teeth begin to cut in the clean, newly cut surface 
of the work and cut upwards toward the scale — showed a decided advan- 
tage in favor of running the cutter against the feed. The result is 
directly opposite to that obtained in tests of a Pratt & Whitney machine 
by experts of the Pratt & Whitney Co. 

In the tests with the Brown & Sharpe machine the cutters used were 6 
inchesfaceby 41/2 and 3 inches diameter, respectively, 15 teeth in each 
mill, 42 revolutions per minute in each case, or nearly 50 feet per minute 
surface speed for the 41/2-inch and 33 feet per minute for the 3-inch mill. 
The revolution marks were 6 to the inch, giving a feed of 7 inches per 
minute, and a cut per tooth of 0.011 inch. When the machine was 
forced to the limit of its driving the depth of cut was 11/32 inch when the 
cutter ran in the "old" way, or against the feed, and only 1/4 inch when 
it ran in the "new" way, or with the feed. The endurance of the mill- 
ing cutters was much greater when they were run in the "old" way. 
The Brown & Sharpe Mfg. Co. says that it is sometimes advisable to 
mill with the feed, as in surfacing two sides of a piece with straddle 
mills, the cutters will then tend to hold the work down. In milling 
deep slots or cutting off stock with thin cutters or saws, milling with the 
feed is less likely to crowd the cutter sidewise and make a crooked slot. 



MILLING MACHINE PRACTICE. 1281 

Lubricant for Milling Cutters. (Brown & Sharpe Mfg. Co., 1007.) — 
An excellent lubricant, to use with a pump, for milling cutters is made 
by mixing together and boiling for one-half hour, 1/4 lb. sal soda, 1/2 
pint lard oil, 1/2 pint soft soap and water enough to make 10 quarts. 
t)il is also frequently used in milling steel, wrought iron, malleable iron 
or tough bronze. 

Typical Milling Jobs — Speeds — Feeds. — The notes below compiled 
from data furnished by the Brown & Sharpe Mfg. Co. and the Cin- 
cinnati Milhng Machine Co. (1915) show examples of what is con- 
sidered good commercial milling practice. 

Bars of 0.60 Carbon steel, s/s in. tMck, 21/2 in. wide, 11 3/4 in. long, 
had 22 rack teeth, 7/iq in. pitch and Vs in. deep milled in the edge. 
The bars were locked four at a time in a vise. A gang of four cutters 
was used, at 41 r.p.m. and a feed of 0.023 in. per revolution, equivalent 
to 15/16 in. per minute. Two vises were used, the operator loading one 
while the bars in the other were being machined. The time required 
per piece including chucking and removing, was 0.71 minute. For 
milling two recesses in the upper edges of these same bars, after the rack 
teeth were cut, they were mounted two in a vise with distance pieces 
between, and a gang of four 31/2-in. side mills was used, milling all four 
recesses at once. The mills rotated at 50 r.p.m., and the feed was 
0.068 per revolution, equivalent to 3.4 in. per minute. Two vises were 
used as before, and the total time per rack was 2.2 minutes. The final 
operation was the milling of a slot in the bar, for which purpose it was 
held at the ends in two vises. Two holes were first drilled in the piece 
through one of which the cutter was threaded. The slot was 1-in. 
wide and 9 in. long. A i5/i6-in. helical cutter was used at 160 r.p.m. 
A roughing cut was first taken at a feed of 0.015 per revolution, equiv- 
alent to 2.4 in. per min., after which the piece was removed and 
allowed to cool before the finishing cut was taken at a feed of 0.068 in. 
per revolution, or 10.8 in. per minute. The roughing cut removed 
11/2 cu. in. of steel per minute. The total time, including chucking, 
removing, etc., was 7.5 minutes. 

Gray iron castings 8 1/4 in. long, 8 1/2 in. wide, 4 1/4 in. thick, with 
two flanges 7/8 in. high and 7 Is in. thick projecting above the upper 
face, were milled on the entire upper surface and the two sides, includ- 
ing top and sides of flanges at one operation by a gang of straddle mills, 
the largest cutter being 10 1/2 in. diameter and running at 21 r.p.m., 
with 6.3 in. feed per minute. Metal was removed at the rate of 19 cu. in. 
per minute, the maximiun depth of cut being 3/i6 in. The pieces were 
held in a string jig, removed as fast as they were traversed by the gang 
of cutters, and others were chucked in their places. They were milled 
in lots of 125 without resharpening of the cutters. Time per piece, 
2 minutes. 

A gray iron casting 22 in. wide and 9 in. long was milled on its upper 
surface by a gang of three 6-in. spiral mills with a total face width of 
24 in., mounted on a 2-in. arbor. The depth of cut was s/g in. and the 
table feed was 7 3/4 in. per minute. 

A surface about 1 in. wide all around an aluminum transmission 
case 12 X 14 in. was milled by means of a 10 1/2-in. inserted tooth face 
mill at 236 r.p.m. Depth of cut, i/g in., table feed, 0.068 in. per revolu- 
tion or 20 in. per minute. A double fixture was used, one piece being 
inserted while the other was being milled. Time, including chucking 
and removal, 2 I/2 minutes per piece. 

Gray iron castings, 10 1/4 in. wide, 14 in. long X 1 3/4 in. thick, finished 
all over, and a slot o/g x 1 in. cut from the solid. A gang of five cutters 
was used, two of 8 in., two of 3 1/2 in. and one of 53/4 in. diameter, re- 
spectively. These took a cut 3/i6 in. deep across the top, and two 
edges, and milled the slot in one operation. The table travel was 
4.2 in. per minute. The average time, including chucking, was 15.6 
minutes. 

Gray iron castings, 3 in. and 6 1/2 in. wide X 25 1/4 in. long, 1 1/4 in. 
thick, were surfaced by a face mill 8 in. diameter at a surface speed of 
80 feet per minute. The cut was ^/u in., and the table travel 11.4 in. 
per minute in the 3-in. part and 8 in. per minute in the 6 1/2-in. part. 
The total time for finishing, including chucking, was seven minutes. 
The planer required 23 minutes for the same operation. In finishing 



1282 



THE MACHINE-SHOP. 



the opposite side of these castings, two castings were milled at one setting, 
3/i6 in. of stock being removed all over and two slots s/g x s/g in. 
milled from the sohd. A gang of seven cutters, 3 of 3 in., 2 of 4 1/4 in., 
and 1 of 8 1/4 in. diameter was used at 38 r.p.m. and a feed of 0.1 in., 
giving a table travel of 3.8 in. per minute. These two castings were 
finished in 18 minutes, including chucking, the actual milhng time being 
eight minutes on each piece. A planer working at 55 ft. cutting speed 
finished the same job in 36 minutes. 

An inserted- tooth face mill 12 in. diameter took a 9-in. cut, i/g in. 
deep across the entire face of a gray iron casting at a table travel of 

5 in. per minute. The length of cut was 18 in. and the time required 

6 1/2 minutes. 

The foUowing table summarizes a number of typical jobs of milling: 





Typical Milling Jobs. 
















Cut, 


In. 


Cutte.-. 


ia 






1 




Material 










w^ 


U.3 


h. 


Nature of 










Work. 


Cut. 


1 


4 


i . 






Ti > 


0) ft 


|l5 


Face Milling 


Cast Iron 


1/8 


6 


8 


26 


54 


0.168 


4.36 


3.27 


" 


" 


1/8 


8 


9.51 


26 


64 


0.58 


15.0 


15.0 


** 


'* 


0.150 


8 


9.51 


24 


60 


0.625 


15. 


18.0 


** 


Mall. Iron 


1/16-3/32 


62 


7.5 


56 


110 


0.223 


12.5 




** 


Steel3 


7/162 


5 


61 


32 


50 


0.148 


4.75 


■92 •■ 


** 


*< 6 


1/8 


6 


9.51 


24 


60 


0.52 


12.5 


9.375 


Surfacing 


Cast Iron 


1/32 


3 


4 


68 


71 


0.18 


12.75 


1.75 


** 


" 


0.1 


12 


4.54 


45 


52 


0.266 


12.0 


14.4 


*' 


" 


0.1 


4 


35 


104 


81 


0.144 


15.0 


6.0 , 


** 


'* 


1/8 


4 


35 


104 


81 


0.078 


8.125 


4.06 


** 


** 


1/8 


8 


3.55 


90 


83 


0.167 


15.0 


15.00 


** 


'* 


1/8 


12 


3.5* 


53 


55 


0.226 


12.0 


14.4 


** 


** 


0.225 


8 


3.55 


85 


77 


0.118 


10.0 


18.0 


it 


" 


1/4 


8 


3.55 


81 


75 


0.154 


12.5 


25.0 


" 


" 


1/4 


8 


3.55 


94 


86 


0.159 


15.0 


30.0 


" 


Tool Steel 


1/16 


2 1/2 


37 


37 


29 


0.05 


1.85 


0.289 


** 


Steele 


0.1 


6 


35 


104 


81 


0.037 


3.875 


2.32 


** 


« 6 


0.15 


6 


35 


104 


81 


0.037 


3.875 


3.48 


** 


« 6 


0.166 


6 


3.55 


90 


83 


0.083 


7.5 


7.5 


** 


" 6 


0.222 


6 


3.55 


105 


96 


0.071 


7.5 


10.0 


** 


«« 6 


0.240 


6 


3.55 


94 


86 


0.133 


12.5 


18.0 


** 


" 6 


0.311 


6 


3.55 


100 


92 


0.075 


7.5 


14.0 


♦* 


Brass 


0.01 


21/2 


37 


100 


78 


0.25 


25.0 


0.675 


*t 


Bronze 


1/64 


3 


38 


166 


130 


0.05 


8.3 


0.389 


T-Slotting 


Cast Iron 


See No 


te? 


1 I/16 


252 


75 


0.05 


12.6 


6.693 


Slottingio 


Steel 




13/16 


1.511 


163 


65 


0.007 


1.25 


2.2 


Sawing 


" 




3/64 


5 


70 


91 


0.05 


3.5 





1 Inserted teeth, high-speed steel. 2 Maximum. » Chrome nickel 
steel. 4 Carbon steel, nicked spiral cutter, s High-speed steel, spiral 
nicked cutter, e Machinery steel, tensile strength, 65,000 lb. ' End 
mill. 8 End mill with spiral teeth; work done by peripheral teeth. 
* Both sides of cutter engaged, making slot width equal to cutter 
diameter; slot IVie X 1/2 in. 10 Milhng slots from sohd plate 13/i6 in. 
thick. 11 Helical end mill, front of which is formed as a regular twist 
drill. Operator first drills through the plate with it, and then uses it . 
as a milling cutter. 

High Speed Milling. — L. P. Alford describes (Am. Mach., April 16, 
1914) a system of high-speed milling developed by the Cincinnati 
Milling Machine Co., which permits of cutter speeds and feeds from 
8 to 12 times as great as are ordinarily used. The fundamental con- 
(iition for this practice is the provision of ample lubrication of the 



MILLING MACHINE PRACTICE. 



1283 



cutter and work. The cutter is deluged with about 12 gal. per minute 
of lubricant, which is delivered through a hood which completely sur- 
rounds the cutter. The lubricant is delivered under pressure, and 
in addition to cooling the cutter and work, washes away the chips 
from the teeth of the cutter, preventing them from being carried back 
into the cut, clogging it, duUing the cutter and marring the finished 
surface. Other requisites for liigh-speed milling are powerful, heavy 
and rigid machines, and cutters with wide spaced teeth which will 
permit the use of heavy feeds and high speeds. The following tests 
were cited to show what is possible with this system of milling.' The 
material cut was machinery steel, 0.2 carbon, 0.5 manganese, with a 
tensile strength of 55,000 to 65,000 lb. per sq. in. The cutters were 
of high speed steel. 







Data and Results of High Speed Milling Tests. 










Cutter. 


& 


Cut. 


Cutter 
Speed. 






a; 






1 . 














fl 




4S 
o 




Q 


No. of 
Teeth. 

Rake, 
Degree 


to . 


S 

-go 
< 




^ 

-S 

g 




1^ 


Id 




1 


S 


25 


3 1/2 


9 


10 


6 


1 1/2 


1/8 


5 


18 


500 


458 


30 1/2 


2 


s 


23 


3 1/2 


9 


10 


6 


1 V2 


0.02 


5 


18 


500 


458 


7.23 


3 


H 


69 


31/2 


3 


15 


6 


1 1/2 


(1/16 j. 

) 3/16 i 






510 


470 


30 1/2 


4 


T. 




6 5/16 


16 


15 


1 


1 1/2 






510 


835 


30 1/2 


















1 1/4 f 

I 7-Tooth ) 










5 


G 


71 


31/2 


12 


10 




11/4 


^30-PitchV.. 
) Gear, i 


18 1/4 


218 


200 


112 


62 


S 


25 


31/2 


9 


10 


6 


11/2 


1/4 1 5 


21/2 


87 


80 


20 



1 Diametral Pitch. 2 Same cutter and block as in Test No. 1, but 
run without lubricant. Test stopped when cutter showed signs of 
distress after cutting 2V2 in. Edges of teeth blued. 

Note. — S, spiral mill; H, helical mill; L, slotting cutter; G, gear 
cutter. 

As a criterion of the life of cutters under the above conditions, a cutter 
of the type used in test No. 5, was run to destruction. It milled 6700 
in., not including cutter approach, the equivalent of cutting 223 gears 
of 1-in. face, 7 pitch, 30 teeth. 

Limiting Factors of Milling Practice. — Discussing the above tests 
Mr. Alford gives the following as the limiting factors of milling ma- 
chine practice: (1) Power of the machine. Increased speed requires 
greater power per cubic inch of metal removed; according to the 
Cincinnati ^Milling ISIachine Co., doubling the speed necessitates a 10% 
increase of power per cubic inch of metal removed. (2) Ability of the 
cutter to remove metal. Increased speed, with the same feed increases 
the ability of the cutter to cut, due to the smaller chip removed by 
each tooth. This means a decrease of strain, wear and heating effect. 
The total or final heating effect is increased, but this may be coimter- 
acted by copious lubrication. (3) Size and spring of arbor. The size 
of the arbor is limited by the size of commercial cutters. The strain 
on the arbor depends on the feed per minute. An increase of speed, 
lessening the pressure per tooth, reduces the arbor strain, and tends 
to do away with the limitation imposed by the arbor. (4) Heating of 
the cutter, often the most important limitation. This can be over- 
come by sufficient lubricant to remove all heat as fast as it is generated. 
(5) Wear of the cutter. This is dependent on the number of lineal 
inches milled, depth of cut and feed per revolution being constant. 
Increased speed increases the wear per unit of time. Wear may be 
somewhat reduced with high speed by copious lubrication which washes 
away the chips, thus preventing the grinding action due to cutting 
up chips. (6) Breakage of cutters. Frail cutters limit production, 
as only a certain maximum feed per revolution, dependent on their 



1284 



THE MACHINE-SHOP. 



strength, can be taken. Increased speed, with constant feed, will 
increase production without increasing the cutter strain or danger of 
breakage. (7) Heating of work. Uneven local heating when milling 
will produce uneven surfaces, for the swelled portions will be cut away. 
This action is progressive as the total heat increases as the cut advances. 
The absence or prevention of heating by copious lubrication does 
away with tliis limitation. (8) Spring of work. This limitation is 
minimized for the same reasons given in (6). (9) Spring of fixture. 
The same analysis applies as in (6). If the pressure per tooth is re- 
duced, the pressure for holding may be reduced, and clamping fixtures 
may be made to operate more quickly. An increase in cutting speed 
therefore will tend to increase the speed of operation of the clamping 
devices and fixtures. (10) Spring of the machine. The same argu- 
ments apply as in (9). (11) Distance of revolution marks on the work. 
This is the limiting feature in perhaps 90% of milling work, which is 
governed by polishing or some subsequent operation. If the marks 
are far apart, polishing cannot be satisfactorily done. Increased 
speed, with constant feed will bring these marks closer together. (12) 
Smoothness of cut. High speed milling, both by the action of centrif- 
ugal force and by copious flooding removes the chips completely from 
the cutter and eliminates the grinding effect on the finished surface. 
With a given distance between revolution marks, high speed will give 
a smoother surface. 

Speeds and Feeds for Gear Cutting. — The speeds and feeds which 
can be used in gear cutting are affected by many variables, among 
which may be noted: The material and shape of the cutter, the latter 
condition involving both the strength and the ability of the teeth to 
clear themselves of chips; the material and shape of the gear, shape 
influencing the speed and feed in that a heavy rugged gear will permit 
higher speeds and heavier feeds, even in hard material than will a light 
springy one; accuracy of finish required; quality of lubricant used; 
rigidity of machine. The following table shows tentative speeds 
recommended by Gould and Eberhardt, which may serve as a pre- 
liminary guide, pending the determination of the best combination 
for each particular case. They represent average practice in medium 
grades of cast iron and steel. 





High-Speed Steel Cutters. 


Carbon Steel Cutters. 




Min. 


Max. 


Average . 


Min. 


Max. 


Average . 


Cast iron, ft. per min. . 
Steel, ft. per min 


60 
45 


70 
50 


80 
55 


35 
25 


60 
40 


45 
30 



The feeds in inches per minute recommended by the same company, 
depend on the capacity of the machine and on the size of the teeth. 
Thus, in a machine whose maximum capacity is for gears with teeth 
of one diametral pitch in cast iron and of 1 1/4 diametral pitch in steel, 
the feeds range from 2.3 in. per minute in cast iron for gears of 1 
diametral pitch to 6.9 in. for gears of 6 diametral pitch, carbon steel 
cutters being used. For high-speed steel cutters, the corresponding fig- 
ures are 3.5 and 11.0 in. In steel, the feeds under the same conditions 
are 1.9 in. and 4. .5 in. per minute with carbon steel cutters and 2.8 in. 
and 6.9 in. per minute with high-speed steel cutters. Likewise in a 
machine whose maximum capacity is teeth of 4 diametral pitch for 
cast iron gears and 5 diametral pitch for steel gears, the feed given for 
carbon steel cutters for gears of 4 diametral pitch is 2.6 in. per minute 
in cast-iron and 1.5 in. per minute in steel. For gears of 24 diametral 
pitch the figures are for cast iron 7.6 in. per minute, and for steel 5.8 in. 
per minute. Using high-speed steel cutters, the corresponding figures 
are: 4 diametral pitch, cast iron 4.5 in. per minute; steel, 3.5 in. per ■ 
minute; 24 diametral pitch, cast iron 10 in. per minute; steel, 7.6 in. per 
nainute. These figures merely show the range of feeds that are possible > 
in gear cutting, and the tables furnished by the manufacturers of gear- 
cutting machines should be consulted for the proper feeds for particular 



DRILLS AND DRILLING. 



1285 



DRILLS AND DRILLING. 

' Constant for Finding Speeds of Drills. — For finding the speed in 
feet when the number of revolutions is given; or the number of revolu- 
tions, when the speed in feet is given. 

Constant = \2 -~ (size of drill X 3.1410). 

Number of revolutions = Constant X speed in feet. 

Speed in feet = Number of revolutions -^ constant. 



Size 

Drill., 

In. 


Con- 
stant. 


Size 

Drill., 

In. 


Con- 
stant. 


Size 

Drill., 

In. 


Con- 
stant. 


Size 

Drill., 

In. 


Con- 
stant. 


Size 

Drill., 

In. 


Con- 
stant. 


1/8 

3/16 

1/4 

5/16 

3/8 

7/16 

1/2 

9/16 

5/8 

11/16 


30.55 
20.38 
15.28 
12.22 
10.19 
8.73 
7.64 
6.79 
6.11 
5.56 


3/4 

13/16 

7/8 

15/16 
1 

11/16 
1 1/8 
13/16 
1 
1 5/16 


5.09 
4.70 
4.36 
4.07 
3.82 
3.59 
3.39 
3.22 
3.06 
2.91 


13/8 
1 7/16 
1 1/2 
19/16 
1 5/8 
1 11/16 
1 3/4 
1 13/16 
17/8 
1 15/16 


2.78 
2.66 
2.55 
2.44 
2.35 
2.26 
2.18 
2.11 
2.04 
1.97 


2 

2 1/16 
2 1/8 
2 3/16 
2 1/4 
2 5/16 
2 3/8 
2 7/16 
2 1/2 
2 9/16 


1.91 
1.85 
1.80 
1.75 
1.70 
1.65 
1.61 
1.57 
1.53 
1.49 


2 5/8 
2 11/16 
2 3/4 
2 13/16 
2 7/8 

2 15/16 

3 1/16 
3 1/8 

3 1/4 


1.45 
1.42 
1.39 
1.36 
1.33 
1.30 
1.27 
1.25 
1.22 
1.18 



The Cleveland Twist Drill Co., Cleveland, states (1915) that it is 
safe to start carbon steel drills with a peripheral speed of 30 ft. per 
minute in soft tool and machinery steel, 35 ft. per min. in cast iron, and 
GO ft. per min. in brass. In all cases a feed of from 0.004 to 0.007 in. 
per revolution should be used for drills 1/2 in. diam. and smaller, and of 
from 0.005 to 0.015 in. per revolution for drills larger than H in. In 
the case of high speed steel drills these feeds should not be changed, but 
the peripheral speed may be increased from 2 to 2 1/2 times. The table 
below is calculated on the basis of the speeds given above for carbon 
steel drills, and on the basis of speeds 2 1/3 times higher for high-speed 
drills. The running speed may be higher or lower than the starting 
speed, and must be determined by good individual judgment for each 
case. 

Starting Speeds for Carbon and Higti-Speed Steel Drills in 
Steel, Cast Iron and Brass, R. P. M. 





Steel. 


Cast 
Iron. 


Brass. 


Drill 


Steel. 


Cast 
Iron. 


Brass. 


Drill 






















. 


Diam., 


5 


'2 i 




r! 


T3 


Diam., 


c 


'^ 


c 


5> 


c 


Si a 


In. 


a 


x^l i 


^%. 


^ 


pfl a 


In. 





^^ 


:^ 


s,t 


:^ 




f;? 


.^w 


^ 


.^m 


;;; 


tcm 




"^ 


M72 


!« 


torn 


^ 


MW 




u 


w 


U 


W 


u 


X 







X 


u 


278 




204 


a 


1/16 


1833 


4278 


2139 


4991 


3667 




11/8 


102 


238 


119 


475 


1/8 


917213911070 


2496 


1833 4278 


1 1/4 


92 


214 


107 


249 


183 


428 


3/I6 


611 1426 


71311664 


1222 2852 


13/8 


83 


194 


97 


227 


167 


389 


1/4 


458 1070 


535 1248 


917 2139 


11/2 


76 


178 


89 


208 


153 


357 


5/I6 


367' 856 


428! 998 


733 1711 


15/8 


7U 


165 


82 


192 


141 


329 


3/8 


306' 713 


357 832 


61 r 1426 


13/4 


65 


153 


76 


178 


131 


306 


7/16 


2621 611 


306 714 


524 1222 


17/8 


61 


143 


71 


166 


122 


285 


1/2 


229 535 


263 614 


458 1070 


2 


57 


134 


67 


156 


115 


267 


5/8 


183 428 


215 500 


367 856 


21/4 


51 


119 


60 


139 


102 


238 


3/4 


153 357 


178 415 


306 713 


21/2 


46 107 


54 


125 


92 


214 


7/8 


131 306 


153 357 


262 611 


23/4 


42 97 


49 


114 


83 


194 




1151 267 


1341 312 


229 535 


3 


381 89 


45 


104 


76 


178 



A drill with a tendency to wear away on the outside^ is running too fast; 
if it breaks or chips on the cutting edges it has too much feed. 

Forms of Drills. — The common form of twist drill is a cylinder with 
two spiral flutes milled in it. Another type, for heavy duty, consists 
of a twisted bar of flat steel. The angle that the cutting edges makes 
with the axis of the drill has been fixed at about 59°. A decrease 
in this angle decreases the pressure required for feeding the drill, but 
increases the power required to turn it. The cutting edge of a six)tting 



1286 



THE MACHINE-SHOP. 



drill should make an angle of about 50° with the axis of the drill. 
The clearance angle, that is, the angle between the surface back of the 
cutting edge and a plane perpendicular to the axis of the drill, ranges 
from 12 to 15°, the angle increasing slightly toward the center. In 
general, the small clearance is best for hard metals and the large 
clearance for soft metals. 

Drilling Compounds. — The following drilling compounds or lubri- 
cants are recommended when drilling the materials given below: 

-soda water. 



Steel (hard) — kerosene, turpentine, 

soda water. 
Steel (soft) — soda water, lard oil. 
Iron (wrought) — soda water, lard 

oil. 



Iron (mall cable) - 

Iron (cast) — none or air blast. 

Brass — parafflne oil. 

Aluminum — soda water, kerosene. 



Warming the lubricant before applying it to high-speed drills is 
recommended, and precautions should be taken against suddenly chilling 
high-speed drills by the lubricant after they have become heated. 

Twist Drill and Steel Wire Gages. — Three standards of gages for 
twist drills and steel wire are in use — the Manufacturers' Standard, 
used by the Morse Twist Drill Co., Brown & Sharpe, and other manu- 
facturers, the Stubs gage, and that of the Standard Tool Co. The 
Stubs and Manufacturers' gages are given in the table on page 30. 
The Standard Tool Co. gage agrees with the Manufacturers' gage for 
sizes from Nos. 1 to 60, inclusive, and with the Stubs gage for sizes 
from Nos. 61 to 80. In addition it has additional H sizes interpolated 
at Nos. 601/2, 681/2, 691/2, 711/2, 731/2, 741/2, 781/2, and 791/2. 

Power Required to Drive High-Speed Drills. — H. M. Norris, me- 
chanical engineer of the Cincinnati-Bickford Tool Co., found (1914) 
that the power absorbed by a 6-foot, high-speed, high-power, plain 
radial drill fitted with a variable speed motor, in driving drills in 
machine steel under a stream of water, varied in accordance with the 
formula: 

H.P. = 0.152 (R + 2.1) di.25/0.74 I r - I — - + 6.8 1 

R = ratio between speed of the intake shaft and speed of the spindle; 
d = diameter of drill, in.; /= feed in thousandths of an inch per revolu- 
tion; r = rev. per min. 

The values deduced from this formula are given in the table, p. 1287; 
the figures 1, 2, and 4 in the column " Ratio R" represent the ratios of 
1 to 1, 1 to 2, and 1 to 4 respectively. The table also gives the results 
obtained in drilling medium cast-iron, but these, at this writing, have 
not been reduced to a formula. 

The American Tool Works Co., Cincinnati, has furnished the 
author with the tests given in the table below, made in 1912, showing 
the power required to drive drills in a 6-foot plain triple-geared radial 
drill made by that company. This table shows the results obtained 
with speeds and feeds higher than those given by Mr. Norris. 



')] 



Power Required to Drive Drills. (Amer. Tool Works Co., 1912.) 




Cast Iron. 


Steel. 


Size 

of 

Drill, 


Speed. 


Feed. 


Horse- 


Speed. 


Feed. 




Rev. 


Ft. 


Per 


In. 


Rev. 


Ft. 


Per 


In. 


Horse- 


In. 


per 


per 


Rev., 


per 


power 


per 


per 


Rev., 


per 


power. 




Min. 


Min. 


In. 


Min. 




Min. 


Min. 


In. 


Min. 




1 


430 


111.25 


0.049 


21.07 


8.26 


335 


88 


0.036 


12.06 


13.50 


11/4 


430 


140 


.049 


21.07 


11.65 


258 


84.5 


.026 


6.70 


10.43 


n/2 


430 


157 


.049 


21.07 


18.65 


229 


90 


.018 


4.12 


14.86 


13/4 


430 


197 


.049 


21.07 


19.75 


178 


81.5 


.018 


3.20 


9.91 


2 


297 


156 


.049 


14.56 


19.79 


143 


75 


.018 


2.57 


12.32 


21/4 


202 


119 


.036 


7.27 


14.82 


143 


84.2 


.018 


2.57 


15.06 


21/2 


178 


116.5 


.036 


6.40 


11.24 


143 


93.6 


.013 


1.86 


13.51 


3 


143 


112 


.036 


5.14 


14.31 


47.5 


37.2 


.026 


1.21 


12.46 



DRILLS AND DRILLING. 



1287 



Power Eequired for Drilling Cast Iron and Steel. (H. M. Norris, 1915.) 










Cast Iron. j Machinery Steel. 


d 


0.020 in. 


0.030 in. 


0.040 in. 


0.012 in. 


0.016 in. 


0.020 in. 


"r 








Feed. 


Feed. 


Feed. 


Feed. 


Feed. 


Feed. 


B 


^ 




t~, . 




(-< , 




^ 












s 


C/2 . 


K 


^ 


^.s 




la 




^.s 



1 ^ 


^•5 


i 
^ 


IB 


1 


&-H 






3 


a, 

i 




•si 





5d 


i 



5 c 





5 c 


i 
w a 




5 c 





Ji r-* 


2 0, 



Q 


o 


« 


Pi 


Q 


w 


Q 


K 


Q 


W 


Q 


W 


Q 


ffi 


Q 


W 


~yl 


60 


306 


I 


6.12 


2.76 


9.18 


3.52 


12.24 


4.203.67 


2.84 


4.90 


3.53 


6.12 


4.15 


3/4 


70 


357 


1 


7.14 


3.36 


10.71 


4.29 


14.28 


5.104.28 


3.49 


5.72 


4.32 


7.14 


5.09 


3/4 


80 


408 


1 


8.16 


3.98 


12.24 


5.08 


16.32 


6.0414.90 


4.12 


6.53 


5.10 


8.16 


6.02 


3/4 


90 


459 


1 


9.18 


4.60 


13.77 


5.86 


18.35 


6.965.51 


4.76 


7.34 


5.89 


9.18 


6.95 


3/4 


lUO 


509 


' 


10.18 


5.21 


15.27 


6.64 


20.36 


7.89j6.11 


5.40 


8.14 


6.68 


10.18 


7.88 


1 


60 


229 


2 


4.58 


2.88 


6.87 


3.67 


9.16 


4.3612.75 


4.0l'3.66 


4.96 


4.58 


5.85 


1 


70 


267 


1 


5.34 


3.09 


8.00 


3.94 


10.67 


4.683.21 


3.724.27 


4.60 


5.34 


5.43 


I 


80 


306 


1 


6.12 


3.66 


9.18 


4.66 


12.24 


5.54 3.67 


4.39 4.89 


5.44 


6.12 


6.42 


1 


90 


344 


1 


6.88 


4.22 


10.32 


5.38 


13.76 


6.394.13 


5.165.50 


6.39 


6.88 


7.54 


1 


100 


382 


1 


7.64 


4.79 


11.46 


6.11 


15.27 


7.26|4.59 


5.796.11 


7.17 


7.64 


8.46 


11/4 


60 


183 


2 


3.66 


3.10 


5.49 


3.95 


7.32 


4.702.19 


4.21 2.93 


5.21 


3.66 


6.15 


11/4 


70 


214 


2 


4.28 


3.80 


6.42 


4.84 


8.56 


5.75 2.57 


5.173.42 


6.40 


4.28 


7.55 


11/4 


80 


245 


2 


4.90 


4.50 


7.36 


5.74 


9.80 


6.82 2.94 


5.96 3.92 


7.57 


4.90 


8.93 


11/4 


90 


275 


I 


5.48 


3.95 


8.22 


5.04 


11.00 


5.99 3.29 


5.354.38 


6.62 


5.48 


7.81 


11/4 


100 


306 


1 


6.12 


4.49 


9.18 


5.73 


12.24 


6.81 3.67 


6.084.89 


7.52 


6.12 


8.87 


11/2 


60 


153 


2 


3.12 


3.27 


4.59 


4.17 


6.12 


4.96*1.84 


4.36'2.45 


5.39' 


3.12' 


6.36 


11/2 


70 


178 


2 


3.56 


4.02 


5.34 


5.12 


7.02 


6.082.14 


5.35 2.85 


6.62 


3.56 


7.81 


11/2 


80 


204 


2 


4.08 


4.77 


6.06 


6.08 


8.16 


7.23 2.45 


6.35 3.26 


7.86 


4.08 


9.27 


11/2 


90 


230 




4.60 


5.51 


6.90 


7.03 


9.20 


8.36 2.76 


7.35 3.68 


9.10 


4.60 


10.73 


11/2 


100 


254 




5.04 


6.27, 


7.62 


7.99 


10.16 


9.50 3.05: 


8.344.07 


10.32: 


5.04 


12.17 


13/4 


60 


131 


- 


2.62 


3.42' 


3.93 


4.36 


5.24 


5.18'l.57' 


4.48'2.10 


5.55! 


2.62' 


6.55 


13/4 


70 


153, 




3.06 


4.21, 


4.59 


5.37 


6.12 


6.38 1.84 


5.53 2.45 


6.84, 


3.06 


8.07 


13/4 


80 


175 




3.50 


5.00' 


5.25 


6.38 


7.00 


7.582.10 


6.56 2.80 


8.12 


3.50 


9.58 


13/4 


90 


196 




2.92 


5.80! 


5.88 


7.39 


7.84 


8.78 2.35 


7.602.14 


9.41 


3.92 


11.10 


13/4 


100 


218 




4.36 


6.59 


6.52 


8.40 


9.12 


9.98 2.62' 


8.63 3.49 


10.68, 


4.36 


12.60 


2 


60 


115' 




2.30 


4.87! 


3.45 


6.22! 


4.60 


7.39'l.38! 


6.82'l.84' 


8.44' 


2.30' 


9.96 


2 


70 


134 




2.68 


4.38; 


4.04 


5.59 


5.36^ 


6.64 I.6I1 


5.662.14 


7.00 


2.68 


8.26 


2 


80 


153 




3.06 


5.21I 


4.59 


6.65 


6.12 


7.90 1.84 


6.73 2.451 


8.33 


3.06 


9.83 


2 


90 


172 




3.44 


6.04 


5.16 


7.71 


6.881 


9.162.06 


7.81 2.75 


9.66 


3.44 


11.40 


2 


100 


19r 




3.82, 


6.87 


5.73 


8.77^ 


7.64 


10.322.29 


8.87|3.06 


10.98. 


3.82 


12.95 


21/4 


60 


102' 


4 


2.04' 


5.18 


3.06 


6.60 


4.08! 


7.84'l.22' 


6.95 1.63' 


8.60' 


2.04' 


10.14 


21/4 


70 


119 




2.38 


6.40' 


3.57 


8.16 


4.76! 


9.70 1.43 


8.60 1.90 


10.64 


2.38 


12.55 


21/4 


80 


136 




2.68 


5.40 


4.08 


6.88 


5.44' 


8.18 1.63 


6.882.18 


8.52 


2.68 


10.05 


21/4 


90 


153 




3.06 


6.27 


4.59 


7.99 


6.12 


9.50 1.84 


7.98 2.45 


9.88 


3.06 


11.65 


21/4 


100 


170 




3.40 


7.13, 


5.10 


9.09 


6.80 


10.802.04 


90.9 2.72, 


11.25, 


3.40 


13.27 


21/2 


60 


92' 


. 


1.83 


5.461 


2.75' 


6.96' 


3.67 


8.27'l.lo' 


7.06' 


1.47' 


8.74I 


1.83' 


10.31 


21/2 


70 


107 




2.14 


6.76 


3.21 


8.63 


4.28 


10.26 1.28 


8.75 


1.71 


10.83 


2.14 


12.77 


21/2 


80 


122 




2.44 


8.06 


3.66 


10.29 


4.88 


12.23 1.46 


10.43 


1.95 


12.91; 


2.44 


15.23 


21/2 


90 


138 




2.76 


6.46 


4.14 


8.24 


5.52 


9.79 1.66| 


8.14 


2.21 


10.08; 


2.76 


11.89 


21/2 


100 


'^^1 




3.06 


7.36j 


4.59 


9.39 


6.12 


11.16 1.84 


9.28 


2.45 


11.49 


3.06, 


13.55 


23/4 


60 


83' 




1.67' 


5.73' 


2.50' 


7.30' 


3.34' 


8. 68' 1.00' 


7.15' 


1.33 


8.85' 


1.67' 


10.44 


23/4 


70 


97 




1.94 


7.11 


2.92 


9.06 


3.89 


10.77 1.17 


8.87 


1.55 


10.98 


1.94 


12.95 


23/4 


80 


111 




2.22 


8.49 


3.33 


10.83 


4.44 


12.87 1.33 


10.62 


1.78 


13.14 


2.22 


15.50 


23/4 


90 


125 




2.50 


9.90 


3.75 


12.62 


5.00 


15.00 1.50 


12.34 


2.00 


15.27 


2.50 


18.00 


23/4 


100 


139 




2.78 


7.59 


4.17, 


9.68 


5.56 


11.50 1.67 


9.46 


2.23 


11.71 


2.78 


13.81 


3 


60 


76' 




1.53 


5.96' 


2.29' 


7.60' 


3.06' 


9.03 0.92 


7.22' 


1.22 


8.94' 


1.53' 


10.55 


3 


70 


89 




1.78 


7.42 


2.67 


9.46 


3.56 


11.25 1.07 


8.98 


1.43 


11.12 


1.78 


13.12 


3 


80 


102 




2.04 


8.88 


3.06 


11.32 


4.08 


13.45 1.27 


10.75 


1.63 


13.31 


2.04 


15.71 


3 


90 


115 




2.30 


10.33 


3.45 


13.17 


4.60 


15.65 1.38 


12.52 


1.84 


15.48 


2.30 


18.26 


3 


100 


127 




2.54 


11.75 


3.81 


15.00 


5.08 


17.82 


1.52. 


14.26 


2.03 


17.651 


2.54 


20.82 



1288 



THE MACHINE-SHOP. 



Feeds for Drills. — According to Mr. Norris, the rate at which a drill 
may be advanced per revolution depends upon the toughness of the 
material to be drilled, the ability of the machine to resist thrust without 
forfeiture of alignment and upon the knowledge that is exercised in the 
grinding of the drill — the size of its included angle, the width of its 
chisel point, and the keenness and evenness of its cutting edges, all being 
deciding factors. Were it not for the weakening effect on the drill it 
could be said that the stiffer the machine, the less the included angle; 
the narrower the chisel point, the smaller the degree of the spiral; the 
greater the uniformity of the cutting lips and the more efficacious the 
lubricant in minimizing the frictional resistance of the chips, the coarser 
becomes the feed it is permissible to use. But, inasmuch as the 
durability of the drill must not be impaired, the advantage obtainable 
through the application of these axioms has its limitations. The 
keenness of edges needed to attain maximum efficiency in cutting cast- 
iron disquahfies for work in steel a drill suitable for use in cast-iron. 
The highest rate of feed at which drills of from 3/8 to 3 in. diam. may 
be operated in steel appears to be about 0.060 in. per revolution, but 
the employment of such feeds increases, rather than decreases the cost of 
work. The feeds provided in the product of the Cincinnati-Bickford 
Tool Co. range from 0.006 in. to 0.040 in. per revolution, which, under 
favorable conditions, may be utilized as follows: 

Hard 0.006 to 0.010 in. Hard. 0.015 to 0.020 in. 

Medium 0.012 to 0.018 in. Medium 0.020 to 0.030 in. 

Soft 0.020 to 0.028 in. | Soft . 030 to . 040 in. 

Speed of Drills. — Mr. Norris says further that while an occasional 
drill is found that will withstand for days a cutting speed of 150 ft. 
per minute, in either ca.st-iron or steel (the latter under a lubricant), 
it is rarely expedient to drive any but very small ones faster than 100 
ft. per min. Operating drills at an excessive speed is an expensive fad. 
It is more economical to err in the other direction. The most satis- 
factory results have been obtained at a cutting speed of 80 ft. per min. 

12 
In cast-iron and -r + 76 ft. in steel. This formula will decrease 

the cutting speed from 100 ft. per min. for a V^-in. drill to 80 ft. for a 
3-in. drill. The reason for this- reduction is that a stream of liquid 
sufficient to keep a small drill cool is insufficient to prevent overheating 
In a large one. 

In order to facilitate the use of the formulae for horse-power there 

52 2 
is given in the following table the deduced values for /"-^S d^-^^, ~~r- 

+ 6.8 and ^ + 76. 

Values of /0.74, fZi.25, 5^ 4. q.s and of ^ + 76. 



i 







C 




00 








u 




C30 




a 




S 




so 




& 




S . 




sO 




i 


^ 


2 c 


S 


+ 






^ 




s 


+ 


+ 


^ 





Q"^ 


ts 


in 


:iN 





«>-. 


Q 


'^ 


^l-^ 


j:il-a 


0.008 


0.02807 


y?. 


0.421 


111.2 


100.0 


0.022 


0.05934 


17/8 


2.194 


34.6 


82.4 


.009 


.03063 


5/8 


.556 


90.3 


95.2 


.024 


.06329 


2 


2.378 


32.9 


82.0 


.010 


.03312 


3/4 


.698 


76.4 


92.0 


.026 


.06715 


21/8 


2.566 31.4 


81.6 


.011 


.03553 


7/8 


.846 


66.6 


89.7 


.028 


.07094 


21/4 


2.756! 30.0 


81.3 


.012 


.03789 


1 


1.000 


59.0 


88.0 


.030 


.07466 


23/8 


2.9481 28.8 


81.0 


.013 


.04021 


11/8 


1.158 


53.2 


86.9 


.032 


.07831 


21/^ 


3.144 27.7 


80.0 


.014 


.04248 


n/4 


1.322 


48.5 


85.6 


.034 


.08190 


25/8 


3.342: 26.7 


80.6 


.015 


.04470 


13/8 


1.489 


44.8 


84.7 


.036 


.08544 


23/4 


3.5411 25.8 


80.4 


.016 


.04689 


11/^ 


1.660 


41.6 


84 


.038 


.08894 


27/8 


3.741 25.0 


80.2 


.018 


.05115 


15/8 


1.833 


38.9 


83.4 


.040 


.09237 


3 


3.948 24.2 


80.0 


.020 


.05530 


13/4 


2.013 


36.6 


82.9 













DRILLS AND DRILLING. 



1289 



Extreme Results with Drills.— The Cleveland Twist Drill Co. 
furnishes the following table of results of drilling tests made at the 
convention of Railway Master Mechanics' Association at Atlantic City, 
N. J., June. 1911 The object of the tests was to demonstrate good 
shop practice, dnlhng being done at speeds and feeds considered 
economical under average shop conditions, and also to show what were 
the ultimate possibilities of drills and machines. Tlu' drills uschI w(to 
flat twisted drills, and the ordinary milled drill. Th(» n^cord per- 
formance for high-speed drilling is test No. 4. in wliich a 1 1/4 in. drill re- 
peatedly drilled through a casting at 57 1/2 in. per minute. In the tests 
to demonstrate good shop conditions, the drill in tt^st No. 17 drilled (iS 
holes, removing 1418 cu. in. of mental without ))eing rc^grotmd, and was 
in good condition at the close of the test. The Cleveland Twist Drill 
Co. does not recommend the high speeds and heavv fcvds attained as 
economical shop practice, but points out that the results can be duplicat- 
ed by carefully established ideal conditions of absolute rigidity in the 
machine, solid clamping of the work, perfect grinding of the drill and 
expert handling. 

Record Performances of High-Speed Drills. 





Sizes of 






Feed 


Inches 


Rev., 


1 Cu. In. 


No. 


Drill, 
In. 


Material 


R.P.M. 


Rev. 


Drilled 
per Min. 


Speed in 

Feet 
per Min. 


Metal 
Removed 
per Min. 


1 


1 1/4 


jirf 


500 


0.050 


25 


163.6 


30.68 


2 


11/4 





325 


0.100 


321 2 


106 


39.88 


3 


U/4 




475 


0.100 


471/2 


155 


58.29 


4 


n/4 




575 


0.100 


571/2 


188 


70.56 


5 


IV2 


^ 


300 


0.030 


9 


117 


15.90 


6 


11/2 


7k 


325 


0.100 


321/2 


127.6 


57.43 


7 


11/2 




335 


0.100 


331/2 


131.5 


59.19 


8 


11/2 





355 


0.100 


351/2 


139.4 


62.73 


9 


13/4 


^-^ 


235 


0.100 


231/2 


107.6 


56.52 


10 


13/4 


^ 


350 


0.100 


35 


160 


84.19 


11 


25/16 


rt 


190 


0.050 


91/2 


115 


39.90 


12 


3 





120 


0.100 


12 


94 


84.82 


13 


11/4 




350 


0.030 


101/2 


113.7 


12.88 


14 


15/8 


1. 


225 


0.040 


9 


94.8 


18.66 


15 


25/16 


165 


0.020 


31/4 


100 


13.86 


16 


25/16 


W « 


200 


0.020 


4 


121 


16.80 


17 


21/2* 


fe*^ 


150 


0.015 


21/4 


98 


11.04 


18 


21/2* 


S'- 


150 


0.040 


6 


98 


29.45 


19 


21/2* 


^^ 


175 


0.040 


7 


114.5 


34.36 


20 


13/4 


S^ 


275 


0.030 


8 1/4 


125 


19.84 


21 


•7 

-> 


^ 


150 


0.030 


41/2 


117.8 


31.81 


22 


31/4 


150 


0.C30 


41/2 


127 


37.33 



* Milled drills; all other drills are flat twisted drills. 

Experiments on Twist Drills. — An extensiv^e series of expiM'iments 
on the forces acting on twist drills of high-sp(H^d steel wh(>n oi)erating 
on cast-iron and steel is reported by DempstiM* Smith and A. l\>liak()n", 
in Proc. Inst. M. E., 1909. Abstracted in Am. Mach., May. 1909, and 
Indust. Eng., May, 1909. Approximate equations derived from the 
first set of experiments are as follows: 

Torque in pounds-feet, /= (1800^4-9)^^ for medium cast-iron; 
T = (3200 t + 20) rf^ for medium steel. End thrtist, lb., P = 115,000 
i - 200, for medium cast-iron; P = 160, 000(rf - 0.5)^ — 1000, for 
medium ."^teel; d = diam., t = feed per revolution of drill, both in inches. 
The steel was of medium hardness, 0.29 C, 0.625 Mn. 

The end thrust in enlarging holes in medium steel from one size to 
a larger was as follows: 3/4 in. to 1 in., P = 15,200 f -}- 60; 1 in. to II/2 in., 
P = 25,500 ^ + ; 3/4 in. to 1 1/2 in., P = 30,000 t + 200. 

A second series of experiments with soft cast-iron of C.C, 0.2; G.C., 
2.9; Si, 1.41; Mn, 0.68; S, 0.035; P, 1.48, and medium steel of C, 0.31; 



1290 



THE MACHINE-SHOP. 



Si, 0.07; Mn, 0.50; S, 0.018; P, 0.033; tensile strength, 72,600 lb. per 
sq. in., gave results from which were derived the following approximate 
equations : 
Torque, Ib.-ft., T = 740 di-8^0.7, or 10 d2 + 100 ^(14 d2 + 3) for cast iron, 

T = 1640 rfi.8^0.7, or 28 d2(l + 100 t) for medium steel, 
End thrust, lb. P = 35,500 do.7 ^0.75, or 200 d + 10,000 t for cast iron, 

P = 35,500 do.7^0.3, or 750 d + 1000 ^ (75 d + 50) for 
medium steel, 
and for different sizes of driU the following equations: 



Drill. 


V4 


1 


IV2 


Cast iron T = 

Cast iron P = 

Steel T = 


5+1.100^ 
125 +82.000 i 
7.5+3.350^ 
550 + 1 09.000 i 


10 + 1.750^ 
200+89.000^ 
17.5+4.400^ 
750 + 131.000 ; 


25+3.700^ 

350 + 1 03.000 i 

40+9.000^ 


Steel P = 


1.250 + 162,000^ 



DrUl. 


2 


21/2 


3 


Cast iron T = 

Cast iron P = 

Steel T = 


40+5,900^ 

500 + 1 10.000 f 

75+12.500 < 

1,500 + 181.250 < 


60 +8.800 t 
600 + 126.000 f 
112.5 + 19.050 t 
], 125 +224,315 1 


90 + 12,900 < 
850 + 140,000 < 
175+26,250 < 


Steel P = 


2,350 +280.000 < 



The tests above referred to were made without lubricants. When 
lubricants were used in drilling steel the average torque varied from 
72 % with 1/400 in. feed to 92 % with 1/35 in. feed of that obtained when 
operating dry. The thrust for soft, medium and hard steel is 26%, 
37%, and 12% respectively less than when operating dry, no marked 
difference being found, as in the torque, with different feeds. The horse- 
power varies as ^07 and as dO-S for a given drill and speed. The torque 
and horse-power when drilling medium steel is about 2.1 times that 
required for cast iron with the same drill speed and feed. The horse- 
power per cu. in. of metal removed is inversely proportional to dO-2 tO-3, 
and is independent of the revolutions. 

While the chisel point of the drill scarcely affects the torque it is ac- 
countable for about 20% of the thrust. Tests made with a preliminary 
hole drilled before the main drill was used to enlarge the hole showed 
that the work required to drill a hole where only one drill is used is 
greater than that required to drill the hole in two operations, with drills 
of different diameter. 

For economy of power a drill with a larger point angle than 120° is to 
be preferred, but the increased end thrust strains the machine in propor- 
tion, and there is more danger of breaking the drill. 

Cutting Speeds for Tapping and Tiireading. (Ajii. Mach., Aug. 3, 
1911.) — The National Machine Co., for tapping and threading, uses 
speeds of 233 r.p.m. for sizes and holes up to 1/4 in. diameter, and 140 
r.p.m. for sizes from 1/4 in. to 1/2 in. diameter, with a lubricant of 
screw-cutting oil. Both the Bignall & Keeler Co. and the Standard 
Engineering Co. recommend a cutting speed of 15 ft. per minute. 
The former recommends lard oil as a lubricant. The practice of the 
F. E. Wells Co. in tapping and the Landis Machine Co. m threading 
in machines of the bolt cutter type is as follows: 

Speeds for Tapping and Threading — r. p. m. 



Mate- 
rial. 


F. E. Wells. 


Landis. 


Mate- 
rial. 


F. E. Wells. 


Landis. 


Steel. 


Cast 
Iron. 


Steel. 


Cast 
Iron. 


Steel. 


Cast 
Iron. 


Steel. 


Cast 
Iron. 


Lubri- 
cant. 


Oil. 


Oil or 
Soda 
Comp. 


Oil. 


Petro- 
leum. 


Lubri- 
cant. 


Oil. 


Oil or 
Soda 
Comp. 


Oil. 


Petro- 
leum. 


1/4 in. 

8/8 " 


299 
153 
115 
91 


382 
255 
191 
153 


280 
220 
175 


200 
150 
125 


3/4 in. 
I 
1 1/2 " 


76 


127 


140 

115 

75 

6 


100 

85 


1/2 " 






55 


5/8 " 






45 



CASE-HARDENINQ. 1291 

SAWING METALS. 

Speeds and Feeds for Cold Sawing Metals. — (Mach'y, Jan., 1914). 
— For sawing 0.30 carbon, open-hearth machine steel bars in a cold 
sawing machine, a feed of 1 in. per minute and a peripheral speed of 
approximately 45 ft. per minute was used. The bars were 5 in. diam- 
eter, and an average of 145 were sawed with one shari)ening of the 
saw. P'or some classes of work a feed of 2 in. per minute can be used, 
but 3/4 in. per minute is advisable for 0.30 carbon steel with the saw 
in good condition. For tool steel and alloy steel the best economy 
will be obtained with a feed of 1/2 in. per minute and a surface speed 
of 30 ft. per minute, with a grinding every 100 pieces. 

Hack Sawing Machines. — Charles AVicksteed {Proc. Inst. Mech. 
Engrs., 1912) says that the important considerations to be observed in 
using hack sawing machines are: For ordinary work, a coarse pitch 
tooth, not less than 10 to the inch is best; extra strength of the saw is 
to be obtained by extra depth, not extra thickness, of blade; the greatest 
weight that a blade will take without injury is 7 lb. per tooth or 70 lb. 
per in. ; a 6-in. machine thus will use the full capacity of the blade on 
4-in. bars with a weight of 210 lb. on the blade. As the size of the 
machine increases, the weight increases proportionately, a 15-in. ma- 
chine employing 700 lb. and using the full capacity of the blade when 
sawing a 10-in. surface. A hack sawing machine will cut true to 0.01 
in. in a mild steel bar at a speed roughly of 1 to 2 sq. in. per minute. 

Saws for Copper. — A special saw for cutting copper has teeth with 
a front rake of 10°. The metal is ground away at the sides of the 
teeth to provide clearance. The number of teeth should be com- 
paratively smaU. A pitch of about 1 in. giving 10 teeth in 3-in. saw 
renders good service. 

CASE-HARDENING, ETC. 
Case-hardening of Iron and Steel, Cementation, Harveyizing. — 
When iron or soft steel is heated to redness or above in contact with 
charcoal or other carbonaceous material, the carbon gradually penetrates 
the metal, converting it into high carbon steel. The depth of penetra- 
tion and the percentage of carbon absorbed increase with the tempera- 
ture and with the length of time allowed for the process. In the old 
cementation process for converting wrought iron into "blister steel" for 
re-melting in crucibles flat bars were packed with charcoal in an oven 
which was kept at a red heat for several days. In the Harvey process of 
hardening the surface of armor plate, the plate is covered with charcoal 
and heated in a furnace, and then rapidly cooled by a spray of water. 

In case-hardening, a very hard surface is given to articles of iron or 
soft steel hy covering them or packing them in a box or oven with a ma- 
terial containing carbon, heating them to redness while so covered, and 
then chilling them. Many different substances have been used for the 
purpose, such as wood or bone charcoal, charred leather, sugar, cyanide 
of patassium, bichromate of potash, etc. Hydrocarbons, such as illu- 
minating gas, gasolene or naphtha, are also used. Amer. Machinist, 
Feb. 20, 1908, describes a furnace made by the American Gas Furnace 
Company of Elizabeth, N. J., for case-hardening by gas. The best results 
are obtained with soft steel, 0.12 to 0.15 carbon, and not over 0.35 man- 
ganese, but steel of 0.20 to 0.22 carbon may be used. The carbon begins 
to penetrate the steel at about 1300° F., and 1700° F. should never be 
exceeded with ordinary steels. A depth of carbonizing of i/64 in. is 
obtained with gas in one hour, and 1/4 in. in 12 hours. After carbonizing 
the steel should be annealed at about 1625° F. and cooled slowly, then 
re-heated to about 1400° F. and quenched in water. Nickel-chrome steels 
may be carbonized at 2000° F. and tungsten steels at 2200° F. 

Change of Shape due to Hardening and Tempering. — J. E. Storey, 
Am. Mach., Feb. 20, 1908, describes some experiments on the change of 
dimensions of steel bars 4 in. long, 7/8 in. diam. in hardening and temper- 
ing. On hardening the length increased in different pieces .0001 to 
.0014 in., but in two pieces a slight shrinkage, maximum .00017, was found. 
The diameters increased .0003 to .0036 in. On tempering the length 
decreased .0017 to .0108 in. as compared with the original 4 ins. length, 
while the diameter was increased .0003 to .0029; a few samples showing 
a decrease, max. 0009 in. The general effect of hardening is a slight 
increase in bulk, which increase is reduced by tempering. 



1292 



THE MACHINE-SHOP. 



POWER REQUIRED FOR MACHINE TOOLS. 

Resistance Overcome in Cutting Metal. (Trans. S. M. E., 
viii, 308.) — Some experiments made at the works of William Sellers 
& Co. showed that the resistance in cutting steel in a lathe would vary 
from 180,000 to 700,000 pounds per square inch of section removed, 
while for cast iron the resistance is about one-third as much. The 
power required to remove a given amount of metal depends on the 
shape of the cut and on the shape and sharpness of the tool used. If 
the cut is nearly square in section, the power required is a minimum; 
if wide and thin, a maximum. The dullness of a tool affects but little 
the power required for a heavy cut. 

F. W. Taylor, in the Art of Cutting Metals {Trans. A. S. M. E., 
xviii) gives the tangential pressure of the chip on the tool as ranging 
from 70,000 lb. per sq. in. when cutting soft cast iron with a coarse 
feed, to 198,000 lb. per sq. in. when cutting hard cast iron with a fine 
feed. In cutting steel, the pressure of the chip on the tool per sq. in. 
ranged from 184,000 lb. to 376,000 lb. The pressure, he found, is 
independent of the speed, and in the case of steel is independent of 
the hardness of the steel. It increases as the quaUty of the steel grows 
finer; that is, high grade steel, whether hard or soft, will give higher 
pressures than low grade steel. He also found that an increase in 
the tensile strength and ductility of the steel increases the pressure, 
the former having the greater effect. 

Horse-power Required to Run Lathes. — The power required to 
do useful work varies with the depth and breadth of chip, with the 
shape of tool and with the nature and density of metal operated upon ; 
and the power required to run a machine empty is often a variable 
quantity. For instance, when the machine is new, and the working 
parts have not become worn or fitted to each other as they will be after 
running a few months, the power required will be greater than will be 
the case after the running parts have become better fitted. 

Another cause of variation of the power absorbed is the driving-belt,* 
a tight belt will increase the friction. 

A third cause is the variation of journal-friction, due to slacking up 
or tightening the cap-screws, and also the end-thrust bearing screw. 

Owing to the demand imposed by high speed tool steels stouter 
machines are more necessary than formerly; these possess more rigid 
frames and powerful driving gears. The most modern (1915) forms 
of lathes obtain all speed changes by means of geared head-stocks, 
power being delivered at a single speed by a belt, or by a motor. If a 
motor drive is used, a speed variation may be obtained in addition to 
those available in the head, by using a variable speed motor, whose 
range usually is about 3:1. The tables on p. 1293 show the results of 
tests made by the Lodge & Shipley Co. in 1906 to determine the power 
required to remove metal in a 20-in. lathe with a cone pulley drive, and 
also in a similar lathe with a geared head. 

Power Required to Drive Macliine Tools. — The power required 
to drive a machine tool varies with the material to be cut. There is 
considerable lack of agreement among authorities on the power re- 
quired. Prof. C. H. Benjamin (Mach'y, Sept., 1902) gives a formula 
H.P. = cW, c being a constant and W the pounds of metal removed 
per hour, c varies both with the quality of metal and the type of 
machine. 

Values of c. 





Lathe. 


Planer. 


Shaper. 


Milling 
Machine. 


Cast iron 

Machinery steel 


0.035 
0.067 


0.032 


0.030 


0.14 


Tool steel 






0.30 


Bronze 








0.10 



In each case the power to drive the machine without load should be 
added. G. M. Campbell (Proc. Engr. Soc. W., Pa., 1906) gives, ex- 
clusive of friction losses, H.P. = Kw, K being a constant and w the 
pounds of metal removed per minute. For hard steel K = 2.5; for soft 



POWER REQUIRED FOR MACHINE TOOLS. 



1293 



Horse-power Required to Remove Metal in Lathes. 

(Lodge & Shipley Mach. Tool Co., 1906.) 
20-Inch Cone-Head Lathe. 



Material 


Cutting 
Speed, 
ft. per 


Cut, In. 


Diam. 

of 
work. 


Cu. in. 
remov- 
ed per 


Lb. 
remov- 
ed per 


H.P. used 
by Lathe. 


Cu.in. 
remov- 


Cut. 










eti per 




mm. 


Depth. 


Feed. 


m. 


min. 


hour. 


Idle. 


With 
Cut. 


HP. 


Crucible 


( 35 


0.109 


1/8 


227/32 


5.74 


96 


0.48 


3.90 


1.471 


Steel 


) 65 


0.055 


1/8 


35/8 


5.33 


90 


0.74 


4.60 


1.158 


0.60 


) 62.5 


0.109 


1/1 R 


3 5/16 


5.125 


86 


0.49 


4.65 


1.102 


Carbon 


( 32.5 


0.094 


VlO 


35/18 


3.656 


62 


0.49 


2.64 


1.384 




C 62.5 


0.273 


1/12 


35/32 


17.09 


266 


0.66 


5.44 


3.141 


Cast 


) 60 


0.430 


1/19 


221/64 


16.27 


253 


0.59 


4.77 


3.410 


Iron 


) 37.5 


0.334 


1/16 


221/32 


10.76 


167 


0.45 


3.91 


2.751 




( 115 


0.086 


1/12 


155/64 


9.88 


153 


0.21 


2.54 


3.889 


Open- 
hearth 
Steel 
0.30 

Carbon 


r 50 


0.109 


1/8 


223/32 


8.2 


138 


0.69 


5.34 


1.535 


) 45 


0.117 


1/8 


21/2 


7.91 


134 


0.53 


5.11 


1.547 


) 45 


0.217 


1/19 


217/64 


6.439 


109 


0.69 


4.10 


1.570 


t 32.5 


0.109 


1/8 


223/64 


5.33 


90 


0.36 


4.04 


1.319 



Average H.P. running idle 0.53; average H.P. with cut 4.25. 
20-Inch Geared-Head Lathe, 



Material. 


Cutting 

Speed, 

ft. per 

min. 


Cut, in. 


Diam. 

of 
work 

in. 


Cu. in. 
remov- 
ed per 
min. 


Lb. 
remov- 
ed per 
hour. 


H.P. used 
by Lathe. 


Cu. in. 

remov- 


Cut. 


Depth. 


Feed. 


Idle. 


With 
Cut. 


t.r 


0.50 

Carbon 

Crucible 

Steel. 

Cast 
Iron 

Open- 
hearth 
Steel 
0.15 

Carbon 


( 40 
) 50 
) 75 

' 85 

(45 
) 62.5 
)85 
( 80 

( 125 
) 105 
) 40 
( 180 


0.266 
0.281 
0.281 
0.109 

0.609 
0.609 
0.641 
0.281 

0.250 
0.188 
0.172 
0.094 


l/io 
1/15 

1/15 

l/lD 

1/16 
1/16 
1/16 
1/8 

1/28 
1/12 
1/6 
Vl6 


227/32 
227/32 
227/32 

2 1/4 

721/32 
721/32 
721/32 

3 3/32 

4 21/32 
4 5/32 
327/32 
3 1/16 


12.75 
11.25 
16.87 
7.43 

20 57 
28.56 
40.82 
33.75 

13.4 
19.68 
13.75 
12.65 


215 
190 
285 
126 

320 

.445 . 

636 

526 

226 
332 
232 
213 


2.11 
1.58 
1.58 
1.28 

1.34 
1.35 
1.64 
1.18 

1.62 
0.94 
1.75 
2.15 


11.1 

8.35 
12.69 

8.98 

6 94 
9.50 
12.69 
10.49 

10.60 
11.56 
12.49 
11.20 


1.142 
1.347 
1.329 
0.827 

2.963 
3.006 
3.216 
3.217 

1.265 
1.702 
1.100 
1.129 



Average H.P. running idle 1.543; average H.P. with cut 10.55. 

steel K = 1.8; for wroiieht iron, K = 2.0; for cast iron, K = 1.4. This 
formula gives results about 50% lower than Prof. Benjamin's. 

L. L. Pomeroy (Gen. Elec. Rev., 1908) gives: H.P. required to drive = 
12 FDSNC, in which F = feed and D = depth of cut, in inches, S = 
speed in ft. per min., N= number of tools cutting, C= a constant, 
whose values with ordinary carbon steel tools are: for cast iron, 0.35 to 
0.5; soft steel or wrought iron, 0.45 to 0.7; locomotive driving-wheel 
tires, 0.7 to 1.0; very hard steel, 1.0 to 1.1. This formula is based on 
Prof. Flather's dynamometer tests. An analysis of experiments by 
Dr. Nicholson of Manchester, which confirm the formula, showed the 
average H.P. required at the motor per pound of metal removed per 
minute to be as follows: Medium or soft steel, or wrought iron, 2.4 H.P. ; 
hard steel, 2.65 H.P.; cast iron, soft or medium, 1.00 H.P.; cast iron, 
hard, 1.36 H.P. 



1294 



THE MACHINE-SHOP. 



Actual tests (1906) of a number of machine tools in the shops of the 
Pittsburg and Lake Erie R.R. showed the horse-power absorbed in 
driving under the conditions given in the table on p. 1295. The 
results obtained are compared with those computed by Campbell's 
formula on p. 1292. It will be observed that the sizes of motors actu- 
ally used on the various machines in the table agree quite closely with 
the sizes recommended in the tables, pp. 1294 to 1298. 

Sizes of Motors for Machine Tools. — The size of motor applied to 
machine tooJs which are driven by an individual motor is usually deter- 
mined by the experience of the manufacturer, rather than by any 
formula. The same lathe, for instance, will be fitted with a larger 
motor if it is required to take heavy roughing cuts continuously in 
tough steel, than if it is to have a more general run of hghter work in 
cast iron. Even if it does, under the latter conditions of service, 
occasionally receive a job up to the limit of its capacity, the motor will 
be able to stand the temporary overload, w^hereas a continuous overload 
would soon ruin it. The conditions under which the machine will 
operate should therefore be stated when it or the motor to drive it 
is purchased. The tables given on pages 1294 to 1298 show the 
sizes of motors for machine tools as recommended by the Westinghouse 
Elect. «fe Mfg. Co. The sizes given embody average practice. The 
type of motor to be used varies with the conditions of service, and the 
type suitable for the different classes of machinery are indicated by 
the following symbols: 

A. Adjustable speed, shunt wound, direct current motor; used where 
a number of speeds are essential. 

B. Constant speed, shunt wound, direct current motor; used when 
the desired speeds are obtainable by a cone pulley or gear box, or where 
only a single speed is required. 

C. Squirrel cage induction motor; used where direct current is not 
available. A cone pulley or gear box is necessary if more than one 
speed is desired. 

D. Constant speed, compound wound, direct-current motor, used 
when different speeds are obtainable by means of a cone pulley or 
gear box, or where but one speed is necessary. 

E. Wound secondary or squirrel cage induction motor with about 
10% slip; used where direct current is not available, or where one 
speed is required. 

F. Adjustable speed, compound wound, direct current motor; used 
where a number of speeds are necessary. 

G. Standard bending roll motor. 

H. Standard machine tool traverse motor. 

Turning and Boring Machines. 

Engine Lathes — Motor .4, B or C, 

Swing, in 12 14 16 18 20-22 24-27 

Horse-power, average 1/2 3/4-I ]-2 2-3 3 5 

Horse-power, heavy 2 2-3 2-3 3-5 7.5-10 7.5-10 

Swing, in 30 32-36 38-42 48-54 60-84 

Horse-power, average 5-7.5 7.5-10 10-15 15-20 20-25 

Horse-power, heavy 7.5-10 10-15 15-20 20-25 25-30 

Wheel Lathes — Motor A, B or C. 

Size, in 48 51-60 79-84 90 100 

Horse-power 15-20 15-20 25-30 30-40 40-50 

H.P. of tail stock motor (H) 5 5 5 5-7.5 5-7.5 

Axle Lathes — Motor A, B or C, 

Single 5, 7.5, 10 Horse-power 

Double 10, 15, 20 

Buffing Lathes — Motor B or C. 

Number of wheels 2 2 2 2 

Diameter of wheels, in 6 10 12 14 

Horse-power 1/4-I/2 1-2 2-3 3-5 

For brass tubing and other special work use about double the 
above H.P. 



POWER REQUIRED FOR MACHINE TOOLa. 



1295 





Horse 


-power 


to Drive Machine Tools. 








Cut, 


Inches. 






H.P. Re- 












C 




quired. 


t 










^ 


0^ 








-3 






u 


oNfe 


. 


S 


2 


^ 


fe 


^3 


^ 


i^ 


f^u 


c3 

3 


S 


S 


& 


03 
IS 




a 


p Jt. 

m 




1 


u 





1^ 


72-in. wheel 


Hard steel 


Vl2 


3/l6«fel/4 


13.7 


1.69 


4.5 


A2 


25 H.P. shunt 


lathe 


.4 <> 


1/8 


3/16&1/4 


11.6 


2.15 


6.^ 


5.4 


wound vari- 




" " 


3/16 


5/16&3/8 


13.2 


5.55 


8.^ 


13.9 


able speed. 




" " 


3/16 


3/8 &3/8 


13.2 


6.3 


12.0 
12.0 


15.7 




90-in. wheel 


Hard steel 


3/16 


3/16&3/16 


13.0 


3.1 


7.7 


25 H.P. shunt 


lathe 


(i it 


3/16 


5/16&5/16 


8.8 


3.5 


8.1 


8.7 


wound vari- 




" 


1/5 


1/4 &I/4 


15.5 


5.3 


9.0 
3.8 


13.2 


able speed. 


42-in. lathe 


Soft steel 


1/16 


1/4 


44 


2.33 


4.2 


15 H.P. shunt 




<( ii 


1/16 


1/8 


44 


1.17 


1.7 


1.9 


wound vari- 




(t <( 


1/16 


1/8 


44 


1.17 


2.6 


1.9 


able speed. 




Cast iron 


1/16 


1/8 


108 


2.63 


5.8 


i.'J 






<( it 


1/16 


3/16 


46 


1.74 


2.9 


2.5 






«( t( 


1/16 

1/8 


3/16 


58 


2.12 


2.2 
6.6 


3.0 




30-in. lathe 


Wro't iron 


3/16 


54 


4.2 


8.4 


10 H.P. shunt 




" " 


1/8 


3/16 


42 


3.2 


4.0 


6.4 


wound vari- 




Cast iron 


3/32 


5/32 


42 


1.92 


3.0 


2.7 


able speed. 




'* *' 


3/32 


I/16 


61 


1.12 


1.5 


1.6 






<( <i 


1/64 


1/4 


47 


2.30 


2.0 
5.9 


3.2 




Axle lathe 


Soft steel 


3/16 


1/4 


27 


4.3 


7.7 


35H.P.sh.w'd 




" " 


1/16 


1/4 


51 


2.7 


5.0 
2.9 


4.9 
3.2 


var. speed. 


72-in. boring 


Soft steel 


1/8 


I/I6&I/32 


44 


1.76 


25 H.P. shunt 


mill . . 




3/16 


I/32&I/16 


40 


2.38 


2.6 


4.3 


wound vari- 




a n 


1/8 


1/8 &1/8 


51 


5.41 


9.6 


9.7 


able speed. 




ii ii 


1/8 


3/16 


47 


3.y5 


7.2 


6.8 






Cast iron 


1/16 


3/8 


28 


2.05 


2.6 


2.9 








1/16 


1/4 


39 


1.90 


2.7 
2.3 


2.7 




24-in. drill 


Wro't iron 


1/64 


li/4to3* 


25.1 


0.81 


1.6 




press 




1/64 


ll/4to3* 


29.7 


0.96 


2.7 


1.9 






<( ii 


1/64 


ll/4to3* 


25.9 


0.83 


1.3 


1.7 






it it 


1/64 


11/4 drill 


74.5 


0.52 


3.5 


1.0 






t( it 


1/64 


11/4 drill 


20.9 


0.54 


1.2 
5.9 


I.l 




60-in. planer 


Soft steel 


1/6 


1/4 


25.5 


3.62 


6.5 


20 H.P. com- 




it it 


1/6 


1/4 


25.7 


3.65 


6.5 


6.6 


pound 




Wro't iron 


3/16 


5/16&5/16 


23 


8.95 


21.0 


17.9 


wound vari- 




it it 


1/2 


1/32&1/32 


17.5 


1.82 


2.7 


3.6 


able speed. 




Cast iron 


1/8 


1/8 &I/16 


22.2 


1.72 


6.5 


3.4 






it it 


1/8&1/16 


1/4 &5/16 


30 


4.74 


9.3 


6.6 






" '* 


1/7 


V4 &I/4 


22.6 


5.03 


7.6 


7.1 








1/4 


7/I6&3/8 


28.9 


18.3 


23.2 
12.1 


25.6 




42-in. planer 


Soft steel 


5/32 


3/8 


24.3 


4.73 


9.5 


15 H.P. com- 




«t it 


1/8 


3/8 


36 


3.7 


7.8 


11.4 


pound 




Cast iron 


3/16 


3/16 


37 


4.06 


4.7 


5.7 


wound vari- 




it 


3/16 


1/8 


37 
30.0 


2.71 


4.1 
2.0 


3.8 


able speed. 


19-in.slotter 


Hard steel 


1/32 


1/4 


0.8 


2.0 


13 HP. comp. 
w'd var. speed. 




Soft steel 


1/82 


V8 


23.3 


0.93 


1.3 


1.7 



* Enlarging hole from smaller dimensions to larger. 



1296 



THE MACHINE-SHOP. 



6 


8 


30 


40 


10 


15 



Boring and Turning Mills — Motor A, B or C. 

In. In. In. Ft. Ft. Ft. Ft. 

Size 37-42 50 60-84 7-9 10-12 14-16 16-25 

H. P., average.. 5-7.5 7.5 7.5-10 10-15 10-15 15-20 20-25 
H.P., heavy... 7.5-10 7.5-10 10-15 30-40 

Cylinder Boring Machines — Motor A, B or C. 

Diameter of spindle, in 4 

Maximum boring diameter, in 10 

Horse-power 7.5 

Horizontal Boring, Drilling and INIilling Machines — 
Motors A, B or C. 

Size of spindle, in 3.5-4.5 4.5-5.5 5.5-6.5 

Horse-power per spindle. . . 5-7.5 7.5-10 10-15 

Drilling Machines. 

Sensitive Drills up to 1/2 in Mi-^k H.P. Motor A, B or C. 

Upright Drii^ls — Motor A, B or C. 

Size, in 12-20 24-28 30-32 

Horse-power 1 2 3 

Eadial Drills — Motor ^, B or C. 

Length of arm, ft 3 

Horse-power, average 1-2 

Horse-power, heavy 3 

Multiple Spindle Drills — Motor ^, B or C. 
Size of drill, in. 1/32-I/4 i/ie-S/s 3/i6-l/o 1/4-3/4 s/g-l 
No. of spindles, 

up to 6-10 10 10 10 10 4 

Horse-power. . 3 5 



4 

2-3 

5-7.5 



36-40 
5 



5-7 

3-5 

5-7.5 



50-60 
5-7.5 



8-10 
5-7.5 
7.5-10 



2 2 



7.5 



10 



10-15 7.5 



6 
10 



8 
15 



Planing Machinery. 

Planers — Motor C, B or F. 



Width, in 22 

Distance imder rail, in. 22 

Horse-power 3 

Width, in 48 

Distance under rail, in. . 48 

Horse-power 15-20 

Shapers— 



24 
24 
3-5 
54 
54 
20-25 



27 

27 
3-5 
60 
60 
20-25 



30 
30 

5-7.5 
72 
72 

25-30 



36 

36 
10-15 
84 
84 
30 



42 
42 
15-20 
100 
100 
40 



Motor A, B or C. 



Traverse Head. 



Stroke, in 12-16 18 

H.P., single head 2 2-3 

Slotters — Keyseaters— 

Stroke, in 6 

Horse-power 3 

Stroke, in 16 

Horse-power 7.5 



30 
5-7.5 



20-24 
3-5 

-Motor ^ , B or C 

8 10 

3-5 5 

18 20 



20 
7.5 



12 

5 

24 



7.5-10 10-15 10-15 



24 
10 



14 

5-7 1/2 

30 
10-15 



Milling Machinery. 

Plain Milling Machines — Motor A, B or C. 

Table feed, in 34 42 50 

Cross feed, in 10 12 12 

Vertical feed, in 20 20 21 

Horse-power 7.5 10 15 

Universal Milling Machines — Motor ^4, B or C. 

Machine number 1 IV2 2 3 4 5 

Horse-power 1-2 1-2 3-5 5-7.5 7.6-10 10-15 



POWER REQUIRED FOR MACHINE TOOLS. 1297 

Vertical Milling Machines — Motor A, B or C. 

Height under Spindle, in 12 14 18 20 24 

Horse-power 5 7.5 10 15 20 

Vertical Slabbing Machines — Motor A, B or C. 

Width of work, in 24 32-36 42 

Horse-power 7.5 10 15 

Horizontal Slabbing Machines — Motor A, B or C. 

Width between housings, in . . 24 30 36 60 72 

Horse-power, average 7.5-10 7.5-10 10-15 25 25 

Horse-power, heavy 10-15 10-15 20-25 50-60 75 

Gear Cutters — Motor ^4, B or C. 

Size, in 36X9 48X10 30X12 60X12 72X14 64X20 

Horse-power.. 2-3 3-5 5-7.5 5-7.5 7.5-10 10-15 

Rotary Planers — Motor A, B or C. 

Diam. of cutter, in 24 30 36-42 48-54 60 72 84 96-100 

Horse-power 5 7.5 10 15 2Q 25 30 40 

Saws, Cold and Cut-off — Motor A, B or C. 

Size of saw, in 20 26 32 36 42 48 

Horse-power 3 5 7.5 10-15 20 25 

Bolt and Nut Machinery. 

Bolt Cutters — Motor A, B or C. 

Single. Double. Triple. 



Size, in . . . 1,1 1/4. 1 1/2 l 1 3/4. 212 1/4, 3 1/2 1 4. 6 11. 1 1/2 I 2. 2 1/2 1 1, 1 1/2, 2 
H.P 1-2 [2-3 1 3-5 1 5-7.5 | 2-3 [ 3-5 I 3-7.5 

Bolt Pointers — Motor B or C. 

Size, in 1 1/2, 2 1/2 Horse-power 1-2 

Nut Tappers — Motor A, B or C. 

4 Spindle. 6 Spindle. 10 Spindle. 

Size, in 1, 2 2 2 

Horse-power 3 3 5 

Nut Facing Machine — Motor B or C. 

Size, in 1,2 Horse-power 2-3 

Bolt Heading, Upsetting and Forging — Motor Z), E or F. 

Size, in 3/4-1 1 /2 U2~2 2 1 <y-^ 4-6 

Horse-power 5-7.5 1(>-15 20-25 30-40 

Bending or Forming Machinery — Hammers. 

Bulldozers — Motor D or E. 

Width, in 29 34 39 45 63 

Head movemont, in 14 16 16 18 20 

Horse-power 5 7.5 10 15 20 

Bending and Straightening Bolls — Motor E or.G. 

Width, ft 4 6 6 6 S 10 10 24 

Thickness, in s/g 5 '^^ T/ig 3 4 7 /g ii/g II/2 1 

Horse-power 5 5 7.5 15 25 35 50 50 

Hammers — Motor D or E. 

Size, lb 15 to 75 100 to 200 

Horse-power 1/2 to 5 5 to 7 .5 

Bliss drop hammers require approximately 1 H.P. for every 100 lb. 
weight of hamnuT head. 

Pipe Threading and Cutting-off Machinery. 

Motor ^, B or C. 
Pipe size. in.. 1/4-2 1/2-3 1-4 II/4-6 2-8 3-10 4-12 8-18 24 
Horse-power. 2 3 3 3-5 3-5 5 5 7.5 10 



1298 THE MACHINE-SHOP. 

Punching and Shearing Machinery. 

Presses for notching sheet-iron — Alotor A, B or C — 1/2 to 3 H.P. 

Punches — Motor D or E. 

Diameter, in. . 3/8 1/2 s/g 3/4 7/3 1 1 II/4 13 /4 2 21/2 

Thickness, in.. I/4 1/2 Vs 3/4 3/4 1/2 1. 1 1 1 11/2 

Horse-power.. 1 2-3 2-3 3-5 5 5 7.5 7.5-10 10-] 5 10-15 15-25 

Shears — Motor D or E, 

Width, in 30-42 50-60 72-96 

Horse-power to cut i/s-in. iron. 3 4 5 

Horse-power to cut 1/4-in. iron.. 5 7.5 10 

Bolt shears 71/2 H.P. Double angle shears.. . . 10 H.P, 

Lever Shears — Motor D or E. 

Size, hi 1X1 11/2X11/2 2X2 6X1 21/2X21/2 

Horse-power 5 7.5 10 15 15 

Size, in 1X7 213/4X23/4 II/2X8 31/2X31/2 41/2 round 

Horse-power 15 20 25 30 30 

Plate Shears — Motor D or E. 
Size of plate, in., 

3/8 X 24 1 X 24 2 X 14 1 X 42 1 1/2 X 42 1 1/4 X 54 1 I/2 X 72 1 1/4 X 100 
Cuts per min., 

35 20 15 20 15 18 20 10-12 

Stroke, in., 

3 3 41/4 4 41/2 6 :51/2 71/2 

Horse-power, 

10 15 30 20 60 75 10 75 

Hydrostatic Wheel Presses — Motor B or C. 

Size, tons 100 200 300 400 600 

Horse-power 5 7.5 7.5 10 15 

Grinding Machinery. 

Grinding Machines (For Shafts, Etc.) — Motor A, B or C. 
Wheels diameter, in. .. . 10 10 10 10 14 18 18 IS 

Length of work, in 50 72 96 120 72 120 144 168 

H.P., average work 5 5 5 5 10 10 10 10 

" heavy work 7.5 7.5 7.5 7.5 15 15 15 15 

Emery Wheel Grinders, Etc. — Motor B or C 

Number of wheels 2 2 2 2 2 2 

Size of wheels, in 6 10 12 18 24 26 

Horse-power 1/2-I 2 3 5-7.5 7.5-10 7.5-10 

Miscellaneous Grinders — Motor B or C. 

Wet tool grinder, 2 to 3 H.P.; flexible swinging grinding and polish- 
ing machine, 3 H.P. ; angle cock grinder, 3 H.P. ; piston rod grinder, 
3 H.P.; twist drill grinder, 2 H.P.; automatic tool grinder, 3 to 5 H.P. 

In selecting a motor for a machine tool, advantage should be taken 
of the fact that motors will stand considerable overloads for short 
periods. This will lead to the selection of smaller motors than are 
usual. The tendency is to select a motor to fit the maximum capacity 
of the machine, rather than one whose capacity is more nearly that of 
the average capacity of the tool. 

A. G. Popcke (Am. Mach., Sept. 26 and Oct. 3, 1912) outlines more 
accurate methods of determining the sizes of motors required for 
driving machine tools, based upon an analysis of the working condi- 
tions, and also the considerations other than those of power which 
govern the selection of the motor. To determine motor capacity, 
the following data are necessary: Horse-power, speed and voltage; and 
in addition for alternating current, frequency and phase. To estimate 
the horse-power the following must be known: Type of tool; depth of 
cut (all tools being considered), inches; feed, in. per revolution; speed, 
ft. per minute; duration of both average and maximum cuts; duration 
of peak of maximum load ; number of peaks per hour. From the area 
of the cut (depth X feed) and the cutting speed, the cubic inches of 



POWER REQUIRED FOR MACHINE TOOLS. 1299 

metal removed per minute can be calculated for both average and 
maximum cuts, and these flgiu*es, multiplied by the constants below 
give the horse-power required, to which the friction load of the machine 
must be added. 

Horse-power Constants for Cutting Metal. 

H.P. per Cu. H.P. per Cu. 

In. per Min. In. per Min. 

Cast iron 0.3 to 0.5 Steel, 50 carbon or more. . 1.0 to 1.25 

Wrought iron 0.6 Brass and similar alloys. . 0.2 to 0.25 

Machinery steel 0.6 

These constants apply to round nose tools used in accordance with 
the conditions recommended by F. W. Taylor (see p. 1261). For 
twist drills the power requirements per cubic inch are about double 
the figures given above. 

The size of the motor selected will depend on the heating of the 
motor while under load, and as the load is usually intermittent, the 
heating will depend upon the square root of the mean square value of 
the power required. In a given cycle in which the several power values 
are Pi, P2, Ps, utilized during periods of ti, U, tz, respectively, the square 
root of the mean square will be 



V 



Pl2 h + P22 t2 -f P32 U 



U-\-k-\- tz 



The heating of the motor will be the same as if it were run constantly 
at a load equal to the square root of the mean square load. In making 
the motor selection, however, it should be observed whether or not the 
duration of the maximum load will be greater than the motor can suc- 
cessfully withstand. Thus a 100% overload for a period of 10 seconds 
can easily be carried by a properly designed motor, while if prolonged 
such a load may burn it out. When selecting motors for widely fluctu- 
ating intermittent loads, the limits above rated load which must be 
taken into consideration are for alternating current, pull at starting 
torque, and speed regulation; and for direct current motors, commuta- 
tion, speed regulation and stability. The pull at the starting torque 
of an induction motor is from 2.5 to 3.5 times the full-load torque, and 
the speed regulation, or percentage drop in speed between no load and 
full load, known as the slip, is, at full load, from 5 to 7%. At other 
loads it is approximately proportional to the load. Commutating pole, 
direct current motors will stand 100% to 125% overload without 
sparking. The speed regulation at full load is 10 to 15%, depending 
on the speed of the motor. With non-commutating pole motors the 
speed decreases with overloads in proportion to the loads, while on 
commutating pole motors it increases up to 100% overload, thus giving 
approximately the same speed at double load as at full load. A com- 
mutating pole motor can be made stable at overloads, which will in- 
crease the drop in speed. The better the speed regulation, however, 
the less certain is the stability and the motor for driving machine tools 
must be a compromise between these two factors. Motors, however, 
are available which can be safely operated on intermittent loads where 
the maximum load is 200%, of the rated load. In machine tool work, 
a large speed reduction, giving a stable motor is advisable when varia- 
tions occur in the work done by the cutting tool on long jobs, thus 
protecting the cutting tools, the machines and the work. An adjust- 
able speed motor with a speed reduction of 25 % is of advantage under 
such circumstances. 

In applying the principles outlined above to the selection of a machine 
tool motor, the average and maximum conditions of service of the 
machine should be determined by laying out typical jobs in which 
these conditions are present. The power cycles are determined from 
the amount of metal removed on each cut as previously explained and 
the duration of each cut is ascertained from the length of the cut, the 
spindle speed and the feed per revolution. The square root of the 
mean square value of the power required is next determined, the time 
while the machine is idle during the periods of adjustment being added 
in the denominator of the formula for this value. A motor whose 



1300 THE MACHINE-SHOP. 

capacity is in the neighborhood of the value ascertained is then selected, 
and the relation of the maximum load to the rated motor capacity is 
observed to ascertain whether or not the motor, in addition to carry- 
ing the average load, is capable of carrying the maximum load without 
injury. For instance, if the square root of the mean square value is 
5.5 H.P. a 5-H.P. motor would be under an overload of 10%, which 
is well within the capacity of a well designed machine. If the maxi- 
mum load requires 8.3 H.P. for a period of three minutes the motor 
will be overloaded 66% for this period which is also within the limits 
set by good motor design. 

According to Mr. Popcke, other questions than horse-power govern 
the selection of a motor for a machine tool. The speed of the motor 
depends upon the speed of the machine shaft, which ranges from 50 to 
60 r.p.m. on forging machines to 200 to 300 r.p.m. on machine tools, 
and as high as 1000 to 2000 r.p.m. on grinding and wood-working ma- 
chinery. The speeds usually obtainable with 60-cycle alternating 
current motors are 1700-1800, 1100-1200, 850-900, 650-720 and 
550-600 r.p.m. The speeds available on standard direct current 
motors are approximately the same. On 25-cycle alternating current 
motors the usual speeds are 700-750, 550-600, and 350-375 r.p.m. 
The following factors are considered in selecting motors for belt drives: 
Speed reductions, pulley sizes, belt speeds, motor speeds, distance 
between pulley centers, arc of contact, use of idler pulleys, mounting 
of motor. Involved in the speed reductions are the sizes of the motor 
and machine pulleys and the belt speed. The standard sizes of motor 
pulleys which have been adopted in connection with standard speed 
ratings of the various sizes of motors have standardized the belt speeds. 
The maximum and minimum standard speed ratings of the motors, 
together with the maximum and minimum pulley diameters are given 
in the following table: 

HORSE-POWER OF MOTOR. 

1 2 3 5 7 1/2 10 15 20 25 30 35 40 50 

R.P.M , Maximum. 

1700 1700 18C0 1800 1700 1700 1700 1700 1400 1700 1700 1700 1700 
Pulley Diameter, standard. 

3 1/2 3 1/2 4 4 5 6 7 8 9 9 10 11 11 

Pulley Diameter, minimum. 

3 3 3 3 1/2441/25 6 6 1/2 6 I/2 7 7 1/2 8 

R.P.M., Minimum. 

850 850 850 650 600 600 650 600 600 675 600 565 

Pulley Diameter, standard. 

4 5 6 8 9 11 11 12 13 13 14 16 

Pulley Diameter, minimum. 

31/2 4 41/2 6 6 1/2 71/2 8 9 10 10 12 13 I/2 

The minimum size of pulley is specified on account of the reduction 
of pulley size increasing the strains on the motor bearings and shaft. 
The arc of contact has great effect on the success of a belt-driven motor 
installation. The arc of contact depends on the distance between the 
pulley centers and on the speed reduction. Where it is necessary to 
increase the arc of contact, idler pulleys are of service. In machine 
work the size of the motor pulley is sometimes fixed by the necessity 
of belting the motor to the machine fiy wheel, in which case care must 
be taken that the diameter of the motor pulley is not less than the 
minimum size specified. The arc of contact must also be considered, 
as in a large speed reduction this will be decreased and will seriously 
affect the amount of power transmitted. The effect of decreasing the 
arc of contact is shown below, the power transmitted by a 180 deg. arc 
of contact being taken as 100. 

Arc of contact, deg 180 170 160 150 140 130 120 

Power transmitted, % . . 100 94 89 83 78 72 67 
The cost of a motor per horse-power increases as the speed decreases. 
Therefore, for maximum economy in first cost as high a speed as 
possible should be selected without, however, going below the minimum 
pulley diameter. Back geared motors are useful where extremely low 
speeds are required. A speed ratio of 6:1 between the armature and 
the motor countershaft is usually satisfactory, any further speed 
reduction to the machine pulley being obtained by means of the pulley 



POWER BEQUIRED FOR MACHINE TOOLS. 



1301 



Data for Standard Geared Connections for Constant Speed Motors. 




Maximum Speed Rating. 


Minimum Speed Rating. 


u 






No. of Teeth. 




,c 






No. of Teeth. 




.S 


% 


% 


t 






1. 




i 

5 


i 










il 

PhC/3 




g 


Q^ 


y 


^•s 


1^ 


•s-s 


s s 


C 


^ 




^^ 


•s-l 


. 0) 
73 C 


c 


W 


^ 


Q 


wfi. 


^;s 


Sfi; 


^.^ 


S 


^ 


Q 


w£ 


Sx 


SS 


^J 


^ 


1 


1700 


8 


17 


15 


13 


940 


1.63 


1200 


8 


17 


15 


n 


665 


1.63 


2 


1700 


8 


17 


15 


13 


940 


1.63 


850 


6 


18 


71 


19 


615 


2.38 


3 


1800 


8 


22 


20 


19 


1300 


2.38 


850 


6 


18 


18 


18 


670 |3.0 


5 


1800 


8 


22 


21 


19 


1300 


2.38 


850 


6 


21 


19 


18 


990 3.0 


7.5 


1700 


6 


18 


18 


18 


1400 


3.0 


650 




20 


18 


18 


685 '3.6 


10 


1700 




21 


19 


18 


1420 


3.0 


600 




21 


19 


19 


665 


3 8 


15 


1700 




19 


18 


18 


1700 


3.6 


600 


4 1/1^ 


22 


19 


19 


770 


4.22 


20 


1700 




20 


18 


18 


1780 


3.6 


650 




21 


18 


18 


890 


4 5 


25 


1400 




21 


19 


19 


1550 


3.8 


600 




22 


19 


18 


864 


4 5 


30 


1700 




21 


19 


19 


1880 


3.8 


600 


31/4 


20 




18 


970 


5.53 


35 


1700 


4 1/:^ 


22 


18 


18 


2180 


4.0 


675 


3 1/4 


20 




18 


1080 


5.53 


40 


1700 


41/:? 


22 


19 


19 


2180 


4.22 


600 




18 




15 


940 


5.0 


50 


1700 




21 


18 


18 


2340 


4.5 


565 




20 




18 


990 


6.0 



Data for Standard Geared Connections for Adjustable Speed Motors. 



Horse- 
Power . 



Maximum Speed Rating. 



Min. 
R.P.M. 

of 
Motor. 



Speed 
Ratio. 



Min. 
Diam. 

of 
Pulley, 



Gear Data. 



Min. 
No. of 
Teeth. 



Min. 
Diam., 



Diam. 
Pitch. 



Pitch Line 

Speed at 

Min. Diam. 



Min. 



Max. 



1 

2 
3 
5 

7 1/2 

10 
15 
20 
25 
30 
40 
50 



740 
1100 
1000 
1000 
900 
850 
780 
650 
550 
550 
550 
500 



3 
3 
3 

4 
5 

6 

6 1/2 

7 1/2 

9 
10 
12 

12 1/2 



19 
19 
19 
18 
18 
18 
19 
19 
18 
18 
15 
18 



2.38 

2.38 

2.38 

3.0 

3.0 

3.6 

3.8 

4.22 

4.5 

5.53 

5.0 

6.0 



8 
6 
6 
5 

5 

4 1/2 
4 

31/4 

3 1/2 

3 



460 
690 
625 
790 
705 
800 
780 
720 
645 
800 
720 
790 



1380 
1380 
1250 
1580 
1410 
1600 
1560 
1440 
1290 
1600 
1440 
1580 



1 
2 
3 
5 

7 1/2 

10 
15 
20 
25 
30 
40 
50 



450 
450 
375 
375 
350 
375 
375 
300 
300 
250 
250 
325 



Minimum Speed Rating. 



3 


19 


4 


18 


5 


18 


6 


18 


6 1/2 


19 


7 


18 


9 


18 


12 


15 


121/2 


18 


14 


18 


16 


19 


16 


19 



2.38 

3.0 

3.0 

3.6 

3.8 

4.0 

4.5 

5.0 

6.0 

6.0 

6.33 

6.33 



8 
6 
6 
5 
5 

4 1/2 

4 
3 
3 
3 
3 
3 



280 
355 
294 
355 
350 
390 
440 
390 
470 
390 
415 
540 



1120 
1420 
1176 
1420 
1400 
1560 
1760 
1560 
1880 
1560 
1660 
1620 



1302 



THE MACHINE-SHOP. 



on the motor countershaft. Back geared motors are used where the 
machine speed is below 150 to 100 r.p.m. The initial speed of the 
back geared motor should not exceed 1200 r.p.m. when the horse-power 
is from 10 to 20 and should not exceed 900 or even 720 r.p.m. when 
the horse-power is greater than this figure. 

For equipment where the motor is geared to the machine, the follow- 
ing are the governing considerations: Speed reduction, pitch hue 
speed, number of teeth on gears, width of face of gears, center distances, 
use of idler gears, motor mounting. Noise limits the pitch line speed 
to about 1000 feet per minute with steel gears. For speeds of 1000 
to 2000 feet per minute, cloth or rawhide pinions should be used and 
speeds in excess of 2000 feet per minute should be avoided if possible. 
Stresses in bearings and motor shafts limit the minimum size of motor 
pinions jvist as they limit the size of pulleys. The maximum and 
minimum speed ratings and the corresponding standard and minimum 
sizes of pinions for constant speed and adjustable speed motors are 
, given in the tables on the preceding page. The second tabic also gives 
the minimum pulley diameters for adjustable speed motors. 

For additional data on machuie tool motors see Electrical Engineer- 
ing, p. 1466. 

Motor Requirements for Milling Machines. — See p. 1278. 

Power Required for Drilling. — See p. 1286. 

Motor Requirements of Planers. (A. G. Popcke, Am. Mach., Sept. 
26, 1912.) — Manufacturers usually specify motors for planers that are 
larger than necessary, due to the heavy peak load imposed at the instant 
of reversal. Before the advent of interpole, commutating motors, this 
peak load caused sparking unless a large motor was used. The com- 
mutating motor eliminates this trouble and permits the use of a smaller 
motor. A flywheel on the countershaft, from which the forward and 
reverse belts are driven, will assist in the carrying of the peak loads, 
and will allow the use of a smaller driving motor than otherwise. The 
table below shows the results of tests of planers with a graphic record- 
ing ammeter, and gives the power required at different portions of the 
planer cycle. It also shows the motors recommended and installed, 
which are handling the work satisfactorily, and also the size of motors 
specified by the makers of the tools. 

Power Requirements of Planers. 





Motor 

Used 

for 

Test. 


Observed Power 
Requirements. 


Remarks. 


Motor 

In- 
stalled, 
Based 

on 
Test. 




Size of 
Planer. 


a; 




1^ 


1 g 


Motor 
Speci- 
fied. 


In. Ft. 
56 X 15 

54 X 16 

48 X 12 

24 X 10 

42 X 12* 
48 X 12 
37 X8 
36 X8 
36 X 8 


H.P. 

3 

5 

5 

30 
30 

5 

5 

7 1/2 

5 

30 
5 
5 

5 


K.W. 
1.3 
1.8 
2.5 
4 
4 

1.8 
2 

2 

1.5 

5 

1.8 

1.5 

1.8 


K.W. 

li 

"e" 

7 

2.3 
7 

4.5 

2.5 
10 
3 
2 
2 


K.W. 
4.0 
3.5 
6 
8 
10 
3.5 
8 

4.3 

5 
14 
4 
2.5 

3 


K.W. 

5.3 

5.3 

6 

10.5 
12 

5.5 

9 

5.5 { 

7 
19 
6 
4 
5 


Average work 
5 Tons on table 
Short stroke 
Average stroke 
Short stroke 
Average stroke 
Average work 
Motor geared 
balance wheel 
Average work 
No. bal. wheel 
Average work 


H.P. 
I 5 

7 1/2 
1 5 

7 1/2 
7 1/2 

5 
3 

3 


H.P. 
15 

15 
15 

7 1/2 

15 
15 
10 

5 
5 



* Open side. 

The Cincinnati Planer Co. has furnished the author with the results 
of a test of 72 in. X 24 ft. planer, fitted with a reversible motor drive, 
cutting cast iron. To run the table in the direction of the cut required 



POWER REQUIRED FOR WOOD-WORKING MACHINES. 1303 

2.06 H.P.; reversing from cutting to return stroke, 13 H.P. ; reversing 
from return to cutting stroke, 14.4 H.P. 



Test on 72 X 24-in. Reversible Motor-Driven Planer. 









Cutting 


H.P. 


Pressure 


Depth 
of Cut, 


Feed. 
In. 


Number 
of Tools 


Speed, 
Ft. per 


Required, 
Including 


per Sq. In. 
in 


In. 




Cutting. 


Min. 


Friction. 


Cast Iron. 


1/2 


3/16 


2 


30 


23 


123.200 


1/2 


3/16 


2 


40 


26.7 


108.680 


1/2 


3/16 


2 


60 


37.5 


104.133 


1/2 


3/32 


2 


30 


11.5 


111.419 


1/2 


3/32 


2 


60 


23 


123.200 


1/4 


3/16 


2 


30 


10.1 


95.090 


1/4 


3/16 


2 


60 


20.2 


106.830 


1/4 


3/32 


2 


30 


7.3 


124.572 


1/4 


3/32 


2 


60 


14.4 


145.726 



Power Required for Wood-Working Maoliinery. (E. G. Fox, EL 

Rev., June 13, 1914.). — The factors influencing the power required 
for wood- working machines are: Design, speed of working, including 
feed and depth of cut, condition of machine and cutters, nature of 
material, ^lachines handling one kind of material may be motored 
for their ordinary load, while those having diverse work must be 
motored for their heaviest service. The data below are based upon 
tests as well as on figures furnished by manufacturers. 

Band Saws. — The motors should have good starting torque, and 
with resaws should be capable of developing 1.5 full load torque 
at starting, and should have good overload characteristics. Belted 
motors are recommended for most Installations. 

Band- Saws. 

Wheel diameter, in 42 

R.P.M 400-500 

Maximum depth of timber, in. . 20 
HP. of motor 5 



Wheel diameter, in 60 

R.P.M 550 

Width saw blade, in 8 

IXIaximum depth of timber, in . . 36 

H.P. of motor 50 

R.P.M. of motor 600 t>uu /zu /zu 

Add for jointing attachment on 48-in. saw, 7.5 H.P. 





38 


36 


36 


34 


30 


500 


450 


500 


400 


500 


500 


) 


16 


16 


14 


12 


12 


> 


5 


5 


3 


3 


3 


\ws. 












54 


48 


44 


42 


40 


38 


600 


650 


650 


650 


700 


450 


6 


5 


4 


4 


3 


2 


.SO 


26 


24 


24 


20 


12 


40 


30 


20 


15 


15 


7.5 


600 


720 


720 


720 


720 


514 



Band Rip Saws — Power Feed. 

Max. Timber Motor Motor 

R.P.M. Depth, in. H.P. R.P.M. 

650 12 15 720 

600 15 10 600 

for return rolls, if used. Speeds given are for direct 



Wheel Diam., 

in. 

42 

40 

Add 2 H.P. 

connection. 

Circular Saws. — Circular saws are not as widely used as band-saws 
for resawing, as they require more power, run at lower speeds and waste 
more stock. Splitting with circular saws requires from 15 to 20% 
more power than cross-cutting. Band-saws require about the same 
power for both. 

Circular Saws. 

Maximum diameter of saw, in 42 

R.P.M. of saw 000 

Maximum capacity, in., horizontal ... 17 

" vertical 

Horse-power 25 



36 


32 


30 


24 


1000 


1225 


1200 


1225 


14 


11 


10 


8 




8 


6 


6 


25 


20 


20 


20 



1304 THE MACHINE-SHOP. 

Circular Rip-Saws. 

Maximum diameter of saw, in 20 16 12 

Maximum R.P.M. of saw 2100 2600 2400 

Maximum thickness of stock, in 6 5 2 

Feed, ft. per min 60-180 64-194 50-100 

Horse-power ,. . 15 15 7.5 

Hand-Feed Circular Rip-Saws. 
Maximum diameter of saw, in. 14 16 20 24 30 36 

R.P.M. of saw 2700 2400 2000 1600 1250 ' 1000 

Horse-power 7.5 10 15 15 20 20 

Power-Feed Gang Ripping-Machine. 

Number of saws 2 3 4 8 

Maximum R.P.M 3400 2300 2500 2500 

Diameter of saws, in 10 15 14 14 

Feed, ft. per min 180 200 100-180 90-200 

Horse-power 15 30 25 35 

Circular Cut-off Saws. 

Maximum saw diameter, in 14 16 

R.P.M. of saws 2700 2600 

Horse-power 5 7.5 

Inside Molders. 

Maximum capacit3% in 8X4 10X4 12 X 6 14 X 6 

Horse-power 25 25 35 35 

Outside Molders. 
Maximum capacity, in. 4X4 6X4 8X4 10 X4 12 X5 14 X6 

Horse-power 10 15 20 25 30 35 

Stickers. 
Maximum size of timber, in... 16X4 18X4 20 X4 

Horse-power 5 7.5 10 

Jointers. 

Maximum width of timber, in 8 12 16 20 24 36 

Horse-power 2 2 3 5 7.5 7.5 

The recommendations for molders, stickers and jointers are based 
on a maximum depth of cut of 3/32 in. If the cut is greater, the size of 
motor should be correspondingly increased. 

Surfacers. — The motor sizes given below are for medium work with 
maximum depths of cut of i/g in. For planing mill work, on heavy 
stock with deep cuts the sizes should be increased about 5 H.P. 
Single Surfacers. 
Maximum width of timber, in. 16 20 24 30 36 

Horse-power 7.5 10 10 15 15 

Double Surfacers. 

Maximum width of timber, in 26 30 36 

Horse-power, heavy work 35 35 

Horse-power, medium work 20 25 30 

Timber Sizcrs. — The following figures apply to heavy service in 
dressing timber to size, surfacing four sides simultaneously. 
Max. size of timber, in. . 20 X 16 20 X 18 20 X 20 30 X 18 30 X 20 

Horse-power 60 60-75 60-75 75 75 

Drum Sanders. 

Number of drums 1 1 1 2 2 2 2 

Max. Width of Stock, in 30 36 42 30 36 42 48 

Horse-power 10 15 15 20 20 20 25 

Number of drums 3 3 3 3 3 3 3 

Maximum width of stock, in .. . 30 36 42-48 54-66 72 78 84 

Horse-power 20 25 30 35 40 40 50 

When material is sanded to size and full width of sander is used with 
panels fed continuously, add 5 H.P. to above motor sizes. 
Tenoners — Hand-Feed. 

Length of tenon, in 7 single 7 double 

Horse-power 7.5 10 



POWER REQUIRED FOR MACHINES IN GROUPS. 1305 

Shapers. — For ordinary service on reversible single- or two-spindle 
machines, use a 5 H.P. motor. For extra heavy work, as in carriage 
factories, railroad shops, etc., use a 7.5 H.P. motor. 

Scraping Machines. 
Maximum width of stock, in. . . 12 26 30 42 
Horse-power 2 3 3 5 

Automatic Lathes. 

Maximum diameter and length of stock, in. 2.75 X 72 3 X 50 5 X 50 

Horse-power 10 15-20 20 

Borers. 

Number of bits 1 1 2 3 4 8 

Maximum diameter of bits, in 1 2 0.75 0.75 0.5 0.5 

Horse-power 3 5 3 5 5 10 

Chisel Mortising-Machines. 

Maximum number of chisels 1 1 l ] 2 

Maximum size of chisel square, in 0.5 0.75 0.75 1.25 1 

Horse-power 2 2 3 5 3 

IMaximum number of chisels 3 4 5 6 7 

INIaximum size of chisel square, in 1 1 i3/i6 i3/i6 i3/i6 

Horse-power 5 5 5 7.5 7 . 5 

Planers and IVIatchers. 
For planing and matching timber at one operation. 
Maximum size of timber, in. . 9X6 15 X 6 20 X 6 24 X 6 26 X 8 
Horse-power 35 40 45 45 45 

Box board matchers are similar to planers and matchers, but the 
work is much lighter. Hand-fed machines u.sually require a 7.5 H.P- 
motor, while power-fed machines require 10 H.P. 

Horse-power Required to Drive Shafting. — Samuel Webber in his 
"Manual of Power" gives, among numerous tables of power required 
to drive textile machinery, a table of results of tests of shafting. A line 
of 21/8-in. shafting, 342 ft. long, weighing 4098 lb., with pulleys weigh- 
ing 5331 lb., or a total of 9429 lb., supported on 47 bearings, 216 rev- 
olutions per minute, required 1.858 H.P. to drive it. This gives a 
coefficient of friction of 5.52 % . In seventeen tests the coefficient ranged 
from 3.34% to 11.4%, averaging 5.73%. J. T. Henthorn states {Trans. 
A. S. M. E., vi, 462) that in print-mills which he examined the friction 
of the shafting and engine was in 7 cases below 20% and in 35 cases 
between 20% and 30%, in 11 cases from 30% to 35% and in 2 cases 
above 35%, the average being 25.9%. Mr. Barrus in eight cotton- 
mills found the range to be between 18% and 25.7%, the average being 
22%. Mr. Flather (Dynamometers) believes that for shops using 
heavy machinery the percentage of power required to drive the shafting 
will average from 40% to 50% of the total power expended. Under 
the head of shafting are included elevators, fans and blowers. 

Power Required to Drive Machines in Groups. — L. P. Alford 
(Am. Mach., Oct. 31, 1907) gives the results of an investigation to 
determine the power required to drive machinery in groups. The 
method employed comprised disconnecting parts of the shafting in a 
belt-diiven plant, and driving the disconnected portion with its ma- 
chines by an electric motor, readings of the power required being taken 
every 5 minutes. The avernge power required for the entire factory 
was considerably less than the sum of the powder roquired for the in- 
dividual machines, due to tools being stopped at some portion of the 
day for adjustment, replacement of work. etc. The conditions of 
group driving are such that fixed rules cannot be laid down, but a study 
must be made of each individual case. The results of the several thou- 
sand observations made in the investigation are given in the accom- 
panying table. The observations were made before the introduction 
of high speed steel, and the figures probably should be modified some- 
what for more modern practice. The sum of the individual horse-power 
values as given in the table is about 20% higher than the power actually 
used m the factory, due to a lessening of the average horse-power in 
each department. The reason for this is the working conditions exist- 
ing, in that all tooliS were not used to their maximum or even average 



1306 



THE MACHINE-SHOP. 



capacity at the same time. In determining the size of motor for each 
department, the total horse-power required by the tools in that depart- 
ment, as given in the table, was diminished by 20%, and the friction 
load of line and comitershafts was added. 

Power Required by Machine Tools in Groups. 



Size. 



Maxi- 


Aver- 


mum 
H.P. 


age 
H.P. 



Size. 



Maxi- 


Aver- 


mum 
H.P. 


age 
H.P. 



Size, 



Maxi- 
mum 
H.P. 



Aver- 
age 
H.P. 



Boring Machines. 
36in.i I 0.78 I 0.52 
42 "2 1.72 1.08 



Cam Cutters. 



No. 2 
** 4 
" 5 

Note 3 
" 4 



0.48 
0.48 



0.67 
0.32 
0.32 
0.32 
0.32 



Cutting-off Machine. 



1 15/i6 in. 

2 in. 

3 in. 
Drilling 

Note 5 
" 6 



" 9 
" iO 
" 11 
16 in. 
18 " 
20 " 
22 " 
24 " 
26 " 
28 " 
30 " 
34 " 
36 " 
46 " 
50 " 

Gear 
No. 4 1/2 
" 3 
" 3 



I 0.12 
0.28 10.14-0.18 
0.34 10.20-0.22 
Machines. 
0.72 



3.18 



1.12 
0.31 
0.32 
0.35 
0.48 
0.71 
0.25 
0.35 
0.42 
0.59 
0.47 
0.22 
0.25 
0.30 
0.45 
0.53 
0.63 
0.83 
Cutters. 

0.15-0.32 
0.20 
0.20 



Grinders. 
No. 312 



4 

1113 

214 

314 

1 15 

215 



i.42 



0.32 
0.53 
0.80 
0.40 
0.50 
0.60 
0.76 



Grinders (Cont.) 
Note 16 I 3.29 1 0.97 

" 17 1 10.41-0.82 

Drop Hammers. 
401b. 
250 " 
400 *' 
600 " 
800 " 
1000 " 
1500 ** 



O.IO 
2.00 
2.50 
3.00 
3.50 
4.00 
5.00 
Power Hammers. 

1001b. I I 1.50 

150 " I I 1.75 

Keyseater. 
No. 4 I 0.64 10.28-0.32 
Lathes. 

0.35 
0.41 
0.24 
0.26 
0.34 
0.36 
0.39 
0.44 
0.32 
0.25 
0.31 
0.31 
0.58 
0.10 
0.12 
0.25 
0.70 
0.33-0.63 
1.20-1.80 
0.31 
0.36 
1.30 



Milling Machines. 



20 in.18 




30 *' 18 




12 ** 




14 " 


0.48 


16 " 




16 " 


0.48 


18 " 




20 " 




22 '* . 


0.37 


24 " 




24 " 




28 " 




38 ** 




10 " 19 




14 '* 19 




15 " 20 




H2l 




No. 122 


1.63 


2X24 in. 23 


1.97 


14in.24 




16 " 24 




36 " 25 


i.'5b J 



No. 



1 


0.47 


3 


0.64 


4 





41/2 





6 





0.30 

0.26 
0.19-0.29 
0.13-0.1 

0.26 



Milling Machines (Cont.) 



No. 



7 
14 
15 

326 

526 

3 

1 

2 

5 

7 

U/22- 

Planers. 



0.83 
0.25 
0.25 
0.26 
0.55 
0.17-0.25 
0.15 
0.25 
0.30 
0.83 
0.20 

1.0 -0.43 
1.16-0.53 
0.70 
0.84 
0.81 
1.31 
1.56 
1.60 
1.14 
3.70 
2.00 
Polishing Stands. 

No. 3 I I 1.00 

"5 I I 1.09 

Punch Presses. 
No. 3 1 2.59 i 1.26 
Profiling Machines. 

No. 1 I I 0.50 

" 6 I I 0.40 

Band-Saw.30 
36 in. I 3.00 1 0.87 

Circular Saw. 

9 in. 3.77 1.05 

13 " 3.75 1.04 

13 " 5.82 1.21 

Hack Saw. 

12-14 in. I I 0.06 

Screw Machines. 



17 in. 


2.01 


22 X 60 in. 


2.34 


22 X 60 '' 


1.44 


24 X 72 '' 




26 X 60 " 


1.59 


30 X 72 " 


4.91 


30 X 96 " 


5.46 


36X120 " 


4.00 


50X108 *' 


2.94 


34 in.28 


7.75 


24 '* 29 


3.40 



No. 1 

" 2 
" 2 



0.60 
0.37 
0.72 



Notes. — 1 Single head. 2 Double head. ^ Lathe type, single head. * Lathe 
type, double head. & No. radial. ^ No. 1 radial. ^ single spindle, 
sensitive. » 2-spindle. 9 3-spindle, sensitive. 10 4-spindle. n 6-spindle. 
12 Cutter and reamer. i3 Plain, i^ Surface. is Universal, i^ -^jVet tool, 

carrying 20-in. wheel, i^ Wet grinder with two 24-in. wheels, i^ Boring 
lathe. 19 Speed lathe. 20 Squaring-up lathe. 21 Gisholt turret lathe. 
'2 Potter & Johnson semi-automatic. 23 Jones & Lamson flat turret. 24 Wood 
turning. 25 Putnam gap lathe, used for wood turning. 26 Vertical. 27 Hand. 
28 Wood panel planar, 29 Wood surfacer. ^o Used for pattern work. 



i 



MACHINE TOOL DRIVES, SPEEDS AND FEEDS. 1307 

A similar investigation, reported by H. C. Spillman (Mach'y, June, 
1913), showed that but 20% of the total power supplied to the motor 
is applied in useful work in the machines, 72% being absorbed in friction 
losses in machines and shafting, and 8% disappearing as electrical 
losses. 

MACHINE TOOL DRIVES, SPEEDS AND FEEDS. 

Geometrical Progression of Speeds and Feeds. — It has become 
generally accepted that the speeds available on a given machine tool 
should be in a geometric progression. There is, however, by no means 
a uniformity in the ratio of the various geometric series adopted by 
the different makers. This ratio will be found to range from 1.3 to 1.7 
on the usual types of cone-driven machines, and the speeds available 
under different conditions of open belt and back gear operation present 
many duplications and are often far from a true geometric progression 
when considered over the entire range of speeds. Carl G. Barth {Am. 
Mach., Jan. 11, 1912) suggests a ratio of ^v^= 1.1S9. With this ratio, 
the revolutions per minute of the spindle are doubled every fourth 
speed. An editorial {Am. Mach., Dec. 3, 1914) discussing the advan- 
tage of adopting this ratio for a speed series shows that it will fulfill 
all the ordinary requirements of machine tool work, and that practically 
any desired speed in either lathe or drill press can be obtained when 
the machine is speeded according to a geometric progression based 
on the ratio 1.189. At the present writing (1915) this ratio has been 
adopted by several machine tool builders. 

The necessity for the adoption of a standard ratio for speeds and 
feeds on machine tools is discussed in Am. Mach., Dec. 3 and 10, 1914, 
in describing the respeeding of machines at the Watertown arsenal and 
elsewhere. The speeds originally available on many of the machines 
presented many duplications of open belt speeds when back-geared, and 
the speeds on any one machine considered as a whole were not in any 
regular series. Thus a lathe with supposedly 20 speeds had practically, 
due to duplication of speeds in the open belt and back-gear series, only 
12 speeds. The rearrangement of the gearing and the pulleys made 
all 20 speeds available, and in practical accord with a geometric series 
with a ratio of 1.189. In the same article there are tabulated the 
speeds of nine 16-in. lathes offered in response to a request for bids. 
In no case did the speeds available on one lathe correspond with those 
on any other, nor did any set of speeds even approximate the ideal 
speeds. Even three machines offered by one maker had wide variations 
in their speeds. Such a condition precludes the possibility of using 
machines interchangeably for the same service, and, as stated by Mr. 
Barth, is the basis of much of the trouble regarding piece rates in machine 
shop work. See also article by Robert T. Kent, Iron Age, July 3, 1913. 

A geometrical progression of the feeds available on machine tools is 
also desirable, and Mr. Barth has recommended the same ratio for 
the feed series as for the speed series, >y2"= 1.189. The reasons for 
adopting this ratio are given in the article above cited, Am. Mach., 
Jan. 11, 1912. 

Methods of Driving Machine Tools. — F. A. Halsey in a lecture at 
Columbia University {Indust. Eng., Sept., 1914) compares the relative 
advantages of the ordinary 5-step cone pulley, the 3-step cone pidley, 
the constant speed pulley and the individual motor as a drive for 
machine tools. In the 5-step cone pulley drive the large intervals 
between the speeds available on the different cone steps decrease the 
output of the machine, due to the fact that except in those few cases 
where the cone speed is nearly equal to the cutting spiuxl the next 
lower cone speed must be used. Also on account of the proportions 
of the cone, the belt speed is unnecessarily low, and as the belt is moved 
to the largest cone step its speed is still further decreased. On the 
larger steps the belt is frequently incapable of delivering the power 
required by the heavier cuts which go with large work. This defect 
is remedied in the 3-step cone pulley, in which the difference in the 
diameters of the steps is not so pronounced, the additional number of 
speed changes being obtained by double back gears. 

Mr. Halsey compares two specific cases: (1) A 5-step cone with 
single back gears, the cone step diameters being respectively 4, 6, 8, 10, 



1308 THE MACHINE-SHOP. 

and 12 in. (2) A 3-step cone with double back gears, the cone step 
diameters being respectively 11 17/32, 12 9/32, and 13 in. In case 1 a 2 1/2- 
in. belt, and in case 2 a 4-in. belt, is used. The change from 3 to 5 steps 
reduces the ratio of the highest to the lowest speed on the cone, and it 
increases the belt speed and therefore the power on all steps, but 
particularly on the large ones where it is most needed. The effect of 
these changes can be shown by calculating the respective powers with 
the belts on the largest steps of the two cones. Assume (case 1) that 
the speed with the belt on the 4-in. step is 100. Then the speed with 
the belt on the largest step will be 100 X ^/u = 331/3. To maintain 
the same cone speed in case 2, the highest belt speed will be 
100 (11 17/32 -^ 4) = 288 +; the lowest will be 288 (11 17/32 -^ 13) = 255+. 
The smallest step in case 1 is too small for a double belt, while in case 2 
a double belt can be used on the smallest step. In order to compare 
the power capacities of the two machines the belt speed must be 
multiplied by a factor representing the greater pulling power of the 
double belt, say 1.43, and also by the ratio of the belt widths, 1.6. If 
Li and L2 represent respectively the power capacities of the large steps 
of cases 1 and 2, and Si and S2 the power capacities of the small steps, 
then 

1 = 1^X^-43X1.6 = 6.5 

l! = Sx 1-43X1.6= 17.5 

That is, the power capacity of the 3-step cone is 6.5 times as great 
as that of the 5-step cone with the belt on the small step, and 17.5 times 
as great with the belt on the large step. The defect of the arrange- 
ment given in case 2 is that it provides a smaller number of speeds 
and a smaller range of speeds than does case 1. The remedy is the 
provision of additional back gears if the additional speeds or greater 
range is necessary.. Mr. Halsey further points out that direct connec- 
tion between the cone pulley and the work spindle has been retained 
in many cases where it should have been discarded, since with large 
work the belt speed will become too low to transmit adequate power, 
and it is better practice to interpose gearing between the pulley and the 
spindle, and thus speed up the belt and pulley. In changing machines 
in accordance with the above suggestions, it is advisable to so design 
the gearing as to obtain speeds which will be in geometric progression 
as explained in a previous paragraph. For methods of laying out cone 
pulleys, see p. 1136. For methods of laying out the driving gears of 
machine tools see "Halsey's Handbook for Machine Designers and 
Draftsmen," p. 77. 

In the Constant Speed Pulley drive, the belt pulley of the machine is 
driven at a constant speed and the power is transmitted to the machine 
from the pulley through a train of gears arranged in a gear box. By 
the shifting of appropriate levers any particular set of gears can be put 
in engagement, thus making instantly available any speed in the range 
of the machine. This arrangement makes the obtaining of a geometric 
series of speeds a particularly easy matter. The constant speed pulley 
drive possesses the advantage of giving a self-contained machine, 
particularly adapted to the individual motor drive. It has found 
wide application in the miUing machine and in certain types of lathes. 

The Individual Motor Drive has, according to Mr. Halsey, a field in 
the driving of portable floor plate tools, for machines in isolated posi- 
tions, or for tools so located that line shafts cannot be conveniently 
laid out for them, and for large machines where the cost of the motor 
is a relatively small part of the total cost of the tool. The disadvantage 
of the individual motor for the small or medium size tool is that the 
power capacity of the motor must be equal to the maximum power 
requirement of the machine and that no advantage can be taken of 
the average power requirements of several machines as is possible in 
the group drive where one motor drives several machines. This in- 
creases the first cost of the motors, and they are also usually worked 
at low efficiency, due to the fact that they are most of the time 
underloaded. 



ABRASIVE PROCESSES. 1309 

ABRASIVE PROCESSES. 

Abrasive cutting is performed by means of stones, sand, emery, glass, 
corundum, carborundum, crocus, rouge, chilled globules of iron, and in 
some cases by soft, friable iron alone. (See paper by John Richards, 
read before the Technical Society of the Pacific Coast, Am. Mach.^ Aug. 
20, 1891, and Eng. & M. Jour., July 25 and Aug. 15, 1891.) 

The " Cold Saw." — For sawing any section of iron while cold 
the cold saw is sometimes used. Tliis consists simply of a plain soft 
steel or iron disk without teeth, about 42 inches diameter and s/^e inch 
thick. The velocity of the circumference is about 15,000 feet per minute. 
One of these saws will saw through an ordinary steel rail cold in about 
one minute. In this saw the steel or iron is ground off by the friction 
of the disk, and is not cut as with the teeth of an ordinary saw. It has 
generally been found more profitable, however, to saw iron with disks or 
band-saws fitted with cutting-teeth, which run at moderate speeds and 
cut the metal as do the teeth of a milling-cutter. 

Reese's Fusing-disk. — Reese's fusing-disk is an application of the 
cold saw to cutting iron or steel in the form of bars, tubes, cylinders, 
etc., in wiiich the piece to be cut is made to revolve at a slower rate of 
speed than the saw. By this means only a small surface of the bar to 
be cut is presented at a time to the circumference of the saw. The 
saw is about the same size as the cold saw above described, and is rotated 
at a velocity of about 25,000 feet per minute. The heat generated by 
the friction of this saw against the small surface of the bar rotated against 
it is so great that the particles of iron or steel in the bar are actually fused, 
and the "sawdust" welds as it falls into a solid mass. This disk will cut 
either cast iron, wrought iron, or steel. It will cut a bar of steel is/g 
inch diameter in one minute, including the time of setting it in the machine, 
the bar being rotated about 200 turns per minute. 

Cutting Stone vs^ith Wire. — A plan of cutting stone by means 
of a wire cord has been tried in Europe. While retaining sand as the 
cutting agent, M. Paulin Gay, of Marseilles, has succeeded in applying 
it by meclianical means, and as continuously as formerly the sand-blast 
and band-saw, with both of which appliances his system — that of the 
**helicoidal wire cord" — has considerable analogy. An engine puts in 
motion a continuous wire cord (varying from five to seven tliirty-seconds 
of an inch in diameter, according to the w^ork), composed of three mild- 
steel wires twisted at a certain pitch, that is found to give the best results 
in practice, at a speed of from 15 to 17 feet per second. 

The . Sand-blast. — In the sand-blast, invented by B. F. Tilghman, 
of Philadelphia, and first exhibited at the American Institute Fair, 
New York, in 1871, common sand, powdered quartz, emery, or any sharp 
cutting material is blown by a jet or air or steam on glass, metal, or other 
comparatively brittle substance, by which means the latter is cut, drilled, 
or engraved. To protect those portions of the surface which it is desired 
shall not be abraded it is only necessary to cover them with a soft or 
tough material, such as lead, rubber, leather, paper, wax, or rubber- 
paint. (See description in App. Uyc. Mech.; also U. iS. report of Vienna 
Exhibition, 1873, vol. iii. 316.) 

A "jet of sand" impelled by steam of moderate pressure, or even by 
the blast of an ordinary fan, depoUshes glass in a few seconds: wood is 
cut quite rapidly; and metals are given the so-called ''frosted ' surface 
with, great rapidity. With a jet issuing from under 300 pounds pressure, 
a hole was cut through a piece of corundum 1 1/2 inches thick in 25 minutes. 

The sand-blast has been applied to the cleaning of metal castings and 
sheet metal, the graining of zinc plates for Uthographic purposes, the 
frosting of silverw^are, the cutting of figures on stone and glass, and the 
cutting of devices on monuments or tombstones, the recutting of files, 
etc. The time required to sharpen a worn-out 14-inch bastard file is 
about four minutes. About one pint of sand, passed through a No. 
120 sieve, and 4 H.P. of 60-lb. steam are required for the operation. 
For cleaning castings, compressed air at from 8 to 10 pounds pressure 
per square inch is employed. Chilled-iron globules instead of quartz 
or flint-sand are used with good results, both as to speed of working and 
cost of material, when the operation can be carried on under proper 
conditions. With the expenditure of 2 H.P. in compressing air, 2 square 
feet of ordinary scale on the surface of steel and iron plates can be 



1310 THiE MACHINE-SHOI>. 

removed per minute. The surface thus prepared is ready for tinning, 
galvanizing, plating, bronzing, painting, etc. By continuing the opera- 
tion the hard skin on the surface of castings, which is so destructive to 
the cutting edges of milling and other tools, can be removed. Small 
castings are placed in a sort of slowly rotating barrel, open at one or 
both ends, through which the blast is directed downward against them 
as they tumble over and over. No portion of the surface escapes the 
action of the sand. Plain cored work, such as valve-bodies, can be 
cleaned perfectly both inside and out. One hundred lbs. of castings 
can be cleaned in from 10 to 15 minutes with a blast created by 2 H.P. 
The same weight of small forgings can be scaled in from 20 to 30 minutes. 
— Iron Age, March 8, 1894. 

Polishing and Bufflng. — The type of polishing wheel to be used de- 
pends on the class of work. For rough polishing on flat surfaces or 
where the corners are to be square, a paper or a wooden wheel, faced 
with leather to which emery or some other abrasive is glued is used. 
For large flat work, or curved surfaces, bull neck, solid canvas, sohd 
sheepskin, paper or wooden wheels are used. These wheels are also 
used for such work as stove trimmings, agricultuial implements, tools, 
cast iron and brass parts, etc. Loose or stitched sheepskin, loose or 
stitched canvas and solid or stitched laminated felt wheels are used 
for roughing irregular shapes requiring a soft faced wheel which will 
come in contact with every crevice of the work. Bull neck or wooden 
wheels are used whenever coloring or finishing is to be done on cast 
or sheet metal. For work requiring a high polish, as gims, cutlery, 
etc., sea horse is often employed. The hardness of the wheel depends 
on the service in which it is to be used, and in the case of linen, canvas, 
leather, or other built-up wheels on steel centers, is governed by the 
depth of the flanges clamping the wheel on the arbor; the larger the 
flanges the harder is the wheel. For most polishing operations, a 
peripheral speed of the wheel of from 3000 to 6000 ft. per minute is 
suflBcient, and 4000 ft. will serve for most purposes. These are the 
speeds recommended for muslin, felt or sea horse wheels, although 
some claims are advanced for speeds as high as 7500 ft., it being stated 
that lower speeds will scratch the work. 

Buffing is the process of obtaining a grainless finish of high luster 
on plated sm-faces. The degree of luster depends on the finish of the 
surface prior to plating. The work is done on a soft wheel to which 
a polishing composition has been applied. The polishing composition 
comprises a heavy grease containing polishing material, as flour-emery, 
rouge, tripoli, crocus, etc. According to the Chicago Wheel and Mfg. 
Co. the following compositions are adapted to the different varieties 
of work. For cutting down and polishing brass, bronze and Britannia 
metal preparatory to plating, tripoli composition; for smooth surfaces 
on nickel and brass, crocus composition; for coloring brass, copper, 
nickel, bronze, German silver, etc., either in solid or plated metal. 
White Diamond XXX composition; for chased or embossed parts, or 
for cutting down silver-plated pieces which are afterward to be colored 
with rouge and alcohol. White Diamond XXXX composition is used; 
for nickel-plated pieces with a high luster. White Coloring composition, 
made of Vienna lime is used. Where rapid, sharp, even cutting is 
desired, emery cake is used. Chandelier rouge is used to produce a 
deep color on brass and bronze parts. 

Laps and Lapping. — A series of tests was made by W. lA. Knight 
and A. A. Case {Jour. A. S. M. E., Aug., 1915) to determine the effect 
on the rate of cutting with different combinations of abrasive lubricant 
and lap material. The tests were made with hardened steel speci- 
mens, and comparative results were obtained with emery, alundum and 
carborundum used in connection with lard oil, machine oil. gasohne, 
kerosene, turpentine, alcohol and soda water. The lap materials were 
cast iron, soft steel and copper. The following conclusions were 
derived from the invesigation : The initial rate of cutting is not 
greatly different for the different abrasives; carborundum maintains 
its rate better than either of the others, alundum next, and emery the 
least; carborundum wears the lap about twice as fast, and alundum 
11/4 times as fast as emery; there is no advantage in using an abrasive 
coarser than No. 150; the rate of cutting is practically proportional to 



EMERY WHEELS AND GRINDSTONES. 1311 

the pressure; the wear of the laps is in the proportions of cast iron 
1.00, steel 1.27, copper 2.62, and this wear is inversely proportional to 
the hardness by the Brinell test; in general, copper and steel cut faster 
than cast iron, but where permanence of form is a consideration, cast 
iron is the superior metal; gasoline and kerosene are the best lubricants 
to use with cast-iron lap, kerosene, on accoimt of its non-evaporative 
qualities, being first choice; machine and lard oil are the best lubri- 
cants to use with copper or steel lap, but they are least eft'ective on the 
cast lap; for all laps and all abrasives (of those tested) the cutting is 
faster with lard oil than with machine oil; alcohol shows no particular 
merit for the work; turpentine does fairly good work with carborundum, 
but in general, is not as good as kerosene or gasoline ; soda water com- 
pares favorably with other lubricants, and on the whole it is slightly 
better than alcohol or turpentine; wet lapping is from 1.2 to 6 times 
as fast as dry lapping, depending on the material of the lap and the 
method of charging. 

EMERY WHEELS AND GEINDSTONES. 

References. — "American Machinist Grinding Book"; "Grits and 
Grinds," Norton Company; "Points about Grinding Wheels and their 
Selection," Brown & Sharpe Mfg. Co.; "Table of Causes of Grinding 
Wheel Accidents," Independence Inspection Bureau; "Safeguarding 
Grinding Wheels," Report of Committee of National Machine^ Tool 
Builders' Association; Bulletin, "Safeguarding High Speed Grinding 
Wheels," National Foimders' Association ; " Operation of Grinding Wheels 
in Machine Grinding," Geo. I. Alden, Journal A.S.M.E., Jan., 1915. 

Selection of Abrasive Wheels. (Contributed by the Norton Com- 
pany, 1915.) — The user of a modern grinding wheel should thoroughly 
understand these essential features; the definition of grain and grade, 
the particular conditions of grinding which catise them to vary; the 
methods of balancing and moimting; truing and dressing; the effect of 
machine vibration and arc of contact upon grain and grade; the rela- 
tion of work speed and wheel speed for production and finish; safe- 
guards and dust removal systems. 

Grain. — Abrasive grains are niunbered according to the meshes per 
Uneal inch of the screen through which they have been graded. The 
nimabers used in wheels are 8, 10, 12, 14, 16, 20. 24, 30, 36, 46, 54, 60. 
70, 80, 90, 120, 150, 180, 200; when finer than 200, the grains are termed 
flours, being designated as F, 2F, 3F, 4F, XF, 65C, 65F, F being the 
coarsest and 65F, the finest. Grits from 12 to 30 are generally used 
on all heavy work such as snagging; 36 to 80 cover nearly all tool grind- 
ing, saw gumming, and other operations where precision in measurement 
is sought; 90 and finer are used for special work such as grinding steel 
balls and fine edge work; the flour sizes are used mostly for sharpening 
and rubbing stones. The number representing the grades of abrasive 
leave a degree of smoothness of surface which may be compared to that 
left by flies as follows: 8 and 10 represent the cut of a wood rasp; 
16, 20, coarse-rough file; 24, 30, ordinary rough file; 36. 40, bastard file; 
46, 60, second-cut file; 70, 80, smooth file; 90, 100, superfine file; 
120F, 2F, dead-smooth file. 

Grade. — When the retentive properties of the bond are great, the 
wheel is called hard; when the grains are easily broken out, it is called 
soft. A wheel is of the proper grade when its cutting grains are auto- 
matically replaced when dulled. Wheels that are too hard glaze. Dress- 
ing re-sharpens them, the points of the dresser breaking out and break- 
ing off the cutting grains by percussion. 

Soft wheels are used on hard materials, like hardened steel. Here the 
cutting particles are quickly dulled and must be renewed. On softer 
materials, like mild steel and wrought iron, harder grades can be used, 
the grains not dulling so quickly. 

The area of surface to be groimd in contact with the wheel is of the 
utmost importance in determining the grade. If it is a point contact 
like grinding a ball or if an extremely narrow fin is to be removed, we 
must use a very strongly bonded wheel, on account of the leverage ex- 
erted on its grain, which tends to tear out the cutting particles before 



1312 



THE MACHINE-SHOP, 



Revolutions per Minute Required for Specified Rates of 

Periphery Speed. Also Stress per Square Inch on 

Norton Wheels at the Specified Rates. 











Surface Speeds, Feet per Minute. 






d 

HI 


1000 


2000 


3000 


4000 


5000 


6000 


7000 


8000 


9000 


lOOOC 


fc 


Stress per Square Inch, Pounds. 


O 


3 


12 


27 


48 


75 


108 


147 


192 


243 


300 


5 


Revolutions per Minute. 


1 


3820 


7639 


11459 


15279 


19099 


22918 


26738 


30558 


34377 


38197 


2 


1910 


3820 


5730 


7639 


9549 


11459 


13369 


15279 


17189 


19098 


3 


1273 


2546 


3820 


5093 


6366 


7639 


8913 


I0I86 


11459 


12732 


4 


955 


1910 


2865 


3820 


4775 


5729 


6684 


7639 


8594 


9549 


5 


764 


1528 


2292 


3056 


3820 


4584 


5347 


6111 


6875 


7639 


6 


637 


1273 


1910 


2546 


3183 


3820 


4456 


5093 


5729 


6366 


7 


546 


1091 


1637 


2183 


2728 


3274 


3820 


4365 


4911 


5457 


8 


477 


955 


1432 


1910 


2387 


2865 


3342 


3820 


4297 


4775 


10 


382 


764 


1146 


1528 


1910 


2292 


2674 


3056 


3438 


3820 


12 


318 


637 


955 


1273 


1591 


1910 


2228 


2546 


2865 


3183 


14 


273 


546 


818 


1091 


1364 


1637 


1910 


2183 


2455 


2728 


16 


239 


477 


716 


955 


1194 


1432 


1671 


1910 


2148 


2387 


18 


212 


424 


637 


849 


1061 


1273 


1485 


1698 


1910 


2122 


20 


191 


382 


573 


764 


955 


1146 


1337 


1528 


1719 


1910 


22 


174 


347 


521 


694 


868 


1042 


1215 


1389 


1563 


1736 


24 


159 


318 


477 


637 


796 


955 


1114 


1273 


1432 


1591 


30 


127 


255 


382 


509 


637 


764 


891 


1018 


1146 


1273 


36 


106 


212 


318 


424 


530 


637 


743 


849 


955 


1061 



Table to Figure Surface Speeds of Wheels. 
(Circumferences in Feet, Diameters in Inches.) 





-kj 




_^ 




-M 




-t-s 




-(^ 




^ 




px, 




fe 




f^ 




^ 


, 


^ 




1^ 


c 




fi 




a 




fl 




fl 




c 




IH 


i. 


t—i 


^ 


I— 1 


% 


1— 1 


1 


1— 1 


t 


(—1 


i 


i 


i 


i 


3 
2 


i 


o 


1 


^ 


i 


B 


i 


:3 


tt 


'6 


P 
13 


o 


25 


O 


37 


o 


p 

49 


o 


p 


O 


1 


.262 


3.403 


6.546 


9.687 


12.828 


61 


15.970 


2 


.524 


14 


3.665 


26 


6.807 


38 


9.948 


50 


13.090 


62 


16.232 


3 


.785 


15 


3.927 


27 


7.069 


39 


10.210 


51 


13.352 


63 


16.493 


4 


1.047 


16 


4.189 


28 


7.330 


40 


10.472 


52 


13.613 


64 


16.755 


5 


1.309 


17 


4.451 


29 


7.592 


41 


10.734 


53 


13.875 


65 


17.017 


6 


1.571 


18 


4.712 


30 


7.854 


42 


10.996 


54 


14.137 


66 


17.279 


7 


1.833 


19 


4.974 


31 


8.116 


43 


11.257 


55 


14.499 


67 


17.541 


8 


2.094 


20 


5.236 


32 


8.377 


44 


11.519 


56 


14.661 


68 


17.802 


9 


2.356 


21 


5.498 


33 


8.639 


45 


11.781 


57 


14.923 


69 


18.064 


10 


2.618 


22 


5.760 


34 


8.901 


46 


12.043 


58 


15.184 


70 


18.326 


11 


2.880 


23 


6.021 


35 


9.163 


47 


12.305 


59 


15.446 


71 


18.588 


12 


3.142 


24 


6.283 


36 


9.425 


48 


12.566 


60 


15.708 


72 


18.850 



To find surface speed, in feet, per minute, of a wheel. 

Rule. — Multiply the circumference (see above table) by its revolu- 
tions per minute. 

Surface speed and diam. of wheel being given, to find number of revo- 
lutions of wheel spindle. 

Rule. — Multiply surface speed, in feet, per min., by 12 and divide the 
product by 3.14 times the diam, of the wheel in inches. 



ABRASIVES. 1313 

they have done their work. If the contact is a broad one, as in grind- 
ing a hole, or where the work brings a largo part of the surface of 
the wheel into operation, softer grades must be used, because the depth 
of cut is so infinitely small that the cutting points in work become 
duUed quickly and must be renewed, or the wheel glazes and loses its 
efiBciency. 

Vibrations in grinding machines cause percussion on the cutting 
grains, necessitating harder wheels. Wheels m.ounted on rigid machines 
can be softer in grade and are much more efficient. 

Speeds of Grinding Wlieels. — The factor of safety in vitrified wheels 
is proportional to the grade of hardness. Bursting limits are from 12,000 
to 25,000 feet per minute, siurface speed. Wheels are tested by standard 
makers at speeds in excess of 9000 feet surface speed per minute. 
Running speeds in practice are from 4000 to 6000 feet, depending on 
work, condition of machine, and mounting. 

Generally speaking, grinding of tools, reamers, cutters, and surface 
grinding is done at about 4000 feet, snagging and rough forms of hand 
grinding at 5000 to 5500 feet, cyhndrical grinding, or where the work is 
rigidly held and where the wheel feed is under control, from 5500 to 6500 
feet, and in some instances as high as 7500 feet. 

These speeds are all for vitrified wheels. The same speeds will apply 
to wheels made by the elastic and silicate processes. 

Grain Depth of Cut. — An analysis of the action of the wheel when 
in operation shows how theoretical considerations bear out the truth of 
the empirical rules for the use of grinding wheels in macliine grinding. 
A paper by Geo. I. Alden {Jour. Am. Soc. J\I. E., Jan., 1915) gives the 
essential distinction between the radial or real depth at which the 
wheel cuts and the depth which the abrasive grain in the wheel cuts 
into the material being ground. The latter depth is termed the "grain 
depth of cut." This grain depth of cut is the controlling factor in se- 
curing the correct working of the wheel. A formula is deduced for com- 
puting the grain depth of cut, the application of the analysis is explained 
and these conclusions reached by Prof. Alden : 1 — Other factors remain- 
ing constant, increase of work speed increases grain depth of cut. and 
makes a wheel appear softer. 2 — A decrease of wheel speed increases 
grain depth of cut. 3 — Diminishing the diameter of the wheel increases 
the grain depth of cut; increasing the diameter of the wheel decreases 
the grain depth of cut. 4 — Decreasing the diameter of work increases 
the grain depth of cut; conversely, increasing the diameter of work de- 
creases the grain depth of cut. 

A table of arcs of contact of wheel and work for a limited range of 
diameters is given, also a table of values of one of the factors in the 
formula for grain depth of cut. 

Artificial Abrasives. — Since 1900 artificial abrasives, made in 
various types of electric furnaces, have been displacing natural abra- 
sives, and they are to-day almost exclusively used. This has been due 
largely to the abiUty to control the purity of the raw material and to 
insure uniformity of cutting action of the finished products. Artificial 
abrasives are divided into the aluminous group (examples, Alundum, 
Aloxite and Boro-Carbone) , and the sihcon carbide group (examples, 
Crystolon, Carborundum, Carbolite). The abrasive action of the 
aluminous group is due to the amount of oxide of aluminum, which in 
these artificial abrasives is in excess of 90%, slightly more than the best 
corundum and considerably in excess of the alumina content of emery, 
which rarely exceeds 70%. The aluminous abrasives are characterized 
by a high degree of toughness and are particularly adapted for grinding 
materials of high tensile strength such as steel and its alloys. The siU- 
cate carbide group is not duplicated by Nature and is somewhat harder 
and more brittle than the aluminous group. The silicon carbide abra- 
sives are now recognized as standard for grinding materials of low 
tensile strength such as cast Iron, brass pearl, marble, granite and 
leather. 

Selection of Emery Wheels.* — The Norton Co. (1915) publishes the 
accompanying table showing the proper grain and grade of wheel for 
different services. The column headed grain indicates the coarsencos of 
the material composing the wheel, being designated by the number of 



1314 



THE MACHINE-SHOP. 



meshes per inch of a sieve through which the grains pass. A No, 20 
grain will pass through a 20mesh sieve, but not through a SOmesh, etc. 

EXPLANATION OF GRADE LETTERS. 



Extremely- 


Soft. 


Medium 


Medium. 


Medium 


Hard. 


Extremely- 


Soft. 




Soft. 




Hard. 




Hard. 


A 


E 


I 


M 


Q 


U 


Y 


B 


F 


J 


N 


R 


W 


Z 


C 


G 


K 


O 


S 






D 


H 


L 


P 


T 







For Grinding Higti-speed Tool Steel, The American Emery Wheel 
Co. recommends a wheel one number coarser and one grade softer than 
a wheel for grinding carbon steel for the same service. 

Balancing. — The standard makers of grinding wheels send out 
wheels balanced within narrow limits, accompUshed by inserting lead 
near the hole. As the wheels wear down it frequently becomes necessary 
for the user to balance them by removing some of the lead. 

Mounting Grinding Wheels— Safety Devices. — A code for the mount- 
ing of grinding wheels was adopted by 23 manufacturers of grinding 
wheels in the U. S. and Canada in 1914, and approved by the Na- 
tional Machine Tool Builders' Association. An abstract of the code is 
given in Indust. Eng., Jan., 1915. The code recognizes as safety devices 
protection flanges, protection hoods, and protection chucks. 

Protection flanges of the double or single concave type, used in con- 
junction with wheels having double or single convex tapered sides or 
side are recommended. For double tapered wheels they shall have a 
taper of not less than 3/4 in. per foot for each flange. For single tapered 
wheels they shall have a taper of not less than 3/4 in. per foot. Each 
flange, whether straight or tapered, shall be recessed at the center at 
least I/16 in. on the side next to the wheel. All tapered flanges over 10 in. 
diameter shall be of steel or material of equal strength. Both flanges in 
contact with the wheels shall be of the same diameter. Wheels should 
never be run without flanges. 

The following table gives the dimensions of flanges to be used where 
no hoods are provided: A = Maximum flat spot at center of flange. 
B = Flat spot at center of wheel. C = Minimum diameter of flange. 
Z) = thickness of flange at bore. S = minimum diameter of recess. 
F = Minimum thickness of each flange at bore; all dimensions are 
in inches, 

Dia. of 

Wheel. 6 8 

A 

B 1 1 

C 3 5 



10 12 14 16 18 20 22 

4 4 4 4 4 4 

2 41/2 41/2 6 6 6 6 

6 6 8 10 12 14 16 



D 3/8 3/8 1/2 5/8 5/8 5/8 3/4 3/4 3/4 



24 


26 


28 


30 


4 


4 


4 


4 


6 


6 


6 


6 


18 


20 


22 


24 


3/4 


3/4 


7/8 


7/8 



F 3/8 



2 31/2 4 



51/27 8 9 101/2 12 131/2 141/2 16 



1/2 5/8 3/4 7/8 1 



11/8 11/8 11/8 11/4 11/4 



Where protection hoods are provided, straight flanges and straight 
wheels may be used, the dimensions being as foUows, and the reference 
letters having the same meaning as above: 

Dia. of 

Wheel. 6 8 10 12 14 16 18 20 22 24 26 28 30 

C 2 3 31/2 4 41/2 51/2 6 7 71/28 8I/2IO 10 

^12 21/4 23/4 3 31/2 4 41/2! 5 51/2 6 7 7 

F 3/8 3/8 3/8 1/2 1/2 1/2 5/8 Vs Vs Vs Vs 8/4 3/4 

Protection hoods shall be used where practical with wheels not 
provided with protection flanges, and shall be sufficiently strong to 
retain all pieces of a broken grinding wheel. They shall conform as 
nearly as possible to the periphery of the wheel, and leave exposed the 



EMERY WHEELS AND GRINDSTONES. 



1315 



Table for Selection of Grades. 



Class of Work. 



Aluminum castings 

Brass or bronze castings (large) . 

Brass or bronze castings (small) . 

Cast iron, cylindrical 

Cast iron, surfacing 

Cast iron (small) castings. . . . 

Cast iron (large) castings .... 

Chilled iron castings 

Dies, chilled iron 

Dies, steel 

Drop forgings 

Hammers, cast steel 

Interior of Automobile Cylinders, 
(cast iron) 

Internal grinding, hardened steel 

Knives (paper;, automatic grinding 

Knives (planer), automatic grinding 

Knives (planing mill), hand grind- 
ing 

Knives, shear and shear blades . 

Lathe centers 

Lathe and planer tools 

Machine-shop use, general . . . 

Malleable iron castings (large) 

Malleable iron castings (small) . 

Milling cutters, automatic or semi- 
automatic grinding 

Milling cutters, hand grinding . . 

Plows (steel), surfacing 

Pulleys (C.I.), surfacing faces of . 

Radiators (cast iron ) , edges of . . 

Reamers, taps, milling cutters, 
etc., hand grinding 

Reamers, taps, milling cutters, 
etc., special machines 

Rolls, (cast iron) wet 

Rolls (chilled iron), finishing . . 

Rolls (chilled iron), roughing. . . 

Rubber 

Saws, gumming and sharpening . 
Saws, cold cutting-ofif 

Steel (soft), cylindrical grinding . 

Steel (soft), surface grinding . . 

Steel (hardened), cylindrical grind- 
ing 

Steel (hardened) , surface grinding 

Steel, large castings 

Steel, small castings 

Steel (manganese), safe work . . 

Steel (manganese), frogs and 
switches 

Structural steel 

Twist drills, hand grinding . . . 

Twist drills, special machines . . 

Wrought iron 

Woodworking tools 



Alundum. 


Cry stolon. 


Grain. 


Grade. 


Grain. 


Grade. 


36 to 46 


3to4EIas. 


20 to 24 


P to R 






20 " 24 


Q " R 






24 " 36 


P " R 


24 comb. 


J to K 


30 " 46 


I " L 


16 to 46 


H " K 


16 " 30 


I " L 


24 " 30 


P " R 


20 " 30 


Q " S 


16 " 20 


Q " R 


16 " 24 


Q " S 


20 " 30 


P " U 


20 " 30 


Q " R 






20 " 30 


O " Q 


36 to 60 


J to L 






20 " 30 


P " R 






30 


P " Q 










36 ** 60 


I " L 


46 to 60 


J to M 






36 " 46 


J " K 






30 " 46 


J " K 






46 " 60 


J to M 






30 *' 60 


J " M 






46 "120 


J " M 






j 20 " 24 
1 20 " 36 


PSil. 






O toP 






20 " 36 


O " Q 




' 


14 " 20 


P " U 


16 " 20 


R " S 


20 " 30 


P " R 


20 " 30 


Q " S 


46 " 60 


I " M 






46 " 60 


J " M 






16 " 24 


Q " S 










30 "36 


K " L 


46 to 1 20 




24 " 30 


R " S 


46 *' 60 


K " 






46 " 60 


J " M 






24 " 36 


J " M 


24 " 46 


J " M 


70 ] 


13^ " 2 
Elas. 


J 70 " 80 
1 80 


1^ to 2 

Elas 

J 







30 to 46 


\2 to 5 
) Elas. 


30 to 50 


J toK 


30 " 50 


KtoM 


36 " 50 


M " N 






60 


" Q 






( 24 comb. 
\ 30 to 60 


L " P 






L " O 






16 "36 


H " K 






24 comb. 
"i 46 to 60 


K 






J to L 






16 *' 46 


H " K 






10 " 20 


Q " W 






20 " 30 


P " R 






16 " 46 


L " P 






14 " 16 


Q " U 






16 " 24 


P " R 






46 " 60 


M 






36 " 60 


K to M 






12 "30 


P " U 






46 "60 


K " M 







1316 THE MACHINE-SHOP. 

least portion of the wheel compatible with the work. A sh'ding tongue 
to close the opening in the hood as the wheel is reduced in diameter 
should be provided. Protruding ends of the wheel arbors and their 
nuts shall be guarded. 

Cups, cylinders and sectional ring wheels shall be either protected with 
hoods, enclosed in protection chucks, or surrounded with protection 
bands. Not more than one-quarter of the height of such grinding 
wheels shall protrude beyond the provided protection. 

Grinding wheels shall fit freely on the spindles. Wheel arbor holes 
shall be made 0.005 in. larger than the machine arbor. The soft metal 
bushing shall not extend beyond the sides of the wheel at the center. 
Ends of spindles shall be threaded left and right so that the nuts on 
both ends will tend to tighten as the spindles revolve. Care should 
be taken that the spindles are arranged to revolve in the proper 
direction. 

Wheel washers of compressible material, such as blotting paper, 
rubber or leather, not thicker than 0.025 in., shall be fitted between the 
wheel and its flanges. It is recommended that the wheel washers be 
sUghtly larger than the diameter of the flanges used. 

When tightening clamping nuts, care shall be taken to tighten them 
only enough to hold the wheel flrmly. Flanges must be frequently in- 
spected to guard against the use of those which have become bent or 
out of balance. If a tapered wheel has broken, the flanges must be 
carefully inspected for truth before using with a new wheel. Clamping 
nuts shall also be inspected. 

Minimum Sizes of Machine Spindles in Inches for Various 
Diameters and Thickness of Grinding Wheels. 



Is 


'A 


M 


1 


IM 


1 iii( 

IM 


:Kiiess 01 
IH 2 


vvneei in 

2M 2A 


IIICI 

3 


Les — 
33/2 


4 


4:A 


5 


Q 
6 


¥2 


3^ 


¥2 


Vs 


Vs 


H H 


H H 


H 


H 


1 


1 


1 


7 


Vi 


% 


% 


H 


H 


H H 


H H 


1 


1 


1 


1 


1 


8 


% 


% 


% 


H 


H 


H 1 


1 1 


1 


1 


IM 


IH 


IH 


9 


% 


% 


y^ 


H 


H 


1 1 


1 1 


IH 


IM 


IM 


IH 


IH 


10 


^ 


H 


K 


H 


H 


1 , 1 


1 IH 


IH 


IM 


IM 


I A 


lA 


12 


M 


^ 


1 


1 


1 


1 1 


1 IH 


IH 


-iH 


IM 


lA 


lA 


14 


Vs 


1 


1 


IH 


IH 


IH IH 


IH IH 


lA 


lA 


IH 


lA 


lA 


16 




IM 


IK 


IH 


IM 


IH IH 


lA lA 


lA 


IH 


IH 


IH 


IH 


18 




IH. 


1V4. 


IH 


IM 


lA lA 


I'A lA 


lA 


IH 


IH 


VA 


lA 


20 






I'A 


I'A 


lA 


lA lA 


lA lA 


IH 


m 


VA 


VA 


1% 


24 






I'A 


lA 


lA 


IH IH 


IH IH 


IH 


2 


2 


2 


2 


26 








lA 


lA 


IH IH 


IH IH 


2 


2 


2H 


2H 


2H 


30 










IH 


IH 2 


2 2 


2 


2H 


2H 


2A 


2A 


36 












2 2H 


2H 2H 


2A 


2H 


2H 


3 


3 



Safe Speeds. — A peripheral speed of 5,000 "ft. per min.. is recom- 
mended as the standard operating speed for vitrified and silicate 
straight wheels, tapered wheels and shapes other than those known as 
cup and cylinder wheels, which are used on bench, floor, swing frame 
and other machines for rough grinding. In no case shall a peripheral 
speed of 6500 ft. be exceeded. 

A peripheral speed of 4500 ft. per min. is recommended as the 
standard operating speed for vitrified and silicate wheels of the cup and 
cylinder shape, used on bench, floor, swing frame, and other machines 
for rough grinding. In no case shall 5500 ft. be exceeded. 

For elastic, vulcanite and wheels of other organic bonds, the recom- 
mendations of individual wheel manufacturers shall be followed. 

For precision grinding an operating peripheral speed of 6500 ft. per 
min. may be recommended. 

If a wheel spindle is driven by a variable-speed motor some device 
shall be used which will prevent the motor from being run at too high 
speeds. Cone pulleys determining the speed of a wheel should never 
be used unless belt-locking devices are provided. Machines should 



EMERY WHEELS AND GRINDSTONES. 1317 

be provided with a stop or some method of fixing the maximum size 
of wheel which may be used, at the speed at which the wheel spindle 
is running. 

If wheels become out of balance through wear and cannot be balanced 
by truing or dressing, they should be removed from the machine. 

A wheel used in wet grinding shall not be allowed to stand partly 
immersed in the water. The water-soaked portion may throw the 
wheel dangerously out of balance. 

Wheel dressers shall be equipped with rigid guards over the tops of 
the cutters, to protect operator from flying pieces of broken cutters. 

Goggles shall be provided for use of grinding wheel operators where 
there is danger of eye injury. 

Work shall not be forced against a cold wheel, but applied gradually, 
giving the wheel an opportunity to warm and thereby eliminate possible 
breakage. This applies to starting work in the morning in grinding 
rooms which are not heated in winter and new wheels wliich have been 
stored in a cold place. 

Grinding as a Substitute for Finish Turning in the Lathe. — 
C. H. Norton (Trans. Am. Soc. M. E. 1912) recommends the use 
of the grinding machine as a substitute for the lathe for many forms 
of cylindrical work. He advocates the elimination of the finishing 
cut in the lathe, claiming it is more economical to grind to size immedi- 
ately after the roughing cut than to finish turn and then grind. For 
this practice, work should not be turned closer than 1/32 in. of finish 
diameter, and coarse feeds, often as coarse as four to the inch, should 
be used. He cites instances where this method produced pieces in 18 
minutes, where the former method of rough and finish turning and then 
grinding to size required 28 }/2 minutes. In 191.3, the Norton Grinding 
Co. was using the grinding machine to the exclusion of the lathe for 
automobile crank-shafts and similar pieces, grinding to size from the 
rough forging. Instances and methods are shown in Indust. Eng., 
April, 1913. 

Truing and Dressing. — (Norton Co., 1915). — A wheel is trued to 
make it concentric and to give it an accurate surface. Dressing is to 
sharpen or renew the surface of the wheel when glazed or loaded. 
Truing on precision grinding machines is performed by a diamond held 
rigidly in a fixed tool post — never in the hand. There should always 
be a hberal supply of lubricant or water flowing on the diamond while 
the truing is being done. In modern practice, truing is for two other 
purposes, as well as to make the wheel perfectly true: one for sharpening 
the wheel to obtain production and the other for dulUng the wheel to 
obtain finish. Truing in rough grinding operations is performed by 
using a dresser, usually an instrmnent containing steel-cutting wheels, 
and in practice the rest is adjusted to form a rigid support for the lugs 
on the dresser, care being taken to see that the dresser is not caught 
between the wheel and the rest. In using the dresser to sharpen up 
the surface of the wheel, the rest is left in its usual close adjustment to 
the wheel. Truing and dressing are two of the most neglected and 
least understood features in the proper use of grinding wheels. 

Special Wheels. — Rim wheels and iron-center wheels are specialties 
that require the maker's guarantee and assignment of speed. 

Safe Speeds for Grindstones and Emery Wheels. — G. D. Hiscox 
{Iron Age, April 7, 1892), by an application of the formula for centri- 
fugal force in fly-wheels (see Fly-wheels) , obtains the figures for strains 
in grindstones and emery wheels which are given in the tables below. 
His formulae are: 

Stress per sq. in. of section of a grindstone = (0.7071DXAO 2X0.0000795 
Stress per sq. in. of sectionof an emery wheel=(0.7071i)xA0 2X0.00010226 

D = diameter in feet, N = revolutions per minute. 

He takes the weight of sandstone at 0.078 lb. per cubic inch, and that 
of an emery wheel at 0.1 lb. per cubic inch; Ohio stone weighs about 
0.081 lb. and Huron stone about 0.089 lb. per cubic inch. The Ohio 
stone will bear a speed at the periphery of 2500 to 3000 ft. per mm., 
which latter should never be exceeded. The Huron stone can be 
trusted up to 4000 ft., when properly clamped between flanges and 
not excessively wedged in setting. Apart from the speed of grindstones 



1318 



THE MACHINE-SHOP. 



as a cause of bursting, probably the majority of accidents have really 
been caused by wedging them on the shaft and over-wedging to true 
them. The holes being square, the excessive driving of wedges to true 
the stones starts cracks in the corners that eventually run out until 
the centrifugal strain becomes greater than the tenacity of the remain- 
ing solid stone. Hence the necessity of great caution in the use of 
wedges, as well as the holding of large quick-running stones between 
large flanges and leather washers. 

The Iron Age says the strength of grindstones when wet is reduced 
40 to 50%. A section of a stone soaked all night in water broke at a 
stress of 80 lb. per sq. in. A section of the same stone dry broke at 
146 lb. per sq. in. A better quaUty stone broke at stresses of 186 and 
116 lb, per sq. in. when dry and wet respectively. 

Strains in Grindstones. 

Limit of Velocity and Approximate Actual Strain per Square 

Inch of Sectional Area for Grindstones of 

Medium Tensile Strength. 



Diam- ' 


Revolutions per Minute. 


eter. 


100 

lbs. 


150 


200 


250 


300 


350 


400 


feet. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


lbs. 


2 


1.58 


3.57 


6.35 


9.93 


14.30 


18.36 


25.42 


2 1/2 


2.47 


5.57 


9.88 


15.49 


22.29 


28.64 


39.75 


3 


3.57 


8.04 


14.28 


22.34 


32.16 






31/2 


4.86 


10.93 


19.44 


30.38 








4 


6.35 


14.30 


27.37 










4V2 










9 93 


22 34 




Approximate breaking strain ten 


6 


14 30 


32 17 




times the strain for size opposite the 


7 


19!44 






bottom figure in each column. 



The figures at the bottom of columns designate the limit of velocity 
(in revolutions per minute at the head of the columns) for stones of the 
diameter in the first column opposite the designating figure. 

A general rule of safety for any size grindstone that has a compact and 
strong grain is to limit the peripheral velocity to 47 feet per second. 

Joshua Rose (Modern Machine-shop Practice) says: The average cir- 
cmnferential speed of grindstones in workshops may be given as follows: 

For grinding machinists' tools, about 900 feet per minute. 

carpenters' " " 600 " 

The speeds of stones for file-grinding and other similar rapid grinding 
is thus given in the "Grinders' List." 

Diam. ft 8 71/2 7 61 /2 6 51 /2 5 41 /2 4 31/2 3 

Revs, per min 135 144 154 166 180 196 216 240 270 308 360 

TAPER BOLTS, PEVS, REAMERS, ETC. 

Standard Steel Mandrels. (The Pratt & Whitney Co.)— These 
mandrels are made of tool-steel, hardened, and ground true on their 
centers. Centers are also ground to true 60 degree cones. The ends are 
of a form best adapted to resist injury hkely to be caused by driving. 
They are slightly taper. Sizes, 1/4 inch diameter by 33/4 inches long to 
4 inches diameter by 17 inches long, diameters advancing by 16ths. 

Taper Bolts for Locomotives. — Bolt-threads, U. S. Standard, ex- 
cept stay-bolts and boiler-studs, V-threads, 12 per inch; valves, cocks, 
and plugs, V-threads, 14 per inch, and i/s-inch taper per 1 inch. 
Standard bolt taper i/ie inch per foot. 

Taper Reamers. — The Pratt & Whitney Co. makes standard taper 
reamers for locomotive work taper i/io inch per foot from 1/4 inch diam- 
eter; 4-inch length of flute to 2-inch diameter, 18-inch length of fiute, 
diameters advancing by 16ths and 32ds. P. & W. Co.'s standard taper 
pin reamers taper 1/4 inch per foot, are made in 15 sizes of diameters, 
0.135 to 1.250 inches; length of flute, 1 7/i6 inches to 14 inches. 



TAPER PINS, BOLTS, REAMERS, ETC. 



1319 



Morse Tapers. 



i 


^52 


L 

J. 

356 


■go 

P 

2 




1 
1 


it 

'So 






a; 




II 

-a 
H 


6 

T3 O 


•it 


Q 
eg 


1' 
a 


2; 




B 


H 


K 


L 


TF 


r 


d 


^ 


R 


a 


>S 









211/32 


21/32 


115/16 


9/16 


.160 


1/4 


.235 


5/32 


5/32 


.04 


27/32 


.625 





I 


.369 


.475 


21/8 


29/16 


23/16 


21/16 


3/4 


.213 


3/8 


.343 


13/64 


3/16 


.05 


2 7/16 


.600 


I 


2 


.572 


.700 


29/16 


31/8 


25/8 


21/2 


7/8 


.26 


7/16 


17/32 


1/4 


1/4 


.06 


215/16 


.602 


2 


3 


.778 


.938 


33/16 


37/8 


31/4 


31/16 


13/16 


.322 


9/16 


23/32 


5/16 


9/32 


.08 


311/16 


.602 




4 


1.020 


1.231 


41/16 


47/8 


41/8 


37/8 


11/4 


.478 


5/8 


31/32 


15/32 


5/16 


.10 


4 5/8 


.623 




5 


1.475 


1.748 


53/16 


61/8 


51/4 


415/16 


11/2 


.635 


3/4 


113/32 


5/8 


3/8 


.12 


57/8 


.630 




6 


2.116 


2.494 


71/4 


89/16 


73/8 


7 


13/4 


.76 


n/s 


2 


3/4 


1/2 


.15 


81/4 


.626 




7 


2.75 


3^7 


10 


115/8 


101/8 


91/2 


25/8 


1.135 


13/8 


25/8 


11/8 


3/4 


.18 


111/4 


.625 





Brown & Sharpe Mfg. Co. publishes {Machy's Data Sheets) a list of 
18 sizes of tapers ranging from 0.20 in. to 3 in. diam. at the small end; 
taper 0.5 in. to 1 ft., except No. 10, which is 0.5161 in. per ft. 




Fig. 216. — Morse Tapers. See table'above. 

The Jarno Taper is 0.05 inch per inch = 0.6 inch per foot. The 
number of the taper is its diameter in tenths of an inch at the small end, 
in eighths of an inch at the large end, and the length in halves of an inch. 
Thus, No. 3 Jarno taper is II/2 inches long, 0.3 inch diameter at the small 
end and 3/8 inch diameter at the large end. 



1320 



THE MACHINE-SHOP. 






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PinsrCHES AND DIES, PRESSES, ETC 



1321 



standard Steel Taper-pins. — The following sizes are made hy The 

Pratt & Whitney Co.: Taper 1/4 inch to the foot. 
Number: 

123 456780 10 

Diameter large end: 

0.156 0.172 0.193 0.219 0.250 0.289 0.341 0.409 0.492 0.591 0.706 
Approximate fractional sizes: 

5/32 11/64 3/16 7/32 I/4 19/64 11/32 13/32 1/2 19/32 23/32 

Lengths from 

3/4 3/4 3/4 3/4 3/4 3/4 3/4 1 11/4 11/2 11/2 

To* 

1 11/4 11/2 13/4 2 21/4 31/4 33/4 41/2 51/4 6 

Diameter small end of standard taper-pin reamer :t 

0.135 0.146 0.162 0.183 0.208 0.240 0.279 0.331 0.398 0.482 0.581 

Dimensions of T-SIots, T-Bolts and T-Nuts. 

(Pratt & Whitney Standard — Dimensions in Inches). 




i:^% 



O 



Slot. 


Bolt and Nut. 












Diam. 


Thick- 


1 












Diam. 


of 


ness of 


Width 


Height 


Diam. 


Width 


w 


Bt 


c 


of 


Head 


Head 


of 


of 


of 


S 


Min. 


Bolt. 


or 


or 


Stem. 


Stem. 


Hole. 












Nut. 


Nut. 
















D 


H 


T 


J 


N 


K 


1/4 


1/2 


3/16 


5/32 


3/16 


7/16 


1/8 


3/16 


3/32 


1/8 


5/16 


5/8 


3/16 


5/32 


1/4 


9/16 


1/8 


1/4 


1/8 


1/8 3/16 


3/8 


11/16 


1/4 


7/32 


5/16 


5/8 


3/16 


5/16 


1/8 


3/16 1/4 


7/16 


13/16 


.9/32 


7/32 


3/8 


3/4 


3/16 


3/8 


5/32 


1/4 5/16 


1/2 


15/16 


5/16 


9/32 


7/16 


7/8 


1/4 


7/16 


3/16 


5/16 3/8 


5/8 


13/16 


3/8 


13/32 


9/16 


1 1/8 


11/32 


9/16 


3/16 


7/16 1/2 


3/4 


I 5/16 


1/2 


17/32 


11/16 


1 1/4 


15/32 


11/16 


1/4 


9/16 5/8 


7/8 


15/8 


9/16 


11/16 


3/4 


1 1/2 


9/16 


3/4 


5/16 


5/8 3/4 


1 


1 7/8 


5/8 


13/16 


7/8 


13/4 


11/16 


7/8 


5/16 


3/4 7/8 



t Maximum thicknesses: Up to S/g-in. bolts, S+I/16 in.; H/ie-in. bolt, 
1 in.; 3/4-in. bolt, 1 l/ie in.; 7/8-in. bolt, 1 3/i6 in. 

PUNCHES AND DIES, PRESSES, ETC. 

Clearance between Punch and Die. — For computing the amount 
of clearance that a die should have, or, in other words, the difference 
in size between die and punch, the general rule is to make the diam- 
eter of die-hole equal to the diameter of the punch, plus 2/10 the thickness 
of the plate. Or, D = d -h 0.2t, in which D = diameter of die-hole, 
d = diameter of punch, and t = thickness of plate. For verj^ thick 
plates some mechanics prefer to make the die-hole a little smaller than 
called for by the above rule. For ordinary boiler- work the die is made 
from Vio to s/^q of the thickness of the plate larger than the diameter 
of the punch; and some boiler-makers advocate making the punch fit 



* Lengths vary by 1/4 inch each size, 
t Taken 1/2 inch from extreme end . 
about 1/2 inch. 



Each size overlaps smaller one 



1322 



THE MACHINE-SHOP. 



the die accurately. For punching nuts, the punch fits in the die. 
iAm. Alach.) 

The clearance between the punch and die when blanking, perforating 
and forming flat thin stock of different materials in the power press 
for light machine parts such as typewriters, adding machines, etc., 
are shown in the following table compiled by E. Dean (Am. Mach., 
May 4, 1905). In using the table, the class of work to be done must 
be considered. For perforating work, the punch is made to the de- 
sired size, and the clearance is made on the die. For blanking, the 
die is of the desired size and the clearance is obtained by making the 
piuich smaller. 

Punch and Die Clearances for Different Materials and Thicknesses. 



Thick- 


Clearance 


Clearance ' Clearance 


Thick- 


Clearance 


Clearance 


Clear- 


ness 


for 


for 


for 


ness 


for 


for 


ance for 


of 


Brass 


Medium 


Hard 


of 


Brass 


Medium 


Hard 


Stock, 


and Soft 


Rolled 


Rolled 


Stock, 


and Soft 


Rolled 


Rolled 


In. 


Steel, In. 


Steel, In. 


Steel, In. 


In. 


Steel, In. 


Steel, In. 


Steel, In. 


0.01 


0.0005 


0.0006 


0.0007 


0.11 


0.0055 


0.0066 


0.0077 


.02 


.001 


.0012 


.0014 


.12 


.006 


.0072 


.0084 


.03 


.0015 


.0018 


.0021 


.13 


.0065 


.0078 


.0091 


.04 


.002 


.0024 


.0028 


.14 


.007 


.0084 


.0098 


.05 


.0025 


.003 


.0035 


.15 


.0075 


.009 


.0105 


.06 


.003 


.0036 


.0042 


.16 


.008 


.0096 


.0112 


.07 


.0035 


.0042 


.0049 


.17 


.0085 


.0102 


.0119 


.08 


.004 


,0048 


.0056 


.18 


.009 


.0108 


.0126 


.09 


.0045 


.0054 


.0063 


.19 


.0095 


.0114 


.0133 


.10 


.005 


.006 


.007 


.20 


.010 


.0120 


.0140 



Kennedy's Spiral Punch. (The Pratt & Whitney Co.) — B. Mar- 
tell, Chief Surveyor of Lloyd's Register, reported tests of Kennedy's 
spiral punches in winch a T/g-inch spiral punch penetrated a s/g-inch 
plate at a pressure of 22 to 25 tons, while a flat punch required 33 to 35 
tons. Steel boiler-plates punched with a flat punch gave an average 
tensile strength of 58,579 pounds per square inch, and an elongation in 
two inches across the hole of 5.2 per cent, while plates punched with a 
spiral punch gave 63,929 pounds, and 10.6 per cent elongation. 

The spiral shear form is not recommended for punches for use in metal 
of a thickness greater than the diameter of the punch. This form is of 
greatest benefit when the thickness of metal vrorked is less than two 
thirds the diameter of punch. 

Size of Blanks used in the Drawing-press. — Oberlin Smith 
(Jour. Frank. Inst., Nov. 1886) gives three methods of finding the 
size of blanks. The first is a tentative method, and consists simply in a 
series of experiments with various blanks, until the proper one is found. 
This is for use mainly in complicated cases, and when the cutting por- 
tions of the die and punch can be finally sized after the other work is 
done. The second method is by weighing the sample piece, and then, 
knowing the weight of the sheet metal per square mch, computing the 
diameter of a piece having the required area to equal the sample in 
w eight. Th e third method is by computation, and the formula is a: = 
V d2 + 4:dh for a sharp-cornered cup, where x = diameter of blank, 
d = diameter of cup, h = height of cup. For a round-cornered cup 
where the corner is sm all, say radi us of corner less than 1/4 height of cup, 
the formula is a; = (V((/2 4- 4 dli)— r, about; r being the radius of the 
corner. This is based upon the assumption that the thickness of the 
metal is not to be altered by the drawing operation. 

Pressure attainable by the Use of the Drop-press. (R. H. 
Thurston, Trans. A. S. M. E., v, 53.) — A set of copper cyhnders 
was prepared, of pure Lake Superior copper; they were subjected to the 
action of presses of different weights and of different heights of fall. 
Companion specimens of copper were compressed to exactly the same 
amount, and measures were obtained of the loads producing compression, 
and of the amount of work done in producing the compression by the 
drop. Comparing one with the other it was found that the work done 
witn the hammer was 90 per cent, of the work which should have been 



FLY-WHEELS FOR PUNCHES, PRESSES, ETC. 1323 

done with perfect efficiency. That is to say, the work done in the test- 
ing-machine was equal to 90 per cent of that due the weight of the drop 
falling the given distance. 

Formula: Mean pressurein pounds ^ Weight of drop X fall X efficiency . 

compression 
For pressures per square inch, divide by the mean area opposed to 
crusliing action during the operation. 

Similar experiments on Bessemer steel plugs by A. W. Moseley and 
J. L. Bacon (Trans. A. S. M. E.j xxvii, 605) indicated an efficiency for the 
drop hammer of about 70 per cent. 

An extensive series of experiments is reported in Am. Mach.. ATar. 
10, 1910. These were made by W. T. Sears, and consisted of the 
compression of lead plugs under a falling weight, ranging from 20 to 
200 lb., dropped from heights ranging up to 360 in. The tests showed 
that after a certain velocity of the falling weight had been attained, 
the speed had little effect on the compression of the plug. This speed 
was" fixed at 10 ft. per second, but its exact value is uncertain. 

Flow of 3Tetals. (David Townsend, Jour. Frank. Inst., March, 
1878.) — In punching holes 7/i6-inch diameter through iron blocks 13/4 
Inches thick, it was found that the core punched out was only 1 i/i6 
inches thick, and its volume was only about 32 per cent of the volume 
of the hole. Therefore, 68 per cent of the metal displaced by punching 
the hole flowed into the block itself, increasing its dimensions. 

Fly-wheels for Presses, Punches, Shears, etc. — The function of the 
fly-wheel on punching and other machinery in which action is inter- 
mittent is to store up energy during that portion of the stroke when 
no work is being done and to give it out during the period of actual 
working. The giving up of energy is accompanied by a reduction in 
the velocity of the fly-wheel. 
. Notation: 

E = total energy in the wheel at maximum velocity, ft. -lb. 

El = energy given out by the wheel during speed reduction, 

ft.-lb. 
VI = initial velocity of the center of gravity of fly-wheel rim, 

ft. per sec. 
V2 = velocity of center of gravity of fly-wheel rim at end of period 
in which energy is given out. 
H.P. = horse-power required. 

N = strokes of press or shear per min. 
T = time required per stroke, sees. 

t = time required for actual cutting of metal per stroke, sees. 
w = weight of fly-wheel rim, lb. 
d = diameter of rim at center of gravity. 
R = r.p.m. of fly-wheel at initial velocity. 
c and ci = constants. 

a = width of fly-wheel rim, in. 
b = depth of fly-wheel rim, in. 
y = ratio of depth to width of rim. 
g = acceleration due to gravity = 32.2 
Formulx: 

^ _ W V\^ _ WV\^ 
2g ~ 64.4 
(?;i2 - ^22) X W 



Ei=- 



64.4 
■El X 64.4 

Vi^ - V2- 

2tt RN 



"- 60 
A simplified method for calculating fly-wheels for punches and shears 
is given in Machinery's Handbook, p. 289. Using the notation as above, 
„^_ EN _ E . r = r (i --L\- 
^'^'~ 33,000 ~ r X 550 ' ' \ T I ' 






El ^ 1 1.22 W , 

c D^ R^' ^ \ 12 Dy 



1324 



THE MACHINE-SHOP. 



For cast-iron fly-wheels with maximum stresses of 1000 lb. per sq. in., 
W=ciEi; R= 1940-^£>. 







Values of c and ci. 






Per Cent 
Reduction. 


2 1/2 


5 


7 1/2 


10 


15 


20 


c 


0.00000213 


0.00000426 


0.00000617 
0.0432 


0.00000810 


0.00001180 


0.00001535 


Ci 


0.1250 


0.0625 


0.0328 


0.0225 


0.0173 



For belt-driven machines, the limiting low velocity V2 is the speed 
at which the belt will rmi off the pulley. Wilfred Lewis, Trans. A. S. 
M. E., vol. vii, shows that this takes place when the slip exceeds 20 
per cent of the belt speed. This gives a limiting condition for belt 

drives of punches and shears of W = 180 



(5) 



FORCING, SHRINKING AND RUNNING FITS. 

Forcing Fits of Pins and Axles by Hydraulic Pressure. — A 

4-inch axle is turned 0.015 inch diameter larger than the hole into which 
it is to be fitted. They are pressed on by a pressure of 30 to 35 tons. 
(Lecture by Coleman Sellers, 1872.) 

For forcing the crank-pin into a locomotive driving-wheel, when the 
pmhole is perfectly true and smooth, the pin should be pressed in with a 
pressure of 6 tons for every inch of diameter of the wheel fit. When the 
hole is not perfectly true, which may be the result of shrinking the tire on 
the wheel center after the hole for the crank-pin has been bored, or if the 
hole is not perfectly smooth, the pressure may have to be increased to 9 
tons for every inch of diameter of the wheel-fit. (Am. Machinist.) 

Pressure Table for Mounting Wheels and Crank Pins. 

(Santa Fe R.R. System, 1915.) 



Driving Axles. 


Eng. Truck Axles. 


Crank Pins. 


Car Truck Axles. 




Pressure, Tons. 

Wheel 

Centers. 


1 

3 


Pressure, Tons. 

Wheel 

Centers. 


1 

t 

s 


Pressure, Tons. 

Wheel 

Centers. 


1 

5 


Pressure, 
Tons. 
Wheels. 




Cast 
Iron. 


Steel 


Cast 
Iron. 


Steel 


Cast 
Iron. 


Steel 


Cast 
Iron. 


Steel 

or 

Steel 

Tired* 


41/2 

6 
7 
8 
9 


45- 50 
50- 55 
60- 65 
70- 75 
80- 85 
90- 95 


72- 80 
80- 88 
96-104 
112-120 
128-136 
144-152 


41/2 
51/2 

6 

6V2 


20-25 
25-30 
30-35 
35-40 
40-45 
45-50 
50-55 
55-60 
60-65 
65-70 


35- 42 
42- 50 
50- 57 
57- 65 
65- 72 
72- 80 
80- 87 
87- 95 
95-102 
102-110 


3 

4 

5 
6 
7 

71/2 
8 

8 1/2 
9 

91/2 


30 
40 
50 
60 
70 
75 
80 
85 
90 
95 


36- 45 
53- 60 
68- 75 
83- 90 
98-105 
105-113 
113-120 
120-128 
128-135 
135-143 


4 
5 

51/2 

6 

6 1/2 
7 


25-35 
35-45 
40-50 
45-55 
50-60 
55-65 


30-40 
45-55 
50-60 
50-65 
55-70 
60-75 


10 
11 
12 


100-105160-168 
110-115176-184 
120-125192-200 


Crank Axles. 

All crank discs, 
110-150 tons. 


* Tires on. 


Allc 

150 


enter v 
-200 tor 


;ebs 1 
1 



Note. — In mounting wheels and crank pins, care should be taken to 
see that for at least two-thirds of the wheel fit the pressure required 
shall be between the maximum and minimum limits given in the table, 
or if only one pressure is shown in the table, the actual pressure re- 
quired should be as near as possible to that pressure. 

In mounting driving wheels with tires on, the maximum pressures 
given in the tables or even 10 per cent higher pressure than the maxi- 
mum pressure may be used. 

Shrinkage of Tires. — Allow 1/54 inch for each 12 in. in diameter. 



FORCE AND SHRINK FITS. 



1325 



Ground Fits for Machine Parts. — The practice of the Brown & 
Sharpe Mfg. Co. in tolerances and allowances for ground fits is gi\ en in 
a paper by W. A. Viall (Trans. A. S. M. E., xxxii) from which the 
table below has been prepared. The liinits given can he recommended 
for satisfactory commercial work in the production of machine parts 
and may be followed under ordinary conditions. In soecial cases it 
may be necessary to vary slightly from the tallies. 

Allowances and Tolerances for Fits— Practice of the Brown & 
Sharpe Mfg. Co. 





Diameter, Up to and Including 


TCind of Fif 






1/2 In. 


I In. 2 In. 


RuNNiNG Fits 








Ordinary speed 


-.00025 to -.00075 


-.00075 to -.0015 


-.0015 to -.0025 


High speed, heavy 








pressure, rocker 








shafts 


-.0005 to -.001 
-.00025 to -.0005 
Oto -.00025 


-.001 to -.002 
-.0005 to -.001 
Oto -.0005 


-.002 to -.003 


Sliding Fits 


— .001 to — 002 


Standard Fits 


Oto -.001 


Driving Fits 








For pieces to be 








taken apart 


to +.00025 


+.00025 to .0005 


+ 0005 to +.00075 


Ordinary . ... 


+.0005 to +.001 


+.001 to +.002 


+.002 to + 003 


Forcing Fits 


+.00075 to +.0015 


+.0015 to +.0025 


+.0025 to +.0C4 


Shrinking Fits 








For pieces to take ' 






hardened shells S/g 








in. thick or less. . . . 


+.00025 to +.0005 


+.0005 to +.001 


+.001 to +.0015 


For pieces to take 








shells more than 








3/8 in. thick 


+.0005 to +.001 


+.001 to +.0025 


+.0025 to +.0035 


Grinding Limits for 








Holes 


Oto +.0005 


to +.00075 


to +.001 



Kind of Fit. 


Diameter Up to and Including 


3 1/2 In. 


6 In. 


12 In. 


Running Fits 
Ordinary speed 


- .0025 to - .0035 

- .003 to - .0045 

- .002 to - .0035 

Oto -.0015 

+.00075 to +.001 
+.003 to +.004 
+.004 to +.006 

+.0015 to +.002 

+.0035 to +.005 
Oto +.0015 


- .0035 to - .005 

- .0045 to - .0065 

- .003 to - .005 

to - .002 

+.001 to +.0015 
+.004 to +.005 
+.006 to +.009 

+.002 to +.003 

+.005 to +.007 
to +.002 




High speed, heavy 
pressure, rocker 
shafts 




Sliding Fits 




Standard Fits 




Driving Fits 
For pieces to be 

taken apart 

Ordinary 






Forcing Fits 




Shrinking Fits 
For pieces to take 
hardened shells S/g 
in thick or less. 




For pieces to take 
shells more than 

% in. thick 

Grinding Limits for 
Holes 




to +.0025 



Running Fits. — Wm. Sangster (Am. Mach., July 8, 1909) gives the 
practice of different manufacturers as follows: 

An electric manufacturing Co. allows a clearance of 0.003 to 0.004 in. for 
shafts 1 1/2 to 2 1/4 in. diam. ; 0.003 to 0.006 for 2 1/2 in. ; 0.004 to 0.006 for 



1326 



THE MACHINE-SHOP. 



23/4 to 31/2 ins.; 0.005 to 0.007 in. for 4 and 41/2 ins.: 0.006 to 008 in 
for 5 ins.; 0.009 to 0.011 in. for 6 ins. Dodge Mfg. Co. allows from i/rI 
for 1-in. ordinary bearings to a little over 1/32 in. for 6-in. Clutch sleeves 
0.008 to 0.015 in.; loose pulleys as close as 0.003 in. in the smaller sizes! 
and about 1/64 in. on a 2V2-in. hole. 

Watt Mining Car Wheel Co. allows i/ie in. for all sizes of wheels, and 
1/16 in. end play. A large fan-blower concern allows 0.005 to 0.01 in 
on fan journals from Q/ig to 2 7/i6 ins. 

Limits of Diameters for Fits. C. W. Hunt Co. (Am. Mach., July 16, 
1903.) — For parallel shafts and bushings (shafts changing): d = diam. 
in ins. 

Shafts: Press fit, + 0.001 d + (0 to 0.001 in.). Drive fit. + 0.0005 d + 

(0. to 0.001 in.). 
Shafts: Hand fit, + 0.001 to 0.002 in. for shafts 1 to 3 in.; 0.002 to 0.003 

in. for 4 to 6 in.; 0.003 to 0.004 in. for 7 to 10 in. 
Holes: all fits to - 0.002 in. for 1 to 3 in.; to - 0.003 in. for 4 to 6 in • 
to - 0.004 in. for 7 to 10 in. 

Parallel journals and bearings (journals changing): 

Close fit - 0.001 d + (0.002 to 0.004 in.); Free fit - 0.001 d +(0 007 
to 0.01 in.); Loose fit, - 0.003 d+ (0.02 to 0.025). Limits of diameters 
for taper shaft and bushings (holes changing). Shaft turned to standard 
taper 3/ig in. per ft., large end to nominal size ± 0.001 in. Holes are 
reamed until the large end is small by from 0.001 d + 0.004 to 0.005 in. 
for press fit, from 0.0005 d + 0.001 in. for drive fit, and from to 0.001 in. 
for hand fit. In press fits the shaft is pressed into the hole until the 
true sizes match, or V16 in. for each Viooo in. that the hole is small. 
The above formulae apply to steel shafts and cast-iron wheels or other 
members. 

Shaft Allowances for Electrical Machinery. — The General Electric 
Co. (1915) gives the following table of allowances for sliding and press 
fits. 









Press Fit 


Press Fit 






Nominal 

Diam., 

In. 


Sliding 
Fit. 


Com- 
mutator 
and Split 

Hub. 


for 

Armature 

Spider 

' Solid 

Steel. 


for 
Armature 

Spider 

Solid 
Cast Iron. 


Press 

Fit for 

Coupling. 


Shrink 
Fit. 


2 


-0.0015 


+0.0005 


+0.00075 


+0.0015 


+0.00175 


+0.0025 


4 


- .002 


+ .0005 


+ .0015 


+ .0025 


+ .003 


+ .004 


8 


- .004 


+ .001 


+ .002 


+ .0035 


+ .0045 


+ .006 


12 


- .005 


+ .001 


+ .0025 


+ .0045 


+ .0055 


+ .0075 


16 


- .0055 


+ .001 


+ .003 


+ .005 


+ .006 


+ .009 


20 


- .006 


+ .0015 


+ .0035 


+ .0055 


+ .007 


+ .010 


24 


- .007 


+ .0015 


+ .0035 


+ .006 


+ .0075 


+ .011 


28 


- .0075 


+ .0015 


+ .004 


+ .0065 


+ .0085 


+ .012 


32 


- .008 


+ .0015 


+ .0045 


+ .007 


+ .009 


+ .0125 


36 


- .0085 


+ .002 


+ .0045 


+ .0075 


+ .0095 


+ .0135 


40 


- .009 


+ .002 


+ .005 


+ .008 


+ .010 


+ .014 


44 


- .0095 


+ .002 


+ .005 


+ .0085 


+ .0105 


+ .0145 


48 


- .010 


+ .002 


+ .0055 


+ .009 


+ .011 


+ .015 



Pressure Required for Press Fits. {Am. Mach., March 7, 1907.) — 
The following approximate formulae give the pressures required for press 
fits of cranks and crank-pins, as used by an engine-building firm. P= total 
pressure on ram, tons; Z) = diameter inches. 

Crank fits up to D =10. P = 9.9 D - 14. 

Crank fits D = 12 to 24. P -= 5 D -{- 40. 

Straight crank-pins. P = 13 Z). 

Taper crank-pins. P = 14 Z> — 7. 

The allowance for cranks and straight pins is 0.0025 inch per inch or 
diameter Taper cranks, taper V16 inch per inch, are fitted on the 
lathe to within i/s inch of shoulder and then forced home. 

Stresses due to Force and vShrink Fits. — S. H. Moore, Trans. 
A, S, M, E., vol. xxiv, gives the following allowances for different fits: 



FOBCE AND SHRINK FITS. 



1327 



For shrinkage fits, d =(i7/i6 D+ 0.5) -^ 1000. For forced fits d = 
(2D + 0.5) -^ 1000. For driven fits, d = (I/2 D + 0.5) -v- 1000 ' d = 
allowance or the amount the diameter of the shaft exceeds the diameter 
of the hole in the ring and D = nominal diameter of the shaft A L 
Jenkins, Eng. News, Mar. 17, 1910, says the values obtained from 'the 
formula for forced fits are about twice as large as those frequently used 
in practice, and in many cases they lead to excessive stresses in the ring. 
He calculates from Lame's formula for hoop stress in a ring subjected tc 
internal pressure the relation between the stress and the allowance foi 
fit, and deduces the following formulae. 



15,000,000 d -^ 
= 30,000,000 d 



(1+ 0.6//:); for a 
- (1+ 1/K); for a 



.S^j = 15,000,000 d -i- (k+ 0.6); 5/^2 ., 

cast-iron ring on a steel shaft. 
Sh^ = 30,000,000 d -^ a -hk); Sh^ 

steel ring on a steel shaft. 
8^^= radial unit pressure between the surfaces; 8}^^= unit tensile 01 

hoop stress in the ring; 
d = allowance per inch of diameter, K a constant whose value depends 
on t, the thickness, and r, the radius of the ring, as follows. 
Values of i -T- r, 

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.25 1.5 1.75 2.0 3.0 
Values of K, 
3.083 2.600 2.282 2.058 1.892 1.766 1.666 1.492 1.380 1.300 1.250 1.133. 

The allowances for forced and shrinkage fits should be based on the 
stresses they produce, as determined by the above formula, and not on 
the diameter of the shaft. 

Force Required to Start Force and Shrink Fits. (Am. Mack., 
Mar. 7, 1907.) — A series of experiments was made at the Alabama Poly- 
technic Institute on spindles 1 in. diam, pressed or shrunk into cast-iron 
disks 6 in. diam., IV4 in. thick. The disks were bored and finished with 
a reamer to 1 in. diam. with an error beheved not to exceed 0.00025 in. 
The shafts were ground to sizes 0.001 to 0.003 in. over 1 in. Some of the 
spindles were forced into the disks by a testing machine, the others had 
the disks shrunk on. Some of each sort were tested by pulling the 
spindle from the disk in the testing machine, others by twisting the disk 
on the spindle,. The force required to start the spindle in the twisting 
tests was reduced to equivalent force at the circumference of the spindle, 
for comparison with the tension tests. The results were as follows: 
D = diam. of spindle; F = force in lbs.: 



Force Fits, 
Tension. 


Force Fits, 
Torsion. 


Shrink Fits, 
Tension. 


Shrink Fits, 
Torsion. 


D 


F,lbs. 


Per 

sq.in. 


D 


F,lbs. 


Per 

sq.in. 


D 


F,lbs. 


Per 

sq.in. 


D 


F,lbs. 


Per 
sq.in. 


1.001 
1.0015 
1.002 
1.0025 


1000 
2150 
2570 
4000 


318 
685 
818 
1272 


1.0015 
1.0015 
1.002 
1.0025 


2200 
2800 
4200 
4600 


700 
892 
1335 
1465 


1.001 

1.001 

1.002 

1.002 

1.0025 

1.0025 


5320 
5820 
7500 
8100 
9340 
9710 


1695 
1853 
2385 
2580 
2974 
3090 


1.001 

1.0015 

1.0015 

1.0025 

1.003 


2200 
7200 
9800 
13800 
17000 


700 
2290 
3118 
4395 
5410 


















1 








' 



1328 THE MACHINE-SHOP. 

KEYS. 

Formulae for Flat and Square Keys. — Great divergence exists in 
the dimensions of square and flat keys as given by various authorities. 
The following are the formulae in common use: 

Notation. — D = diameter of shaft; w = width of key; t = thickness 
of key ; I = length of key, all dimensions being in inches. 
E. G. Parkhui-st's rule: z^ = i/s -D; ^ = i/9-D; taper i /sin. per ft. 

ISIichigan saw-mill practice: w = i/i D; t = w. 
J. T. Hawkins's rule: w = i/z D\ t = '^/i D. 

Machinery's Handbook, rule 1: w = l/iD; t = ^/q D\ I = 1.5 D. 
Machinery's Handbook, rule 2: w = ^/iq D + i/ie; t = i/s £> + Vs; 

I = 0.3 D2 -^ t. 

For sphnes or feather keys interchange w and t. 

F. W. Halsey ("Handbook for Machine Designers and Draftsmen") 
says: The common driven key for securing a crank or gear to a shaft 
is commonly made with a width of 1/4 -D up to about a, 4-in. shaft, 
about 13/8 in. for a 6-in., 1 3/4 in. for an 8-in., and 21/4 in. for a 10-in. 
shaft. The depth should be from s/g w to 3/4 w. If the work is at 
all severe the length should be at least 1.5 D. The taper is commonly 
1/8 in. per ft. 

Unwin ("Elements of Machine Design ") gives: Width = 1/4 D-\- i/g in. 
Thickness = i/s D + 1/8 in. When wheels or pulleys transmitting only 
a small amount of power are keyed on large shafts, he says, these 
dimensions are excessive. In that case, if H.P. = horse-power trans- 
mitted by the wheel or pulley, N = r.p.m., P = force acting at the cir- 
cumference, in pounds, and B = radius of pulley in inches, take 



■=^' 



„ 100 H.P. PR , 



John Richards, in an article in Gassier' s Magazine, writes as follows: 
There are two kinds or systems of keys, both proper and necessary, but 
widely different in nature. 1. The common fastening key, usually made 
in width one fourth of the shaft's diameter, and the depth five eighths 
to one- third the width. These keys are tapered and fit on all sides, or, 
as it is commonly described, "bear all over." They perform the double 
function in most cases of driving or transmitting and fastening the 
keyed-on member against movement endwise on the shaft. Such keys, 
when properly made, drive as a strut, diagonally from corner to corner. 

2. The other kind or class of keys are not tapered and fit on their 
sides only, a slight clearance being left on the back to insure against 
wedge action or radial strain. These keys drive by shearing strain. 

For fixed work where there is no sliding movement such keys are com- 
monly made of square section, the sides only being planed, so the depth 
Is more than the width by so much as is cut away in finishing or fitting. 

For sliding bearings, as in the case of drilling-machine spindles, the 
depth should be increased, and in cases where there is heavy strain 
there should be two keys or feathers instead of one. 

The following tables are from proportions adopted in practical use. 

Flat keys, as in the first table, are employed for fixed work when the 
parts are to be held not only against torsional strain, but also against 
movement endwise ; and in case of heavy strain the strut principle being 
the strongest and most secure against movement when tliere is strain 
each way, as in the case of engine cranks and first movers generally. 
The objections to the system for general use are, straining the work out 
of truth, the care and expe^nse required in fitting, and destroying the 
evidence of good or bad fitting of the keyed joint. When a wheel or 
other part is fastened with a tapering key of this kind there is no means 
of knowing whether the work is well fitted or not. For this reason such 
keys are not employed by machine-tool-makers, and in the case of 
accurate work of any kind, indeed, cannot be, because of the wedging 
strain, and also the difficulty of inspecting completed work. 

I. Dimensions of Flat Keys, in Inches. 

Diam. of shaft.... 1 1 I/4 1 1/2 1 3/4 2 2 1/2 3 3 1/2 4 5 6 7 8 
Breadth of keys... I/4 5/i6 3/8 Vu ^2 % ^k Vs 1 1 Vs i 3/8 1 I/2 1 3/4 
Depth of keys.... 5/32 3/l6 I/4 Q/32 5/i6 3/8 VlQ I/2 5/8 H/lG 13/l6 7/8 1 



KEYS. 



1329 



II. Dimensions of Square Keys, in Inches. 



Diameter of shaft . 
Breadth of keys . . 
Depth of keys .... 



1 

5/32 
3/16 


1 1/4 
7/32 
1/4 


I 1/2 
9/32 
5/16 


1 3/4 

11/32 
3/8 


13/32 
7/16 


2 1/2 
15/32 

1/2 


3 

17/32 
9/16 


3 1/2 
9/32 
5/8 



11/16 

3/4 



III. Dimensions of Sliding Feather Keys, in Inches. 



Diameter of shaft . . 
Breadth of keys . . . 
Depth of keys 



1 1/4 


1 1/2 


13/4 


2 


2 1/4 


2 1/2 


3 


3 1/2 


4 


1/4 


1/4 


5/16 


5/16 


3/8 


3/8 


V?, 


9/16 


9/16 


3/8 


3/8 


7/l6 


7/16 


1/2 


1/2 


5/8 


•3/4 


3/4 



4 1/2 

5/8 
7/8 



Depth of Key Seats. — The depth of a fiat or square key is equaUy 
divided between the shaft and the hub. The depth to which a milling 
cutter is sunk into the shaft in milling a keyway is equal to one-half 
the depth of the key plus the height of the arc projecting above the 
intersection of the side of the keyway with the circumference of the 
shaft. This height can be calculated from the formula 



h = r- \/r2 - (1/2 w)2 
in which r is the radius of the shaft, h the height of the arc, and w the 
width of the key. 

The Lewis Key. — The disadvantage of the ordinary flat key is that 
it must be carefully fitted. A key fitting tight on top and bottom of 
the keyway drives partly by friction. If fitted only on the sides of 
the keyway it exerts a prying action on the hub and shaft, and is sub- 
jected to severe bending and shearing stresses. Square or flat keys 
should fit tight on all four sides, but in practice this is prohibitive on 
account of the expense. To avoid the difficulty inherent in ordinary 
flat keys, the Lewis key shown in Fig. 217 was devised by Wilfred 
Lewis. It is subject to compression only, but is expensive to fit. 





Fig. 217. 



Fig. 218. 



The Barth Key. ( Fred. Oyen, Am. Mach., Nov. 14, 1907, and Feb. 
20, 1908.) — The key shown in Fig. 218 was devised by Carl G. Barth 
to combine the advantages of the Lewis key with thos(^ of the ordinary 
rectangular key. The Barth key is rt^ctangular with onc-lialf of both 
sides bevelled at 45°. The key does not need to fit tightly . as pressure 
tends to drive it into its seat. There is no tendency to turn it, and 
the only stress to which it is subject is compression. This key has 
been used in many cases as a feather to replace rectangular feather 
keys which have given trouble. It has found wide application as a 
feather key in drill sockets and drill shanks, reamers, etc., which are 
commonly driven with a tang. 

Reducing sockets for drill presses are fitted with a Barth key dove- 
tailed inside and a similar keyway on the outside. No. 1 Morse taper 
shank has a keyway for No. 1 Barth key and fits into a No. 1 reducing 
socket. No. 2 shank has No. 2 Morse taper and a keyway for No. 2 
Barth key, etc. Dimensions of the various sizes of the Barth key are 
shown in the following table: 



1330 



THE MACHINE-SHOP. 



Dimensions of Dovetailed Bartli Keys. 




No. of 
Barth Key. 


No. of Morse 

Taper in 
Which Used. 


In. 


In. 


In. 


1 

2 
3 
4 
5 


1 

2 
3 

4 

5 


1/8 
5/32 
3/16 
1/4 
5/16 


0.132 
0.165 
0.199 
0.264 
0.329 


5/128 
3/64 
1/16 
5/64 
3/23 



The Barth key has been adapted to a complete line of standard taper 
sockets, shanks, driving keys, holdback 
keys, drifts, adapters, and reducers at the 
Watertown Arsenal. The standards, which 
cover both Brown & Sharpe and Morse 
tapers are given in Am. Mach., Dec. 24, 
1914. 

Detrick & Harvey Keys. (Am. Mach., 
"Feb. 11, 1915.) — The Detrick & Harvey 
Machine Co., Baltimore, uses square keys 
of dimensions shown in Fig. 219 and the 
following table. Although these are smaller 
than the square key generally used, there 
is no case known in which one of them has 
sheared off. The dimension C is for setting 
the key, and the dimension D gives the 
diameter across the corners of the key. AU 
dimensions are In inches. 




Fig. 219. 







Dimensions of Detrick & Harvey Keys. 






D 


A 


B 


C 


D 


A 


B 


C 


D 


A 


B 


C 


V?. 


1/8 


0.623 


0.555 


13/8 


9/32 


1.652 


1.501 


31/2 


11/16 


4.177 


3.808 


9/16 


1/8 


.685 


.618 


1 1/2 


5/16 


1.806 


1.640 


3 3/4 


3/4 


4.487 


4.087 


.5/8 


5/32 


.778 


.693 


1 5/8 


5/16 


1.931 


1.766 


4 


13/16 


4.797 


4.364 


11/16 


5/32 


.841 


.756 


13/4 


7/16 


2.176 


1.941 


4 1/4 


13/16 


5.049 


4.616 


3/4 


3/16 


.933 


.832 


1 7/8 


7/16 


2.302 


2.067 


4 1/2 


13/16 


5.303 


4.868 


13/16 


3/16 


.996 


.895 


2 


7/16 


2.428 


2.194 


4 3/4 


7/8 


5.619 


5.147 


7/8 


3/16 


1.058 


.958 


2 1/4 


9/16 


2.796 


2.496 


5 


7/8 


5.864 


5.399 


15/16 


3/16 


1.122 


1.022 


2 1/2 


9/16 


3.050 


2.749 


5 1/4 


7/8 


6.115 


5.650 


1 


1/4 


1.242 


1.109 


2 3/4 


5/8 


3.361 


3.027 


5 1/2 


15/16 


6.422 


5.928 


1 1/8 


1/4 


1.368 


1.236 


3 


5/8 


3.616 


3.280 


5 3/4 


15/16 


6.676 


6.180 


11/4 


9/32 


1.524 


1.375 


3 1/4 


11/16 


3.925 


3.556 


6 


15/16 


6.927 


6.432 




Fig. 220. 



Tlie Kennedy Key. — The Kennedy 
key, largely used in rolling mill work, is 
shown in Fig. 220. In these keys w = 
t = i/i D. They are tapered 1/8 in. per 
ft. on top, while the sides are a neat fit. 
The keys are so set in the shaft that 
diagonals through them intersect at the 
axis of the shaft. The hub is bored for 
a press fit and then is rebored eccen- 
trically about 1/64 D off center. The 
keyways are cut in the eccentric side. 
General practice is to use single keys 
for diameters up to and including 6 in. 
where the torque is constant and the 
power transmitted always in one direc- 
tion. For shafts above 6 in. diameter 
double keys should be used, and if the 
torque is intermittent and in alternate 
directions, double keys should be used 
down to shaft diameters of 4 in. 



KEYS. 



1331 



The Nopdberg Key. — The Nordberg 
Mfg. Co. has adopted for the ends of 
shafts round keys shown in Fig. 221. 
The advantages of this key are: No 
tendency toward deformation ; they are 
a driven fit in the direction of the 
shear; they are always in true shear and 
are cheaper than the square key. In 
manufacturing a hole A is drilled in the 
joint and next a hole B as large as the 
size of the keyway will admit is drilled 
in the shaft in order to avoid the ten- 
dency of the drill used for driUing the 
keyway to size to crowd into the soft 
cast iron. In the table the reamer 
diameters given are of the small end. 
The taper is i/ie in. per ft., measured 
on the diameter. 




Fig. 221. 



Dimensions of Nordberg Standard R ound Keys. 



Diam. 

of 
Shaft, 

In. 


Diam. 

of 
Reamer 

In. 


Cutting 
Length 

of 
Reamer 

In. 


Diam. 

of 

Shaft, 

In. 


Diam. 

of 

Reamer 

In. 


Cutting 
Length 

of 

Reamer 

In. 


Diam. 

of 

Shaft, 

In. 


of Length 

^7"^^^ Reader 
^^- , In. 


2 15/16-3 

3 7/16-3 1/2 

3 7/8 -4 

4 3/8 -4 1/2 

5 

5 1/2 

6 


3/4 
7/8 
1 

1 1/8 
11/4 
1 3/8 
11/2 


4 1/4 
4 1/2 

4 7/8 

4 5/8 
4 7/8 
61/8 


12i 

14V 
15 ( 


15/8 

2 

2 9/16 


6 7/8 & 8 
10 1/4 

12 


I6i 
17V 

18) 
19) 

20 t 

21 i 
22) 

23 I 

24 i 


31/8 12 
311/16 13 
4 1/4 14 1/4 











The Woodruff Key. — The Woodruff key shown in Fig. 222 is exten- 
sively used in machine construction. Dimensions are given in the 
following table. The key should project above the shaft a distance 
equal to one-half the thickness. For ordinary practice mediiun-sized 
keys should be used: 

_^5j^ *k a- 

I ,--- --. I , . ;i' >i ,. 




xy 









Standard. 


Fig. 


222. 




Special. 








Dimensions of Woodruff Standard Keys— Inclies. 










D, 










o 










a 
o 


No. 


out 

1/9 


Si 

l/l6 


1/3? 


lis 


No. 


0\4 






Uw o 


No. 






Q. >> 




1 


3/64 


12 


7/8 


7/3? 


7/64 


1/16 


20 


1 1/4 


7/32 


7/64 


5/64 


2 


1/9 


3/39 


3/64 


3/64 


A 


7/8 


1/4 


1/8 


1/16 


21 


1 1/4 


1/4 


1/8 


5/64 


3 


1/9 


1/8 


l/lfi 


3/64 


13 




3/16 


3/3? 


l/lfi 


D 


1 1/4 


5/16 


5/32 


5/64 


4 


5/8 


3/s? 


3/R4 


1/16 


14 




7/3? 


7/64 


1/16 


E 


1 1/4 


3/8 


3/16 


5/64 


5 


5/8 


1/8 


1/16 


1/16 


15 




1/4 


1/8 


l/lfi 


22 


13/8 


1/4 


1/8 


3/32 


6 


5/8 


5/S9 


5/64 


1/16 


B 




5/16 


5/3? 


l/lfi 


23 


1 3/8 


5/16 


5/32 


3/32 


7 


3/4 


1/8 


1/16 


1/16 


16 


1 1/8 


3/16' 3/32 


5/64 


F 


13/8 


3/8 


3/16 


3/32 


8 


3/4 


5ho 


5/64 


1/16 


17 


1 1/8 


7/3? 


7/64 


5/64 


24 


1 1/2 


1/4 


1/8 


V/64 


9 


3/4 


3/16 


3/3? 


1/16 


18 


1 1/8 


1/4 


1/8 


5/64 


25 


1 1/2 


5/16 


5/32 


V/64 


10 


7/8 


5/8? 


5/64 


1/16 


C 


I 1/8 


5/16 


5/32 


5/64 


G 


1 1/2 


3/8 


3/16 


vy64 


11 


7/8 


3/16 


3/32 


1/16 


19 


I 1/4 


3/161 3/32 


5/64 





.... 







1332 



THE MACHINE-SHOP. 





Dimensions of Woodruff Special Keys- 


-Inches. 




No. 


26 


27 


28 


29 


30 


31 


32 


33 


34 


Dimension 




















a 


21/8 


2 1/8 


2 1/8 


2 1/8 


31/2 


3 1/2 


31/2 


31/2 


31/2 


b 


3/16 


1/4 


5/18 


3/8 


3/8 


7/16 


1/2 


9/16 


5/8 


c 


3/32 


1/8 


5/32 


3/16 


3/16 


7/32 


1/4 


9/32 


5/16 


d 


17/32 


17/32 


17/32 


17/32 


13/16 


13/16 


13/16 


13/16 


13/16 


e 


3/32 


3/32 


3/32 


3/32 


3/16 


3/16 


3/16 


3/16 


3/16 





Woodruff Keys Suitable for Different Shaft Diameters. 




Sbaft 
Diam. 


Key 

Nos. 


Shaft 
Diam. 


Key 
Nos. 


Shaft 
Diam. 


Key 

Nos. 


Shaft 
Diam. 


Key 

Nos. 


5/16-3/8 
7/16-1/2 
9/16-5/8 
11/16-3/4 


1 

2.4 

3.5 

3.5.7 


13/16 

7/8-15/16 

1 

1 1/16-1 1/8 


6,8 
6,8, 10 
9. 11, 13 
9.11.13.16 


1 3/16 
1 1/4-1 5/16 
1 3/8-1 7/16 
1 1/2-1 5/8 


11. 13, 16 
12.14.17.20 

14. 17.20 
15.18.21.24 


1 11/16-1 3/4 

1 13/16-2 

2 1/16-2 1/2 


18.21.24 

23.25 

25 



B- 






Gib Keys. — '' Machinery's Handbook " gives the following formulae' for 
dimensions of gib keys. (See Fig. 223). All dimensions are in inches. 

D = diameter of shaft ; w = width 
of key; T = thickness of key, large 
end; S = safe shearing strength of 
material in key; G = length of gib; 

h = projection of gib above top oi* k.W-^ ^ ^Length- 
key. 

w = i/i D up to 6 in. ; over 6 in. 
w = 0.211 D. 

r = 1/6 D up to 6 in. ; over 6 in. T = i/s D. Minimum value 3/i6 in. 

G = w. 

Length = length of hub + 1/2 in. Taper i/s in. per ft. 

Safe twisting moment per in. of length of key = 1/2 D X TT X 5. 

Keyways for Milling Cutters. — For keyways for milling cutters 
see p. 1277. 



Fig. 223. 



HOLDING-POWER OF KEYS AND SET-SCREWS. 

Tests of tlie Holding-power of Set-screws in Pulleys. (G. Lanza, 
Trans. A. S. M. E., x, 230.) — These tests were made by using a puUey 
fastened to the shaft by two set-screws with the shaft keyed to the 
holders; then the load required at the rim of the pulley to cause it to 
slip was determined, and this being multiplied by the number 6.037 
(obtained by adding to the radius of the pulley one-half the diameter 
of the wire rope, and dividing the sum by twice the radius of the shaft, 
since there were two set-screws in action at a time) gives the holding- 
power of the set-screws. The set-screws used were of wrought iron, 
5/8 of an inch in diameter, and ten threads to the inch; the shaft used 
was of steel and rather hard, the set-scrcAvs making but little impression 
upon it. They were set up with a force of 75 pounds at the end of a 
ten-inch monkey-wrench. The set-screws used were of four kinds, 
marked respectively A, B, C, and D. The results were as follows; 

A, ends perfectly fiat, 9/i6-in. diam. 1412 to 2294 lbs.; average 2064. 

B, radius of rounded ends about 1/2-in. 2747 to 3079 lbs.; average 2912. 

C, radius of rounded ends about 1/4-in. 1902 to 3079 lbs.; average 2573. 

D, ends cup-shaped and case-hardened 1962 to 2958 lbs.; average 2470. 

Remarks. — A. The set-screws were not entirely normal to the shaft; 
hence they bore less in the earlier trials, before they had become flattened 
by wear. 

B. The ends of these set-screws, after the first two trials, were found 
to be flattened, the flattened area having a diameter of about 1/4 inch. 



DYNAMOMETERS. 1333 

r. The ends were found, after the first two trials, to be flattened, as 
InB. 

D. The first test held well because the edpres were sharp, then the 
holding-power fell off till they had become flattened in a manner similar 
to B, when the holding-power increased again. 

Tests of the Holding-power of Keys. (Lanza.) — The load was 

applied as in the tests of set-screws, the shaft being firmly keyed to the 
holders. The load required at the rim of the pulley to shear the kevs 
was determined, and this, multipUed by a suitable constant, determined 
in a similar way to that used in the case of set-screws, gives us the shear- 
ing strength per square inch of the keys. 

The keys tested were of eight kinds, denoted, respectively, by the 
letters A, B, C, D, E, F, G and H, and the results were as follows: A, B, D, 
and F, each 4 tests; E, 3 tests; C, G, and H, each 2 tests. 

A, Norway iron, 2" X V/ X 15/32", 40,184 to 47,760 lbs.; average, 42,726 

B, refined iron, 2" X V^' X 15/32", 36,482 to 39,254 lbs. ; average, 38,059 

C, tool steel, 1'' X V/ X 15/32'', 91,344 & 100,056 lbs. ; 

D, mach'y steel, 2" X V/ X 15/32" 64,630 to 70,186 lbs. ; average, 66,875 

E, Norway iron, 1 1/3" X S/g" X 7/i6'' 36,850 to 37,222 lbs. ; average, 37,036 

F, cast-iron, 2'' X 1/4'' X 15/32'', 30,278 to 36,944 lbs.; average, 33,034 

G, cast-iron, 1 1/3" X W X Vie", 37,222 & 38,700. 
H, cast-iron, \" X V2" X 7/i6", 29,814 & 38,978. 

The first dimension is the length, the second the width and the third 
the height. 

In A ana B some crushing took place before shearing. In E, the 
keys, being only 7/i6 inch deep, tipped slightly in the key-way. In H, in 
the first test, there was a defect in the key-way of the pulley. 

DYNAMOMETERS. 

Dynamometers are instruments used for measuring power. They are 
of several classes, as: 1. Traction dynamometers, used for determining 
the power required to pull a car or other vehicle, or a plow or harrow. 
2. Brake or absorption dynamometers, in which the power of a rotating 
shaft or wheel is absorbed or converted into heat by the friction of a 
brake; and 3. Transmission dj^namometers, in which the power in a 
rotating shaft is measured during its transmission through a belt or other 
connection to another shaft, without being absorbed. 

Traction Dynamometers generally contain two principal parts: (1) A 
spring or series of springs, through which the pull is exerted, the exten- 
sion of the spring measuring the 
amount of the pulling force; and 
(2) a paper-covered drum, rota- 
ted either at a uniform speed by 
clockwork, or at a speed propor- 
tional to the speed of the trac- 
tion, through gearing, on which 
the extension of the spring is reg- 
istered by a pencil. From the 
average height of the diagram 
drawn by the pencil above the 
Fig 224 zero-line the average pulling 

force in pounds is obtained, and 
this multiplied by the distance traversed, in feet, gives the work done, in 
foot-pounds. The product divided by the time in minutes and by 33,000 
gives the horse-power. 

The Prony brake is the typical form of absorption dynamometer. 
(See Fig. 224, from Flather on Dynamometers.) 

Primarily this consists of a lever connected to a revolving shaft or pul- 
ley in such a manner that the friction induced between the surfaces in 
contact will tend to rotate the arm in the direction in which the shaft 
revolves. This rotation is counterbalanced by weights P, hung in the 
scale-pan at the end of the lever. In order to measure the power for a 
given niunber of revolutions of pulley, we add weights to the scale-pan 




"- L * * — 




1334 DYNAMOMETERS. 

and screw up on bolts b,b, until the friction induced balances the weights 
and the lever is maintained in its horizontal position while the revolu- 
tions of the shaft per minute remain constant. 

For small powers the beam is generally omitted — the friction being 
measured by weighting a band or strap thrown over the pulley. Ropes 
or cords are often used for the same purpose. 

Instead of hanging weights in a scale-pan, as in Fig. 224, the friction 
may be weighed on a platform-scale; in tliis case, the direction of rotation 
being the same, the lever-arm will be on the opposite side of the shaft. 

In a modification of this brake, the brake-wheel is keyed to the shaft, 
and its rim is provided with inner flanges which form an annular trough 
for the retention of water to keep the pulley from heating. A small 
stream of water constantly discharges into the trough and revolves with 
the pulley — the centrifugal force of the particles of water overcoming the 
action of gravity ; a waste-pipe with its end flattened is so placed in the 
trough that it acts as a scoop, and removes all surplus water. The brake 
consists of a flexible strap to which are fitted blocks of wood forming the 
rubbing-surface; the ends of the strap are connected by an adjustable 
bolt-clamp, by means of which any desired tension may be obtained. 

The horse-power or work of the shaft is determined from the following: 

Let W - work of shaft, equals power absorbed, per minute; 

P = imbalanced pressure or weight in pounds, acting on lever- 
arm at distance L; 
L = length of lever-arm in feet from center of shaft; 
V = velocity of a point in feet per minute at distance L, if arm 

were allowed to rotate at the speed of the shaft; 
N = number of revolutions per minute; 
H.P. = horse-power. 

Then will TT = P7 =2 ::LNP. 

Since H.P. = P7 -^ 33,000, we have H.P. = 2 rtLNP •«- 33,000. 

If 1/ = 33 -^ 2 ;r, we obtain H.P. = NP -^ 1000. 33-^2 tt is practically 
5 ft. 3 in., a value often used in practice for the length of arm. 

If the rubbing-surface be too small, the resulting friction will show 
great irregularity — probably on account of insufficient lubrication — • 
the jaws being allowed to seize the pulley, thus producing shocks and 
sudden vibrations of the lever-arm. 

Soft woods, such as bass, plane-tree, beech, poplar, or maple, are all 
to be preferred to the harder woods for brake-blocks. The rubbing-sur- 
face should be well lubricated with a heavy grease. 

The Alden Absorption-dynamometer, (G. I. Alden, Trans. A. S. 
M. E., vol. xi, 958; also xii, 700 and xiii, 429.) — This dynamometer is a 
friction-brake, which is capable in quite moderate sizes of absorbing 
large powers with unusual steadiness and complete regulation. A 
smooth cast-iron disk is keyed on the rotating shaft. Tliis is inclosed 
in a cast-iron shell, formed of two disks and a ring at their circumference, 
which is free to revolve on the shaft. To the interior of each of the sides 
of the shell is fitted a copper plate, inclosing between itself and the side a 
water-tight space. Water under pressure from the city pipes is admitted 
into each of these spaces, forcing the copper plate against the central disk. 
The chamber inclosing the disk is fiUed with oil. To the outer shell is 
fixed a weighted arm, which resists the tendency of the shell to rotate 
with the shaft, caused by the friction of the plates against the central 
disk. Four brakes of this type, 56 in. diam., were used in testing the 
experimental locomotive at Purdue University (Trans. A. S. M. E.^ 
xiii, 429). Each was designed for a maximum moment of 10,500 foot- 
pounds with a water-pressure of 40 lbs. per sq. in. The area in effective 
contact with the copper plates on either side is represented by an annular 
surface having its outer radius equal to 28 ins. and its inner radius equal 
to 10 ins. The apparent coefiBcient of friction between the plates and the 
disk was 3V2%. 

Capacity of Friction-brakes. — W. W. Beaumont (Proc. Inst. C. E., , 
1889) has deduced a formula by means of which the relative capacity of 
brakes can be compared, judging from the amount of horse-power ascer- • 
tained by their use. 

If W = width of rubbing-surface on brake-wheel in inches; T = vol. 
of point on circum. of wheel in feet per minute; K = coefficient; then 
K= WV -i- H.P. 



DYNAMOMETERS. 



1335 



Prof. Flather obtains the values of K given in the last column of 
subjoined table: 



the 



W 



21 
19 

20 
40 
33 
150 

24 
180 
475 
125\ 
250 f 

401 
125r 



<b 


Brake- 


^ 


pulley. 


u 






M . 




<u . 


^'1 




.£2 c 


tx^- 


Q"^ 



;2 



150 
148.5 
146 
180 
150 
150 
142 
100 
76.2 
290\ 

250 r 

3221 
290 f 



7 


5 


7 


5 


7 


5 


!0.5 


5 


10.5 


5 


10 


9 


12 


6 


24 


5 


24 


7 


24 


4 


13 


4 



33 

33.38 

32.19 

32 

32 



38.31 
126.1 
191 

63 
273/4 



Design of Brake. 



Royal Ag. Soc, compensating 

McLaren, compensating 

McLaren, water-cooled and comp . 
Garrett, water-cooled and comp . . 
Garrett, water-cooled and comp . . 

Schoenheyder. water-cooled 

Balk 

Gately & Kletsch, water-cooled ... 
Webber, water-cooled , 

Westinghouse, water-cooled 

Westinghouse, water-cooled 



785 
858 
802 
741 
749 
282 
1385 
209 
847 

465 
847 



The above calculations for eleven brakes give values of K varying from 
84.7 to 1385 for actual horse-powers tested, the average being K = 655. 

Instead of assuming an average coefficient. Prof. Flather proposes the 
following: 

Water-cooled brake, non-compensating, i^ = 400; TF = 400 H.P. h- V. 

Water-cooled brake, compensating, X = 750; TF = 750 H.P. -^ V. 

Non-cooUng brake, with or without compensating device, K = 900: W — 
900 H.P. H- 7. 

A brake described in Am. Mach., July 27, 1905, had an iron water- 
cooled drum, 30 in. diam., 20 in. face, with brake blocks of maple attached 
to an iron strap nearly surrounding the drum. At 250 r.p.m., or a cir- 
cumferental speed of 1963 ft. per min., the limit of its capacity was about 
140 H.P.; above that power the blocks took fire. At 140 H.P. the total 
surface passing under the brake blocks per minute was 3272 sq. ft., or 
23.37 per H.P. This corresponds to a value of K = 285. 

Several forms of Prony brake, including rope and strap brakes, are 
described by G. E. Quick in Am. Mach., Nov. 17, 1908. Some other 
forms are shown in Am. Electrician, Feb., 1903. 

A 6000 H.P. Hydraulic Absorption Dynamometer, built by the West- 
inghouse Machine Co., is described by E. H. Longwell in Eng. A'ews, 
Dec. 30, 1909. It was designed for testing the efficiency of the Melville 
and McAlpine turbine reduction gear (see page 1095). This dynamometer 
consists of a rotor mounted on a shaft coupled to the reduction gear and 
rotating within a closed casing which is prevented from turning by a 
6| ft. lever arm, the end of which transmits pressure through an I-beam 
lever to a platform scale. The rotor carries several rows of steam turbine 
vanes and the casing carries corresponding rows of stationary vanes, so 
arranged as to baffle and agitate the water passing through the brake, 
which is heated to boiling temperature by the friction. The dynamom- 
eter was run for 40 hours continuously, and proved to be a highly- 
accurate instrument. 

Transmission Dynamometers are of various forms, as the Batchelder 
dynamometer, in which the power is transmitted through a "train-arm" 
of bevel gearing, with its modifications, as the one described by the author 
in Trans, A, I, M. E., viii, 177, and the one described by Samuel Webber 
in Trans. A. S. M, E., x, 514; belt dynamometers, as the Tatham; the 
Van Winkle dynamometer, in wliich the power is transmitted from a 
revolving shaft to another in line with it, the two almost toucliing, 
through the medium of coiled springs fastened to arms or disk keyed to 
the shafts; the Brackett and the Webb cradle dynamometers, used for 
measuring the power required to run dynamo-electric macliines. De- 
scriptions of the four last named are given in Flather on Dynamometers. 

The Kenerson transmission dynamometer is described in Trans. A. S. 
M, E., 1909. It has the form of a shaft coupling, one part of which con- 



1336 ICE-MAKING OR REFRIGERATING-MACHINES. 

tains a cavity filled with oil and covered by a flexible copper diaphragm. 

The other part, by means of bent levers and a thrust baU-bearing, brings 
an axial pressure on the diaphragm and on the oil, and the pressure of the 
oil is measured by a gauge. 

Much information on various forms of dynamometers will be found in 
Trans, A. S. M. E., vols, vii to xv, inclusive, indexed under Dynamometers. 

ICE-MAKINQ OR REFRIGERATING 
MACHINES. 

References. — An elaborate discussion of the thermodynamic theory 
of the action of the various fluids used in the production of cold was 
published by ^I. Ledoux in the Annates des Mines, and translated in Van 
Nostrand's Magazine in 1879. This work, revised and additions made 
in the light of recent experience by Professors Denton, Jacobus, and 
Riesenberger, was reprinted in 1892. (Van Nostrand's Science Series, 
No. 46.) The work is largely mathematical, but it also contains much 
information of immediate practical value, from which some of the mat- 
ter given below is taken. Other references are Wood's Thermody- 
namics, Chap. V. and numerous papers by Professors Wood, Denton, 
Jacobus, and Linde in Trans. A. S. M. E., vols, x to xiv; Johnson's 
Cyclopaedia, article on Refrigerating-machines ; and the following books: 
Siebel's Compend of Mechanical Refrigeration; Modem Refrigerating 
Machinery, by Lorenz, translated by Pope; Refrigerating Machines, by 
Gardner T. Voorhees; Refrigeration, by J. Wemyss Anderson, and Re- 
frigeration, Cold Storage and Ice-making, by A. J. AVallis-Taylor. For 
properties of Ammonia and Sulphur Dioxide, see papers by Professors 
Wood and Jacobus, Trans. A. S. M. E., vols, x and xii. 

For illustrated descriptions of refrigerating-machines, see catalogues of 
builders, as Frick & Co., Waynesboro, Pa.; De La Vergne Refrigerating- 
machine Co., New York; Vilter Mfg. Co., Milwaukee; York Mfg., York, Co., 
Pa.; Henry Vogt Machine Co., Louisville, Ky.; Carbondale Machine Co., 
Carbondale, Pa. ; and others. See also articles in Ice and Refrigeration. 

Operations of a Refrigerating-machine. — Apparatus designed for 
refrigerating is based upon the following series of operations: 

Compress a gas or vapor by means of some external force, then relieve 
it of its heat so as to diminish its volume; next, cause this compressed gas 
or vapor to expand so as to produce mechanical work, and thus lower 
its temperature. The absorption of heat at tliis stage by the gas, in 
resuming its original condition, constitutes the refrigerating effect of the 
apparatus. 

A refrigerating-machine is a heat-engine reversed. 

From tills similarity between heat-motors and freezing-machines it 
results that all the equations deduced from the mechanical theory of heat 
to determine the performance of the first, apply equally to the second. 

The efficiency depends upon the difference between the extremes of 
temperature. 

The useful effect of a refrigerating-machine depends upon the ratio 
between the heat-units eliminated and the work expended in compressing 
and expanding. 

This result is independent of the nature of the body employed. 

Unlike the heat-motors, the freezing-machine possesses the greatest 
efficiency when the range of temperature is small, and when the final 
temperature is elevated. 

If the temperatures are the same, there is no theoretical advantage in 
employing a gas rather than a vapor in order to produce cold. 

The choice of the intermediate body would be determined by practical 
considerations based on the physical characteristics of the body, such as 
the greater or less facility for manipulating it, the extreme pressures 
required for the best effects, etc. 

Air offers the double advantage that it is everywhere obtainable, and 
that we can vary at will the higher pressures, independent of the tempera- 
ture of the refrigerant. But to produce a given useful effect the apparatus 
must be of larger dimensions than that required by liquefiable vaDors. 

The maximum pressure is determined by the temperature of the con- 
denser and the nature of the volatile liquid ; this pressure is often high. 



BOILING POINTS OF REFRIGERATING LIQUIDS. 1337 



When a change of volume of a saturated vapor is made under constant 
pressure, the temperature remains constant. The addition or subtraction 
of heat, which produces the chanpre of volume, is represented by an 
increase or a diminution of the quantity of Uquid mixed with the vapor. 

On the other hand, when vapors, even if saturated, are no longer in 
contact with their liquids, and receive an addition of heat either through 
compression by a mechanical force, or from some external source of heat, 
they comport themselves nearly in the same way as permanent gases, 
and become superheated. 

It results from this property, that refrigerating-machines using a 
liquefiable gas will afford results differing according to the method of 
working, and depending upon the state of the gas, whether it remains 
constantly saturated, or is superheated during a part of the cycle of 
working. 

The temperature of the condenser is determined by local conditions. 
The interior will exceed by 9° to 18° the temperature of the water fur- 
nished to the exterior. This latter will vary from about 52° F., the 
temperatiye of water from considerable depth below the surface, to 
about 95° F., the temperature of surface-water in hot cUmates. The 
volatile liquid employed in the machine ought not at this temperature to 
have a tension above that which can be readily managed by the apparatus. 

On the other hand, if the tension of the gas at the minimum temperature 
is too low, it becomes necessary to give to the compression-cylinder 
large dimensions, in order that the weight of vapor compressed by a 
single stroke of the piston shall be suflBcient to produce a notably useful 
effect. 

These two conditions, to which may be added others, such as those 
depending upon the greater or less facility of obtaining the liquid, upon 
the dangers incurred in its use, either from its inflammability or unhealth- 
fulness, and finally upon its action upon the metals, limit the choice to a 
small number of substances. 

The gases or vapors generally available are: sulphuric ether, sulphurous 
oxide, ammonia, methylic ether, and carbonic acid. 

The following table, derived from Regnault, shows the tensions of the 
vapors of these substances at temperatures between - 22<^ and -j- 104®. 

Pressures and Boiling-points of Liquids available for Use 
in Refrigerating-machines. 



Temp. 

of 
Ebulli- 
tion. 



Tension of Vapor, in lbs. per sq. in., above Zero. 



Deg. 

Fahr. 



Sul- 
phuric 
Ether. 



BSlJSk™-- 



Methylic 

Ether. 



Carbonic 
Acid. 



10.22 

13.23 

16.95 

21.51 

27.04 

33.67 

41.58 

50.91 

61.85 

74.55 

89.21 

105.99 

125.08 

146.64 

170.83 

197.83 

227.76 



Pictet 
Fluid. 



Ethyl 
Chlonde 



-40 

-31 

-22 

-13 

- 4 

5 

14 

23 

32 

41 

50 

59 

68 

77 

86 

95 

104 









5.56 




7.23 


1.30 


9.27 


1.70 


11.76 


2.19 


14.75 


2.79 


18.31 


3.55 


22.53 


4.45 


27.48 


5.54 


33.26 


6.84 


39.93 


8.38 


47.62 


10.19 


56.39 


12.31 


66.37 


14.76 


77.64 


17.59 


90.32 



11.15 
13.85 
17.06 
20.84 
25.27 
30.4/ 
36.34 
43.13 
50.84 
59.56 
69.35 
80.28 
92.41 



251.6 
292.9 
340.1 
393.4 
453.4 
520.4 
594.8 
676.9 
766.9 
864.9 
971.1 
1085.6 
1207.9 
1338.2 



13.5 
16.2 
19.3 
22.9 
26.9 
31.2 
36.2 
41.7 
48.1 
55.6 
64.1 
73.2 
82 9 



2.13 

2.80 

3.63 

4.63 

5.84 

7.28 

9.00 

11.01 

13.36 

16.10 

19.26 

22.90 

27.05 

31.78 

37 12 



The table shows that the use of ether does not readily lead to the 
production of low temperatures, because its pressure becomes then very 
feeble. Ammonia, on the contrary, is well adapted to the production 
of low temperatures. 



1338 ICE-MAKING OR REFRIGERATING-MACHINES. 

Metliylic ether yields low temperatures "Without attaining too great 
pressures at the temperature of the condenser. Sulphur dioxide readily 
affords temperatures of — 14 to — 5, while its pressure is only 3 to 4 
atmospheres at the ordinary temperature of the condenser. These latter 
substances then lend themselves conveniently for the production of cold 
by means of mechanical force. 

The " Pictet fluid" is a mixture of 97% sulphur dioxide and 3% carbonic^ 
acid. At atmospheric pressure it affords a temperature 14° lower than 
sulphur dioxide. (It is not now used — 1910.) 

Carbonic acid is in use to a limited extent, but the relatively greater 
compactness of compressor that it requires, and its inoffensive character, 
are leading to its recommendation for service on shipboard. 

Certain ammonia plants are operated ^ath a surplus of liquid present 
during compression, so that superheating is prevented. This practice is 
known as the "cold " or " wet " system of compression. 

Ethyl chloride, C0H5CI. is a colorless gas which at atmospheric pressure 
condenses to a liquid at 54.5° F. The latent heat at 23° F. is given at 174 
B.T.U. Density of the gas (air = l) = 2.227. Specific heat at constant 
pressure, 0.274; at constant volume, 0.243. 

Nothing definite is known regarding the application of methyUc ether or 
of the petroleum product chymogene in practical refrigerating service. 
The inflammabihty of the latter and the cumbrousness of the compressor 
required are objections to its use. 



PROPERTIES OF SULPHUR DIOXIDE AND 
AI^OIONIA GAS. 

Ledoux's Table for Saturated Sulphur-dioxide Gas, 

Heat-units expressed in B.T.U. per pound of sulphur dioxide. 





• u 


1 Total Heat 
reckoned from 
32° F. 


Heat of Liquid 
reckoned from 
32° F. 


^ 


^ 




. 


■^ 


Temperature 
of Ebullition 
in deg. F. 
t 


Absolute Pres 
sure in lbs. pe 
sq. in. 
1 P -- 144 


Latent Heat 
Evaporation. 
r 


HeatEquivale 
of External 
Work. 
APu 


Internal La- 
tent Heat. 
P 


Increase of 
Volume dur- 
ing Evapo- 
ration. 
u 


Density of Va- 
por or Weigh 
of 1 cu. ft. 

1 -^v 


Deg. F. 


Lb. 


B.T.U. 


B.T.U. 


B.T.U. 


B.T.U. 


B.T.U. 


Cu.ft. 


Lb. 


-22 


5.56 


157.43 


-19.56 


176.99 


13.59 


163.39 


\3A7 


0.076 


-13 


7.23 


158.64 


-16.30 


174.95 


13.83 


161.12 


10.27 


.097 


- 4 


9.27 


159.84 


-13.05 


172.89 


14.05 


158.84 


8.12 


.123 


5 


11.76 


161.03 


- 9.79 


170.82 


14.26 


156.56 


6.50 


.153 


14 


14.74 


162.20 


- 6.53 


168.73 


14.46 


154.27 


5.25 


.190 


23 


18.31 


163.36 


- 3.27 


166.63 


14.66 


151.97 


4.29 


.232 


32 


22.53 


164.51 


0.00 


164.51 


U.84 


149.68 


3.54 


.282 


41 


27.48 


165.65 


3.27 


162.38 


15.01 


147.37 


2.93 


.340 


50 


33.25 


166.78 


6.55 


160.23 


15.17 


145.06 


2.45 


.407 


59 


39.93 


167.90 


9.83 


158.07 


15.32 


142.75 


2.07 


.483 


68 


47.61 


168.99 


13.11 


155.89 


15.46 


140.43 


1.75 


.570 


77 


56.39 


170.09 


16.39 


153.70 


15.59 


138.11 


1.49 


.669 


86 


66.36 


171.17 


19.69 


151.49 


15.71 


135.78 


1.27 


.780 


95 


77.64 


\72.24 


22.98 


149.26 


15.82 


133.45 


1.09 


.906 


104 


90.31 


173.30 


26.28 


147.02 


15.91 


131.11 


0.91 


1.046 



E. F. Miller (Trans. A. S. M. E., 1903) reports a series of tests on the 
pressure of SO2 at various temperatures, the results agreeing closely with 
those of Regnault up to the highest figure of the latter, 149° F., 178 lbs. 
absolute. He gives a table of pressures and temperatures for every 
degree between — 40° and 217°. The results obtained at temperatures 
between 113° and 212° are as below: 
Temp. °F. 

113 122 131 140 149 158 167 176 194 203 212 
Pres. lbs. persq. in. 

104.4 120.1 137.5 156.7 179.5 203.8 230.7 260.5 331.1 371.8 418. 



PROPERTIES or AMMONIA. 



1339 



Properties of Ammonia. — For a discussion of the properties of am- 
monia and a bibliography of investigations of ammonia, see Bulletin 66 
of the University of Ilhnois Experiment Station. See also "Properties 
of Steam and Ammonia," by G. A. Goodenough (John Wiley & Sons, 
1915). Prof. Goodenough says that experiments on the properties of 
ammonia are by no means as complete or as concordant as the experi- 
ments on water vapor; hence any formulation for ammonia must be 
regarded as tentative and subject to revision as further experimental 
evidence becomes available. 



Properties of Saturated Ammonia. 

(From Goodenough 's Tables.) 



JQ 


2 


6i 




Total Heat 


Latent 


Heat 








1^ 


3^ 

id 


B.T.U. 


B.T.U. 


Entropy. 




73 


C 


^ S 


^ 


'6 


is 


hjD 




«♦-( o 


«*H o o 


0)-^ 




««-i o o 


III 


B^ 
^Q 


$i 




'1 


> 










1 


-103.7 
- 62.0 


225.0 
49.3 


0.0044 
0.0203 






644.6 
617.2 


603.0 
571.5 


-6.2207 


1.8107 


5 


-98.V ' 


519.Y 


1.5523 


10 


- 40.4 


25.75 


0.0388 


-75.7 


526.4 


602.2 


554.6 


-0.1661 


1.4363 


15 


- 26.4 


17.60 


0.0568 


-61.2 


530.9 


592.1 


543.3 


-0.1324 


1.3669 


20 


- 15.9 


13.45 


0.0744 


-50.3 


534.0 


584.3 


534.7 


-0.1075 


1.3168 


25 


- 7.2 


10.88 


0.0919 


-41.3 


536.5 


577.8 


527.4 


-0.0876 


1.2771 


30 


+ 0.1 


9.17 


0.1090 


-33.6 


538.5 


572.1 


521.3 


-0.0708 


1.2447 


35 


6.5 


7.93 


0.1260 


-26.9 


540.3 


567.1 


515.8 


-0.0561 


1.2167 


40 


12.2 


6.99 


0.1430 


-20.8 


541.8 


562.6 


511.0 


-0.0433 


1.1924 


45 


17.4 


6.25 


0.1598 


-15.3 


543.1 


558.4 


506.4 


-0.0319 


1.1707 


50 


22.1 


5.66 


0.1765 


-10.3 


544.3 


554.6 


502.3 


-0.0216 


1.1512 


55 


26.4 


5.18 


0.1931 


- 5.7 


545.3 


551.1 


498.6 


-0.0122 


1.1338 


60 


30.5 


4.77 


0.2096 


- 1.3 


546.3 


547.7 


495.0 


-0.0033 


1.1175 


65 


34.3 


4.42 


0.2261 


+ 2.7 


547.2 


544.5 


491.6 


+0.0051 


1.1023 


70 


37.9 


4.12 


0.2425 


6.6 


548.1 


541.4 


488.4 


0.0128 


1.0883 


75 


41.3 


3.86 


0.2589 


10.3 


548.8 


538.5 


485.3 


0.0201 


1.0751 


80 


44.5 


3.63 


0.2753 


13.8 


549.5 


535.8 


482.3 


0.0271 


1.0627 


85 


47.6 


3.43 


0.2917 


17.2 


550.2 


533.1 


479.5 


0.0336 


1.0511 


90 


50.5 


3.25 


0.3081 


20.4 


550.9 


530.5 


476.8 


0.0398 


1.0400 


95 


53.3 


3.08 


0.3246 


23.5 


551.5 


528.0 


474.3 


0.0458 


1.0295 


100 


56.0 


2.93 


0.3409 


26.5 


552.1 


525.6 


471.8 


0.0516 


1.0195 


110 


61.1 


2.678 


0.3735 


32.1 


553.1 


521.0 


467.0 


0.0625 


1.0006 


120 


65.8 


2.466 


0.4056 


37.4 


554.1 


516.7 


462.5 


0.0725 


0.9834 


130 


70.4 


2.283 


0.4381 


42.5 


555.0 


512.5 


458.2 


0.0820 


0.9672 


140 


74.5 


2.124 


0.4707 


47.3 


555.9 


508.6 


454.2 


0.0910 


0.9521 


150 


78.5 


1.989 


0.5028 


51.8 


556.7 


504.8 


450.3 


0.0993 


0.9382 


160 


82.3 


1.868 


0.5353 


56.2 


557.4 


501.1 


446.6 


0.1074 


0.9249 


170 


85.9 


1.763 


0.5673 


60.5 


558.1 


497.6 


443.0 


0.1152 


0.9121 


180 


89.4 


1.666 


0.6000 


64.6 


558.8 


494.1 


439.5 


0.1226 


0.9001 


190 


92.7 


1.580 


0.6330 


68.6 


559.4 


490.9 


436.2 


0.1296 


0.8887 


200 


95.9 


1.504 


0.665 


72.3 


560.0 


487.6 


433.0 


0.1363 


0.8779 


220 


101.8 


1.370 


0.730 


79.5 


561.0 


481.5 


426.8 


0.1488 


0.8578 


240 


107.4 


1.258 


0.795 


86.4 


562.0 


475.6 


421.0 


0.1609 


0.8389 


260 


112.7 


1.161 


0.861 


93.0 


562.9 


470.0 


415.4 


0.1722 


0.8213 


280 


117.6 


1.079 


0.927 


99.2 


563.8 


464.6 


410.2 


0.1829 


0.8048 


300 


122.4 


1.007 


0.993 


105.3 


564.6 


459.3 


405.0 


0.1932 


0.7893 


350 


133.2 


0.863 


1.159 


119.6 


566.4 


446.8 


392.8 


0.2171 


0.7538 


400 


142.9 


0.752 


1.330 


132.9 


567.9 


435.0 


381.5 


0.2390 


0.7220 


450 


151.8 


0.665 


1.504 


145.6 


569.3 


423.8 


370.8 


0.2593 


0.6931 


500 


160.0 


0.597 


1.675 


157.5 


570.5 


413.0 


360.5 


0.2786 


0.6664 


550 


167.6 


0.539 


1.855 


169.2 


571.7 


402.5 


350.8 


0.2965 


0.6419 


600 


174.7 


0.491 


2.038 


180.4 


572.7 


392.3 


341.3 


0.3138 


0.6186 


650 


181.4 


0.449 


2.227 


191.4 


573.6 


382.2 


332.0 


0.3307 


0.5963 


700 


187.7 


0.414 


2.416 


202.1 


574.4 


372.2 


322.8 


0.3469 


0.5758 


761.4 


195.0 


0.376 


2.660 


215.2 


575.4 


360.2 


311.8 


0.3664 


0.5503 



1340 ICE-MAKING OR REFRIGERATING-MACHINES. 



Properties of Superheated Ammonia. 

(From Goodenough's Tables.) 
V = volume, cu. ft. per lb., n = entropy, h = total heat, B.T.U. per lb. 
Pressure in lb. per sq. in. ; temperatures in deg. F. 



Pressure, 15 


20 


25 


30 


Temp. (-26.4°F.) 


(-15.9°) 


(-7.2°) 


(+0.1°) 




V 


n 


h 


V 


n 


h 


V 


n 


h 


V 


n 


h 


Sat. 


17.6 


1.234 


530.9 


13.4 


1.209 


534.0 


10.9 


1.190 


536.5 


9.17 


1.174 


538.5 


0° 


18.9 
21.1 


1.267 
1.320 


545.2 
571.1 


14.0 
15.8 


1.229 
1.284 


542.9 
569.8 


11.1 
12.6 


1.199 
1.256 


540.8 
568.4 








50 


10.41 


1.733 


567.1 


100 


23.3 


1.367 


596.4 


17.5 


1.332 


595.5 


13.9 


1.305 


594.5 


11.55 


1.783 


593.7 


150 


25.5 


1.410 


621.4 


19.1 


1.376 


620.8 


15.2 


1.349 


620.1 


12.65 


1.327 


619.5 


200 


27.7 


1.449 


646.5 


21.4 


1.431 


656.2 


16.5 


1.389 


645.6 


13.74 


1.367 


645.7 


240 


29.3 


1.479 


666.9 


22.0 


1.446 


666.4 


17.6 


1.419 


666.0 


14.59 


1.398 


665.7 


Pressure, 40 


50 


60 


70 


Temp. (12.2°) 


(22.1°) 


(30.5°) 


(37.9°) 


Sat. 


6.99 


1.149 


541.8 


5.67 


1.130 


544.3 


4.77 


1.114 


546.3 


4.12 


1.101 


548.1 


50 


7.72 


1.195 


564.3 


6.11 


1.165 


561.5 


5.03 


1.139 


558.8 


4.27 


1.117 


556.0 


100 


8.59 


1.247 


591.8 


6.83 


1.218 


590.0 


5.65 


1.194 


588.2 


4.81 


1.174 


586.5 


150 


9.44 


1.292 


618.2 


7.51 


1.264 


617.0 


6.22 


1.242 


615.8 


5.31 


1.222 


614.6 


200 


10.26 


1.333 


644.3 


8.17 


1.306 


643.3 


6.79 


1.283 


642.4 


5.80 


1.265 


641.5 


300 








9.47 


1.380 


695.7 


7.87 


1.358 


695.1 


6.73 


1.339 


694.6 












Pressure, 80 


90 


100 


120 


Temp-. (44.5°) 


(50.5°) 


(56.0°) 


(65.8°) 


Sat. 


3.63 


1.090 


549.5 


3.25 


1.080 


550.9 


2.94 


1.071 


552.1 


2.47 


1.056 


554.1 


100 


4.18 


1.156 


584.7 


3.69 


1.140 


582.9 


3.29 


1.125 


581.1 


2.71 


1.099 


577.5 


150 


4.62 


1.205 


613.4 


4.09 


1.190 


612.1 


3.66 


1.176 


610.8 


3.02 


1.152 


608.4 


200 


5.04 


1.248 


640.6 


4.47 


1.233 


639.8 


4.01 


1.220 


638.9 


3.31 


1.197 


637.1 


300 


5.87 


1.323 


694.1 


5.21 


.1.309 


693.5 


4.67 


1.297 


693.0 


3.87 


1.275 


692.1 


340 








5.50 


1.337 


714.9 


4.93 


1.324 


714.6 


4.09 


1.302 


713.9 










Pressure, 140 


160 


200 


240 


Temp. (74.5°) 


(82.3°) 


(95.9°) 


(107.4°) 


Sat. 


2.12 


1.043 


555.9 


1.87 


1.032 


557.4 


1.50 


1.014 


560.0 


1.26 


1.000 


562.0 


100 


2.29 
2.56 


1.076 
1.131 


573.9 
605.9 


1.97 

2.22 


1.056 
1.112 


570.3 
603.5 


1.52 
1.73 


1.020 
1.080 


563.1 
598.4 








150 


1.42 


1.053 


593.5 


200 


2.82 


1.177 


635.3 


2.44 


1.160 


633.6 1.92 


1.130 


630.0 


1.57 


1.105 


626.4 


300 


3.30 


1.256 


691.1 


2.66 


1.202 


662.1 2.27 


1.212 


687.7 


1.87 


1.189 


685.6 


360 


3.58 


1.297 


723.9 


3.12 


1.2811 


722.9 2.47 


1.254 


721.0 


2.04 


1.232 


719.3 



Thermal Properties of Liquid Ammonia. 

(From Goodenough's Tables.) 





Satu- 










Satu- 










ration 


Vol. 


Weight 






ration 


Vol. 


Weight 




Temp. 


Pres- 


of 


of 


144 X 


Temp. 


Pres- 


of 


of 


144 X 


Deg.F. 


sure, 


1 Lb., 


1 Cu. 


Apv. 


°F. 


sure, 


1 Lb., 


1 Cu. 


Apv, 




Lb. per 


Cu. Ft. 


Ft., Lb. 






Lb. per 


Cu. Ft. 


Ft., Lb. 






Sq. In. 










Sq. In. 








-110 


0.758 


0.02202 


45.42 


0.003 


60 


107.7 


0.03609 


38.33 


0.520 


-100 


1.176 


.02220 


45.04 


.005 


70 


129.2 


.02643 


37.85 


.632 


- 80 


2.626 


.02258 


44.28 


.011 


80 


153.9 


.02678 


37.35 


.76 


- 60 


5.358 


.02299 


43.51 


.023 


90 


181.8 


.02714 


36.84 


.92 


- 40 


10.12 


.02342 


42.71 


.044 


100 


213.8 


.02754 


36.32 


1.09 


- 20 


17.91 


.02388 


41.88 


.079 


120 


289.9 


.02839 


35.23 


1.52 





29.95 


.02437 


41.04 


.135 


140 


384.4 


.02936 


34.06 


2.09 


10 


38.02 


.02463 


40.61 


.173 


160 


500.1 


.0305 


32.80 


2.82 


20 


47.75 


.02490 


40.17 


.220 


180 


639.5 


.0318 


31.5 


3.77 


30 


59.35 


.02518 


39.72 


.247 


200 


805.6 


.0335 


29.9 


4.99 


40 


73.03 


.02547 


39.27 


.344 


250 


1357.4 


.0404 


24.8 


10.2 


50 


89.1 


.02577 


38.81 


.425 


273.2 


1690.0 


.0678 


14.75 


21.2 



A = reciprocal of Joule's equivalent = 1/777.6; p = pressure, lb. per 
sq. in.; v = vol. of 1 lb., cu ft. 



PROPEETIES OF AMMONIA. 



1341 



Solubility of Ammonia. (Siebel.) — One pound of water will dis- 
solve the following weights of ammonia at the pressures and tempera- 
tures F° stated. 



Abs. 








Abs. 








AKs. 








I^ess. 


32° 


68° 


104° 


Press. 


32° 


68° 


104° 


Press. 


32° 


68° 


104° 


per 








per 








per 








sq.m. 








sq.m. 








sq. m. 








lb. 


lb. 


lb. 


lb. 


lb. 


lb. 


lb. 


lb. 


lb. 


lb. 


lb. 


lb. 


14.67 


0.899 


0.518 


0.338 


21.23 


1.236 


0.651 


0.425 


27.99 


1.603 


0.780 


0.486 


13.44 


0.937 


0.635 


0.349 


22.19 


1.283 


0.669 


0.434 


28.95 


1.636 


0.801 


0.493 


16.41 


0.980 


0.556 


0.363 


23.16 


1.330 


0.685 


0.445 


30.88 


1.758 


0.842 


0.511 


17.37 


1.029 


0.574 


0.378 


24.13 


1.388 


0.704 


0.454 


32.81 


1.861 


0.881 


0.530 


18.34 


1.077 


0.594 


0.391 


25.09 


1.442 


0.722 


0.463 


34.74 


1.966 


0.919 


0.547 


19.30 


1.126 


0.613 


0.404 


26.06 


1.496 


0.741 


0.472 


36.67 


2.070 


0.955 


0.565 


20.27 


1.177 


0.632 


0.414 


27.02 


1.549 


0.761 


0.479 


38.60 




0.992 


0.579 



Strength of Aqua Ammonia at 60° F. 

% NHs by wt. 2 4 6 8 

Sp. gr. 0.986 .979 .972 .966 

% NH3 20 22 24 26 

Sp. gr. 0.925 .919 .913 .907 

Properties of Saturated Vapors. — The 
are given by Lorenz, on the authority of 



10 12 14 16 18 
.960 .953 .945 .938 .931 

28 30 32 34 36 
.902 .897 .892 .888 .884 
figures in the following table 
M oilier and of Zeuner. 





Heat of 
Vaporization, 


Heat of Liquid, 
B.T.U. per lb. 


Absolute 
Pressure, 


Volume of 
1 lb.. 


°F. 


B.T.U. per lb. 


lbs. per sq. in. 


cubic feet. 




NH3 


CO2 


SO2 


NH3 


CO2 


SO2 


NH3 


CO2 


SO2 


NH3 


CO2 


SO2 


- 4° 


589 


117 6 


171 


-31.21 


-17.19 


-11.16 


27.1 


288.7 


9.27 


10.33 


0.312 


8.06 


+ 14° 


580 


110.7 


168.2 


-15.89 


- 9.00 


- 5.69 


41.5 


385.4 


14.75 


6.92 


0.229 


5.27 


32° 


569 


99,8 


164,2 


C 








61.9 


503.5 


22.53 


4.77 


0.167 


3.59 


50° 


555 5 


86 


158.9 


16.51 


10.28 


5.90 


89.1 


650.1 


33.26 


3.38 


0.120 


2.44 


68° 


539 9 


66 5 


152 5 


33.58 


23.08 


12.03 


125.0 


826.4 


47.61 


2.47 


0.083 


1.71 


86° 


57.1 4 


27.1 


144.8 


51.28 


45.45 


18.34 


170.8 


1040. 


66.36 


1.83 


0.048 


1.22 


104° 


500.4 




135.9 


69.58 


. . .. 


24.88 227.7 




90.30 


1.39 




88 



The figures for CO2 in the above table differ widely from those of 
Regnault, and are no doubt more reliable. 

Heat Generated by Absorption of Ammonia. (Berthelot, from 
Siebel.) — Heat developed when a solution of 1 lb. NH3 in n lbs. water 
is diluted with a great amount of water = Q = 142/71 B.T.U. Assumins: 
925 B.T.U. to be developed when 1 lb. NH3 is absorbed by a great deal 
(say 200 lbs.) of water, the heat developed in making solutions of different 
strengths (1 lb. NH3 to n lbs. water) = Qi= 925 - 142/n B.T.U. Heat 
developed when h lbs. NH3 is added to a solution of 1 lb. NH3 + n lbs. 
water = ^3= 9255- 142 (2&+ 62) /^ B.T.U. 

Let the weak liquor enter the absorber with a strength of 10%,= 1 lb. 
NH3 + 9 lbs. water, and the strong liquor leave the absorber with a 
strength of 25%, = 3 lbs. NH3 + 9 lbs. water, ?> = 2, n = 9; C>3 = 925 X 
2 - 142 (4 + 4)/9 = 1724 B.T.U. Hence by dissolving 2 lbs. of ammonia 
gas or vapor in a solution of 1 lb. ammonia in 9 lbs. water we obtain 
12 lbs. of a 25% solution, and the heat generated is 1724 B.T.U. 

Cooling Effect, Compressor Volume, and Power Required. — The 
following table gives the theoretical results computed on the basis of 
a temperature in the evaporator of 14° F. and in the condenser of 68° F.; 
in the first three columns of figures the cooling agent is supposed to flow 
through the regulating valve with this latter temperature; in the last 
three it is previously cooled to 50° F. 

From the stroke-volume per 100,000 B.T.U. the minimum theoretical 
horse-power is obtained as follows: Adiabatic compression is assumed 
for the ratio of the absolute condenser pressure to that of the vaporizer, 
and the mean pressure through the stroke thus found, in lbs. per sq ft.; 
multiplying this by the stroke volume per hour and dividing by 1,980,000 
gives the net horse-power. The ratio of the mean effective pressure, 
M.P., to the vaporizer pressure, V.P., for different ratios of condenser 
pressure, C.P., to vaporizer pressure is given on the next page. 



1342 ICE-MAKING OR REFRIGERATING-MACHINES. 



Cooling Effect, Compressor Volume, and Power Required, with 
Different Cooling Agents. (Lorenz.) 



Cooling Agent. 



1. Temp, in front of regulating 

valve 

2. Vaporizer pressure, lbs. per 

sq. in 

3. Condenser pressure, lbs. per 

sq. in 

4. Heat of evaporation, B.T.U. 

per lb 

5-. Heat imparted to the liquid 

6. Cold produced per lb. B.T.U 

7. Cooling agent circulated for 

yield of 100,000 B.T.U. per 
hour, lbs 

8. Stroke volume for 100,000 

B.T.U. per hour, cu. ft 

9. Minimum H.P. per 100,000 

B.T.U. per hour 

10. Ratio Heat of evap. -r- cold 

produced 

1 1 . Ratio total work to minimum 

12. Total I.H.P. per 100,000 

B.T.U. per hour 

13. Cooling effect per I.H.P. hr.. 



NHs 



68 

41.5 

125.0 

580.2 
49.47 
530.73 

188.4 

1,300 

4.98 

t.093 
1.175 

5.85 
17.100 



CO2 



68 

385.4 

826.4 

110.7 
32.08 
78.62 

1272. 

292 

4.98 

1.408 
1.513 

7.53 
13,300 



SO2 



68 

14.75 

47.61 

168.2 
17.72 
150.48 

664.3 

3,507 

4.98 

1.118 
1.202 

5.99 
16,700 



NH3 



50 

41.5 

125.0 

580.2 
32.4 
547.8 

182.5 

1,264 

4.98 

1.059 
1.133 

5.67 
17,600 



CO2 



50 

385.4 

826.4 

110.7 
19.28 
91.42 

1094. 

242 

4.98 

1.211 
1.302 

6.48 
15,400 



SO2 



50 

14.75 

47.61 

168.2 

11.59 

156.61 

638.5 

3,365 

4.98 

1.074 
1.155 

5.75 
17,400 



Ratios of Condenser Pressure, C. P., and Mean Effective Pres- 
sure, M. P., TO Vaporizer Pressure, V. P. 



&■ 


fin 
> 


> 


> 


> 


> 
'I* 


Pk 
> 


P^ 

;> 
•I- 


Ph 

;> 


P4 
> 
•1- 


Ph 
> 


Ph 
> 
•1- 


^ 


Q^ 


P-i 


fU 


Ph 


PL| 


Ph 


p^ 


Ph 


Ph 


Ph 


Ph 





^ 





^ 





^ 



4.0 


^ 





^ 


Q 


^ 


1.0 


0. 


2.0 


0.752 


3.0 


1.249 


1.684 


5.0 


1.947 


6.0 


2.210 


1.2 


0.186 


2.2 


0.865 


3.2 


1.344 


4.2 


1.711 


5.2 


2.006 


7.0 


2.454 


1.4 


0.350 


2.4 


0.970 


3.4 


1.414 


4.4 


1.766 


5.4 


2.062 


8.0 


2.666 


1.6 


0.487 


2.6 


1.070 


3.6 


1.491 


4.6 


1.829 


5.6 


2.116 


9.0 


2.858 


1.8 


0.630 


2.8 


1.163 


3.8 


1.564 


4 8 


1.891 


5.8 


2.168 


10 


3.036 



The minimum theoretical horse-power thus obtained is increased by 
the ratio of the heat of evaporation to the available cooling action (line 
4 -^ line 6, = line 10 of the table) and by an allowance for the resistance 
of the valves taken at 7.5% to obtain the total H.P. given in the table. 

To the theoretical horse-power given in line 12 Lorenz makes numerous 
additions, viz.: friction of the compression and driving machine 0.90, 
1.10, 0.90, 0.85, 0.95, 0.85 respectively for the six columns in the table; 
also H.P. for stirring 0.3; for cooling-water pumps, 0.45; for brine pumps, 
2.2; for transmission of power, 0.6, making the total H.P. for the six cases 
10.30, 12.18, 10.44, 10.07, 10.98, 10.15. He also makes deductions from 
the theoretical generation of cold of 100,000 B.T.U. per hour, for a brewery 
cooling installation, for irregularities of valves, etc., for NH3 and SO2 
machines 10% and for CO2 machines 5%; for cooling loss through stirring 
765 B.T.U., through brine pumps 5610 B.T.U., and through radiation 
4500 B.T.U., making the net cooling for NH3 and SO2 machines 79,125 
B.T.U. and for CO2 machines 84,125 B.T.U., and the cold generated per 
effective H.P. in tlie six cases, 7682, 6908, 7578, 7848, 7662, and 7796 
B.T.U. 

The figures given in the tables are not to be considered as holding 
generally or extended to other condenser and evaporator temperatures. 
Each change of condition requires a separate calculation. The final 
results indicate that for the various cooling systems no appreciable 
difference exists in the work required for the same amount of cold 
delivered at the place where it is to be applied. 



PROPERTIES OF DIFFERENT COOLING AGENTS. 



1343 



Properties of Brine Used to Absorb Refrigerating EflTect of 
Ammonia. (J. E. Denton, Trans. A. S. M. E., x, 799). — A solution of 
Liverpool salt in well-water having a specific gravity of 1.17, or a weight 
per cubic foot of 73 lbs., will not sensibly tliicken or congeal at 0° F. 

The mean specific heat between 39° and 16° Fahr. was found by 
Denton to be 0.805. Brine of the same specific gravity has a specific 
heat of 0.805 at 65° Fahr., according to Naimiann. 

Naumann's values {Lehr-und Handbuch der Thermochemie, 1882) are: 

Specific heat 0.791 0.805*0.863 0.895 0.941 0.962 0.978 

Specific gravity.... 1.187 1.170 1.103 1.072 1.044 1,023 1.012 

Properties of Salt Brine (Carbondale Calcium Co.) 

Deg. Baumg 60° F 1 5 10 15 19 23 

Deg. Salinometer 60° F 4 20 40 60 80 100 

Sp. gravity 60° F 1.007 1.037 1.073 1.115 1.150 1.191 

Per cent of salt, by wt.. . . 1 5 10 15 20 25 

Wt. of 1 gallon, lbs 8.40 8.65 8.95 9.30 9.60 9.94 

Wt. of 1 cu. ft., lbs 62.8 64.7 66.95 69.57 71.76 74.26 

Freezing point ° F , . 31.8 25.4 18. 6 12.2 6.86 1.00 

Specific heat 0.992 0.960 0.892 0.855 0.829 0.783 

Chloride of Calcium solution is commonly used instead of brine. 
According to Naumann, a solution of 1.0255 sp. gr. has a specific heat of 
0.957. A solution of 1.163 sp. gr. in the test reported in Eng'g, July 22, 
1887, gave a specific heat of 0.827. 

H. C. Dickinson (Science, April 23, 1909) gives the following values of the 
specific heat of solutions of chemically pure calcium chloride. 

Density Specific Heat Temperature, C. 

1.07 0.869 + 0.00057 « (- 5° to + 15°) 

1.14 0.773 + 0.00064 fc (- 10° to + 20°) 

1.20 0.710 + 0.00064i (- 20° to + 20°) 

1.26 0.662 + 0.00064 i (- 25° to + 20°) 

The advantages of chloride of calcium solution are its lower freezing point 
and that it has little or no corrosive action on iron and brass. Calcium 
cliloride is sold in the fused or granulated state, in steel drums, contain- 
ing about 75% anhydrous chloride and 25% water, or in solution contain- 
ing 40 to 50% anhydrous chloride^ in tank cars. The following data 
are taken from the catalogue of the Carbondale Calcium Co. 

Properties of '* Solvay " Calcium Chloride Solution. 



vy 


. 






^c 


, 






su 


. 






g 


> 




-t.3 


f, 


> 




■*3 


s 


> 




.«^ 


3 


2 


h 


0) • 


3 


2 




N bJO 


3 
PQfa 


Ofa 






^1 


^1 


^.6 




1^2 


^S 


sa 




qO 


r2 


i6 


2Q 


Q 


m 


p-i 


fa 


o 


m 


^ 


fa 


Q 


m 




fa 


1. 


1.007 


1 


+ 31.10 


21 


1.169 


19 


+ 1.76 


32 


1.283 


30 


-54.40 


«> 5 


1.041 


5 


27.68 


22 


1.179 


20 


- 1.48 


35 


1.316 


33 


-25.24 


11 


1.085 


10 


22.38 


23 


1.189 


21 


- 4.90 


35.5 


1.327 


34 


- 9.76 


17 


1.131 


15 


12.20 


26 


1.219 


24 


-17.14 


36.5 


1.338 


3:> 


+ 2.84 


20 


1.159 


18 


4.64 


29 


1.250 


27 


-32.62 


37.5 


1.349 


36 


14 36 



Quantity of 75% calcium chloride required to make solutions of different 

specific gravities and freezing points. 

Sp. gravity^ 1.250 1.225 1.200 1.175 1.150 1.125 1.100 

Lbs. per cu ft. solu- 
tion 28.06 25.06 22.05 19.15 16.26 13.47 10.70 

Lbs. per gallon 3.76 3.36 2.95 2.56 2.18 1.80 1.43 

Freezing point ° F. .-32.6 -19.5 -8.7 Zero +7.5 +13.3 +18.5 

Boiling points of calcium chloride solutions : 

Sp. Gr. at 59° F 1.104 1.185 1.238 1.341 

Boiling point ° F. . . 215.6 221.0 230.0 240.8 
Sp.gr.atboilmg point 1.085 1.119 1.209 1.308 



1.383 solid at 59°. 
248.0 266.0 282.2 306.5 
1.365 1.452 1.526 1.619 



* Interpolated. 



1344 ICE-MAKING OR REFRIGERATING-MACHINES 

"Ice-melting Effect." — It is agreed that the term "ice-melting 
effect" means the cold produced in an insulated bath of brine, on the 
assumption that each 144 B.T.U. represents one pound of ice, this 
being the latent heat of fusion of ice. or the heat required to melt a pound 
of ice at 32° to water at the same temperature. The performance of a 
machine, expressed in pounds or tons of "ice-melting capacity," does 
not mean that the refrigerating-machine would make the same amoimt 
of actual ice, but that the cold produced is equivalent to the effect of the 
melting of ice at 32° to water of that temperature. 

m maKing arunciai ice the water frozen is generally about TU*^ b\ when 
submitted to the refrigerating effect of a macliine; second, the ice is 
chilled from 12° to 20° below its freezing-point; third, there is a dissipa- 
tion of cold, from the exposure of the brine tank and the manipulation of 
the ice-cans: therefore the weight of actual ice made, multipUed by its 
latent heat of fusion, 144 thermal units, represents only about three- 
fourths of the cold produced in the brine by the refrigerating fluid per 
I.H.P. of the engine driving the compressing-purnps. Again, there is 
considerable fuel consumed to operate the brine-circulating pump, the 
condensing-water and feed-pumps, and to reboil, or purify, the condensed 
steam from which the ice i'S frozen. This fuel, together with that wasted 
in leakage and drip water, amounts to about one-half that required to 
drive the main steam-engine. Hence the pounds of actual ice manu- 
factured from distilled water is just about half the equivalent of the 
refrigerating effect produced in the brine per indicated horse-power of the 
steam-cylinders. 

When ice is made directly from natural water by means of the '* plate 
system," about half of the fuel, used with distilled w^ater, is saved by 
avoiding the reboiling, and using steam expansively in a compound 
engine. 

Ether-machines, used in India, are said to have produced about 6 lbs. 
of actual ice per pound of fuel consumed. 

The ether machine is obsolete, because the density of the vapor of ether, 
at the necessary working-pressure, requires that the compressing-cylinder 
shall be about 6 times larger than for sulphur dioxide, and 17 times 
larger than for ammonia. 

Air-machines require about 1.2 times greater capacity of compressing 
cylinder, and are, as a whole, more cumbersome than ether machines, 
but they remain in use on shipboard. In using air the expansion must 
take place in a cylinder doing work, instead of through a simple expansion- 
cock which is used with vapor machines. The work done in the expansion- 
cylinder is utilized in assisting the compressor. 

The Allen Dense Air Machine takes for compression air of considerable 
pressure which is contained in the machine and in a system of pipes. The 
air at 60 or 70 lbs. pressure is comi^ressed to 210 or 240 lbs. It is then 
passed through a coil immersed in circulating water and cooled to nearly 
the temperature of the water. It then passes into an expander, which is, 
in construction, a common form of steam-engine with a cut-off valve. 
This engine takes out of the air a quantity of heat equivalent to the 
work done by the air while expanding, to the original pressure of 60 or 
70 lbs., and reduces its temperature to about 90° to 120° F. below the 
temperature of the cooling water supply. The return stroke of the piston 
pushes the air out through insulated pipes to the places that are to be 
refrigerated, from which it is returned to the compressor. 

The air pushed out by the expander is commonly about 35 to 55 below 
zero F. In arrangements where not all the cold is taken out of the air 
by the refrigerating apparatus, the highly compressed air after cooling 
in the coil is further cooled by being brought in surface contact with the 
returning and still cold air, before entering the expander. By this means 
temperatures of 70 to 90 below zero may be obtained. 

The refrigerating effect in B.T.U. per minute is: Lbs. of air handled per 
min. X 0.2375 X difference of temperature of air passing out of ex- 
pander and of that returning to the machine. 

Carbon-dioxide Machines are in extensive use on shipboard. S. H. 
Bunnell (Eng. News, April 9, 1903) says there are over 1500 CO2 plants 
on shipboard. He describes a large duplex CO2 compressor built by the 
Brown-Cochrane Co., Lorain, O. Tests of CO2 machines by a comniittee 
of the Danish Agricultural Society were reported in 1899, in "Ice and 



MACHINES USING DIFFERENT COOLING AGENTS. 1345 

Cold Storage," of London. Carbon-dioxide machines are built also by 
Kroeschel Bros., Chicago. 

Methyl-Chloride machines are made by Railway and Stationary Re- 
frigerating Co., New York City. The compressor is a rotary pump. 
When driven by an electric motor the complete apparatus is very com- 
pact, and is therefore suitable for refrigerator cars or other places where 
space is restricted 

Sulphur-Dioxide Machines. — Results of theoretical calculations 
are given in a table by Ledoux showing an ice-melting capacity per hour 
per horse-power ranging from 134 to 63 lbs., and per pound of coal rang- 
ing from 44.7 to 21.1 lbs., as the temperature corresponding to the pres- 
sure of the vapor in the condenser rises from 59° to 104° F. The theoret- 
ical results do not represent the actual. 

Prof. Denton says concerning Ledoux's theoretical results: The 
figures given are higher than those obtained in practice, because the 
effect of superheating of the gas during admission to the cylinder is not 
considered. This superheating may cause an increase of work of about 
25%. There are other losses due to superheating the gas at the brine- 
tank, and in the pipe leading from the brine-tank to the compressor, so 
that in actual practice a sulphur-dioxide machine, working under the 
conditions of an absolute pressure in the condenser of 56 lbs. per sq. in. 
and the corresponding temperatiu-e of 77° F., will give about 22 lbs. of 
ice-melting capacity per pound of coal, which is about 60% of the theor- 
etical amount neglectiner friction, or 70% including friction. 

Sulphur-dioxide machines are not (1910) used in the United States. 

ttefrigera ting-Machines using Vapor of Water. (Ledoux.) — In 
these machines, sometimes called vacuum machines, water, at ordinary 
temperatures, is injected into, or placed in connection with, a chamber 
in which a strong vacuum is maintained. A portion of the water vapor- 
izes, the heat to cause the vaporization being supplied from the water not 
vaporized, so that the latter is chilled or frozen to ice. If brine is used 
instead of pure water, its temperature may be reduced below the freez- 
ing-point of water. The water vapor is compressed from, say, a pressure 
of 0.1 lb. per sq. in. to 1 M lbs. and discharged into a condenser. It is 
then condensed and removed by means of an ordinary air-pump. The 
principle of action of such a machine is the same as that of volatile- 
vapor machines. 

A theoretical calculation for ice-making, assuming a lower temperature 
of 32° F., a pressure in the condenser of 1 3^2 lbs. per sq. in. and a coal 
consumption of 3 lbs. per I.H.P. per hour, gives an ice-melting effect of 
34.5 lbs. per pound of coal, neglecting friction. Ammonia for ice-making 
conditions gives 40.9 lbs. The volume of the compressing cylinder is 
about 150 times the theoretical volume for an ammonia machine for 
these conditions. 

[The Patten Vacuum Ice Co., of Baltimore, has a large plant on this 
system in operation (1910).] 

Ammonia Compression-machines. — "Cold"' vs» *'Dry'* Systems of 
Compression. — In the "cold" system or "humid" system some of the 
ammonia entering the compression cylinder is liquid, so that the heat 
developed in the cylinder is absorbed by the liquid and the temperature 
of the ammonia thereby confined to the boiling-point due to the con- 
denser-pressure. No jacket is therefore required about the cylinder. 

In the "dry" or "hot" system all ammonia entering the compressor is 
gaseous, and the temperature becomes by compression several hundred 
degrees greater than the boiling-point due to the condenser-pressure. A 
water-jacket is therefore necessary to permit the cylinder to be properly 
lubricated. 

Dry, Wet and Flooded Systems. (York Mfg. Co.) — An expansion 
system, or one where the ammonia leaves the coil slightly superheated, 
requires about 33 5^% more pipe surface than a wet compression system, 
in which the ammonia leaves the coils containing sufficient entrained 
liquid to maintain a wet compression condition in the compressor. 

The flooded system is one where the ammonia is allowed to flow through 
the coils and into a trap, where the gas is separated from the liquid, tlie 
gas passing on to the compressor, while the liquid goes around through 
the coils again, together with the fresh liquid, which is fed into the trap. 
Such a system requires only about one-half the evaporating surface that 



1346 ICE-MAKING OR REFRIGERATING-MACHINES. 

an expansion system does to do the same work. The relative proportions 
of the three systems may be expressed as follows: 

A Dry Compression plant will need, with an Expansion Evaporating 
System, a medimn size compressor, a large size evaporating system, a 
small amount of ammonia. 

A Dry Compression plant will need, with a Flooded Evaporating Sys- 
tem, a small size compressor, a small size evaporating system, a large 
amount of ammonia. 

A Wet Compression plant will need, with a Wet Compression Evapo- 
rating System, a large size compressor, a medium size evaporating sys- 
tem, a medium amount of ammonia. 

The Ammonia Absorption-machine comprises a generator which 
contains a concentrated solution of ammonia in water; this generator 
is heated either directly by a fire, or indirectly by pipes leading from a 
steam-boiler. The vapor passes first into an " analyzer," a chamber con- 
nected with the upper part of the generator which separates some of the 
water from the vapor, then into a rectifier, where the vapor is partly 
cooled, precipitating more water, which returns to the generator, and 
then to the condenser. The upper part of the cooler or brine-tank is in 
communication with the lower part of the condenser. 

An absorption-chamber is filled with a weak solution of ammonia; a 
tube puts this chamber in communication with the cooling-tank. 

The absorption-chamber communicates wirh the boiler by two tubes: 
one leads from the bottom of the generator to the top of the chamber, the 
other leads from the bottom of the chamber to the top of the generator. 
Upon the latter is mounted a piunp, to force the liquid from the absorp- 
tion-chamber, where the pressure is maintained at about one atmosphere 
into the generator, where the pressure is from 8 to 12 atmospheres. 

To work the apparatus the ammonia solution in the generator is first 
heated. This releases the gas from the solution, and the pressure rises. 
When it reaches the tension of the saturated gas at the temperature of 
the condenser there is a hquef action of the gas, and also of a small 
amount of steam. By means of a cock the flow of the hquefied gas into 
the refrigerating coils contained in the cooler is regulated. It is here 
vaporized by absorbing the heat from the substance placed there to be 
cooled. As fast as it is vaporized it is absorbed by the weak solution in 
the absorbing-chamber. 

Under the influence of the heat in the boiler the solution is unequally 
saturated, the stronger solution being uppermost. The weaker portion 
is conveyed by the pipe entering the top of the absorbing-chamber, the 
flow being regulated by a cock, while the pump sends an equal quantity 
of strong solution from the chamber back to the boiler. 

The working of the apparatus depends upon the adjustment and regu- 
lation of the flow of the gas and liquid ; by these means the pressure is 
varied, and consequently the temperature in the cooler may be controlled. 

The working is similar to that of compression-machines. The absorp- 
tion-chamber fills the office of aspirator, and the generator plays the part 
of compressor. The mechanical force producing exhaustion is here re- 
placed by the affinity of water for ammonia gas, and the mechanical force 
required for compression is replaced by the heat which severs this affinity 
and sets the gas at liberty. 

Recce's absorption apparatus (1870) is thus described by Wallis-Taylor. 
The charge of Hquid ammonia (26° Baume) is vaporized by the apphcation 
of heat, and the mixed vapor passed to the analyzer and rectifier, wherein 
the bulk of the water is condensed at a comparatively elevated temperature 
and returned to the generator. The ammoniacal vapor or gas is then 
passed to the condenser, where it is liquefied under the combined action 
of the cooling-water and of the pressure maintained in the generator. The 
hquid ammonia, practically anhydrous, is then used in the refrigerator, 
and the vapor therefrom, still under considerable pressure, is admitted to 
the cyUnder of an engine used to drive a pump for returning the strong 
solution to the generator, after which it is passed to the absorber, where 
it meets and is absorbed by the weak liquor from the generator, and the 
strong liquor so formed is forced back into the generator by means of the 
pump. The temperature exchanger, introduced in 1875, provides for 
the hot liquor on its way from the generator to the absorber giving up 
its heat to the cooler liquid from the absorber on its way to the generator. 

Wallis-Taylor describes also marine refrigerating, ice-making cold 



AAIMONIA MACHINES. 



1347 



Storage, the application of refrigeration in breweries, dairies, etc.; and the 
management and testing of apparatus. 

For the best results the following conditions are necessary (Voorhees): 
1. The generator should have ample liquid evaporating surface to make 
dry gas. 2. The temperature of the gas to the rectiher should be as low 
as possible. 3. The drip liquor returned to the generator from the recti- 
fier should be as hot as possible. 4. The gas from the rectifier to the 
condenser should not be over 10° to 50° hotter than the condensing tem- 
perature of the gas. 5. The exchanger should exchange upwards of 
90% of the heat of the hot weak liquor to the cold strong liquor. The 
weight of strong liquor pumped should be from 7 to 8 times that of the 
anhydrous ammonia circulated in the refrigerator. 

To produce one ton of refrigeration at 8.5 lbs. suction and 170 lbs. gauge 
condenser pressure, about 3.5 times as manjr heat units are actually used 
by an absorption machine as by a compression machine (compound con- 
densing engine driven), but, owing to the low efficiency of the steam 
engine, due to the heat wasted in the exhaust and in cylinder condensation, 
the actual weight of steam used per hour per ton of refrigeration is the 
same for both the absorption machine and the compressor. 

Relative Performance of Ammonia Compression- and Absorp- 
tion- machines, assuming no Water to be Entrained with the 
Ammonia-gas in the Condenser. (Denton and Jacobus, Trans. A. S. 
M. E., xiii.) — It is assumed in the calculation for both machines that 
1 lb. of coal imparts 10,000 B.T.U. to the boiler. The condensed steam 
from the generator of the absorption-machine is assumed to be returned 



Condenser. 


Refrigerat- 
ing Coils. 


^ 


Pounds of Ice-melting Effect 
per lb. of Coal. 


S^'2 




u 




u 


Compress. 


Abso 


rption- 


2H^ 




73 


1 

TO 


ft 

DO 

i 


1 


Machine. 


Machine.* 


g«3 


1 




-3 


achine in 
ammonia 

ump ex- 
the gen- 


be amm. 

exhausts 

mosphere 

heater, 

temp, to 


2-S.2 


1 




1 


ft 


1 

< 






bion-m 
the 

ting-p 
into 


ich tJ 
pump 
he at 
:h a 
g 212° 
d-wat( 


3 t. O 


1 


1 a 


d 





ft 

S 


tr, ft 


•" o 
.£ S3 


A-bsorpi 
which 
cireula 
hausts 
era tor. 


In wh 
circ. ] 
into t 
throug 
yieldin 
the fee 


Heat f 
of abso 
per lb. 


61.2 


110.6 


5 


33.7 


61.2 


38.1 


71.4 


38.1 


33.5 


969 


59.0 


106.0 


5 


33.7 


59.0 


39.8 


74.6 


38.3 


33.9 


967 


59.0 


106.0 


5 


33.7 


130.0 


39.8 


74.6 


39.8 


35.1 


931 


59.0 


106.0 


-22 


16.9 


59.0 


23.4 


43.9 


36.3 


31.5 


1000 


86.0 


170.8 


5 


33.7 


86.0 


25.0 


46.9 


35.4 


28.6 


988 


86.0 


170.8 


5 


33.7 


130.0 


25.0 


46.9 


36.2 


29.2 


966 


86.0 


170.8 


-22 


16.9 


86.0 


16.5 


30.8 


33.3 


26.5 


1025 


86.0 


170.8 


-22 


16.9 


130.0 


16.5 


30.8 


34.1 


27.0 


1002 


104.0 


227.7 


5 


33.7 


104.0 


19.6 


36.8 


33.4 


25.1 


1002 


104.0 


227 7 


-22 


16 9 


104.0 


13.5 


25.3 


31.4 


23.4 


1041 



*5% of w^ater entrained in the ammonia will lower the economy of 
the absorption-machine about 15% to 20% below the figures given in 
the table. 

to the boiler at the temperature of the steam entering the generator. 
The engine of the compression-machine is assumed to exhaust through a 
feed- water heater that heats the feed-water to 212° F. The engine is 
assumed to consume 26 1/4 lbs. of water per hour per horse-power. The 
figures for the compression-machine include the effect of friction, which 
is taken at 15% of the net work of compression. 

(For discussion of the efficiency of the absorption system, see Ledoux's 
work; paper by Prof. Linde, and discussion on the same by Prof. Jacobus, 
Trans. A. S. M. E., xiv. 1416. 1436; and papers by Denton and Jacobus, 
Trans. A. S. M. E., x. 792, xiii. 507. 



1348 ICE-MAKING OR REFRIGERATING-MACHINES. 



Relative Efficiency of a Refrigerating-Machine. — The efficiency 
of a refrigerating-machine is sometimes expressed as the quotient of 
the quantity of heat received by the ammonia from the brine, that is, the 
quantity of useful work done, divided by the heat equivalent of the 
mechanical work done in the compressor. Thus in column 1 of the table 
of performance of the 75-ton machine (page 1363) the heat given by the 
brine to the ammonia per minute is 14,776 B.T.U. The horse-power of 
the ammonia cyhnder is 65.7, and its heat equivalent = 65.7 x 33,000 -^- 
778 = 2786 B.T.U. Then 14,776 -^ 2786 = 5.304, efficiency. The ap- 
parent paradox that the efficiency is greater than unity, which is im- 
possible in any machine, is thus explained. The working fluid, as 
ammonia, receives heat from the brine and rejects heat into the condenser. 
(If the compressor is jacketed, a portion is rejected into the jacket-water.) 
The heat rejected into the condenser is greater than that received from the 
brine; the difference (plus or minus a small difference radiated to or from 
the atmosphere) is heat received by the ammonia from the compressor. 
The work to be done by the compressor is not the mechanical equivalent 
of the refrigeration of the brine, but only that necessary to supply the dif- 
ference between the heat rejected by the ammonia into the condenser and 
that received from the brine. If cooling water colder than the brine were 
available, the brine might transfer its heat directly into the cooling water, 
and there would be no need of ammonia or of a compressor; but since such 
cold water is not available, the brine rejects its heat into the colder 
ammonia, and then the compressor is required to heat the ammonia to 
such a temperature that it may reject heat into the cooling water. 

The maximum theoretical efficiency of a refrigerating machine is ex- 
pressed by the quotient To -^ (Ti - To), in which Ti is the highest and To 
the lowest temperature of the ammonia or other refrigerating agent. 

The efficiency of a refrigerating plant referred to the amount of fuel 
consumed is 

/^Tspefflct*lt r/ange'l °' brine or other 
Ice-melting capacity J ^ i of t?m%e?a'iurl '^"'" / circulating fiuld 
per pound of fuel j 



144 X pounds of fuel used per hour 



Cold Watef 



1 1 



Condenser 



I 1 



Compressor ' 



209 '^ 



ao Brine Oatlet 



Ammonia 
Coils 



Cold Room 



85^ 



Warm Water 
Heat rejected 



Heat received 
from compression. 



W 



Heat received 
from brine 



Inlet 



DIAGRAM OF AMMONIA COMPRESSION MACHINE. 



llw 



Condenser 



Gener- 
ator 



Cold 
Room 



u 



J^=C3== 



80°ll i ""=. 



Torce Pump 



DIAGRAM OF AMMONIA ABSORPTION MACHINC. 



EFFICIENCY OF REFRIGERATING SYSTEMS. 1349 

The Ice-raelting capacity is expressed as follows: 

Tons (of 2000 lbs.) ^ { ^^ x Fpedfic heat | ^^ ^""^ honr^^^^^ ^^' 
ice-melting ca- t^ ^ x range of temp. ) '^^^ 



Ti 



pacity per 24 hours J 144 x 2000 

The analogy between a heat-engine and a rcfngerating-machine is as 
follows: A steam-engine receives heat from the boiler, converts a part 
of it into mechanical work in the cylinder, and throws away the differ- 
ence into the condenser. The ammonia in a compression refrigerating- 
machine receives heat from the brine-tank or cold room, receives an 
additional amount of heat from the mechanical work done in the com- 
pression-cyhnder, and throws away the sum into the condenser. The 
efficiency of the steam-engine = work done -i- heat received from boiler. 
The efficiency of the refrigerating-machino = heat received from the 
brine-tank or cold-room ^ heat required to produce the work in the 
compression-cylinder. In the ammonia absorption-apparatus, the 
ammonia receives heat from the brine-tank and additional heat from 
the boiler or generator, and rejects the sum into the condenser and into 
the cooling water supplied to the absorber. The efficiency = heat 
received from the brine -^ heat received from the boiler. 

The Efficiency of Refrigerating Systems depends on the tempera- 
ture of the condenser water, whether there is sufficient condenser 
surface for the compressor and whether or not the condenser pipes are 
free from uncondensable foreign gases. With these things right, con- 
denser pressure for different temperatures of cooling water should be 
approximately as follows: 

1 gallon per minute per ton per 24 hours 

—Cooling water, ° F 60 65 70 75 80 85 90 

Condenser pressure, gage, lb 183 200 220 235 255 280 300 

Condensed liquid ammonia, °F 95 100 105 110 115 120 125 

2 gallons per minute per ton per 24 

hours — Condenser pressure, gage, lb . 130 153 168 183 200 220 235 
Condensed Uquid ammonia, ° F 77 85 90 93 100 105 110 

3 gallons per minute per ton per 24 

hours — Condenser pressure, gage, lb. 125 140 155 170 185 200 215 

Condensed Uquid ammonia, ° F 75 85 90 93 95 100 105 

The evaporating or back pressure within the expansion coils of a re- 
frigerating system depends upon the temperatures on the outside of such 
coils, i.e., the air or brine to be cooled. For average practice back pres- 
sures for the production of required temperatures should be approxi- 
mately as follows: 

Temperature of room. ° F 10 15 20 28 32 36 40 50 60 

Back pressure, gage, lb 10 12 15 22 25 27 30 35 40 

Temperature of ammonia, ° F. —10 —5 8 12 14 17 22 26 
The condenser pressure should be kept as low as possible and the back 
pressure as high as possible, narrow limits between such pressures being 
as important to the efficiency of a refrigerating system as wide ones are 
to that of a steam engine in which the economy increases with the range 
between boiler pressure and condenser pressure. (F. E. Matthews, 
Power, Jan. 26, 1909.) 

Cylinder-lieating. — In compression-machines employing volatile 
vapors the principal cause of the difference between the thc^orotical and 
the practical result is the heating of the ammonia, by the warm cylinder 
walls, during its entrance into the compressor, thereby expanding it. so 
that to compress a pound of ammonia a greater number of revolutions 
must be made by the compressing-pumps than corresponds to the density 
of the ammonia-gas as it issues from the brine-tank. t 

Volumetric Efficiency. — The volumetric efficiency of a compressor 
is the ratio of the actual weight of ammonia pumped to the amount 
calculated from the piston displacement. Mr. Voorhees deduces from 
Denton's experiments the formula: Volumetric efficiency = JS = 1 — 
(h— ^o)/1330, in which h = the theoretical temperature of gas after 
compression and ^i = temperature of gas delivered to the compressor. 
The temperature h, = Ti — 460, is calculated from the formula for adia- 
batic compression, Ti = To (Pi/Po) 0*2*, in which Ti and To are absolute 
temperatures and Pi and Po absolute pressures. In eight tests by Prof. 
Denton the volumetric eflaciency ranged from 73.5% to 84%, and they 



1350 ICE-MAKING OR REFRIGERATING-MACHINES. 



vary less than 1 % from the efficiencies calculated by the formula. The 
temperature of the gas discharged from the compressor averaged 57° less 
than the theoretical. 

The volumetric efficiency of a dry compressor is greatest when the va- 
por comes to the compressor with little or no superheat; 30° superheat of 
the suction gas reduces the capacity of the compressor 4% , and 100° 9%. 

The following table (from Voorhees) gives the theoretical discharge, 
temperatures (h) and volumetric efficiencies (E) by the formula, and the 
actual cubic feet of displacement of compressor (F) per ton of refrigera- 
tion per minute for the given gage pressures of suction and condenser. 

Suction Pressures. 



Cond. press., 140. . 
Cond. press., 170. . 
Cond. press., 200. . 












15 






30 


tl 

323° 
221° 
167° 


E 
0.76 
0.83 
0.87 


F 
10.35 
4.57 
2.96 


tl 
358° 
254° 
192° 


E 
0.73 
0.81 
0.86 


F 
11.02 
4.78 
3.07 


tl 

388° 
280° 
216° 


E 
0.71 
0.79 
0.84 



F 
11.57 
5.03 
3.21 



Pounds of Ammonia per Minute to Produce 1 Ton of Refrigeration, 
and Percentage of Liquid Evaporated at the Expansion Valve. 



Condenser Pressure and 
Temperature. 



Refrigerator, pressure and 
temperature lbs., -29°... 

Refrigerator pressure and 
temperature 15 lbs.,-0°... 

Refrigerator pressure and 
temperature, 30 lbs. ,-17''.. 



140 lbs., 80° 



170 lbs., 90°. 



200 lbs., 100° 



0.431 lb., 19% 
0.420 lb., 14.4% 
0.415 lb., 11.6% 



0.441 lb., 20.8% 
0.4301b., 16.2% 
0.425 lb., 13.4% 



0.451 lb.\ 22.5% 
0.4401b., 18.0% 
0.4341b., 15.2% 



Mean Effective Pressure, and Horse-power. — Voorhees deduces 
the following {Ice and Refrig., 1902) : M.E.P. = 4.333 po [{pi/po) o-23i — i], 
Pq = suction and pi condenser pressure, abs. lbs. per sq. in. The maxi- 
miun M.E.P. occurs when po = pi -^ 3.113. The percentage of stroke 
during which the gas is discharged from the compressor is Vi = (po/pi)^'''^^. 

The compressor horse-power, C.H.P., is 0.00437 F X M.E.P. 

The friction of the compressor and its engine combined is given by 
Voorhees as 33V3% of the compressor H.P. or 25% of the engine H.P. 
Values of the mean effective pressure per ton of refrigeration (M), the 
compressor horse-power (C) and the engine horse-power (E) are given 
below for the conditions named. 



Suction Pressure. 





15 


30 


Cond. press., 140... 
Cond. press., 170.. . 
Cond. press., 200... 


(M) 
46.5 
50.5 
55.0 


(C) 
2.10 
2.42 
2.78 


(E) 
2.80 
3.23 
3.71 


(M) 
59.5 
67.0 
74.5 


(C) 
1.19 
1.40 
1.64 


(E) 
1.59 
1.87 
2.19 


(M) (C) 
64.5 0.83 
75.0 1.00 
85.0 1.19 


(E) 
1.11 
1.33 
1.59 



By cooling the liquid between the condenser and the expansion valve 
the capacity will be increased and the horse-power per ton reduced. With 
compression from 15 to 170 lbs., if the hquid at the expansion valve is 
cooled to 76° instead of 90° the H.P. per ton will be reduced 3%. 

Prof. Lucke deduces a formula for the I. H.P. per ton of refrigerating 
capacity, as follows: 

p = mean effective pressure, lbs. per sq. in. ; L = length of stroke in 
ft.; a = area of piston in sq. ins. ; n = no. of compressions per minute; 
Ec = apparent volumetric efficiency, the ratio of the volume of ammonia 
apparently taken in per stroke to the full displacement of the piston; 
Wc = weight of 1 cu.ft. of ammonia vapor at the back pressure, as it 
exists in the cylinder when compression begins; Lc — latent heat of 
vaporization available for refrigeration; 288.000 = B.T.U. equivalent 
to 1 ton of refrigeration ; T = tons refrigeration per 24 hours. 
I. HP. ^ pLan -?- 33.000 0.87 ^ _p_ 

T ~ LaEc nwc X I^c X 60 X 24 ~ WcLc Ec 
144 X 288,000 

The Voorhees Multiple Effect Compressor is based upon the fact 
that both the economy and the capacity of a compression machine vary 
with the back pressure. In the past it has always been necessary to run a 
compressor at a gas suction pressure corresponding to the lowest required 



QUANTITY OF AMMONIA EEQUIRED. 



1351 



temperature. » The multiple effect compressor takes in gas from two or 
more refrigerators at two or more different suction pressures and tem- 
peratures on the same suction stroke of the compressor. The suction gas 
of the higher pressure helps to compress the lower suction pressure gas. 
There are two sets of suction valves in the compressor cjiindcr ; the low 
temperature and corresponding low back pressure being connected to 
one suction port, usually in the cylinder head, and the high back pres- 
sure connected to the other. At the beginning of the stroke the cylinder 
is filled with the low pressure gas and as the piston reaches the end of its 
suction stroke, the second or high back pressure port is uncovered, the 
low pressure suction valve closing automatically, and the cylinder is 
completely filled with gas at the high pressure. By this means the 
C9mpressor operates with an economy and capacity corresponding to the 
higher back pressure, making a gain in capacity of often 50% or more. 
{Trans. Am, Soc. Refrig. Engrs., 1906.) 

Quantity of Ammonia Required per Ton of Refrigeration.— 
The tollowing table is condensed from one given by F. E. Matthews in 
Trans. A. S ME., 1905. The weight in lbs. per minute is calculated 
from the formula P = (144 X 2000) ^ [1440 Z - {ht - /io)J in which 
2 IS the latent heat of evaporation at the back pressure in the cooler, and 
hi and /?o the heat of the liquid at the temperatures of the condenser and 
the cooler respectively. The specific heat of the liquid has been taken 
at unity. The ton of refrigeration is 2000 lbs. in 24 hours = 288,000 

js.r.u. 

B = rounds of ammonia evaporated per minute. 

C = Cubic feet of gas to be handled per minute by the compressor. 



I 




Head or Condenser Gauge Pressure and Corresponding 
Temperature. 


w. 
B.P. 


100 

lb. 
63.5° 


110 

lb. 
68° 


120 

lb. 
72.6° 


130 

lb. 
77.4° 


140 

lb. 
80.3° 


150 

lb. 

83.8° 


160 

lb. 
87.4° 


170 

lb. 
90.8° 


180 

lb. 
93.8° 


190 

lb. 
96.9° 


200 

lb. 
100° 


572.78 ) 
.0556 



B 
C 


.4159 
7.482 


.4199 
7.551 


.4240 
7.626 


.4284 
7.703 


.4310 
7.761 


.4343 
7.812 


.4376 
7.870 


.4408 
7.929 


.4440 
7.986 


.4470 
8.041 


.4501 
8.095 


566.14 ) 
.0>33J 


B 
C 


.4122 
5.636 


.4160 
5.675 


.4202 
5.732 


.4243 
5.790 


.4271 
5.826 


.4308 
5.878 


.4335 
5.914 


.4366 
5.970 


.4397 
5.999 


.4437 
6.039 


.4458 
6.081 


560.69 ) 

.0910 } 

10 ) 


B 
C 


.4093 
4.502 


.4130 
4.543 


.4171 
4.587 


.4204 
4.625 


.4237 
4.662 


.4271 
4.698 


.4302 

4.733 


.4332 
4.766 


.4363 
4.799 


.4392 
4.833 


.4423 
4.865 


556.11) 

.1083 } 

15 ) 


B 
C 


.4068 
3.756 


.4106 
3.791 


.4145 
3.827 


.4186 
3.866 


.4211 
3.889 


.4244 
3.918 


.4276 
3.948 


.4288 
3.975 


.4336 
4.003 


.4365 
4.030 


.4394 
4.058 


552.83 ) 

.1258 ; 

20 ) 


B 
C 


.4040 
3.2! 1 


.4077 
3.241 


.4116 

3.272 


.4158 
3.305 


.4182 
3,324 


.4214 
3.350 


.4245 
3.375 


.4275 
3.398 


.4304 

3.422 


.4333 
3.444 


.4362 
3.467 


548.40) 
.1429 } 
25 ) 


B 
C 


.4025 
2.819 


.4062 
2.843 


.4102 
2.870 


.4140 
2.898 


.4167 
2.916 


.4198 
2.938 


.4229 
2.959 


.4258 
2.980 


.4287 
3.000 


.4316 
3.020 


.4345 
3.040 


545.13 ) 
.1600 S 
30 ) 


B 
C 


.4013 
2.507 


.4049 
2.530 


.4088 
2.555 


.4128 
2.580 


.4152 
2.600 


.4184 
2.615 


.4213 
2.633 


.4243 
2.653 


.4273 
2.671 


.4300 
2.687 


.4329 
2.706 


542.80 ) 
.1766 S 
35 ) 


B 
C 


.3991 
2.260 


.4028 
2.280 


.4066 
2.302 


.4105 
2.925 


.4130 
2.338 


.4161 
2.356 


.4188 
2.373 


.4220 
2.390 


.4249 
2.406 


.4277 

2.422 


.4305 
2.443 


539.35 ) 
.1941 { 
40 \ 


B 
C 


.3984 
2.052 


.4020 
2.071 


.4058 
2.090 


.4098 
2.111 


.4122 
2.123 


.4153 
2.139 


.4183 
2.155 


.4211 
2.175 


.4240 
2.185 


.4269 
2.200 


.4296 
2.214 



I, Latent heat of volatilization, w, weight of vapor per cubic foot. 
B.P. back pressure or suction gauge pressure. 

Back pressures 5 10 15 20 25 30 35 40 

Temperatures. -28.5° -17.5° -8.5° -1°5.66° 11.5° 16.8° 21.7° 26.1° 

Mr. INIatthews defines a standard ton of refrigeration as the equiva- 
lent of 27 lbs. of anhydrous ammonia evaporated per hour from liquid 



1352 ICE-MAKING OR REFRIGERATING-MACHINES. 



at 90° F. into saturated vapor at 15.67 lbs. gauge pressure (0° F.). 
which requires 12,000 B.T.U.; or 20,950 units of evaporation, each of 
wliich is equal to 572.78 B.T.U., the heat required to evaporate 1 lb. 
of ammonia from a temperature of — 28.5° F. into saturated vapor at 
atmospheric pressure. 

Size and Capacities of Ammonia Refrigerating - Machines. — 
York Mfg. Co. Based on 15.67 lbs. back pressure, 185 lbs. condensing 
pressure, and condensing water at 60° F. 



SiNGLE-ACTING COMPRESSORS. 


DOUBLE-ACTING COMPRESSORS. 


Compressors . 


Engine. 


Capacity 


Compressors. 


Engine. 


Capacity 








Tons 






I 


Tons 


Bore. 


Stroke. 


Bore. Stroke. 


Refrig- 
eration. 


Bore. 


Stroke. 


Bore. [Stroke. 


Refrig- 
eration. 


7 1/2 10 


lll'o 10 


10 


9 


15 


13 1/2 


12 


20 


9 


12 


13l/>i 12 


20 


11 


18 


16 


15 


30 


11 


15 


16 


15 


30 


12 1/2 


21 


18 


18 


40 


12 1/^ 


18 


18 


18 


40 


14 


24 


20 


21 


65 


14 


21 


20 


21 


65 


16 


28 


24 


24 


90 


16 


24 


24 


24 


90 


18 


32 


26 


28 


125 


18 


28 


26 


28 


125 


21 


36 


28 1/2; 32 


175 


21 


32 


28 1/2 


32 


175 


24 


40 


34 


36 


250 


24 


36 


34 


36 


250 


26 


60 


38 


54 


350 


27 


42 


36 


42 


350 












30 


48 


44 


48 


500 













For larger capacities the machines are built with duplex compressors, 
driven by simple, tandem or cross compound engines. 

Displacement and Horse-power per Ton of Refrigeration 
Dry Compression. S.A., Single-acting; D.A., Double-acting. 





Suction Gauge Pressure and Corresponding Temp. 




5 1b. = 


10 1b. = 


15.67 lb. 


20 lb. = 


25 lb. = 


Condenser Gauge 


- 17.5° F. 


- 8.5° F. 


= 0° F. 


5.7° F. 


11.5°F. 


Pressure and 


























Corresp. Temp. 






















g 


of Liquid at 
Expansion Valve. 


5& 






Kg, 


5& 




w 1 • fc- 








u 






9.811 


h-t 


U 




1 HH 


u 




1451b. 82° F.,S.A... 


12.608 


1.654 


1.4 7829 


1.195 


6765^ 1.065 5836 0.943 


1451b. 82°F., D.A.. 


14.645 


1.921 


11,300 


1.612 8901 


1.358 


7625 1.2 ,6522 1.054 


1651b. 89° F.,S.A.. 


13.045 


1.834 


10.148 


1.56 !8092 


1.341 


6990 1.201602711.071 


1651b. 89° F., D.A. 


15.203 


2.137 


11.720 


1.802 9224 


1.529 


7898 1.357 6751 1.2 


1851b. 95.5° F.,S.A. 


13,491 


2.013 


10.487 


1.72 18362 


1 .4865 


7219 


1.336,6223 1.197 


1851b. 95.5° F.,D.A. 


15,774 


2.354 


12.150 


1.993:9555 


1.7 


8176 


1.513 6985|1.344 


2051b.l01.4°F.,S.A. 


13.947 


2.192 


10.834 


1.879 8630 


1.631 


7450 


1.47 6420 1.323 


2051b.l01.4°F.,D.A. 


16.362 


2.571 


12.590 


2.184,9890 


1.87 


8459 


1.67 72221 1. 488 



* Cu. in. Displacement per Min. per Ton of Refrigeration. 

The volumetric efficiency ranges from 63.5 to 76.5% for double-acting 
and from 74.5 to 85.5 % for single-acting compressors, increasing with the 
decrease of condenser pressure and with the increase of suction pressure. 

Where the liquid is cooled lower than the temperature corresponding 
to the condensing pressure, there will be a reduction in horse-power and 
displacement proportional to the increase of work done by each poimd 
of liquid handled. The I. H.P. is that of the compressor. For Engine 
Horse-power add 17% up to 20 tons capacity and 15% for larger machines. 

Small Sizes of Refrigerating-Machtnes. 



Capacity, tons 

Compressor, diam., in. 
Compressor, stroke, in 

Engine, diam., in 

Engine, stroke, in ... . 



Single-acting, 


Double-acting, 


Vertical. 


Horizontal. 


1 1/4 


3 


6 


21/2 
4 


6 


10 


41/?, 


6 


2-6 


51/2 


7 


5 


6 


6 


6 


8 


10 


5 


6 


8 


6 


8 


10 


5 


6 


6 


8 


8 


10 



CONDENSERS FOR REFRIGBRATING-MACHINES. 



1353 



Rated Capacity of Refrigerating-3Iachines. — It is customary to 
rate refrigerating machines in tons of refrigerating capacity in 24 hours, 
on the basis of a suction pressure of 15.67 lbs. gauge, corresponding to 
0° F. temperature of saturated ammonia vapor, and a condensing pressure 
of 185 lbs. gauge, corresponding to 95.5'^ F. The actual capacity increases 
with the increase of the suction pressure, and decreases with the increase 
of the condensing pressure. The following table shows the calculated 
capacities and horse^power of a machine rated at 40 H.P., when run at 
different pressures. (York Mfg. Co.) The horse-power required increases 
with the increase of both the suction and the condensing pressure. 



Condenser Press. 
Temp. 



145 1b. = 82° F. . 
165 1b. = 89° F. . 
185 1b. = 95.5° F. 
205 1b. = 101.4° F. 



Suction Gauge Pressure and Corresponding Temp. 
5lbr^ TOlb. = 1576ribr"20lb7= 25 Ib.^, 30 Ib.^ 
-17.5°F -8.5°F. =0°F. 5.7° F. 11.5°F.I 16.8°F. 



H 

26.6 
25.7 
24.8 
24 



a 

50.6 
54.2 
57.4 
60.5 



34.2 
33.1 
32 
31 



a 

55.1 
59.4 
63.3 
67 



Eh 

42.8 
41.4 
40 
38.9 



a 

58.8 
63.8 
68.6 
72.9 



H 

49.6 
48 
46.5 
45 



Ph 

a 

60.7 
66.3 
71.4 
76.1 



Eh 
57.5 

55.7 
53.9 



a_ 

62.3 
6 
74.2 



65.3 
63.2 



a 

63.4 
70.1 



61.3 76.5 
52.3:79.6|59.4i86.2 



Piston Speeds and Revolutions per Minute. — There is a great diver- 
sity in the practice of difJerent builders as to the size of compressor, the 
piston speed and the number of revolutions per minute for a given 
rated capacity. F. E. Matthews, Trans. A. S. M. E., 1905, has plotted 
a diagram of the various speeds and revolutions adopted by four promi- 
nent builders, and from average curves the following figures are obtained : 

Tons 20 30 40 50 60| 80 100 120 140 160 180^00 240! 300]40^ ^500 

R.P.M 90 78 73 68 64 60 581/2 57| 56 55 54 53 52 51 481/2 46 

Piston speeds. 200 215 228 240 250 1270 280 2861290 293 296 300 31 5|340, 378 i425 

Mr. Matthews recommends a standard rating of machines based on 
these revolutions and speeds and on an apparent compressor displace- 
ment of 4.4 cu. ft. per minute per ton rating. 

Condensers for Refrigerating'-3Iachines are of two kinds: sub- 
merged, and open-air evaporative. The submerged condenser requires 
a large volume of cooling water for maximum efficiency. According 
to Siebel the amount of condensing surface, the water entering at 70° 
and leaving at 80°, is 40 sq ft. for each ton of refrigerating capacitv, or 
64 lineal feet of 2-in. pipe. Frequently only 20 sq. ft., or 90 ft. of lV4-in. 
pipe, is used, but this necessitates higher condenser pressures. If F = 
sq. ft. of cooling surface, h = heat of evaporation of 1 lb. ammonia at 
the condenser temperature, K = lbs. of ammonia circulated per minute, 
m = B.T.U. transferred per minute per sq. ft. of condenser surface, 
t = temperature ot the ammonia in the coils and ti the temperature of 
the water outside, F = JiK -r m{t - ti). For t = SO and U = 70, m 
may be taken at 0.5. Practically the amount of water required will 
vary from 3 to 7 gallons per minute per ton of refrigeration. When 
cooling water is scarce, cooling towers are commonly used. 

E. T. Shinkle gives the average surface of several submerged con- 
densers as equal to 167 lineal feet of 1-in. pipe per ton of refrigeration. 

Open air or evaporation surface condensers are usually made of a stack 
of parallel tubes with return bends, and means for distributing the water 
so that it will flow uniformly over the pipe surface. tShinkle gives as the 
average surface of open-air coolers 142 ft. of 1-in. pipe, or 99 ft. of 11/4 in. 
pipe per ton of refrigerating capacity. 

Capacity of Condensers. (York Mfg. Co.) — The following table 
shows the capacities and horse-power per ton refrigeration of one section 
counter-current double-pipe condenser, 1 i/i-in. and 2-in. pipe, 12 pipes 
high, 19 feet in length outside of water bends, for water velocities 100 ft. 
to 400 ft. per minute: initial temperature of condensing water 70°. 

The horse-power per ton is for single-acting compressor with 15.67 
lbs. suction pressiu-e. 

The friction in water pump and connections should bo added to 
water horse-power and to total horse-power. 



1354 ICE-MAKING OR REFRIGERATING-MACHINES. 



Capacity of Condensers 



High Pressure Constant. 



Condensing Water. 


Capy 
Tons 
Refrig. 
per 24 
hours. 


Con- 
densing 
Pressure 
Lbs. per 
sq. in. 


Horse-power per Ton 
Refrigeration. 


Veloc- 
ity 

thr'gh 

il/4-in. 
pipe. 

Ft. per 
min. 


Total 

gallons 

used 

per 

mm. 


Gallons 
per min 
per ton 
Refrig. 


Fric- 
tion 

thr'gh 

Coil. 

Lbs. 

per 

sq.m. 


Engine 
driving 
Com- 
pressor 


Circu- 
lating 
Water 
thr'gh 
Con- 
denser. 


Total 
Engine 

and 
Water 
Circu- 
lation. 


100 
150 
200 
250 
300 
400 


7.77 
11.65 
15.54 
19.42 
23.31 
31.08 


1.16 

1.165 

1.165 

1.18 

1.24 

1.30 


2.28 
5.75 
9.98 
15. 
21.6 
37.8 


6.7 
10. 
13.4 
16.4 
18.8 
24. 


185 
185 
185 
185 
185 
185 


1.71 
1.71 
1.71 
1.71 
1.71 
1.71 


0.0016 

0.004 

0.007 

0.011 

0.016 

0.030 


1.7116 

1.714 

1.717 

1.721 

1.726 

1.74 



Capacity Constant. 



100 


7.77 


0.777 


2.28 


10. 


225 


2.04 


0.001 


2.041 


150 


11.65 


1.165 


5.75 


10. 


185 


1.71 


0.004 


1.714 


200 


15.54 


1.554 


9.98 


10. 


165 


1.54 


0.009 


1.549 


250 


19.42 


1.942 


15. 


10. 


155 


1.46 


0.018 


1.478 


300 


23.31 


2.331 


21.6 


10. 


148 


1.40 


0.030 


1.43 


400 


31.08 


3.108 


37.8 


10. 


140 


1.33 


0.071 


1.401 



Cooling-Tower Practice in Refrigerating - Plants. (B. F. Hart, 
.Jr., Southern Engr., Mar., 1909.) — The efiQciency of a cooling-tower de- 
pends on exposing the greatest quantity of water surface to the cooling 
air-currents. In a tower designed to handle 100 gallons per minute the 
ranges of temperature found when handling different quantities of 
water were as follows: 

Gallons of water per minute ' 

Temperature of the atmosphere 

Relative humidity, % 

Initial temperature 85.5° 

Final temperature 

Range 

The final temperatures which may be obtained 
temperature does not exceed 100° are as foUows: 



148 


109 


58 


78° 


78.5° 


78^ 


47 


49 


47 


85.5° 


85° 


86' 


78° 


76° 


75' 


7.5° 


9° 


ir 


when 


the ii 


litia 



Atmosphere Temp. 


95° 1 90° 1 85° 1 80° | 75° 1 70° 




Final temperature of water leaving tower. 




r9o 


100 


95 


90 


85 


80 


75 




80 


98 


92 


88 


83 


78 


73 


Humidity, % - 


70 
60 


95 
92 


90 
88 


86 
83 


80 
78 


76 

74 


71 
69 




50 


89 


84 


79 


75 


70 


66 




L40 


85 


80 


76 


71 


67 


63 



For ammonia condensers we figure on supplying 3 gallons per minute of 
circulating water per ton of refrigeration, or 6 gallons per minute per ton of 
ice made per 24 hours, and guarantee a reduction range from 150° to 160° 
down to about 100° when the temperature of the atmosphere does not 
exceed 80° nor the relative humidity 60%. When the temperature of the 
atmosphere and the humidity are both above 90° the speed of the pumps 
and the ammonia pressure must be increased. 

The Refrigerating-Coils of a Pictet ice-machine described by Ledoux 
had 79 sq. ft. of surface for each 100,000 theoretic negative heat-units 
produced per hour. The temperature corresponding to the pressure of 
the dioxide in the coils is 10.4° F., and that of the bath (calcium chloride 
solution) in which they were immersed is 19.4°. 



TEST-TRIALS OF REFRIGERATING-MACHINES. 1355 



Comparison of Actual and Theoretical lee-melting Capacity.— 

The following is a comparison of the theoretical ice-melting capacity of 
an ammonia compression machine with that obtained in some of Prof. 
Schroter's tests on a Linde macliine having a compression-cylinder 
9.9-in. bore and 16.5 in. stroke, and also in tests by Prof. Denton on a 
machine having two single-acting compression-cylinders, 12 in. x 30 in.: 



No of 


Temp, in Degrees F. 
Corresponding to 
Pressure of Vapor. 


Ice-melting Capacity per lb. of Coal, 

assuming 3 lbs. per hour per 

Horse-power. 


Test. 


Condenser. 


Suction. 


Theoretical 
Friction* 
Included. 


Actual. 


Per cent of 
Loss Due to 
Cylinder 
Superheating. 


Ij 2 

lb 

1 (24 
1^26 
^125 


72.3 
70.5 
69.2 
68.5 

84.2 
82.7 
84.6 


26.6 

14.3 

0.5 

-11.8 

15.0 
- 3.2 
-10.8 


50.4 
37.6 
29.4 
22.8 

27.4 
21.6 
18.8 


40.6 
30.0 
22.0 
16.1 

24.2 
17.5 
14.5 


19.4 
20.2 
25.2 
29.4 

11.7 
19.0 
22.9 



* Friction taken at figures observed in the tests, which range from 
14 % to 20 % of the work of the steam-cylinder. 

TEST-TRIALS OF REFRIGERATEVG-MACHINES. 

(G. Linde, Trans. A. S. M. E., xiv, 1414.) 
The pm-pose of the test is to determine the ratio of consumption and 
production, so that there will have to be measured both the refrigera- 
tive effect and the heat (or mechanical work) consumed, also the cool- 
ing water. The refrigerative effect is the product of the number of 
heat-units (Q) abstracted from the body to be cooled, and the quotient 
{Tc— T) -7- T: in which Tc = absolute temperature at which heat is 
transmitted to the coohng water, and T = absolute temperature at 
which heat is taken from the body to be cooled. 

The determination of the quantity of cold will be possible with the 
proper exactness only when the machine is employed during the test to 
refrigerate a liquid; and if the cold be found from the quantity of hquid 
circulated per unit of time, from its range of refrigeration, and from its 
specific heat. Sufficient exactness cannot be obtained by the refrigera- 
tion of a current of circulating air, nor from the manufacture of a certain 
quantity of ice, nor from a calculation of the fluid circulating within the 
machine (for instance, the quantity of ammonia circulated by the com- 
pressor). Thus the refrigeration of brine will generally form the basis 
for tests making any pretension to accuracy. The degree of refrigeration 
should not be greater than necessary for allowing the range of temperature 
to be measured with the necessary exactness; a range of temperature of 
from 5° to 6° Fahr. will suffice. 

The condenser measurements for cooling water and its temperatures 
will be possible with sufficient accuracy only with submerged condensers. 
The measurement of the quantity of brine circulated, and of the cool- 
ing water, is usually effected by water-meters inserted into the conduits. 
If the necessary precautions are observed, this method is admissible. 
For quite precise tests, however, the use of two accurately gauged 
tanks which are alternately filled and emptied must be advised. 

To measure the temperatures of brine and cooling water at the entrance 
and exit of refrigerator and condenser respectively, the employment of 
specially constructed and frequently standardized thermometers is in- 
dispensable; no less important is the precaution of using at each spot si- 
multaneously two thermometers, and of changing the position of one such 
thermometer series from inlet to outlet (and vice versa) after the expiration 
of one-half of the test, in order that possible errors may be compensated. 
It is important to determine the specific heat of the brine used in 
each instance for its corresponding temperature range, as small differ- 
ences in the composition and the concentration may cause considerable 
variations. {Continued on page 1358.) 



1356 ICE-MAKING OR REFRIGERATING-MACHINES. 



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TEST-TRIALS OF REFRIGERATING- MACHINES. 1357 



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1358 ICE-MAKING OR REFRIGERATING-MACHINES. 

As regards the measurement of consumption, the programme will not 
have any special rules in cases where only the measurement of steam and 
cooling water is undertaken, as will be mainly the case for trials of absorp- 
tion-machines. For compression-machines the steam consumption 
depends both on the quality of the steam-engine and on that of the 
refrigerating-machine, while it is evidently desirable to know the con- 
sumption of the former separately from that of the latter. As a rule 
steam-engine and compressor are coupled directly together, thus render- 
ing a direct measurement of the power absorbed by the refrigerating- 
machine impossible, and it will have to suffice to ascertain the indicated 
work both of steam-engine and compressor. By further measuring 
the work for the engine running empty, and by comparing the differences 
in power between steam-engine and compressor resulting for wide varia- 
tions of condenser-pressures, the effective consumption of work L^ for 
the refrigerating-machine can be found very closely. In general, it will 
suffice to use the indicated work found in the steam-cylinder, especially 
as from this observation the expenditure of heat can be directly deter- 
mined. Ordinarily the use of the indicated work in the compressor- 
cylinder, for purposes of comparison, should be avoided; firstly, because 
there are usually certain accessory apparatus to be driven (agitators, etc.), 
belonging to the refrigerating-machine proper; and secondly, because 
the external friction would be excluded. 

Report of Test. — Reports intended to be used for comparison with 
the figures found for other machines will have to embrace at least the 
following observations: 
Refrigerator: 

Quantity of brine circulated per hour 

Brine temperature at inlet to refrigerator 

Brine temperature at outlet of refrigerator T 

Specific gravity of brine (at 64° Fahr.) 

Specific heat of brine 

Heat abstracted (cold produced) Qq 

Absolute pressure in the refrigerator 

Condenser: 

Quantity of cooling water per hour 

Temperature at inlet to condenser 

Temperature at outlet of condenser Tf. 

Heat abstracted Qi 

Absolute pressure in the condenser 

Temperature of gases entering the condenser 



Absorption-machine . 
Still: 



Steam consumed per hour 

Abs. pressure of heating steam 

Temperature of condensed steam at 
outlet 

Heat imparted to still Q'e 

Absorber: 

Quantity of coohng water per hour. . 

Temperature at inlet 

Temperature at outlet 

Heat removed O2 

Pump for Ammonia Liquor: 

Indicated work of steam-engine .... 

Steam-consumption for pump 

Thermal equivalent for work of 
pump ALv 

Total sum of losses by radiation and 

convection ± Qz 

Heat Balance: 

Qe + Q'e = <?i + Q2 ± Qz, 

For the calculation of efficiency and for comparison of various tests, 
the actual efficiencies must be compared with the theoretical maximum 
of efficiency Q ^ {AL) max. = T ^ (Tc - T) corresponding to the 
temperature range. 



Compression-machine . 



Compressor: 

Indicated work Li 

Temperature of gases at inlet 

Temperature of gases at exit 
Steam-engine: 

Feed-water per hour 

Temperature of feed-water . . 

Absolute steam-pressure be- 
fore steam-engine 

Indicated work of steam-en- 
gine Lg 

Condensing water per hour.. . 

Temperature of do 

Total sum of losses by radia- 
tion and convection. . ± Qz 
Heat Balance: 

Qe + ALc = Qi ± <?s. 



PERFORMANCES OF ICE-MAKING MACHINES. 1359 



Heat Balance. — We possess an important aid for checking the cor- 
rectness of the results found in each trial by forming the balance in each 
case for the heat received and rejected. Only those tests should be re- 
garded as correct beyond doubt which show a sufficient conformity in 
the heat balance. It is true that in certain instances it may not be easy 
to account fully for the transmission of heat between the several parts of 
the machine and its environment by radiation and convection, but gener- 
ally (particularly for compression-machines) it will be possible to obtain 
for the heat received and rejected a balance exhibiting small discrepancies 
only. 

Temperature Range. — For the temperatures {T and Tc) at which the 
heat is abstracted in the refrigerator and imparted to the condenser, it is 
correct to select the temperature of the brine leaving the refrigerator and 
that of the cooling water leaving the condenser, because it is in principle 
impossible to keep the refrigerator pressure higher than would correspond 
to the lowest brine temperature, or to reduce the condenser pressure 
below that corresponding to the outlet temperature of the cooling water. 
Prof. Linde shows that the maximum theoretical efficiency of a com- 
pression-machine may be expressed by the formula 
Q -f- UL) = T-^iTc- T), 
in which Q = quantity of heat abstracted (cold produced): 

AL = thermal equivalent of the mechanical v/ork expended; 
L = the mechanical work, and ^ = 1 -7- 778- 
T = absolute temperature of heat abstraction (refrigerator); 
Tf. = absolute temperature of heat rejection (condenser). 
If w = ratio between the heat equivalent of the mechanical w^ork AL 
and the quantity of heat Q' w^hich must be imparted to the motor to 
produce the work L, then 

^L -^ Q' = u, and Q'/Q - (T^ - T) -^ (uT), 

It follows that the expenditure of heat Q' necessary for the production 
of the quantity of cold Q in a compression-machine will be the smaller, 
the smaller the difference of temperature Tq — T. 

Metering the Ammonia. — For a complete test of an ammonia 
refrigerating-machine it is advisable to measure the quantity of ammonia 
circulated, as w-as done in the test of the 75-ton machine described by 
Prof. Denton. (Trans. A. S. M. E., xii, 326.) 

ACTUAL PERFOR3IANCES OF ICE-MAKING IVIACHINES. 

The table given on page 1360 is abridged from Denton, Jacobus, and 
Riesenberger's translation of Ledoux on Ice-making Machines. The 
following shows the class and size of the machines tested, referred to by 
letters in the table, with the names of the authorities: 



Class of Machines. 


Authority. 


Dimensions of Com- 
pression-cylinder in 
inches. 




Bore. 


Stroke. 


A. Ammonia cold-compression 

B. Pictet fluid dry-compression 

C. Bell-Coleman air 


Schroter. 

( Ren wick & 
\ Jacobus. 
Denton. 


9.9 

11.3 
28.0 

10.0 

12.0 


16.5 

24.4 
23.8 


D. Closed cycle air 


18.0 


E. Ammonia dry-compression 


30.0 


F. Ammonia absorption 





In class A, a German double-acting machine with compression cylinder 
9.9 in. bore, 16 in. stroke, tested by Prof. Schroter, the ice-melting capac- 
ity ranges from 46.29 to 16.14 lbs. of ice per pound of coal, according as 
the suction pressure varies from about 45 to 8 lbs. above the atmosphere, 
this pressure being the condition which mainly controls the economy of 
compression machines. These results are equivalent to reaUzing from 
72% to 57% of theoretically perfect performances. The higher per cents 
appear to occur with the higher suction-pressures.- indicating a greater 
loss from cylinder-heating (a phenomenon the reverse of cylinder conden- 



1360 ICE-MAKING OR REFRIGERATING-MACHINES. 



sation in steam-engines), as the range of the temperature of the gas in 
the compression-cylinder is greater. 

In E, an American single-acting compression-machine, two compression 
cylinders each 12X 30 in., operating on the "dry system," tested by 
Prof. Denton, the percentage of theoretical effect reahzed ranges from 
69.5% to 62.6%. The friction losses are higher for the American machine. 
The latter's higher efficiency may be attributed, therefore, to more perfect 
displacement. 

The largest ' 'ice-melting capacity" in the American machine is 24. 16 lbs. 

Actual rerformance of lee-making 3Iachines. 







k'^ 


bc-S . 


^ 












b/) 


.j^ 








Absolute Pre 
sure, in lbs. p 
square inch. 


Temperature 
corresponding 
to Pressure, 
degrees Fahr 


Temperature < 
Brine, in de- 
grees Fahr. 


6 


0) 

o 

B 




a 
S 


■§:!j 
II 


. between theoretical Ice-melt- 
g Capacity, no Cylinder Heatin 
Friction, and actual, %.% 


t 
o 
o 

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u 

1 

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1 

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A 


1 


135 


55 


72 


27 


43 


37 


44.9 


17.9 


14.4 


26.2 


40.63 


30.8 


19.1 


54.8 


(( 


2 


131 


42 


70 


14 


28 


23 


45.1 


18.0 


16.7 


19.5 


30.01 


33.5 


20.2 


53.4 


•« 


3 


128 


30 


69 


1 


14 


9 


45.1 


16.8 


16.0 


13.3 


22.03 


37.1 


25.2 


50.3 


«* 


4 


126 


22 


68 


-12 


30 


- 5 


44.8 


15.5 


19.5 


9.0 


16.14 


42.9 


29.1 


44.7 


«« 


5 


200 


42 


95 


14 


28 


23 


45.0 


24.1 


10.5 


16.5 


19.07 


36.0 


28.5 


77.0 


<c 


6 


136 


60 


72 


30 


44 


37 


45.2 


17.9 


10.7 


29.8 


46.29 


28.5 


19.9 


56.8 


*i 


7 


131 


45 


71 


18 


28 


•23 


45.1 


18.0 


12.1 


21.6 


33.23 


31.3 


21.9 


56.4 


«» 


8 


126 


24 


68 


- 9 





- 6 


44.7 


15.6 


18.0 


9.9 


17.55 


41.1 


28.3 


46.1 


«« 


9 


117 


41 


64 


13 


28 


23 


45.0 


16.4 


13.5 


20.0 


33.77 


33.1 


22.9 


50.6 


«« 


10 


130 


60 


70 


31 


43 


37 


31.7 


12.0 


14.8 


19.5 


45.01 


35.2 


23.8 


52.0 


B 


11 


57 


21 


77 


28 


43 


37 


57.0 


21.5 


22.9 


25.6 


33.07 


39.9 


22.2 


24.1 


(( 


12 


56 


15 


76 


14 


28 


23 


56.8 


20.6 


22.9 


17.9 


24.11 


41.3 


24.0 


23.1 


it 


13 


55 


10 


75 


- 2 


14 


9 


57.1 


18.5 


24.0 


11.6 


17.47 


42.2 


25.2 


20.4 


«( 


14 


60 


7 


81 


-16 





- 6 


57.6 


15.7 


25.7 


5.7 


10.14 


54.5 


38.5 


16.8 


<( 


15 


91 


15 


104 


U 


28 


23 


59.3 


27.2 


16.9 


15.7 


16.05 


36.2 


23.1 


31.5 


(C 


16 


61 


22 


81 


31 


44 


37 


57.3 


21.6 


14.0 


28.1 


36.19 


33.4 


22.5 


26.8 


** 


17 


59 


16 


80 


16 


28 


23 


57.5 


20.5 


12.8 


19.3 


26.24 


34.6 


25.0 


25.6 


i« 


18 


59 


7 


79 


-16 





- 6 


57.8 


15.9 


21.1 


6.8 


11.93 


47.5 


33.4 


18.0 


«« 


19 


54 


22 


75 


31 


43 


37 


35.3 


12.4 


22.3 


17.0 


38.04 


39.5 


22.6 


22.6 


(« 


20 


89 


16 


103 


16 


28 


23 


42.9 


19.9 


14.7 


11.9 


16.68 


37.7 


27.0 


32.7 


«« 


21 


62 


6 


82 


-17 





- 5 


34.8 


9.9 


24.3 


3.5 


9.86 


54.2 


39.5 


17.7 


C 


22 


59 


15 


65* 


-53* 






63.2 


83.2 


21.9 


10.3 


3.42 


71.7 


56.9 


26.6 


D 


23 


175 


54 


81* 


-40* 






93.4 


38.1 


32.1 


4.9 


3.0 


80.0 


63.0 


89.2 


E 


24 


166 


43 


84 


15 


*37' 


■"28 


58.1 


85.0 


22.7 


73.9 


24.16 


32.8 


11.7 


65.9 




25 


167 


23 


85 


-11 


6 


2 


57.7 


72.6 


18.6 


37.9 


14.52 


37.4 


22.7 


57.6 


«« 


26 


162 


28 


83 


- 3 


14 


2 


57.9 


73.6 19.3 


46.5 


17.55 


34.9 


18.6 


59.9 


«' 


27 


176 


42 


88 


14 


36 


28 


58.9 


88.6 19.7 


74.4 


23.31 


30.5 


13.5 


70.5 


F 


28 


152 


40 


79 


13 


21 


16 






42.2 


20.1 


47.8 















* Temperature of air at entrance and exit of expansion-cylinder. 

t On a basis of 3 lbs. of coal per hour per H.P. of steam-cylinder of 
compression-machine and an evaporation of 11.1 lbs. of water per pound 
of combustible from and at 212° F. in the absorption-machine. 

t Per cent of theoretical with no friction. 

§ Loss due to heating during aspiration of gas in the compression- 
cylinder and to radiation and superheating at brine-tank. 

II Actual, including resistance due to inlet and exit valves. 



PERFORMANCES OF ICE-MAKING MACHINES. 1361 



This corresponds to the highest suction-pressures used in American 
practice for such refrigeration as is required in beer-storage cellars using 
the direct-expansion system. The conditions most nearly corresponding 
to American brewery practice in the German tests are those in line 5, 
which give an "ice-melting capacity" of 19.07 lbs. 

For the manufacture of artificial ice, the conditions of practice are those 
of hnes 3 and 4, and hues 25 and 26. In the former the condensing pres- 
sure used requires more expense for cooling water than is common in 
American practice. The ice-melting capacity is therefore greater in the 
German machine, being 22.03 and 16.14 lbs. against 17.55 and 14.52 for 
the American apparatus. 

Class B. Sulphur Dioxide or Pictet Machines. — No records are 
available for determination of the "ice-melting capacity" of machines 
using pure sulphur dioxide. In the " Pictet fluid, " a mixture of about 97 % 
of sulphur dioxide and 3% of carbonic acid, the presence of the carbonic 
acid affords a temperature about 14 Fahr. degrees lower than is obtained 
with pure sulphur dioxide at atmospheric pressure. The latent heat of 
this mixture has never been determined, but is assumed to be equal to 
that of pure sulphur dioxide. 

For brewery refrigerating conditions, Line 17, we have 26.24 lbs. ••ice- 
melting capacity," and for ice-making conditions, line 13, the "ice- 
melting capacity" is 17.47 lbs. These figures are practically as econom- 
ical as those for ammonia, the per cent of theoretical effect realized 
ranging from 65.4 to 57.8. At extremely low temperatures, - 15° 
Falir., lines 14 and 18, the per cent reahzed is as low as 42.5. 

Performance of a 75-toii Ammonia Compression-machine. (J. E. 
Denton, Trans. A. S. M. E., xii, 326.) — The machine had two single- 
acting compression cylinders 12 X 30 in., and one Corliss steam- 
cylinder, double-acting, 18 X 36 in. It was rated by the manufac- 
turers as a 50-ton machine, but it showed 75 tons of ice-refrigerating 
effect per 24 hours during the test. 

The most probable figures of performance in eight trials are as follows: 





Ammonia 


Brine 




oo,^| 


ump- 
. of 
min. 

I Ca- 


Isi 




m 


Pressures, 


Tempera- 


^^'^^ 


r.<^ 


A 




lbs. above 


tures, 




=;±;f^ 


c-S^^ 


< « 


o 


H 


Atmosphere. 


Degrees F. 


a rtj c3 aj u, 


lim 






o 
o 


Con- 
densing 


Suc- 
tion. 


Inlet. 


Outlet. 


.2 2 
1'^ 


I 


151 


28 


36.76 


28.86 


70.3 


22.60 


0.80 


1.0 


1.0 


8 


161 


27.5 


36.36 


28.45 


70.1 


22.27 


1.09 


I.O 


1.0 


7 


147 


13.0 


14.29 


2.29 


42.0 


16.27 


0.83 


1.70 


1.60 


4 


152 


8.2 


6.27 


2.03 


36.43 


14.10 


1.1 


1.93 


1.92 


6 


105 


7.6 


6.40 


-2.22 


37.20 


17.00 


2.00 


1.91 


1.88 


2 


135 


15.7 


4.62 


3.22 


27.2 


13.20 


1.25 


2.59 


2.57 



The principal results in foiu* tests are given in the table on page 
1363. The fuel econom.y under different conditions of operation is 
showTi in tlie following table: 







Pounds of Ice-melting Effect with 


B.T.U.per Ib.of Steano 


1 


2 
S 


Engines — 


with Engines — 


Ph 


Non-con- 
densing. 


Non-com- 


Compound 


^ 








2 . 
o 


pound Con- 
densing. 


Con- 
densing. 


o.S 


to 

a 
o 

r3 


3 S 


1' 


^ . 


Ab 


£ . 


S> ;5 


^ . 


:2a 


!- 


"S 


»- c3 


^§ 


t~, d 


^ ^, 


t- a 


^ s^ 


a 


C 


B a 


i 


O O 


<D O 




<v o 


a, « 


o 





c o 


& 


PhU 


f^c/i 


P^O 


Ph^ 


P^O 


f^OJ 


^ 


6 


oo 


150 


28 


24 


2.90 


30 


3.61 


37.5 


4.51 


393 


513 


640 


150 


7 


14 


1.69 


17.5 


2.11 


21.5 


2.58 


240 


300 


366 


105 


28 


34.5 


4.16 


43 


5.18 


54 


6.50 


591 


725 


923 


105 


7 


22 


2.65 


27.5 


3.31 


34.5 


4.16 


376 


470 


591 



1362 ICE-MAKING OR REFRIGERATING-MACHINES. 

The non-condensing engine is assumed to require 25 lbs. of steam 
per I.H.P. per hour, the non-compound condensing 20 lbs., and the 
compound condensing 16 lbs., and the boiler eflQciency is assumed at 
8.3 lbs. of water per lb. coal under working conditions. The following 
conchisions were derived from the investigation: 

1. The capacity of the machine is proportional, almost entirely, to the 
weight of ammonia circulated. This weight depends on the suction- 
pressure and the displacement of the compressor-pumps. The practical 
suction-pressures range from 7 lbs. above the atmosphere, with which a 
temperature of 0° F. can be produced, to 28 lbs. above the atmosphere, 
with wliich the temperatures of refrigeration are confined to about 28° F. 
At the lower pressure only about one-half as much weight of ammonia 
can be circulated as at the upper pressure, the proportion being about in 
accordance with the ratios of the absolute pressures, 22 and 42 lbs. 
respectively. For each cubic foot of piston-displacement per minute a 
capacity of about one-sixth of a ton of refrigerating effect per 24 hours 
can be produced at the lower pressure, and of about one-third of a ton at 
the upper pressure. No other elements practically affect the capacity 
of a machine, provided the cooling-surface in the brine-tank or other space 
to be cooled is equal to about 36 sq. ft. per ton of capacity at 28 lbs. back 
pressure. For example, a difference of 100% in the rate of circulation of 
brine, while producing a proportional difference in the range of tempera- 
ture of the latter, made no practical difference in capacity. 

The brine-tank was 10 1/2 X 13 X 10 2/3 ft., and contained 8000 lineal 
feet of 1-in. pipe as cooling-surface. The condensing-tank was 12 XlO 
X 10 ft., and contained 5000 hneal feet of 1-in. pipe as cooling-surface. 

2. The economy in coal-consumption depends mainly upon both the 
suction-pressures and condensing-pressures. Maximum economy with a 
given type of engine, where water must be bought at average city prices, 
is obtained at 28 lbs. suction-pressure and about 150 lbs. condensing- 
pressure. Under these conditions, for a non-condensing steam-engine 
consuming coal at the rate of 3 lbs. per hour per I.H.P. of steam-cylinders, 
24 lbs. of ice-refrigerating effect are obtained per lb. of coal consumed. 
For the same condensing-pressure, and with 7 lbs. suction-pressure, which 
affords temperatures of 0° F., the possible economy falls to about 14 lbs. of 
refrigerating effect per lb. of coal consumed. The condensing-pressure is 
determined by the amount of condensing-water suppUed to liquefy the 
ammonia in the condenser. If the latter is about 1 gallon per minute 
per ton of refrigerating effect per 24 hours, a condensing-pressure of 
150 lbs. results, if the initial temperature of the water is about 56° F. 
Twenty-five per cent less water causes the condensing-pressure to in- 
crease to 190 lbs. The work of compression is thereby increased about 
20%, and the resulting "economy" is reduced to about 18 lbs. of "ice 
effect " per lb. of coal at 28 lbs. suction-pressure and 11.5 at 7 lbs. If, on 
the other hand, the supply of water is made 3 gallons per minute, the 
condensing-pressure may be confined to about 105 lbs. The work of 
compression is thereby reduced about 25%, and a proportional increase 
of economy results. Minor alterations of economy depend on the initial 
temperature of the condensing-water and variations of latent heat, but 
these are confined witliin about 5% of the gross result, the main element 
of control being the work of compression, as affected by the back pressure 
and condensing-pressure, or both. If the steam-engine supplying the 
motive power may use a condenser to secure a vacuum, an increase of 
economy of 25% is available over the above figures, making the lbs. of 
"ice effect" per lb. of coal for 150 lbs. condensing-pressure and 28 lbs. 
suction-pressure 30.0, and for 7 lbs. suction-pressure, 17.5. It is, however, 
impracticable to use a condenser in cities where water is bought. The 
latter must be practically free of cost to be available for this purpose. 
In this case it may be assumed that water will also be available for con- 
densing the ammonia to obtain as low a condensing-pressure as about 
100 lbs., and the economy of the refrigerating-machine becomes, for 
28 lbs. back pressure, 43.0 lbs. of ** ice-effect " per lb. of coal, or for 7 lbs. 
back pressure 27.5 lbs. of ice effect per lb. of coal. If a compound con- 
densing-engine can be used with a steam-consumption per hour per 
horse-power of 16 lbs. of water, the economy of the refrigerating-machine 
may be 25% higher than the figures last named, making for 28 lbs. back 
pressure a refrigerating-effect of 54.0 lbs. per lb. of coal, and for 7 lbs. 
back pressure a refrigerating effect of 34.0 lbs. per lb. of coal. 



PERFORMANCES OF ICE-MAKING MACHINES. 1363 



Performance of a 75-ton Refrigerating-machine. 


(Denton.) 




'O tn 


-0 0-^ 


-0 n*-^ 


'^ T> 




c^ 


^ 2 " 


= ° 2 


C^ 




03 =i 


c3 5^ 


33 OJ^ 


03=: 




^S 


^"^^ 


>.N« 


^^ 






a"c«zr 


l^l 


1^ • 




rt c^ 3 


a « 


r^ 


03 rt 3 




o^ 


-C! 


^ ^ 


o^S 




•Goo 


timum 
onomy 
ine, an 
essure. 


y 0.- CI 


300 




|w^ 




2 t- u 


|h(S 


Av. high ammonia press, above atmos 


ISIlbs. 


152 lbs. 


147 lbs. 


161 lbs. 


Av. back ammonia press, above atmos 


28 '* 


8.2 " 


13 " 


27.5 ♦• 


Av. temperature brine inlet 


36.76° 


6.27° 


14.29° 




Av. temperature brine outlet 


28.86° 


2.03° 


2 29° 


"28 '.45^ 
7 91° 


Av. range of temperature 


7 .9° 


4 24° 


12.00° 


Lbs. of brine circulated per minute » . . . 


2281 


2173 


943 


2374 
54.00° 


Av. temp, condensing-water at inlet 


44.65° 


56.65° 


46.9° 


Av. temp, condensing-water at outlet 


83.66° 


85.4° 


85.46° 


82. 86*^ 


Av. range of temperature 


39.01° 


28.75° 


38.56° 


28.80° 


Lbs. water circulated p. min. thro' cond'ser 


442 


315 


257 


601.5 


Lbs. water per min. through jackets 


25 


44 


40 


14 


Range of temperature in jackets 


24 0° 


16.2° 


16 4° 


29 1° 


Lbs. ammonia circulated per min 


'^28.17 


14!68 


16.67 


28! 32 


Probable temperature of liquid ammonia, 










entrance to brine-tank 


♦71 30 

+ 14° 


*68° 
-8° 


*63.7° 
-5° 


76 7° 


Temp, of amm. corresp. to av. back press. 


14° 


Av. temperature of gas leaving brine-tanks 


34.2° 


14.7° 


3.0° 


29.2° 


Temperature of gas entering compressor 


*39° 


25° 


10.13° 


34° 


Av. temperature of gas leaving compressor 


213° 


263° 


239° 


221° 


Av. temp, of gas entering condenser 


200° 


218° 


209° 


168° 


Temperature due to condensing pressure. . . 


84.5° 


84.0° 


82.5° 


88.0° 


Heat given ammonia: 










By brine, B.T.U. per minute 


14776 


7186 


8824 


14647 


By compressor, B.T.U. per minute 


2786 


2320 


2518 


3020 


By atmosphere, B.T.U. per minute 


140 


147 


167 


141 


Total heat rec. by amm., B.T.U. per min.... 


17702 


9653 


11409 


17708 


Heat taken from ammonia: 










Bv condenser B T U. Der min 


17242 


9056 


9910 


17359 


By jackets, B.T.U. per min 


608 
182 


712 
338 


656 
250 


406 


By atmosphere, B.T.U. per min 


252 


Total heat rej. by amm., B.T.U. per min.. . . 


18032 


10106 


10816 


18017 


Dif . of heat rec'd and rej., B.T.U. per min.. . 


330 


453 


407 


309 


% work of compression removed by jackets 


22% 


31% 


26% 


13% 


Av. revolutions per min 


58.09 
32.5 


57.7 
27.17 


57.88 
27.83 


58 89 


Mean eff. press, steam-cyl., lbs. per sq. in.. . 


32.97 


Mean eff. press, amm.-cyl., lbs. per sq. in. . . 


65.9 


53.3 


59.86 


70.54 


Av. H.P. steam-cylinder 


85.0 
65.7 
23.0 


71.7 
54.7 
24.0 


73.6 

59.37 

20.0 


88.63 


Av. H.P. ammonia-cylinder 


71.20 


Friction in per cent of steam H.P 


19.67 


Total cooling water, gallons per min. per 




ton per 24 hours 


0.75 
74.8 


1.185 
36.43 


0.797 
44 64 


0.990 


Tons ice-melting capacity per 24 hours 


74.56 


Lbs. ice-refrigerating eff. per lb. coal at 3 










lbs. per H.P. per hour 


24.1 


14.1 


17.27 


23.37 


Cost coal per ton of ice-refrigerating effect 




at $4 per ton 


$0,166 


$0,283 


$0,231 


$0,170 


Cost water per ton of ice-refrigerating effect 




at $1 per 1000 cu.ft 


$0,128 
$0,294 


$0,200 
$0,483 


$0,136 
$0,467 


$0,169 


Total cost of 1 ton of ice-refrigerating eff. . . 


$0,339 



Figures marked thus (*) are obtained by calculation; all other figures 
obtained from experimental data; temperatures in Fahrenheit are degrees- 



1364 ICE-MAKING OR REFRIGERATING-MACHINES. 



Ammonia Compression-machine. 

Actual Results Obtained at the Munich Tests. 
(Prof. Linde, Trans. A. S. M. E., xiv, 1419.) 



No. of Test 


1 


2 


3 


4 


5 


Temp, of refrig- ) Inlet, deg. F ... . 
erated brine j Outlet, deg. F... 


43.194 


28.344 


13.952 


-0.279 


28.251 


37.054 


22.885 


8.771 


-5.879 


23.072 


Specific heat of brine 


0.861 


0.851 


0.843 


0.837 


0.851 


Brine circ. per hour, cu. ft 


1,039.38 
342,909 


908.84 
263,950 


633.89 
172,776 


414.98 
121,474 


800.93 


Cold produced, B.T.U. per hour. . . 


220,284 


Cooling water per hour, cu. ft 


338.76 


260.83 


187.506 


139.99 


97.76 


I.H.P. in steam-engine cylinder. . . 


15.80 


16.47 


15.28 


14.24 


21.61 


Cold pro- ) Per I.H.P. in comp.-cyl 


24,813 


18,471 


12,770 


10,140 


11,151 


duced per { Per I.H.P. in steam-cyl 


21,703 


16,026 


11,307 


8,530 


10,194 


h.,B.T.U. ) Per lb. of steam 


1,100.8 


785.6 


564.9 


435.82 


512.12 



A test of a 35-ton ahsorption-inachine in New Haven, Conn., by Prof. 
Denton {Trans. A. S. M. E., x, 792), gave an ice-melting effect of 20.1 
lbs. per lb. of coal on a basis of boiler economy equivalent to 3 lbs. of 
steam per I.H.P. in a good non-condensing steam-engine. The ammonia 
was worked between 138 and 23 lbs. pressure above the atmosphere. 

Performance of a Single-acting Ammonia Compressor. — Tests 
were made at the works of the Eastman Kodak Co., Rochester, N.Y., of 
a machine fitted with two York IMfg. Co.'s single-acting compressors, 
15 in. diarh., 22 in. stroke, to determine the horse-power per ton of 
refrigeration. Following are the principal average results (Bulletin 
of York Mfg. Co.): 



Date of Test, 1908. 



Mar. 6 


Mar. 7 


Mar. 8 


Mar. 9 


Mar. 
10. 


Mar. 
11. 


216.2 


217.8 


250.6 


245.8 


253.0 


242.9 


15.2 


14.3 


16.8 


14.8 


13.5 


18.2 


9.33 


9.36 


10.37 


9.29 


9.90 


13.20 


74.85 


74.16 


71.98 


77.91 


76.61 


82.88 


22.89 


23.19 


25.26 


22.73 


27.35 


28.41 


13.58 


13.96 


14.44 


13.02 


15.53 


16.06 


45.1 


'45.0 


45.1 


34.3 


56.0 


67.8 


20.76 


20.43 


21.04 


15.59 


25.99 




20.11 


19.90 


19.97 


20.04 


20.18 


18.13 


183.96 


184.41 


186.99 


187.27 


187.90 


186.8 


69.35 


69.80 


70.05 


52.57 


89.48 


105.11 


49.08 


48.79 


50.38 


37.01 


61.39 


66.65 


1.418 


1.427 


1.389 


1.422 


1.425 


1.439 



Mar. 
14. 



Temp, dischg. gas, av 

Temp, suction gas, av . . . . 
Temp, suction at cooler. . 
Temp, liquid at exp. valve 

Temp, brine, inlet 

Temp, brine, outlet 

Revs, per min 

Lbs. liquid NH3 per min. . 
Sue. press, at mach. lb. . . 

Condenser pressure 

Indicated H.P.... 

Tons Refrig. Capy, 24 hrs. 
I.H.P. per ton capacity . . 



255.5 
17.9 
9.13 

76.98 
23.43 
12.87 
44.8 
20.40 
20.38 
183.81 
68.61 
49.31 
1.375 



Full details of these tests were reported to the Am. Socy. of Refrig. 
Engrs. and published in Ice and Refrigeration, 1908. 

Performance of Absorption Machines. — From an elaborate review 
by Mr. Voorhees of the action of an absorption machine under certain 
Stated conditions, showing the quantity of ammonia circulated per hour 
per ton of refrigeration, its temperature, etc., at the several stages of 
the operation, and its course through the several parts of the apparatus, 
the following condensed statement is obtained: 

Generator. — 30.9 lbs. dry steam, 38 lbs. gauge pressure condensed, 
evaporates 32.2% strong liquor to 22.3% weak liquor. 

Exchanger. — 3.01 lbs. weak hquor at 264° cools to 111°. 

Absorber. — Adds 0.43 lbs. vapor from the brine cooler, making 3.44 
lbs. strong liquor at 111° to go to the pump. 

Exchanger. — 3.44 lbs. heated to 224°, some of it is now gas, and the 
rest liquor of a little less than 32% NH3. 

Analyzer. — (A series of shelves in a tank above the generator) delivers 
strong liquor to the generator, while the vapor, 91% NH3, 0.4982 lb., goes 
to the rectifier. 

Rectifier. — Cools the gas to 110° separating water vapor as 0.0682 lb. 
drip liquor which returns through a trap to the generator. 

Conclenser. — 0.43 lb. NH3 gas at 110° cooled and condensed to liauid 
at 90° by 2 gals, of water per min. heated from 73° to 86°. , 



I 



PERFORMANCES OF ICE-MAKING MACHINES. 1365 



Expansion Valve and Cooler. — Reduces liquid to 0° and boils it at 0°, 
cooling 3 gals, of brine per min. from 12° to 3°. Gas passes to absorber 
and the cycle is repeated. 

Of the 2 gals, per min. of cooling water flowing from the condenser, 
0.2 gal. goes to the rectifier, where it is heated to 142°, and 1.8 gal. through 
the absorber, where it is heated to 110°. 

Heat Balance. — Absorbed in the generator 496; in the brine cooler, 
200, Total 696 B.T.U. Rejected; condenser, 220; absorber, 383; rectifier, 
93; Total 696 B.T.U. 

The following table shows the strength of the liquoFs and the quantity 
of steam required per hour per ton of refrigeration under the conditiona 
stated: 







Condenser Pressures. 












140 1 170 




200 






Suction Pressures. 







15 


80 





15 


30 





15 


30 


SI per cent 

Wl per cent 

SG, pounds 

SL, pounds 


24 

13.13 
30.1 

1.7 


35 
25.75 
27.9 

1.6 


42 
33.70 
22.9 

1.4 


22 

10.85 
41.3 

2.1 


32 
22.3 
30.9 

1.9 


38 
29.15 
26.2 

1.8 


18 

6.28 
48.7 
2.4 


28 
17.7 
34.1 

2.3 


36 
26.9 
27.9 

2.2 



SI, strong liquor; Wl, weak liquor; SG, lbs. of steam per hour per ton 
of refrigeration for the generator, SL, do. for the liquor pump. Pressures 
are in lbs. per sq. in., gauge. 

The following table gives the steam consumption in lbs. per hour per 
ton of refrigeration, for engine-driven compressors and for absorption 
machines with liquor pump not exhausting into the generator at the suc- 
tion and condenser pressures (gauge) given: SC, simple non-condensing 
engine, CC. compound condensing engine. A, absorption machine. 







Condenser Pressures. 














140 1 170 1 


200 






Suction Pressures. 







15 30 





15 


30 





15 


30 


SC 


78.3 
42.0 
31.8 


44.5 31.1 
23.8 16.6 
29.5 24.3 


90.5 
48.4 
43.4 


52.5 
28.0 
32.8 


37.2 
19.0 
28.0 


104.0 
55.6 
51.1 


61.4 
32.7 
36.4 


44.5 


CC 


23.9 


A 


30.1 

















The ecoiiomy of the absorption machine is much better for all condi- 
tions than that of a simple non-condensing engine-driven compressor. 
At suction gauge pressures above 8 to 10 lbs. the economy of the com- 
pound condensing engine-driven compressor exceeds that of the absorp- 
tion macliine, the absorption macliine giving the superior economy at 
suction pressures below 8 to 10 lbs. 

Means for Applying the Cold. (M. C. Bannister, Liverpool Eng'g 
Soc'y, 1890.) — Tne most useful means for applying the cold to various 
uses is a saturated solution of brine or chloride of magnesium, wliich 
remains liquid at 5° Fahr. The brine is first cooled by being circulated 
in contact with the refrigerator-tubes, and then distributed through 
coils of pipes, arranged either in the substances requiring a reduction of 
temperature, or in the cold stores or rooms prepared for them; the air 
coming in contact with the cold tubes is immediately chilled, and the 
moisture in the air deposited on the pipes. It then falls, making room 
for warmer air, and so circulates until the whole room is at the tempera- 
ture of the brine in the pipes. 

The Direct Expansion 3Iethod consists in conveying the compressed 
cooled ammonia (or other refrigerating agent) directly to the room to be 
cooled, and then expanding it through an expansion cock into pipes in the 
room. Advantages of this system are its simplicity and its rapidity of 



1366 ICE-MAKING OR REFRIGERATING-MACHINES. 

action in cooling a room; disadvantages are the danger of leakage of the 
gas and the fact that the machine cannot be stopped without a rapid rise 
in the temperature of the room. With the brine system, with a large 
amount of cold brine in the tank, the machine may be stopped for a con- 
siderable time without serious cooling of the room. 

Air has also been used as the circulating medium. The ammonia-pipes 
refrigerate the air in a cooling-chamber, and large conduits are used to 
convey it to and return it from the rooms to be cooled. An advantage of 
this system is that by it a room may be refrigerated more quickly than by 
brine-coils. The returning air deposits its moisture on the ammonia- 
pipes, in the form of snow, which is removed by mechanical brushes. 

ARTIFICIAL-ICE MANUFACTURE. 

Under summer conditions, with condensing water at 70°, artificial-ice 
machines use ammonia at a condenser pressure, about 190 lbs. above the 
atmosphere and 15 lbs. suction-pressure. 

In a compression type of machine the useful circulation of ammonia, 
allowing for the effect of cylinder-heating, is about 13 lbs. per hour per 
indicated horse-power of the steam-cylinder. This weight of ammonia 
produces about 32 lbs. of ice at 15° from water at 70°. If the ice is made 
from distilled water, as in the **can system," the amount of the latter 
supplied by the boilers is about 33% greater than the weight of ice 
obtained. This excess represents steam escaping to the atmosphere 
from the re-boiler and steam-condenser, to purify the distilled water, or 
free it from air; also, the loss through leaks and drips, and loss by melting 
of the ice in extracting it from the cans. The total steam consumed per 
horse-power is, therefore, about 32 x 1.33 = 43.0 lbs. About 7.0 lbs. 
of this covers the steam-consumption of the steam-engines driving the 
brine circulating-pumps, the several cold-water pumps, and leakage, 
drips, etc. Consequently, the main steam-engine must consume 36 lbs. of 
steam per hour per I.H.P., or else live steam must be condensed to supply 
the required amount of distilled water. There is, therefore, nothing to be 
gained by using steam at high rates of expansion in the steam-engines, in 
making artificial ice from distilled water. If the cooling water for the 
ammonia-coils and steam-condenser is not too hard for use in the boilers, 
it may enter the latter at about 175° F., by restricting the quantity to 
11/2 gallons per minute per ton of ice. With good coal 8V2 lbs. of feed- 
water may then be evaporated, on the average, per lb. of coal. 

The ice made per pound of coal will then be 32 -=- (43.0 ~ 8.5) = 6.0 
lbs. This corresponds with the results of average practice. 

If ice is manufactured by the "plate system," no distilled water is 
used for freezing. Hence the water evaporated by the boiler may be 
reduced to the amount which will drive the steam-motors, and the latter 
may use steam expansively to any extent consistent with the power 
required to compress the ammonia, operate the feed and filter pumps, 
and the hoisting macliinery. The latter may require about 15% of the 
power needed for compressing the ammonia. 

If a compound condensing steam-engine is used for driving the com- 
pressors, the steam per indicated steam horse-power, or per 32 lbs. of 
net ice, may be 14 lbs. per hour. The other motors at 50 lbs. of steam 
per horse-power will use 7.5 lbs. per hour, ma_king the total consumption 
per steam horse-power of the compressor 21.5 lbs. Taking the evapora- 
tion at 8 lbs., the feed-water temperature being limited to about 110°, the 
coal per horse-power is 2.7 lbs. per hour. The net ice per lb. of coal is 
then about 32 -h 2.7 =11.8 lbs. The best results with "plate-system" 

f)lants, using a compound steam-engine, have thus far afforded about IOV2 
bs. of ice per lb. of coal. 

In the " plate system" the ice gradually forms, in from 8 to 10 days, to 
a thickness of about 14 inches, on the hollow plates, 10x14 feet in area, in 
which the cooling fluid circulates. 

In the "can system" the water is frozen in blocks weighing about 
300 lbs. each, and the freezing is completed in from 40 to 48 hours. The 
freezing-tank area occupied by the "plate system" is, therefore, about 
twelve times, and the cubic contents about four times, as much as required 
in the "can system." 

The investment for the "plate" is about one-third greater than for the 
"can" system. In the latter system ice is being drawn throughout the 



ARTIFICIAL-ICE MANUFACTURE. 1367 

24 hours, and the hoisting is done by hand tackle. Some "can" plants 
are equipped with pneumatic hoists and on large hoists electric cranes are 
used to advantage. In the "plate system" the entire daily product is 
drawn, cut, and stored in a few hours, the hoisting being performed 
by power. The distribution of cost is as follows for the two systems, tak- 
ing the cost for the "can" or distilled-water system as 100, which repre- 
sents an actual cost of about $1.25 per net ton: 
„ . Can System. Plate System. 

Hoisting and storing ice 14.2 2.8 

Engineers, firemen, and coal-passer 15.0 13.9 

Coal at $3.50 per gross ton 42 .2 20 .0 

Water pumped directly from a natural source 

at 5 cts. per 1000 cubic feet 1.3 2 6 

Interest and depreciation at 10% 24 .6 32 7 

Repairs 2.7 3.4 

100.00 75.4 

A compound condensing engine is assumed to be used by the "plate 
system." 

Test of the New York Hygeia Ice-making Plant. — (By Messrs. 
Hupfel, Griswold, and Mackenzie: Stevens Indicator, Jan., 1894.) 

The final results of the tests were as follows: 

Net ice made per pound of coal, in pounds 7.12 

Pounds of net ice per hour per horse-powder 37 .8 

Net ice manufactured per day (12 hours) in tons 97 

Av. pressure of ammonia-gas at condenser, lbs. per sq. in. above 

atmos 135 . 2 

Average back pressure of amm.-gas, lbs. per sq. in. above atmos. 15 .8 

Average temperature of brine in freezing-tanks, degrees F 19 .7 

Total number of cans filled per week 4389 

Ra.tio of cooling-surface of coils in brine-tank to can-surface 7 to 10 

An Absorption Evaporator Ice-making System, built by the Carbon- 
dale Machine Co. is in operation at the ice plant of the Richmond Ice Co., 
Clifton, Staten Island, N, Y., which produces the extra distilled water by 
an evaporator at practically no fuel cost, and thus about 10 tons of dis- 
tilled water ice per ton of coal is obtained. Steam from the boiler at 
100 lbs. pressure enters an evaporator, distillmg off steam at 70 lbs., 
which operates the pumps and auxiliary machinery. These exhaust 
into the ice machine generator under 10 lbs. pressure, where the exhaust 
is condensed. In a 100-ton plant the evaporator will condense 43 tons 
of live steam, distilling off 40 tons of steam to operate the auxiliaries, 
which exhaust into the generator: 20 tons of live steam has to be added 
to this exhaust, making 60 tons in all, which is the amount required to 
operate the generator. The 60 tons of condensation from the generator 
and 43 tons from the evaporator go to the re-boiler, making 103 tons of 
distilled water to be frozen into ice. The total steam consumption is the 
60 tons condensed in the generator plus 3 tons for radiation, or 63 tons 
in all. Hence if the boiler evaporates 6.6 lbs. water per pound of coal 
the economy of the plant will be 10 V2 lbs. ice per pound of coal, a result 
which cannot be obtained even with compound condensing engines and 
compression machines. 

Heat-excnangmg colls, on the order of a closed feed-water heater, are 
used to heat the feed-water going to the boiler. The condensation leav- 
ing the generator and evaporator at a high temperature is utilized for 
this purpose; by this means securing a feed-water temperature con- 
siderably in excess of 212°. 

Ice-Making with Exhaust Steam. — The exhaust steam from electric 
light plants is being utilized to manufacture ice on the absorption system. 
A 10-ton plant at the Holdredge Lighting Co., Holdredge, Neb., built by 
the Carbondale Machine Co., is described in Elec. World, April 7, 1910. 
Here 11 tons of ice were made per day with exhaust steam from the 
electric engines at 21/2 lbs. pressure, using 6V3 K.W., or 8V2 H.P., for 
driving the circulating pumps. 

Tons of Ice per Ton of Coal. — From a long table by Mr. Voorhees, 
showing the net tons of plate ice that may be made in well-designed 
plants under a variety of conditions as to type of engine, the following 
figures are taken: 



1368 



MARINE ENGINEERING. 



Compression, Simple Corliss engine, non-condensing 6.1 tons 

Absorption liquor pump and auxiliaries not exhausting into 

generator, simple, non-condensing engine 10.0 

Compression, compound condensing engine 11.2 

Compression triple-expansion condensing engine 12.8 

Absorption, pump and auxiliaries exiiausting into generator, 

Corliss non-conden<ing engine 13.3 

Compression and absorption, compound engine, non-condensing 16.0 

Compression, triple-expansion condensing engine, multiple effect 16.5 
Compression and absorption, triple-expansion non-condensing 

engine, multiple effect 19.5 

Standard Ice Cans or 3Ioulds, 

(Buffalo Refrigerating Machine Co.) 



Weight of 
Block. 


Size of Can. 


Time of 
Freezing. 


Weight of 
Block. 


Size of Can. 


Time of 
Freezing. 


pounds 

50 
100 
150 
150 
200 


4x10x24 
6x12x26 
8x15x32 
8x15x44 
10x15x36 
10x20x36 


hours 
12 
20 
36 
36 
48 
48 


pounds 
100 
200 
300 
400 
200 


11x11x32 
11x22x32 
11x22x44 
11x22x56 
14x14x40 


hours 
48 
54 
54 
54 
66 



The above given time of freezing is with a brine temperature of 15° F 

Cubic Feet of Well-insulated Space per Ton of Refrigeration. 

(F. W. Niebling Co., Cincinnati, O.) 



Room Temperature. 


0°F. 


5° 1 10° 


20° 


32° 


36° 


Size of Room. 




Cubic Feet 


per Ton 






Up to 1.000 cu. ft 

1.000 to 10.000 cu. ft 

Over 10.000 cu. ft 


200 
600 
1000' 


400 
1200 
2000 


800 
2500 
4000 


1400 
4500 
6000 


2000 
6000 
8000 


2500 

8000 

10.000 



MARINE ENGINEBRINQ. 

Rules for Pleasuring Dimensions and Obtaining Tonnage of 
Vessels. (Record of American and Foreign Shipping. American Bureau 
of Shipping, N. Y., 1S90.) — The dimensions to be measured as follows; 

I. Length, L. — From the fore-side of stem to the after-side of stern- 
post measured at middle line on the upper deck of all vessels, except 
those having a continuous hurricane-deck extending right fore and alt, 
in wliich the length is to be measured on the range of deck immediately 
below the hurricane-deck. 

Vessels ha\dng clipper heads, raking forward, or receding stems, or 
raking stern-posts, the length to be the distance of the fore-side of stem 
from aft-side of stern-post at the deep-load water-line measured at middle 
line. (The inner or propeller-post to be taken as stern-post in screw- 
steamers.) 

II. Breadth, B. — To be measured over the widest frame at its widest 
part: in other words, the molded breadth. 

III. Depth, D. — To be measured at the dead-flat frame and at middle 
line of vessel. It shall be the distance from the top of floor-plate to the 
upper side of upper deck-beam in all vessels except those having a con- 
tinuous hurricane-deck, extending right fore and aft, and not intended 
for the American coasting trade, in which the depth is to be the distance 
from top of floor-plate to midway between top of hurricane deck-beam 
and the top of deck-beam of the deck immediately below hurricane-deck. 

In vessels fitted with a continuous hiu-ricane-deck, extending right 
fore and aft, and intended for the American coasting trade, the depth is 



MARINE ENGINEERING. 1369 

to be the distance from top of fioor-plate to top of deck-beam of deck 
immediately below hurricane-deck. 

Rule for Obtaining Tonnage. — Multiply together the length, breadth, 
and depth, and their product by 0.75; divide the last product by 100; 
the quotient will be the tonnage. LX BX DX 0.75 -h 100 = tonnage. 

The U. S. Custom-house Tonnage Law, May 6, 1804, provides that 
"the register tonnage of a vessel shall be her entire internal cubic capacity 
in tons of 100 cubic feet each." This measurement includes all the space 
between upper decks, however many there may be. ExpUcit directions 
for making the measurements are given in the law. 

The Displacement of a Vessel (measured in tons of 2240 lbs.) is 
the weight of the volume of w^ater which it displaces. For sea-water it is 
equal to the volume of the vessel beneath the water-hne, in cubic feet, 
divided by 35, which figure is the number of cubic feet of sea- water at 
60° F. in a ton of 2240 lbs. For fresh water the divisor is 35.93. The 
U. S. register tonnage will equal the displacement when the entire internal 
cubic capacity bears to the displacement the ratio of 100 to 35. 

The displacement or gross tonnage is sometimes approximately esti- 
mated as follows: Let L denote the length in feet of the boat, B its extreme 
breadth in feet, and D the mean draught in feet; the product of these 
three dimensions will give the volume of a parallelopipedon in cubic feet. 
Putting V for this volume, we have V = LX BX D. 

The volume of displacement may then be expressed as a percentage 
of the volume V, known as the " block coefficient. " This percentage varies 
for different classes of ships. In racing yachts with very deep keels it 
varies from 22 to 33: in modern merchantmen from 55 to 90; for ordinary 
small boats probably 50 will give a fair estimate. The volume of dis- 
placement in cubic feet divided by 35 gives the displacement in tons. 

Coefficient of Fineness. — A term used to express the relation between 
the displacement of a sliip and the volume of a rectangular prism or box 
whose lineal dimensions are the length, breadth, and draught. 

Coefficient of fineness = DX S5-r-(LX B X W); D being the displace- 
ment in tons of 35 cubic feet of sea-water to the ton, L the length between 
perpendiculars, B the extreme breadth and W the mean draught, all in feet. 

Coefficient of AVater-lines. — An expression of the relation of the dis- 
placement to the volume of the prism whose section equals the midship 
section of the ship, and length equal to the length of the ship. 

Coefficient of water-hnes = D X35-^ (area of immersed water sectionXL). 
Seaton gives the following values: 

Coefficient Coefficient of 
of Fineness. Water-lines 

Finely-shaped ships .55 .63 

Fairly-shaped ships .61 .67 

Ordinary merchant steamers 10 to 11 knots. . . 0.65 0.72 

Cargo steamers, 9 to 10 knots , .70 .76 

Modern cargo steamers of large size .78 .83 

Resistance of Ships. — The resistance of a ship passing through water 
mav vary from a number of causes, as speed, form of body, displacement, 
midship dimensions, character of wetted surface, fineness of lines, etc. 
The resistance of the water is twofold; 1st. That due to the displacement 
of the water at the bow^ and its replacement at the stern, with the con- 
sequent formation of waves. 2d. The friction between the wetted sur- 
face of the ship and the water, known as skin resistance. A common 
approximate formula for resistance of vessels is 
Resistance = speed2 X \/ displacement X a constant, or R= S'^D^f^ X C. 

If Di = displacement in pounds, Si = speed m feet per mmute, R re- 
sistance in pounds, R = cSi^Di ^1^. The work done in overcoming the re- 
sistance through a distance equal to SiisRXSi = cS{-^Di^f^; and if E is 
the efficiency of the propeller and machinery combined, the indicated 
horse-power I.H.P. = cSiWi^f^ ^ (E X 33.000). 

If s = speed in knots, D = displacement in tons, and C a constant 
which includes all the constants for form of vessel, efficiency of mechan- 
ism, etc., I.H.P. = 531)2/3 ^ c. 

The wetted surface varies as the cube root of the square of the displace- 
ment; thus, let L be the length of edge of a cube just immersed, whose 



1370 



MARINE ENGINEERING. 



displacement is D and wetted surface W. Then D — L^ or L = ^ D, 
and Tf = 5 X L2 = 5 X (-^d)^. That is, W varies as D^^3. 

Another approximate formula is 

I.H.P. = area of immersed midship section X S^ -^ K, 

The usefulness of these two formulae depends upon the accuracy of the 
so-called "constants" C and K, which vary with the size and form of the 
ship, and probably also with the speed. Seaton gives the following, 
which may be taken roughly as the values of C and K under the condi- 
tions expressed; 



General Description of Ship. 



iSpeed, 


Value 


knots. 


of C. 


15 to 17 


240 


15 ♦* 17 


190 


13 •• 15 


240 


11 " 13 


260 


11 ♦• 13 


240 


9 " 11 


260 


13 *• 15 


200 


11 •• 13 


240 


9 " 11 


260 


11 ♦• 13 


220 


9 ♦• 11 


250 


11 •* 12 


220 


9 •* 11 


240 


9 " 11 


220 


11 " 12 


200 


10 •• 11 


210 


9 " 10 


230 


9 •* 10 


200 



Value 
of K. 



Shipa over 400 feet long, finely shaped . 
300 



Ships over 300 feet long, fairly shaped . . 
Ships over 250 feet long, finely shaped.. 

Ships over 250 feet long, fairly shaped . . 
t« •» •• 

Ships over 200 feet long, finely shaped . . 

Ships over 200 feet long, fairly shaped . . 
Ships under 200 feet long, finely shaped. 



Ships under 200 feet long, fairly shaped . 



620 
500 
650 
700 
650 
700 
580 
660 
700 
620 
680 
600 
640 
620 
550 
580 
620 
600 



Coeflacient of Performance of Vessels. 

^(displacement;2 x (speed in knots)3~- 



— The quotient 

tons of coal in 24 hours 



gives a coefficient of performance which represents the comparative cost 
of propulsion in coal expended. Sixteen vessels with three-stage expan- 
sion-engines in 1890 gave an average coefficient of 14,810, the range being 
from 12,150 to 16,700. 

In 1881 seventeen vessels with two-stage expansion-engines gave an 
average coefficient of 11,710. In 1881 the length of the vessels tested 
ranged from 260 to 320, and in 1890 from 295 to 400. The speed in knots 
divided by the square root of the length in feet in 1881 averaged 0.539; 
and in 1890, 0.579; ranging from 0.520 to 0.641. (Proc. Inst. M. E., 
July, 1891, p. 329.) 

Defects of the Common Formula for Resistance. — Modern 
experiments throw doubt upon the truth of the statement that the resist- 
ance varies as the square of the speed. (See Robt. Mansel's letters in 
Engineering, 1891: also his paper on The Mechanical Theory of Steam- 
ship Propulsion, read before Section G of the Engineering Congress, 
Chicago, 1893.) 

Seaton says: In small steamers the chief resistance is the skin resistance. 
In very fine steamers at high speeds the amount of power required seems 
excessive when compared with that of ordinary steamers at ordinary 
speeds. 

In torpedo-launches at certain high speeds the resistance increases at a 
lower rate than the square of the speed. 

In ordinary sea-going and river steamers the reverse seems to be the 
case. 

Rankine's Formula for total resistance of vessels of the "wave-line" 
type is: 

R = ALBV2 (1 + 4 sin2 9 + sin4 0), 

in which equation 9 is the mean angle of greatest obliquity of the stream- 
lines, A is a constant multiplier, B the mean wetted girth of the surfaco 
exposed to friction, L the length in feet, and V the speed in knots. The 



MARINE ENGINEERING. 1371 

power demanded to impel a sliip is thus the product of a constant to be 
determined by experiment, the area of the wetted surface, the cube of 
the speed, and the quantity in tlie parenthesis, wliich is known as the 
"coefficient of augmentation." In calculating the resistance of ships the 
last term of the coefficient may be neglected as too small to be practically 
Important. In applying the formula, the mean of the squares of the 
sines of the angles of maximum obliquity of the water-hnes is to be taken 
for sin2 e, and the rule will then read thus: 

To obtain the resistance of a ship of good form, in pounds, multiply the 
length in feet by the mean immersed girth and by the coefficient of aug- 
mentation, and then take the product of this "augmented surface," as 
Rankine termed it, by the square of the speed in knots, and by the proper 
constant coefficient selected from the following; 

For clean painted vessels, iron hulls A = 0.01 

For clean coppered vessels A = 0.009 to 0.008 

For moderately rough iron vessels A = 0.011 + 

The net, or effective, horse-power demanded will be quite closely 
obtained by multiplying the resistance calculated, as above, by the speeo 
in knots and dividing by 326. The gross, or indicated, power is obtained 
by multiplying the last quantity by the reciprocal of the efficiency of the 
machinery and propeller, which usually should be about 0.6. Rankine 
uses as a divisor in this case 200 to 260. 

The form of the vessel, even when designed by skillful and experienced 
naval architects, will often vary to such an extent as to cause the above 
constant coefficients to vary somewhat: and the range of variation with 
good forms is found to be from 0.8 to 1.5 the figures given. 

For well-shaped iron vessels, an approximate formula for the horse- 
power required is H. P. = *S73^ 20,000, in which S is the "augmented 
surface." The expression SV^ -ir H.P. has been called by Rankine the 
coefficient of propulsion. In the Hudson River steamer "Mary Powell," 
according to Thurston, this coefficient was as high as 23,500. 

The expression D^V^ -e- H.P. has been called the locomotive performance. 
(See Rankine's Treatise on Shipbuilding, 1864; Thurston's Manual of the 
Steam-engine, part ii, p. 16; also paper by F. T. Bowles, U. S. N., Proc. 
U. S. Naval Institute, 1883.) 

Rankine's metnod for calculating the resistance is said by Seaton to 
give more accurate and reliable results than those obtained by the older 
rules, but it is criticised as being difficult and inconvenient of appUcation 

Empirical Equations for Wetted Surface. (Peabody, Naval Archi- 
tecture, page 411). — L = length, feet; B = beam; II = mean draught; 
D = displacement in tons ; K = block coefficient. 

Taylor Surface = C\/DL. Values of C for different ratios B ^ H are: 

B^H= 2 2.2 2.4 2.6 2.8 3.0 3.2 3.4 

C = 15.63 15.54 15.50 15.51 15.55 15.62 15.71 15.83 

Normand Surface = 1.52 LH + (3.74 + 0.85 K'-) LB. 
Mumford Surface = L (1.74 + KB). 

Errors of these approximate equations as applied to several types of 
vessels are shown by Professors Durand and AIcDermott (Trans. 
Soc. Nav. Archts. & Mar. Engrs., Vol. 2), as follows: Taylor - 2.69 to 
+ 2.52%; Normand, - 1.55 to + 2.57%; Mumford, to - 0.95%, 
except one lake freight vessel, L = 299, B = 40.9, D = 15.9, K = 0.S25. 
on which Mumford's formula was — 12.55% in error. 

E. R. Mumford's Method of Calculating Wetted Surfaces is given 
in a paper by Archibald Denny, Eng'g, Sept. 21, 1894. The following 
is his formula, which gives closely accurate results for medium draughts, 
beams, and finenesses; 

S = (LXDX 1.7) + (L X B X C). 

in which S = wetted surface in square feet ; L •= length between perpen- 
diculars in feet; D = middle draught in feet; B = beam in feet; C — 
block coefficient. 

The formula may also be expressed in the form S = L(1.7 D + EC). 

In the case of twin-screw ships having projecting shaft-casings, or in 



1372 



MARINE ENGINEERING. 



the case of a ship having a deep keel or bilge keels, an addition must be 
made for such projections. The formula gives results which are in 
general much more accurate than those obtained by Kirk's method. It 
underestimates the surface when the beam, draught, or block coefficients 
are excessive; but the error is small except in the case of abnormal forms, 
such as stern-wheel steamers having very excessive beams (nearly one- 
fourth the length), and also very full block coefficients. The formula 
gives a surface about 6% too small for such forms. 

The wetted surface of the block is nearly equal to that of the ship of 
the same length, beam and draught; usually 2% to 5% greater. In 
exceedingly tine hoilow-hne sliips it may be 8% greater. 

Area of bottom of block = (F -h M) X B; 

Area of sides = 2 M X H, 

Area of sides of ends = 4 X J F^ + {-^ X H\ 

Tangent of half angle of entrance = y2B/F = B/{2 F), 
From this, by a table of natural tangents, the angle of entrance may be 
obtained: 

Angle of Entrance Fore-body in 
of the Block Model, parts of length. 
Ocean-going steamers, 14 knots and upw'd 18° to 15° 0.3 to .36 

12 to 14 knots 21° to 18° 0.26 to 0.3 

cargo steamers, 10 to 12 knots.. 30° to 22° .22 to .26 

Dr. Kirk's Method. — This method is generally used on the Clyde. 

The general idea proposed by Dr. Kirk is to reduce all ships to so 
definite and simple a form that they may be easily compared; and the 
magnitude of certain features of this form shall determine the suitabihty 
of the ship for speed, etc. 

The form consists of a m.iddle body, which is a rectangular parallelo- 

giped, and fore-body and after-body, prisms having isosceles triangles for 
ases, as shown in Fig. 225. 

D E 




Fig. 225. 



This is called a block model, and is such that its length is equal to that 
of the ship, the depth is equal to the mean draught, the capacity equal 
to the displacement volume, and its area of section equal to the area of 
immersed midsliip section. The dimensions of the block model may be 
obtained as follows: Let AG = HE = length of fore- or after-body = F; 
GH = length of middle body = M: KL = mean draught = H; EK = 
area of immersed midship section ^KL =5. Volume of block = (i^+ikf) X 
BX H- midship section = BX H\ displacement in tons = volume in 
cubic ft. -5- 35. 

AH = AG -{- GH == F+ M = displacement X 35 -4- (B X H), 

To find the Indicated Horse-power from the Wetted Surface. 

(Seaton.) — In ordinary cases the horse-power per 100 feet of wetted 
surface may be found by assuming that the rate for a speed of 10 knots 
is 5, and that the quantity varies as the cube of the speed. For example: 
To find the number of I.H.P. necessary to drive a ship at a speed of 15 
knots, having a wetted skin of block model of 16,200 square feet: 

The rate per 100 feet = (15/10)3 X 5 = 16.875. 
Then I.H.P. reauired = 16.875 X 162 = 2734. 
When the ship is exeptionally well-proportioned, the bottom quite 



MARINE ENGINEERING. 



1373 



Clean, and the efficiency of the machinery high, as low a rate as 4 I.H.P. 
per 100 feet of wetted skin of block model may be allowed. 

The gfross indicated horse-power includes the power necessary to over- 
come the friction and other resistance of the engine itself and the shafting, 
and also the power lost in the propeller. In other words, I.H.P. is no 
measure of the resistance of the ship, and can only be relied on as a means 
of deciding the size of engines for speed, so long as the efficiency of the 
engine and propeller is known definitely, or so long as similar engines and 
propeUers are employed in ships to be compared. The former is difiicuii 
to obtain, and it is nearly impossible in practice to know how much of 
the power shown in the cyhnders is employed usefully in overcoming the 
resistance of the sliip. The following example is given to show the vari- 
ation in the efficiency of propellers: 

Knots. I.H.P. 

H.M.S. "Amazon," with a 4-bladed screw, gave 12.064 with 1940 

H.M.S. "Amazon," with a 2-bladed screw, increased 

pitch, and fewer revolutions per minute 12.396 " 1663 

H.M.S. " Iris, " with a 4-bladed screw 16.577 " 7503 

H.M.S. "Iris." with 2-bladed screw, increased pitch, 

fewer revolutions per knot 18.587 " 7556 

Relative Morse-power Required for Different Speeds of Vessels. 
(Horse-power for 10 knots = 1.) — The horse-power is taken usually to 
vary as the cube of the speed, but in different vessels and at different 
speeds it may vary from the 2.8 power to the 3.5 power, depending upon 
the lines of the vessel and upon the efficiency of the engines, the pro- 
peller, etc. (The power may vary at a much higher rate than the 3.5 
power of the speed when the speed is much less than normal, and the 
machinery is therefore working at less than its normal efficiency.) 





4 


6 


8 


10 


12 


14 


16 


18 


20 


22 


24 


26 


28 


30 


aiM 






























HPoc 






























82-8 


.0769 


.239 


.535 




1.666 


2.565 


3.729 


5.185 


6.964 


9.095 


11.60 


14.52 


17.87 


21.67 


S2.9 


.0701 


.227 


.524 




1.697 


2.653 


3.908 


5.499 


7.464 


9.841 


12.67 


15.97 


19.80 


24.19 


S3 


.0640 


.216 


.512 




1.728 


2.744 


4.096 


5.832 


8. 


10.65 


13.82 


17.58 


21.95 


27. 


S3-1 


.0584 


.205 


.501 




1.760 


2.838 


4,293 


6.185 


8.574 


11.52 


15.09 


19.34 


24.33 


30.14 


S3.2 


.0533 


.195 


.490 




1.792 


2.935 


4.500 


6.559 


9.189 


12.47 


16.47 


21.28 


26.97 


33.63 


S3.3 


.0486 


.185 


.479 




1.825 


3.036 


4.716 


6.957 


9.849 


13.49 


17.98 


23.41 


29.90 


37.54 


83-4 


.0444 


.176 


.468 




1.859 


3.139 


4.943 


7.378 


10.56 


14.60 


19.62 


25.76 


33.14 


41.90 


S3.5 


.0405 


.167 


.458 




1.893 


3.247 


5.181 


7.824 


11.31 


15.79 


21.42 


28.34 


36.73 


46.77 



Example in Use of the Table. — A certain vessel makes 14 knots 
speed with 587 I.H.P. and 16 knots with 900 I.H.P. What I.H.P. will 
be required at 18 knots, the rate of increase of horse-power with increase 
of speed remaining constant? The first step is to find the rate of 
increase, thus: 14^ : 16^ :: 587 : 900. 

X log IQ- X log 14 = log 900 - log 587; 
X (0.204120 - 0.146128) = 2.954243 - 2.768638, 
whence x (the exponent of S in formula H.P.oc S^) = 3.2. 

From the table, for S^-s and 16 knots, the I.H.P. is 4.5 times the 
I.H.P. at 10 knots; .-. H.P. at 10 knots = 900 ^ 4.5 = 200. 

From the table for S^-"^ and 18 knots, the I.H.P. is 6.559 times the 
I.H.P. at 10 knots; .'. H.P. at 18 knots = 200 X 6.559 = 1312 H.P. 

Resistance per Horse-power for Different Speeds. (One horse- 
power = 33.000 lbs. resistance overcome through 1 ft. in 1 min.) — The 
resistances per horse-power for various speeds are as follows: For a 
speed of 1 knot, or 6080 feet per hour = IOII/3 ft. per min., 33,000 -^ 
1011/3 = 325.658 lbs. per horse-power; and for any other speed 325.658 
lbs. divided by the speed in knots; or for 

1 knot 325.66 lbs. 

2 knots 162.83 " 

3 ** 108.55 ♦* 

4 " 81.41 *• 
6 " 65.13 •* 

6 *• 54.28 •' 

7 " 46.52 '♦ 



8 knots 40.71 lbs. 


15 knots 


21.71 lbs. 


9 " 36.18 ♦• 


16 " 


20.35 " 


10 •• 32.57 •* 


17 •' 


19.16 •» 


11 •• 29.61 " 


18 *' 


18.09 •• 


12 " 27.14 •' 


19 •• 


17.14 *• 


13 •• 25.05 •• 


20 " 


16.28 •• 


14 ♦• 23.26 " 







1374 



MAKiNE ENGINEERING. 



More accurate methods than those above given for estimating the horse- 
power required lor any proposed ship are: 1. Estimations calculated 
from the results of trials of "similar" vessels driven at "corresponding" 
speeds; "similar'! vessels being those that have the same ratio oi iengiii 
to breadth and to draught, and the same coefficient of fineness, and 
"corresponding" speeds those wMch are proportional to the square roots 
of the lengths of the respective vessels. Froude found that the resistances 
of such vessels varied almost exactly as wetted surface X (speed)^ 

2. The method employed by the British Admiralty and by some Clyde 
shipbuilders, viz., ascertaining the resistance of a model of the vessel, 
12 to 20 ft. long, in a tank, and calculating the power from the results 
obtained. 

Estimated Displacement, Horse-power, etc. — The table on the 
next page, calculated by the author, will be found convenient for making 
approximate estimates. 

The figures in 7th column are calculated by the formula H.P. =S^D'3-7- c 
in which c = 200 for vessels under 200 ft. long when C =0.65, and 210 
when C = 0.55; c = 200 for vessels 200 to 400 ft. long when C =0.75, 
220 when C = 0.65, 240 when C = 0.55; c = 230 for vessels over 400 ft. 
long when C = 0.75, 250 when C = 0.65, 260 when C = 0.55. 

The figures in the 8th column are based on 5 H.P. per 100 sq. ft. of 
wetted surface. 

The di ameters of screw in the 9th column are from formu la D = 3.31 
^I.H.P., and in the 10th column from formula D = 2.71 ^I.H.P. 
^ To find the diameter of screw for any other speed than 10 knots, revolu- 
tions being 100 per minute, multiply the diameter given in the table by 
the 5th root of the cube of the given speed -^ 10. For any other revolu- 
tions per minute than 100, divide by the revolutions and multiply by 100. 

To find the approximate horse-power for any other speed than 10 knots, 
multiply the horse-power given in the table by the cube of the ratio of the 
given speed to 10, or by the relative figure from table on p. 1373. 

F. E. CarduUo, Mach'y, April, 1907. gives the following formula as 
clo sely ap proximating the speed of modern types of hulls: S = 6.35 
'/t it t* 
1/ 2/ ' " » ^ which S = speed in knots, D = displacement in tons. If 

we take S = 10 knots, then I.H.P. ~ D^/3 = 3.906. Let D = 10,000, and 
S = 10, then H.P. = 1813. The table on page 1375 gives for a displace- 
ment of 10,400 tons and a coefficient of fineness 0.65, 1966 and 1760 H.P., 
averaging 1863 H.P. 

Internal Combustion Marine Engines. — Linton Hope (Eng'g, 
April 8, 1910), in a paper on the application of internal combustion engines 
to fishing boats and fine-lined commercial vessels, gives a table showing 
the brake H.P. required to propel such vessels at various speeds. The 
following table is an abridgment. L = load water line; Z) = displacement 
in tons. 







Block Coefficient. 










5peed 


in Knots 






0.25 


0.3 


0.35 


0.4 


4 


5 1 6 


7 1 8 


9 1 10 


L 1 D 


L I D 


L I D 


L I D 


Brake Horse-power. 


78 
71 
65 
59 
54 
50 


105 

81 

62 

47 

36 

28 

22 

17 

13 
9 

6V2 
41/2 
31/4 


75 
69 
63 
57 
52 
48 
44 
40 
37 
34 
31 
29 
27 


100 

77 

60 

45 

35 

27 

21 

16 

12 

81/2 

6 

4V. 


72 
66 
60 
54 
50 
46 
42 
38 
35 
32 
30 
28 
26 


95 
73 

58 

44 

34 

26 

20 

15 

11 1/2 
8 

51/2 
33/4 
23/4 


69 
63 
57 
52 
48 
44 
40 
37 
34 
31 
29 
27 
25 


90 
70 
55 
42 
32 
25 
19 
14 

71/2 

31/2 
21/2 


20 
17 
15 
13 
11 

9 

8 

7 

6 

5 

4 

3 

21/2 


30 
25 
22 
19 
16 
13 
12 
11 

9 

7 

41/2 


43 
37 
32 
27 
24 
20 
17 
15 
13 
11 

9 

7 

61/2 


60 
51 

44 

11 

29 
25 
22 
19 
16 
14 
12 
11 


81 
69 
60 
53 
48 
44 
40 
37 
34 


110 
93 

82 
76 
71 


150 


46 






41 






38 






35 






^?. 








30 








7^ 

















MARINE ENGINEERING. 



1375 



Estimated Displacement, Horse-power, etc., of Steam-vessels of 
Various Sizes. 







«,- 


a . O 


Displacement. 

LBDX C 

35 




Estimated Horse- i 


Diam. of Screw for 10. 


5« 


5^ 


U 


1 o S 


Wetted Surface 

/. (1.7 D+ JiC) 

sq. ft. 


power at 10 kDotd. | 


knots speec 
rets, per 


and 1(10 


is^ 


Calc. 
from Dis- 


Calc. from 
Wetted 


minute. 


J^ 


If Pitch -.. 1 


If Pitch =i 


tt 




O B 


tons. 




placem't. 


Surface. 


Diam. 


1.4 Diam. 


12 


3 


1.5 


0.55 


0.85 


48 


4.3 


2.4 


4.4 


3.6 


16 


3 


1.5 


.55 


1.13 


64 


5.2 


3.2 


4.6 


3.8 


4 


2 


.65 


2.38 


% 


8.9 


4.8 


5.1 


4.2 


20{ 


3 


1.5 


.55 


1.41 


80 


6.0 


4.0 


4.7 


3.9 


4 


2 


.65 


2.97 


120 


10.3 


6,0 


5.3 


4.3 


24 { 


3.5 


1.5 


.55 


1.98 


104 


7.5 


5.2 


5 


4.1 


4.5 


2 


.65 


4.01 


152 


12.6 


7.6 


5.5 


4.5 


30 { 


4 


2 


.55 


3.77 


168 


11.5 


8.4 


5.4 


4.4 


5 


2.5 


.65 


6.96 


224 


18.2 


11.2 


5.9 


4.8 


-{ 


4.5 


2 


.55 


5.66 


235 


15.1 


11.8 


5.7 


4.7 


6 


2.5 


.65 


11.1 


326 


24.9 


16.3 


6.3 


5.2 


50 { 


6 


3 


.55 


14.1 


420 


27.8 


21.0 


6.4 


5.4 


8 


3.5 


.65 


26 


558 


43.9 


27.9 


7.1 


5.8 


60 { 


8 


3.5 


.55 


26.4 


621 


42.2 


31.1 


7.0 


5.7 


10 


4 


.65 


44.6 


798 


62.9 


39.9 


7.6 


6.2 


70{ 


10 


4 


.55 


44 


861 


59.4 


43.1 


7.5 


6.1 


12 


4.5 


.65 


70.2 


1082 


85.1 


54.1 


8.1 


6.6 


8o{ 


12 


4.5 


.55 


67.9 


1140 


79.2 


57.0 


7.9 


6.5 


14 


5 


.65 


104.0 


1408 


111 


70.4 


8.5 


7.0 


,o{ 


13 


5 


.55 


91.9 


1408 


97 


70.4 


8.3 


6.8 


16 


6 


.65 


160 


1854 


147 


92.7 


9 


7.3 


100 


13 


5 


.55 


102 


1565 


104 


78.3 


8.4 


6.9 


15 


5.5 


.65 


153 


1910 


143 


95.5 


8.9 


7.3 


17 


6 


.75 


219 


2295 


202 


115 


9.6 


7.8 


120 1 


14 


5.5 


.55 


145 


2046 


131 


102 


8.8 


7.2 


16 


6 


.65 


214 


2472 


179 


124 


9.4 


7.6 


18 


6.5 


.75 


301 


2946 


250 


147 


10 


8.2 


140 1 


16 


6 


.55 


211 


2660 


169 


133 


9.2 


7.4 


18 


6.5 


65 


306 


3185 


227 


159 


9.8 


8.0 


20 


7 


.75 


420 


3766 


312 


188 


10.5 


8.5 


160 I 


17 


6.5 


.55 


278 


3264 


203 


163 


9.6 


7.8 


19 


7 


.65 


395 


3880 


269 


194 


10.1 


^■\ 


( 


21 


7.5 


.75 


540 


4560 


368 


228 


10.8 


8.8 




20 


7 


.55 


396 


4122 


257 


206 


10.1 


8.2 


180 


22 


7.5 


.65 


552 


4869 


337 


243 


10.6 


8.7 




24 


8 


75 


741 


5688 


455 


284 


11.3 


9.2 




22 


7 


55 


484 


4800 


257 


240 


10. 1 


8.2 


200 


25 


8 


.65 


743 


5970 


373 


299 


10.8 


8.8 




28 


9 


75 


1080 


7260 


526 


363 


11.6 


9.5 




28 


8 


55 


880 


7250 


383 


363 


10.9 


8.9 


250 


32 


10 


65 


1486 


9450 


592 


473 


11.9 


9.7 




36 


12 


.75 


2314 


11850 


875 


593 


12.8 


10.5 




32 


10 


55 


1509 


10380 


548 


519 


11.7 


9.6 


300 


36 


12 


65 


2407 


13140 


806 


657 


12.6 


10.4 




40 


14 


75 


3600 


17140 


1175 


857 


13.6 


11.1 




38 


12 


55 


2508 


14455 


769 


723 


12.5 


10.2 


350 


42 


14 


65 


3822 


17885 


nil 


894 


13.5 


11.0 




46 


16 


75 


5520 


21595 


1562 


1080 


14.4 


11.8 




44 


14 


55 


3872 


19200 


1028 


960 


13.3 


10.8 


400 


48 


16 


65 


5705 


23360 


1451 


1168 


14.2 


11.6 




52 


18 


75 


8023 


27840 


2006 


1392 


15.2 


12.4 




50 


16 


55 


5657 


24515 


1221 


1226 


13.7 


11.2 


450 


54 


18 


.65 


8123 


29565 


1616 


1478 


14.5 


11.9 




58 


20 


75 


11157 


34875 


2171 


1744 


15.4 


12.6 




52 
56 


18 


55 


7354 


29600 


1454 


1480 


14.2 


11.6 


500 


20 


65 


10400 


35200 


1966 


1760 


15.1 


12.4 




60 


22 


75 


14143 


41200 


2543 


2060 


15.9 


13.0 


( 


56 


20 


55 


9680 


36245 


1747 


1812 


14.7 


12.0 


550 


60 


22 


65 


13483 


42735 


2266 


2137 


15.5 


12.7 


( 


64 


24 


75 


18103 


49665 


2998 


2483 


16.4 


13.4 


( 


60 


22 


55 


12446 


42900 


2065 


2145 


15.2 


12.5 


600 5 


64 


24 


'65 


17115 


50220 


2656 


2511 


15.4 


13.1 


1 


68 


26 


.75 


22731 


58020 


3489 


2901 


16.9 


13.8 



1376 



MARINE ENGINEERING. 



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j,: 



THE SCREW-PROPELLER. 1377 

THE SCREW-PROPELLER. 

The "pitch" of a propeller is the distance which any point in a blade 
describing a heUx will travel in the direction of the axis during one revolu- 
tion, the point being assumed to move around the axis. The pitch of a 
propeller with a uniform pitch is equal to the distance a propeller will 
advance during one revolution, provided there is no sUp. In a case of 
this kind, the term " pitch" is analogous to the term "pitch of the thread" 
of an ordinary single-threaded screw. 

Let P = pitch of screw in feet, R = number of revolutions per second, 
V = velocity of stream from the propeller = P X R, v = velocity of the 
ship in feet per second, V — v = slip, A = area in square feet of section 
of stream from the screw, approximately the area of a circle of the same 
diameter, A X V = volume of water projected astern from the ship in 
cubic feet per second. Taking the weight of a cubic foot of sea-water 
at 64 lbs., and the force of gravity at 32, we have from the common for- 

vi W vi W 

m.ula for force of acceleration, viz.: F^Mj = — y.oi F ^ —vu when 

t =1 second. 

6^ AV 
Thrust of screw in pounds = — ^T~ iV — v) = 2 AV iV — v), 

Rankine (Rules, Tables, and Data, p. 275) gives the following: To 
calculate the thrust of a propelling instrument (jet, paddle, or screw) in 
pounds, multiply together the transverse sectional area, in square feet, 
of the stream driven astern by the propeller; the speed of the stream 
relatively to the ship in knots; the real slip, or part of that speed which is 
impressed on the stream by the propeller, also in knots; and the constant 
5.66 for sea-water, or 5.5 for fresh water. If *S = speed of the screw in 
knots, s = speed of ship in knots, A = area of the stream in square feet 
(of sea-water), 

Thrust in pounds = AXS (S - s) X 5. 66. 

The real slip is the velocity (relative to water at rest) of the water pro- 
jected sternward; the apparent slip is the difference between the speed of 
the ship and the speed of the screw; i.e., the product of the pitch of the 
screw by the number of revolutions. 

This apparent slip is sometimes negative, due to the working of the 
screw in disturbed water which has a forward velocity, follo\nng the ship. 
Negative apparent slip is an indication that the propeller is not suited 
to the ship. The apparent slip should generally be about 8% to 10% at 
full speed in well-formed vessels with moderately fine lines; in bluff cargo 
boats it rarely exceeds 5%. 

The effective area of a screw is the sectional area of the stream of water 
laid hold of by the propeller, and is generally, if not always, greater than 
the actual area, in a ratio which in good ordinary examples is 1.2 or there- 
abouts, and is sometimes as high as 1.4: a fact probably due to the stiffness 
of the water, which communicates motion laterally amongst its particles. 
(Rankine's Shipbuilding, p. 89.) 

Prof. D. S. Jacobus, Trans. A. S. M. E., xi, 1028, found the ratio of the 
effective to the actual disk area of the screws of different vessels to be as 
follows: 

Tug-boat, with ordinary true-pitch screw 1 .42 

Tug-boat, with screw having blades projecting backward 0.57 

Ferryboat "Bergen," with or- ( at speed of 12.09 stat. miles perhr.. 1 .53 
dinary true-pitch screw ( at speed of 13.4 stat. miles per hr. . 1 .48 

Steamer "Homer Ramsdell," with ordinary true-pitch screw 1 .20 

Size of Screw. — Seaton says: The size of a screw depends on so 
many things that it is very difficult to lay down any rule for guidance, 
and much must alwaj^s be left to the experience of the designer, to allow 
for all the circumstances of each particular case. The following rules are 
given for ordinary cases (Seaton and Rounthwaite's Pocket-book): 

10133 /S 
p = pitch of propeller in feet = ^ .■,^„ r , in wliich S = speed in 

K (.iUU — X) 

knots, R = revolutions per minute, and x = percentage of apparent 
slip. For a sUp of 10%, pitch = 112.6 S -h R. 



1378 



MARINE ENGINEERING. 



D = diameter of propeller = K 



I I.H.P. 

'^ V 100 / 



, K being a coefficient given 



in the table below. liK=20, D = 20,000 Vi.h.P. ~{Px R)^. 

, Total developed area of blades = C Vi.h.P. --i2, in which C is a coeffi- 
cient to be taken from the table. 

Another formula for pitch, given in Seaton's Marine Engineering is 
o **/t h p ' 
^^R\ i)2 ' i^ which C= 737 for ordinary vessels, and 660 for slow- 
speed cargo vessels with full lines.^ 

Thickness of blade at root = i/^ X fc, in which d = diameter of tail 
shaft in inches, n = number of blades, b = breadth of blade in inches 
where it joins the boss, measured parallel to the shaft axis; k = 4 for cast 
^^^rS,!..-^;^ ^^^ ^^^^ st^^^' 2 for gun-metal, 1.5 for high-class bronze 

Thickness of blade at tip: Cast iron 0.04 D -r 0.4 in.; cast steel 03 D 4- 
0.4 in.; gun-metal 0.03 Z) + 0.2 in.; high-class bronze 0.02 D +03 in 
where D = diameter of propeller in feet. 

Propeller Coefficients. 



Description of Vessel. 




CO 

■si 


No. of 

Blades 
per Screw 


1^ 


3^ 


Usual 
Mate- 
rial of 
Blades. 


Bluff cargo boats 


8-10 
10-13 
13-17 
13-17 
17-22 
17-22 
16-22 
16-22 
20-26 


One 

Twin 
One 
Twin 

One 


4 
4 
4 
4 
4 
3 
4 
3 
3 


17 -17.5 

18 -19 
19.5-20.5 
20.5-21.5 

21 -22 

22 -23 

21 -22.5 

22 -23.5 
25 


19 -I/. 5 
17 -15.5 
15 -13 
14.5-12.5 
12.5-11 
10.5- 9 
11.5-10.5 
8.5-7 
7-6 


Cast iron 


Cargo, moderate lines 

Pass, and mail, fine lines. . 

** ** ** very fine. . . 

Naval vessels, " ** . . 

<( ti «t «t 

Torpedo-boats, ** ** . . 


C.I. or S. 
G.M.orB 

B.orF.S. 



C. I., cast iron; G. M., gun-metal; B., bronze; S., steel; F.S., forged steel. 



V (PxRy 



and P 



/737I.H.P. 



From the formulae D = 20,000 
P = /) and i2 = 100, we obtain D = ^ 400 X I.hTr = 3.31 -y/l. H.P. 



R 



if 



If P = 1.4 D and i2 = 100, then D = ^145.8 X I.H.P. = 2.71 v^I.H.P. 

From these two formulae the figures for diameter of screw in the table 
on page 1375 have been calculated. They may be used as rough approx- 
imations to the correct diameter of screw for any given horse-power, for 
a speed of 10 knots and 100 revolutions per minute. 

For any other number of revolutions per minute multiply the figures 
in the table by 100 and divide by the given number of revolutions. For 
any other speed than 10 knots, since the I.H.P. varies approximately as 
the cube of the speed, and the diameter of the screw as the 5th root of the 
I.H.P., multiply the diameter given for 10 knots by the 5th root of the 
cube of one-tenth of the given speed. Or, multiply by the following 
factors: 

For speed of knots: 

_4 5_ 6 7 8 9 11 12 13 14 15 16 

^(S -^ 10)3 

= 0.577 0.660 0.736 0.807 0.875 0.939 1.059 1.116 1.170 1.224 1.275 1.327 

Speed : 

17 18 19 20 21 22 23 24 25 26 27 28 
N^ (S -^ 10)3 
= 1.375 1.423 1.470 1.515 1.561 1.605 1.648 1.691 1.733 1.774 1.815 1.855 

For more accurate determinations of diameter and pitch of screw, the 
formulae and coefficients given by Seaton, quoted above, should be used. 



THE SCREW-PROPELLER. 



1379 



Efficiency of the Propeller. — According to Rankine, if the slip of 
the water be s, its weight W, the resistance K, and the speed of the sliip v. 
R= Ws -i-g; Rv = Wsv-i- g. 

This impeUing action must, to secure maximum efficiency of propeller, 
be effected by an instrument which takes hold of the fluid without shock 
or disturbance of the surrounding mass, and, by a steady acceleration, 
gives it the required final velocity of discharge. The velocity of the 
propeller overcoming the resistance R would then be 

[v-\- {v-h s)]-i- 2 = v-\- s/2; 
and the work performed would be 

R (v-h s/2) = Wvs -h g+ Ws^ ■&• 2 g, 
the first of the last two terms being useful, the second the minimum lo«?t 
work; the latter being the wasted energy of the water thrown backward. 
The efficiency is E = v -i- (v+s/2); and this is the hmit attainable with 
a perfect propeUing instrument, which Umit is approached the more nearly 
as the conditions above prescribed are the more nearly fulfilled. The 
efficiency of the propeUing instrument is probably rarely much above 
0.60, and never above 0.80. 

In designing the screw-propeller, as was shown by Dr. Froude, the 
best angle for the surface is that of 45° with the plane of the disk; but as 
all parts of the blade cannot be given the same angle, it should, where 
practicable, be so proportioned that the "pitch-angle at the center of 
effort" should be made 45°. The maximum possible efficiency is then, 
according to Froude, 77%. In order that the water should be taken on 
without shock and discharged with maximum backward velocity, the 
screw must have an axially increasing pitch. 

The true screw is the usual form of propeller in all steamers, both mer- 
chant andnaval. (Thurston, Manual of the Steam-engine, part ii, p. 176.) 

The combined efficiency of screw, shaft, engine, etc., is generally taken 
at 50%. In some cases it may reach 60% or 65%. Rankine takes the 
effective H.P. to equal the I.H.P. -^ 1.63. 

Results of Researches on the efficiency of screw-propellers are sum- 
marized by S. W. Barnaby, in a paper read before section G of the Engi-* 
neering Congress, Chicago, 1893. He states that the following general 
principles have been established: 

(a) There is a definite amount of real slip at which, and at which only, 
maximum efficiency can be obtained with a screw of any given type, 
and this amount varies with the pitch-ratio. The slip-ratio proper to a 
given ratio of pitch to diameter has been discovered and tabulated for a 
screw of a standard type, as below : 

Pitch-ratio and Slip for Screws of Standard Form. 



Pitch-ratio. 


Real Slip of 
Screw. 


Pitch-ratio . 


Real Slip of 
Screw. 


Pitch-ratio. 


Real Slip of 
Screw. 


0.8 


15.55 


1.4 


19.5 


2.0 


22.9 


0.9 


16.22 


1.5 


20.1 


2.1 


23.5 


1.0 


16.88 


1.6 


20.7 


2.2 


24.0 


I.I 


17.55 


1.7 


21.3 


2.3 


24.5 


1.2 


18.2 


1.8 


21.8 


2.4 


25.0 


1.3 


18.8 


1.9 


22.4 


25 


25.4 



(6) Screws of large pitch-ratio, besides being less efficient in them- 
selves, add to the resistance of the hull by an amount bearing some pro- 
portion to their distance from it, and to the amount of rotation left in 
the race. 

(c) The be.st pitch-ratio lies probably between 1.1 and 1.5. 

1^) The fuller the lines of the vessel, the le.=?s the pitch-ratio should be, 

(e) Coarse-pitched screws should be placed further from the stern 
than fine-pitched ones. 

(/) Apparent negative sfip is a natural result of abnormal proportions 
of propellers. 

Cg) Three blades are to be preferred for high-speed vessels, but when 
the diameter is unduly restricted, four or even more may be advantageously 
employed. 

(h) An efficient form of blade is an ellipse having a minor axis equal 
to four-tenths the major axis. 

(i) The pitch of wide-bladed screws should increase from forward to 
aft, but a uniform pitch gives satisfactory results when the blades are 



1380 



MARINE ENGINEERING. 



narrow, and the amount of the pitch variation should be a function of the 

width of the blade. 

0") A considerable inclination of screw-shaft produces vibiation, and 
with right-handed twin-screws turning outwards, if the shafts are incUnea 
at all, it should be upwards and outwards from the propellers. 

For results of experiments with screw-propellers, see F. C. Marshall, 
Proc. Inst. M. E., 1881; R. E. Froude, Trans. Inst. Nav. Archs., 1886; 
G. A. Calvert, Trans. Inst. Nav. Archs., 1887; S. W. Barnaby, Proc. Inst. 
C. E., 1890, vol. ch, and D. W. Taylor's " Resistance of Ships and Screw 
Propulsion." Also Mr. Taylor's paper in Proc. Soc. Nav. Arch. & Marine 
Engrs., 1904. Mr. Taylor found the highest efficiencies, exceeding 70%, 
in propeUers with pitch ratios from 1.0 to 1.5 ratio of width of blade to 
diameter of Vs to i/5, and ratio of developed area of blade to disk area of 
0.201 to 0.322. 

One of the most important results deduced from experiments on model 
screws is that they appear to have practically equal efficiencies through- 
out a wide range both in pitch-ratio and in surface-ratio; so that great 
latitude is left to the designer in regard to the form of the propeller. 
Although these experiments are not a direct guide to the selection of the 
most ^efficient propeller for a particular ship, they supply the means of 
analyzing the performances of screws fitted to vessels, and of thus in- 
directly determining what are likely to be the best dimensions of screw 
for a vessel of a class whose results are known. {Proc. Just. M. E., July, 
1891.) 

Mr. Barnaby in Proc. Inst. C. E., 1890, gives a table to be used in cal- 
culations for determining the best dimensions of screws for any given 
speed and H.P. from which the following table is abridged. It is deduced 
from Froude's experiments at Torquay. (Trans. Inst. Nav. Archs., 1886.) 

Ca = disk area in sq. ft. X FVH.P. Cr = revs, per min. X D/V, 
V = speed in knots, D = diam. of screw in ft. H.P. = effective H.P. 
on the screw shaft. Disk area = 0.7854 2)2= CaX I.B..V./VK Revs, 
per min. = CrX V/D. The constants Ca and Cji assume a standard 
value of the speed of the wake, equal to 10% of the speed of the ship. 
In a verj^ full ship it may amount to 30%, therefore V should be reduced 
when using the constants by amounts varying from 20% to as the 
form varies from "very full" to "fairly fine." 



Effy. of 
Screw, %. 


63 


67 


68 


69 


68 


66 


63 


Pitch ratio. 


Ca 


Cr 


Ca 


Cr 


Ca 


Cr 


Ca 


Cr 


Ca 


Cr 


Ca 


Cr 


Ca 


Cr 


0.80 
1.00 
1.20 
1.40 
1.60 
1.80 


468 
546 
625 
704 
780 


122 
99 
83 
72 
63 


304 
355 
405 
456 
507 
558 
609 
660 
710 


128 
104 
87 
76 
67 
60 
55 
50 
47 


215 
251 
288 
325 
360 
396 
432 
469 
505 


134 
109 
92 
80 
71 
64 
58 
54 
50 


157 
184 
210 
236 
263 
290 
315 
342 
369 


142 
115 
97 
85 
75 
68 
62 
57 
53 


115 
135 

154 
173 
193 
212 
231 
250 
270 


150 
123 
104 
90 
80 
73 
67 
62 
57 


86 
100 
115 
129 
144 
159 
173 
187 
202 


160 
131 
111 

97 
87 
78 
72 
67 
62 


65 
76 
87 
98 
109 
120 
131 
142 
153 


171 

140 
119 
104 
93 

84 


2,00 






77 


2.20 






7? 


2.40 






67 



Comparison of Marine Engines for tlie Years 1872, 1881, 1891, 1901. 

J Jas . McKechnie. Proc. Inst. M. E. 1901.) 



Boilers, Engines and Coal. 


Average Results. 


1872. 1881. 1 1891. 


1901. 


Boiler press., lbs. per sq. in 


52.4 


77.4 
30.4 

3.917 
13.8 
59.76 

467 

1.83 

2.0 


158.5 

31.0 

3.275 

15.0 

63.75 

529 

1.52 

1.75 


197 


Heating surface, per sq. ft. grate 


38 & 43* 


Heat'g surf., per I.H.P., sq. ft 


4.41 


3.0 


Coal, per sq. ft. of grate, lbs. per hr 


18&28* 


Revolutions per minute 


55.67 
376 
2.11 


87 


Piston speed, ft, per min 


654 


Coal per I.H.P. per hr., lbs 

Av. consumption, long voyage 


1.48 
1.55 



* Natural and forced draft respectively. 
Summary of Results. (1891 to 1901). — Steam pressures have been 
increased in the merchant marine from 158 lbs. to 197 lbs. per sg. in* 



MARINE PRACTICE. 



1381 



the maximum attained being 267 lbs. per so in nnfl "inn ihc f« .),„ 
from'sirto •fi.J'?? P,j'*°" ?P^f^ Of mefcaVt^e ma<^5ncry^i^'go'?c.*up 

}^rZ iVe"a*s°u?flte-'^a°n1 atr^°"-' '-^'^ ^^Tgr'i^lft'.rpot'l'^ 

InJ^'mv'A^tts'^'iZl ?' ^*J;* "Lu?»aniaf"'' (Thomaf BeTl/ P?o i 
t^ij^l^^olfers^o'f'^fhl-a Of ^''e 



Turbines. 



H.P. . . 
L.P. . . . 

Astern . 



Diameter 
of Rotor, 

Ins. 

96 
140 
104 



Length of Bla des, In"sr 



In First 
Expansion. 



2 3/4 
8J/4 
21/4 



In Last 
Exp ansion. 



12 3/8 
22 
8 



total length of boiler-rooms, 336 f t ; total length of m^^^^^^ 

engine rooms, 149 ft. 8 in. ^^11^1,11 oi mam ana auxiliary 

ci J^^^f following are the Weights of the various revolving parts and the 
size of bearings and the pressiu-e: Weight of one H P tnrhinp rntnr 
complete, 86 tons: one L.P. rotor, 120 tgSs; one^'astern rotor^^^^^ Cs' 



H.P. rotor... 
L.P. rotor. . . 
Astern rotor. 



Main Bearing 
Journals. 



Diameter. 



27 1/8 in. 
33 1/8 in. 
24 1/8 in. 



Effective 
Length. 



44 3/4 in. 
56 1/2 in. 
34 3/4 in. 



Pressure 
per Sq. In. 
of Bearing 

Surface. 



80 lbs. 
72 lbs. 
83 lbs. 



At. 190 Revs. 

Surface Speed 

of Journal. 



1350 ft. per min. 
1650 ft. per min. 
1200 ft. per min. 



A^ht,^'''TSn^-%n'*JJ\ "Lusitania." (Thos. Bell, Proc. Inst. Nav. 
tlined-in'?h^officfartriils^ ''' ^^^^'^-The following records were ob- 



Speed in knots 15 77 

Shaft horse-power. ...*.*.!!** 13 *400 
Steam cons, per shaft, H.P. hr. 

of turbines, lbs 21 23 

of auxiliaries, lbs .'**.* 53 

^ total lbs * 9f\\'^ 

Temp, of feed-water, ° F*.*.*.\ 200 
Coal cons. lbs. per shaft 

H.P. hr 



18 

20,500 

17.24 
3.72 
20.96 
200 



21 

33,000 

14.91 

2.6 
17.51 

190 



23 

48,000 

13.92 

2.01 

15.93 

179 



2.52 2.01 1.68 1.56 



25.4 
68,850 

12.77 

1.69 

14.46 

1()5 

1.43 



Estimated steam and coal consumption under service conditions at 
same speeds: • 

Steam cons, of auxiliaries, 

per shaft H.P. hr., lbs.. 6.97 4.92 3.41 
Steam cons, of total per 

shaft H.P. hr., lbs 28.20 22.16 18.32 

Coal cons., lbs. per shaft 

H.P. hr., lbs 2.76 2.17 1.8 

Est. coal cons., on a voyage 

of 3100 nautical miles, 

gross tons 3,270 3,440 3,930 4.700 5.490 

The following figures are taken from tiie records of a voyage from 



2.65 
16.57 
1.62 



2.17 
14.94 
1.46 



1382 



MARINE ENGINEERING, 









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THE PADDLE-WHEEL. 1383 

Queenstown to Sandy Hook, 2781 nautical miles, Nov. 3-8, 1908, 4 days, 
18 lirs., 40 m.: Averages: Steam pressure at boilers, 168 lbs.; temperature 
hot-well, 74.5°; feed-water, 197°; vacuum, 28.1 in.; speed, 24.25 knots; 
speed, best day, 24.8 knots; revolutions, 181.1; slip, 13.9%. Total coal, 
4976 tons. Steam consumption: main turbines, 851,500 lbs., = 13.1 lbs. 
??^ ?.^?;^,V^-^\^J; (on a basis of 65,000 shaft H.P.); auxiliary macUinery. 
^^^.'WJ°^" = Jx^5 ^F H-P- ^^^-J evaporating plant and heating, 32.500 lbs. 
= 0.0 lb. per H.P. hr. Total, 998,000 lbs., = 15.35 lbs. per shaft H P 
hour. Average coal burned, 431/2 tons per hour. Water evaporated 
per lb., coal 10.2 lbs. from feed at 196°, = 10.9 lbs. from and at 212° 
Coal for all purposes per shaft H.P. hour, 1.5 lbs. Coal per sq ft of 
grate per hom\ 24.1 lbs. The coal was half Yorkshire, half South Wales. 

In September, 1909, the "Lusitania" made the westward passage, 2784 
miles from Daunt's Hock near Queenstown to Ambrose Channel Lightship 
off Sandy Hook, m 4 days 11 h. 42 m., averaging 25.85 knots for the entire 
passage. Four successive days runs, from noon to noon, were 650. 652. 
651 and 674 miles. 

Reciprocating Engines with a Low-Pressure Turbine. —The 

Laurentic," built for the Canadian trade of the White Star Line, 
14,000 tons gross register, is a triple-screw steamer, with the two outer 
screws driven by four-cylinder triple-expansion engines, and the central 
screw by a Parsons turbine. The steam, of 200 lbs. boiler pressure, first 
passes to the reciprocating engines, where it expands to from 14 to 17 lbs. 
absolute, and then passes to the turbine. For manoeuvering the ship 
into and out of port the turbine is not used, and the steam passes directly 
from the engines to the condensers. During the trial trip the combined 
engine-tufbine outfit developed 12,000 H.P., with a speed of 17i/'> knots, 
and showed a coal consumption of 1.1 lbs. and a water consumption of 
11 lbs. per indicated horse-power hour. (Power, May 18, 1909.) 

The *' Kronprinzessin Cecilie" of the North German Lloyd Co., is 
probably the last high-speed transatlantic steamer of very great power 
that will be built with reciprocating engines. Its dimensions are: length, 
706 ft.; beam, 72 ft.; depth, 44 ft. 2 in.; displacement, 26,000 tons. Four 
12,000 H.P. engines, two on each shaft, in tandem. Cylinders, 373/8, 
491/4, 74"/8 and 112V4 ins., by 6 ft. stroke. Steam, 230 lbs., delivered 
from 19 cylindrical boilers, through four 17-in. steampipes. Coal used 
in 24 hours, 764 tons, in 124 furnaces; 1.4 lbs. per H.P. hour, including 
auxiliaries. Speed on trial trip on a 60-mile course, 24.02 knots, (iSci. 
Am., Aug. 24, 1907.) 

THE PADDLE-WHEEL. 

Paddle-wheels with Radial Floats. (Seaton's Marine Engineering.) — 
The effective diameter of a radial wheel is usually taken from the centers 
of opposite floats; but it is difficult to say what is absolutely that diameter, 
as much depends on the form of float, the amount of dip, and the waves 
set in motion by the wheel. The sUp of a radial wheel is from 15 to 30 
per cent, depending on the size of float. 

Area of one float = C X I.H.P. ■*■ D, 
D is the effective diameter in feet, and C is a multiplier, varying from 0.25 
in tugs to 0.175 in fast-running fight steamers. 

The breadth of the float is usually about 1/4 its length, and Its thickness 
about 1/8 its breadth. The number of floats varies directly with the diam- 
eter, and there should be one float for every foot of diameter. 

(For a discussion of the action of the radial wheel, see Thurston, 
Manual of the Steam-engine, part n, p. 182.) 

Feathering Paddle-wheels. (Seaton.) — The diameter of a feather- 
ing-wheel is found as follows: The amount of slip varies from 12 to 20 
per cent, although when the floats are small or the resistance great It 
is as high as 25 per cent; a well-designed wheel on a well-formed ship 
should not exceed 15 per cent under ordinary circumstances. 

If K is the speed of the ship in Imots, S the percentage of sUp, and R 
the revolutions per minute, 

Diameter of wheel at centers = K (100 + S) ^ (3.14 X R). 

The diameter, however, must be such as will suit the structure of the 
ship, so that a modification may be necessary on this account, and the 
revolutions altered to suit it. The diameter will also depend on the 
amount of "dip" or immersion of float. 



1384 MARINE ENGINEERING. 

When a ship is working always in smooth water the immersion of the 
top edge should not exceed i/g the breadth of the float; and for general 
service at sea an immersion of 1/2 the breadth of the float is sufficient. 
If the ship is intended to carry cargo, the immersion when light need not 
be more than 2 or 3 inches, and should not be more than the breadth of 
float when at the deepest draught; indeed, the efficiency of the wheel falls 
off rapidly with the immersion of the wheel. 

Area of one float = C X I.H.P. -s- D. 
C is a multiplier, varying from 0.3 to 0.35; D is the diameter of the 
wheel to the float centers, in feet. 

The number of floats = I/2 (/> + 2). 
The breadth of the float- 0.35 X the length. 
The thickness of floats = Vi2 the breadth. 
Diameter of gudgeons = thickness of float. 
Seaton and Rounthwaite's Pocket-book gives: _ 
Number of floats = 60 -^ ^R, 
where R is number of revolutions per minute. 

- fl w ^ ^N I.H.P. X 33,000 X it 
Area of one float (in square feet) = — m x (Dx R)^ ' 

where N = number of floats in one wheel. 

For vessels plying always in smooth water K = 1200. For sea-going 
steamers K = 1400. For tugs and such craft as require to stop and 
start frequently in a tide-way K = 1600. 

It will be quite accurate enough if the last four figures of the cube 
(D X R)^ be taken as ciphers. 

For illustrated description of the feathering paddle-wheel see Seaton's 
Marine Engineering, or Seaton and Rounthwaite's Pocket-book. The 
diameter of a feathering- wheel is about one-half that of a radial wheel 
for equal efficiency. (Thurston.) 

Eflaciency of Paddle-vs^heels. — Computations by Prof. Thurston of 
the efficiency of propulsion by paddle-wheels give for hght river steamers 
with ratio of velocity of the vessel, v, to velocity of the paddle-float at 
center of pressure, V, or v/V, = 3/4, with a dip = 3/20 radius of the wheel 
and a sUp of 25 per cent, an efficiency of 0.714; and for ocean steamers 
with the same shp and ratio of v/V, and a dip = 1/3 radius, an efficiency of 
0.685. 

JET-PKOPUXSION. 

Numerous experiments have been made in driving a vessel by the 
reaction of a jet of water pumped through an orifice in the stern, but 
they have all resulted in commercial failure. Two-jet propulsion steamers, 
the *' Waterwitch, " 1100 tons, and the "Squirt," a small torpedo-boat, 
were built by the British Government. The former was tried in 1867, 
and gave an efficiency of apparatus of only 18 per cent. The latter gave 
a speed of 12 knots, as against 17 knots attained by a sister-ship having a 
screw and equal steam-power. The mathematical theory of the efficiency 
of the jet was discussed by Rankine in The Engineer, Jan. 11, 1867, and 
he showed that the greater the quantity of water operated on by a jet- 
propeller, the greater is the efficiency. In defiance both of the theory 
and of the results of earlier experiments, and also of the opinions of many 
naval engineers, more than S200,000 were spent in 1888-90 in New York 
upon two experimental boats, the "Prima Vista'* and the "Evolution,** 
in which the jet was made of very small size, in the latter case only s/g-inch 
diameter, and with a pressure of 2500 lbs. per square inch. As had been 
predicted, the vessel was a total failure. (See article by the author in 
Mechanics, March, 1891.) 

The theory of the jet-propeller is similar to that of the screw-propeller. 
If A == the area of the jet in square feet, V its velocity with reference to 
the orifice, in feet per second, v = the velocity of the ship in reference to 
the earth, then the thrust of the jet (see Screw-propeller, ante) is 2 AV 
(V — v). The work done on the ve.ssel is 2 AViV — v)v, and the work 
wasted on the rearward projection of the jet is 1/2 X 2 AF(F — v)K 
2 4V (V — v) V 2 V 

The efficiency is o ^t//-t/ ^ \ \ a\z r^r To = ifr" * This expression 

'' 2 AV {V — v) v-\- AV {V —vY V-^v 
equals unity when V — v, that is, when the velocity of the jet with refer- 
ence to the earth, or V — v, = 0; but then the thrust of the propeller is 
also 0. The greater the value of V as compared with v, the less the 



CONSTRUCTION OF BXTILDINGS. 



1385 



efficiency. For F = 20 2;, as was proposed in the "Evolution," the 
efficiency of the jet would be less than 10 per cent, and this would be 
further reduced by the friction of the pumping mechanism and of the 
water in pipes. 

The whole theory of propulsion may be summed up in Rankine's 
words: "That propeller is the best, other tilings beine: equal, which drives 
astern the largest body of water at the lowest velocity." 

It is practically impossible to devise any system of hvdraulic or jet 
propulsion wliich can compare favorably, under these conditions, with 
the screw or the paddle-wheel. 

Reaction of a Jet. — If a jet of water issues horizontally from a vessel, 
the reaction on the side of the vessel opposite the orifice is equal to the 
weight of a column of water the section of which is the area of the orifice, 
and the height is twice the head. 

The propeUing force in iet-propulsion is the reaction of the stream 
issuing from the orifice, ana it is the same whether the jet is discharged 
under water, in the open air, or against a solid wall. For proof, see 
account of trials by C. J. Everett, Jr., given by Prof. J. Burkitt Webb, 
Trans. A, S. M. E., xii, 904. 

CONSTRUCTION OF BUILDINGS.* 

FOUNDATIONS. 



Bearing Power of Soils. - 

Construction. " 



-Ira O. Baker, "Treatise on Masonry 



Kind of Material. 



Bearino; Power in 
Tons per Square Foot. 



Minimum. 


Maximum. 


200 




25 


30 


15 


?0 


5 


10 


4 


6 


2 


4 




2 


8 


10 


4 


6 


2 


4 


0.5 


1 



Rock — the hardest — in thick layers, in native bed. 

Rock equal to best ashlar masonrj' 

Rock equal to best brick masonry , 

Rock equal to poor brick masonry 

Clay on thick beds, always dry 

Clay on thick beds, moderately dry 

Clay, soft 

Gravel and coarse sand, well cemented 

Sand, compact, and well cemented 

Sand, clean, dry. 

Quicksand, alluvial soils, etc 



The building code of Greater New York specifies the following as the 
maximum permissible loads for different soils: 

*' Soft clay, one ton per square foot; 

*' Ordinary clay and sand together, in layers, wet and springy, two 
tons per square foot; 

"Loam, clay or fine sand, firm and dry, three tons per square foot; 

*' Very firm coarse sand, stiff gravel or hard clay, four tons per square 
foot, or as otherwise determined by the Commissioner of Build- 
ings having jurisdiction." 



* The limitations of space forbid any extended treatment of this subject. 
Much valuable information upon it will be found m Trautwine's \ Civil 
Engineers' Pocket-book." and in Kidder's " Architects and Builders 
Pocket-book." The latter in its preface mentions the follo\ymg works of 
reference: "Notes on Building Construction," 3 vols., Rivingtons pub- 
lishers, London; "Building Superintendence.' by TM. Chirk (J. K. 
Osgood &Co., Boston); " The American House Carpenter." and The Theory 
of Transverse Strains," both by R. G. Hatfield; "Graphical Analysis of 
Roof-trusses," by Prof. C. E. Greene: "The Fire Protection of MiUs, by 
C J H Woodbiirv; "House Drainage and Water Service," by James C. 
Bayies- "The Builder's Guide and Estimator's Price-book." and "Plaster- 
ing Mortars and Cements,' by Fred.T. Hodgson; "Foundations and Con- 
crete Works." and "Art of Building," by E. Dobson, Weale s Series, 
London. 



1386 



CONSTBUCTION OF BUILDINGS. 



Bearing Fower of Tiles. — Engineering JSews i^'ormula: Safe load in 
tons = 2 Wh H- (^ + 1). TF = weight of hammer in tons, h = height of fall 
of hammer in feet. S = penetration under last blow, or the average under 
last five blows, in inches. 

Safe Strength of Brick Piers, exceeding six diameters in height. 
(Kidder.) 

Piers laid with rich lime mortar, lbs. per sq. in., 110 — 5 H/D. 
Piers laid with 1 to 2 natural cement mortar, 140 — 5V2 H/D, 
Piers laid with 1 to 3 Portland cement mortar, 200 - 6 H/D, 
H = height; D = least horizontal dimension, in feet. 



Thickness of Foundation Walls 


. (Kidder.) 




Height of Building. 


DweUings, 
Hotels, etc. 


Warehouses. 


Brick. 


Stone. 


Brick. 


Stone. 


Two stories 


Inches. 
12 or 16 

16 

20 

24 

28 


Inches. 
20 
20 
24 
28 
32 


Inches. 
16 
20 
24 
24 
28 


Inches. 
20 


Three stories 


24 


Four stories 


28 


Five stories .. 


28 


Six stories 


32 







3IASONRY. 

Allowable Pressures on Masonry in Tons per Square Foot, 



(Kidder.) 



Different Cities.* 


(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 


Granite, cut 


60 
40 
30 




72-172 

50-165 

28-115 

18 

15 

111/2 
8 








40 


Marble and limestone, cut 










Sandstone, hard, cut 








12 


Hard-burned brick in Portland cement. . . 


121/2 
9 

61/2 


15 

iii/2 






Hard-burned brick in natural cement 

Hard-burned brick in cement and lime . . . 

Hard-burned brick in lime mortar 

Pressed brick in Portland cement 


15 
12 
8 


9 

'*6' 
12 
9 
5 

6 

4 


15 
12 
S 


9 
"8* 


Pressed brick in natural cement 












P 


Rubble stone in natural cement 




8 
...... 

8 


5-7 
"4 




10 


12 


In foundations: 
Dimension stone 




30 


Portland cement concrete 






15 


10 


Natural cement concrete 




4 



*From building laws, (1) Boston, 1897; (2) Buffalo, 1897; (3) New 
York, 1899; (4) Chicago, 1893; (5) St. Louis, 1897; (6) Philadelphia, 
1899; (7) Denver, 1898. 

Crushing Strength of 12-in. Cubes of Concrete. (Kidder.) — 
Pounds per square foot. The concrete was made of 1 part Portland 
cement, 2 parts sand, with average concrete stone and gravel, as below. 





10 days. 


45 days. 


3 mos. 


6 mos. 


1 year. 


6 parts stone 


130,750 
136.750 


172.325 
266.962 


324.875 


361.600 
298,037 


440,040 


3 parts stone, 3 gravel 


396.200 


4 parts stone, 2 gravel . . 




408.300 


6 parts (3/4 stone, 1/4 grano- 
lithic) 










388.700 


6 parts average gravel 

6 parts coarse stone, no fine. 


99.900 


234.475 


385,612 
L34.475 


i265.55d 
220.350 


406,700 
266.300 



Reinforced Concrete. — The building laws of New York, St. Louis, 
Cleveland and Buffalo, and the National Board of Fire Underwriters agree 
in prescribing the following as the maximum allowable working stresses: 



BEAMS AND GIRDERS. 



1387 



Extreme fiber stress in compression in con- 
crete 500 lbs. per sq. in. 

Shearme: stress in concrete 50 

Direct compression in concrete 350 '* 

Adhesion of steel to concrete 50 '* 

Tensile stress in steel 16,000 ** 

Shearing stress in steel 10^000 

BEAMS AND GIRDERS. 

Safe Loads on Beams. — Uniformly distributed load: 

Safe load in lbs. = ^ X breadth X square of depth X A ^ 
span in feet 
Breadth in inches - span in feet X load ^ 
2 X square of depth X A 

The depth is taken in inches. The coefficient A, is Vis the maximum 
fiber stress for safe loads, and is the safe load for a beam 1 in square 1 ft 
span. The following values of A are given by Kidder as one-third of 
the breakmg weight of timber of the quality used in first-class buildings. 
The values for stones are based on a factor of safety of six. 
Values for a. — Coefficient for Beams. 



Cast iron 308 

Wrought iron 666 

Steel 888 

American Woods: 

Chestnut 60 

Hemlock 55 

Oak, white 75 

Pine, Georgia yellow 100 

Pine, Oregon 90 

Pine, red or Norway 70 

Pine, white. Eastern 60 

Pine, white. Western 65 



Pine, Texas yellow 90 

Spruce 70 

Whitewood (poplar) 65 

Redwood (California) 60 

Bluestone flagging (Hudson 

River) 25 

Granite, average 17 

Limestone 14 

Marble 17 

Sandstone 8 to 11 

Slate 50 



Safe Loads in Tons, Uniformly Distributed, for White-oak Beams. 

(In accordance with the Building Laws of Boston.) 

W = safe load in pounds; P, extreme fiber- 



Formula: W = 



4 PBD^ stress = 1000 lbs. per square inch, for white 

3 2;, * oak; 5, breadth in inches; D, depth in inches; 
L, distance between supports in inches. 



4 


Distance between Supports in Feet. 


6 


8 


10 


11 


12 


14 


15 


16 


17 


18 


19 


21 


23 


25 


26 


.2^ 

02^ 


Safe Load in Tons of 2000 Pounds. 


2x6 


0.67 


0.50 


0.40 


0.36 


0.33 


0.29 


0.27 


0.25 


0.24 


0.22 












2x8 


1.19 


0.89 


0.71 


0.65 


0.59 


0.51 


0.47 


0.44 


0.42 


0.40 


0.37 


0.34 


0.31 


0.28 




2x10 


1.85 


1.39 


1.11 


1.01 


0.93 


0.79 


0.74 


0.69 


0.65 


0.62 


0.58 


0.53 


0.48 


0.43 


6.43 


2x12 


2 67 


2.00 


1.60 


1.45 


1.33 


1.14 


1.07 


1. 00 


0.94 


0.89 


0.84 


0.76 


0.70 


0.64 


0.62 


3x6 


1.00 


0.75 


0.60 


0.55 


0.50 


0.43 


0.40 


0.37 


0.35 


0.33 


0.32 


0.29 


0.26 






3x8 


1.78 


1.33 


1.07 


0.97 


0.89 


0.76 


0.71 


0.67 


0.63 


0.59 


0.56 


0.51 


0.46 


0.43 


0.41 


3x10 


2.78 


2.08 


1.67 


1.52 


1.39 


1.19 


1.11 


1.04 


0.98 


0.93 


0.88 


0.79 


0.72 


0.67 


0.64 


3x12 


4.00 


3.00 


2.40 


2.18 


2.00 


1.71 


1.60 


1.50 


1.41 


1.33 


1.26 


1.14 


1.04 


0.96 


0.92 


3x14 


5.45 


4.08 


3.27 


2.97 


2,72 


2.37 


2.18 


2.04 


1.92 


1.82 


1.72 


1.56 


1.42 


1.31 


1.25 


3x16 


7.11 


5.33 


4.27 


3.88 


3.56 


3.05 


2.84 


2.67 


2.51 


2.37 


2.25 


2.03 


1.86 


1.71 


1.64 


4x10 


3.70 


2.78 


2.22 


2.02 


1.85 


1.59 


1.48 


1.39 


1.31 


1.23 


1.17 


1.06 


0.97 


0.89 


0.85 


4x12 


5.33 


4.00 


3.20 


2.91 


2.67 


2.29 


2.13 


2.00 


1.88 


1.78 


1.68 


1.52 


1.39 


1.28 


1.23 


4x14 


7.26 


5.44 


4.36 


3.96 


3.63 


3.11 


2.90 


2.72 


2.56 


2.42 


2.29 


2.07 


1.90 


I 74 


1.68 


4x16 


9.48 


7.11 


5.69 


5.17 


4.74 


4.06 


3.79 


3.56 


3.35 


3.16 


3.00 


2.71 


2.47 


2.28 


2.19 


4x18 


12.00 


9.00 


7.20 


6.55 


6.00 


5.14 


4.80 


4.50 


4.24 


4.00 


3.79 


3.43 


3.13 


2.88 


2.77 



For other kinds of wood than white oak multiply the figures in the 
table by a figure selected from those given below (which represent the 



1388 



CONSTRUCTION OF BUILDINGS. 



safe stress per square inch on beams of different kinds of wood accord- 
ing to the building laws of the cities named) and divide by 1000. 





Hem- 
lock. 


Spruce. 


White 
Pine. 


Oak. 


Yellow 
Pine. 


New York 


800 


900 
750 


900 
750 
900 


1100 

lOOOt 

1080 


1100* 


Boston 


1250 


Chicago 




1440 











* Georgia pine. t White oak. 

Maximum Permissible Stresses in Structural 3Iaterials used in 
Buildings. (Building Ordinances of the City of Chicago, 1893.) — Cast 
iron, crushing stress: For plates, 15,000 lbs. per square inch; for lintels, 
brackets, or corbels, compression 13,500 lbs. per square inch, and tension 
3000 lbs. per square inch. For girders, beams, corbels, brackets, and 
trusses, 16,000 lbs. per square inch for steel and 12,000 lbs. for iron. 

For plate girders: 

Flange area = maximum bending moment in ft.-lbs. -^(CD). 

D = distance between center of gravity of flanges in feet, 

C = 13,500 for steel, 10,000 for iron. 

Web area = maximum shear -r- C. 

C = 10,000 for steel; 6,000 for iron. 

For rivets in single shear per square inch of rivet area: 

If shop-driven, steel, 9000 lbs., iron, 7500 lbs.; if field-driven, steel 
7500 lbs., iron, 6000 lbs. ^ 

For timber girders: S = chd- -^ I. 

h = breadth of beam in inches, d = depth of beam in inches, I = length 
of beam in feet, c = 160 for long-leaf yeUow pine, 120 for oak, 100 for 
white or Norway pine. 

WALLS. 

Thickness of Walls of Buildings. — Kidder gives the following gen- 
eral rule for mercantile buildings over four stories in height : 

For brick equal to those used in Boston or Chicago, make the thickness 
of the three upper stories 16 ins., of the next three below 20 ins., the next 
three 24 ins., and the next three 28 ins. For a poorer quality of material 
make only the two upper stories 16 ins. thick, the next three 20 ins. and 
so on down. 

In buildings less than five stories in height the top story may be 12 
ins. in thickness. 

Thickness of Walls in Inches, for Mercantile Buildings and for 
ALL Buildings over Five Stories in Height . (The figures show the 
range of the thicknesses required by the ordinances of eight different 
cities. — Condensed from Kidder.) 



Stories 


Stories. 


High. 


1st. 


2d. 


3d. 


4th. 


5th. 


6th. 


7th. 


8th. 


9th. 


10th 


11th 

13-17 
16-20 


12th 


2 
3 
A 
5 
6 
7 
8 
9 
K) 
11 
12 


12-18 
13-20 
16-22 
18-22 
20-26 
20-28 
22-32 
24-32 
24-36 
28-36 
28-40 


12-13 
12-18 
16-18 
16-22 
18-22 
20-26 
20-28 
24-32 
24-32 
28-36 
28-36 


12-16 
12-18 
16-20 
16-22 
18-24 
20-26 
20-28 
24-32 
24-32 
28-36 


12-16 
12-20 
16-20 
16-22 
18-24 
20-26 
20-28 
24-30 
24-32 


12-16 
13-20 
16-20 
16-22 
20-24 
20-26 
24-28 
24-32 


12-16 
13-20 
16-20 
16-22 
20-24 
20-26 
24-28 


12-17 
13-20 
16-20 
16-22 
20-24 
20-26 


12-17 
16-20 
16-20 
20-22 
20-24 


12-17 
16-20 
16-20 
20-22 


12-17 
16-20 
16-20 


13-17 



(Extract from the Building Laws of the City of New York, 1893.) 
Walls of Warehouses, Stores, Factories, and Stables. — 25 feet 
or less in width between walls, not less than 12 in. to height of 40 ft. 
If 40 to 60 ft. in height, not less than 16 in. to 40 ft., and 12 in. thence 
to top; 



COLUMNS AND POSTS. 1389 

60 to 80 ft. in height, not less than 20 in. to 25 ft., and 16 in. thence to 

top; 
75 to 85 ft. in height, not less than 24 in. to 20 ft.; 20 in. to 60 ft., and 

16 in. to top; 
85 to 100 ft. in height, not less than 28 in. to 25 ft.; 24 in. to 50 ft • 

20 in. to 75 ft., and 16 in. to top; 

Over 100 ft. in height, each additional 25 ft. in height, or part thereof, 
next above the curb, shall be increased 4 inches in thickness, the 
upper 100 feet remaining the same as specified for a wall of that 
height. 

If walls are over 25 feet apart, the bearing- walls shall be 4 inches 
thicker than above specified for every 12 1/2 feet or fraction thereof that 
said walls are more than 25 feet apart. 

Strength of Floors, Koofs, and Supports. 

Floors calculated to 
bear safely per sq. ft., in 
addition to their own wt. 
Floors of dwelling, tenement, apartment-house or hotel, not 

less than 70 lbs. 

Floors of office-building, not less than: 100 *' 

Floors of public-assembly building, not less than 120 ** 

Floors of store, factory, warehouse, etc., not less than 150 '* 

Roofs of all buildings, not less than 50 " 

iLlvery tloor shall be ot sutticisnt strengtT^ to bear sateiy the weight to be 
imposed thereon, in addition to the weight of the materials of which the 
floor is composed. 

Columns and Posts. — The strength of all columns and posts shall 
be computed according to Gordon's formulae, and the crushing weights in 
pounds, to the square inch of section, for the following-named materials, 
shall be taken as the coefficients in said formulae, namelv: Cast iron, 80,000; 
wrought or rolled iron, 40,000: rolled steel, 48,000: white pine and spruce, 
3500; pitch or Georgia pine, 5000; American oak, 6000. The breaking 
strength of w^ooden beams and girders shall be computed according to 
the formulae in which the constants for transverse strains for central load 
shall be as follows, namely: Hemlock, 400: white pine, 450: spruce, 150; 
pitch or Georgia pine, 550; American oak, 550: and for wooden beams and 
girders carrying a uniformly distributed load the constants will be doubled. 
The factors of safety shall be as one to four for all beams, girders, and 
other pieces subject to a transverse strain; as one to four for all posts, 
columns, and other vertical supports when of wrought iron or rolled steel; 
as one to five for other materials, subject to a compressive strain; as one 
to six for tie-rods, tie-beams, and other pieces subject to a tensile strain. 
Good, solid, natural earth shall be deemed to sustain safely a load of four 
tons to the superficial foot, or as otherwise determined by the super- 
intendent of buildings, and the width of footing-courses shall be at least 
sufficient to meet this requirement. In computing the width of walls, 
a cubic foot of brickwork shall be deemed to weigh 115 lbs. Sandstone, 
white marble, granite, and other kinds of building-stone shall be deemed 
to weigh 160 lbs. per cubic foot. The safe-bearing load to ai)ply to 
good brickwork shall be taken at 8 tons per superficial foot when good 
lime mortar is used, 11 1/2 tons per superficial foot when good lime and 
cement mortar mixed is used, and 15 tons per superficial foot when good 
cement mortar is used. 

Fire-proof Buildings — Iron and Steel Columns. — All cast-iron, 
wrought-iron, or rolled-steel columns shall be made true and smooth at 
both ends, and shall rest on iron or steel bed-plates, and have iron or 
steel cap-plates, which shall also be made true. All iron or steel trimmer- 
beams, headers, and tail-beams shall be suitably framed and connected 
together, and the iron girders, columns, beams, trusses, and all other iron- 
work of all floors and roofs shall be strapped, bolted, anchored, and con- 
nected together, and to the walls, in a strong and substantial manner. 
Where beams are framed into headers, the angle-irons, which are bolted 
to the tail-beams, shall have at least two bolts for all beams over 7 inches 
in depth, and three bolts for aU beams 12 inches and over in depth, and 
these bolts shall not be less than 3/4 inch in diameter. Each one of such 



1390 CONSTRUCTION OF BUILDINGS. 

angles or knees, when bolted to girders, shall have the same number of 
bolts as stated for the other leg. The angle-iron in no case shall be less 
in thickness than the header or trimmer to which it is bolted, and the 
width of angle in no case shall be less than one third the depth of beam, 
excepting that no angle-knee shall be less than 21/2 inches wide, nor 
required to be more than 6 inches wide. All wrought-iron or. rolled-steel 
beams 8 inches deep and under shall have bearings equal to their depth, 
if resting on a wall; 9 to 12 inch beams shall have a bearing of 10 inches, 
and all beams more than 12 inches in depth shall have bearings of not 
less than 12 inches if resting on a wall. Where beams rest on iron sup- 
ports, and are properly tied to the same, no greater bearings shall be 
required than one third of the depth of the beams. Iron or steel floor- 
beams shall be so arranged as to spacing and length of beams that the 
load to be supported by them, together with the weights of the materials 
used in the construction of the said floors, shall not cause a deflection of 
the said beams of more than 1/30 of an inch per linear foot of span; and 
they shall be tied together at intervals of not more than eight times the 
depth of the beam. 

Under the ends of all iron or steel beams, where they rest on the walls, a 
stone or cast-iron template shall be built into the w^alls. Said template 
shall be 8 inches wide in 12-inch walls, and in all walls of greater thickness 
said template shall be 12 inches wide; and such templates, if of stone, 
shall not be in any case less than 21/2 inches in thickness, and no template 
shall be less than 12 inches long. 

No cast-iron post or columns shall be used in any building of a less 
average thickness of shaft than three quarters of an inch, nor shall it 
have an unsupported length of more than twenty times its least lateral 
dimensions or diameter. No wrought-iron or rolled-steel column shall 
have an unsupported length of more than thirty times its least lateral 
dimensions or diameter, nor shall its metal be less than one fourth of an 
inch in thickness. 

Lintels, Bearings and Supports. — All iron or steel lintels shall 
have bearings proportionate to the weight to be imposed thereon, but no 
lintel used to span any opening more than 10 feet in width shall have a 
bearing less than 12 inches at each end, if resting on a wall; but if resting 
on an iron post, such lintel shall have a bearing of at least 6 inches at each 
end, by the thickness of the wall .to be supported. 

Strains on Girders and Rivets. — Rolled iron or steel beam girders, 
or riveted iron or steel plate girders used as lintels or as girders, carrying 
a wall or floor or both, shall be so proportioned that the loads which may 
come upon them shall not produce strains in tension or compression upon 
the flanges of more than 12,000 lbs. for iron, nor more than 15,000 lbs. 
for steel per square inch of the gross section of each of such flanges, nor 
a shearing strain upon the web-plate of more than 6000 lbs. per square 
inch of section of such web-plate, if of iron, nor more than 7000 pounds 
if of steel; but no web-plate shall be less than 1/4 inch in thickness. Rivets 
in plate girders shall not be less than o/g inch in diameter, and shall not be 
spaced more than 6 inches apart in any case. They shall be so spaced 
that their shearing strains shall not exceed 9000 lbs. per square inch, on 
their diameter, multiplied by the thickness of the plates through which 
they pass. The riveted plate girders shall be proportioned upon the 
supposition that the bending or chord strains are resisted entirely by the 
upper and lower flanges, and that the shearing strains are resisted en- 
tirely by the web-plate. No part of the web shall be estimated as flange 
area, nor more than one half of that portion ol the angle-iron which lies 
against the web. The distance between the centers of gravity of the 
flange areas will be considered as the effective depth of the girder. 

The building laws of the city of New York contain a great amount of 
detail in addition to the extracts above, and penalties are provided for 
violation. See An Act creating a Department of Buildings, etc.. Chapter 
275, Laws of 1892. Pamphlet copy published by Baker, Voorhies & Co., 
New York. 

FLOORS. 
Maximum Load on Floors. {Eng'g, Nov. 18, 1892, p. 644.) — Maxi- 
mum load per square foot of floor surface due to the weight of a dense 
crowd. Considerable variation is apparent in the figures given by many 
authorities, as the following table shows: 



STRENGTH OF FLOORS. 1391 

Authorities. Weight of Crowd, 

lbs. per sq. ft. 

French practice, quoted by Trautwine and Stoney 41 

Hatfield (" Transverse Strains, " p. 80) 70 

Mr. Page, London, quoted by Trautwine 84 

Maximum load on American highway bridges according to 

Waddell's general specifications 100 

Mr. Nash, architect of Buckingham Palace 120 

Experiments by Prof. W. N. Kernot, at Melbourne | \a^i 

Experiments by Mr. B. B. Stoney ("On Stresses," p. 617) 147! 4 

Experiments by Prof. L, J. Johnson, Eng. News, April 14, ( 134.2 

1904 I to 156 .9 

The highest results were obtained by crowding a number of persons 
previously weighed into a small room, the men being tightly packed so as 
to resemble such a crowd as frequently occurs on the stairways and plat- 
forms of a theatre or other public building. 

Safe Allowances for Floor Loads. (Kidder.) Lbs. per square foot. 

For dwellings, sleeping and lodging rooms 40 lbs. 

For schoolrooms 50 ** 

For offices, upper stories 60 ** 

For offices, first story 80 " 

For stables and carriage houses 65 ** 

For banking rooms, churches and theaters 80 '* 

For assembly halls, dancing halls, and the corridors of all 

public buildings, including hotels 120 " 

For drill rooms 150 ** 

For ordinary stores, light storage, and light manufactur- 
ing 120* " 

* Also to sustain a concentrated load at any point of 4000 lbs. 

STRENGTH OF FLOORS. 

(From circular of the Boston Manufacturers' Mutual Insurance Co.) 

The tables on p. 1393 were prepared by C. J. H. Woodbury, for deter- 
mining safe loads on floors. Care should be observed to select the 
figure giving the greatest possible amount and concentration of load as 
the one which may be put upon any beam or set of floor-beams; and 
in no case should beams be subjected to greater loads than those speci- 
fied, unless a lower factor of safety is warranted under the advice of a 
competent engineer. These tables are computed for beams one inch in 
width, because the strength of beams increases directly as the width 
when the beams are broad enough not to cripple. 

Beams or heavy timbers used in the construction of a factory or ware- 
house should not be painted, varnished or oiled, filled or encased in 
impervious concrete, air-proof plastering, or metal for at least three years, 
lest fermentation should destroy them by what is called "dry rot." 

It is, on the whole, safer to make floor-beams in two parts with a 
small open space between, so that proper ventilation may be secured. 

These tables apply to distributed loads, but the first can be used in 
respect to floors which may carry concentrated loads by using half the 
figure given in the table, since a beam will bear twice as much load 
when evenly distributed over its length as it would if the load was 
concentrated in the center of the span. 

The weight of the floor should be deducted from the figure given in 
the table, in order to ascertain the net load which may be placed upon 
any floor. The weight of spruce may be taken at 36 lbs. per cubic 
foot, and that of Southern pine at 48 lbs. per cubic foot. 

Table I was computed upon a working modulus of rupture of South- 
em pine of 2160 lbs., using a factor of safety of six. It can also be 
applied to ascertaining the strength of spruce beams if the figures 
given in the table are multiplied by 0.78; or hi d(^signing a fioor to be 
sustained by spruce beams, multiply the required load by 1.28, and 
use the dimensions as given by the table. 

Example. — Required the safe load per square foot of floor, which 
may be safely sustained by a floor on Southern pine 10 X 14 in. beams, 
8 ft. on centers, and 20 ft. span. In Table I a 1 X 14 in. beam, 20 ft. 



1392 CONSTRUCTION OF BUILDINGS. 

span, will sustain 118 lbs. per foot of span; and for a beam 10 ins. wide 
the load would be 1180 lbs. per foot of span, or 1471/2 lbs. per sq. ft. of 
floor for Southern-pine beams. From this should be deducted the 
weight of the floor, 171/2 lbs. per sq. ft., leaving 130 lbs. per sq. ft. as a 
safe load. If the beams are of spruce, multiply 1471/2 by 0.78, reduc- 
ing the load to 115 lbs. Deducting the weight of the floor, 16 lbs., 
leaves the safe net load as 90 lbs. per sq. ft. for spruce beams. 

Table II applies to floors whose strength must be in excess of that 
necessary to sustain the weight, in order to meet the conditions of deli- 
cate or rapidly moving machinery, to the end that the vibration or 
distortion of the floor may be reduced to the least practicable limit. 

In the table the limit is that of a load which would cause a bending 
of the beams to a curve of which the average radius would be 1250 ft. 

This table is based upon a modulus of elasticity obtained from obser- 
vations upon the deflection of loaded storehouse floors, and is taken at 
2,000,000 lbs. for Southern pine; the same table can be applied to spruce, 
whose modulus of elasticity is taken as 1,200,000 lbs., if six tenths of 
the load for Southern pine is taken as the proper load for spruce; or, in 
the matter of designing, the load should be increased one and two thirds 
times, and the dimension of timbers for this increased load as found in 
the table should be used for spruce. 

It can also be applied to beams and floor-timbers supported at each 
end and in the middle, remembering that the deflection of a beam sup- 
ported in that manner is only 0.4 that of a beam of equal span which 
rests at each end; that is to say, the floor-planks are 2 1/2 times as stiff, 
cut two bays in length, as they would be if cut only one bay in length. 
When a floor-plank two bays iit length is evenly loaded, 3/ig of the load 
on the plank is sustained by the beam at each end of the plank, and lo/ig 
by the beam under the middle of the plank; so that for a completed floor 
3/8 of the load would be sustained by the beams under the joints of the 
plank, and s/g of the load by the beams under the middle of the plank: 
this is the reason of the importance of breaking joints in a floor-plank 
every 3 ft. in order that each beam shall receive an identical load. If 
it were not so, 3/8 of the whole load upon the floor would be sustained 
by every other beam, and 5/8 of the load by the alternate beams. 

Repeating the former example for the load on a mill floor on Southern- 
pine beams 10 X 14 ins., and 20 ft. span, 8 ft. centers: In Table II a 
1 X 14 in. beam should receive 61 lbs. per foot of span, or 75 lbs. per 
sq. ft. of floor, for Southern-pine beams. Deducting the weight of the 
floor, 171/2 lbs. per sq. ft., 57 lbs. per sq. ft. is the advisable load. 

If the beams are of spruce, the result of 75 lbs. should be multiplied 
by 0.6, reducing the load to 45 lbs. The weight of the floor, in this 
instance amounting to 16 lbs., would leave the net load as 29 lbs. for 
spruce beams. 

If the beams were two spans in length, they could, imder these con- 
ditions, support two and a half times as much load with an equal amount 
of deflection, unless such load should exceed the limit of safe load as found 
by Table I, as would be the case under the conditions of this problem. 

Maximum Spans for 1, *^and 3 Inch Plank. (Am. Mach., Feb. 11, 
1904.) — Let w -= load per sq. ft.; I = length in ins.; W = wl/12; S = 
safe fiber stress, using a factor of safety of 10; h = width of plank; d = 
thickness; p = deflection, E = coefficient of elasticity, / = moment of 
inertia = V12 bd^- 

Then Wl/S = Sbd^/Q: s = 5 WP -^ 384 EI. Taking S at 1200 lbs., E 
at 850,000 and s = i -^ 360 for long-leaf yellow pine, the following figures 
for maximum span, in inches, are obtained: 

Unifonnload, lbs. per sq.ft.. 40 60 80 100 150 200 250 300 

1 in Tilankl^^orst^^^^t*^-- 75 61 53 48 39 33 

i-iii. pidiiK I jp^jj, dellection .37 33 30 28 24 22 

For strength. .151 123 107 96 78 67 60 55 
~- 38 



^■^"- 1^^^^^ 1 For deflection . 75 66 60 55 48 44 41 



/For strength. .227 185 161 144 117 101 91 83 

73 66 61 58 



•^■"^- P^*^"^^} For deflection. 113 99 90 83 
For white oak S may be taken at 1000 and B at 550,000; for Canadian 
spruce, S = 800, E = 600,000; for hemlock, 5 = 600. E = 450,000. 



STRENGTH OF FLOORS. 



1393 



I. Safe Distributed Loads upon Southern-pine Beams One Inch 
in Width. 

(C. J. H. Woodbury.) 
(If the load is concentrated at the cent(n- of the span, the beams 
will sustain half the amount given in the table.) 











Depth of Beam in 


inches. 










2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


15 


16 








Load in 


pounds per foot of Span. 






5 
6 
7 
8 
9 
10 
11 


38 
27 
20 
15 


86 
60 
44 
34 
27 
22 


154 
107 
78 
60 
47 
38 
32 
27 


240 
167 
122 
94 
74 
60 
50 
42 
36 
31 
27 


346 
240 
176 
135 
107 
86 
71 
60 
51 
44 
38 
34 
30 


470 
327 
240 
!84 
145 
118 
97 
82 
70 
60 
52 
46 
41 
36 


614 
427 
314 
240 
190 
154 
127 
107 
90 
78 
68 
60 
53 
47 
43 
38 


778 

540 

397 

304 

240 

194 

161 

135 

115 

9Q 

86 

76 

67 

60 

54 

49 

44 


960 

667 

490 

375 

296 

240 

198 

167 

142 

123 

107 

94 

83 

74 

66 

60 

54 

50 

45 


807 

593 

454 

359 

290 

240 

202 

172 

148 

129 

113 

101 

90 

80 

73 

66 

60 

55 

50 


705 

540 

427 

346 

286 

240 

205 

176 

154 

135 

120 

107 

96 

86 

78 

71 

65 

60 


828 

634 

501 

406 

335 

282 

240 

207 

180 

158 

140 

125 

112 

101 

92 

84 

77 

70 


735 

581 

470 

389 

327 

278 

240 

209 

184 

163 

145 

130 

118 

107 

97 

89 

82 

75 


667 
540 
446 
375 
320 
276 
240 
211 
187 
167 
150 
135 
122 
112 
102 
94 
86 


759 
614 
508 


12 






474 


13 






364 


14 








314 


15 








273 


16 








240 


17 










217 


18 










190 


19 












170 


20 














154 


21 














139 


22 
















127 


23 


















116 


24 


















107 


25 




















46 


55 


98 

















n. Distributed Loads upon Southern 
Produce Standard Limit 


-pine Reams Sufficient 
of Deflection. 


to 




Depth of Beam in inches. 




C 


2 


3 


4 


5 


6 j 7 


8 


9 


10 


11 


12 13 


14 


15 


16 






Load in pounds per foot of Span. 


Q-- 


5 
6 
7 
8 
9 


3 

2 


10 
7 
5 
4 


23 
16 
12 
9 
7 
6 


44 
31 
23 
17 
14 
11 
9 


77 
53 
39 
30 
24 
19 
16 
13 


122 
85 
62 
48 
38 
30 
25 
21 
18 
16 
14 


182 
126 
93 
71 
56 
46 
38 
32 
27 
23 
20 
18 
16 


259 

180 

132 

101 

80 

65 

54 

45 

38 

33 

29 

25 

22 

20 

18 


247 
181 
139 
110 
89 
73 
62 
53 
45 
40 
35 
31 
27 
25 
22 
20 


241 
185 
146 
118 
98 
82 
70 
60 
53 
46 
41 
37 
33 
30 
27 
24 
22 


240 
190 
154 
127 
107 
91 
78 
68 
60 
53 
47 
43 
38 
35 
32 
29 
27 
25 


305 
241 
195 
161 
136 
116 
100 
87 
76 
68 
60 
54 
49 
44 
40 
37 
34 
31 


301 
244 
202 
169 
144 
124 
108 
95 
84 
75 
68 
61 
55 
50 
46 
42 
39 


300 
248 
208 
178 
153 
133 
117 
104 
93 
83 
75 
68 
62 
57 
52 
48 


301 

253 

215 

186 

162 

147 

126 

112 

101 

91 

83 

75 

69 

63 

58 


.0300 
.0432 
.0588 
.0768 
0972 


10 






1200 


n 






,1452 


1? 








.1728 


n 










,2028 


14 










2352 


15 












2700 


16 












3072 


17 














3468 


18 














.3888 


19 
















.4332 


?n 
















4800 


?i 


















5292 


22 


















5808 


?3 




















6348 


24 




















6912 


25 






















.7500 



Mill Columns. — Timber posts offer more resistance to fire than iron 
pillars, and have generally displaced them in millwork. Experiments 



1394 



CONSTHUCTION OF BUILDINGS. 



at the U. S. Arsenal at Watertown, Mass., show that sound timber posts 
of the proportions customarily used in millwork yield by direct crush- 
ing, the strength being directly as the area at the smallest part. The 
columns yielded at about 4500 lbs. per sq. in., confirming the general 
practice of allowing 600 lbs. per sq. in. as a safe load. Square columns 
are one fourth stronger than round ones of the same diameter. 

COST OF BUILDINGS. 

Approximate Cost of Mill Buildings. — Chas. T. Main (Eng. News, 
Jan. 27, 1910) gives a series of diagrams of the cost in New England 
Jan., 1910, per sq. ft. of floor space of different sizes of brick mill build- 
ings, one to six stories high, of the type known as "slow-burning," cal- 
culated for total floor loads of about 75 lbs. per sq. ft. Figures taken 
from the diagrams are given in the table below. The costs include 
ordinary foundations and plumbing, but no heating, sprinklers or lighting. 
Cost of Brick Mill Buildings per sq. ft. of Floor Area. 



Length, feet. 



50 100 150 200 250 300 350 400 500 



One Story. 



Width 25 ft. 


$1.90 


$1.66 


$1.58 


$1.54 


$1.51 


$1.49 


$1.48 


$1.47 


$1.46 


50 


1.52 


1.29 


1.21 


1.18 


1.16 


1.15 


1.14 


1.13 


1.13 


75 


1.41 


1.21 


1.12 


1.08 


1.06 


1.04 


1.03 


1.02 


1.02 


125 


1.32 


1.09 


1.02 


0.98 


0.96 


0.94 


0.94 


0.93 


0.92 



Two Stories. 



25 


2.00 


1.62 


1.52 


1.47 


1.44 


1.41 


1.39 


1.38 


1.36 


50 


1.50 


1.21 


1.13 


1.09 


1.06 


1.05 


1.04 


1.03 


1.02 


75 


1.34 


1.08 


1.01 


0.97 


0.94 


0.92 


0.92 


0.91 


0.90 


125 


1.22 


0.97 


0.90 


0.86 


0.84 


0.82 


0.81 


0.80 


0.80 



Three Stories. 



25 


1.98 


1.57 


1 47 


1.42 


1.39 


1.38 


1.36 


1.35 


1.34 


50 


1.47 


1.17 


1.07 


1.03 


1.01 


1.00 


0.98 


0.98 


0.98 


75 


1.30 


1.05 


0.98 


0.94 


0.91 


0.89 


0.88 


0.87 


0.86 


125 


1.18 


0.93 


0.86 


0.82 


0.80 


0.78 


0.77 


0.76 


0.76 



Four Stories. 



25 


2.00 


1.61 


1.50 


1.45 


1.42 


1.40 


1.38 


1.37 


1.36 


50 


1.38 


1.17 


1.10 


1.05 


1.02 


1.00 


1.00 


0.99 


0.98 


75 


1.32 


1.08 


97 


0.93 


0.90 


0.88 


0.88 


0.87 


0.87 


125 


1.20 


0.93 


0.85 


0.81 


0.78 


0.77 


0.76 


0.75 


0.74 



Six Stories. 



25 


2.10 


1.72 


1.57 


1.51 


1.48 


1.46 


1.44 


1.43 


1.42 


50 


1.53 


1.21 


1.12 


1.08 


1.05 


1.04 


1.03 


1.02 


1.02 


75 


1.35 


1.08 


0.98 


0.94 


0.92 


0.90 


0.89 


0.88 


0.86 


125 


1.22 


0.96 


0.86 


0.82 


0.79 


0.78 


0.77 


0.76 


0.76 



The cost per sq. ft. of a building 100 ft. wide will be about midway 
between that of one 75 ft. wide and one 125 ft. wide, and the cost of a 
five-story building about midway between the costs of a four- and a six- 
story. The data for estimating the above costs are as follows : 





Stories High. 




1 


2 


3 


4 


5 


6 


Foundations, includ- ) Onf sidp walk 

Brick walls, cost per ) Outside walls. . 
sq. ft. of surface. . . ) Inside walls — 


$2.00 
1.75 

0.40 
0.40 


$2.90 
2.25 

0.44 
0.40 


$3.80 
2.80 

0.47 
0.40 


$4.70 
3.40 

0.50 
0.43 


$5.60 
3.90 

0.53 
0.45 


$6.50 
4.50 

0.57 
0.47 



Columns, including piers and castings, cost each $15. 

Assumed Height of Stories. — From ground to first floor, 3 ft. Buildings 



COST OF BUILDINGS. 1395 

25 ft. wide, stories 13 ft. high; 50 ft. wide, 14 ft. high; 75 ft. wide, 15 ft 
high; 100 ft. and 125 ft. wide, 16 ft. high. 

Floors, 32 cts. per sq. ft. of gross floor space not including columns 
Columns included, 38 cts. 

Roof, 25 cts. per sq. ft., not including columns. Columns included 
30 cts. Roof to project 18 ins. all around buildings. 

Stairways, including partitions, SlOO each flight. Two stairways and 
one elevator tower for buildings up to 150 ft. long; two stairways and two 
elevator towers for buildings up to 300 ft. long. In buildings over two 
stories, three stairways and three elevator towers for buildings over 300 ft. 
long. 

m buildings over two stories, plumbing $75 for each fixture including 

giping and partitions. Two fixtures on each floor up to 5000 aq. ft. ol 
oor space and one fixture for each additional 5000 sq. ft. of floor oi 
fraction thereof. 
Modifications of the above Costs: 

1. If the soil is poor or the conditions of the site are such as to require 
more than ordinary foundations, the cost will be increased. 

2. If the building is to be used for ordinary storage purposes with low 
stories and no top floors, the cost will be decreased from about 10% for 
large low buildings to 25% for small liigh ones, about 20% usually being 
a fair allowance. 

3. If the building is to be used for manufacturing and is substantially 
built of wood, the cost will be decreased from about 6% for large one- 
story buildings to 33% for high small buildings; 15% would usually be a 
fair allowance. 

4. If the building is to be used for storage with low stories and built 
substantially of wood, the cost will be decreased from 13% for large 
one-story buildings to 50% for small high buildings; 30% would usually 
be a fair allowance. 

5. If the total floor loads are more than 75 lbs. per sq. ft. the cost is 
increased. 

6. For ofiBce buildings, the cost must be increased to cover architectural 
features on the outside and interior finish. 

Reinforced-concrete buildings designed to carry floor loads of 100 lbs. 
per sq, ft. or less will cost about 25% more than the slow-burning type 
of mill construction. 



1396 ELECTRICAL ENGINEERING. 

ELECTRICAL ENGINEERING-.^ 

STANDARDS OF MEASURE3IENT. 

C.6.S. (Centimeter, Gramme, Second) or " Absolute '* System 
of Physical Measurements 8 

Unit of space or distance = 1 centimeter, cm.; 

Unit of mass = 1 gramme, gm.; 

Unit of time = 1 second, sec; 

Unit of velocity = space -v- time = 1 centimeter in 1 second; 
Unit of acceleration = change of 1 unit of velocity in 1 second; 
Acceleration due to gravity, = 980.665 centimeters per sec. per sec. 

unit offeree = 1 dyne= ^^1^^ g°^-- "gST '^- 0-0000022481 lb. 

A dyne is that force which, acting on a mass of one gramme during one 
second, will give it a velocity of one centimeter per second. The weight 
of one gramme in latitude 40° to 45° is about 980 dynes, at the equator 
973 dynes, and at the poles nearly 984 dynes. Taking the value of g, 
the acceleration due to gravity, in British measures at 32.1740 feet per 
second at lat. 45° at the sea level, and the meter = 39.37 inches, we have 

1 gramme = 32.174 X 12 -^ 0.3937 = 980.665 dvnes. 
Unit of work = 1 erg =1 dyne-centimeter = 0.000000073756 ft. -lb.; 
Unit of power = 1 watt = 10 million ergs per second, 

= 0.73756 foot-pound per second. 

^ 550 "" 745^ horse-power = 0.0013410 H.P. 

C.G.S. unit magnetic pole is one which reacts on an equal pole at a 
centimeter's distance with the force of 1 dyne. 

C.G.S. unit of magnetic field strength, the gauss, is the intensity of 
field which surrounding unit pole acts on it with a force of 1 dyne. 

C.G.S. unit of electro-motive force = the force produced by the cutting 
of a field of 1 gauss intensity at a velocity of 1 centimeter per second (in 
a direction normal to the field and to the conductor) by 1 centimeter of 
conductor The volt is 100,000,000 times this unit. 

C.G.S. unit of electrical current = the current in a conductor (located 
in a plane normal to the field) when each centimeter is urged across a 
magnetic field of 1 gauss intensity with a force of 1 dyne. One-tenth of 
this is the ampere. 

The C.G.S. unit of quantity of electricity is that represented by the 
flow of 1 C.G.S. unit of current for 1 second. One-tenth of this is the 
coulomb. 

The Practical Units used in Electrical Calculations are: 

Ampere, the unit of current strength, or rate of flow, represented by /. 

Volt, the unit of electro-motive force, electrical pressure, or difference 
of potential, represented by E. 

Ohm, the unit of resistance, represented by R. 

Coulomb (or ampere-second), the unit of quantity, Q. 

Ampere-hour = 3600 coulombs, Q'. 

Watt (volt-ampere), the unit of power, P. 

Joule (or watt-second), the unit of energy or work, W. 

Farad, the unit of electrostatic capacity, represented by C. 

Henry, the unit of inductance, represented by L. 

Using letters to represent the units, the relations between them may 
be expressed by the following formulae, in which t represents one second 
and T one hour: 

/=|, Q = It, Q'==IT, C = ^. W==QE, P^IE, 
rC hi 

As these relations contain no coefficient other than unity, the letters 
may represent any quantities given in terms of those units. For exam- 
ple, if E represents the number of volts electro-motive force, and R the 
number of ohms resistance in a circuit, then their ratio E -r- R will give 
the number of amperes current strength in that circuit. 

The above six formulae can be combined by substitution or elimination, 

* In the revision of this chapter the author has had the assistance 
of Mr. David B. Rushmore. 



STANDARDS OF MEASUREMENTS. 1397 

so as to give the relations between any of the quantities. The most 
important of these are the following: 

/ ti it 

The definitions of these units as adopted at the International Electrical 
Congress at Chicago in 1893, and as estabhshed by Act of Congress of 
the United States, July 12, 1894, are as follows: 

The ohm is substantially equal to 10^ (or 1,009,000,000) units of resist- 
ance of the C.G.S. system, and is represented by the resistance offered 
to an unvarying electric current by a column of mercury at 32° F., 14.4521 
grammes in mass, of a constant cross-sectional area, and of the length of 
106.3 centimeters. 

The ampere is Vio of the unit of current of the C.G.S. system, and is 
the practical equivalent of the unvarying current wliich when passed 
through a solution of nitrate of silver in water in accordance with standard 
specifications deposits silver at the rate of 0.001118 gramme per second. 

The volt is the electro-motive force that, steadily applied to a con- 
ductor whose resistance is one ohm, will produce a current of one ampere, 
and is practically equivalent to 1000/1434 (or 0.6974) of the electro- 
motive force between the Doles or electrodes of a Clark's cell at a tem- 
perature of 15° C, and prepared in the manner described in the standard 
specifications. [The e.m.f. of a Weston normal cell is 1.0183 volts at 20° C] 

The coulomb is the quantity of electricity transferred by a current of one 
ampere in one second. 

The farad is the capacity of a condenser charged to a potential of one 
volt by one coulomb of electricity. 

The joule is equal to 10,000,000 units of work in the C.G.S. system, and 
is practically equivalent to the energy expended in one second by an 
ampere in an ohm. 

The watt is equal to 10,000,000 units of power in the C.G.S. system, and 
is practically equivalent to the work done at the rate of one joule per 
second. 

The henry is the induction in a circuit when the electro-motive force 
induced in this circuit is one volt, while the inducing current varies at the 
rate of one ampere per second. 

The ohrn, volt, etc., as above defined, are called the ••international" 
ohm, volt, etc., to distinguish them from the "legal" ohm, B.A. unit, etc. 

The value of the ohm, determined by a committee of the British Asso^ 
elation in 1863, called the B.A. unit, was the resistance of a certain piece 
of copper wire. The so-called "legal" ohm, as adopted at the Inter- 
national Congress of Electricians in Paris in 1884. was a correction of the 
B.A. unit, and was defined as the resistance of a column of mercury 
1 square millimeter in section and 106 centimeters long, at a temperature 
of 32° F. 1 legal ohm =1.0112 B.A. units; 1 international ohm =1.0023 
legal ohm: 1 legal ohm =0.9977 int. olim. 

Derived Units. 
1 megohm = 1 million ohms; 
1 microhm = 1 millionth of an ohm; 
1 milliampere = i/iooo of an ampere; 
1 micro-farad = 1 millionth of a farad. 

Relations of Various Units. 

1 ampere =1 coulomb per second : 

1 volt-ampere (direct current) = 1 watt = 1 volt-coulomb per sec. ; 

' = 0.73756 foot-pound per second. 
= 0.00094859 heat-unit per sec. (Fahr.), 
= 1/745 7 of one horse-power; 
= 0.73756 foot-pound, 
= work done by one watt in one sec, 
= 0.00094859 heat-unit; 
= 0.23904 gram calories; 
= 1054.2 joules; 
= 777.54 foot-pounds; 
= 25.200 gram calories; 



1 watt 

1 joule = 107 ergs 

1 British thermal unit , 



1398 ELECTRICAL ENGINEERING. 

1 mpnn eram ralorie ^ = 4. 1834 X 10^ ergs * ; 

1 mean gram caiorie ^ ^ 0.0039683 B. T. U.; 

1 kilowatt, or 1000 watts. ... = 1000/745.7 or 1.3410 horse-powers; 

1 kilowatt-hour f = 1.3410 horse-power hours, 

1000 volt-ampere hours \ = 2,655,220 foot-pounds, 

1 British Board of Trade unit 1 =3415 heat-units; 

1 v.^..o^ r^r.T,r^r. J = 745.7 watts = 745.7 volt-amperes, 

i norse-power j ^ 33,000 foot-pounds per minute. 

The ohm, ampere, and volt are defined in terms of one another as 
follows: Ohm, the resistance of a conductor through which a cm-rent of 
one ampere will pass when the electro-motive force is one volt. Ampere, 
the quantity of current which will flow through a resistance of one ohm 
when the electro-motive force is one volt. Volt, the electro-motive force 
required to cause one ampere to flow through a resistance of one ohm. 

For Methods of Making Electrical Measurements, Testing, etc., 
see "American Handbook for Electrical Engineers"; Karapetoff's 
"Experimental Electrical Engineering"; BedeU's "Direct and Alter- 
nating Current Manual"; 1914 Standardization Rules of A. I. E. E. 

Equivalent Electrical and Mechanical Units. — H. Ward Leonard 
pubhshed in The Electrical Engineer, Feb. 25, 1895, a table of useful 
equivalents of electrical and mechanical units, from which the table on 
page 1399 is taken, with some modifications. 

Units of the Magnetic Circuit. 

Unit magnetic pole is a pole of such strength that when placed at a dis- 
tance of one centimeter from a similar pole of equal strength it repels it 
with a force of one dyne. 

Magnetic Moment is the product of the strength of either pole into the 
distance between the two poles. 

Intensity of Magnetization is the magnetic moment of a magnet divided 
by its volume. 

Intensity of Magnetic Field is the force exerted by the field upon a unit 
magnetic pole. The unit is the gauss. 

Gauss = unit of field strength, or density, symbol H is that intensity 
of field which acts on a unit pole with a force of one dyne, = one line of 
force per square centimeter. One gauss produces 1 dyne of force per 
centimeter length of conductor upon a current of 10 amperes, or an 
electro-motive force of 1/100,000,000 volt in a centimeter length of con- 
ductor when its velocity across the field is 1 centimeter per second. A field of 
H units is one which acts with H dynes on unit pole, or H lines per 
square centimeter. A unit magnetic pole has 4;r lines of force proceeding 
from it. 

Maxwell = unit of magnetic flux, is the amount of magnetism passing 
through a square centimeter of a field of unit density. Symbol, <^. 

In non-magnetic materials a unit of intensity of flux is the same as 
unit intensity of field. The name maxwell is given to a unit quantity 
of flux, and one maxwell per square centimeter in non-m9.gnetic materials 
is the same as the gauss. In magnetic materials the flux produced by 
the molecular magnets is added to the field (Norris). 

Magnetic Flux, ^, is equal to the average field intensity multiplied by 
the cross-sectional area. The unit is the maxwell. Maxwehs per square 
inch = gausses X 6.45. 

Magnetic Induction, symbol B, is the flux or the number of magnetic 
lines per unit of area of cross-section of magnetized material, the area 
being at every point perpendicular to the direction of the flux. It i3 
equal to the product of the field intensity, H, and the permeability, ft. 

Gilbert = umt of magnetomotive force, is the amount of M.M.F. that 
would be produced by a coil of 10 h- 4;r or 0.7958 ampere-turns. Symbol F. 

The M.M.F. of a coil is equal to 1.2566 times the ampere-turns. 

If a solenoid is wound with 100 turns of insulated wire carrying a current 
of 5 amperes, the M.M.F. exerted will be 500 ampere-turn^ X 1.2566 = 
628.3 jg:ilberts. 

Oersted = unit of magnetic reluctance; a magnetic circuit has a re- 
luctance of 1 oersted when unit m.m.f. produces unit flux. Symbol, R. 

Reluctance is that quantity in a magnetic circuit which limits the flux 

* Mean of the values of Reynolds and Moorby and of Barnes — 
Marks & Davis, Steam Tables, 1909. 



EQUIVALENT ELECTRICAL AND MECHANICAL UNITS. 1399 






•i s 



5 «« r 



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oo 
oo 



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c>o"o 



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2^1 




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fl O 0) ftoa 






J fl <=> 
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o) w -j^ ^- j2 :2 

^ CO -^ m ir> *«-i 
3 — «J^ t>« f*^ -^ 

— Or<Soo-<t- 



-2 fe fc 
c . a . ^ 

S.S£.e^ 

o i^ CT^ 

CM "^^ — 
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no nO 

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: -^j «r! ^ ^ r-r* 



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a> o; g 
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g ^ p |x5 a5 o 
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£ t. I. . F2 3^ 
K 0) a; m.ti i rt 






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— ^ ^. in r>, tt 



8: 



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ft^-a 



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1400 



ELECTRICAL ENGINEERING. 



under a given M.M.F. It corresponds to the resistance in the electric cir- 
cuit. 

Permeance is the reciprocal of reluctance. 

The reluctivity of any medium is its specific reluctance, and in the O.G.S. 
system is the reluctance offered by a cubic centimeter of the body between 
opposed parallel faces. The reluctivity of nearly all substances, other 
than the magnetic metals, is sensibly that of vacuum, is equal to unity, 
and is independent of the flux density. 

Permeability is the reciprocal of magnetic reluctivity. It is a number 
and the symbol is //. 

Materials differ in regard to the resistance they offer to the passage 
of lines of force; thus iron is more permeable than air. The permeability 
of a substance is expressed by a coefficient, n, which denotes its relation 
to the permeability of air, which is taken as 1. If H = number of mag- 
netic lines per square centimeter which will pass through an air-space 
between the poles of a magnet, and B the number of lines which will 
pass through a certain piece of iron in that space, then /i = B -r- H. The 
permeability varies with the quality of the iron, and the degree of satura- 
tion, reaching a practical limit for soft wrought iron when B= about 
18,000 and for cast iron when B = about 10,000 C.G.S. lines per square 
centimeter. 

The permeability of a number of materials may be determined by means 
of the table on page 1431. 



ANALOGIES BETWEEN THE FLOW OF WATER AND 
ELECTRICITY. 



Water, 

Head, difference of level, in feet. 

Difference of pressure, lbs. per sq. in. 

Resistance of pipes, apertures, etc., 
increases with length of pipe, with 
contractions, roughness, etc.: de- 
creases with increase of sectional 
area. 

Rate of flow, as cubic ft. per second, 
gallons per min., etc., or volume 
divided by the time. In the min- 
ing regions sometimes expressed 
in "miners' inches." 

Quantity, usually measured in cubic 
ft. or gallons, but is also equiva- 
lent to rate of flow X time, as cu. 
ft. per second for so many hours. 

Work, or energy, measured in foot- 
pounds; product of weight of fall- 
ing water into height of faU; in 
pumping, product of quantity in 
cubic feet into the pressure in lbs. 
per square foot against which the 
water is pumped. 

Power, rate of work. Horse-power = 
ft.-lbs. of work in 1 min. -^ 33,000. 
In water flowing in pipes, rate of 
flow in cu. ft. per second X resist- 
ance to the flow in lbs. per sq. ft. 
-V- 550. 



Electricity. 

1 Volts; electro-motive force; differ- 
J ence of potential; E. or E.M.F. 

IOhms, resistance, R. Increases di- 
rectly as the length of the conduc- 
■ tor or wire and inversely as its sec- 
tional area, R <^l-^ s. It varies 
with the nature of the conductor. 
! Amperes; current; current strength; 
intensity of current; rate of flow; 
1 ampere = 1 coulomb per second > 
volts y £J ^ ,„ 

1 Coulomb, unit of quantity, Q, = 
I rate of flow X time, as ampere- 
j seconds. 1 ampere-hour = 3600 
J coulombs. 

^ Joule, volt-coulomb, W, the unit of 
work, = product of quantity by 
the electro-motive force = volt- 
ampere-second. 1 joule = 0.7373 
foot-pound. 
If C (amperes) = rate of flow, and 
E (volts) = difference of pressure 
between two points in a circuit, 
energy expended = lEt, = PRt. 

Watt, unit of power, P, = volts X 
amperes, = current or rate of 
flow X difference of potential. 

1 watt = 0.7373 foot-pound per sec. 
= 1/746 of a horse-power. 



ELECTRICiL RESISTANCE. 

Laws of Electrical Resistance. — The resistance, R, of any con- 
ductor varies directly as its length, I, and inversely as its sectional area, s, 
01 R ^ I -^ s. 

If r = the resistance of a conductor 1 unit in length and 1 square unit 
in sectional area, R = rl -7- s. The common unit of length for electrical 



ELECTRICAL RESISTANCE. 



1401 



calculations in English measure is the foot, and the unit of area of wires 
is the circular mil = the area of a circle 0.001 in. diameter. 1 rail-foot = 
1 foot long 1 circ.-mil area. 

Resistance of 1 mil-foot of soft copper wire at 51° F. = 10 international 
ohms. 

Example. — What is the resistance of a wire 1000 ft. longr. 0.1 in diam •? 
0.1 in. diam, = 10,000 circ. mils. ' i*"^.. 

R = rl-~ s = 10 X 1000 ~- 10,000 = 1 ohm. 

Specific resistance, also called resistivity, is the resistance of a material 
of umt length and section as compared with the resistance of soft coDner 

Conductivity is the reciprocal of specific resistance, or the relative 
conducting power compared with copper taken at 100. 

Conductance is the reciprocal of resistance. 

Eelative Conductivities of Different Metals at 0° and 100° C. 

(Matthiessen.) 





Conductivities. 


Metals. 


Conduc 
At 0°C. 
At 32° F. 


tivities. 


Metals. 


At 0°C. 
At 32° F. 


At 100^ C. 
At 212° F. 


At 100° C. 
At 212° F. 


Silver, hard 


100 
99.95 
77.96 
29.02 
23.72 
18.00 
16.80 


71.56 
70.27 
55.90 
20.67 
16.77 


Tin ... 


12.36 
8.32 
4.76 
4.62 
1.60 
1.245 


8.67 


Copper, hard .... 


Lead 


5.86 


Gold, hard 


Arsenic 


3.33 


Zinc, pressed .... 

Cadmium 

Platinum, soft. . . 


Antimony 

Mercury, pure . . 
Bismuth 


3.26 
d.'87'8* * 


Iron, soft 













Resistance of Various Metals and Alloys. — Condensed from a 
table compiled by H. F. Parshall and H. M. Hobart from different 
authorities. R = resistance in ohms per mil foot = resistance per centi- 
meter cube X 6.015. C = per cent increase of resistance per degree C. 



Aluminum, 99% pure 

Aluminum, 94; copper, 6., 
Al. bronze, Al 10; Cu, 90 . 
Antimony, compressed. . 
Bismuth, compressed — 

Cadmium, pure 

Copper, annealed, (D) 

Copper, annealed, (M) ... 

Copper, 88; silicon, 12 

Copper, 65.8; zinc, 34.2 

Copper, 90; lead, 10 

Copper, 97; aluminum, 3. , 

Cu, 87;Ni, 6.5;A1, 6.5 

Copper, 65; nickel, 25 

Cu, 70; manganese, 30 

German silver 
Cu, 60;Zn, 25;Ni, 15... 

Gold, 99.9% pure , 

Gold, 67; silver, 33 , 

Iron, very pure , 



R 


C 


15.4 


0.423 


17.4 


.381 


75.5 


.105 


211 


.389 


780 


.354 


60 


.419 


9.35 


.428 


9.54 


.388 


17.7 




37.8 


.158 


31.7 




53.0 


.090 


89.5 


.065 


205 


.019 


605 


.004 


180 


.036 


13.2 


.377 


61.8 


.065 


54.5 


.625 



12. 



White cast iron 

Gray cast iron 

Wrought iron 

Soft steel, C, 0.045 .. 

Manganese steel, Mr 

Nickel steel, Ni, 4.35 

Lead, pure 

Manganin, 
Cu, 84;Mn, 12;Ni, 4.... 
Cu, 80.5;Mn, 3;Ni, 16.5 
Cu, 79.5; Mn, 19.7; Fe.O. 

Mercury 

Nickel 

Palladium, pure 

Platinum, annealed 

Platinum, 67; silver, 33 . . 

Phosphor bronze 

Silver, pure 

Tin, pure 

Zinc, pure 



R 



340 
684 

82.8 

63 
401 
177 
123 

287 

294 

393 

566 
73.7 
61.1 

539 

145 
33.6 
8.82 
78.5 
34.5 



.127 
.201 
.411 

.000 

.000 

.000 

.072 

.62 

.354 

.247 

.133 

.394 

.400 

.440 

.406 



(D) Dewarand Fleming; (M) Matthiessen. 

Conductivity of Aluminum. —J. W. Richards (Jour. Frank.. Inst., 
Mar., 1897) gives for hard-drawn aluminum of purity 98.5, 99.0, 99.5, 
and 99.75% respectively a conductivity of 55, 59, 61, and 63 to 64%, 
copper being 100%. The Pittsburg Reduction Co. claims that its purest 
aluminum has a conductivity of over 64.5%. (Eng'g News, Dec. 17, 
1896.) 

German Silver. — The resistance of German silver depends on its 
composition. Matthiessen gives it as nearly 13 times that of copper, 
with a temperature coefficient of 0.0004433 per degree G. Weston, how- 



1402 ELECTRICAL ENGINEERING. 

ever (Proc. Electrical Congress, 1893, p. 179), has found copper-nickel- 
zinc alloys (German silver) which had a resistance of nearly 28 times 
that of copper, and a temperature coefficient of about one-half that 
given by Matthiessen. 

Conductors and Insulators in Order of Their Value. 



INSULATOKS (NON-CONDUCTORS) . 

Dry air Ebonite 

Shellac Gutta-percha 

Paraffin India-rubber 

Amber Silk 

Resins Dry paper 

Sulphur Parchment 

Wax Dry leather 

Jet Porcelain 

Glass Oils 
Mica 



CONDUCTORS. 

All metals 

Well-burned charcoal 

Plumbago 

Acid solutions 

SaUne solutions 

]\Ietallic ores 

Animal fluids 

Living vegetable substances 

Moist earth 

Water 

According to Culley, the resistance of distilled water is 6754 million 
times as great as that of copper. Impurities in water decrease its 
resistance. 

Resistance Varies with Temperature. — For every degree Centi- 
grade the resistance of copper increases about 0.4%, or for every degree 
F., 0.2222%. Thus a piece of copper wire having a resistance of 10 
ohms at 32° would have a resistance of 11.11 ohms at 82° F. 

The following table shows the amount of resistance of a few sub- 
stances used for various electrical purposes by which 1 ohm is increased 
by a rise of temperature of 1° C. 

Platinoid 0.00021 I Gold, silver 0.00065 

Platinum silver . 00031 Cast iron . 00080 

German silver (see above) . . . 00044 * Copper . 00400 

Annealing. — Resistance is lessened by annealing. Matthiessen gives 
the following relative conductivities for copper and silver, the comparison 
being made with pure silver at 100° C: 

Metal. Temp. C. Hard. Annealed. Ratio. 

Copper 11*^ 95.31 97.83 1 to 1.027 

Silver 14.6° 95.36 103.33 1 to 1.084 

Dr. Siemens compared the conductivities of copper, silver, and brass 
with the following results. Ratio of hard to annealed: 

Copper 1 to 1.058 Silver 1 to 1.145 Brass 1 to 1.180 

STANDARD VALUES FOR RESISTIVITY AND TEMPERATURE 
COEFFICIENT OF COPPER. 

Bureau of Standards, 1914. 

The Bureau of Standards made measurements of a large number of 
representative samples of copper and established standard values of 
resistivity and temperature coefficients, which have been adopted by 
the International Electrochemical Commission. 

Conductivity of Copper. 

The following rules of the International Electrical Commission have 
been adopted by the American Institute of Electrical Engineers. 

The following shall be taken as normal values for standard annealed 
copper: 

(1) At a temperature of 20° C. the resistance of a wire of standard 
annealed copper one meter in length and of a uniform section of 1 square 
miUimeter is 1/58 ohm = 0.017241. . . .ohm. 

(2) At a temperature of 20° C. the density of standard annealed 
copper is 8.89 grams per cubic centimeter. 

(3) At a temperatm-e of 20° C. the "constant mass" temperature 
coefficient of resistance of standard annealed copper, measured between 
two potential points rigidly fixed to the wire, is 0.00393 = 1/254.45 
, . . . per degree centigrade. 



RESISTANCE OF COPPER. 1403 

(4) As a consequence it follows from (1) and (2) that, at a temper- 
ature of 20° C. the resistance of a wire of standard annealed copp(T of 
uniform section, one meter in length and weighing one gram, is (1/58) 
X 8.89 = 0.15328 ohm. 

Paragraphs (1) and (4) define what are sometimes called "volume 
resistivity" and "mass resistivity" respectively. This may be ex- 
pressed in other units as follows: Volume resistivity = 1.7241 
microhm-cm. (or microhms in a cm. cube) at 20° C. = 0.67879 microhm 
inch at 20° C. and mass resistivity = 875.20 ohms (mile, pound) at 
20 C 

The new value is known as the International Annealed Copper 
Standard, and is equivalent to 

0.017241 ohm (meter, mm2) at 20° C. 
The units of mass resistivity and volume resistivity are interrelated 
through the density; this was taken as 8.89 grams per cm^ at 20° C. by 
the International Electrochemical Commission. The International 
Annealed Copper Standard, in various imits of mass resistivity and 
volume resistivity, is: 

0.15328 ohm (meter, gram) at 20° C. 
875.20 ohms (mile, pound) at 20° C. 

0.017241 ohm (meter, mm2) at 20° C. 

1.7241 microhm-cm. at 20° C. 

0.67879 microlim-inch at 20° C. 
10.371 ohms (mil, foot) at 20° C. 
The Temperature Coefficient of Resistance of Copper. — The Bureau of 
Standards' investigation of the temperature coefficient showed that 
the coeflacient varies with different samples, but that the relation of 
conductivity to temperature coefficient is substantially a simple pro- 
portionality. 

The general law may be expressed by the following practical rule: 
The 20° C. temperature coefficient of a sample of copper is the product 
of the per cent, conductivity by 0.00393. There are sometimes cases 
when the temperature coefficient is more easily measured than the 
conductivity, and the conductivity can be computed from the relation: 
per cent, conductivity = 254.5 X temperature coefficient. 

When a temperature coefficient of resistance must be assumed the 
best value to assume for good commercial annealed copper wire is that 
corresponding to 100 per cent, conductivity, viz. : 

ao = 0.00427, an = 0.00401, a2o = 0.00393, 025 = 0.00385 

Rt -Rio , \ 
, etc. I 



l«20 = 



R20 it - 20) ' 

This value was adopted as standard by the International Electro- 
chemical Commission in 1913. It would usually apply to instruments 
and macliines, since they are generally wound with anneaUxl wire. 
Experiment has shown that distortions such as those caused by winding 
and ordinary handling do not affect the temperature coefficient. 

Similarly, when assumption is unavoidable, the temperature coeffi- 
cient of good commercial hard-drawn copper wire may be taken as 
that corresponding to a conductivity of 97.3 per cent., viz.: 

«o = 0.00414, Gig = 0.00390, ^20 = 0.00382. a2s = 0.00375 

Rule for reducing resisti\ity from one temperature to another: 
The change of resistivity of copper per degree C. is a constant, inde- 
pendent of the temperature of reference and of the sample of copper. 
This " resistivitv-temperature constant" may be taken, for general 
purposes, as 0.00060 ohm (meter, gram), or 0.(X)68 microhm-cm. 
More exactly, it is: 

0.000.597 ohm (meter, gram) 
or, 0.000.0681 ohm (meter, mm2) 
or, 0.006.81 microhm-cm. 
or, 3.41 ohms (mile, pound) 

or, 0.002.68 microhm-inch, 
or, 0.040.9 ohm (mil, foot). 

Continued on p. 1406. 



1404 



ELECTEICAL ENGINEERING. 



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WIRE TABLE. 



1405 



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1406 ELECTRICAL ENGINEERING. 

Resistivity of Hard-Drawn Copper ^Vires. — In general the resistivity 
of hard-drawn wires varies with the size of the wire, while the resistivity 
of annealed wires does not. The difference between the resistivity of 
annealed and hard-drawn wires increases as the diameter of the wire 
decreases. This general conclusion is, however, comphcated in any 
particular case by the number of drawings between anneahngs, amount 
of reduction to each drawing, etc. For No. 12 A.W.G. (B. & S.), the 
conductivity of hard-drawn wires was found to be less than the con- 
ductivity of annealed wires by 2.7 per cent. 

Density of Copper. — The international standard density for copper, 
at 20° C, is 8.89 grams per cubic centimeter. This is the value which 
has been used by the A. I.E. E., and most other authorities in the past. 
Recent measurements have indicated this value as a mean. This den- 
sity, 8.89, at 20° C, corresponds to a density of 8.90 at 0° C. In 
English imits, the density at 20° C. = 0.32117 pounds per cubic inch. 

For a complete treatise on this subject, see Bulletin No. 31, Bureau 
of Standards. 

Approximate Rules for the Resistance of Copper Wire. — The re- 
sistance of any copper wire at 20° C. or 68° F., according to Matthies- 

sen's standard, lis i? = — ^^^— , in which R is the resistance in inter- 
national ohms, I the length of the wire in feet, and d its diameter in 
mils. (1 mil = Viooo inch.) 

A No. 10 wire, A.W.G. , 0.1019 in. diam (practically 0.1 in.), 1000 
ft. in length, has a resistance of 1 ohm at 68° F. and weighs 31.4 lbs. 

If a wire of a given length and size by the American or Brown & 
Sharpe gauge has a certain resistance, a wire of the same length and 
three numbers higher has twice the resistance, six numbers higher 
four times the resistance, etc. 

Wire gauge, A.W.G. No 000 1 4 7 10 13 16 19 22 

Relative resistance 16 8 4 2 1 1/2 1/4 Vs Vie 

section or weight .. . i/ie Vs V4 V2 1 2 4 8 16 



DIRECT ELECTRIC CURRENTS. 

Ohm's Law. — This law expresses the relation between the three 
fundamental units of resistance, electrical pressure, and current. It is: 

^ ^ electrical pressure ^^ E , „ ^ r, ^ n ^ 

Current = ~- ; J = ^ ; whence E = I R, and R = -y. 

resistance R I 

In terms of the units of the three quantities, 

volts ,, ,, , , volts 

Amperes = — r; — ; volts = amperes X ohms ; ohms = - 



ohms amperes 

Examples: Simple Circuits. — 1. If the source has an effective electrical 
pressure of 100 volts, and the resistance is two ohms, what is the current? 

/= -s = -77- = 50 amperes. 

2. What pressure will give a current of 50 amperes through a resistance 
of 2 ohms? ^ = /i2 = 50 X 2 = 100 volts. 

3. What resistance is required to obtain a current of 50 amperes when 
the pressure is 100 volts? ie = ^ ~ / = 100 4- 50 = 2 ohms. 

Ohm's law apphes equally to a complete electrical circuit and to any 
part thereof. 

Series Circuits. — If conductors are arranged one after the other they 
are said to be in series, and the total resistance of the circuit is the sum of 
the resistances of its several parts. Let A, Fig. 226, be a source of current, 
such as a battery or generator, producing a difference of potential or 



DIKECT ELECTRIC CURRENTS. 1407 

E.M.F. of 120 volts, measured across ab, and let the circuit contain four 
conductors whose resistances, n, n, n, n, are 1 ohm each, ana three 
r2 f^-\ other resistances, R\, R2, R3, each 2 ohms. The 



-O^H3i 



Tl 



:A "1 



Ri R 



Ro 




total resistance is 10 ohms, and by Ohm's law 
the current / = J5; -4- /? = 12O -^ 10 = 12 am- 
peres. This current is constant throughout the 
circuit, and a series circuit is therefore one of 
constant current. The drop of potential in the 
,3 whole circuit from a around to b is 120 volts, 

Fig. 226. or E = RI. The drop in any portion depends 

_ . . ^ on the resistance of that portion: thus from a to 

Ri the resistance is 1 ohm, the constant current 12 amperes, and the drop 
IX 12 = 12 volts. The drop in passing through each of the resistance 
Ru Rz, i?3 IS 2 X 12 = 24 volts. 

Parallel, Divided, or 3Iultiple Circuits.— Let B, Fig. 227, be a 
generator producing an E.M.F. of 220 volts across the terminals ab 
The current is divided, so that part 
flows through the main wires ac and 
part through the "shunt'* s, having a 
resistance of 0.5 ohm. Also the current 
has three paths between c and d, viz.. ^ 
through the three resistances in parallel S^ 
Ri, R2, Rz, of 2 ohms each. Consider 
that the resistance of the wires is so small 
that it may be neglected. Let the con- 
ductances of the four paths be repre- 
sented by Cg. Ci, C2, Cz. The total Fig. 227. 
conductance is C^ 4- Ci+ C2 + Cs = C and the total resistance R = 
1 -*- C The conductance of each path is the reciprocal of its resistance, 
the total conductance is the sum of the separate conductances, and the 
resistance of the combined or "parallel" paths is the reciprocal of the 
total conductance. 

« = ^^(0^5 + 1 + 1+!)=^^ 3.5 = 0.286 ohm. 

The current I = E -r- R - 770 amperes. 

Conductors in Series and Parallel. — Let the resistances in parallel 
be the same as in Fig. 227, with the additional resistance of 0.1 ohm 
in each of the six sections of the main wires, ac, bd, etc., in series. The 
voltage across ab being 220 volts, determine the drop in voltage at the 
several points, the total current, and the current through each path. 
The problem is somewhat complicated. It may be solved as follows: 
Consider first the points eg: here there are two paths for the current, 
efgh and eg. Find the resistance and the conductance of each and the 
total resistance (the reciprocal of the joint condiictance) of the parallel 
paths. Next consider the points cd; here there are two paths — one 
through e and the other through cd. Find the total resistance as before. 
Finally consider the points ab; here there are two paths — one through 
c, the other through s. Find the conductances of each and their sum. 
The product of tliis sum and the voltage at ab will be the total amperes 
of current, and the current through any path will be proportional to the 
conductance of that path. The resistances, R, and conductances, C, 
of the several paths are as follows: 

R C 

Ra of efRshg = 0.1 + 2 + 0.1 = 2.2 0.4545 

Rl, of eRig = 2 0.5 

0.9545 



Rd of ce+dg+ Re = 1.248 0.8013 

Rg of cRid = 2 0.5 

Joint Rf= 0.7687 1,3013 



1408 ELECTRICAL ENGINEERING. 

Rg of ac+M+ Rf = 0.9687 1.0332 

RhOts = 0.5 2 

Joint R(i+ Rj^ = 0.330 3.0332 

Total current = 220 X 3.0332 = 667.3 amperes. 
Current through s = 220 X 2 = 440 amp.; through c = 227.3 amp. 
''cRid = 227.3 X 0.5 -^ 1.3013 = 87.34 amp. 

e = 227.3 X 0.8013 -^ 1.3013 = 139.96 " 

•• eR^g = 139.96 X 0.5 h- 0.9545 = 73.31 ** 

•• ** fRi = 139.96 X 0.4545 -j- 0.9545 = 66.65 " 

The drop in voltage in any section of the line is found by the formula 
E = RI, R being the resistance of that section and / the current in it. 
As the R of each section is 0.1 ohm we find E for ac and bd each = 22.7 
volts, for ce and dg each 14.0 volts, and for ef and gh each 6.67 volts. 
The voltage across cd is 220 - 2 X 22.7 = 174.6 volts; across 6^,174.6- 2 
X 14.0 = 146.6, and across fh 146.6 - 2 X 667 = 133.3 volts. Taking 
these voltages and the resistances Ri, R2, Rs, each 2 ohms, we find from 
I = E -i- R the current through each of these resistances 87.3, 73.3, and 
66.65 amperes as before. 

Internal Resistance. — In a simple circuit we have two resistances, 
that of the circuit R and that of the internal parts of the source of electro- 
motive force, called internal resistance, r. The formula of Ohm's law 
when the internal resistance is considered is I = E -r- {R -h r). 

Power of the Circuit. — The power, or rate of work, in watts = 
current in amperes X electro-motive force in volts = I X E. Since 
I = E -^ R, watts = E^ -^ R = electro-motive force2 ~ resistance. 

Example. — What H.P. is required to supply 100 lamps of 40 ohms 
resistance each, requiring an electro-motive force of 60 volts? 

The number of volt-amperes for each lamp is "b" = 7?r t 1 volt-ampere 

K 40 
602 
= 0.00134 H.P.; therefore — X 100 X 0.00134 = 12 H.P. (electrical) 

very nearly. 

Electrical, Brake, and Indicated Horse-power. — The power given 
by a dynamo = volts X amperes -^ 1000 = kilowatts, kw. Volts X out 
amperes -~ 746 = electrical horse-power, E.H.P. The power put into a 
dynamo shaft by a direct-connected engine or other prime mover is 
called the shaft or brake horse-power, B.H.P. If ei is the efficiency of the 
dynamo, B.H.P. = E.H.P. -^ ei. If €2 is the mechanical efficiency of the 
engine, the indicated horse-power, I. H.P. = brake H.P. -t- 62 = E.H.P. H* 
(61X62). 

If ei and €2 each = 91.5%, I.H.P. = E.H.P. X 1.194 = kw. X 1.60. In 
direct-connected units of 250 kw. or less the rated H.P. of the engine is 
commonly taken as 1.6 X the rated kw. of the generator. 

Electric motors are rated at the H.P. given out at the pulley or belt. 
H.P. of motor = E.H.P. suppUed X efficiency of motor. 

Heat Generated by a Current. — Joule's law shows that the heat 
developed in a conductor is directly proportional, 1st, to its resistance; 
2d, to the square of the current strength; and 3d, to the time during 
which the current flows, or H = PRt. Since I = E -r- R, 

E E EH 

PRt =%IRt== Elt = E%t = ^' 

Or, heat = current2 x resistance X time 

= electro-motive force X current X time. 
= electro-motive forced x time 4- resistance. 
Q = quantity of electricity flowing = It = {Et ~ R), 
H = EQ\ or heat = electro-motive force X quantity. 

The electro-motive force here is that causing the flow, or the differ- 
ence in potential between the ends of the conductor. 

The electrical unit of heat, or "joule" = 10^ ergs = heat generated in 
one second by a current of 1 ampere flowing through a resistance of one 



DIRECT ELECTRIC CURRENTS. 1409 

ohm = 0.239" gramme of water raised 1° C. i/ •= PRt X 0.239 gramme 
calories = PRt X 0.0009478 British thermal units. 

In electric lighting the energy of the current is converted into heat in 
the lamps. The resistance of the lamp is made great so that the required 
quantity of heat may be developed, while in the wire leading to and from 
the lamp the resistance is made as small as is commercially practicable, 
so that as little energy as possible may be wasted in heating the wire. 

Heating of Conductors. (From Kapp's Electrical Transmission of 
Energy.) — It becomes a matter of great importance to determine before- 
hand what rise in temperature! is to be expected in each given case, and 
if that rise should be found o be greater than appears safe, provision must 
be made to increase the rate at which heat is carried off. This can gen- 
erally be done by increasing the superficial area of the conductor. Say 
we have one circular conductor of 1, square inch area, and find that with 
1000 amperes flowing it would become too hot. Now by splitting up this 
conductor into 10 separate wires each one-tenth of a square inch cross- 
sectional area, we have not altered the total amount of energy trans- 
formed into heat, but we have increased the surface exposed to the cooling 
action of the surrounding air in the ratio of 1: v^lO, and therefore the ten 
thin wires can dissipate more than three times the heat, as compared with 
the single thick wire. 

Prof. Forbes states that an insulated wire carries a greater current with- 
out overheating than a bare wire if the diameter be not too great. Assum- 
ing the diameter of the cable to be twice the diam. of the conductor, a 
greater current can be carried in insulated wires than in bare wires up to 
1.9 inch diam. of conductor. If diam. of cable = 4 times diam. of con- 
ductor, this is the case up to 1.1 inch diam. of conductor. 

Heating of Bare Wires. — The following formulae are given by 
Kennelly: 



r= ^^ X 90.000 + t\ rf=44.8 

T = temperature of the wire and t that of the air, in Fahrenheit degrees; 
I - current in amperes, d = diameter of the wire in mils. 



\ T -I 

ai 
in 

If wetaJie T - i = 90° F., -n/So = 4.48, then 

d «= 10 ^P and / » V# -*- 1000. 

This latter formula gives for the carrying capacity in amperes of bare 
wires almost exactly the figures given for weather-proof wires in the 
Fire Underwriters' table, except in the case of Nos. 18 and 16, B. & S. 
gauge, for which the formula gives 8 and 11 amperes, respectively, instead 
of 5 and 8 amperes, given in the table. 

Heating of Coils. — The rise of temperature in magnet coils due to 
the passage of current through the wire is approximately proportional to 
the watts lost in the coil per unit of effective radiating surface, thus: 
, PR , PR 

t being the temperature rise in degrees Fahr.; *S, the effective radiating 
surface; and k a coefficient which varies widely, according to condition. 
In electromagnet coils of small size and power, k may be as large as 0.015. 
Ordinarily it ranges from 0.012 down to 0.005; a fair average is 0.007. 
The more exposed the coil is to air circulation, the larger is the value of k\ 
the larger the proportion of iron to copper, by weight, in the core and 
winding, the tliinner the winding with relation to its dimension parallel 
with the magnet core, and the larger the "space factor" of the winding, 
the larger will be the value of k. The space factor is the ratio of the 
actual copper cross-section of the whole coil to the gross cross-section of • 
copper, insulation, and interstices. 

Fusion of Wires. — W. H. Preece gives a formula for the current 
required to fuse wires of different metals, viz., J = ad'/2 in which d is the 
diameter in inches and a a coefficient whose value for different metals 
is as follows: Copper, 10,244; aluminum, 7585; platinum, 5172; German 
silver, 5230; platinoid, 4750; iron, 3148; tin, 1462; lead, 1379; alloy of 2 
lead and 1 tin, 1318. 



1410 



ELECTRICAL ENGINEERING. 



Allowable Carrying Capacity of Copper Wires. 

(For inside wiring, National Board of Fire Underwriters' Rules.) 



B.&S. 


Circular 


Amperes. 


Circular 


Amperes. 










Gauge. 


Mils. 


Rubber 


Other In- 


Mils. 


Rubber 


Other In- 






Covered. 


sulation. 




Covered. 


sulation. 


18 


1,624 


3 


5 


200,000 


200 


300 


16 


2,583 


6 


8 


300,000 


270 


400 


14 


4,107 


12 


16 


400,000 


330 


500 


12 


6,530 


17 


23 


500,000 


390 


590 


10 


10,380 


24 


32 


600,000 


450 


680 


8 


16,510 


33 


46 


700,000 


500 


760 


6 


26,250 


46 


65 


800,000 


550 


840 


. 5 


33,100 


54 


77 


900,000 


600 


920 


4 


41,740 


65 


92 


1,000,000 


650 


1,000 


3 


52,630 


76 


110 


1,100,000 


690 


1,080 


2 


66,370 


90 


131 


1,200,000 


730 


1,150 


1 


83,690 


107 


156 


1,300,000 


770 


1,220 





105,500 


127 


185 


1,400,000 


810 


1,290 


00 


133,100 


150 


220 


1,600,000 


890 


1,430 


000 


167,800 


177 


262 


1,800,000 


970 


1,550 


0000 


211,600 


210 


312 


2,000,000 


1,050 


1,670 



Wires smaller than No. 14 B. & S. gauge must not be used except in fix- 
tures and pendant cords. 

The lower limit is specified for rubber-covered wires to prevent deteriora- 
tion of the insulation by the heat of the wires. 

For insulated aluminum wire the safe-carrying capacity is 84 per cent of 
that of copper wire with the same insulation. 

See pamphlets published by the National Board of Fire Underwriters, 
New York, for complete specifications and rules for wiring. 

Underwriters' Insulation, — The thickness of insulation required 
by the rules of the National Board of Fire Underwriters varies with the size 
of the wire, the character of the insulation, and the voltage. The thick- 
ness of insulation on rubber-covered wires carrying voltages up to 600 
varies from 1/32 inch for a No. 18 B. & S. gauge wire to 1/8 inch for a wire of 
1.000.000 circular mils. Weather-proof insulation is required to be slightly 
thicker. For voltages of over 600 the insulation varies from i/ie inch 
for No. 14 B. & S. gage to 9/54 inch for 1,000,000 CM. and over. 

ELECTEIC TRANSMISSION, DIRECT CURRENTS. 

Cross-section of Wire Required for a Given Current. — 

Let R = resistance of a given line of copper wire, in ohms ; 
r - *' *' 1 mil-foot of copper; 

L = length of wire, in feet; 
e = drop in voltage between the two ends; 
I = current, in amperes; 
A = sectional area of wire, in circular mils; 

then I =^^; R = 4^; R = r ~; whence A = ^—. 
R I A e 

The value of r for soft copper wire at 68° F. is 10.371 international 
ohms. For ordinary drawn copper wire the value of 10.8 is commonly 
taken, corresponding to a conductivity of 97.2 per cent. 

For a circuit, going and return, the total length is 2 L, and the formula 
becomes A = 21.67L -t- e, L here being the distance from the point of 
supply to the point of deUvery. 

If E is the voltage at the generator and a the per cent of drop in the 
line, then e = Ea -^ 100, and A = 2160 IL -^ aE. 

If P = the power in watts, = EI, then 7 = ^, and A = iS . 

If P^ = the power in kilowatts, A = 2,160.000 P]j:^ h- aE"^. 

If L^ = the distance in miles and Af. the area in circular inches, then 



ELECTRIC TRANSMISSION, DIRECT CURRENT. 1411 

Af. = 6405 PjcLjfi ~ aE^. If A^ = area in square inches, A^ = 5030 
Pj^Lj^ 4- aE\ When the area in circular mils has been determined by 
either of these formulae reference should be made to the table of Allow- 
able Capacity of Wiras, to see if the calculated size is sufficient to avoid 
overheating. For all interior wiring the rules of the National Board of 
Fire Underwriters should be followed. 

Weight of Copper for a Given Povrer. — Taking? the weight of 
a mil-foot of copper at 0.000003027 lb., the weight of copper in a circuit of 
length 2 Land cross-section A, in circ. mils, is 0.000006054 LA lbs., = W, 
Substituting for A its value 2160 PL -^ aE- we have 

TF = 0.0130766 PL2 -^ aE^; P in watts, L in ft. 

W = 13.0766 P^L^ -i- aE^\ Pj^ in kilowatts, L in ft. 

TF = 364,556,000 Pj^U^-^ aE^; Pj^ in kilowatts, L^ in miles. 

The weight of copper required varies directly as the power transmitted; 
inversely as the percentage of drop or loss; directly as the square of the 
distance; and inversely as the square of the voltage. 

From the last formula the following table has been calculated: 

Weight of Copper Wire to Carry 1000 Kilowatts with 10% Loss. 



Distance 
in Miles. 


1 


5 


10 


20 


50 


100 


Volts. 






Weight 


in Lbs. 






500 


145.822 

36.456 

9.114 

1.458 

365 

91 


3.645.560 
911.390 

227.848 

36.456 

9.114 

2.278 

570 










1.000 


3.645.560 

911.390 

145,822 

36.456 

9.114 

2.278 

1.013 









2.000 




3.645.560 

593.290 

145.822 

36.456 

9.114 

4.051 






5.000 


3.645.560 

911.390 

227,848 

56.962 

25.316 




10.000 
20.000 
40.000 


3.645.560 
911.390 
227.848 


60.000 




101.266 











In calculating the distance, an addition of about 5 per cent should 
be made for sag of the wires. 

Short-circuiting. — From the law I = E/R it is seen that with any 
pressure E, the current I will become very great if R is made very 
small. In short-circuiting the resistance becomes small and the current 
therefore great. Hence the dangers of short-circuiting a current. 



ECONOMY OF ELECTRIC TRANSMISSION. 

The loss of power in a transmission line is ordinarily given in per 
cent of the total power consumed in the conductors at maximum load. 
Whatever the line pressure may be, the size of the conductors varies 
inversely with the percentage of loss. Consequently the maximum line 
loss which can be allowed is dependent on the most economical size of 
the Une conductors. 

In 1881 Lord Kelvin gave out a statement in regard to the most 
economical size of conductors. This statement, which is known as 
** Kelvin's law," was as follows: 

"The most economical area of conductor will be that for which the 
annual interest on the capital outlay equals the annual cost of energy 
wasted." 

According to this rule, the cheaper the cost of power, the less should 
be the capital outlay for the conductors, thus allowing a smaller size 
to be used. George Forbes states that the most economical section of 
the conductor is independent of the voltage and the distance, and is 
proportional to the current. 

It is generally assumed that the cost of the pole line and the insula- 
tors is constant and not affected by the variation in the size of the line 
conductors. 

If A = interest cost per year of conductors erected, in dollars, 
B = value of the line loss per year, in dollars; then for the most 
economical cross-section of the conductors 

A = B, 



1412 ELECTRICAL ENGINEERING. 

If K" = Cost per kilowatt-year of lost power, in dollars, 

K\ = Cost per pound of wires erected, in dollars, 

L = Length of line in 1000 ft., 

Z)2 = Cross-section of conductor in circular mils, 

I = Line current in amperes, 

p = per cent interest, 

then A^ ^ XKiX 0.003 XLXD^ 
B^KXI^X 10.5 X ^2 
Y^ X Ki X 0.003 XLXD^ = KXI^X 10.5 X ^^ 
D2 = 592I \\ZE1 

D^ is the cross-section, in circular mils, that will give the most eco- 
nomical Une loss. 

In the following, the above equation is worked out for three different 
rates of interest : 

IK- 



For 4%. D2 = 296 I \ — ; For 5%, D^ = 265 I \l^ 



For 6%, D2 = 242 I -^E. 

In determining the value of 7, care must be taken that the annual 
mean value of the current is used. The value of K must also be the 
one for which the power, representing the Une loss, can be produced, 
and not that for which it can be sold. 

Wire Tables. — The tables on the following page show the relation 
between load, distance, and "drop" or loss by voltage in a two- wire 
direct-current circuit of any standard size of wire. The tables are based 
on the formula 

(21.6 IL) -i- A = Drop in volts. 
I = current in amperes, L = distance in feet from point of supply to 
point of deUvery, A = sectional area of wire in circular mils. The 
factors I and L are combined in the table, in the compound factor 
"ampere feet." 

Examples in the Use of the "Wire Tables. — 1. Required the max- 
imum load in amperes at 220 volts that can be carried 95 feet by No. 6 
wire without exceeding 11/2% drop. 

Find No. 6 in the 220- volt column of Table I; opposite this in the 
11/2% column is the number 4005, which is the ampere-feet. Dividing 
this by the required distance (95 feet) gives the load, 42.15 amperes. 

Example 2. A 500- volt line is to carry 100 amperes 600 feet with a 
drop not exceeding 5 % ; what size of wire will be required? 

The ampere-feet will be 100 X 600 = 60,000. Referring to the 5% 
column of Table II, the nearest number of ampere-feet is 60,750, which 
is opposite No. 3 wire in the 500-volt column. 

These tables also show the percentage of the power dehvered to a line 
that is lost in non-inductive alternating-current circuits. Such circuits 
are obtained when the load consists of incandescent lamps and the cir- 
cuit wires he only an inch or two apart, as in conduit wiring. 

Efficiency of Electric Systems. — The efficiency of a system is the 
ratio of the power dehvered by the electric motors at the distant end of 
the line to the power delivered to the dynamo-electric machines at the 
other end. The efficiency of a generator or motor varies with its load 
and with the size of the machine, ranging about as follows: 

Average Full-load Efficiency of Generators: 

K.W 25 50 100 200 500 1000 2000 3000 

Eff . % 88 90 91 92 93 94 94 . 5 95 

Average Full-load Efficiency of Motors: 

H.P 1 2 5 10 25 50 100 200 500 

Eff. % 80 82 85 87 88 90 91 92 93 

The efficiency of both generators and motors decreases, at first very 



ELECTRIC TRANSMISSION, DIRECT CURRENT. 1413 



Wire Table — Relation bet^'een Load, Distance, Loss, and 
Size of Conductor. 
Note. — The numbers in the body of the tables are Ampere-Feet, i.e., 
Amperes X Distance (length of one wire). See examples below. 

Table I. — 110-volt and 220-volt Two-wire Circuits. 



Wire Sizes; 


Line Loss in Percentage of the Rated Voltage; and Power 


B.&S. 


Gauge. 


Loss in Percentage of the Del 


ivered Power. 


IIOV. 


220 V. 


1 


11/2 


2 


3 


4 


5 


6 


8 


10 




OOOD 


21,550 


32,325 


43,100 


64,650 


86,200 


107,750 129,300 172,400 


215.500 




000 


17,080 


25,620 


34,160 


51,240 


68,320 


85,400 102,480 136,6^0 


170.800 




00 


13,5!?0 


20,325 27,100 


40,650 


54,200 


67,750 


81,300 


108,400 


135,500 


0000 





10,750 


16,125 


21,500 


32,250 


43,000 


53,750 


64,500 


86,000 


107,500 


000 


1 


8,520 


12,780 


iy,040 


25,560 


34,080 


42,600 


51,120 


68,160 


85,200 


00 


2 


6,750 


10,140 


13,520 


20,280 


27,040 


33,800 


40,560 


54,080 


67,600 





3 


5,360 


8,040 


10,720 


16,080 


21,4^0 


26,800 


32,160 


42,880 


53,600 


1 


4 


4,250 


6,375 


8,500 


12,y50 


iy,ooo 


21,250 


25,500 


34,000 


42,500 


2 


5 


3,370 


5,055 


6,740 


10,110 


13,480 


16,850 


20,220 


26,Q^ 


33,700 


3 


6 


2,670 


4,005 


5,340 


8,010 


10,680 


13,350 


16,020 


21,360 


26,700 


4 


7 


2,120 


3,180 


4,240 


6,360 


8,480 


10,600 


12,720 


16,960 


21,200 


5 


8 


1,680 


2,520 


3,360 


5,040 


6,720 


8,400 


10,800 


13,440 


16,800 


6 


9 


1,330 


1,995 


2,660 


3,990 


5,320 


6,650 


7,980 


10,640 


13,300 


7 


10 


1,055 


1,582 


2,110 


3,165 


4,220 


5,275 


6,330 


8,440 


10.550 


8 


11 


838 


1,257 


1,675 


2,514 


3,350 


4,190 


5,028 


6,700 


8,380 


9 


12 


665 


997 


1,330 


1,995 


2,660 


3,320 


3,990 


5,320 


6.650 


10 


13 


527 


790 


1,054 


1,580 


2,108 


2,635 


3,160 


4,215 


5,270 


11 


14 


418 


627 


836 


1,254 


1,672 


2,090 


2,508 


3,344 


4.180 


12 





332 


498 


665 


997 


1,330 


1,660 


1,995 


2,660 


3,325 


14 





209 


313 


418 


627 


836 


1.045 


1.354 


1.672 


2.090 





Table II. — 


500, 1000, and 2000 Volt Circuits 


. 




Wire Sizes; 
B. & S. Gauge. 


Line Loss in Percentage of the Rated Voltage: and 
Power Loss in Percentage of the Delivered Power. 


500 V. 


lOOOV. 


2000 V. 


1 


11/2 


2 


2V2 


3 


4 


5 


0000 
000 

00 


1 
2 
3 

4 
5 
6 

7 
8 

9 
10 

n 

12 


0000 
000 

'^ 

1 

2 
3 
4 

5 
6 

7 
8 
9 
10 

n 

12 
13 
14 



1 

2 
3 
4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 


97,960 
77,690 
61,620 
48,880 
38,750 

30,760 
24,370 
19,320 
15,320 
12,150 

9,640 
7,640 
6,060 
4,805 
3,810 

3,020 
2,395 
1,900 
1,510 
950 


146,940 
116,535 
92,430 
73,320 
58,125 

46,140 
36,555 
28,980 
22,980 
18,225 

14,460 
11,460 
9,090 
7,207 
5,715 

4,530 
3,592 
2,850 
2,265 
1,425 


195,920 
155,380 
123,240 
97,760 
77,500 

61,520 
48.740 
38.640 
30,640 
24,300 

19,280 
15,280 
12,120 
9,610 
7,620 

6,040 
4,790 
3,800 
3,020 
1,900 


244,900 
194,225 
154,050 
122,200 
96,875 

76,900 
60,925 
48,300 
38.300 
30,375 

24.100 
19,100 
15,150 
12,010 
9,525 

7,550 
5,985 
4,750 
3,775 
2,375 


293,880 
233,970 
184,860 
146,640 
116,250 

92.280 
73.110 
57,960 
45,960 
36,450 

28,920 
22,920 
18.180 
14,415 
11,430 

9,060 
7,185 
5,700 
4,530 
2,850 


391,840 
310,760 
246,480 
195,420 
155,000 

123,040 
97,480 
77,280 
61,280 
48,300 

38,560 
30,560 
24.240 
19,220 
15,220 

12,080 
9,580 
7,600 
6,040 
3,800 


489,800 
388,450 
308,100 
244.400 
193,750 

153,800 
121,850 
96,600 
76,600 
60,750 

48.200 
38,200 
30,300 
24.025 
19,050 

15,100 
11.975 
9,500 
7,550 


14 






4.750 



1414 



ELECTRICAL ENGINEERING. 



slowly and then more rapidly, as the load decreases. Each machine 
has its "characteristic" curve of efficiency, showing the ratio of output 
to input at different loads. Roughly the decrease in efficiency for direct- 
current machines at half-load varies from 3 % to 10 % for the smallest 
sizes. The loss in transmission, due to fall in electrical pressure or 
"dop" in the line, is governed by the size of the wires, the other 
conditions remaining the same. For a long-distance transmission 
plant this will vary from 5% upwards. 

With generator efficiency and motor efficiency each 90%, and trans- 
mission loss 5 %, the combined efficiency is 0.90 X 0.90 X 0.95 = 76.95%. 

Resistances of Pure Aluminum Wire.* 

Conductivity 62 in the Matthiesen Standard Scale. Pure aluminum 
weighs 167.111 pounds per cubic foot. 



oo 


Resistances at 70° 


F. 


(iTo 


Resistances at 70 


o Y, 


5P/^ 








^^ 








CJ*^ 


















Ohms 

per 1000 

Feet. 


Ohms 
per 
MUe. 


Feet 

per 

Ohm. 


Ohms per 
Pound. 




Ohms 

per 1000 

Feet. 


Ohms 

per 

Mile. 


Feet 
Ohm. 


Ohms per 
Pound. 


0000 


0.07904 


0.41730 


12652. 


0.00040985 


19 


12.985 


68.564 


77.05 


11.070 


000 


.09966 


.52623 


10034. 


.00065102 


20 


16.381 


86.500 


61.06 


17.595 


00 


.12569 


.66362 


7956. 


.0010364 


21 


20.649 


109.02 


48.43 


27.971 





.15849 


.83684 


6310. 


.0016479 


22 


26.025 


137.42 


38.44 


44.450 


1 


.19982 


1.0552 


5005. 


.0026194 


23 


32.830 


173.35 


30.45 


70.700 


2 


.25200 


1.3305 


3968. 


.0041656 


24 


41.400 


218.60 


24.16 


112.43 


3 


.31778 


1.6779 


3147. 


.0066250 


25 


52.200 


275.61 


19.16 


178.78 


4 


.40067 


2.1156 


2496. 


.010531 


26 


65.856 


347.70 


15.19 


284.36 


5 


.50526 


2.6679 


1975. 


.016749 


27 


83.010 


438.32 


12.05 


452.62 


6 


.63720 


3.3687 


1569. 


.026628 


28 


104.67 


552.64 


9.55 


718.95 


7 


.80350 


4.2425 


1245. 


.042335 


29 


132.00 


697.01 


7.58 


1142.9 


8 


1.0131 


5.3498 


987.0 


.067318 


30 


166.43 


878.80 


6.01 


1817.2 


9 


1.2773 


6.7442 


783.0 


.10710 


31 


209.85 


1108.0 


4.77 


2888.0 


10 


1.6111 


8.5065 


620.8 


.17028 


32 


264.68 


1397.6 


3.78 


4595.5 


11 


2.0312 


10.723 


492.4 


.27061 


33 


333.68 


1760.2 


3.00 


7302,0 


12 


2.5615 


13.525 


390.5 


.43040 


34 


420.87 


2222.2 


2.38 


11627. 


13 


3.2300 


17.055 


309.6 


.68437 


35 


530.60 


2801.8 


1.88 


18440. 


14 


4.0724 


21.502 


245.6 


1.0877 


36 


669.00 


3532.5 


1.50 


29352. 


15 


5.1354 


27.114 


194.8 


1.7308 


37 


843.46 


4453.0 


1.19 


46600. 


16 


6.4755 


34.190 


154.4 


2.7505 


38 


1064.0 


5618.0 


0.95 


74240. 


17 


8.1670 


43.124 


122.5 


4.3746 


39 


1341.2 


7082.0 


0.75 


118070. 


18 


10.300 


54.388 


97.10 


6.9590 


40 


1691.1 


8930.0 


0.59 


187700. 



* Calculated on the basis of Dr. Matthiessen's standard, viz.: The 
resistance of a pure soft copper wire 1 meter long, having a weight of 
1 gram = 0.141729 International Ohm at 0° C. 
(From Aluminum for Electrical Conductors; Pittsburgh Reduction Co.) 

ELECTRIC RAILWAYS. 

While 600 volts is still maintained as a standard for street railway 
systems, experience has shown that the most economical operation of 
lugh-speed suburban and interurban railroads can be obtained with 
1200 to 1500 volts on the trolley. Steam railroad electrifications will, 
however, be accomphshed most satisfactorily with 2400 or 3000 volts 
direct current. 

Schedule Speeds, Miles per Hour. 
City Service. 



Max. 


Stops per Mile. 


Speed. 


1 


2 


3 


4 


5 


6 


7 


8 


15 

20 

25 

30 


10.8 
13.7 
16.3 
18.5 


9.9 
12.1 
14.2 
15.6 


9.3 
11.1 
12.7 
13.8 


8.7 
10.3 
11.5 
12.4 


8.3 
9.6 
10.6 
11.3 


7.9 
9.0 
9.9 
10.5 


7.5 
8.6 
9.3 
9.8 


7.2 
8.1 
8.7 
9.2 



ELECTRIC RAILWAYS. 



1415 



Interurban Service. 



Max. 


Miles between Stops. 


Speed. 


1/2 


3/4 


I 


1.5 i 2 


3 


4 


5 


10 


30 

40 

50 

60 


14.0 
15.4 
16.2 
17.0 


15.5 
18.1 
19.5 
20.8 


16.7 
20.0 
21.9 
23.6 


18.5 
22.7 
25.6 
27.9 


19.7 
24.5 
27.9 
30.9 


21.0 
26.7 
31.0 
34.8 


22.0 
28.0 
32.9 
37.5 


22.5 
28.9 
34.2 
39.3 


23.9 
30.8 
37.2 
43.6 



The figures in the above tables include stops of 5 seconds eac^h for the 
city service and of 15 seconds for the interurban service, besides a 15 % 
margin for Une drop and traffic delays. The ratio of acceleration is 
approximately 1.5 miles per hour per second for the city service and 
1.2 miles per hour per second for the interurban service, the braking 
being 1.5 miles per hour per second and the coasting approximately 
10% of the running time exclusive of stop. 

Train Resistance. (General Electric Co.) — The horse-power output 
at the rim of the wheels is equal to, 

H p _ T XF X Feet _T XF XV 



33,000 X Minutes 
When reduced to Kilowatts, 

TXFX VX 746 



375 



Kw. 



2x rx Fx V 

1000 



approx. 



375 X 1000 
The kilowatt input to train is equal to, 

jr = 2X TXFX V 
1000 XEff. 
Where T = Total weight of train in tons. 

F = Train resistance, including that due to grades and curves, 

in lbs. per ton. 
V = Speed in miles per hour. 
Eff = Efficiency of motors at speed V. 
The train resistance may be found from the following formula: 

F. = ^ + 0.03V-|-^«^^a(i4-^) 



Where F = Train resistance in lbs., per ton. 

T = Total weight of train in tons. 

V = Speed in miles per hour. 

A = End cross-section in sq. ft. 

N = Number of cars in train. 

50 
— — is limited to a value of 3.5. 

\/T 
Tractive Resistance of a 28-ton Electric Car (Harold H. Dunn, 
Bull. 74, Univ'y of 111. Expt. Station, April, 1914). — JNIean of all tests: 
Miles per hr. . 5 10 15 20 25 30 35 40 45 

Lb. per ton.. 5.25 6.80 8.62 10.75 13.03 15.75 18.75 22.13 26.12 
Two formulae have been derived from the results: 
i^ = 4 + 0.222 S + 0.00582 S\ 
i2 = 4 + 0.222 5 + 0.00181 -^ S'\ 
A = cross-sectional area of the car in sq. ft. W = weight of the car 

The formulae should not be used beyond the limit of 45 miles per hour. 

Rates of Acceleration.— Electric Locomotive Passenger Service. 0.3 to 
0.6 mile per hour per second. 

Electric Motor Cars, Interurban Service, 0.8 to 1.3 miles per hour 
per second. ., , 

Electric Motor Cars. City Service, 1.5 milr\s per hour per second. 

Electric Motor Cars, Rapid Transit Service, 1.5 to 2.0 miles per hour 
per second. .. , 

Highest Practical Bate, 2.0 to 2.5 miles per hour per second. 



1416 



ELECTRICAL ENGINEERING. 



Safe Maximum Speed on Curves. — 

Radius of Curve, Ft. 10,000 5000 2000 1000 500 200 100 50 
Speed, miles per hr., 100 75 50 35 25 15 10 6 

The above values apply only when full elevation is given the outer 
rail. For city service such elevation is not possible and the maxi- 
mum speed will, therefore, be less under such conditions. The same 
restriction applies with steel wheel flanges of 3/4 inch or less. 

Coefflcient of Adhesion. — The following are the average values of 
the coefficient of adhesion between wheels and rails, based on a uniform 
torque: 

Clean, dry rail, 30%. 

Wet rail, 18%; with sand, 22%. 

Rail covered with sleet, 15%; with sand, 20%. 

Rail covered with dry snow, 10%; with sand, 15%. 
Electrical Resistance of Steel Rails. — The resistance of steel rails 
varies considerably, due to the difference in chemical composition. 
Ordinary traction rails have a specific resistance averaging 12 times 
that of copper, while for contact rails (third rails) the average is only 
8 times. The values given in the following table are in ohms at 75° F. 
and with no joints. 



Weight of Rails, 
Lbs. per Yard. 


Actual 
Area, 
Sq. In. 


Actual Area 

in 

Circular Mils. 

4,918,300 


Resistance 

per Mile, 

8 to 1 Ratio. 


Resistance 

per Mile, 

12 to I Ratio. 


40 


3.92 


0.09118 


0.13395 


45 


4.42 


5,627,700 


0.07915 


0.11905 


50 


4.90 


6,238,800 


0.07135 


0.10710 


60 


5.88 


7,486,600 


0.05955 


0.08920 


70 


6.86 


8,734,400 . 


0.05105 


0.07660 


75 


7.35 


9,230,900 


0.04780 


0.07185 


80 


7.84 


9,982,100 


0.04465 


0.06695 


90 


8.82 


11,229,900 


0.03975 


0.05955 


100 


9.80 


12,477.700 


0.03750 


0.05365 



Resistance of Rail Bonds. — The resistance of bonded rails will 
vary, depending on the amount of contact made by the splice bars and 
rail ends, but in selecting bonds this element of the return circuit 
should be disregarded, as it is quite unrehable and frequently neghgible. 



Size of Conductor. 



:' 


00 


000 


0000 


250,000 C. 


M 


300,000 C. 


M 


350,000 C. 


M 


400,000 C. 


M 


450,000 C. 


M 


500,000 C. 


M 



Diameter of 


Resistance per In. 


Carrying 


Terminal, 


of Conductor. 


Capacity, 


in Inches. 


75° Fahr. 


Amp. 


1/2 


.00000829 


210 


5/8 


.00000657 


265 


3/4 


.00000521 


335 


7/8 


.00000414 


425 


7/8 


.00000350 


500 


1 


.00000275 


600 


1 


.00000250 


700 


1 


.00000219 


800 


1 


.00000196 


900 


1 


.00000175 


1000 



Electric Locomotives. — In selecting an electric locomotive the prin- 
cipal points to be determined are the weight of the locomotive, the 
type and capacity of the equipment, and the mechanical features. 
The weight upon the drivers must be enough to pull the heaviest 
trains under the most adverse conditions. Therefore the weight of the 
heaviest train, the maximum grade and curvature nmst be ascertained. 
It must be known whether the locomotive is expected to start the train 
under these conditions, or whether it will start upon the level and only 
meet maximum grade conditions when running. 

In order to determine the motor equipment all the data of the service 
conditions are required, such as the speed required under various condi- 
tions of load and grade. The maximum free-running speed will be ap- 
proximately 50 to 75 per cent greater than the rated full load speed. 
Mechanical limitations must also be considered, such as track clear- 
ances, limiting weight on drivers, type of couplings, etc. 



ELECTRIC RAILWAYS. 



1417 









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1418 



ELECTRICAL ENGINEERING. 



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ELECTRIC WELDING. 



1419 



Relative Efficiencies of Electric Railway Distributing: Systems.— Tho 

table on p. 1417 shows the approximate all-day combiiK^d efficiencies 
from prime mover to train wheels for various mc^thods of trunk lino 
electrifications. The trains are supposed to hv handled by electric 
locomotives, and in each instance a considerable k^ngth of line is con- 
templated, making it necessary to have a l()0,()0()-volt high-tension 
primary distribution or a multiphcity of power sources. 

Space will not permit a complete treatment of the subject of Electric 
Railways in this work. For further information consult: "American 
Handbook for Electrical Engineers"; Standard Handbook for Electrical 
Engineers"; "Foster's Electrical Engineer's Pocket Book"; Burch, 
"Electric Traction for Railway Trains"; Harding, "Electric Railway 
Engineering." 

ELECTRIC WELDING. 

Electric welding is divided into two general classes, arc heating 
and resistance heating. 

Arc Welding. — In this process the heat of the arc is utilized to 
bring the metals to be welded to the melting temperature, when tho 
joint is filled with molten metal, usually introduced in the form of a 
rod. Tliis system is usually operated by direct current, and as the 
positive side of a direct current arc generates heat at a rate approxi- 
mately three times that of the negative side, the positive side is used for 
performing the welding operation. 

Two kinds of arcs may be used for this class of welding, the carbon 
arc and the metallic arc. The former requires an e. m. f. varying from 
50 to 100 volts and the value of the current is varied over a range of 
100 to 750 amperes, 300 being the average. The metallic arc, how- 
ever, requires an e. m. f. of only from 15 to 30 volts, the length of the 
arc being very short as compared with the carbon arc. 

The arc should be as stable as possible, and the current should, 
therefore, be of a constant value. The regulation may be accomplished 
by inserting resistance in series in the circuit, but this system is nat- 
urally very wasteful and greater economy may be obtained by pro- 
viding motor-generator sets, with the generator of the variable voltage 
type. 

The following costs, Table I (from Electrical World) were compiled 
from the records of an electric railway repair shop: 

TABLE I. 

Data on Electric Welding Repairs in Railway Shops. 



Gear-case lugs 

Armature shaft (broken) 2-in 

Dowel-pin holes 

Broken motor cases 

Broken lugs on a compressor cover, doors 

and grease-cup hinges 

Broken truck frames 

Worn bolt holes in motors and trucks 

Enlarged and elongated holes in brake levers 
Armature shafts, 2-in., worn in journals . . . 

Armature shafts, worn in key ways 

Armature shaft, worn thread 

Air-brake armature shafts (broken) 

Leaking axle boxes 



Time in 
Minutes. 



10 
60 
5-12 
150-200 

2-5 
30-60 

5-10 

2-4 

120-180 

10-15 

20-30 

20-30 

5-15 



Kw. 



6 

20-30 

4-8 

75-90 

1-3 
20-35 

3-5 
I i/o-3 
60-90 

7-12 
10-15 
10-20 

3-7 



Average 
Costs. 
$0.07^ 

0.80 

0.07 

4.98 

0.03 
0.63 
0.05 
0.03 
3.75 
0.10 
0.24 
0.27 
0.08 



Resistance Welding. — Resistance welding is done by the heat 
developed by a large amperage carrying through the joining metals by 
means of a low voltage. Single-phase alternating current is generally 
used for the operation, which may be broadly divided into two classes — 
butt-welding and spot-welding. The former covers all work on which 
the ends or the sides of the material are welded together, while spot- 
welding is used for joining metal sheets together at any point by a 
spot the size of a rivet, without punching holes or using rivets. 

For resistance welding a very low voltage is used, varying from 2 
to 8 volts, the line voltage being stepped down by special transformers. 



1420 



ELECTRICAL ENGINEERING. 



The current consumption, in amperes, varies with the work and the 
time taken to make the weld. 

The foUowing tables (from Iron Trade Review) give the cost of 
resistance welding. Table II gives the results obtained by butt- 
welding round stock ranging from 1/4 to 1 inch diameter, in the short- 
est and longest time possible. The difference in current consumption 
is very great and in most cases the shorter time in seconds was the most 
economical of the two, although neither is the most economical rate 
at which the material can be welded. 

TABLE n. — Shortest and Longest Butt-welding Periods. 



Size, In. 


Time, 
Seconds. 


Current 
Amperes. 


Volts per 
Square 
Inch. 


Size, In. 


Time, 
Seconds. 


Current 
Amperes. 


Volts per 
Square 
Inch. 


1/4 


2.7 


1960 


39.5 


5/8 


3.5 


9400 


33.7 


1/4 


5 


1645 


35.5 


5/8 


10.85 


5510 


18.85 


3/8 


4 


4330 


45.5 


3/4 


4 


10000 


16.26 


3/8 


5.27 


2190 


19.7 


3/4 


22.2 


9400 


19.7 


1/2 


4 


6600 


36.6 


7/8 


7 


11900 


27.7 


1/2 


15.8 


1800 


13 


Vs 


17 


10550 


19.6 


9/I6 


3.6 


8400 


8 


1 


33 


7740 


10.35 


9/I6 


21.5 


3400 


12.25 


1 


114 


4450 


16.1 



Table III contains the results of tests made to determine the cost of 
power for making electric butt welds on material ranging from 1/4 to 
2 inches in diameter. 

TABLE m.— Cost of Power. 



Area, 
Sq. In, 




Welding 


Cost per 


Area, 
Sq. In. 




Welding 


Cost per 


Kw. 


Time, 


1000 


Kw. 


Time, 


1000 




Seconds. 


Welds* 




Seconds. 


Welds* 


0.05 


5 


5 


$0.07 


0.79 


18 


30 


$1.50 


0.11 


71/2 


6 


0.13 


0.99 


20 


30 


1.66 


0.20 


8 


10 


0.22 


1.23 


26 


40 


2.89 


0.31 


10 


12 


0.33 


1.77 


40 


60 


6.67 


0.44 


12 


15 


0.50 


2.41 


45 


70 


8.75 


0.60 


15 


20 


0.83 


3.14 


56 


80 


12.44 



Table IV gives the time, power and! cost per 100 spot- welds, with 
current at 1/4 cent per Kw.-hr., for welding Nos. 10 to 28 gage sheets. 

TABLE IV.— Cost of Welding. 



Gage. 


Kw. 


Time in 
Seconds. 


Cost per 

1000 Welds, 

Cents.* 


Gage. 


Kw. 


Time in 
Seconds. 


Cost per 
1000 Welds, 

Cents. 


10 
12 

14 
16 
18 


18 
16 
14 
12 
10 


1.5 
1.3 

1.0 
0.9 
0.8 


3.5 

3 

2.75 

2.5 

2.25 


20 
22 
24 
26 
28 


9 

8 
7 
6 
5 


0.7 
0.6 
0.5 
0.4 
0.3 


2 

1.75 
1.5 
1.25 

1 



* Current at 1 cent per Kw.-hr. 

ELECTRIC HEATERS. 

Wherever a comparatively small amount of heat is desired to be auto- 
matically and uniformly maintained, and started or stopped on the 
instant without waste, there is the province of the electric heater. 

The elementary form of heater is some form of resistance, such as 
coils of thin wire introduced into an electric circuit and surrounded with 
a substance which will permit the conduction and radiafion of heat, and 
at the same time serve to electrically insulate the resistance. 

This resistance should be proportional to the electro-motive force of 
the current used and to the equation of Joule's law: 
H = I2JW X 0.24, 



ELECTRIC HEATING. 1421 

where I is the current in amperes; R, the resistance in ohms; t, the time 
in seconds; and //, the heat in gram-cent igracii> units. 

Since the resistance of metals increases as tlieir temperature increases, 
a thin wire heated by current passing through it will resist more, and 
grow hotter and hotter until its rate of loss of heat by conduction and 
radiation equals the rate at which heat is supphed by the current. In a 
short wire, before heat enough can be dispelled for commercial purposes, 
fusion will begin; and in electric heaters it is necessary to use either long 
lengths of thin wire, or carbon, which alone of all conductors resists 
fusion. In the majority of heaters, coils of thin wire are used, separately 
embedded in some substance of poor electrical but good thermal 
conductivity. 

Relative Efficiency of Electric and of Steam Heating. — Suppose 
that by the use of good coal, careful firing, well-designed boilers and 
triple-expansion engines we are able in daily practice to generate 1 H.P. 
at the fly-wheel with an expenditure of 2 1/2 lb. of coal per hour. 

We have then to convert this energy into electricity, transmit it by 
wire to the heater, and convert it into heat by passing it through a 
resistance-coil. We may set the combined efficiency of the dynamo and 
line circuit at 85%, and will suppose that all the electricity is converted 
into heat in the resistance-coils of the radiator. Then 1 brake H.P. at 
the engine = 0.85 electrical H.P. at the resistance coil = 1.683.000 
ft. -lb. energy per hour = 2180 heat-units. But since it required 2 1/2 
lbs. of coal to develop 1 brake H.P., it follows that the heat given out 
at the radiator per pound of coal burned in the boiler furnace will be 
2180 -7-21/2 = 872 H.U. An ordinary steam-heating system utiUzes 
9652 H.U. per lb. of coal for heating; hence the efficiency of the electric 
system is to the efficiency of the steam-heating system as 872 is to 9652, 
or about 1 to 11. {Eng'g News, Aug. 9, '90; Mar. 30. '92; May 15. '93.) 

Heat Required to Warm and Ventilate a Room. — The heat re- 
quired to raise the temperature of a given space or room to a certain 
value depends upon the ventilation, the character of the walls, the di- 
mensions, proportions of the room, etc. One watt-hour of electrical 
energy will raise the temperature of one cubic foot of air (measured at 
70°) 191° F., or 1 watt will raise the temperature of a cubic foot of air 
at the rate of 0.0531° F. per second, or approximately 3.2° per minute. 
In addition to raising the temperature of the air to the desired value, 
the loss of heat through conduction and ventilation must be supplied. 
(See Heating and Ventilation.) 

Example. Assume a room of a capacity of 3000 cu. ft., in which 
the air is changed every 20 minutes, the temperature to be main- 
tained 30° above the outside air. 

3000 -T- 20 = 150 cu. ft. per minute. 

(150 X 30) ~ 3.2 = 1406 watts necessary to supply the ventilation 
loss. To begin with, to raise the air in the room 30° will require 

(3000 X 30) 4- 191 =471 watt-hours 

and therefore the total energy used during the first hour will be 
1406 + 471 = 1877 watt-hours or 1.88 Kw.-hoiU"s. 

Domestic Heating. — Electric heating is extensively used for house- 
hold cooking apparatus. The time taken to heat water in any quantity 
to any definite temperature not exceeding boihng point can be deter- 
mined by the formula: 

V (T2 - Ti) 1831 
^ P X Eff. 

Where t = time in minutes, V = number of pints, Ti = initial tem- 
perature, °F., T2 = final temperature. °F.. P = energy consumption 
m watts, Eff. = Efficiency of cooking utensil, per cent. 

Example. To heat 1 pint of water 100° F. with a 220-watt heater 
with 50% efficiency, time = (1 X 100 X 1831) ^ (220 X 50) = 16.6 min. 

The following table (compiled by the National Electric Light Asso 
ciation) gives the watts consumed and cost of operation of different 
domestic heating devices, the cost of current being.at the rate of 5 cents 
per Kw.-hr. 



1422 ELECTRICAL ENGINEERING. 

Cost of Operation of Domestic Heating Appliances. 

Apparatus. Watts. Cents per hr. 

Broilers, 3 heat* 300 to 1200 1.5 to 6 

Chafing dishes, 3 heat 200 to 500 1 to 2.5 

Coffee percolators for 6-in. stove 100 to 440 0.5 to 2.2 

Curling-iron heaters 60 0.3 

Double boilers for 6-in., 3-heat stove 100 to 440 0.5 to 2.2 

Flatiron (domestic size) , 3 lb 275 1 

Flatiron (domestic size), 4 lb 350 1.4 

Flatiron (domestic size) , 5 lb 400 2 

Flatiron (domestic size) , 6 lb 475 2.4 

Flatiron (domestic size), 7.5 lb. . , 540 2.7 

Flatiron (domestic size), 9 lb 610 3.05 

Frying kettles, 8 in. diameter 825 4.125 

Griddle-cake cookers, 9 in. by 12 in., 3-heat 330 to 880 1.7 to 4 4 

Griddle-cake cookers, 12 in. by 18 in., 3-heat 500 to 1500 2.5 to 7.5 

Ornamental stoves 250 to 500 1.25 to 2.5 

Ovens 1200 to 1500 6 to 7.5 

Plate warmers 300 J .5 

Radiators 700 to 6000 3.5 to 30 

Ranges: 3-heat, 4 to 6 people 1000 to 4515 5 to 22 

Ranges: 3-heat, 6 to 12 people 1100 to 5250 5.5 to 26 

Ranges: 3-heat, 12 to 20 people 2000 to 7200 10 to 36 

Toasters, 9 in. by 12 in., 3-heat 330 to 880 1.6 to 4.4 

Urns, 1-gal., 3-heat 110 to 440 0.5 to 2.2 

Urns, 2-gal., 3-heat 220 to 660 1.1 to 3.3 

Experience has shown that 300 watt-hours per meal per person is a 

liberal allowance for electric cooking; or in a family of five, four kilo- 
watt hours per day is an average. 

ELECTRIC FURNACES. 

In the combustion furnace, no matter what form of fuel is used, the 
temperature cannot exceed 2000° C. (3632° F.), and for higher temper- 
atures the electric furnace must be used. The intensity of the heat 
in this type of furnace depends on the amount of current that passes, 
and as most substances are conductors when hot, the degree of intensity 
possible is theoretically unhmited. In practice, however, the conduct- 
ing substance begins to fuse when heated to its melting point, and one 
is then confronted with the physical difficulty of keeping the con- 
ducting medium in place, or, if this be accompUshed, the conducting 
medium ultimately vaporizes, the gaseous materials escape, and heat 
is thus carried away from the furnace as rapidly as it is suppUed. The 
temperature of the electric arc, which is somewhere between 3600° 
and 4000° C. (6512° - 7232° F.), is perhaps the highest temperature 
attainable at present. 

Electric furnaces may be divided in two broad classes, arc furnaces 
and resistance furnaces. In the former the heat is generated by passing 
an electric current through the space between the ends of two elec- 
trodes, forming the so-called arc. In the resistance furnace the heat 
is generated in the interior of a body due to its electrical resistance. 

There are three typical forms of arc furnaces, their common feature 
being that most. and sometimes all of the heat is transmitted to the 
material by radiation, which extends in aU directions. In aU the fur- 
naces the arc must be started by a quick movement of the electrodes and 
afterwards these must be continuously fed together as they are 
consumed. 

The chief characteristics of the three main types of arc furnaces are: 

1. The direct-heating type, in which two or more electrodes are 
used and the heating is accomplished by conduction and radiation. 
The current passes from one electrode down through the slag, across 
through the bath and up through the slag to the other electrode. The 
Heroult furnace belongs to this type. 

The Girod furnace is also of the direct-heating type, the current 
arcing from the electrodes, which are connected to one side of the cir- 
cuit, to a fixed electrode in the bottom. 



* The apparatus can be set at three different heats or temperatures, 



4 



ELECTRIC FURNACES. 1423 

2. The indirect-heating type. To this type belongs the Stassano 
furnace, in which the arc extends between two or more carbon elec- 
trodes above the charge, and therefore passe>i over but does not come 
in contact with the charge, the heating being accomplished by radiation. 

3. The smothered type, in which the arc extends from the end of tho 
upper electrode, which extends beneath the surface of the charge, to 
the lower fixed electrode in the bottom of the furnace. 

The direct and indirect heating arc furnaces are extensi^^ely used 
for melting and refining metals, while examples of the smothered type 
are the ferro-silicon and calcium carbide furnaces. 

Resistance furnaces may also be divided in two distinct types, those 
of direct and indirect heating. 

1. Direct heating. In these the heat is produced in the material by 
its own resistance, and enters the material at the highest efficiency. 

The material may be placed in a channel between two electrodes at 
the ends which lead the current to and from it, the charge being sur- 
rounded with insulating material to reduce the loss of heat. The 
Acheson graphite furnaces are of this type. 

Under this classification also come the induction furnaces in which 
the terminal electrodes are eliminated and the heat generated solely 
by induction. The furnace consists essentially of an iron core, around 
one leg of which is wound a primary winding enclosed in a refractory 
case and usually cooled ])y means of forced draft. The annular hearth 
surrounds this primary coil and is separated from it by means of 
refractory material. This hearth contains the metal and acts as a 
secondary winding of one turn. The voltage induced in this turn is 
quite small so that the energy transformed from the primary coil 
results in a very large current in the secondary, wliich heats the metal 
and thus nearly all the electrical energy is converted into heat in tho 
metal to be melted. The Kjellin and the Rochling-Rodenhauser fur- 
naces belong to this type. They are extensively used for steel refining. 

2. Indirect heating furnaces have the heat generated in an internal 
or external resistor and it is transferred to the charge by conduction 
and radiation. Such furnaces are used for small moderate temperature 
work. 

Uses of Electric Furnaces. 

Pig Iron. — When the electric furnace is used for smelting of iron 
ore it is only necessary to supply enough carbon for the reduction, this 
amount being approximately one-third of what is required in the 
ordinary blast furnace for both the heating and reduction. From re- 
peated trial runs with electric smelting furnaces in Norway and Sweden 
it has been found that coke as a reducing agent does not give satisfac- 
tory results, and charcoal is therefore used exclusively. 

The table on p. 1424 gives a summary of the most important figures 
relating to the economical results which were obtained with the electric 
iron ore furnaces in Sweden. 

Steel Reflning. — Electric furnaces are used in the manufacture of 
crucible quality steel, and the number is constantly increasing, both 
arc and induction furnaces being in general use. 

The following data as to the cost of electric steel refining are taken 
from an article in Stahl und Eisen, April 10, 1913. This article gives 
the results which have been obtained in Germany by the Heroult 
furnace and it contains a discussion of electric steel production from a 
large-industry point of view. 

The total refining cost must include many items as well as the cost 
of current; for example, the cost of fluxes (ore, lime, sand, etc.), the 
additions of ferro-alloys, relining, maintenance, and repairs, electrode 
consumption, wages, and, finally, interest and depreciation. The totals 
of these items and the cost of current, which is the largest item, are 
given below: 

Total Refining Costs (Per Ton). 

5- ton 10- ton 15-ton 20- ton 

Basic. Acid. Basic. Acid. Basic. Acid. Basic. Acid. 

Total costs $2.79 $1.79 $2.45 $1.45 $2.28 $1.34 $2.15 $1.25 

Cost of current 1.19 0.77 1.07 0.59 1.01 0.54 0.95 0.48 
The figures are based on prevailing market prices. Current is taken 



1424 



ELECTRICAL ENGINEERrNG. 



Data on 


Electric Smelting of Pig Iron in Sweden. 




Nov. 15, 1910, 


Aug. 4, 1911, 


Aug. 12, 1912, 


October to 




to 


to 


to 


December, 




May 29, 1911. 


June21,1912. 


Sept. 30, 1912. 


1912. 


Ore, concentrates 










and briquettes, kg. 


4,336,338 


7,917,214 


1,406,530 


2,914,830 


Limestone kg. 


345,405 


647,479 


108,150 


169,944 


Charcoal hi.* 


65,474 


107,282 


21,859 


44,934 


Coke kg. 




70,854 
10,845,180 






Elec. energy, kw. hrs. 


6;339,r3r" 


1 ,939,673 " 


3",957,565 


Iron in ore, per cent. 


60.79 


60.75 


68.67 


65.38 


Iron produced . . kg. 


2,636,098 


4,809,670 


965,915 


1,905,865 


Slag per ton of 










iron kg. 


350 


324 


192 




Electrodes per ton 




of iron, gross. kg. 


10.00 


6.08 


3.02 


2.78 


Electrodes per ton 










of iron, net. .kg. 


4.95 


5.17 


3.02 


2.78 


Charcoal per ton 










of iron hi. 


24.84 


22.31 


22.63 


23.58 




Hr. Min. 


Hr. Min. 


Hr. Min. 


Hr. Min. 


Working time 


4,441 20 


7,218 23 


1,173 08 


2,158 30 


Repairs 


236 53 


506 07 


13 47 


49 30 


Repairs in per cent. 










of total time .... 


5.06 


6.55 


1.16 


2.24 


Average load, kw . . 


1,427 


1,502 


1,653 


1,833 


Kw.-hrs. per ton of 










iron 


2,405 


2,255 


2,007 


2,076 


Iron per kw. year. 










tons 


3.64 


3.88 


4.36 


4.22 


Iron per h.p. year. 










tons 


2.68 


2.86 


3.20 


3.10 



* 1 hectoliter = 3.53 cu. ft. = 2.84 U. S. bushels. 

at 0.595c. per Kw.-hr., which is a figure that should be easy of attain- 
ment for most steel plants. The time per heat is taken as 2 1/4 to 2 1/2 
hours. Three-phase furnaces are considered, and in the installation 
cost of the plant must be included transformers, cables, and switch- 
boards. The amount of current required is as follows: 
Size of Furnace, Tons 1 2 5 10 25 

Kilowatts 300-350 400-450 750-800 1000-1200 3000-3500 

Ferro- Alloys. — The electric furnace has clearly demonstrated its 
advantages in the manufacture of ferro-alloys. The production of a 
ferro-alloy low in carbon or with a high percentage of the alloying 
element is hmited in the blast furnace by three difficulties — first, the 
temperature is too low for the reduction of some of the oxides of the 
alloying metals; second, it is difficult to obtain an alloy containing 
a high percentage of the special metal; and third, it is impossible to 
produce a ferro-alloy low in carbon, because of the great excess of 
carbon in the charge. With the crucible, owing to the small scale of 
operation necessary, the process is expensive. Owing to the temper- 
ature limitation, certain oxides can not be reduced and metals of high 
melting point can not be melted ; it is difficult to obtain an alloy with a 
high percentage of the special metal; and if a graphite crucible is used, 
the percentage of carbon tends to be high in the ferro-alloy. 

Non-ferrous Metals. — In the metallurgy of non-ferrous metals the 
electric furnace has had a greater application for the treatment of zinc 
ores than in the metallurgy of any of the other non-ferrous metals 
except aluminum. Since 1885, when an electric furnace for the treat- 
ment of zinc ores was patented by the Cowles brothers, experimental 
work has been done on a very large scale. However, the process has 
not b(3en applied to any grcsat extent because of the difficulty of con- 
densing the zinc vapor produced in smelting in the electric furnace, and 



ELECTRIC ACCTJMUIiATORS. 



1425 



SO it may be said that the electric smelting of zinc ores is yet in the 
experimental stage. 

Silundum, or silicified carbon, is a product obtained when carbon is 
heated in the vapor of sihcon in an electric furnace. It is a form of car- 
borundum, and has similar properties; it is very hard, resists high 
temperatures, and is acid-proof. It is a conductor of electricity, its 
resistance being about three times that of carbon. It can be heated in 
the air up to 1600° C without showing any sign of oxidation. At about 
1700°, however, the silicon leaves the carbon and combines with the 
oxygen of the air. Silundum can not be melted. The first use to which 
the material was applied was for electric cooking and heating. For 
heating purposes the silundum rods can be used single, in lengths up to 
32 in., depending on the diameter, as solid, round, flat, or square rods or 
tubes, or in the form of a grid mounted in a frame and provided with 
contact wires. — {El. Review, London. Eng. Digest, Feb., 1909.) 



PRI3IARY BATTERIES. 

Following is a partial list of some of the best known primary cells or 
batteries. 



Name. 



Daniell 

Gravity 

Grove 

Fuller 

Edison-Lalande . . 

Leclanche 

Clark 

Weston 

Dry battery .... 



Elements. 
+ 



Cu 

Cu 

Pt 

C 

Cu 

C 

Pt 

Pt 

C 



Zn 
Zn 
Zn 
Zn 
Zn 
Zn 
Zn 
Cd 
Zn 



Electrolyte. 



Dilute H2SO4 

ZnS04 
Dilute H2SO4 
Dilute H2SO4 
Cone. NaOH 

NH4CI 

ZnS04 

CdS04 



Depolarizer. 



Concent. CUSO4 
Concent. CUSO4 

HNO3 

K2Cr207 

CuO 

Mn02 

Hg2S04 
Hg2S04 



Various electrolyte pastes. 



E.M.F. 

volts. 



1.07 
1. 

1.9 
2.1 
0.7-0.9 
1.4 
1.44 
1.02 
1^1.8 



The gravity cell is used for telegraph work. It is suitable for closed 
circuits, and should not be u&ed where it is to stand for a long time on 
open circuit. 

The Fuller cell is adapted to telephones or any intermittent work. It 
can stand on open circuit for months without deterioration. 

The Edison-Lalande cell is suitable for either closed or open circuits. 

The Leclanche cell is adapted for open circuit intermittent work, such 
as bells, telephones, etc. 

The Clark and Weston cells are used for electrical standards. The 
AVeston cell has largely superseded the Clark. 

Dry cells are in common use for house ser\ice, igniters for gas engines, 
etc. , . - 

Batteries are coupled in series of two or more to obtain an e.m.i. 
greater than that of one cell, and in multiple to obtain more amperes 
without change of e.m.f. . 

Spark coils, or induction coils, with interrupters, are used to obtam 
ignition sparks for gas engines, etc. 

ELECTRIC ACCUMULATORS OR STORAGE BATTERIES. 

Secondarv or storage batteries may be divided in two general 
classes: viz.. the lead battery and the Edison alkaline battery. They 
are composed of a number of cells connected in series or multiple. The 
voltage is independent of the size of the cell and is a function of the 
electro -chemical properties used for the electrodes and electrolytes, 
being approximatelv two volts per cell. The current, however, is ap- 
proximately proportional to the surface of the electrodes that are sub- 
merged in the electrolyte. 

Lead Batteries. — The lead battery consists of two electrodes, the 
positive and negative, immersed in the electrolyte. The two electrodas 
are sponge lead (Pb) for the negative, and peroxide of lead (PbO:) for 
the positive, these forming the active couple, the electrolyte being di- 
lute sulphuric acid. The two sets of electrodes are called an element, 
and they can be readily distinguished by their colors, the positive per- 



1426 ELECTEICAL ENGINEERING. 

oxide plate being of a velvety brown chocolate color and the negative 
lead sponge plate of a light gray. 

Inside of the cell the current starts from the negative electrode to- 
ward the positive, and the positive electrode, therefore, is that por- 
tion of the battery from which the electric current passes out into the 
load circuit, this being termed "discharge,", as compared to the storing 
of energy, which is termed "charge." When the cell gives out current, 
the elements gradually change in composition, becoming mixtures or 
compounds of lead and lead sulphate at the negative electrode, and lead 
peroxide and lead sulphate at the positive electrode, the chemical 
change caused by the giving out of electrical energy being a gradual 
formation of lead sulphate. 

Lead batteries are made with two different types of plates, the 
"formed" or Plante plate, and the "pasted" or Faure plate. In the 
former, the active material is formed electro-chemicaUy on the surface of 
the plate body, while in the latter it is first apphed mechanically in the 
form of lead oxide and afterward} subjected to the forming process. As 
a rule the negative plates are always of the Faure type. Positive Plante 
plates have a long life, while the life of positive Faure plates is limited 
to a considerable extent by the number of charges. The latter, how- 
ever, give a greater capacity for the same weight than the formed plate, 
and are, therefore, used where light weight is required, such as for elec- 
tric vehicles. Positive plates have ordinarily a shorter hfe than 
negative. 

The capacity of a storage battery is measured in ampere-hours, and 
varies with the discharge rate. An arbitrary standard of the 8-hour 
rate is now universally adopted, but if the rate is increased, the capacity 
is diminished. So, for example, at a one-hour discharge rate only about 
half the number of ampere-hours can be obtained from a cell that it can 
supply at the 8-hour rate. An 80-ampere-hour battery thus means one 
which will discharge 10 amperes continuously for eight hours without 
falling below the minimum allowable voltage. 

When a battery is being discharged, the voltage sinks gradually and 
it should never be discharged below some fixed limit, because an ex- 
cessive quantity of sulphate will then form, which may injure the plates 
both electrically and mechanically, tending to crack and loosen the 
active material. This condition is indicated by the deposit of white 
sulphate on the surfaces of the plates. The voltage at which a lead 
battery is assumed to be completely discharged depends on the dis- 
charge rata and may be computed from the formula 

E = 1.66+0.0175^ 
where t = time of discharge in hours. 

Thus for an 8-hour rate the discharge should be stopped when the 
voltage has dropped to 180, while for an 1-hour rate, it should be 
stopped when it has dropped to 168. 

The voltage rises gradually during the charging from about 2.15 per 
cell at the beginning to about 2.55 at the end. The rate of charging is 
usually specified by the manufacturer. In certain instances it is equal 
to the 8-hour discharge rate, while in others the instructions may be to 
start the charge between the 3- and 5-hour rate, reducing the current 
to the 8-hour rate as soon as the plates gas freely. The time required 
for a charge will, of course, depend upon the amount of the previous 
discharge. If this has been two-thirds of the rated capacity of the bat- 
tery, about three hours at the starting rate and an hour and a half or two 
hours at the finishing rate will be necessary; i.e., from 10 to 15 per cent 
more charge than the amoimt taken out on the discharge is ordinarily 
required. 

At regularly weekly or bi-weekly intervals the battery should be 
given an overcharge for the purpose of equalizing all cells, reducing 
all sulphate, and keeping the plates in good general condition. Such 
overcharge is a regular charge continued until the voltage does not 
show any rise for four or five consecutive readings 15 minutes apart, 
all cells then gasing freely. A charging voltage of 2.7 volts should be 
provided for such overcharges. 

The specific gravity of the electrolyte, will reach a maximum in 
the same manner as the voltage, and readings of this in the various 
cells of the battery should be taken toward the end of the charge 



ELECTRIC ACCUMULATORS. 1427 

with a hydrometer. These readings will act as a check on those taken 
on the voltage, and while it may not be found practicable to do this 
every time the battery is charged, it is very important and should be 
done at least once a week. If batteries are used intermittently and 
allowed to stand some time without charge or discharge, the electrolyte 
should be of low density, not over 1.210. 

Several different methods may be adopted for controUing the dis- 
charge voltage and maintaining a uniform pressure at the hghts, viz.: 
(1) by connecting in additional or "end" cells one at a time, as the 
voltage drops, by means of an end cell switch; (2) by a rheostat, whoso 
resistance is cut out step by step; (3) by counter eloctro-motive force 
cells, which, hke a rheostat, cut down the battery voltage at the be- 
ginning of discharge, and are cut out of circuit one by one by means 
of an end cell switch. 

Also, several methods may be employed for obtaining the necessary 
increase of voltage for charging, viz.; (1) by dividing the battery into 
two equal parts and charging these in parallel through a suitable re- 
sistance, the generator running at normal (lamp) voltage; (2) by 
raising the voltage of the generator sufficiently to charge all the cells in 
one series; (3) by means of a booster, whose voltage is added to that 
of the generator, and is varied to give the total required. 

In a lead storage-cell, if the sm-face and quantity of active material 
be accurately proportioned, and if the discharge be commenced imme- 
diately after the termination of the charge, then a current efficiency of 
as much as 98 % may be obtained, provided the rate of discharge is low 
and well regulated. Since the current efficiency decreases as the dis- 
charge rate increases, and since very low discharge rates are seldom used 
in practice, efficiencies as high as this are never obtained practically, the 
average being about 90%. 

After a battery has been erected and all connections made and the 
current ready, the electrolyte may be pom*ed into the jars, and as soon 
thereafter as possible the initial charging should commence. Never 
allow a battery to stand longer than two hours after the acid is put in, 
before starting the charge. This should be as continuous as possible, 
until all cells gas freely and the specific gravity and voltage show no 
rise over a period of 10 hours. The duration of such a charge may vary 
from 30 to 100 hours, and is always given by the manufacturer. The 
temperature in any one cell should not be permitted to go above 100° F. ; 
if this occurs, the charging rate must be reduced or the charge tem- 
porarily stopped. 

The level of the electrolyte should be kept above the top of the plates 
by adding pure fresh water. Addition of new electrolyte is seldom 
necessary and should be done only on advice from the manufacturer. 

The sediment which collects in the bottom of the cells should always 
be removed before it touches the plates. 

The batterv room should be weU ventilated, especiaUy when charging, 
and great care taken not to bring an exposed flame near the cells when 
charging or shortly after. 

Metals or impurities of any kind must not be aUowed to get mto 
the cells. If this should happen, the impurity should be removed at once, 
and if badly contaminated, the electrolyte replaced with new. If m 
doubt as to the purity of elec^trolyte or water, the manufacturers should 
be consulted. ^ ^ ^ 

To take cells out of commission, the electrolyte should be drawn off; 
the ceUs fiUed with water and allowed to stand for 12 or 15 hours. The 
water can then be drawn off and the plates aUowed to dry. When 
putting into service again, the same procedure should be followed as 
with the initial charge. ^ ^ , ^ „ • ,. 

Lead storage batteries are extensively used for the foUowmg appli- 
cations : 

Stand-by service in central stations. 

Voltage regulation on D. C. distribution fines. 

To carry peak loads of central stations. 

Voltage regulation in isolated building plants. . , , 

To carry load of isolated plant, when the plant is shut down for 
the night. , ^ , ^ ^, 

To furnish country places with power where such places are off the 
fine of central stations. 



1428 ELECTRICAL ENGINEERING. 

To furnish current for talking circuits in telephone service. 

To furnish current for signal work. 

To light trains in connection with a generator system. 

To operate submarine torpedo boats. 

For ignition, starting and hghting on gas cars. 

To propel electric pleasure and commercial vehicles. 

To regulate long distance transmission hnes. 

For a complete treatise on lead storage batteries see Lyndon, ** Storage 
Battery Engineering." 

Edison Alkaline Battery. — The Edison storage bat'tery is considerably 
Hghter, although not as efficient as the lead battery, and for that 
reason it is extensively used for vehicle service. Its weight varies from 
14 to 18 watt-hours per pound. 

The active materials of this battery are oxides of nickel and iron in 
the positive and negative grids respectively, the electrolyte being a 
solution of caustic potash in water with a small amount of lithium 
hydrate. The first charging of a cell reduces the iron oxide to metallic 
iron while converting the nickel hydrate to a very high oxide of nickel, 
black in color. On discharge, the metallic iron goes back to iron 
oxide and the high nickel oxide goes to a lower oxide, but not to its orig- 
inal form of green nickel hydrate, and every cycle thereafter during 
charging the positive changes to a high nickel oxide. Current passing 
in either direction (charge or discharge) decomposes the potassium 
hydrate of the electrolyte and the oxidation and the reduction at the 
electrodes are brought about by the action of its elements. An amount 
of potassium hydrate equal to that decomposed is always reformed at 
one of the electrodes by a secondary chemical reaction, and con- 
sequently there is none of it lost and its density remains constant. The 
eventual results of charging, therefore, are a transference of oxygen from 
the iron to the nickel electrode and that of discharging is a transference 
back again. 

The density of the electrolyte does not change during charge or dis- 
charge and consequently hydrometer readings are unnecessary. 

To give the best output and efficiency, the manufacturer gives the 
normal rate of charge as 7 hours and discharge as 5 hours. The rates 
are, however, optional, and may with certain restrictions be based on 
the operating conditions. The discharge starts at 1.44 volte per cell, 
faUs rapidly for the first hour, and slowly for 4 V2 hours. The voltage at 
the end of 5 hours, the normal discharge period, is 1.11 per cell. 

The charge starts at 1.54 volts per cell, rises rapidly for three- 
quarters of an hour, and then slowly until it becomes practically con- 
stant at the end of 7 hours. The voltage is then 1.81 per cell. 

ELECTROLYSIS. 

Electrolysis is the separation of a chemical compound into its con- 
stituents by an electric current. Faraday gave the nomenclature of 
electrolysis. The compound to be decomposed is the electrolyte, and 
the process electrolysis. The plates or poles of the battery are elec- 
trodes. The plate where the greatest pressure exists is the anode, and 
the other pole is the cathode. The products of decomposition are ions. 

Lord Rayleigh found that a current of one ampere wiU deposit 
0.017253 grain, or 0.001118 gram of silver per second on one of the 
plates of a silver voltameter, the Uquid employed being a solution of 
silver nitrate containing from 1 5 % to 20 % of the salt. The weight of 
hydrogen similarly set free by a current of one ampere is 0.00001038 
gram per second. 

Knowing the amount of hydrogen thus set free, and the chemical 
equivalents of the constituents of other substances, we can calculate 
what weight of their elements will be set free or deposited in a given 
time by a given current. Thus, the current that hberates 1 gram of 
hydrogen will liberate 8 grams of oxygen, or 107.7 grams of silver, the 
numbers 8 and 107.7 being the chemical equivalents for oxygen and 
silver respectively. 

To find the weight of metal deposited by a given current in a given 
time, find the weight of hydrogen liberated by the given current in the 
given time, and multiply by the chemical equivalent of the metal. 



ELECTROLYSIS. 



1429 



The table below (from "Practical Electrical Engineering") Is calcu- 
lated upon Lord Rayleigh's determination of the electro-chemical 
equivalents and Roscoe's atomic weights. 

ELECTRO-CHEMICAL EQUH ALENTS. 



'Elements. 


•3f 

§ 


+7 

•4.9 

■a 
1 

1 

< 


1 
1. 

6^ 


Electro-chemical 
Equivalent (mil- 
ligrams per 
coulomb). 


o a 




Electro-positive, 
Hydrogen 


%' 

Mg2 
AU3 

CU2 

Cui 
Hg, 
Hgi 

Sn4 
Sn2 

l^' 
Fe2 

Ni2 

a 
'A 

N3 


1.00 
39.04 
22.99 
27.3 
23.94 
196.2 
107.66 
63.00 
63.00 
199.8 
199.8 
117.8 
117.8 
55.9 
55.9 
58.6 
64.9 
206.4 

15.96 
35.37 
126.53 
79.75 
14.01 


1.00 
39.04 
22.99 
9.1 
11.97 
65.4 

107.66 
31.5 
63.00 
99.9 

199.8 
29.45 
58.9 
18.64t 
27.95 
29.3 
32.45 

103.2 

7.98 

35.37 

126.53 

79.75 

4.67 


0.010384 

0.40539 

0.23873 

0.09449 

0.12430 

0.67911 

1.11800 

0.32709 

0.65419 

1 .03740 

2.07470 

0.30581 

0.61162 

0.19356 

0.29035 

0.30423 

0.33696 

1.07160 

0.08286 
0.36728 
1.31300 
0.82812 
0.04849 


96293.00 
2467.50 
4188.90 
1058.30 

804.03 
1473.50 

894.41 
3058.60 
1525.30 

963.99 

481 .99 
3270.00 
1635.00 
5166.4 
3445.50 
3286.80 
2967.10 

933.26 


03738 


Potassium. 


1 45950 


Sodium^ 


85942 


Aluminum^ 


34018 


Magiiesium 


44747 


Gold 


2 44480 


Silver 


4 02500 


Copper (cupric) 

(cuprous) 

Mercury (mercuric) 

(mercurous). . 
Tin (stannic) 


1.17700 
2.35500 
3.73450 
7.46900 
1 10090 


*' (stannous) 


2 20180 


Iron (ferric) 


69681 


" (ferrous) 


1.04480 


Nickel 


1 .09530 


Zinc 


1.21330 


Lead 


3.85780 


Electro-negativb. 
Oxygen 




Chlorine ..••••••. 






Iodine 






Bromine . . 






Nitroigen 













*Valency is the atom-fixing or atom-replacing power of an element com- 
pared with hydrogen, whose valency is unity. 

fAtomic weight is the weight of one atom of each element compared 
with hydrogen, whose atomic weight is unity. 

JBecquerel's extension of Faraday's law showed that the electro-chemical 
equivalent of an element is proportional to its chemical equivalent. The 
latter is equal to its combining weight, and not to atomic weight -^ valency, 
as defined by Thompson, Hospitaller, and others who have copied their 
tables. For example, the ferric salt is an exception to Thompson's rule, 
as are sesqui-salts in general. 

Thus: Weight of silver deposited in 10 seconds by a current of 10 amperes 
= weight of hydrogen liberated per second X number of seconds X current 
strength X 107.7 = 0.00001038X10X10X107.7 = 0.1 1178 gram. 

Weight of copper deposited in 1 hour by a current of 10 amperes =» 

0.00001038 X 3600 XlOX 31.5 = 11.77 grams. 

Since 1 ampere per second liberates 0.00001038 gram of hydrogen, 
Strength of current in amperes 

= weight in grams of H liberated per second ^ 0.00001038 

^ weight of element liberated per second 
~" 0.00001038 Xchemical equivalent of element 



1430 ELECTRICAL ENGINEERING. 

THE MAGNETIC CIRCUIT. 

For units of the magnetic circuit, see page 1398. 

Lines and Loops of Force. — It is conventionally assumed that the 
attractions and repulsions shown by the action of a magnet or a con- 
ductor upon iron filings are due to " lines of force " surrounding the 
magnet or conductor. The " number of lines " indicates the magnitude 
Oi the forces acting. As the iron filings arrange themselves in concentric 
circles, we may assume that the forces may be represented by closed 
curves or " loops of force." The following assumptions are made con- 
cerning the loops of force in a conductive circuit: 

1. That the lines or loops of force in the conductor are parallel to the 
axis of the conductor. 

2. That the loops of force external to the conductor are proportonal in 
number to the current in the conductor, that is, a definite current gener- 
ates a definite number of loops of force. These may be stated as the 
strength of field in proportion to the current. 

3. That the radii of the loops of force are at right angles to the axis ol 
the conductor. 

The magnetic force proceeding from a point is equal at all points on the 
surface of an imaginary sphere described by a given radius about that 
point. A sphere of radius 1 cm. has a surface of 4;r square centimeters ' 
If ^ = total flux, expressed as the number of lines of force emanating from 
a magnetic pole having a strength M, 

4) = 4inM; M = <^-T-4;r. 
Magnetic moment of a magnet = product of strength of pole M and its 
length, or distance between its poles L. Magnetic moment = <^L-t- 4;:. 

If B = number of lines flowing through each square centimeter of cross- 
section of a bar-magnet, or the " specific induction," and A = cross-section 
Magnetic Moment = LAB^47r. 
If the bar-magnet be suspended in a magnetic field of density H and so 
placed that the lines of the field are all horizontal and at right angles to the 
axis of the bar, the north pole will be pulled forward, that is, in the direc- 
tion in which the lines flow, and the south pole will be pulled in the 
opposite direction, the two forces producing a torsional moment or torque. 
Torque = iVfLH =Z/ABH -f- 4;r, in dyne-centimeters. 
Magnetic attraction or repulsion emanating from a point varies inversely 
as the square of the distance from that point. The law of inverse squares, 
however, is not true when the magnetism proceeds from a surface of appre- 
ciable extent, and the distances are small, as in dynamo-electric machines 
and ordinary electromagnets. 

The Magnetic Circuit. — In the electric circuit 

E.M.F. , E ^ volts 

Current = T=r — r- ■ , or /=-p,; Amperes = — r — 

Resistance R ohms 

Similarly, in the magnetic circuit 

PI _ Magnetomotive Force jl—E. m - il _ Gilberts 

~ Reluctance ' *^ ~~ R * xw s — Qgj-g^g^^g * 

Reluctance is the reciprocal of permeance, and permeance is equal to 
permeability X path area -h path length (metric measure); hence 

One ampere-turn produces 1.257 gilberts of magnetomotive force and 
one inch equals 2.54 centimeters; hence, in inch measure, 
<^= (1.257A^)At6.45aH- 2.54 i= 3.192//aA^^ I. 

The ampere-turns required to produce a given magnetic flux in a given 
path will be 

A^= 4>l-i' S.192 pLa = 0.SlS3 <f>l-^fia. 
Since magnetic flux -^ area of path = magnetic density, the ampere-turn 
required to produce a density B, in lines of force per square inch of area 
of path, will be 

A^= 0.3133 BZ--JM. 

This formula is used in practical work, as the magnetic density must 
be predetermined in order to ascertain the permeability of the material 
under its working conditions. When a magnetic circuit includes several 
Qualities of material, such as wrought iron, cast iron, and air, it is most 
direct to work in terms of ampere-turns per unit length of path. The 



THE MAGNETIC CIRCUIT. 



1431 



ampere-turns for each material are determined separately, and the wind- 
ing is desifrned to produce the sum of all the ampere-turns. Ttic following 
table gives the average results from a number or t(3sts made by Dr. Samuel 
Sheldon: 

Values of B and H 





^1 

3$ 


DO 

a 

(-1 


Cast Iron. 


Cast Steel. 


Wrought Iron. 


Sheet Metal. 






1 ^ 




1 >^ 




t^ 




^^ 


H 


kSA 


k^^ 


00 

9^ 


ga. 


(0 


c3 a . 


i 


1 V 
X p. . 


0) 


AS.. 




1"^ 


4).- *^ 






DO 1 !K 

O 3 


0"Tn • 




H" 


CD « 


H- 




1^ 


|El 


S^ 






5s^ 




^.%^ 
w 


i^' 


10 


7.95 


20.2 


4.3 


27.7 


11.5 


74.2 


13.0 


83.8 


14.3 


92.2 


20 


15.90 


40.4 


5.7 


36.8 


13.8 


89.0 


14.7 


94.8 


15.6 


100.7 


30 


23.85 


60.6 


6.5 


41.9 


14.9 


96.1 


15.3 


98.6 


16.2 


104.5 


40 


31.80 


80.8 


7.1 


45.8 


15.5 


100.0 


15.7 


101.2 


16.6 


107.1 


50 


39.75 


101.0 


7.6 


49.0 


16.0 


103.2 


16.0 


103.2 


16.9 


109.0 


60 


47.70 


121.2 


8.0 


51.6 


16.5 


106.5 


16.3 


105.2 


17.3 


111.6 


70 


55.65 


141.4 


8.4 


59.2 


16.9 


109.0 


16.5 


106.5 


17.5 


112.9 


80 


63.65 


161.6 


8.7 


56.1 


17.2 


111.0 


16.7 


107.8 


17.7 


114.1 


90 


71.60 


181.8 


9.0 


58.0 


17.4 


112.2 


16.9 


109.0 


18.0 


116.1 


100 


79.50 


202.0 


9.4 


60.6 


17.7 


114.1 


17.2 


110.9 


18.2 


117.3 


150 


119.25 


303.0 


10,6 


68.3 


18.5 


119.2 


18.0 


116.1 


19.0 


122.7 


200 


159.0 


404.0 


11.7 


75.5 


19.2 


123.9 


18.7 


120.8 


1.96 


126.5 


250 


198.8 


505.0 


12.4 


80.0 


19.7 


127.1 


19.2 


123.9 


20.2 


130.2 


300 


238.5 


606.0 


13.2 


85.1 


20.1 


129.6 


19.7 


127.1 


20.7 


133.5 



H = 1.257 ampere-turns per cm. = 0.495 ampere-turns per inch. 

Example. — A magnetic circuit consists of 12 ins. of cast steel of 8sq. 
ins. cross-section; 4 ins. of cast iron of 22 sq. ins. cross-section; 3 ins. of 
sheet iron of 8 sq. ins. cross-section; and two air-gpps each I'le in. long and 
of 12 sq. ins. area. Required, the ampere-turns to produce a flux of 
768,000 maxwells, which is to be uniform throughout the magnetic circuit. 

The flux density in the steel is 768,000^8 = 96,000 maxwells; the am- 
pere-turns per inch of length, according to Sheldon's table, are 60.6, so 
that the 12 in. of steel will require 727.2 ampere-turns. 

The density in the cast iron is 768,000-^22 = 34,900; the ampere-turns 
= 4X40=160. 

The density in the sheet iron = 768,000 ^ 8 = 96,000; ampere-turns per 
inch = 30; total ampere-turns for sheet iron = 90. 

The air-gap density is 768,000 -^ 12 = 64,000; ampere-turns per in. = 
0.3133B; ampere-turns required for air-gap = 0.3133 X 64,000 -^ 8= 2506.4. 

The entire circuit will require 727.2 + 160 + 90 + 2506.4 = 3483.6 am- 
pere-turns, assuming uniform flux throughout. 

In practice there is considerable "leakage" of magnetic lines of force; 
that is, many of the Unes stray away from the useful path, there being no 
material opaque to magnetism and therefore no means of restricting it to 
a given path. The amount of leakage is proportional to the permeance 
of the leakage paths available between two points in a magnetic circuit 
which are at different magnetic potentials, such as opposite ends of a 
magnet coil. It is seldom practicable to predetermine with any approach 
to accuracy the magnetic leakage that will occur under given conditions 
unless one has profuse data obtained experimentally under similar con- 
ditions. In dynamo-electric machines the leakage coefficient varies from 
1.3 to 2. 

Tractive or Lifting Force of a Magnet. — The lifting power or 
'* pull " exerted by an electro-magnet upon an armature in actual contact 
with its pole-faces is given by the formula 

Lbs.= B2a-=- 72, 134,000, 
a being the area of contact in square inches and B the magnetic density 
over this area. If the armature is very close to the pole-faces this for- 
mula also applies with sufficient accuracy for all practical puposes, but 
a considerable air-gap renders it inapplicable. 

The design of solenoids for the coil-and-plunger type of electro-magnets 



1432 ELECTRICAL ENGINEERING. 

is described by C. R. Underbill in his book, *' Solenoids, Electro-MagnetSi 
and Electro-Magnetic Windings." 

Various forms of magnetic chucks are illustrated and described by 
O. S. Walker, in Am. Mach., Feb. 11, 1909. 

For magnets used in hoisting, see page 1193. 

Determining tlie Polarity of Electro - Magnets. — If a wire is 
wound around a magnet in a right-handed heUx, the end at which the 
current flows into the heUx is the south pole. If a wire is wound around 
an ordinary wood-screw, and the ciurent flows around the helix in the 
direction from the head of the screw to the point, the head of the screw 
is the south pole. If a magnet is held so that the south pole is opposite 
the eye of the observer, the wire being wound a a right-handed hehx 
around it, the current flows in a right-handed direction, with the hands 
of a clock. 

Determining the Direction of a Current. — Place a wire carrying 
a current above and parallel to a pivoted magnetic needle. If the cur- 
rent be flowing along the wire from N. to S., it will cause the N. -seeking 
pole to turn to the eastward; if it be flowing from S. to N., the pole will 
turn to the westward. If the wire be below the needle, these motions 
wlQ be reversed. 

Maxwell's rule. The direction of the current and that of the resisting 
magnetic force are related to each other as are the rotation and the for- 
ward travel of an ordinary (right-handed) corkscrew. 

DYNAMO-ELECTRIC MACHINES. 

A dyiiamo-electric machine is a machine for converting mechanical 
energy into electrical energy, or vice versa. It may be either a direct 
current or an alternating current machine. 

Rating. — The A. I.E. E. Standardization Rules (1914) recommend 
that in the case of Direct Current Generators, the rating shall be ex- 
pressed in Kilowatts (Kw.) available at the terminals. 

In the case of Alternators and Transformers, the rating shall be 
expressed in kilo volt-amperes (Kv.-a.) available at the terminals, at a 
specified power factor. The corresponding kilowatts should also 
preferably be stated. 

In the case of Motors, it is recommended that the rating shall be 
expressed in kilowatts (Kw.) available at the shaft. Since the input of 
machinery of this class is measured in electrical units and since the out- 
put has a definite relation to the input, it is logical to measure the 
dehvered power in the same units as are employed for the receiving 
power. However, on account of the prevailing practice of expressing 
mechanical output in horse-power, it is recommended that for machin- 
ery of this class the rating should, for the present, be expressed both in 
kilowatts and in horse-power; as follows: 



Kw. approx. equiv. h.p.- 



The horse-power rating of a motor may, for pmctical purposes, be 
taken as 4/3 of the kilowatt rating. 

There are various kinds of ratings, such as: 

Continuous Rating. — A macliine rated for continuous service shall be 
able to operate continuously at its rated output, without exceeding any 
of the limitations specified. 

Short-Time Rating. — A machine rated for short-time service (i.e., 
service including runs alternating with stoppages of suflScient duration 
to ensure substantial cooling) shall be able to operate at its rated out- 
put during a limited period, to be specified in each case, without exceed- 
ing any of the limitations specified. 

Nominal Ratings. — For railway motors and railway sub-station 
machinery, certain nominal ratings are employed. 

Duty-Cycle Operation. — Many machines are operated on a cycle of 
duty which repeats itself v/ith more or less regularity. For purposes of 
rating, either a continuous or a "short-time" " equivalent load " may be 
selected which shall simulate as nearly as possible the thermal condi- 
tions of the actual duty cycle. 

Standard dui-ations of equivalent tests shall be for machines oper- 
ating under specified duty-cycles: 5 min., 10 min., 30 min., 60 min.. 



DYNAMO-ELECTRIC MACHINES. 1433 

120 min., and continuous. Of these the first 5 are short-time ratings 
selected as being thermally equivalent to the specified duty cycle. 
When, for example, a short-time rating of 10 miniite>i' duration is 
adopted, and the thermally equivalent load is 25 kw. for that period, 
then such a machine shall be stated to have a 10-minute rating of 
25 kw. In every case the equivalent short-time test shall commence 
only when the windings and other parts of the machine are within 5° C. 
of the ambient temperature at the time of starting the test. In the 
absence of any specification as to the kind of rating, the continu- 
ous rating shall be understood. 

Temperature Liinitations of the Capacity of Electrical Machinery. — 
The capacity, so far as relates to temperature, is usually limited by the 
maximum temperature at wliich the materials in the machine, espe- 
cially those employed for insulation, may be operated for long periods 
without deterioration. When the safe limits are exceeded, d(^terioration 
is rapid. The insulating material becomes permanently damaged by 
excessive temperature, the damage increasing with the length of time 
that the excessive temperature is maintained, and with the amount of 
excess temperature, until finally the insulation breaks down. 

Ambient Temperature of Reference for Air. — The standard ambient 
temperature of reference, when the cooUng medium is air, shall be 40° C. 
(104° F.). 

The permissible rises in temperature given in column 2 of the table 
on p. 1434 have been calculated on the basis of the standard ambient 
temperature of reference, by substracting 40° C. from the highest tem- 
peratures permissible, which are given in column 1 of the same table. 

Altitude. — Increased altitude has the effect of increasing the temper- 
ature rise of some types of machinery. In the absence of information in 
regard to the height above sea level at which the machine is intended to 
work in ordinary service, this height is assumed not to exceed 1000 
meters (3300 feet). For machinery operating at an altitude of 1000 
meters or less, a test at any altitude less than 1000 meters is satisfactory, 
and no correction shall be anolied to the observed temperatures. 
INIachines intended for operation at higher altitudes shall be regarded as 
special. When a machine is intended for service at altitudes above 
1000 meters (3300 feet) the permissible temperature rise at sea level, 
until more nearly accurate information is available, shall be reduced by 
1 per cent for each 100 meters (130 ft.) by wliich the altitude exceeds 
1000 meters. Water-cooled oil transformers are exempt from this 
reduction. 

Ambient Temperature of Reference for Water-Cooled ]\fachinery. — For 
water-cooled machinery, the standard temperature of reference for in- 
coming cooling water shall be 25° C. (77° F.), measured at the intake of 
the machine. 

Corrections for the Deviation of the Ambient Temperature, at the time 
of test, from the reference value of 40° C. — The effect on tiie temperatiu*e 
rise of the precise value of the ambient temperature at the time of test 
is small, obscure, and of doubtful direction. No correction shall be 
made for ambient temperature deviations from the standard value of 
40° C. It is desirable, however, that tests should be conducted at 
ambient temperatures not lower than 25° C. Exception to tliis rule is 
made in the case of air-blast transformers, in which, if the ipgoing air 
temperature during the test differs from 40° C.,a correction on account 
of difference in resistance and difference in convection shall be made by 
changing the "observable" temperature rise of the windings by 0.5 per 
cent for each degree centigrade. Thus with a room temperature of 
30° C. the "observable" rise of temperature shall be increased by 5 
per cent, and with a room temperature of 15° C. the "observable" rise 
of temperature shall be increased by 12.5 per cent. 

The actual temperatures attained in the different parts of a machine, 
and not the rises in temperature, affect the life of the insulation of the 
machine. The temperatures in the different parts of a machine wliich it 
is desired to ascertain, are the maximum tempera tiu-es reached in those 
parts. 

As it is usually impossible to determine the maximum temperature 
attained in insulated windings, it is convenient to apply a correction to 
the observable temperature, to approximate the difference between 
the actual maximum temperature and the observable temperature by 



1434 



ELECTRICAL ENGINEERING. 



the method used. This correction or margin of security is provided to 
cover the errors due to fallibility in the location of the measm-ing 
devices, as well as inherent inaccuracies in measurement and methods. 

Methods of Determining the Temperature of Different Parts of a 
Machine. — Three methods will be considered. One or other of these 
methods will usually be appropriate for commercial measurements on 
any particular type of macliine. 

No. 1. Thermometer Alethod. — This method consists in the deter- 
mination of the temperature by mercury or alcohol thermometers, by 
resistance thermometers, or by thermo-couples, apphed to the hottest 
accessible part of the completed machine, as distinguished from the 
thermo-couples or resistance coils imbedded in the machine as described 
under Method No. 3. When Method No. 1 is used, the hottest-spot 
temperature for windings shall be estimated by adding a hottest-spot 
correction of 15° C. to the highest temperature observed, in order to 
allow for the impossibiUty of locating any of the thermometers at the 
hottest spot. 

Exception. In cases where the thermometer is applied directly to 
the surfaces of a bare winding, such as an edgewise strip conductor, or a 
cast copper winding, a hottest-spot correction of 5° C. instead of 15° C. 
shall be made. For bare metaUic surfaces not forming part of a winding, 
no correction is to be appUed. 

No. 2. Resistance Method. This method consists in the measurement 
of the temperature of windings by their increase in resistance, corrected 
to the instant of shut-down when necessary. In the appUcation of 
this method thermometer measurements must also be made whenever 
practicable without disassembhng the machine, in order to increase 
the probability of reveahng the highest observable temperature. 
Whichever method yields the higher temperature, that temperatm-e 
shall be taken as the "highest observable" temperature and a hottest- 
spot correction of 10° C. added thereto. 

In the case of resistance measurements, the temperature coeflBlcient 
of copper shall be deduced from the formula 1/(234.5 + t). Thus, at 
an initial temperature t = 40° C, the temperature coefficient or in- 
crease in resistance per degree centigrade rise is 1/(274.5) = 0.00364. 

No. 3. Imbedded Temperature-Detector Method. Thermo-couples or 
resistance coils, located as nearly as possible at the estimated hottest 
spot. This method is only to be used with coils placed in slots. 

Temperature Limits. — In the following table column 1 gives the per- 
missible Umits for the hottest-spot temperatures of insulations, and 
column 2 the highest permissible temperature rise of the hottest spot 
above 40° C. permitted under rated-load conditions, for the purpose of 
fixing the Institute rating. The rise of temperature observed must never 
exceed the limits in column 2 of the table. The liighest temperatures 
attained in any machine corresponding to the output for wliich it is 
rated must not exceed the values indicated in column 1 of the table 
and the clauses following: 



Hottest-Spot Temperatures and Corresponding Permissible Tem- 
perature Rises. 



Class. 



Insulation. 

Cotton, silk, paper, and other fibrous materials, not so 
treated as to increase the thermal limit 

Similar to A 1, but treated or impregnated and in- 
cluding enameled wire 

Mica, asbestos, or other material capable of resisting 
high temperatures, in which any Class A material 
or binder, if used, is for structural purposes only, 
and may be destroyed without impairing the insu- 
lating or mechanical qualities 

Fireproof and refractory materials 



Col. I. Col. 2. 



A 1 
A2 
B 



95° C. 
105° C. 



55° C. 
65° C. 



125° C. 85° C. 
No limit speci- 
fied. 



DYNAMO-ELECTRIC MACHINES. 



1435 



Summary of the Temperature Conditions under tlie Three Methods 
of Measurement for Insulations of Classes Ai, A2, and B. 





Hottest 
Spot 
Temp. 


u 

<v 

s 




1 

1 


Imbedded Thermo-couples or Resistance Coils. 




Double-layer 

Windings. 
All voltages. 


Single-layer 

Windings. 

5000 volts or 

less. 


Single-layer Windings above 5000 
volts. 


6 


a b 


a b 


a b 


a b 


Hottest 

Spot 

Correction. 


Limiting 
Observable 
Temperat'r 


Limiting 
Observable 
Temp. Rise 
above 40^^. 


Ai 
A2 
B 


950 

105° 
125° 


15 80 
15 90 

15 no 


10 85 
10 95 
10 115 


5 90 
5 100 
5 120 


10 85 
10 95 
10 115 


10+(E-5)t 

10+(E-5) 

10+(E-5) 


85 - (E-5) 
95 - (E-5) 
115- (E-5) 


45 - (E-5) 
55 - (E-5) 
75 - (E-5) 



* With thermometer check when practicable. 

a Hottest-spot correction. b Limiting observable temperature. 
The Umit of the observable temperatm-e rise above 40° always = (6 —40°). 

t In this formula E represents the rated pressure between terminals 
in kilovolts. Thus for a three-phase machine with single-layer winding 
of 11 kilovolts between terminals, the hottest spot correction to be added 
to the maximum observable temperature will be 16° C. 

Special Cases of Temperature Limits. — Temperature of Oil. 
The oil in which apparatus is immersed shall in no part have an observ- 
able temperature in excess of 90° C. 

Water-cooled Transformers. The hottest-spot temperature shall not 
exceed 85° C. 

Commutators. The observable temperature shall in no case be per- 
mitted to exceed the values given in the table for the insulation em- 
ployed, either in the commutator or in any insulation whose temper- 
ature would be affected by the heat of the commutator. 

For commutators so constructed that no difficulties from expansion 
can occur, the following temperature limits are suggested: 

Ciirrent per Brush Arm. Maximum Permissible Temp. 

200 amperes or less. 130° C. 

200 to 900 amperes. 130° C. less 5 deg. for each 100 

amperes increase above 200. 
900 amperes and over. 95° C. 

Moving Force of a Dynamo-electric Machine. — A wire through 
which a current j^asses has, when placed in a magnetic field, a tendency 
to move perpendicular to itself and at right angles to the lines of the 
field. The force producing this tendency is F = IBI dynes, in which 
Z = length of the wire, / = the current in C.G.S. units, and jB = the induc- 
tion or flux density, in the field in gausses or lines per square centimeter. 

If'the current / is taken in amperes, P = IBI^10 = IBI X 10"^ 

If Pf^ is taken in kilograms, 

P^ = 257-^9,810,000 = 10.1937 IBIXlQr^ kilograms. 

Example.— The mean strength of field, B, of a dynamo is 5000 C.G.S. 
lines- a current of 100 amperes flows through a wire; the force acts upon 
10 centimeters of the wire = 10.1937 X 10 X 100 X5000 X 10-^ = 0.5097 kUo- 
irrams 

Torque of an Armature. — The torque of an armature is the moment 
tending to turn it. In a generator it is the moment which must be 
applied to the armature to turn it in order to produce current. In a motor 
it is the turning moment which the armature gives to the pulley. 



1436 ELECTKICAL ENGINEERING. 

Let / = current in the armature in amperes, £;=the electromotive force 
in volts, T = the torque in pound-feet, <f>= the flux through the armature 
in maxwells, N = the number of conductors around the armature, and n = 
the number of revolutions per second. Then 

Watts = IE = 27: nTX 1.356.* 
In any machine if the flux be constant, E is directly proportional to the 
speed and = ^Nn -*- 10^; whence 

<i>NI -^10^ =2;r!rX1.356; 

108 X 2 ;r X 1.356 8.52 X 10^ P^^^^-^^^^- 
Let I ~ length of armature in inches, d = diameter of armature in inches, 
B = flux density in maxwells per square inch, and let m = the ratio of the 
conductors under the influence of the pole-pieces to the whole number of 
conductors on the armature. Then 

^ = irrrfX IX BXm. 
These formulae apply to both generators and motors. They show that 
torque is independent of the speed and varies directly with the current and 
the flux. The total peripheral force is obtained by dividing the torque by 
the radius (in feet) of the armature, and the drag on each conductor is 
obtained by dividing the total peripheral force by the number of conductors 
under the influence of the pole-pieces at one time. 

Example. — Given an armature of length I = 20 inches, diameter d = 12 
inches, number of conductors A^ = 120, of which 80 are under the influence 
of the i)ole-pieces at one time; let the flux density B = 30,000 maxwells 
per sq. in. and the current / = 400 amperes. 

^ = -^ X 20 X 30,000 X ^ = 7,540,000. 

^ 7,540,000 X 120 X 400 .^ . _ ... 

^= 8.52 X 100,000,000 = ^^4.8 pound-feet. 

Total peripheral force = 424.8 -^ 0.5 = 849.6 lbs. 
Drag per conductor = 849.6 -^ 120 = 7.08 lbs. 

The work done in one revolution == torque X circumference of a circle 
of 1 foot radius = 424.8 X 6.28 = 2670 foot-pounds. 

Let the revolutions per minute equal 500, then the horse-power 

2670 X 500 .n r u -D 
= 33000 = ^^-^ ^'^' 
Torque, Horse-power and Revolutions. — T= torque in pound-feet, 
H.P. = T X Rpm. X 6.2832 -^ 33,000 = IE -^- 746. Whence Torque 
= 7.0403 EI -^ Rpm. or 7 times the watts -^ the revs, per min. nearly. 
Electromotive Force of the Armature Circuit. — From the horse- 
power, calculated as above, together with the amperes, we can obtain 
the E.M.F.. for /£; = H.P. X 746. whence E.M.F. or £/ = H.P. X 746-^/. 

If H.P., as above, = 40.5, and /= 400, E = ^^4^7^^= 75.5 volts. 

' 400 

The E.M.F. may also be calculated by the following formulse: 

/= Total current through armature; 

C(j= E.M.F. in armature in volts; 

N= Number of active conductors counted all around armature; 

p = Number of pairs of poles (p = 1 in a two-pole machine); 

71= Speed in revolutions per minute; 

^= Total flux in maxwells. 

1 en'=4>N -tt; 10"-8 for two-pole machines. 

Electromotive I ^ "^ 60 

force: | _ p^N n for multipolar machines with series- 

[^ a "" 1Q8 60 wound armature 

Strength of the Magnetic Field. — Let / = current in amperes. N = 
number of turns in the coil. A = area of the cross-section of the core in 

* I ft.-lb. per second = 1.356 watts. 



DIRECT-CURKENT GENERATORS. 1437 

square centimeters, i= length of core in centimeters, ft the permeability of 
the core, and ^= flux in maxwells. Then 

. _ Magnetomotive Force _ 1.257 NI 
Reluctance ~ {l-i-Aii) 

In a dynamo-electric machine the reluctance will be made up of three 
separate quantities, viz.: that of the field magnet cores, that of the air 
spaces between the field magnet pole-pieces and the armature, and that 
of the armature. The total reluctance is the sum of the three. Let Li, 
L2, L2 be the length of the path of magnetic lines in the field magnet 
cores,* m the air-gaps, and in the armature respectively; and let Ai, 
A2, Az be the areas of the cross-sections perpendicular to the path of the 
magnetic lines in the field magnet cores, the air-gaps, and the armature 
respectively. Let the permeability of the field magnet cores benu and of 
the armature fis. The permeability of the air-gaps is taken as unity. Then 
the total reiuctance of the machine will be 

Aifii A2 Asfis* 



(Li -*- Aifx^i) 4- (L2 -»- A2) + (L3 -^ Asms) ' 

The ampere-turns necessary to create a given flux in a machine may be 
found by the formula, 

;^r ^ . [(Lt -^ Aifii) + (Lz-^Az) + (L3 -?• Aztis)] 
^ 1.257 

But the total flux generated by the field coils is not available to produce 
current in the armature. There is a leakage between the field magnets, 
and this must be allowed for in calculations. The leakage coefficient 
varies from 1.3 to 2 in different machines. The meaning of the coefficient 
is that if a flux of say 100 maxwells per square cm. are desired in the field 
coils, it will be necessary to provide ampere turns for 1.3 X 100 = 130 
maxweUs, if the leakage coefficient be 1.3. 

Another method of calculating the ampere-turns necessary to produce a 
given flux is to calculate the magnetomotive force required in each portion 
of the machine, separately, introducing the leakage coefficient in the calcu- 
lation for the field magnets, and dividing the sum of the magnetomotive 
forces by 1.257. 

In the ordinary type of multipolar machine there are as many magnetic 
circuits as there are poles. Each winding energizes part of two circuits. 
The calculation is made in the same manner as for a single magnetic circuit. 

DmECT.CURRENT GENERATORS. 

Direct-current generators may be separately excited, in which case 
the field magnets are excited or magnetized from some external source, 
as, for instance, a storage battery or another continuous-current dynamo. 
Such generators are used to some extent in connection with regulating 
sets, but as a rule almost all direct-current generators are self-excited, 
in which case the magnetizing current for the field-coils is furnished by 
the dynamo itself. 

Direct-cmrent generators (as well as motors) may be classified accord- 
ing to the manner of the field-winding into : 

1. Series-wound Dynamo. — The field- winding and the external circuit 
are connected in series with the armature- winding, so that the entire 
armature current must pass through the field-coils. 

Since in a series-wound dynamo the armature-coils, the field, and the 
external circuit are in series, any increase in the resistance of the exter- 
nal circuit wdll decrease the electro-motive force from the decrease in the 
magnetizing currents. A decrease in the resistance of the external cir- 

* The length of the path in the field-magnet cores Li includes that 
portion of the path which lies in the piece joining the cores of the 
various field-magnets. 



1438 ELECTRICAL ENGINEERING. 

cuit will, in a like manner, increase the electro-motive force from the 
increase in the magnetizing current. The use of a regulator avoids 
these changes in the electro-motive force. 

2. Shunt-wound Dynamo. — The field-magnet coils are placed in a 
shunt to the armature circuit, so that only a portion of the current 
generated passes through the field-magnet coils, but all the difference 
of potential of the armature acts at the terminals of the field-circuit. 

In a shunt-wound dynamo an increase in the resistance of the external 
circuit increases the electro-motive force, and a decrease in the resistance 
of the external circuit decreases the electro- motive force. This is just 
the reverse of the series-wound dynamo. 

In a shunt-wound dynamo a continuous balancing of the current 
occurs, the current dividing at the brushes between the field and the 
external circuit in the inverse proportion to the resistance of these 
circuits. If the resistance of the external circuit becomes greater, a 
proportionately greater current passes through the field magnets, and 
so causes the electro-motive force to become greater. If, on the con- 
trary, the resistance of the external circuit decreases, less current passes 
through the field, and the electro-motive force is proportionately 
decreased. 

3. Compound-wound Dynamo. — The field magnets are wound with 
two separate sets of coils, one of which is in series with the armature 
and the external circuit, and the other in shunt with the armature or 
the external circuit. 

A compound generator is made for the purpose of delivering current 
at constant potential either at the terminals of the machine or at some 
distant receiving point on the hne. In the former case the machine is 
flat-compounded, the ideal being the same terminal voltage at full load 
as at no load, giving a practically horizontal voltage characteristic. 
In the latter case the machine is over-compounded, giving a terminal 
voltage which rises from no load to full load to compensate for hne 
drop, so that at the receiving end of the line the voltage wiU be constant 
at all loads. 

The standard voltages for ordinary fight and power service are 125 
and 250 volts, while for railway service they have been built for voltages 
as high as 1200, and in one particular installation two such machines 
are connected in series furnishing a supply voltage of 2400 volts. 

Many direct-current generators are provided with commutating 
poles, and such machines may be operated over an extremely wide range 
of load and voltage with fixed brush positions and sparkless commu- 
tation. The commutating winding produces a magnetic field which is 
in a direction to assist the reversal of current in the coil imdergoing 
commutation and also directly opposed to the field generated by arma- 
ture reaction which tends to retard the reversal of current in this coil. 
The commutating field thus completely nulhfies the distortive effect of 
armature reaction on the main field fiux in the commutating zone, and 
generates an e.m.f. which helps the brush to commutate the current 
without sparking, and with a consequent increased fife of the commu- 
tator and brushes. 

Commutating poles are placed between the main poles of direct- 
current generators and motors. They are used for the purpose of 
nuUifying the effect of the armature reaction upon the magnetic field 
adjacent to the neutral point. The armature reaction tends to move the 
neutral point from its proper mechanical position, and it is obvious that 
a number of ampere turns setting up magnetic lines of force equal to 
and opposing the directions of those set up by the armature ampere 
turns win nuUify that effect on the neutral occasioned by the armature 
reaction. 

The commutating pole winding is connected in series with the arma- 
ture and has a number of turns per pole sufficient to give a magnetic 
strength that will not only counteract the armature reaction above 
referred to, but will actually reverse the current in the coil when it is 
in the commutating zone. 

The commutating zone is the region over which the brushes may have 
to be moved in order to obtain good commutation between no load and 
full load. With commutating pole machines no such movement is 
necessary and the reversal takes place in the coils short circuited under 
the brushes. 



ALTERNATING CURRENTS. 1439 

Inasmuch as the commutating windings are directly in series with 
the armature, their strength varies directly with the armature current 
and provides the correct rectifying effect for proper reversal of current 
in the coils at all loads. Hence it is unnecessary to shift the brushes as 
the load changes. 

Parallel Operation. — The first requisite for satisfactory parallel 
operation of direct current generators is that they have the same char- 
acteristics. They must have the same degree of compounding for any 
percentage of their rated load. The resistance of series fields with their 
shunt resistances and cable connections to the bus-bar should further- 
more be inversely proportional to the capacities of the machines; i.e., no 
matter what size cables are used, the resistances of the two connections 
must be so proportioned that the drop will be the same for both ma- 
chines between the equaUzer junction and the main bus-bar when each 
machine is deUvering its full-load current. 

Three-Wire System. — The chief advantage of the Edison three- 
wire system over the ordinary two-wire installation is that of econ- 
omy in distribution. In a two-wire system with a given load and a 
given percentage of voltage drop, the distribution at 250 volts requires 
only one-quarter the weight of copper required for a distribution at 125 
volts. A neutral wire in the three-wire system will, however, modify 
this proportion of copper, the final saving depending on the size of the 
neutral. In well-designed systems, the maximum unbalanced current 
carried by the neutral will be about 25 per cent of the full load. There- 
fore the size of the neutral need not be larger than 25 per cent of the 
capacity of the outside mains, and the weight of the copper in this case 
would be 9/32 of that used in distributing the same power by a two- 
wire system. 

The practical methods available for operating direct-current three- 
wire systems are: 1. Two generators. 2. One generator with balancer 
set. 3. One generator with storage battery. 4. One generator with 
balancing coil. 5. Three- wire generator. 

ALTERNATING CURRENTS.* 

The advantages of alternating over direct currents are: 1. Greater 
simpUcity of dynamos and motors, no commutators being required; 2. 
The feasibility of obtaining high voltages, by means of static trans- 
formers, for cheapening the cost of transmission; 3. The facility of 
transforming from one voltage to another, either higher or lower, for 
different purposes. 

A direct current is uniform in strength and direction, while an alter- 
nating current rapidly rises from zero to a maximum, falls to zero, re- 
verses its direction, attains a maximum in the new direction, and again 
returns to zero. This series of changes can best be represented by a 
curve the abscissas of which represent time and the ordinates either 
current or electro-motive force (e.m.f.). The curve usually chosen for 
this purpose is the sine curve. Fig. 228 ; the best forms of alternators give a 
curve that is a very close approximation to the sine curve, and all calcu- 
lations and deductions of formulae are based on it. The equation of the 
sine curve is y = sin x, in which y is any ordinate, and x is the angle 
passed over by a moving radius vector. 

After the flow of a direct current has been once established, the only 
opposition to the flow is the resistance offered by the conductor to the 
passage of current through it. This resistance of the conductor, in 
treating of alternating currents, is sometimes spoken of as ohmic resist- 
ance. The word resistance, used alone, always means the ohmic 
resistance. In alternating currents, in addition to the resistance, sev- 

* Only a very brief treatment of the subject of alternating currents can 
be given in this book. The following works are recommended as val- 
uable for reference: Steinmetz, "Theoretical Elements of Electrical 
Engineering. Alternating Current Phenomena"; Cohen, "Formulae 
and Tables for the Calculation of Alternating Current Problems"; Jack- 
son, "Alternating Currents and Alternating Current Machinery"; 
Bedell, "Direct and Alternating Current Manual"; Timbie, "Alter- 
nating Currents," 



1440 ELECTRICAL ENGINEERING. 

eral other quantities, which affect the flow of current, must be taken 
into consideratioa These quantities are inductance, capacity, and skin 
effect. They are discussed under separate headings. 

The current and the e.m.f. may be in phase with each other, that is, 
they may attain their maximum strength at the same instant, or they 
may not, depending on the character of the circuit. In a circuit con- 
taining only resistance, the current and e.m.f. are in phase; in a cm-rent 
containing inductance the e.m.f. attains its maximum value before the 
current, or leads the current. In a circuit containing capacity the cur- 
rent leads the e.m.f. If both capacity and inductance are present in a 
circuit, they will tend to neutrahze each other. 

Maximum, Average, and Eflfectlve Values. — The strength and the 
e.m.f. of an alternating current being constantly varied, the maximum 
value of either is attained only for an instant in each period. The maxi- 
mum values are little used in calculations, except in deducing formulae 
and for proportioning insulation, which must stand the maximum 
pressure. The average value is obtained by averaging the ordinates of 
the sine curve representing the current, and is 2 4- tt or 0.637 of the 
maximum value. 

The value of greatest importance is the effective, or "square root of 
the mean square, " value. It is obtained by taking the square root of the 
mean of the squares of the ordinates of the sine curve. The effective 
value is the value shown on alternating-current measuring instruments. 
The product of the square of the effective value of the current and the 
resistance of the circuit is the heat lost in the circuit. 

The relation of the maximum, average, and effective values is: 

^Effec. = %ax. X 0.707 ; J^Aver. = %ax. X 0.637 ; %a^. = 1.41 X E^q^^ 

Frequency. — The time required for an alternating current to pass 
through one complete cycle, as from one maximum point to the next {a 
and b, Fig. 228) , is termed the period. The number of periods in a second 
is termed the frequency of the cm"rent. Since the current changes its 
direction twice in each period, the number of reversals or alternations is 
double the frequency. A current of 120 alternations per second has a 
period of Veo and a frequency of 60. The frequency of a current is equal 
to one-half the number of poles on the generator, multiplied by the number 
of revolutions per second. Frequency is denoted by the letter/. 

The frequencies most generally used in the United States are 25, 40, 60, 
125, and 133 cycles per second. The Standardization Report of the 
A I.E.E. recommends the adoption of three frequencies, viz. 25, 60 and 120. 

With the higher frequencies both transformers and conductors will be 
less costly in a circuit of a given resistance but the capacity and inductance 
effects in each will be increased, and these tend to increase the cost. With 
high frequencies it also becomes difficult to operate alternators in parallel. 

A low frequency current cannot be used on lighting circuits, as the lights 
wiU flicker when the frequency drops below a certain figure. For arc lights 
the frequency should not be less than 40. For incandescent lamps it should 
not be less than 25. If the circuit is to supply both power and light a 
frequency of 60 is usually desirable. For power transmission to long dis- 
tances a low frequency, say 25, is considered desirable, in order to lessen 
the capacity effects. If the alternating current is to be converted into 
direct current for lighting purposes a low frequency may be used, as the 
frequency will then have no effect on the lights. 

Inductance. — Inductance is that property of an electrical circuit by 
which it resists a change in the current. A current flowing through a 
conductor produces a magnetic flux 
arouna tne conaucior. ii tne current 
be changed in strength or direction, 
the flux is also changed, producing 
in the conductor an e.m.f. whose direc- 
tion is opposed to that of the current 
in the conductor. This counter e.m.f. 
is the counter e.m.f. of inductance. 
It is proportional to the rate of change 
of current, provided that the perme- 
ability of the medium around the con- 
ductor remains constant. The unit of Fig. 228. 




ALTERNATING CURRENTS. 1441 

inductance is the henry, symbol L. A circuit has an inductance of one 
henty if a uniform variation of current at the rate of one ampere per 
second produces a counter e.m.f. of one volt. 

The effect of inductance on the circuit is to cause the current to lag 
behind the e.m.f. as shown in Fig. 228, in which abscissas represents time, 
and ordinates represent e.m.f. and current strengths respectively. 

Capacity. — Any insulated conductor has the power of holding a quan- 
tity of static electricity. This power is termed the capacity of the body. 
The capacity of a circuit is measured by the quantity of electricity in it 
when at unit potential. It may be increased by means of a condenser. 
A condenser consists of two parallel conductors, insulated from each other 
by a non-conductor. The conductors are usually in sheet form. 

The unit of capacity is ^ farad, symbol C. A condenser has a capacity 
of one farad when one coulomb of electricity contained in it produces a dif- 
ference of potential of one volt, or when a rate of change of pressure of 
one volt per second produces a current of one ampere. The farad is too 
large a unit to be conveniently used in practice, and the micro-farad or 
one-millionth of a farad is used instead. The effect of capacity on a 
circuit is to cause the e.m.f. to lag behind the current. Both inductance 
and capacity may be measured with a Wheatstone bridge by sub- 
stituting for a standard resistance a standard of inductance or a stand- 
ard of capacity. 

Power Factor. — In direct-current work the power, measured in watts, 
is the product of the volts and amperes in the circuit. In alternating-cur- 
rent work this is only true w^hen the current and e.m.f. are in phase. If 
the current either lags or leads, the values shown on the volt and ammeters 
will not be true simultaneous values. Referring to Fig. 228, it will be 
seen that the product of the ordinates of current and e.m.f. at any partic- 
ular instant will not be equal to the product of the effective values which 
are shown on the instruments. The power in the circuit at any instant is 
the product of the simultaneous values of current and e.m.f.. and the volts 
and amperes shown on the recording instruments must be multiplied 
together and their product multiplied by a power factor before the true 
watts are obtained. This power factor, which is the ratio of the volt- 
amperes to the watts, is also the cosine of the angle of lag or lead of 
the current. Thus 

P = I X E X power factor = I X E X cos 9, 
where is the angle of lag or lead of the current. 

A watt-meter, however, gives the true power in a circuit directly. 
The method of obtaining the angle of lag is shown on p. 1442. 

Reactance, Impedance, Admittance. — In addition to the ohmic re- 
sistance of a circuit there are also resistances due to inductance, capacity, 
and skin effect. The virtual resistance due to inductance and capacity 
is termed the reactance of the circuit. If inductance only be present in 
circuit, the reactance will vary directly as the inductance. If capacity 
only be present, the reactance will vary inversely as the capacity. 

Inductive reactance = 2 tt/L ; Condensive reactance = - — 7^. 

The total apparent resistance of the circuit, due to both the ohmic resist- 
ance and the total reactance, is termed the impedance, and is equal to the 
gquare root of the s um of the sq uares of the resistance and the reactance. 
Impedance =Z = ^ K'^ + (2 nfL)^ w hen inductance is present in the circuit. 

Impedance =Z = ^R^+ \o~fr) ^^''^^^^ capacity is present in the circuit. 

Admittance is the reciprocal of impedance, = 1 -^ Z. 

If both inductance and capacity are present in the circuit, the reactance 
of one tends to balance that of the other; the total reactance is the alge- 
braic sum of the two reactances; thus, 

Total reactance =X= 2nfL--^^^; Z='yJR^-h (^2nfL- ^^f' 

In all cases the tangent of the angle of lag or lead is the reactance divided 
by the resistance. In the last case 

tan = 7j . 



1442 



ELECTRICAL ENGINEERING. 



Skin Effect. — Alternating currents tend to have a greater density at 
the surface than at the axis of a conductor. The effect of this is to make 
the virtual resistance of a wire greater than its true ohmic resistance. 
With low frequencies and small wires the skin effect is small, but it be- 
comes quite important with high frequencies and large wires. With 
magnetic material it is much higher than with non-magnetic. 

The skin effect factor, by which the olrniic resistance is to be multi- 
plied to obtain the virtual resistance is given by Berg in the following 
approximate formula: 

T2 



C.= 



^^\^Ht) 



For Copper Cable: ( ^\ =0.0105 d^f; for Aliuninum Cable: f^) =0.0063 

c?2 f where d = diameter of cable, and / = frequency. 

For the same per cent increase, due to skin effect, a cable can have 
13% larger diameter than a solid wire; in other words, the skin effect is 
the same as long as the ohmic resistance is the same, whether a solid 
wire or a cable is used. 

Ohm's Law applied to Alternating- Current Circuits. — To apply 
Ohm's law to alternating-current circuits a shght change is necessary 
in the expression of the law. Impedance is substituted for resistance. 
The law should read 

7= ^ E 

\/ B^ + X2 ^' 

Impedance Polygons. — 1. Series Circuits. — The impedance of a circuit 
can be determined graphically as follows : Suppose a circuit to contain 
a resistance R and an inductance L, and to carry a current I of frequency 
/. In Fig. 229 draw the line ab proportional to R, and representing the 
direction of current. At b erect be perpendicular to ab and propor- 
tional to 2 nfL. Join a and c. The hne ac represents the impedance of 
the circuit. The angle e between ab and ac is the angle of lag of the cur- 
rent behind the e.m.f., and the power factor of the circuit is cosine 0. 
The e.m.f. of the circuit is E = IZ. 

"-- — ^ 





Fig. 230. 



Fig. 231. 




Fig. 232. 



If the above circuit contained, instead of the inductance L, a capacity 
C, then would the polygon be drawn as in Fig. 230. The line be would 

be proportional to x — 27=; and would be drawn in a direction opposite to 

that of be in Fig. 229. The impedance would again be Z, the e.m.f. 
would be Z X I, but the current would lead the e.m.f. by the angle 9. 

Suppose the circuit to contain resistance, inductance, and capacity, 
the lines of the impedance polygon would then be laid off as in Fig. 231. 
The impedance of the circuit would be represented by ad, and the angle 



ALTERNATING CURRENTS, 



1443 



of lag by 9, If the capacity of the circuit had been such that cd was 
less than be, then would the e.m.f. have led the current. 

If between the inductance and capacity in the circuit in the previous ex- 
amples there be interposed another resistance, the impedance polygon will 
take the form of Fig, 232. The lines representing either resistances, in- 
ductances, or capacities in the circuit follow each other in ail cases as do 
the resistances, inductances, and capacities in the circuit, each line having 
its appropriate direction and magnitude. 

Example. — A circuit (Fig. 233) contains a resistance, i?i, of 15 ohms, a 
capacity, Cu of 100 microfarads (0.000100 farad), a resistance, R2, of 12 



Kj =.0001 00 R2=12 Li=.05 




irCyz s/\y\y^ 



Ri=15 



Fig. 233. 

ohms, and inductance of Lt, of 0.05 henry, and a resistance Rz, of 20 ohms. 
Find the impedance and electromotive force when a current of 2 amperes 
is sent through the circuit, and the current when e.m.f. of 120 volts is 
impressed on the circuit, frequency being taken as 60. Also find the angle 
of lag, the power factor, and the power in the circuit when 120 volts are 
impressed. 

The resista nee is represented in Fig. 234 by the horizontal line a&, 1 Fi 
units long. I'he capacity is represented by the line be, drawn downwards 
from b and whose length is 

== = ofi f;5 

2;r/Ci 2X3.1416X60X0.0001 
From the point c a horizontal line cd, 12 units long, is drawn to represent 
R2. From the point d the line de is drawn vertically upwards to represent 

the inductance Li. Its length is 

2;r/Li =2 X3.1416 X60 X0.05 = 18.85. 
From the point e a horizontal line ef, 20 
units long, is drawn to represent R3. The 
line adjoining a and / will represent the 
impedance of the circuit in ohms. The 
angle d, between ab and af, is the angle of 
lag of the e.m.f. behind the current. The 
impedance in this case is 47.5 ohms, and 
the angle of lag is 9° 15'. 

The e.m.f. when a current of 2 amperes 
is sent through is 

JZ = E = 2 X 47.5 = 95 volts. 
If an e.m.f. of 120 volts be impressed on the circuit, the current flowing 
through will be 

^ 120 120 

/= -^7- = -TTT-p = 2.53 amperes. 
Zi 47.0 

The power factor = cos 5 = cos 9° 15' = 0.987o 

The power in the circuit at 120 volts is 

IX Ex cos = 2.53 X 120 X 0.987 = 

2. Parallel Circuits. — If two circuits be ar- 
ranged in parallel, the current flowing in each 
circuit will be inversely proportional to the 
impedance of that circuit. The e.m.f. of each 
circuit is the e.m.f. across the terminals at 
either end of the main circuit, where the vari- 
ous branches separate. Consider a circuit, 
Fig. 235, consisting of two branches. The 
first branch contains a resistance R, and an 
inductance Li in series with it. The second 




299.6 watts. 

Ri U 

Fig. 235. 



1444 



TJLECTRICAL ENGINEERING. 



branch contains a resistance E2 in series with an inductance L^. The 
impedance of the circuit may be determined by treating each of the 
two branches as a separate series circuit, and drawing the impedance 
polygon for each branch on that assumption. Having fotmd the im- 
pedance the current flowing in either branch will be the reciprocal of 
the impedance multipUed by the e.m.f. across the terminals. The 
current in the entire circuit is the geometrical sum of the current in 
the two branches. 

The admittance of the equivalent simple circuit may be obtained by 
drawing a parallelogram, two of whose adjoining sides are made paraUel to 
the impedance lines of each branch and equal to the two admittances 
respectively. 

The diagonal of the parallelogram will represent the admittance of the 
equivalent simple circuit. The admittance multiplied by the e.m.f. gives 
the total current in the circuit. 

Example.— Given the circuit in Fig. 236, consisting of two branches. 
Branch 1 consists of a resistance Ri = 12 ohms, an inductance Li = 0.05 
henry, a resistance i?2 = 4 ohms, and a capacity Ci = 120 microfarads 
(0.00012 farad). Branch 2 consists of an inductance L2 = 0.015 henry, a 
resistance Rz = 10 ohms, and an inductance Lz = 0.03 henry. An e.m.f. 
of 100 volts is impressed on the circuit at a frequency of 60. Find the ad- 
mittance of the entire circuit, the current, the power factor, and the power 



Ri=i2 Li=.05 R2=4 Ki*^ .00012 
/^60 



o- 



E.M.F. -=100 

L2='.015 R3=10 L3=,Q3 




f IG. 237. 



ALTERNATING CURRENTS. 



1446 



in the circuit. Construct the impedance polygons for the two branches 
separately as shown in Fig. 237, a and h. The impedance in branch 
1 is 16.4 ohms, and the current is (1/16.4) X 100 = 6.19 amperes. The 
angle of lead of the current is 1° 45'. The impedance in branch 2 is 
19.5 ohms and the current is (1/19.5) X 100 = 5.13 amperes. The 
angle of lag of the current is 61°. 

The current in the entire circuit is found by taking the admittances of 
the two branches, and drawing them from the point o, in Fig. 237 c, parallel 
to the impedance Unes in their respective polygons. The diagonal from o 
is the admittance of the entire circuit, and in this case is equal to 0.092. 
The current in the circuit is 0.092 X 100 = 9.2 amperes. The power factor 
is 0.944 and the power in the circuit is 100 X 0.944 X 9.2 = 868.48 watts. 

Self-Inductance of Lines and Circuits. — The following formulae 
and table, taken from Crocker's " Electric Lighting," give a method of cal- 
culating the self-inductance of two parallel aerial wires forming part of the 
same circuit and composed of copper, or other non-magnetic material: 

L per foot = (l5.24 + 140.3 log '~\ \Qr^, 

L per mUe = Uo.b + 740 log ^) 10-«. 

in which L is the Inductance in henrvs of each wire, A is the interaxial dis- 
tance between the two wires, and d is the diameter of each, both In inches. 
If the circuit is of iron wire, the formulae become 

L per foot = (2286 4- 140.3 log ~\ IQr^, 

L per mile = (l2070 + 740 log ^) lO-^. 

Inductance, in Millihenrys per Mile, for Each of Two 
Parallel Copper Wires. 



Interaxial 








American ' 


Wire Gauge Number. 








Distance. 




















Ins. 


0000 


000 00 


^ 


1 


2 


3 


4 


6 


8 


10 


12 


6 


1.130 


1.168 1.205|1.242 


1.280 


1.317 


1.354 


1.392 


1.466 


1.540 


1.615 


1.690 


12 


1.353 


1.391 1.428 1.465 


1.502 


1.540 


1.577 


1.614 


1.689 


1.764 


1.838 


1.913 


24 


1.576 


1.614 


1.651 1.688 


1.725 


1.764 


1.800 


1.838 


1.912 


1.986 


2.061 


2.135 


36 


1.707 


1.745 


1.784 


1.818 


1.856 


1.893 


1.931 


1.968 


2.043 


2.117 


2.192 


2.266 


60 


1.871 


1.909 


1.946 


1.982 


2.023 


2.058 


2.095 


2.132 


2.208 


2.282 


2.356 


2.432 


96 


2.02312.059 


2.097 


2,134 


2.172 


2.210 


2.246 


2.283 


2.358 


2.433 


2.507 


2.582 



Capacity of Conductors, — All conductors are included in three 
classes, viz.: 1. Insulated conductors with metallic protection; 2. Single 
aerial conductor with earth return; 3. Metallic circuit consisting of two 
parallel aerial wires. The capacity of the lines may be calculated by 
means of the following formulae taken from Crocker's ** Electric Lighting. ' 



Class 1. C per foot 
Class 2. C per foot = 



7361 k 10-^5 
log(D -^ d)' 
7361 X 10-" 



A' 



log (4/1 -J- 
per foot of each wire 



C per mile = 
C per mile = 



3681 X 10-*« >^ 
log (2 A ^ d) * 
19.42 X 10-9 



38.83 k 10-^ 
log {D ^ d)' 
38.83 X 10-g 
log(4/l-T-d) 



Class 3. 

I C per mile of each wire = -^^^ A^d) 

In which C is the capacity in farads, D the internal diameter of the metallic 
covering, d the diameter of the conductor, h the height of the conductor 
above the ground, and A the interaxial distance between two parallel wires 
all in inches; fc is a dielectric constant which for air Is equal to 1 and for 
pure rubber is equal to 2.5. The formulae in classes 2 and 3 assume the wires 
to be bare. If they are insulated, k must be introduced in the numerator 
and given a value slightly greater than 1. , , ,. 

Single-phase and Polyphase Cvirrents. — A single-phase current 
is a shnple alternating current carried on a single pair of wires and is 



1446 



ELECTRICAL ENGINEERING. 




generated on a machine having a single armature winding. It is repre- 
sented by a single sine curve. 

Polyphase currents are known as two-phase, three-phase, six-phase, or 
any other number, and are represented by a corresponding number of sine 
curves. The most commonly used systems are the two-phase and three- 
phase. 

1. Two-phase Currents. — In a two-phase system there are two single- 
phase alternating currents bearing a definite time relation to each other 
and represented by two sine curves (Fig. 238). 
The two separate currents may be generated by 
the same or by separate machines. If by sepa- 
rate machines, the armatures of the two should 
be positively coupled together. Two-phase cur- 
rents are usually generated by a machine with 
two armature windings, each winding termi- 
nating in two collector rings. The two windings 
are so related that the two currents will be 90° 
two phase-currents are also called " quarter- 
phase " currents. 

Two-phase currents may be distributed on either three or four wires. 
The three-wire system of distribution is shown in Fig. 239. One of the 
return wires is dispensed with, connection being made across to the other 
as shown. The common return wire should be made 1.41 times the area 
of either of the other two wires, these two being equal in size. 

The four-wire system of distribution is shown in Fig. 240. The two 
phases are entirely independent, and for lighting purposes may be operated 
as two single-phase circuits. 

Wi 

.a 



Fig. 238. 
apart. For this reason 




Fig. 239. 



Fig. 240. 



2. Three-phase Currents. — Three-phase currents consist of three alter- 
nating currents, differing in phase by 120°, and represented by three sine 
curves, as in Fig. 241. They may be distributed by three or six wires. If 
distributed by the six-wire system, it is analogous to the four- wire, two- 
phase system, and is equivalent to three single-phase circuits. In the 
three-wire system of distribution the circuits may be connected in two 
different ways, known respectively as the Y or star connection, and the A 
(delta) or mesh connection. 

a 





Fig. 241. 



Fig. 242. 



The Y connection is shown in Fi^. 242. The three circuits are joined 
at the point o, known as the neutral point, and the three wires carrying the 
current are connected at the points a, b, and c, respectively. If tiie three 
circuits ao, bo, and co are composed of lights, they must be equally loaded 
or the lights will fluctuate. If the three circuits are perfectly balanced, 
the lights will remain steady. In this form of connection each wire may 



ALTERNATING CURRENTS. 



1447 



be considered as the return wire for the other 
two. If the three circuits are unbalanced, a 
return wire may be run from the neutral point 
o to the neutral point of the armature wind- 
ing on the generator. The system will then 
be four- wire, and will work properly with un- 
balanced circuits. 

The A connection is shown in Fig. 243. 
Each of the three circuits ab, ac, he, receives 
the current due to a separate coil in the arma- 
ture winding. This form of connection will 
work properly even if the circuits are unbal- 
anced; and if the circuit contains lamps, they 
will not fluctuate when the circuit changes 
from a balanced to an unbalanced condition, 
or vice versa. 

Measurement of Power in Polyphase Circuits. — 1. Two-phase 
Circuits. — The power of two-phase currents distributed by four wires 
may be measured by two wattmeters introduced into the circuit as shown 
in Fig. 240. The sum of the readings of the two instruments is the total 
power. If but one wattmeter is available, it should be introduced first in 
one circuit, and then in the other. If the current or e.m.f. does not vary 
during the operation, the result will be correct. If the circuits are per- 
fectly balanced, twice the reading of one wattmeter will be the total power. 
Wi 





Fig. 244. 




Fig. 245. 



The power of two-phase currents distributed by three wires may be 
measured by two wattmeters as shown in Fig. 239. The sum of the two 
readings is the total power. If but one wattmeter is available, the coarse- 
wire coil should be connected in series with the wire ef and one extremity 
of the pressure-coil should be connected to some point on ef. The other 
end should be connected first to the wire a and then to the wire d, a read- 
ing being taken in each position of the wire. The sum of the readings 
gives the power in the circuits. 

2. Three-phase Circuits. — The power in a three-phase circuit may be 
measured by three wattmeters, connected as in Fig. 244 if the system is 
Y-connected, and as in Fig. 245 if the system is A-connected. The sum 
of the wattmeter readings gives the power in the system. If the circuits 
are perfectly balanced, three times the reading of one wattmeter is the 

total power. 

The power in a A-connected system 
may be measured by two watt-meters, as 
shown in Fig. 246. If the power factor of 
the system is greater than 0.50, the arith- 
metical sum of the readings is the power 
in the circuit. If the power factor is less 
than 0.50, the arithmetical dilference of 
the readings is the power. Whether the 
1''''^''''^ A A power factor is greater or less than 0.50 

— jvv^v^ /AAA \ ^^y ^^ discovered by interchanging the 

•■ yVvW\/ i wattmeters without disturbing the rela- 

' ■■ ' tive connection of their coarse- and fine- 

FiG. 246. wire coils. If the deflections of the needles 

are reversed, the difference of the readings 
is the power. If the needles are deflected in the same direction as at 
first, the sum of the readings is the power. 




1448 ELECTRICAL ENGINEERING. 

ALTEENATEVG-CUKEENT GENERATOES. 

Synchronous Generators. — The function of the alternating-current 
synchronous generator is to transform mechanical energy into electrical 
energy, either single-phase or polyphase. It comprises a comparatively 
constant magnetic field and an armature generating electro-motive forces 
and delivering currents in synchronism with the motion of the machine. 

Alternating-current generators are generaUy designed to operate at 
normal load and 80% power factor without exceeding a specified tem- 
perature rise, and should such a machine have to be operated with a load 
of lower power factor, its rating will be reduced, when based on the same 
temperature guarantee. 

Synchronous generators are almost always of the revolving field type, 
and may be either of a horizontal or vertical design. 

Eating. — The normal full-load rating is usually based on continu- 
ous operation with a certain rated voltage, current, power factor, fre- 
quency and speed. The overload guarantees should refer to the normal 
conditions of operation, and an overload capacity of 25% for two hours 
has generally been accepted as standard, although in several instances 
a 50% two-hour overload is required. Of late (1915), however, gen- 
erators are often given a maximum continuous rating with a temper- 
ature rise not exceeding 50° C. (122° F.). 

The rated full-load current is that current which, with rated terminal 
voltage, gives the rated kilowatts or rated kilo volt-amperes. In ma- 
chines in which the rated voltage differs from the no-load voltage, the 
rated current should refer to the former. The rated output may be 
determined as follows: 

If E = full-load terminal voltage and I = rated ciirrent, then for a 

■pr 

single-phase generator, K.V.A. = , ___ . 

1000 
For a two-phase generator the total output is equal to the output of 
the two single-phase circuits, and if I, in this case, is the rated current 

per circuit, the output for a two-phase generator is, K.V.A. = . 

For a three-phase generator there are three circuits to be considered, 
whether the machine is star or delta connected. If ^ is the terminal 
voltage and I the line current, then for a three-phase generator, 

^•^•^- = 1000 • 

The capacity of a polyphase generator, whether operating two- or 
three-phase, is always the same, while, if operating under the same 
conditions single-phase, in which case one phase is ineffective, the 
rating is only about 71% of what it would be if operated as a poly- 
phase generator. This relation, however, does not hold true for a ma- 
chine which is initially built for single-phase service, and in such a case 
the distribution of the winding can be made such as to increase the 
capacity somewhat. The inherent regulation is generally made poorer 
thereby, but by the use of massive damping devices it can be materially 
improved. 

Efficiency. — The efficiency of a generator is the ratio of the power 
output to the power input, the difference between these two quantities 
being equal to the losses. The method commonly and most readily 
used for obtaining the efficiency is to determine these losses and then 
compute the efficiency by dividing the power output by the siun of the 
power output plus the losses. 

The guaranteed efficiency should always refer to the energy load 
(the energy load is the load doing useful work, and is equal to the total 
K.V.A. X the power factor of the load), and it is most important that 
the power factor of the load is also given. In certain cases the guaran- 
teed efficiency is based on a K.V.A. output, but the inconsistency of 
such a method is apparent, as the following example will illustrate: 

Assume a generator rated 100 K.V.A. (100 Kw. at unity power- 
factor) or 100 K.V.A. (80 Kw. 0.8 P.F.), and that the losses at unity and 
80% power factors are 10 and 11 Kw. respectively, the eflaciency is then: 



ALTERNATING-CURRENT GENERATORS. 1449 

Based on 100 Kw. 1.0 P.F., 

Based on SO Kw. 0.8 P.P., 

Based on 100 K.V.A. 0.8 P.F., 

From the last two values it is seen that for 80 % power-factor if based 
on the K.V.A., a 2% greater efiQciency guarantee can be made, although 
this value has no meaning, as it is based on apparent power. 

The losses in the generator consist of: The copper losses in the 
armature and field, proportional to the square of the armature and field 
currents respectively; the core loss, slightly increasing from no-load to 
full-load; the load loss, having a value approximately one-third of the 
short-circuiting core loss; and finally, the friction and windage losses, 
which are practicaUy constant. 

Regulation. — Such a close inherent voltage regulation as was for- 
merly required is not any longer desirable, since a good voltage regula- 
tion may readily be accomplished by means of automatic voltage regu- 
lators, which perform their function whether the fluctuations are due to 
a change of load, speed, or power factor. 

A close inherent regulation would require a low reactance generator, 
which means an expensive machine. A low reactance machine also, in 
case of short circuits, would allow a very large current to flow through 
the machine and through any other apparatus that may be within the 
circuit enclosed by the short-circuit. These short-circuit currents reach 
enormous values in large central stations, and in order to reduce the 
currents to safe values large reactances are necessary. It is, however, 
not possible to design high-speed turbo-generators for the necessary 
reactance, and external reactances must usually be inserted in the gen- 
erator leads or between the bus-sections. By so hmiting the abnormal 
flow of current the generating system is relieved from the disastrous 
effects of such short circuits. 

Bating of a Generating Unit. — In determining the proper rating 
and capacity of the generators for a power station, the generator and the 
prime mover must of necessity be treated together as a combination so 
as to secure the highest operating efficiency. With steam-engines the 
ratings are usually such that the engine is working under its most eco- 
nomical load at the rating of the electrical generator. With gas engines, 
however, the efficiency increases with the load beyond the capacity of 
the engine, and for this reason the rating of such an engine is generally 
made as nearly as possible to its maximum capacity with only a small 
margin for regulating purposes. With steam turbines the efficiency 
curve is very flat so that it is the desirable overload capacity which 
limits the rating of the turbine. In the water-wheel unit, the efficiency 
usually falls off rapidly above and below the maximum point, so that 
the rating of the generator should correspond to the point of maximum 
efiQciency of the wheel. 

The effect of the power factor shoiUd also be considered when deter- 
mining the prime mover as well as the generator capacity, and many 
mistakes have been made in this respect. The generator may, for ex- 
ample, have been designed and rated on the basis of imity power factor 
operation with a prime mover having a corresponding capacity. After 
installation it is, however, found that the actual operating power factor 
is 0.80, with the result that only 80 per cent of the prime mover capacity 
can be utiUzed without overloading the generator. 

Windings. — The greatest number of all alternating-current gener- 
ators are wound three-phase with the armature windings connected in 
star. This is preferable to delta connection, as a smaller number of 
conductors is required for a given voltage, while on the other hand the 
danger of the circulation of triple-frequency currents in the closed 
armatm*e winding is avoided. 



1450 ELECTRICAL ENGINEERING. 

Voltages. — Standard generator voltages for all frequencies are 240, 
480, 600, 1150, 2300, 4000, 6600, with the corresponding motor voltages 
220, 440, 550, 1040, 2090, 6000. There is no motor voltage corresponding 
to 4000 volts, since this is only used on hghting three-phase, four- wire 
distributing systems. In addition 11,000 volts is also standard for 60 
cycles, and 13,200 volts for 25 cycles. 

Parallel Operation. — In order that an alternating-current generator 
shall be able to carry a load, a current must flow corresponding to this 
load. The e.m.f. required to generate this current is the resultant of the 
terminal and the induced e.m.f. 's of the generator, the displacement be- 
tween these e.m.f. 's being due to the impulse of the prime mover. In 
the same manner when two or more generators are operating in parallel 
the division in load between the different units is entirely dependent on 
the turning efforts of the prime movers, and a change in the field excita- 
tion, as with direct-current generators, will have no effect whatsoever. 

For a satisfactory parallel operation it is important that the e.m.f. 's 
and frequencies of the generators be the same, as, if this is not the 
case, cross currents wiU flow between the units. These cross currents 
may be either wattless or they may represent a transfer of energy, de- 
pending on whether they are caused by a difference in the e.m.f. or in 
the frequency of the machines. 

Exciters (E. A. Lof, in Coal Age). — S5mchronous generators as well as 
synchronous motors are dependent on a direct-current excitation for 
their operation, and the energy for the excitation is generally obtained 
from direct-current generators, termed "exciters." These should have 
a capacity sufficient to excite all of the synchronous apparatus in the 
station when these machines are operating at their maximum load and 
true operating power factor. It is not enough to provide for the 
excitation when operating at unity power factor, because the exci- 
tation which is required at lower power factors is considerably higher 
than at unity power factor. 

For small and mediimi size plants a 125-volt exciter pressure is gen- 
erally chosen, wliile for larger installations a 250- volt excitation will 
prove more economical. 

There are many different ways of driving exciters. They may be 
direct-connected to the main units if these are of moderate speed. Such 
an arrangement may prove satisfactory for two or three imits, but 
when the number of units is higher the system becomes rather compli- 
cated. Another objection is that in case of trouble with an exciter, the 
whole generating unit wiU have to be shut down. When two direct- 
connected units are used, they should each have a capacity sufficiently 
large to excite both the generators, and with three units the capacity of 
either exciter should preferably be such that it can excite two of the 
generators. For four or more units it should only be necessary to give 
each exciter a capacity sufficient for one generator, and if necessary a 
motor-driven exciter unit can be installed as a reserve. 

The system, however, which seems to be the most widely used and 
which offers the greatest reliabihty, is that in which the excitation is 
obtained from a common source, consisting of as few exciters as possible. 
One or two units are then generally provided for normal excitation, de- 
pendiQg on the size of the station, a third unit being installed as a re- 
serve. It is also common practice to have the regular units driven by 
prime movers, such as steam-engines or water-wheels, while the reserve 
imit is motor-driven. 

Still another system which is becoming common is to install low- 
voltage generators, driven either by a non-condensing steam turbine in 
case of a steam-plant or a water-wheel in a hydro-electric plant. The 
exciters are then motor-driven, current for driving them being obtained 
from the low voltage generator. The steam from the tm'bines would 
then, of course, be taken to the feed-water heaters, and in addition to 
the exciters, all the other auxiharies, such as the circulating pumps, 
etc., would also be motor-driven. 

In order to insure a close voltage regulation of the system, automatic 
regulators are commonly installed in connection with the exciters, their 
principle being to automatically increase or decrease the excitation bj' 
rapidly opening or closing a shunt circuit across the exciter-fleld rheo- 
stat, and thus keep a constant bus-bar voltage regardless of the load. 



TRANSFORMERS. 1451 

TRANSFORMERS. 

A transformer consists essentially of two coils of wire, one coarse and 
one fine, wound upon an iron core. Its function is to transform elec- 
trical energy from one potential to another, although it may also be 
used for phase transformation. If the transformer causes a change from 
high to low voltage, it is known as a "step-down" transformer; if from 
low to high voltage, it is known as a "step-up" transformer. 

Primary and Secondary. — In regard to the use of the terms high- 
voltage, low- voltage, primary and secondary, the A.I.E.E. Standardiza- 
tion Rules read as follows: 

**The terms ' high- voltage ' and 'low- voltage' are used to distinguish 
the winding having the greater from that having the lesser number of 
tiu-ns. The terms 'primary' and 'secondary' serve to distinguish the 
windings in regard to energy flow, the primary being that wliich receives 
the energy from the supply circuit, and the secondary that which re- 
ceives the energy by induction from the primary." 

The terms primary and secondary are, however, often confused, and 
in order to avoid any misunderstanding, it is preferable that the terms 
high- voltage and low- voltage be used instead of primary and secondary. 

Voltage Ratio. — The A.I.E.E. Standardization Rules also state that 
*' The voltage ratio of a transformer is the ratio of the r.m.s. (square root 
of mean square) primary terminal voltage to the r.m.s. secondary ter- 
minal voltage under specified conditions of load." It also defines 
*'The ratio of a transformer, unless otherwise specified, as the ratio of 
the number of turns in the high-voltage winding to that in the low- 
voltage winding: i.e., the turn-ratio.'' 

The two ratios are equal when one of the windings is open and the 
transformer does not carry any load. When loaded, the resistance 
and inductance of the windings cause a drop in the voltage, thus modi- 
fying the ratio of transformation slightly. 

Rating. — A transformer should be rated by its kilovolt - ampere 
(K.V.A.) output. It is equal to the product of the voltage and current, 
and is, therefore, the same whether the different coils are connected in 
series or parallel. If the load is of unity power factor, the kilowatt out- 
put is the same as the kilovolt-ampere output, but if the power factor 
is less, the kilowatt output will be correspondingly less. For example, a 
100 K.V.A. transformer will have a full-load rating of 100 K.W. at 100% 
power factor, 90 K.W. at 90% power factor, etc. 

Efficiency. — There are two sources of loss in the transformer, viz., 
the copper loss and the iron loss. The copper loss is proportional to the 
square of the current, being the 72 B loss due to heat. If Ii, R\, be the 
current and resistance respectively of the primary, and 72, R2, the cur- 
rent and resistance respectively of the secondary, then the total copper 
loss is TF^ = 7i2 7?i -f 7227^2 and the percentage of copper loss is 

-^ — W"^ — ^' where W^ is the energy delivered to the primary. The iron 

loss is constant at all loads, and is due to hysteresis and eddy currents. 

The efficiency of a transformer is the ratio of the output in watts at 
the secondary terminals to the input at the primary terminals. At full 
load the output is equal to the input less the iron and copper losses. 
The full-load eflQciency of a transformer is usually very liigh, being from 
92 per cent to 98 per cent. As the copper loss varies as the sciuare of 
the load, the efficiency of a transformer varies considerably at ditrerent 
loads. Transformers on Ughting circuits usually operate at full load 
but a very small part of the day, though they use some current all the 
time to supply the iron losses. For transformers operated only a part of 
the time, the "all-day" efficiency is more important than the full-load 
eflQciency. It is computed by comparing the watt-hours output to the 
watt-hours input. 

The all-day efficiency of a 10-Kw. transformer, whose copper and 
iron losses at full load are each 1.5 per cent, and which operates 3 hours 
at full load, 2 hours at half load, and 19 hours at no load, is computed as 
follows : 

Iron loss, all loads = 10 X 0.015 = 0.15 K.W. 
Copper loss, full load = 10 X 0.015 = 0.15 K.W. 



1452 



ELECTRICAL ENGINEERING. 



Copper loss, 1/2 load = 0.15 X (1/2)2 = 0.0375 K.W. 
Iron loss, K.W. hours = 0.15 X 24 = 3.6. 
Copper loss, full load, K.W. hours = 0.15 X 3 = 0.45. 
Copper loss, 1/2 load, K.W. hours = 0.0375 X 2 = 0.075. 



Output, K.W. hours = (10 X 3) + (5 X 2) 



= 40. 



Input, K.W. hours = 40 + 3.6 + 0.45 + 0.075 = 44.125. 
AU-day efficiency = 40 ^ 44.125 = 0.907. 
Connections. — Among the great variety of transformer manipula- 
tions in power and general distribution worli, either for straight voltage 
transformation or for phase transformation, the following are the most 
generally used: 

Voltage Transformation: 
Single-phase. 
Two-phase. 

Three-phase, delta-delta. 
Three-phase, delta-star, and vice versa. 
Three-phase, star-star. 
Three-phase, open-delta. 
Three-phase, Tee. 
Phase Transformation: 

Two- or three-phase to single-phase. 
Two-phase to six-phase. 
Three-phase to two-phase. 
Three-phase to six-phase. 
The transformer connections mostly used are delta-delta or delta-star 
with neutral grounded. 

For moderate voltage systems, the isolated delta connection is to 
be preferred, although for liigh-tension systems with very high voltages 



s* ^. 



-100- 




FlG. 247. 



Fig. 248. 



Fig. 249. 



practice has proved that the high-tension winding star connected and 
the neutral grounded will give a more satisfactory operation. 

Tee - Connection. — (Fig. 247.) — T - connection requires only two single 
transformers of which one is provided with a 50 per cent tap to which 
the other is connected. The latter may be designed for only 86.6% of 
the line or main transformer voltage, but generally it is made identical 
with the main transformer and operated at reduced flux density. 

Delta-Connection. — (Fig. 248.) — The e.m.f. between the mains is the 
same as that in any one transformer measured between terminals, and 
each transformer must, therefore, be wound for the full Une voltage, but 

only for — =. or 57.7 per cent of the line current. 
\/3 

Star-Connection. — (Fig. 249.) — In the star-connection each trans- 
former has one terminal connected to a common junction, or neutral 
point. Each transformer is wound for only 57.7 per cent of the hne 
voltage, but for the full line current. 

Reactance. — In order to obtain a good voltage regulation, it has been 
the custom to design the transformers with a reactance as low as II/2 to 
2 per cent. Recent experience has, however, shown that in high power 
systems such transformers are unsafe, owing to the enormous mechan- 
ical strain produced on the transformer and system by the excessive 
short-circuit currents permitted by such low impedance transformers. 



SYNCHRONOUS CONVERTERS. 1453 

A 2 per cent reactance means that at full load current, 2 per cent or 1/50 
of the supply voltage is consumed by the reactance. At short circuit 
the total voltage would have to be consumed by the transformer re- 
actance and the short-circuit current at full voltage is then fifty times 
full load current. Safety thus requires that in high power systems the 
transformers should be designed for a much higher reactance and the 
present practice (1915) is, therefore, to design such transformers for 
6 to 8 per cent reactance, and sometimes even for as high as 10 per cent 

Cooling.— Accordmg to the method used in dissipating the heat 
generated by the losses, transformers may be classified as: 1 Oil 
cooled. 2. Water cooled. 3. Air blast. 

Parallel Operation. — In order that two or more transformers or groups 
of transformers shall operate successfuUy in parallel, it is necessary that 
their polarity be the same, that their voltages and voltage ratios be 
identical, and that their impedances be inversely proportional to the 
ratings. 

Auto Transformers. — Auto transformers may be used where the 
required voltage change is small. Their action is similar to that of 
ordinary transformers, the essential difference between the two being 
that in the transformer the high- voltage and low-voltage windings are 
separate and insulated from each other while in the auto-transformer a 
portion of the winding is common to both the high and low voltage 
circuits. 

The high- and low-voltage currents in both types of transformers 
are in opposite direction to each other, and thus in an auto-transformer 
a portion of the winding carries only the difference between the two 
currents. 

Auto transformers are extensively used for alternating current motor 
starters, and also to some extent in moderate voltage generating stations. 

Constant-Current Transformers. — The transformers heretofore dis- 
cussed are constant-potential transformers and operate at a constant 
voltage with a variable current. For the operation of lamps in series a 
constant-current transformer is required. There are a number of types 
of this transformer. That manufactured by the General Electric Co. 
operates by causing the primary and secondary coils to approach or to 
separate on any change in the current. 

SYNCHRONOUS CONVERTERS. 

A synchronous converter is essentially a continuous-current gener- 
ator, which, in addition to its commutator, is supplied with two or more 
collector rings connected to suitable points in the armature winding. If 
such a machine be driven by mechanical power, it will evidently deliver 
either alternating or direct current, and, conversely, if suppUed with 
electric power, it will operate either as a synchronous motor, as a direct- 
current motor, or as a synchronous converter. When operated as a 
converter, the alternating current enters the armature winding tlirough 
the collector rings, and after being rectified by the commutator, is de- 
livered as direct current, or vice versa. 

The alternating and direct current e.m.f. stand in a certain relation 
or ratio to each other, and this depends upon the number of phases and 
frequency of the system used, and also upon the ratio of maximum to 
the square root of the mean square value of the impressed e.m.f. (that 
is, the e.m.f. of the supply circuit). It also depends upon the load of 
the machine, the ohmic armature losses, the position of the direct- 
current brushes on the commutator, the excitation, the ratio of pole arc 
to pole pitch, and upon the operating conditions, that is, whether the 
machine is used to convert from alternating to direct current or vice 
versa. Synchronous converters for 60 cycles, which usually have a 
lower ratio of pole arc to pole pitch than 25 cycle converters, have, as a 
rule, a higher voltage ratio and, when used as inverted converters, a 
lower voltage ratio than corresponding 25 cycle machines. 

In the two-ring or single-phase converter, the two collector rings are 
connected to armature conductors with the same angular distance apart 
as commutator bars under adjacent sets of brushes. At tins instant 
the e.m.f. between the collector rings is at its maximum value and 
equal to the e.m.f. between the direct-current brushes. Therefore, 
the direct-current e.m.f. {E) of a two-ring single-phase synchronous 



1454 ELECTRICAL ENGINEERING. 

converter is equal to the maximum value (\/2 x E2) of the sine wave 
e.m.f. between the two collector rings. Therefore, 

in which E2 is the effective value of the single-phase alternating e.m.f. 

The effective e.m.f. between the two collector rings, which are con- 
nected to the armature winding at points 120 electrical degrees apart, 
that is, between any two rings of a three-ring three-phase converter, is 
represented by that chord of a polygon which subtends an angle of 
120 degrees. Likewise, the e.m.f. between two rings which are con- 
nected to the armature winding at points 90 electrical degrees apart, as 
between two adjacent rings in a four-ring quarter-phase converter, is 
represented by the chord wliich subtends an angle of 90 electrical de- 
grees; and the chord which subtends an angle of 60 electrical degrees 
represents the e.m.f. between two adjacent rings of a six-ring six- 
phase synchronous converter. 

In general, the effective e.m.f., Ei, between adjacent rings of an 
n-ring converter, is represented by that chord of a polygon which sub- 

tends an angle of or — . Therefore, 

° n n 

„ E . 180° 
El = — — : sm 

\/2 ^ 

This gives the following theoretical values of the effective alternating 
e.m.f. between adjacent collector rings of a two-ring, three-ring, four- 
ring and six-ring synchronous converter, expressed in terms of the 
e.m.f., E, between the direct-current brushes: 

For single-phase Ei = — = = 0.707 E, 

\/2 

For three-phase Ei = ^-^ = 0.612 E, 
2 V^ 

For quarter-phase Ei = — = 0.500 E, 

For six-phase Ei = — —=. = 0.354 E. 

2\/2 

The above ratios represent, as before stated, the effective alternating 
e.m.f. between two adjacent collector rings. For quarter- and six-phase 
converters the different phases of the supply circuit, however, are not 
connected as a rule to adjacent rings and the ratios given above are not 
the ones to be used for determining the alternating supply voltage for 
these types of synchronous converters. 

For the four-ring quarter-phase converter, each phase of the supply 
circuit is generally connected to diametrically opposite points of the 
armature winding and the ratio will, under such conditions, be equal 
to the ratio for the two-ring single-phase converters, that is, for quarter- 
phase El = -^ = 0.707 E. 
\/2 

For six-phase synchronous converters two different arrangements of 
the connections are generally used. One is called the "double delta" 
connection and the other the "diametrical" connection. In the first 
case, the voltage ratio is the same as for the three-phase synchronous 
converter and simpfy consists of two "delta" systems. The trans- 
formers can also be connected in "double-star," and in such a case the 
ratio between the three-phase voltage between the terminals of each 
star and the direct voltage will be the same as for "double-delta," 

while the voltage of each transformer coil, or voltage to neutral, is — -= 
times as much. With the diametrical connection the ratio is the same 



SYNCHRONOUS CONVERTERS. 1455 

as for the two-ring single-phase converter, it being analogous to three 
such systems. Therefore 

Six-phase double-delta, Ei = — '-^^^ = 0.612 E. 

2 V 2 

TCI 

Six-phase diametrical, Ei = — — = 0.707 E. 

\/2 

The ratio of the effective e.m.f., Eq, between any collector ring and 
the neutral point is always 

Eo = —-=. = 0.354 E. 
2 \/ 2 

The given voltage ratios are, as stated, only theoretical, as the losses 
in the winding have been neglected and the assumption has been made 
that both the impressed and the counter generated converter e.m.f. 
has a sine wave shape. The ratio between the alternating and direct 
terminal voltages is somewhat different from the theoretical ratio due 
to the voltage drop in the armature and to the wave shapes of the 
e.m.f. 's. The exact ratios are always furnished by the manufacturer. 

Synchronous converters may be either of the shunt- or compound- 
wound type, the choice depending on the character of the service for 
which they are to be used. In the majority of installations, especially 
for power purposes, compound- wound converters are generally used 
because they automatically regulate for a comparatively constant 
direct-current voltage. 

In order to change the direct voltage in the ordinary type of syn- 
chronous converter with constant voltage ratio, it is necessary to 
provide means for changing the applied alternating voltage correspond- 
ingly. This can be done in several ways, one of which is to i)rovi(le taps 
on the step-down transformers and adjust the ratio of transformation 
by means of a dial switch. A much better method, however, is the use 
of an induction regulator between the transformer secondary terminals 
and the synclironous converter. This regulator consists of a stationary 
series winding and a movable potential winding, which can be turned 
through a certain angle, and at each angular position will raise or lower 
the voltage at the collector rings a certain amount, through the mutual 
action of the current and potential windings. Tliis method of control 
is generally used with shunt- wound synchronous converters in order to 
keep the voltage constant, when the line drop is excessive. The induc- 
tion regulator is either hand-operated by means of chain or motor 
drive, or the control can be made automatic by using a contact-making 
voltmeter and relay, which will automatically control the regulator 
motor. 

The voltage regulation can also be accomplished by taking advantage 
of the fact that an alternating current passing over an inductive circuit 
will decrease in potential if lagging, and increase if leading. By pro- 
viding the synchronous converter with a series field winding in addition 
to the shunt field, the excitation can be automatically reguhited as the 
load comes on. The inductance of the supply circuit and step-down 
transformers is, however, frequently not sufficient to cause the required 
boost in the voltage, and in such a case it becomes necessary to ins(Tt 
extra reactance coils in the line or provide the step-down transformers 
with extra high reactance. 

There are three feasible methods of starting synchronous converters: 
First, the application of alternating current at reduced voltage to the 
collection rings; second, the application of direct current to the commu- 
tator and starting the machine as a direct-current motor; tliird, the use 
of an auxiliary starting motor mechanically connected. 

The alternating current starting method has many advantages over 
the other methods. It is self-synchronizing, and. therefore, entirely 
eUminates the difficulty of accurately adjusting tiie speed. When the 
speed of the prime movers is liable to be varial^le. the ability to start a 
machine quickly and get it on the line in the shortest possible time is a 
great advantage inherent to this method of starting. It is possible for 
the converter to drop into step with its direct-current voltage reversed 
from that of the bus to which the machine is to be connected, but the 



1456 ELECTRICAL ENGINEERING. 

machine can easily be made to drop back a pole by a self-exciting field 
reversing switch on the machine frame. This method of starting makes 
the operation of the macliine so simple that the habihty of confusion 
and mistakes by operators is greatly reduced. 

If several synclironous converters are to supply the same direct- 
current system, they can be connected in parallel in the same manner 
as shunt- or compound -wound generators, and they are even frequently 
operated in parallel with such generators and storage batteries. The 
different converters will divide the load according to their direct-current 
voltages, and these can be regulated by changing the applied alternating 
current. It is evidently necessary that all of the macliines operating in 
parallel should have the same voltage regulation from no-load to full- 
load, and if a battery is also operated in parallel the voltage drop should 
be sufficiently large so as to cause the battery to take the excessive 
loads. Synchronous converters operated in parallel should not be con- 
nected to the same transformer secondaries. Such a connection would 
form a closed local circuit in which heavy cross-currents would flow 
when any difference in the operating conditions of the machine occurs, 
as, for example, if the brushes of one of the machines were slightly 
displaced relative to the other. 

Compound-wound converters for parallel operation should be pro- 
vided with equahzer switches. For connecting a compound-wound con- 
verter in parallel with one already running, the equalizer switch is 
closed first, so as to energize the series field from the running machine. 
Next, the shunt field circuit is closed and the field adjusted so that the 
voltage will correspond to that of the first machine, and finally the 
main switch is closed. The load can then be transferred from the first 
to the second converter by weakening the shimt field of the former and 
strengthening that of the latter. 

MOTOR-GENERATOES. 

Motor-generator sets may be divided into three general classes: 

1. Direct current to direct current sets, including balancing sets for 
three- wire lighting systems, and for variable speed motor work, boosters 
for storage battery charging and railway or Ughting feeders. 

2. Alternating current to direct current sets or vice versa. These are 
used for excitation purposes and for supply of lighting, railway or 
power systems. The sets may he driven either with synchronous or 
induction motors, the former being equipped with an auxiliary squirrel 
cage winding on the fields so as to be self-starting at reduced voltage. 

3. Alternating current to alternating current sets between the two 
periodicities; commonly called "frequency changers." 

Balancers. — The balancer set, a form of direct- current compensator, 
is a variation of the regular motor-generator set, in that the units of 
which it is composed may be, alternately, motor or generator, and the 
secondary circuit is interconnected with the primary. On account of 
the latter feature, the efficiency of transformation is higher and a 
larger output is obtainable from a given amount of material than in the 
straight motor-generator set. 

Balancer sets are widely used to provide the neutral of Edison 
three- wire lighting systems. They are also installed for power service 
in connection with the use of 250-volt motors on a 500-volt service 
or 125- volt motors on a 250-volt service. 

The potential of the system being given, the capacity of a three-wire 
balanc(^T set is fixed by the maximum current the neutral wire is required 
to carry. This figure is a more definite specification of capacity than a 
statement in per cent of unbalanced load. 

As designed for power work and generally for lighting service, the 
brushes of each machine are set at the neutral point in order to get the 
best results for operating alternately either as a generator or motor. 
Where the changes of balance are so gradual as to permit of hand ad- 
justment, if desired, a considerable increase in output is obtainable. 

Boosters. — Boosters are ext(^nsively used in railway stations to raise 
the potential of the feeders extending to distant points of the system; 
for storage-battery charging and regulation ; and in connection with the 
Edison three-wire lighting system. The design of the various sets is 
closely dependent upon their apphcation. 



ALTERNATING-CURRENT CIRCUITS. 1457 

Booster sets are constructed in either scries- or shunt-wound types, 
and they may be arranged for cither automatic or hand regulation, 
depending on the nature of the service required. 

Where there are a number of hghting feeders connected and run at 
full load for only a short time each day it will generally be economical 
to install boosters rather than to invest in additional feeder copper. 
It is important, however, to consider each case where the question of 
instaUing a booster arises, as a separate problem, and to dettu-mine if 
the value of the power lost represents an amount lower than the interest 
charge on the extra copper necessary to deUver the same potential 
without the use of a booster. 

Dynamotors. — A dynamotor is a machine for rcxlucing a direct- 
current voltage, and it is extensively used in connection with liigh voltage 
railway equipments for obtaining a moderate voltage for the control. It 
has two armature windings and commutators on one dnmi, with the field 
between them. The control ciu-rent is taken midway between the arma- 
tures and is returned to the ground side of the dynamotor. This insures 
that the maximum potential on the control circuit, under normal condi- 
tions, will be approximately one-half of the line voltage, and the potential 
to grounded parts no greater than when operated directly on a line voltage 
of one-half the amount. 

Frequency Changers. — A periodicity of 25 cycles has been quite gen- 
erally selected for railway service. Also in certain large cities, current of 
the same frequency is generated in central stations and distributed to 
substations in which are installed rotary converters supplying an Edison 
three- wire network. 

Inasmuch as the periodicity of 60 cycles is more favorable than 25 
cycles for alternating current Ughting, frequency changers, similar to that 
shown above, are installed to furnish high tension 60-cycle current for 
distribution to outlying districts beyond the reach of the three-wire 
system. 

In the design of frequency changers speeds must be selected that are 
common to the two periodicities of the system upon which they are to 
be used; since 300 r.p.m. is the highest speed common to 25 and 60 cycles, 
at which speed smaU sets are expensive per kilowatt, a line of sets with 
4 or 8 pole motors and 10 or 20 pole generators has been developed, giving 
62 1/2 cycles from 25 cycles or 60 cycles from 24 cycles. 

Where parallel operation is required between synclironous motor- 
driven frequency changers, a mechanical adjustment is necessary between 
the fields or armatures of the generator and motor to obtain equal division 
of the load. The adjustment is best obtained by the cradle construction. 
The stator of one machine is bolted to a cradle fastened to the base, and 
by taking out the bolts the frame can be tm'ued around tlirougli a small 
angle relatively to the cradle, and therefore to the stator field of the other 
macliine. where the bolts can be replaced. 

The Mercury Arc Rectifier consists of a mercury vapor arc enclosed 
hi an exhausted glass vessel into which are sealed two terminal anodes 
connected to the two wires of an alternating-current circuit. A third 
terminal, at the bottom of the vessel, is a mercury cathode. AVlieii an 
arc is operating, it is a good conductor from either anode to the cathode, 
but practically an insulator in the other direction. The two anodes 
connected across the terminals of the alternating-ciu-rent line become 
alternately positive and negativ^e. "Wliile either anode is ]X)sitive, there 
is an arc carrying the ciirrent between it and the cathode. When the 
polarit>' of the alternating-current reverses, the arc passes from the other 
anode to the mercury cathode, which is always nc^gative. The current 
leading out from the mercury cathodes is uui-diri actional. By means of 
reactances, the pulsations are smoothed out and th(^ current at the cathode 
becomes a true direct current with pulsations of small amplitude. 

ALTERNATING-CURRENT CIRCUITS. 

CalculatioD of Alternating-current Circu5ts. — The following formulae 
and tables are issued by the General Electric Co. They afford a con- 
venient method of calculating the sizes of conductors for. and determining 
the losses in, alternating-current circuits. They apply only to circuits 
in which the conductors are spaced 18 inches apart, but a slight increase 
or decrease in this distance does not alter the figures appreciably. If 



1458 



ELECTRICAL ENGINEERING. 



the conductors are less than 18 inches apart, the loss of voltage is de- 
creased, and vice versa. 
Let W = total power delivered in watts: 

D — distance of transmission (one way) in feet; 

P* = per cent loss of delivered power ( W) ; 

E == voltage between main conductors at consumer*s end of circuit, 

K = a, constant; for continuous current = 2160; 

r == a variable depending on the system and nature of the load; for 
continuous current = 1; 

Jlf = a variable, depending on the size of wire and frequency; for con- 
tinuous current =1; 

A = a, factor; for continuous current = 6.04. 

Area of conductor, circular miUs = — p ^^ ^^ — ; 

Current in main conductors = WX T -i- E; 
Volts lost in Unes = P X -E X A/ -^ 100; 

Z)2 X W "X K y. A 
Pounds copper = p x £2 X l.OOO.OOO ' 



X = 0.000882/ [logio (j^ + 0.109] 



R 



tan a ) cos 2 



X = Reactance. 
R = Resistance, ohms per 1000 ft., 
sen's standard.) 

d = inches between wires. 

r = radius of wire, inches. 

/ = cycles per second. 



at 60° F. (Wire 100 % Matthies- 





Values 


OF M 


—Wires 18 In. 


APART-t 


Wires 36 In. Apart, t 




25 Cycles. 


60 Cycles. 


25 Cycles. 


Power 

Factors. 


0.95 


0.90 


0.85 


0.80 


•0.95 


0.90 


0.85 


0.80 


0.95 


0.90 0.85 0.80 


Wire Sizes. 






















0000 


1.17 


1.16 


1.12 


1.06 


1.53 


1.64 


1.67 


1.66 


1.22 


1.23 1.20 1.15 


000 


1.12 


1.09 


1.05 


0.99 


1.41 


1.49 


1.50 


1.47 


1.16 


1.15 1.11 1.05 


00 


1.08 


1.04 


0.99 


.92 


1.32 


1.36 


1.35 


1.31 


1.11 


1.08 1.04 0.97 





1.05 


1.00 


.94 


.87 


1.24 


1.26 


1.24 


1.19 


1.07 


1.03 0.98 .91 


1 


1.02 


0.96 


.90 


.83 


1.18 


1.17 


1.14 


1.08 


1.04 


0.99 .93 .86 


2 


1.00 


.93 


.86 


.79 


1.12 


1.10 


1.06 


1.00 


1.02 


.95 .89 .82 


3 
4 


0.98 
.96 


.91 

.89 


.84 
.81 


.76 

.74 


1.08 
1.05 


1 05 


0.99 
.94 


0.93 

.87 






1.00 


$For higher volt- 


5 


.95 


.88 


.80 


.72 


1.02 


0.97 


.90 


.83 


ages 


10,000 to 200,- 


6 


.94 


.86 


.78 


.70 


1. 00 


.94 


.87 


.79 


000. 




7 


.94 


.85 


.77 


.69 


0.98 


.91 


.84 


.76 






8 


.93 


.85 


.76 


.68 


.97 


.89 


.82 


.74 






9 


.92 


.84 


.76 


.67 


.95 


.88 


.80 


.72 






10 


.92 


.83 


.75 


.67 


.94 


.86 


.79 


.71 







Per cent of 


Value of K. 


Value of T. 





Power Factor. 


100 95 


85 


80 


100 95 1 85 


80 


>'o 


System: 

Single-phase 


2160 2400 


3onn 


1 1 

3380 1.00 1.05 1.17 
16900.50 0.530 S9 


1.25 
0.62 
0.72 


6 04 


Two-phase, 4- wire 


1080 1200 1500 


12 08 


Three-phase, 3- wire 


1080 I2OOI1SOO 1690l0 58 61 68 


9 06 















* P should be expressed as a whole number, not as a decimal; thus 
a 5 per cent loss should be written 5, not .05. 

t As corrected by Harold Pender, see Elect. World, July 1, 1905. The 
formula for M is approximate, and gives values correct within 2% for 
any case likely to arise in practice. 



ALTERNATING-CURRENT CIRCUITS. 



1459 



aelatlTe Weight of Copper Required in Different Systems for 
Equal Effective Voltages. 

Direct current, ordinary two-w ire system 1 . 000 

** three-wire system, all wires same size 0. 375 

neutral one-half size 0.313 

Alternating current, single-phase two- wire, and two-phase four- wire 1.000 
Two-phase three- wire, voltage between outer and middle wire 

same as in single-phase two-wire . 720 

voltage between two outer wires same. . . 1 .457 

Three-phase three-wire . 750 

four-wire . 333 

The weight of copper is inversely proportional to the squares of the 
voltages, other things being equal. The maximum value of an alter- 
nating e.m.f. is 1.41 times its effective rating. For derivation of the 
above figures see Crocker's "Electric Lighting," vol. ii. 

Approximate Rule for Size of Wires for Three-Phase Transmission 
Lines. (General Electric Co.) 

The table given below is for use in making rough estimates for the 
sizes of wires for three-phase transmission, as in the following example. 

Required. — The size of wires to deliver 500 Kw. at 6000 volts, at the 
end of a three-phase line 12 miles long, allowing an energy loss of 10% 
and a power factor of 85 % . If the example called for the transmission 
of 100 Kw. (on which the table is based), we should look in the 6000- 
volt column for the nearest figure to the given distance, and take the 
size of wire corresponding. But the example calls for the transmission 
of five times this amount of power, and the size of wire varies directly 
as the distance, which in this case is 12 miles. Therefore we look for 
the product 5 X 12 = 60 in the 6000-volt column of the table. The 
nearest value is 60.44 and the size of wire corresponding is No. 00, which 
is, therefore, the size capable of transmitting 100 Kw. over a line 60.44 
miles long, or 500 Kw. over a line 12 miles long, as required by the example. 

If it is desired to ascertain the size of wire which will given an energy 
loss of 5%, or one-half the loss for which the table is computed, it is 
only necessary to multiply the value obtained by 2, since the area 
varies inversely as the per cent energy loss. 

Distances to which 100 Kw. Three-phase Current can be Trans- 
mitted Over Different Sizes of Wires at Different Poten- 
tials, Assuming an Energy Loss of 10% and a Power Factor 

OF 85%. 



Num- 
ber 


AreE in 


Distance of Transmission for Various Potentials at 


Circular 
Mils. 


Receiving End, in Miles. 


B. & S. 


2.000 


4.000 


6.000 


8.000 10.000 


15.000 20.000 


25.000 


30.000 


6 


26,250 


1.32 


5.28 


11.92 


21.12 


33.1 


74.50 132.4 


206.75 


298 


5 


33.100 


1.66 


6.64 


15.00 


26.56 


41.6 


93.75 166.4 


260.00 


375 


4 


41.740 


2.10 


8.40 


18.96 


33.60 


52.6 


118.50 210.4 


328.75 


474 


3 


52.630 


2.54 


10.16 


23.84 


40.64 


66.2 


149.00! 254.8 


413.75 


596 


2 


66.370 


3.33 


13.32 


30.04 


53.28 


83.4 


187.75: 333.6 


521.25 


751 


I 


83.690 


4.21 


16.84 


37.92 


67.36 


105.3 


212.OOI 421.2 


658.00 


948 





105.500 


5.29 


21.16 


47.68 


84.64 


132.4 


298.00 


529.6 


827.50 


1192 


00 


133.100 


6.71 


26.84 


60.44 


107.36 


167.9 


377.75 


671.6 


1049.25 


1511 


000 


167.800 


8.45 


33.80 


76.16 


135.20 


211.4 


476.00 


845.6 


1321.25 


1904 


0000 


211.600 


10.62 


42.48 


95.68 


169.92 


265.7 


598.00 


1062.8 


1660.50 


2392 




250.000 


12.58 


50.32 


113.32 


201.28 


3147 


708.25 


1258.8 


1966.75 


2833 




500.000 


25.17 


1 00.68 


226.64j402.72 


629.4 


1416.50 


2517.6 


3933.75 


5666 



Notes on High-tension Transmission. — The cross-sectional area and, 
consequently, weight of conductors vary inversely as the square of the 
voltage for a given power transmission. The cost of conductors is there- 
fore reduced 75 % every time the voltage is doubled. The cost of other 
apparatus and appliances increases with increasing voltage. For long- 
distance Unes the saving in copper with the "highest practicable voltages 
is so great that the other expenses are rendered practically negligible. In 
the shorter Unes, however, the most suitable voltage must be determined 



1460 



ELECTRICAL ENGINEERING. 



in each individual case. The voltages in the following table will serve as 
a guide. 





Voltages Advisable for Various Line Lengths. 


Miles. 


Volts. 


Miles. 


Volts. 


Miles. 


Volts, 


1 
1-2 
2-3 


500-1000 
1000-2300 
2300-6600 


3-10 
10-15 
15-20 


6600-13,200 
13,200-22,000 
22,000-44,000 


20-40 
40-60 
60-100 


44,000- 66,000 
66,000- 88,000 
88,000-110,000 



Standard machinery is made for 2300, 6600, 13,200, 22,000, 33,000, 
44,000, 66,000, 88,000 and 110,000 volts, and standard generators are 
made for the above voltages up to and including 13,200 volts. When 
the Une voltage is higher than 13,200, step-up transformers must be 
employed. In a given case the saving in cost of conductor by using the 
higher voltage may be more than offset by the cost of transformers, and 
the question of voltage must be determined for each case. 

Line Spacing. — Line conductors should be so spaced as to lessen the 
tendency to leakage and to prevent the wires from swinging together 
or against the towers. With suspended disk insulators the radius of free 
movement is increased, and special account should be taken of spacing 
when these insulators are used. The spacing should be only sufficient 
for safety, since increased spacing increases the self-induction of the line, 
and while it lessens the capacity, it does so only in a slight degree. The 
following spacing is in accordance with average practice. 

Conductor Spacing Advisable for Various Voltages. 



Volts. Spacing. 

33,000 3 feet. 

44,000 4 feet. 

66,000 6 feet. 



Volts. Spacing. 

88,000 8 feet. 

110,000 10 feet. 

140,000 12 feet. 



Aluminum Conductors. — The conductivity of aluminum is generally 
taken at 63.3%, that of hard-drawn copper of the same cross-sectional 
area. The weight of Al is 30.2% that of copper, and therefore an Al 
conductor of the same length and conductivity as a given copper con- 
ductor weighs 47.7% as much. The cost of Al must therefore be 2.097 
times that of hard-drawn copper to give equal cost for the same length 
and conductivity. Omng to the mechanical imrehability of soUd Al 
conductors, stranded conductors are used in all sizes, including even the 
smallest. 

The Size of the Line Conductors depends on both economical and 
electrical considerations, except where the length of the span is the gov- 
erning feature. With expensive steel towers it becomes necessary to 
string the conductors for higher stresses so as to reduce the sags and 
consequently the height of the towers as much as possible. It has, there- 
fore, become a general practice to erect the conductors so that the stress 
at the worst load conditions equals one-half the ultimate strength of the 
conductor material, which gives a factor of safety of two. The load to 
which a Une conductor is subjected, besides its own weight and ice, is 
acting in a vertical direction, the pressure imposed by the wind acting in 
a horizontal direction. It is also evident that the stress will be greater 
in extremely cold weather because of the contnaction of the \vires, and 
it is generally agreed that the worst load condition would occur at 0° F. 
with an actual wind velocity of 56 miles per hour (8 pounds pressure 
per square foot projected area) and with an ice covering one-half inch 
thick. The maximum temperature is considered to be 130° F., and the 
cables should be so supported that at this temperature the sag does not 
become excessive, but allows a clearance between the lowest conductor 
and ground of from 25 to 30 feet. 

Line conductors may be either of copper or aluminum. It is advisable for 
mechanical reasons in spans of 200 to 300 feet never to use smaller cable 
than No. 5 B. & S. copper, or No. 1. B. & S. aluminum (equivalent of 
No. 3 copper). For spans greater than 300 feet, the minimum sizes of 
cable allowable are those which will give a reasonable sag at the most 
severe climatic conditions assumed. Frequently the size of conductors, 



ELECTRIC MOTORS. 1461 

determined by electrical considerations, limits the length of spaas to a 
smaller value than is economical. Tliis may occur even with moderately 
long spans — 500 to 600 feet — when the character of the country is such as 
to make transportation costly or when expensive foundations must be 
used. In such cases it ^vill often be found that a saving can be made by 
increasing the size of conductor, thereby allowing an incrccise in thc^ length 
of span and the use of fewer towers of approximately the same height and 
not greatly increased weight. 

The sag or deflection at the center of a span can be figured by the 
formula: 

where D = deflection in feet; 5 = length of span in feet; W = resultant of 
weight and wind in lbs. per foot of cable; T = tension on cable in lbs. 

A 135,000-Volt Three-phase Transmission System from Cook Falls, 
Mich., to Flint, Mich., 125 miles distant, is described in Power, Aug. 
9, 1910. The generating equipment comprises three 3000-K.W. 
60-cycle alternators, mounted on horizontal shafts driven l)y water- 
wheels. The available head of water is 40 ft., and the flow averages 
1100 cu. ft. per second. The transmission line consists of three No. 
copper wires carried on suspension-type insulators hung from the cross- 
arms of 55-ft. tripod steel towers. The wires are at the angles of an 
isosceles triangle with a 12-ft. base and 17-ft. sides, the lowest wire 
40 ft. above the ground. The insulators have eight disks linked in 
series, each disk having been tested to withstand continuously 75,000 
volts, and subjected to 100,000 volts for a brief period. 

ELECTRIC MOTORS. 

Classification. — Motors maybe classified according to type, speed, and 
mechanical features. The first cover: 

Direct Current — 1. Series. 2. Shunt. 3. Compound. 

Alternating Current (single-phase and polyphase) — 1. Synclironous. 
2. Synchronous Induction. 3. Induction. 3a. Phase-woimd. 3b. Squirrel- 
Cage. 4. Commutator. 
According to their speed, they are classified as — 

Constant Speed: covering cases where the speed is constant or varies 

slightly. 

Adjustable Speed: covering cases where the speed may be varied over a 
considerable range, but when once fixed remains at tliis value independent 
of the load changes. 

Varying Speed: covering cases where the speed changes with the 
load, usually decreasing as the load increases. 

Multi-Speed: covering cases where several distinct speeds may be 
obtained by changing the connections of the windings or by otlier moans. 

According to their mechanical features motors may be classified as: 
(1) Open. (2) Mechanically Protected. (3) Semi-Enclosed. (4) Totally 
Enclosed. (5) Enclosed. Externally Ventilated. (6) Enclosed, Self-Venti- 
lated. (7) Moisture Proof. (8) Splash and Water Proof. (9) Submergiblc. 
(10) Acid Proof. (11) Explosion Proof. 

Limitations. — The principal limitations in the ratings of motors are: 
(1) Mechanical Strength. (2) Heating. (3) Commutation. (4) Reg- 
ulation. (5) Efficiency. 

CHARACTERISTICS OF MOTORS AFFECTING THEIR 
APPLICATIONS. 

(D. B. Rushmore, "American Handbook for Electrical Engineers.") 

Series Motor. — This motor is used when a powerful starting torque and 
rapid acceleration are required, without an excessive instantaneous de- 
mand of energy. The torque is practically independent of the voltage and 
at low-flux densities varies directly as the square of the ciu-rent, but as 
the magnetization approaches saturation it becomes more nearly propor- 
tional to the first power of the current. The ftiaximmn torque exists at 



1462 ELECTRICAL ENGINEERING. 

low speed, this being the most valuable feature of the series motor. 
Dangerously high speeds may be attained by the armature with very 
hght loads, and series motors should for this reason be either geared or 
direct connected to the load. 

Speed Control of Series Motor. — The speed of a series motor on 
constant potential varies automatically with the load, increasing as the 
load decreases. The speed may, however, be adjusted if some means of 
varying the impressed voltage is provided. As the work required of a 
series motor is very often intermittent in character, the insertion of re- 
sistance in the armature circuit to reduce the speed is permissible from an 
economic standpoint in such cases. In others, such as railway work, where 
two or four motors are used, reduced voltage is most readily and economi- 
cally obtained by connecting the motors in series or in series parallel. 

Shunt Motor. — This motor has good starting characteristics and a prac- ■ 
tically constant speed, varying only shghtly with load changes. The speed I 
can, however, be adjusted, either by changing the e.m.f. impressed on the ^ 
armature or by changing the field flux. 

Speed Adjustment by Armature-voltage Control, i.e., by changing 
the e.m.f. impressed on the armature, does not change the full-load torque 
which the motor is capable of exerting, since the rated torque depends only 
upon field flux and rated armature current. These methods are therefore 
constant-torque methods and are properly adapted to loads in which the 
torque remains constant regardless of speed. The method most generally ' 
used for varying the impressed e.m.f. with a single-voltage system is by ' 
means of inserting resistance in series with the armature. The efiflciency ' 
with this method is, of course, very low at slow speeds. The speed regu- 
lation with varying loads may also be very poor. 

There are several systems of controUing the motor speeds by applying 
different voltages, such as by the use of three- wire generators or two-wire 
generators with balancer sets or by the Ward Leonard system. This latter 
system, which is the most practical, consists of a constant-speed motor 
driving a generator which supphes current to the motor whose speed is to 
be adjusted. This arrangement is very satisfactory, but on account of the 
expense of providing three fuU-sized machines instead of one to perform 
the work, the cost may be prohibitive except with very large motors, such 
as for hoists, etc. 

Speed Adjustment by Shunt-field Control, i.e., by inserting resistance 
in the shunt-field circuit, is the simplest of all methods of speed variation, 
but with ordinary shunt motors the range of speed variation by this means 
is small. Where a variation of more than from 20 to 30 per cent is desired, 
a motor of modified design and of a certain increased size is generally re- 
quired, because the field must be more powerful with respect to the arma- 
ture than in the case of standard single-speed motors. Variable-speed 
motors of the field- weakening type are not constant torque, but constant- 
output motors, i.e., the torque falls proportionally as the speed increases. 

A speed variation up to 3 to 1 meets, as a rule, aU requirements, and such 
motors can readily be obtained in commercial sizes. Should a greater 
speed variation be desired, say 4 to 1 or 5 to 1, it is possible to accomphsh 
this by the commutating-pole shunt motor with field control only. A 
combined field and armature control would, however, be a better method. 

Compound Motor. — This motor is provided with both a series and a 
shunt field. The two fields are usually connected so that they act in the 
same direction, in which case the motor is called a "cumulative" com- 
pound motor. "Differential" compound motors, with the two fields 
opposing, are sometimes employed for special services. The cimiulative, 
or ordinary, compound motor combines the characteristics of the shunt 
and series motors, having a speed not extremely variable under load 
changes, but developing a powerful starting torque and an increasing 
torque with decreasing load. Motors having a comparatively weak series 
field are employed extensively in shop practice where the motor may be 
required to start under heavy load, but must maintain an approximately 
constant speed after starting, or when the load is removed. The heavily 
compounded motor is used where powerful starting torque and rapid accel- 
eration are necessary, with a speed not varying too widely imder load 
changes, such as for rolling mills, etc. 

The speed control employed with compound motors may be any of the 
various methods explained in connection with the shunt motor. For 



CHARACTERISTICS OF MOTORS. 1463 

certain service the control may be entirely rheostatic, the scries winding 
being cut out after the motor has come up to speed. 

Induction Motoip. — The induction motor is essentially a constant-speed 
machme, although the speed may be varied either by varying the applied 
stator frequency or by introducing resistance in the rotor circuit. It is 
bmlt in two distmct types, namely, the squirrel-cage and the phase-wound. 

Squirrel-cage Motor. — The squirrel-cage type is used for constant- 
speed service with mfrequent starting. It has a relatively small starting 
torque per ampere and draws a large starting current from the hne. By 
increasmg the resistance of the rotor, it may, however, also be built in the 
smaller sizes for a high starting torque, rapid acceleration and frequent 
starting, for such apphcations as sugar and laundry centrifugals, etc., 
where simpUcity of control is desirable. They are also used for operat- 
ing punches, shears, etc., where a fly-wheel is provided for storing the 
energy. 

Induction Motor with Wound Rotor. — For service requiring high 
starting torque combined with moderate starting current a motor with 
the wound type of rotor is best adapted. A motor with the resistance 
moimted inside the rotor should not be used to operate machinery having 
large inertia or excessive static friction, since full starting current may bo 
required for a long period before the apparatus attains full speed, and, as 
the capacity of the internal resistance is small, excessive temperatures may 
result. This type of motor is, as a rule, not built above 200 horse-power, 
due to mechanical difiSculties involved in connection with the internal 
resistance. 

A motor with external resistance should be used for moderate and large 
.sizes. The rotor must then be provided with collector rings and brushes. 
The contact resistance of these as well as the leads and the controller 
fingers, which are in the circuit all the time, may impair the efficiency and 
regulation of the motor, especially if the controller and the resistance are 
located some distance from the motor. The phase-wound induction motor 
with an external variable-rotor resistance is best adapted for a variable- 
speed service, as the losses necessary to obtain reduced speeds are external 
to the motor itself. 

Multi-speed Induction Motors. — It often happens that the service 
is such that two or three speeds will be satisfactory for the operation of 
the machinery and that these speeds must be independent of the load. 
Under such conditions multi-speed motors can frequently be used. In 
these motors the different synchronous speeds are produced by changing 
the number of poles in the magnetic circuit. Each of these speeds is fixed, 
if no resistance is used in the secondary circuit. With multi-speed motors, 
as with single-speed motors, however, resistance may be used in the sec- 
ondary circuit for varying the speed. 

A change of the number of poles ,may be made in any of the following 
ways: 

1. By the use of single magnetic and electric circuits, changing the 
number of poles by re-grouping the coils. 2. By the use of single mag- 
netic circuits and independent electric circuits. 3. By means of separate 
magnetic and electric circuits, the so-called Cascade connection. 

Synchronous Motor. — The speed of a synchronous motor is constant, 
being fixed by the number of poles and the frequency of the applied volt- 
age. The single-phase type is not self-starting and the polyphase type has 
in itself a very poor starting torque. They may, however, be made self- 
starting in the same manner as squirrel-cage induction motors, by the use 
of an amortissem^ or cage-winding, similar jin construction to that used 
for induction motors. 

The speed-torque curve of a synchronous motor is similar to that of an 
induction motor except that the torque values are lower for a given resis- 
tance of rotor winding on account of the construction of the macliine. The 
starting winding must be designed with both the load at start and the load 
at synchronous speed in mind, because too great a slip may cause the 
motor to shut dowTi when the field is put on. It is, however, seldom that 
the same motor Avill be called upon to start a heavy load and at the same 
time synchronize a heavy load, as the load usually consists principally of 
either static friction, as in the use of motor-generator sets, line shafting, 
etc., or it comes up with the speed as in the case of a fan blower or centrif- 
ugal pump. The former case would be met by a high-resistance squirrel- 
cage winding and the latter would require a low resistance. 



1464 ELECTRICAL ENGINEERING. 

Single-phase Series Motor. — This type of commutator motor has a very 
powerful starting torque, liigli power factor, and relatively high efficiency. 
It is most generally used for traction work, the speed being controlled by 
varying the apphed voltage wliich can most readily be done by means of 
an auto-transformer with a nimaber of taps. 

Repulsion Induction Motor. — This type of cormnutator motor has a 
limited speed and an increase of torque with decrease in speed. The action 
of the compensating field insures a power factor approximately unity at 
full load and closely approaching unity over a wide range in load. In ad- 
dition, it serves to restrict the maximum no-load speed and also permits, 
where varying speed service is involved, an increase over the synchronous 
speed. 

Starting of Repulsion Motors. — A repulsion motor, if started by 
directly closing the Une switch, will develop about 21/2 times full-load 
torque. The starting current corresponding to full-load starting torque is 
from 2 to 21/4 times full-load running current. As a general rule, starting 
boxes are not required up to and including 2-horse-power rating. From 
2 to 5 horse-power the use of a rheostat is optional, dependent upon the 
degree and care to be exercised in maintaining voltage regulation. Start- 
ing boxes should, however, preferably be used on sizes above 5 horse- 
power, especially where Ught and power circuits are combined. 

Reversible Repulsion Motors. — The repulsion motor may be designed 
for reversible service. This is accomplished by adding an auxihary revers- 
ing winding spaced 90° from the main field winding and connected in 
series with it. By reversing the relative polarity of the two windings, 
the direction of rotation is changed in a simpler manner than by mechani- 
cal shifting of the brush holder yoke. Instant reversal may be effected 
from fuU speed in one direction to full speed in the other, about 200 per 
cent of normal running torque being developed at the moment of speed 
reversal in either direction. 

Variable-speed Repulsion Motors. — In addition to the constant-speed 
repulsion motor, two other types are also available, one for constant- 
torque and variable-speed sendee, the other for adjustable speed inde- 
pendent of torque. In general, variable-speed repulsion motors are not 
applicable to lathes, boring mills, or similar machines where the service 
requires adjustable speed and constant horse-power at aU speeds below 
and above normal. When a certain amount of variable speed is required 
at approximately constant torque, such as in driving fans, blowers, print- 
ing presses, etc., the repulsion motor successfully meets a wide field of 
appUcation. 

MOTOR APPLICATIONS. 

Pumps (E. A. Lof, in Coal Age). — Pumps are either of the reciprocating 
or centrifugal type. In the former the volmne of water can be varied 
either by changing the speed or by the use of a by-pass valve. The latter 
method is, of course, less economical, and speed variation is, therefore, 
preferable. In starting large pumps the water may, however, be delivered 
tlirough a by-pass imtil the motor is up to speed, when tliis passage is 
gradually closed and the water deUvered into the pipe system. The load 
at starting, therefore, only consists of the friction losses, and usually does 
not exceed 25 per cent of the full-load torque. 

Either direct- or alternating-current m.otors may be used for dri\dng 
reciprocating pumps. When of the former class, the compound-wound 
type is generally selected for single-acting pimips on account of their 
rather pulsating load, while for duplex and triplex pumps, having steadier 
characteristics of power demand, the shunt- woimd motor is used to ad- 
vantage. Both squirrel-cage and phase-wound induction motors are 
suitable, the latter as a rule being selected where it is desirable to reduce 
the starting current to a minimmn or where a somewhat variable speed 
is required. 

Synchronous motors may also be used for driving large ^pumps of mod- 
erate speed, and are admirably adapted for such service, while their 
characteristics are such that by over-exciting their fields they may be 
made to considerably improve the power factor of the system. By-pass 
valves should preferably be provided on the pumps, when this type of 
motor Is employed, so as to reduce the starting current as much as possible. 

In selecting the motor equipment for a centrifugal pump, its character- 
istics as affected by the service conditions must be carefuUy predetermined, 



MOTOR APPLICATIONS. 1465 

and in some respects the operating features of this type of water lift aro 
entirely opposite to those of reciprocating pumps. 

With constant speed an increase of the resistance against which the 
reciprocating pump operates increases the water pressure and, therefore 
the load on the motor, while with the centrifugal pump an increase of the 
resistance reduces the load. The volume of water deUvered Ijy a recip- 
rocating pump is not affected by the reduction of the head, but the 
required power is lessened. A reduction of the head with a centrifugal 
pump, however, increases the volume of water, and as the efficiency at the 
same tune goes down rapidly, the load increases. It is, therefore, of im- 
portance to know what this overload, caused by a n^ductiori of the head 
amounts to, and the duration of the overload; and the capacity of the 
motor should, £ls a rule, be governed by the low- and not the liigh-head 
conditions. 

The starting condition must be given careful consideration in selecting 
the motors. In starting a centrifugal pump the discharge valve may be 
entirely closed imtil the motor comes up to speed, so that the latter may 
start as nearly light as possible. As the machine accelerates, the water is 
churned around in the casing, causing the motor to load up as it ap- 
proaches full speed, when, with pumps of the usual design, it takes from 
40 to 50 per cent of full-load torque to drive it even though pumping 
no water. 

Shunt- wound, direct-current motors and either squirrel-cage or phase- 
wound induction motors are well adapted for tliis type of pimip and will 
readily meet the above conditions. A synchronous motor may lead to 
difficulties unless precautions are taken in designing the squirrel-cage 
starting winding with a sufficiently low resistance so that it will develop 
enough torque to puU the motor into synclironism. When this is done, 
however, the starting current is increased and a compromise must usually 
be made. 

Fans. — Either direct- or alternating-current motors can be used for 
driving fans. Where the air-supply must be regulated, such as in mines, 
the motors must be of the adjustable-speed type. Direct-current motors 
may be either of the shimt- or compoimd- wound type, the speed rt^gulation 
being accompanied by field control. Shunt-wound motors are generally 
used, but compound- wound motors are preferable for very large fans 
requiring a great starting torque. 

With an alternating-current system, the phase-wound induction motor 
should be used, the speed regulation being accomphshed by uiserting 
resistance in the secondary rotor circuit. 

Air Compressors. — Air compressors may be divided in two classes, 
centrifugal and reciprocating. The former require a high speed for their 
operation, while the speed of the latter is comparatively low. 

Shunt-womid, direct-current motors and both squirrel-cage and phase- 
wound induction motors are used for driving them, the phase-wound type 
being preferable for larger units, where a low starting cm-rent is desirable. 

With direct-current systems, shunt-wound motors are usually used for 
centrifugal compressors and compound-woimd for the reciprocating type. 

Hoists (E. A. Lof, in Coal Age). — The two principal clavsses of electric 
mine-hoist equipments are: The direct-current motor operated from its 
own motor-generator set by generator field control, and the induction 
motor. The direct-current motor lends itself well to direct connection, as 
the characteristics of slow-speed motors of this type are excellent. The 
cost of a direct-connected motor will, in practically all cases, ])e liigher 
than that of a geared motor, but in some instances tliis is largely offset by 
the saving in gearing, etc. Where, however, a considerable saving can be 
made by using a geared motor, and where the mechanical advantages of a 
direct-connected hoist are not an important consideration, a geared direct- 
current motor should be employed. Such a motor should be separat^ily 
excited and shunt-wound, and the current should be o])tained from a 
separately excited generator of similar type, both machines being driven 
by a direct-coupled induction motor where the source of supply is alter- 
nating current, as is almost invariably the case. 

The control of the hoist motor is effected by regulating and reversing 
the exciting current of the direct-current generator, thus varying the 
voltage impressed upon the motor terminals. Tlie current for the motor 
and dynamo fields is supplied from the direct-connected exciter, and in 



1466 ELECTRICAL ENGINEERING. 

the case of the motor it is maintained constant. As the rapidity of hoist- 
ing is practically proportional to the voltage impressed upon the motor 
armatm*e, the controlUng gear is arranged so that the speed will be directly 
proportional to the distance by wliich the controlUng lever is moved away 
from the neutral position. This system of hoisting has the great advan- 
tage that the rheostatic losses are reduced to a minimum and that the 
operator has perfect control over the motor. 

In many cases it is higlily desirable to reduce the instantaneous peak 
loads and equalize the current input to the hoist. This is especially true 
where the power charge is based wholly or partly on the maximum de^ 
mand, and any practicable method, therefore, by which energy may be 
taken from the Une and stored during periods of light load and discharged 
when the hoist load is heavy, makes it possible to greatly reduce the 
maximum input and consequently the charge for power. 

The simplest method of effecting this is by adding a fly-wheel to the 
motor-generator set, previously described. In order to permit the fly- 
wheel to take care of the peaks, and equaUze the load, the speed of the 
set must be varied according to the demand for power. Tliis is accom- 
plished by an automatic sUp regulator connected in the secondary circuit 
of the induction motor, wliich, in this case, must be of the phase-wound 
type. 

The second important class of electric hoisting systems is, as previously 
stated, driven by induction motors. Excessive low-speed motors of this 
type and of moderate capacities do not show particularly good electrical 
characteristics. For large-capacity hoists at high-rope speeds, using as 
small a drum diameter as is consistent with good practice, a direct- 
connected induction motor is, in some instances, entirely feasible, and a 
niunber of such equipments are in actual operation abroad. However, 
the great majority of induction- motor-driven hoists now in use and which 
will be installed in the future are and will continue to be of the geared type. 

The induction motor must be of the phase- wound type, and the speed 
control is accomplished by cutting in or out resistance in the secondary 
circuit. Drum controllers with grid resistances are used up to about 200 
horse-power, while between this and 400 horse-power it is customary to 
provide a complete magnetic-contactor control. Above 400 horse-power 
the liquid rheostat is usuaUy employed as a secondary resistance and 
control. 

For equalizing the load taken by an induction-motor-driven hoist, a 
fly-wheel motor balancer may be used. This consists of a shunt- wound or 
compound- wound direct-current motor, connected to a heavy fly-wheel 
and carrying a direct-connected exciter. The motor balancer is floated 
indirectly across the incoming line circuit, being tied in by means of a 
rotary converter or motor-generator set. A regulator actuated by the 
line current controls the direct-current motor field, so that when the 
power taken by the hoist drops below the average, the field is automati- 
cally reduced, causing the fly-wheel set to speed up and absorb power 
from the supply system and store it in the fly-wheel. When the load on 
the hoist motor exceeds the average, the operation is reversed, the fly- 
wheel set slows down, and power is returned to the system through the 
rotary converter. 

Machine Tools (Abstracted from C. Fair, General Electric Review, 1914). 
— In general, the most satisfactory electrical equipment for machine shops, 
using a large number of motors, would be one having available both A.C. 
and D.C. distribution; A.C. for all constant speed machines and D.C. for 
adjustable speed macliines. 

In the smaller shops, with rare exceptions, the choice of motors would 
depend upon the current available, which in the majority of cases would 
be alternating current. The size and product of the small factory make 
a proper layout a comparatively simple matter, while in larger factories 
skill and ingenuity are essential to obtain the most advantageous equip- 
ment. The standard motor of to-day will answer for the majority of the 
machine tools, although special motors are in some cases necessary. 

When equipping tools with individual drives, the controlling apparatus 
as well as the motor should be attached directly to the tool whenever 
possible. In the case of portables tools this, of course, is a nt^cessity. 

A graphic recording wattmeter in circuit with a tool is of value in 
efficient management, as it not only tells the actual power consumed by 



MOTOR APPLICATIONS. 



1467 



the machine, showing whether or not the tool is properly motored, but it 
also shows whether the tool is operating at its maximum rate, by register- 
ing the time of unproductive cycles or the length of time the tool is idle. 
By analysis, the cause of the lost time may be discovered and a change of 
operating conditions can be made with a corresponding increase in 
production. 

Motors for Machine Tools. 



Tool. 



Bolt cutter 

Bolt and rivet header . 

Bulldozers 

Boring machines 



Boring mills 
Raising and lowering cross rails on bor- 
ing mills and planers 

Boring bars 

Bending machines 



Bending rolls . . . . 
Corrugating rolls . 



D. C. 



Centering machines 

Chucking machines 

Boring, milling and drilling machines. . 

Drill, radial 

Drill press 

Grinder — tool, etc 

Grinder — castings 

Gear cutters 

Hammers — drop 

Keyseater — milling — broach 

Keyseater — reciprocating 

Lathes 

Lathe carriages 

Milling machines 

Heavy slab milling 

Pipe cutters 

Punch presses 

Planers 

Planers — rotary 

Saw — small circular 

Saw — cold bar and I-beam 

Saw — hot 

Screw machine 

Shapers 

Shears 

Slotters 

Swaging 



Tappers 

Tumbhng barrels or mills . 



Shunt. 


Comp. 


V 






^20% 




1 40% 




|20% 
140% 




V 




V 




** 


20% 


V 






J 20% 




(40% 


** 


J 20% 
150% 






J 20% 
150% 




V 




V 




V 




V 




V 




V 




V 


20% 


V 


20% 




(20% 




(40% 


V 






20% 


V 




** 


50% 


V 




V 


20% 


V 






120% 
140% 






§20% 


V 


10% 


V 






20% 




20% 


V 




V 


10% 




(20% 
40% 




V 


20% 




)20% 

140% 


V 

.... 


"20%" 



A.C. 



* Squirrel cage rotor. 

t Squirrel cage rotor — high starting torque. 

% Slip ring induction motor with external rotor resistance. 

§ Does not apply to reversing motors. 

** D. C. series motor. 



1468 ELECTRICAL ENGINEERING. 

The table on p, 1467 will, in a general way, aid in the choice of motors. 
The great variety and size of tools of the same name make it necessary 
in a general Ust, such as this, to double-check a number of tools. It 
must be kept in mind, however, that various circumstances, such as size 
and roughness of work, and fly-wheel capacity, etc., may call for radical 
departures in the choice of motors, this list being compiled to meet average 
conditions. 

Shunt motors, for instance, are used in the following cases: When work 
is of a fairly steady nature, when considerable range of adjustment of 
speed is required, as on lathes and boring mills, and on group and line- 
shaft drives, etc. 

Compound-wound motors are used where there are sudden calls for 
excessive power of short duration, as on planers without reversing 
motor drives, punch presses, bending rolls, etc. 

Series motors should be used where speed regulation is not essential, 
and where excessive starting torque is required, as, for instance, in moving 
carriages of large lathes, in raising and lowering the cross rails of planers 
and boring mills, and for operating cranes, etc., but not where the motor 
can be run without load, through the opening of a clutch, or by a belt 
leaving ics pulley, as the motor would run away if the operator failed to 
shut off the power. 

When in doubt as to the choice of compound or series motors of small 
horse-power, the choice might be determined by the simpUcity of control 
in favor of the series motor. 

The altematiixg-current motor of the squirrel-cage rotor type corre- 
sponds to the constant-speed, shunt, direct-current motor; but with a 
iugh-resistance rotor it approaches more closely the characteristics of a 
compound, direct-current motor. It is understood that the variable- 
speed machines checked in the table above under the alternating-current 
squirrel-cage rotor column have the necessary raechanical speed changas. 

The slip-ring induction motor with external rotor resistance would be 
used for variable speed, but this must not be construed to mean that it 
corresponds to a direct-current, adjustable-speed motor, as it has the 
characteristics of a direct- ciu-rent shunt motor with armature control. 

The self-contained, rotor resistance type could be used for lineshaft 
drives, and for groups when of s,ufQcient size. 

Multi-speed, alternating-current motors are those giving a number of 
definite speeds, usuaUy 600 and 1200, or 600, 900, 1200, and 1800 r.p.m., 
and are made for both constant power and constant torque. These motors 
would be used where alternating current only was available, and where 
the speed ranges of the motor, together with one or two change gears, 
would give the required speeds. These motors should, however, be used 
with discretion, especially on sizes above six horse-power. 

The adjustable speed, A.C., commutator brush-sliifting type of motor 
with shunt characteristics would, on account of high cost, be used mostly 
where an adjustable speed motor was liighly desirable and where A.C 
only wa^ available and where there were not enough machines caUing for 
adjustable speed drive to warrant putting in a motor-generator set. 

ILLUMINATION— ELECTRIC AND GAS LIGHTING.* 

niumination . — Some writers distinguish "lighting" and "illumina- 
tion." Lighting refers to the character of the hghts themselves, as 
dazzling, brilliant, or soft and pleasing, and illumination to the quantity 
of light reflected from objects, by which they are rendered visible. If 
the objects in a room are clearly seen, then the room is well illuminated. 

The quantity of light is estimated in candle-power per square foot of 
area or per cubic foot of space. The amount of illumination given by 
one candle at a distance of 1 ft. is known as a foot-candle. Since the 
illumination varies inversely as the square of the distance, one foot- 
candle is given by a 16-candle-power lamp at a distance of 4 ft., or by a 
25-C.-P. lamp at a distance of 5 ft. 

Terms, Units, Definitions. — Quantity of light proceeding from a 
source of light, measured in units of luminous flux, or lumens. 

Intensity with which the flux is emitted from a radiant in a single 
direction, called candle-power. 

Illumination, density of the light flux incident upon an area. 

^ Contributed by Prof. W. H. Timbie. 



ILLTJMINATION. 1469 

Luminosity, brightness of surface; flux emitted per unit area of 
surface. 

Candle-power, the unit of luminous intensity. A spermaceti candle- 
burning at the rate of 120 grains per hour is the old standard used in 
the gas industry. It is very unsatisfactory as a standard and is being 
displaced by others. 

The hefner lamp, burning amyl acetate, is the legal standard in Ger- 
many. The imit of luminous intensity produced by this lamp when 
constructed and operated as prescribed is called a hefner. The standard 
laboratories of Great Britain, France, and America have agreed upon 
the following relative values of the units used in the several countries: 
1 International Candle = 1 Pentane Candle = 1 Bougie Decimale = 1 
American Candle = 1.11 Hefners = 0.104 Carcei unit. 1 Hefner = 
0.90 International Candle. 

Intrinsic Brilliancy of a source of Ught = candle-power per square 
inch of surface exposed in a given direction. 

Lumen, the unit of liuninous flux, is the quantity of light included in 
a unit solid angle and radiated from a source of imit intensity. A unit 
solid angle is the angular space subtended at the surface of a sphere by 
an area equal to the square of the radius, or by 1 -^477, or 1/12.5664 of 
the surface of the sphere. The light of a source whose average intensity 
in all directions is 1 candle-power, or one mean spherical candle-power, 
has a total flux of 12.5664 lumens. 

Foot-candle, the unit of illumination, = 1 lumen per square foot; the 
illumination received by a surface every point of which is distant one 
foot from a source of one candle-power. 

Lux, or meter-candle, 1 lumen per square meter; 1 foot-candle = 10.76 
meter-candles. 

Law of Inverse Squares. — The illumination of any siu-face is inversely 
proportional to the square of its distance from the source of light. This 
is strictly true when the source of light is a point, and is very nearly 
true in all cases when the distance is more than ten times the greatest 
dimension of the light-giving siu-face. 

Law of Cosines. — When a surface is illuminated by a beam of hght 
striking it at an angle other than a right angle, the illumination is pro- 
portional to the cosine of the angle the beam makes with a normal to 
the surface. 

If E = the illumination at any point in a surface, I the intensity of 
hght coming from a source, the angle of deviation of the direction of 
the beam from a normal to the surface, and I the distance from the 
source, then E = I cos ^ l^. 

Relative Color Values of Various lUuminants. — The light pro- 
ceeding from any source may be analyzed in terms of the elementary 
color elements, red, green and blue, by means of the spectroscope, or by 
a colorimeter. The following relative values have been obtained by 
the Ives colorimeter {Trans. Ill, Eng. Soc, iii, 631). In aU cases the 
red rays in the hght are taken as 100, and the two figures given are 
respectively the proportions of green and blue relative to 100 red. 

Average davUght, 100,100. Blue sky, 106,120. Overcast sky, 92, 85. 
Afternoon suriUght, 91, 56. Direct-current carbon arc, 64. 39. Mercury 
arc (red 100), 130, 190. Moore carbon dioxide tube, 120, 520. Wels- 
bach mantle, 3/4% cerium, 81, 28. Do., li/4 7o cerium, 69, 14.5. Do., 
13/4% ceriimi, 63, 12.3. Tungsten lamp, 1.25 watts per mean horizon- 
tal candle-power, 55, 12.1. Nernst glower, bare, 51.5, 11.3. Tantalum 
lamp, 2 watts per m. h. c.-p., 49, 8.3. Gem lamp, 2.5 watts per m. h. 
c.-p., 48, 8.3. Carbon incandescent lamp, 3.1 watts per m. h. c.-p., 45, 
7.4. Flaming arc, 36.5, 9. Gas flame, open fish-tail burner, 40, 5.8. 
Moore nitrogen tube, 28, 6.6. Hefner lamp, 35, 3.8. 

Relation of Illumination to Vision. — Wickenden gives the following 
summary of the principles of effective vision : 

1. The eye works with approximately normal efficiency upon sur- 
faces possessing an effective luminosity of one foot-candle or more. 

2. Excessive Illumination and inadequate illumination strain and 
fatigue the eye in an effort to secure sharp perception. 

3. Intrinsic brilhancy of more than 5 c.-p. per sq. m. should be re- 
duced by a diffusing medium when the rays enter the eye at an angle 
below 60° with the horizontal. 



1470 ELECTRICAL ENGINEERING. 

4. Flickering, unsteady, and streaky illumination strains the retina 
in the effort to maintain uniform vision. 

5. True color values are obtained only from hght possessing all the 
elements of diffused daylight in approximately equivalent proportions* 

6. An excess of ultra-violet rays is to be avoided for hygienic reasons. 

7. Esthetic considerations commend hght of a faint reddish tint as 
warm and cheerful in comparison with the cold effects of the green tints, 
although the latter are more effective in reveahng fine detail. 

Types of Electric Lamps.— The carbon arc lamp is now rapidly dis- 
appearing on account of the cost of maintenance of the open type and 
the low efficiency of the enclosed type. Gas-fiUed tungsten lamps now 
operate at less cost on the same circuits on which these arcs formerly 
burned. 

The Flaming Arc. — The carbons are impregnated with calcium fluor- 
ide or other luminescent salts. The current is usually 8 to 12 amperes 
and the voltage per lamp 35 to 60. The regenerative flame arc is a 
highly efficient variety of the flame arc. 

The Magnetite Arc has for a cathode a thin iron tube packed with a 
mixture of magnetite, Fe304, and titanium and chromium oxides. The 
anode consists of copper or brass. It is weU adapted to series opera- 
tion with low currents. The 4-ampere lamp, using 80 volts per lamp, 
is highly successful for street iUumination. 

The Tungsten Incandescent {vacuum) depends upon the heating of 
a drawn tungsten filament to incandescence in a vacuum. They are 
made in sizes for 25, 40, 60, 100, 150, 250, 400, 500, 750, and 1000 watts 
and average about 1 candle-power for each watt, with a hfe of 1000 
hours, before the candle-power falls below 80% at rated voltage. 

The Tungsten Incandescent {gas-filled) has the advantage of having 
longer hfe and being smaller than the vacuum lamp of the same watt- 
age. They are filled with an inert gas, generally nitrogen or argon, 
and have an efficiency of 2 candle-power per watt in the larger sizes 
(the average being about 1.7 candle-power per watt), with a hfe of 
1300 hours. 

The Mercury Vapor Lamp is an arc of luminous mercury vapor con- 
tained in a glass tube from which the air has been exhausted. A small 
quantity of mercury is contained in the tube, and platinum wires are 
inserted in each end. When the tube is placed in a horizontal position 
so that a thin thread of mercury hes along it, making electrical con- 
nection with the wires, and a current is passed tlirough it, part of the 
mercury is vaporized, and on the tube being inclined so that the hquid 
mercury remains at one end, an electric arc is formed in the vapor 
throughout the tube. The tubes are made about one inch in diameter 
and of different lengths, as below. The mercury vapor lamp is very 
efficient, ranging from 1.9 c.-p. per watt for the 900 c.-p. size to 1.55 
c.-p. per watt for the 300 c.-p. size. The color of the light is unsatis- 
factory, being deficient in red rays, but it possesses a very penetrating 
quality which makes it valuable in drafting rooms and wherever a 
hght is needed to bring small details out sharply. The spectrum con- 
sists of three bands, of yellow, green, and violet, respectively. The 
intrinsic briUiancy of the lamp is very moderate, about 17 c.-p. per sq. 
in. Commercial lamps are made of the sizes given below. The lamp 
is essentially a direct-current lamp, but it may be adapted to alternat- 
ing-current by use of the principle of the mercury-arc rectifier. The 
tubes have a life ordinarily of about 1000 hours. 

The Quartz-Tube Mercury-Arc Lamp operates at a higher voltage 
and gives much nearer a white light. Owing to the injurious ultra- 
violet rays given out by this form, it must always be enclosed in a 
globe of clear glass. The efficiency ranges from 2.4 to 3.3 c.-p. per 
watt and the hfe averages 3000 hours. It is made in sizes from 1000 
to 3500 c.-p. 

Street Lighting. — Street lighting may be divided into three classes: 

(a) "White- Way" or display illumination. 

(b) Main road illumination. 

(c) Residence district lighting. 

The object of " White-Way'' iUumination is generally advertising and 
many more lights are used than are necessary for proper road illumina- 
tion. The lamps generally used are the titanium arc, the magnetite 



ILLUMINATION. 



1471 



arc, the yellow flaming arc, and the white flaming arc of over 1000 c.-p. 
See last column of Table VI. 

In ''Main-road" illumination the purpose is to illuminate tlie road 
appreciably for night automobile travel. The lamps generally used 
are some type of the 300-watt flaming arc, the magnetite arc, or the 
titanium arc of Table IV. These are usually placed from 200 to 300 
ft. apart at heights varying from 15 to 18 ft. 

For Residential-district Lighting, where vehicle travel is infrequent 
and slow, the smaller sizes (40 to 100 c.-p.) of tungsten lamps are used 
spaced from 100 to 200 ft. at height varying from 15 to 18 ft. according 
to shading of the road by the fohage. Tungsten lamps of the higher 
candle-powers of 200 to 450 are also used with spacings of 200 ft. and 
over, with reflectors designed. to give the best distribution of the Hght. 

Dlumination by Arc Lamps at Diflferent Distances. — Several dia- 
grams and curves showing the light distribution in a vertical plane 
and the illumination at different distances of different types of lamps 
are given by Wickenden. From the latter are taken the approximate 
figures in the table below. The carbon and the magnetite lamps were 
25 ft. high, the flame arcs 21 ft. 

TABLE I. — niumiuation by Arc Lamps. 



Horizontal Distance from Lamp, Feet. 


20 


30 


40 


50 


100 


150 


200 


250 


Kind of Lamp. 


Foot-candles, normal illumination. 


A. Open carbon arc, D.C., 6.6 amp. 

B. Enclosed carbon arc, A.C. 6.6 " 

C. Flame arc, 10 

D. Regenerative arc, 7 ** 

E. Magnetite arc, 6.6 *' 

F. Magnetite arc, 4 " 


6:30 
0A7 


0.40 
0.19 

i'.oo 

0.40 


0.29 
.135 

6!85 
0.69 
0.30 


0.20 
0.10 
1.10 
0.65 
0.51 
0.21 


.032 

.027 

.31 

.15 

.15 

.07 


.0\A 

.013 

.14 

.055 

.075 

.035 


.006 

.006 

.08 

.03 

.045 

.022 


.002 

.002 

.05 

.02 

.025 

.018 



A. 6.6 amp., D.C., open arc, clear globe. 

B. 6.6 amp., A.C, enclosed arc, opal inner and clear outer globe, 
small reflector. 

C. 10 amp., flame arc, vertical electrodes; 50 volts, 1520 M.H. C.-P.*; 
0.33 watt per M.L.H. C.-P.*; 10 hours per trim. 

D. 7 amp., regenerative flame arc, 70 volts, 2440 M.L.H.C.-P., 0.2 
watt per M.L.H.C.-P., 70 hours per trim. 

E. 6.6 amp., D.C. series magnetite arc, 79 volts, 510 watts, 1450 
M.L.H.C.-P. 75 to 100 hours per trim. 

F. 4 amp., D.C. series magnetite arc, 80 volts, 320 watts, 575 M.L.H. 
C.-P., 150 to 200 hours per trim. 

TABLE n. — Data of Some Arc Lamps. 



Type of Lamp. 


Hours 
Trim. 


Am- 
peres. 


Ter- 
minal 
Volts. 


Ter- 
minal 
Watts. 


Watts 

per 

M.L.H. 

C.-P. 


D.C. series carbon, open 

D.C. series carbon, enclosed 

A.C. series carbon, enclosed 

D.C. multiple carbon, enclosed. . 
A.C. multiple carbon, enclosed... 
D.C. flame arcs, open 


9 to 12 

100 to 150 

70 to 100 

100 to 150 

70 to 100 

10 to 16 

70 
10 to 16 
70 to 100 


9.6 
6.6 
7.5 
5.0 
6.0 

10 
5 

10 
6.6 


50 
72 
75 

no 
no 

55 
70 
55 
80 


480 
475 
480 
550 
430 
440 
350 
467 
528 


0.6 

0.9 

1.25 

2.25 

2.40 

0.45 


Regenerative, semi-enclosed 

A.C. flame arcs, open 


0.26 
0.55 


Magnetite, open 


0.45 



Values of watts per M.L.H. C- 
magnetite arcs with clear globes, 
clear outer globes, and for flame 



P. approximate for open carbon arcs and 
enclosed arcs with opalescent inner and 
and regenerative arcs with opal globes. 



*M.H.C.-P. =mean horizontal candle-power; 
M.L.H.C.-P. =mean lower hemispherical candle-power. 



1472 



ELECTRICAL ENGINEERING. 



Relative Efficiency of Illuminants. — The advent of the gas-filled 
tungsten incandescent lamp of high efficiency and high candle-power 
has driven the less efficient arc lamps from the field. At present (1915) 
the incandescent lamp of the 200- or 300-watt size is more efficient than 
the arc lamp of the same candle-power. On the other hand, the 1000- 
c.-p. arcs are more efficient than the incandescent lamps of the same 
size. The field for the arc lamp seems to be in the higher candle-power 
sizes. Dr. Steinmetz in The General Electric Review for March, 1914, 
gives the following tables. 

TABLE m. — Relative Efficiency of Illuminants. 

(Irrespective of Size, in Available Mean Spherical C.-P. per Watt). 





Available 

Mean 

Spherical 

C.-P. per 

Watt. 


(Street 
Lighting) 
10° C.-P.* 
per Watt 


Available 
Mean 

Spherical 
C.-P. 


3.1 watt per h. c.-p. carbon filament. , . . 

2.5 watt per h. c.-p. gem filament 

450 watt 6.6 amp. series enclosed a.c. 
carbon arc 


0.21 
0.26 

0.39 
0.45 

(3.62 

0.64 

0.78 

1.0 

1.1 

1.28 

1.4 

1.5 
1.55 

1.7 

1.9 

1.95 

1.95 

2.0 

2.7 

2.88 

3.1 

3.6 

5.2 


0.4 
0.5 

0.5 

1.0 
1.25 

'"2.'2" 

3.0 
3.2 

3.6 
4.0 
4.0 
4.0 
. . .^.^ . . 

■"6.2 ■■ 
7.0 


Any 
Any 

175 


Nitrogen Moore tube 




480 watt 6.6 amp. series enclosed d.c. 
carbon arc . 


300 


1 watt per h. c.-p. mazda lamp 


Any 

' "ioo"* 


500 watt d.c. "intensified" carbon arc . . . 
4 amp. 300 watt d.c. special magnetite arc 
Neon Moore tube 


0.5 watt per h. c.-p. gas-filled mazda lamp 
4 amp. 300 watt d.c. special magnetite arc 
6.6 amp. 500 watt d.c. standard magnetite 
arc 


Above 350 
(420) 

750 


Mercury lamp in glass tube, best values. 

6.6 amp. 500 watt d.c. special magnetite 

arc 


850 


220 watt a.c. titanium arc 


420 


300 watt yellow flame arc, best value. . . . 
500 watt white flame arc, best values. . . . 
Mercury lamp in quartz tube, best values 

Exper. 350 watt a.c. titanium arc 

Melting tungsten in vacuum 


(585) 
(975) 

■■(950)" 


500 watt yellow flame arc, best value. . . . 

Exper. 500 watt a.c. titanium arc 

Titanium arc, best values (high power) . . 


(1550) 
(1800) 



*The expression 10° c.-p. per watt means the candle-power per watt 
on a circle 10° below the horizontal plane of the filament. 



TABLE IV.— Efficiency of 300-Watt Illuminants. 





Available 

Mean 

Spherical 

C.-P. per 

Watt. 


Available 
Mean 

Spherical 
C.-P. 


Mazda lamp (1 watt per h. c.-p) 

Standard 4 amp. d.c. magnetite arc 


0.64 

1.0 

1.2 

1.28 

1.4 

1.95 

2.4 


190 
300 


White flame carbon arc, best . ... 


360 


Gas-filled mazda lamp (0.5 watt per h. c.-p.) 

Special 4 amp. d.c. magnetite arc 


384 
420 


Yellow flame carbon arc, best 


585 


A.C. titanium arc 


720 



ILLUMINATION. 



1473 



TABLE V.—Efflclency of 500-Watt lUumlnaiits. 




Available 
Mean 

Spherical 
C.-P. 



A.C. series enclosed carbon arc 

Mazda lamp (1 watt per h. c.-p.) 

D.C. series enclosed carbon arc 

Gas-filled mazda lamp (0.5 watt per h. c.-p.) 

Standard 6.6 amp. d.c. magnetite arc 

Special 6.6 amp. d.c. magnetite arc 

White flame carbon arc, best 

Quartz mercury lamp 

Yellow flame carbon arc, best 

A.C. titanium arc 



210 
320 
325 
640 
750 
850 
975 
1000 
1550 
1800 



Characteristics of Tungsten Lamps. Vacuum Type. — The accom- 
panying Table VII refers to tungsten lamps of the 25, 60, and 100 watt 
size. They show the changes which take place in the candle-power, 
watts, watts per candle-power and Ufe when used at the various voltages. 
It is to be noted that a 4% increase in voltage above the normal (100%) 
increases the candle-power 15%, the efficiency 6%, but decreases the 
life 38%. 

TABLE VI.— Relative Efficiency of Various C-P. of Dluminants. 



200 Mean 

Spherical 

C.-P. 


300 Mean 

Spherical 

C.-P. 


400 Mean 

Spherical 

C.-P. 


500 Mean 

Spherical 

C.-P. 


1000 Mean 

Spherical 

C.-P. 


Type. 




Type. 


3i 


Type. 


ii 

1 


Type. 


il 

^ 


Type. 


1 


A.C. 

carbon 

D.C. 

carbon 

Mazda 


490 

380 
310 


A.C. 

carbon 

D.C. 

carbon 

Mazda 

Standard 
magnetite 
Special 
magnetite. . 


620 

480 
470 

300 
250 


Mazda .... 
Standard 
magnetite. 
Gas-filled 

mazda 

Special 
magnetite. . 

Titanium . . 


620 
350 
310 


Standard 
magnetite . . 
Gas-filled 

mazda 

Special 
magnetite . . 
White 


400 

390 

350 

350 

280 
250 


Gas-filled 

mazda 

Standard 
magnetite. . 
Special 
magnetite. . 
White 

Flame 

Yellow 

Flame 

Titanium . . 


780 
700 
550 






290 Flame 

Yellow 


520 






210 


Flame 

Titanium. . 


400 
360 



Interior Illumination. — There are three systems for artificially light- 
ing interiors. All three are easily adapted for the use of either gas or 
electricity or both: (1) Direct hghting; (2) indirect lighthig; (3) semi- 
indirect lighting. 

(1) Direct Lighting. — When the room is illuminated almost entirely 
by the light which comes directly from the lamps without reflection 
from walls and ceiUngs, it is said to be illuminated by direct lighting. 
This is the usual form of hghting. 

(2) Indirect Lighting. — When a room is illuminated by the light of 
concealed lamps which is reflected from the walls and ceiling, the 
system of illumination is said to be indirect. The ceihng and walls 
must be Ught-colored. There is an entire lack of shadows in a room 
thus hghted. 

(3) Semi-indirect Lighting. — When a room is illuminated mostly by 
light reflected from the walls and ceihng but still receives 15 or 20% 
directly from the lamps, the system of illumination is said to be semi- 
indirect. This system produces particularly pleasing effects. 

Tlie Quantity of Electricity and Gas Necessary to Dluminate Various 
Rooms. — Practically all modem illumination is done either by tungsten 
incandescent electric lamps or gas lamps with incandescent mantles. 



1474 



ELECTRICAL ENGINEERING. 





TABLE Vn 


. — Characteristics of Mazda (Vacuum) Lamps. 












■M 


SR 










^ 


_^ 






.1 


.«cC 


i 




"3 


2 




J 


-^ 


-1 




^3 






o'o 


o '. 


1^ 




5:t_Z 


0.i3 


©"o 








o S 


o^ 


01 TJ 


St3 


gft 






=2 




§T3 


r- 






=2 


v^ 


O^ 


O^ 


•s(^ 


o^ 


o^ 


u^ 


U-lii 


U^ 


■t^ 


U5 


OB 


§3^ 


^c^ 


^Ph 


Sn 


"t o 




fc^ 


a3;S 


fctf 


a5p2 


Bn 






^>nl 


PW 


^ 


pm 


w 


h^l 


^ 


Ph 


m 


ti^ 


Ph 


w 


^ ^ 


Ph 


Plh"^ 


50 


8 
15 
27 


33 
44 
57 






67 
72 
82 


77 
80 
87 


102 
104 
106 


108 
115 
123 


103 
106 
110 


0.934 
0.971 
1.01 


80 
62 
48 






60 


0.231 
0.429 








70 


103 


102 


75 


36 
45 


63 
71 


0.500 
0.578 




84 
88 


88 
92 


108 
110 


130 
139 


113 
117 


1.03 
1.08 


35 
25 






80 


106 


104 


85 


57 


77 


0.658 




91 


94 


115 


161 


125 


1.16 




108 


106 


90 


69 


85 


0.736 




94 


96 


120 


187 


n3 


1.27 




112 


108 


97 


75 

81 


88 
91 


0.769 
0.799 








125 
130 


213 
242 


142 


1.35 
1.47 




114 
117 


110 


94 


230 


96 


98 


112 


96 


87 
93 
100 


94 
97 
100 


0.833 
0.880 
0.909 


180 
135 
100 






140 
150 


.... 




1.67 
1.85 




122 
127 


115 


98 






118 


100 


100 


100 

















The following table of electricity and gas necessary to light rooms 
used for given purposes is based on the fact that in the modern mazda 
lamps 1.1 watt produces 1 c.-p., and in the best gas lamps with incan- 
descent mantles, 0.04 cu. ft. per hour of gas produces 1 c.-p. Inasmuch 
as there are no bright spots in the room to fatigue the eye, when in- 
direct and semi-indirect systems are used, a lower degree of illumina- 
tion is sufficient to enable objects to be clearly seen. Hence, although 
the indirect and semi-indirect systems are less eflQcient, the following 
table applies to all these methods: 



TABLE Vm. — Electricity or Gas Necessary to Sufficiently 
Illuminate Booms. 





Watts 


Cu. Ft. 




Watts 


Cu. Ft. 




per Sq. 


per Hour 




per Sq. 


per Hour 


Use of Rooms. 


Ft. of 
Work- 


per Sq. 
Ft. of 


Use of Rooms. 


Ft. of 
Work- 


per Sq. 
Ft. of 




ing 


Working 




ing 


Working 




Plane. 


Plane. 




Plane. 


Plane. 


Assembly hall 


0.8-0.1 


0.032-0.04 


Library (book 






Ball room 


1.2-1.3 


0.05 -0.052 


stacks) 


0.3-0.6 


0.012-0.24 


Barber shop 


1.5-1.7 


0.06 -0.07 


Library (resi- 






Bed room (resi- 






dence) 


1.0-1.1 


0.04 -0.044 


dence) 


0.3-0.35 


0.012-0.014 


Lobby (hotel) 


1.5-1.6 


0.06 -0.065 


Church 


1.0-1.3 


0.04 -0.05 


Machine shop. . . . 


2.0-2.2 


0.08 -0.0:3 


Class room 






Music room (resi- 






(school) 


1.2-1.3 


0.048-0.052 


dence) 


0.5-0.6 


0.02- 0.025 


Corridor 


0.4-0.5 


0.016-0.02 


Office (banking 






Dining room 






and accounting) . 


1.5-1.6 


0.06 -0.065 


(residence) 


0.9-1.0 


0.036-0.04 


Office (general). . . 


1.3-1.5 


0.052-0.06 


Drafting room . . . 


2.5-2.8 


0.10 -0.112 


Operating room 






Drill hall 


0.5-0.6 


0.02 -0.025 


(hospital) 


3.5-3.9 


0.14 -0.15 


Foundry 


3.0-4.0 


0.12 -0.16 


Restaurant 


1.5-1.7 


0.06 -0.07 


Kitchen 


1.2-1.3 


0.05 -0.052 


Store 


1.4-1.7 


0.055-0.07 


Library (public 






Warerooms 


0.3-0.9 


0.012-0.030 


reading room).. . 


1.4-1.5 


0.055-0.06 


Wood-working 












shop 


1.5-1.8 


0.06 -0.072 



For gas-filled tungsten and Welsbach "Kinetic" use 0.6 of abov^ 
values, Data on gas furnished by F. R. Pierce, Welsbach Co. 



ILLUMINATION. 



1475 



Example of Use of Table Vm. 

Specify the proper lighting arrangements for a banking office 25 ft. X 
40 ft. with a 13-ft. ceiUng. 

The four-lamp fixture is an efficient and pleasing arrangement of 
lamps. It does not give quite as uniform distribution of light as 
individual lamps imiformly spaced, but the effect is much more pleasing 
and the distribution is very satisfactory. 
Using Electricity. — 
Watts per sq. ft. needed = 1.5 - 1.6 (Table VIII). 
Total watts needed = 1.5 X 40 x 25. 

= 1500 watts. 
Using four-lamp fixtures, we shall need six fixtures, as in Fig. 250, in 
two rows of 3 each. 

Watts per fixture = i^ = 250. 

D 

250 
Watts per lamp = ■ • = 62.5. 

On consulting Table IX we find we can use 60-watt lamps as the 
standard lamp nearest the size computed. If at any place more light 

is needed, 100-watt lamps may be 
substituted in the nearest fixture. 

Using Gas. — To use gas with the 
same number of similar fixtures, we 
would have to use lamps which 
correspond to the 60-watt mazda. 
Allowing 25 watts to the cu. ft. per 
hour of gas, we would need a lamp 

which would bum j— or 2 1/2 cu. ft. 

Jo 
per hour of gas. By Table IX, we 
see that this is a standard size. 
The foregoing rules are merely 
Fig 250 intended to serve as a guide for 

planning correct illumination. They 
are not intended to take the place of judgment and intelligence. The 
details of each lighting project differ shghtly from the details of every 
other fighting project and due weight should be given to ways in which 
these details affect the appUcation of general rules. 




TABLE EX.— Standard IJnits; Mazda and Welsbach. 



Watts 


C.-P. 

per 

Watt. 


Welsbach 
Inverted. 


Watts 

(105- 

125 

Volts). 


C.-P. 

Watt. 


Welsbach 
Inverted. 


Welsbach 
Upright. 


(105- 
125 

Volts). 


Cu. 
Ft. 


Equiv. 
Watts 

Hour. 


Cu. 
Ft. 


Equiv. 
Watts 

Hour. 


Cu. 
Ft. 


Equiv. 
Watts 

Hour. 


10 


0.77 

0.80 

0.855 

0.88 

0.91 

0.935 

0.98 


















15 






150 
250 
400 
500 
750 
1000 


1.11 
1.11 
1.33 
1.43 
1.67 
1.82 










20 






10 


250 






25 










40 


1.6 
2.5 

4.0 

4.5 


40 

62.5 
100 
112.5 










60 










100 
















5.5 


135.5 



Cost of Electric Lighting. (A. A. Wohlauer, El. World, May 16. 
1908, corrected, July, 1915.) — The following table shows the relative 
cost of 1000 candle-hours of illumination by lamps of different kinds, 
based on costs of 2, 4 and 10 cents per Kw.-hour for electric energy. 
The life, K, is that of the lamp for incandescent lamps, of the electrode 
for arc lamps, and of the vapor tube for vapor lamps. 



1476 



ELECTEICAL ENGINEEKINa. 



Lg = mean spherical candle-power. 
Sg = watts per mean spherical candle. 
P = renewal cost per trim or life, cents. 
K = life in hours. 
Cy= 1000 P/iKLs). 

Ci = {Ss XR) ■^Cj. = cost'per 1000 candle-hours. 
R = rate in cts. per K.W. horn*. 



Illuminant. 



Amp, 



Volts. 



^s\^s 



K 



6, 



Rating. 



Ct=(SsXR) 
+Cr 









Incandescent Lamps. B 


=2 


4 10 


Carbon 

Gem 


0.31 
0.45 
0.91 


110 

no 

110 


13.2 3.8 
16.5 3.05 
72 1.4 


16 
20 
70 


450 
450 
1000 


2.7 16c.-p. 
2.7 20c.-p. 
0.97 100 Watt 


10.3 
8.8 
3.8 


17.9 40.7 
14.9 33.2 


Tungsten 


6.6 15.0 



Direct-Current Arc Lamps. 



Open arc 

Enclosed 

Carbon 

Miniature 

Magnetite. . . . 

Flaming 

Inclined flam- 
ing .. . 

Inclined en- 
closed flaming 



10 
5.0 

)J0 
2.5 
3.5 

10 

10 
5.5 



55 

no 
no 
no 
no 

55 
55 

100 



400 
260 
550 
150 
225 
600 

1100 

1500 



1.3 
2.1 
2.0 
1.8 
1.7 
0.75 

0.5 

0.365 



10 
150 

16 

20 
150 

10 

10 

70 



2 

0.2 

1 

2 

0.31 

2.4 

1.6 

0.1 



10 amp. 


4.6 


7.2 


15 


5 


4.4 


8.6 


21.2 


10 


5 


9 


21 


2.5 


5.6 


9.2 


20 


3.5 


3.71 


7.n 


17.3 


10 


3.9 


5.4 


9.9 


to 


2.6 


3.6 


6.6 


5.5 


1.03 


1.76 


4 



Mercury- Vapor Lamps. 



Cooper Hewitt 3.5 
Quartz 3.5 



no 

220 



770 
1300 



0,5 11200 4000 0.4 
0.6 1 700 3000 0.135 



3.5 amp. 1:4 |2.4 5.4 
3.5 1.3412.54 6.14 



Recent Street Lighting Installations. 

(Preston S. Millar, Proc. A, I. E, E., July, 1915). 



b 






it 








II 


fl 


Lamps.io 


1' 





1 
2 

3 
4 

5 

6 
7 

8 


36 
47 
42 
80 

901] 

109 
60 


50 
90 

102 

222 

82 

(twin) 

123 

2003 


80 
69 
94 
100 

[ 112 

100 
100 
100 
400 
92 
105 
220 
120 


18 
24 
25 
14.5 

14 

15 

19 

13.5 

17.5 

19.8 

22 

22 

10.25 


B 

* b' 

B 

B 

A 
B 
B 
R 
B 

R 




S 

s 


s 

s 
s 

s 


note' 

notes 

S 


K 
P 
P 
P 

P 

P 
P 
P 
P 
K 
P 
P 
P 


D.C., 6.6 amp. LA. 

A.C., SF. 

A.C., SF. 

6.6 amp. Mag. 

600 c.-p. Mazda C. 

6.6 amp. Mag. 

I20v., 400w M.C. 

400 c.-p., 15 amp. M.C. 

1000 c.-p. M.C. 

4.0 amp. D.C. LA. 

120v., 400w., M.C. 

600 c.-p. M.C. 

5.5 amp. series M.C. 


A 
B 
B 
A 

N 

A 
C 
R 


9 
10 

n 

12 
13 


50 
92 
80 
36 
502 


56 
'"79" 
**246" 


A 
A 
C 
B 
B 



(Notes.) — 1 Between building Unes. 2 i^o ft. between building Unes. 
8 Two per post. ^ Along one curb. ^ Kind of buildings: B, business 
structures; A, all kinds; Ap., apartments; R, residences, ^o, both 
curbs, opposite; S, staggered. 7 in center of block (on center isle). On 
curb of intersecting streets at house line of cross-street intersection. 
• East curb only. »K, brackets on trolley poles; P, ornamental posts. 



ELECTRICAL SYMBOLS. 



1477 



10 LA, luminous arc; SF, series flame arc; Mag., inverted magnetite; 
M.C., Mazda C. n A, alabaster; B, alba; N, novulux; C, Carrara; 
R, C.R.I. , globe and translucent glass reflectors. 

Cities. — 1. 5th Ave., Pittsburgh; 2. Federal St., Pittsburgh; 3. 
Dearborn St.^ Chicago; 4. Main St., Rochester, N. Y.; 5. Main St., 
Hartford, Conn.; 6. Penna. Ave., Washington, D. C; 7. 5th Ave., 
New York; 8. Market St., Coming, N. Y.; 9. Lake Ave., Rochester; 
10. Grand Ave., Milwaukee; 11. 7th Ave., New York; 12. Troy St., 
Chicago; 13. 16th St., Washington. 

SYMBOLS USED IN ELECTRICAL DIAGRAMS. 






'SPST 
I^SPDT 
: DPST 



DPDT Galvanometer. Ammeter. 



-©- -^ 



Voltmeter. 



Wattmeter^ 



Switches; 5, single; .^wv^c 
D, double; P. pole; Non-inductive 
2 , throw. Resistance. 



Inductive 
Resistance. 



Capacity 
or Condensef. 



Lamps. 



15 



fc 



Motor Shunt-wound Motor Series-wound 
or Generator. or Generator. Motor or Generator. 




Two-phase Three-phase Battery. Trans- Compound- Separately 
Generator. Generator. former, wound Motor excited Motor 

or Generator, or Generator. 



INDEX. 



ABBREVIATIONS, 1 
Abrasion, resistance to, of 
manganese steel, 495 
Abrasive processes, 1309-1318 
Abrasives, artificial, 1313 
Abscissas, 70 
Absolute temperature, 567 

zero, 567 
Absorption of gases, 605 
of water by brick, 370 
refrigerating machines, 1346, 
1364 
Accelerated motion, 526 
Acceleration, definition of, 521, 
526 
force of, 526 

rates of, on electric railways ,1415 
work of, 529 
Accumulators, electric, 1425 
Acetylene and calcium carbide, 
855 
blowpipe, 857 
flame welding, 488 
generators and burners, 857 
heating value of, 856 
Acheson's deflocculated graphite, 

1246 
Acme screw thread, 234 
Adhesion between wheels and 

rails, 1416 
Adiabatic compression of air, 633 
curve, 959 
expansion, 601 

expansion in compressed air- 
engines, 638 
expansion of air, 635, 638 
expansion of steam, 959 
Admiralty metal, composition of, 

390 
Admittance of alternating cur- 
rents, 1441 
Aerial tramways, track cable for, 

260 
Air (see also Atmosphere) , 606-681 
and vapor mixture, weight of, 

610-613 
-boimd pipes, 748 
carbonic acid allowable in, 681, 

685 
compressed, 623, 632-653 
(see Compressed air) 
Air Compressors, centrifugal, 648 
effect of intake temperatures, 

647 
electric motors for, 1465 



Air compressors, high altitude, 
table of, 639 

hydraulic, 650 

intercoolers for, 648 

steam consumption of, 644 

tables of, 641-643 

tests of, 643 
Air, contamination of, 687 

coolmg of, 594, 710 

density and pressure, 607, 613 
Air, flow of, in pipes, 617-624 

in long pipes, 618-624 

in ventilating ducts, 683 

through orifices, 615-617, 670 
Air, friction of, in miderground 
passages, 714 

head of, due to temperature 
differences, 716 

heating of {see also Heating) 

heating, heat-units absorbed in, 
691 

heating of, by compression, 632 

horse-power required to com- 
press, 637 

in feed-pump discharges, 1074 

inhaled by a man, 687 

leaks in steam boilers, 891 

-lift pump, 808 

-Uft pump for oil wells, 809 

liquid, 605 

loss of pressure of, in pipes, 
617-624 

manometer, 607 

pipes in house heating, capacity 
of, 691 

pressures, conversion table for, 
607 

properties of, 606 

-pump, 1071-1073 

-pump for condenser, 1071, 
1073 

-pump, maximum work of, 1074 

pyrometer, 555 

saturated, temperatures, pres- 
sures and volume, table, 1072 

saturated, volume at different 
vacuums, 1072 

specific heat of, 564 

thermometer. 557 

velocity of, in pipes, by ane- 
mometer, 624 

volume at different tempera- 
tures, 692 

volume transmitted in pipes, 
table, 623, 624 



1479 



1480 



air-alt 



INDEX. 



alt-ana 



Air, volumes, densities, and pres- 
sures, 607, 613 

washing, 687 

water vapor in 1 pound of, 1081 

weight and volume of, 27 

weight of, 176 

weight of (table), 609, 613 
Alcohol as fuel, 843 

denatured, 843 

engines, 1102 

vapor tension of, 844 
Alden absorption dynamometer, 

1334 
Algebra, 33-37 
Algebraic symbols, 1 
Alligation, 9 

Alloy steels, 470-480 (see Steel) 
Alloys, 384-410 

aluminum, 396-399 

aluminum-antimony, 399 

aluminum-copper, 396 

aluminum-silicon-iron, 398 

aluminum, tests of, 398 

aluminum- tungsten, 399 

aluminum-zinc, 399 

antimony, 405, 407 

bearing metal, 405 

bismuth, 404 

caution as to strength of, 398 

composition by mixture and by 
analysis, 388 

composition of, in brass foun- 
dries, 390 

copper-manganese, 401 

copper- tin, 384 

copper-tin-lead, 394 

copper-tin-zinc, 387-390 

copper-zinc, 386 

copper-zinc-iron, 393 

ferro-, 1255 

ferro-, manufacture of, 1424 

for casting under pressure, 395 

fusible, 404 

Japanese, 393 

liquation of metals in, 388 

magnetic, of non-magnetic 
metals, 402 

miscellaneous, analyses and 
properties, 392 

nickel, 402 

the strongest bronze, 389 

vanadium and copper, 395 

white metal, 407 
Alternating currents, 1440-1460 

admittance, 1441 

average, maximum, and effec- 
tive values, 1440 

calculation of circuits, 1457 

capacity, 1440 

capacity of conductors, 1446 

converters, 1453 

delta connection, 1446 

frequency, 1440 

generators, for, 1448 

impedance, 1441 

impedance polygons, 1442 

inductance, 1440 

induction motor, 1463 



Alternating currents, measure- 
ment of power in polyphase 
circuits, 1447 

motors, variable speed, 1463 

Ohm's law applied to, 1442 

power factor, 1440 

reactance, 1441 

single and polyphase, 1445 

skin effect, 1442 

standard voltages of, 1460 

synchronous motors, 1463 

transformers, 1451 

Y-connection, 1446 
Altitude by barometer, 608 
Aluminum, 177, 380 

SiUoys {see g /so Alloys), 396-399 

alloys, tests of, 398 

alloys used in automobile con- 
struction, 400 

brass, 397 

bronze, 396 

bronze wire, 248 

coating on iron, 473 

conductors, cost compared with 
copper, 1459 

effect of, on cast iron, 439 

electrical conductivity of, 1401 

plates, sheets, and bars, weight 
of, tables, 230 

properties and uses, 380 

sheets and bars, table, 230 

solder, 382-383 

steel, 496 

strength of, 381, 383 

thermit process, 400 

tubing, 226 

wire, 248, 381, 383 

wire, electrical resistance of, 
table, 1414 
Ammonia, aqua, strength of, 1341 

-absorption refrigerating ma- 
chine, 1346, 1364 

-absorption refrigerating ma- 
chine, test of, 1364 

carbon dioxide and sulphur 
dioxide, cooling effect, and 
compressor volume, 1341 

-compression machines, tests of, 
1359-1364 

-compression refrigerating ma- 
chines, 1345, 1356 

gas, properties of, 1338 

heat generated by absorption 
of, 1341 

liquid, properties of, 1340 

solubihty of, 1341 

superheated, properties of, 1340 
Ampere, definition of, 1397 
Analyses, asbestos, 270 

boiler scale, 722 

boiler water, 722 

cast iron, 439-450 

coals, 821-830 

crucible steel, 490, 494 

fire-clay. 269 

gas, 854 

gases of combustion, 817 

magnesite, 270 



ana-arm 



INDEX. 



art-baz 



1481 



Analyses of rubber goods, 378 
Analytical geometry, 70-73 
Anchor bolts for chimneys, 957 

forgings, strength of, 353 
Anemometer, 624 
Angle, economical, of framed 
structures, 548 
of repose of building material, 
1220 
Angles, Carnegie steel, properties 
of, table, 317-321 
plotting, without protractor, 53 
problems in, 38 
steel, gage lines for, 321 
steel, tests of, 362 
steel, used as beams, table of 

safe loads, 321 
trigonometrical properties of, 
66 
Angular velocity, 522 
Animal power, 532-534 
Annealing, effect on conductivity, 
1402 
effect of, on steel, 479 
influence of, on magnetic capac- 
ity of steel, 483 
malleable castings, 455 
of steel, 484, 492 (see Steel) 
of steel forgings, 482 
of structural steel, 484 
Annuities, 15-17 
Annular gearing, 1169 
Anthracite, classification of, 819, 
828 
composition of, 819, 820, 828 
gas, 845 
sizes of, 823 
space occupied by, 823 
Anti-friction curve, 50, 1232 

metals, 1223 
Anti-logarithm, 136 
Antimony, in alloys, 405, 407 

properties of, 177 
Apothecaries' measure and weight, 

18, 19 
Arbitration bar, for cast iron, 

441 
Arc, circular, length of, 58 
circular, relations of, 58 
lamps (see Electric lighting) 
hghts, electric, 1469 
Arcs, circular, table, 122-124 
Arches, corrugated, 195 
Area of circles, square feet, di- 
ameters feet and inches, 131, 
132 
of circles, table, 111-119 
of geometric lalplane figures, 

54-61 
of irregular figures, 56, 57 
of sphere, 62 
Arithmetic, 2-32 
Arithmetical progression, 10 
Armature circuit, e.m.f. of, 1436 

torque of, 1435 
"Armco ingot iron," 477 
Armor-plates, heat treatment of, 
482 



Artesian well pumping by com- 
pressed air, 810 
Asbestos, 270 

Asphaltum coating for iron, 471 
Asses, work of, 534 
Asymptotes of hyperbola, 73 
Atmosphere (see also Air) 

equivalent pressures of, 27 

moisture in, 609-613 

pressure of, 607, 608 
Atomic weights (table), 173 
Austenite, 480 
Autogenous welding, 488 
Automatic cut-off engines, water 

consumption of, 967 
Automobile engines, rated capac- 
ity of, 1101 

gears, efficiency of, 1172 

screws and nuts, table, 232 
Automobiles, steel used in, 510 
Avogadro's law of gases, 604 
Avoirdupois weight, 19 
Axles, forcing fits of, by hydrauhc 
pressure, 1324 

railroad, effect of cold on, 465 

steel, specifications for, 507, 509 

steel, strength of, 354 

BABBITT metal, 407. 408 
Bagasse as fuel, 839 
Balances, to weigh on in- 
correct, 20 
Balls and rollers, carrying capac- 
ity of, 340 
for bearings, grades of, 1237 
hollow copper, resistance to 
collapse, 345 
Ball-bearings, 1233, 1235 

saving of power by, 1237 
Band brakes, design of. 1240 
Bands and belts for carrying coal, 
etc., 1198 
and belts, theory of, 1138 
Bank discount, 13 
Bar iron {see Wrought iron) 
Bars, eye, tests of, 360 

iron and steel, commercial sizes 

of, 182 
Lowmoor iron, strength of, 352 
of various materials, weights of, 

181 
steel (see Steel) 

twisted, tensile strength of, 280 
w^rought-iron, compression tests 
of, 359 
Barometer, leveling with, 607 

to find altitude by, 608 
Barometric readings for various 

altitudes, » 608 
Barrels, to find volume of, 65 

number of, in tanks, 134 
Barth key, 1329 
Basic Bessemer steel, strength of, 

476 
Batteries, primarv electric, 1425 

storage, 1425-1428 
Baume's hydrometer, 175 
Bazin's experiments on weirs, 763 



1482 



bea-bel 



INDJEX. 



bel-bio 



Beams and girders, safe loads on, 
1387 

formula for flexure of, 299 

formulae for transverse strength 
of, 299 

of uniform strength, 301 

special, coefficients for loads on, 
300 

steel, formulae for safe loads on, 
298 

wooden, safe loads, by building 
laws, 1387 

yellow pine, safe loads on, 1387, 
1393 
Beardslee's tests on elevation of 

elastic limit, 275 
Bearing-metal alloys, 405 

practice, 407 
Bearing-metals, anti-friction, 1223 

composition of, 390 
Bearing pressure on rivets, 426 

pressure with intermittent 
loads, 1231 
Bearings, allowable pressure on, 
1226, 1230 

and journals clearance in, 1230 

ball, 1233, 1235 

cast-iron, 1223 

conical roller, 1234 

engine, calculating dimensions 
of, 1042-1044 

engine, temperature oi, 1232 

for high rotative speeds, 1231 

for steam turbines, 1232 

knife-edge, 1238 

mercury pivot, 1233 

of Corhss engines, 1232 

of locomotives, 1232 

oil pivot, in Curtis steam tur- 
bine, 1083 

oil pressure in, 1228 

overheating of, 1228 

pivot, 1229, 1232 

roUer, 1233 

shaft, length of, 1034 

steam-engine, 1232. 1238 

thrust, 1232 
Bed-plates of steam-engine, 1044 
Bell-metal, composition of, 390 
Belt conveyors, 1198-1201 

dressings, 1151 

factors, 1142 
Belts and pulleys, arrangement 
of, 1149 

care of, 1150 

cement for leather or cloth, 1152 

centrifugal tension of, 1139 

effect of humidity on, 1150 

endless, 1151 

evil of tight, 1149 

lacing of, 1147 

length of, 1148 

open and crossed, 1136 

quarter twist, 1147 

sag of, 1149 

steel, 1152 
Belting, 1138-1152 

Barth's studies on, 1146 



Belting, formulae, 1139 

friction of, 1138 

horse-power of, 1139-1142 

notes on, 1146 

practice, 1139 

rubber, 1152 

strength of, 357, 1150 

Taylor's rules for, 1143 

theory of, 1138 

vs. chain drives, 1155 

width for given horse-power, 
1140 
Bends, effects of, on flow of water 
in pipes, 747, 748 

in pipes, 624 

in pipes, table, 221, 222 

pipe, flexibihty of, 221 

valves, etc., resistance to flow 
in, 879 
Bending curvature of wire rope, 

1213 
Bent lever, 514, 536 
Bernouilh's theorem, 617, 765 
Bessemer converter, temperature 
in, 555 

steel, 475 (see Steel, Bessemer) 
Bessemerized cast iron, 453 
Bethlehem girder beams, proper- 
ties of, table, 331 

I-beams, table, 332 

steel H-columns, 333 
Bevel wheels, 1169 
Billets, steel, specifications for, 507 
Binomial, any power of, 33 

theorem, 37 
Bins, coal-storage, 1196 
Birmingham gage, 28 
Bismuth alloys, 404 

properties of, 178 
Bituminous coal (see Coal) 

coating for pipe, 206 
Black body radiation, 579 
Blast area of fans, 655 

pipes (see Pipes) 
Blast - furnace, consumption of 
charcoal in, 837 

gas, 855 

steam-boilers for, 899 

temperatures in, 555 
Blechynden's tests of heat trans- 
mission, 593 
Blocks or pulleys, 538, 539, 1181 

or pulleys, strength of, 1181 
Blooms, steel weight of, table, 190 
Blow, force of, 529 . 
Blowers (see also Fans), 663-681 

and fans, comparative efficiency, 
656 

blast-pipe diameters for, 671 

in foundries, 1250 

rotary, 677 

rotary, for cupolas, 678 

steam- jet, 679 
Blowing-engines, dimensions of, 
680 

horse-power of, 680 
Blowing-machines, centrifugal, 
648, 649 



blo-bra 



INDEX. 



bra-bui 



1483 



Blowpipe, acetylene, 857 

Blue heat, effect on steel, 482 

Board measure, 20 

Boats '(see Ships) 

Boats, motor, power required for, 

1101 
Bodies, falUng, laws of, 521 
Boiler compounds, 930 

explosions, 932 

feed-pumps, 792 

feeders, gravity, 938 

furnaces, height of, 889 

furnaces, use of steam in, 854 

heads, 914 

heads, strength of, 337, 338 

heating-surface for steam heat- 
ing, 693-697 

plate, strength of, at high 
temperatures, 463 

scale, analyses of, 722 

tube joints, rolled, sUpping 
point of, 364 

tubes, dimensions of, table, 204 

tubes, expanded, holding power 
of, 364 
Boilers for house heating, 693 

for steam-heating, 694-697 

horse-power of, 885 

incrustation of, 721, 927-932 

locomotive, 1113 

natural gas as fuel for, 847 

of the "Lusitania," 1381 

steam, 885-944 (see Steam- 
boilers) 
Boiling-point of water, 719 

of substances, 559 
Boiling, resistance to, 570 
Bolts and nuts, 231-238 

and pins, taper, 1318 

effect of initial strain in, 347 

hanger, 243 

holding power of in white pine, 
346 

square-head, table of weights 
of, 242 

strength of, tables, 348 

stud, 237 

track, weight of, 244, 245 
Bonds, rail, electric resistance of, 

1416 
Boosters, 1456 
Boyle's or Mariotte's law, 600, 

603 
Braces, diagonal, stresses in, 542, 

545 
Brackets, cast-iron, strength of, 292 
Brake horse-power, 970 

horse-power, definition of, 1017 

Prony, 1333 
Brakes, band, design of, 1240 

electric, 1240 

friction, 1239 

magnetic, 1240 
Brass alloys, 390 

and copper-lined iron pipe, 227 

and copper tubes, coils and 
bends, 222 

influence of lead on, 394 



Brass plates, bars, and wire, tables, 
228, 229 

rolled, composition of, 391 

sheets and bars, table, 228, 229 

tube, seamless, table, 224, 225 

wire, weight of, table, 229 
Brazing metal, composition of, 390 

of aluminum bronze, 397 

solder, composition of, 390 
Brick, absorption of water by, 370 

fire, number required for vari- 
ous circles, table, 267 

fire, sizes and shapes of, 266 

kiln, temperature in, 555 

magnesia, 269 

piers, safe strength of. 1386 

sand-lime, tests of, 371 

specific gravity of, 177 

strength of, 358, 370-372 

weight of, 180, 370 

zirconia, 270 
Bricks and blocks, slag, 268 
Brickwork, allowable pressures 
on, 1386 

measure of, 180 

weight of, 180 
Bridge iron, durability of, 466 

links, steel, strength of, 353 

members, strains allowed in, 
287 

trusses, 543-547 
Brine, boihng of, 570 

properties of, 570, 571, 1343 
Brinell's tests of hardness, 364 
Briquettes, coal, 831 
Britannia metal, composition of, 

407 
British thermal unit (B.T.U.). 

560, 867 
Brittleness of steel (see Steel) 
Bronze, aluminiun, strength of, 
396 

ancient, composition of, 388 

deoxidized, composition of, 395 

Gurley's, composition of, 390 

manganese, 401 

navy-yard, strength of, 398 

phosphor, 394 

strength of, 356 

Tobin, 391, 392 

variation in strength of, 386 
Buffing and polishing, 1310 
Building-laws, New York City, 
1388-1390 

-laws on columns, New York, 
Boston, and Chicago, 292 

-materials, coefficic^nts of fric- 
tion of, 1220 

-materials, sizes and weights, 
177, 180. 191 
Buildings, construction of, 1385- 
1395 

fire-proof. 1389 

heating and ventilation of, 684 

mill, approximate cost of, 1394 

transmission of heat througli 
walls of, 688 

walls of, 1388 



1484 



bul-car 



INDEX. 



caf-cas 



Bulkheads, plating and framing 
for, table, 339 
stresses in due to water-pres- 
sure, 338 
Buoyancy, 719 
Burners, acetylene, 857 

fuel oil, 842 
Burning of steel, 481 
Burr truss, stresses in, 544 
Bush-metal, composition of, 390 
BiLshel of coal and of coke, weight 

of, 834 
Butt-joints, riveted, 428 

CG. S. system of measure- 
ments, 1396 
• CO2, (see also carbon dioxide, 
carbonic acid) 
CO2 recorders, autographic, 891 
CO2, temperature required for 

production of, 852 
Cable, formula for deflection of, 
1207 
traction ropes, 256 
Cables (see Wire rope) 

chain, proving tests of, 264 
chain, wrought-iron, 264, 265 
galvanized steel, 255 
suspension-bridge, 255 
Cable- ways, suspension, 1205 
Cadmium, properties of, 178 
Calcium carbide and acetylene, 
855 
chloride in refrigerating-ma- 
chines, 1343 
Calculas, 73-82 
Caloric engines, 1095 
Calorie, definition of, 560 
Calorimeter for coal, Mahler 
bomb, 826 
steam, 942-944 
steam, coil, 943 
steam, separating, 943 
steam, throttling, 943 
Calorimetric tests of coal, 826, 827 
Cam, 537 
Campbell's formulae for strength 

of steel, 477 
Canals, irrigation, 755 
Candle-power, definition of, 1469 
of electric lights, 1468-1476 
of gas lights, 860 
per watt of lamps, 1475 
Canvas, strength of, 357 
Cap screws, dimensions of, 238 

table of standard, 238 
Capacity, electrical, 1440 

electrical, of conductors, 1445 
Car heating by steam, 702 
journals, friction of. 1228 
wheel, irons used for, 453 
Cars, steel plate for, 507 
Carbon, burning out of steel, 485 
dioxide (see also CO2) 
dioxide exhaled by a man, 687 
dioxide in air, 687 
dioxide, pressure, volume, etc., 
1341 



Carbon, effect of, on sti*ength of 
steel, 476 

gas, 845 
Carbonic acid, allowable in air, 

681, 685 
Carbonizing (see Case-hardening) 
Carborundum, made in the elec- 
tric furnace, 1425 
Cargo hoisting by rope, 414 
Carnegie steel sections, proper- 
ties of, 305-321 
Carnot cycle, 598, 600 

cycle, eflBciency of steam in, 881 
Carriages, resistance of, on roads, 

534 
Carriers, bucket, 1197 
Case-hardening of iron and steel, 

510, 1291 
Casks, volume of, 65 
Cast copper, strength of, 356, 384 
Cast-iron, 437-454 

addition to, of ferro-silicon, 
titanium, vanadiiun, and 
manganese, 450 

analyses of, 439-450 

bad, 453 

bars, tests of, 444 

beams, strength of, 451 

Bessemerized, 453 

chemistry of, 438-443 

columns, eccentric loading of, 
296 

columns, strength of, 289-292 

columns, tests of, 290 

columns, weight of, table, 200 

combined carbon changed to 
graphite by heating, 448 

compressive strength of, 283 

corrosion of, 466 

cylinders, bursting strength of, 
452 

durabihty of, 466 

effect of cupola melting, 450 

expansion in cooling, 448 

growth of by heating, 1254 

hard, due to excessive silicon, 
1254 

influence of length of bar on 
strength, 446 

influence of phosphorus, sul- 
phur, etc., 438 

journal bearings, 1223 

malleable, 454 

manufacture of, 437 

mixture of, with steel, 453 

mobility of molecules of, 449 

permanent expansion of, by 
heating, 453 

pipe, 196-200 (see Pipe, cast- 
iron) 

pipe-fittings, sizes and weights, 
206-216 

relation of chemical composi- 
tion to fracture, 446 

shrinkage of, 438, 447, 1254 

specific gravity and strength, 
452 

specifications for, 441 



cas-cha 



INDEX. 



cha-ctil 



1485 



Cast-iron strength in relation to 
silicon and cross-section, 447 
strength in relation to size of 
bar and to chemical consti- 
tution, 446 
strength of, 445-447 
tests of, 352, 444-447 
theory of relation of strength 

to composition, 446 
variation of density and te- 
nacity, 452 
water pipe, transverse strength 

of, 452 
white, converted into gray by 
heating, 448 
Castings, deformation of, by 
shrinkage, 448 
from blast-furnace metal, 450 
hard, from soft pig, 450 
hard to drill, due to low Mn, 

450 
iron, analysis of, 439 
iron, chemical standards for, 

441 
iron, strength of, 352 
made in permanent cast-iron 

molds, 1255 
shrinkage of, 1254 
specifications for, 441 
steel, 489, 510 

steel, specifications for, 489, 510 
steel, strength of, 355 
weakness of large, 1253 
weight of, from pattern, 1256 
Catenary, to plot, 52 
Cement as a preservative coating, 
471 
for leather belts, 1152 
Portland, strength of. 358 
Portland, tests of, 373 
weight and specific gravity of, 
177 
Cements, mortar, strength of, 372 
Cementation or case-hardening, 

510, 1291 
Cementite, 439, 480 
Center of gravity, 516 

of gravity, of regular figures, 

516 
of gyration, 518 
of oscillation, 518 
of percussion, 518 
Centigrade- Fahrenheit conver- 
sion table, 550, 551 
Centigrade, thermometer scale, 

550, 551 
Centrifugal air compressors, 648, 
649 
fans (see Fans, centrifugal) 
fans, high-pressure, 648, 649 
force, 521 

force in fly-wheels, 1047 
pmnps (see Pmnps, centrifugal), 

796-S02 
tension of belts, 1139 
Chain-blocks, efficiency of, 1181 
Chain-cables, proving tests of, 264 
weight and strength of, 264 



Chain-drives, 1153 

silent, 1156 

vs. belting, 1155 
Chain-hoists, 1181 
Chains, formulic for safe load on, 
348 

link-belt, 1196 

monobar, 1199 

pm, 1199 

pitch, breaking and working 
strains of, 265 

roUer, 1199 

sizes, weights and properties, 
264, 265 

specifications for, 264 

strength of, tables, 264, 265 

tests of, 264, 265 
Chalk, strength of, 371 
Change gears for lathes, 1260 
Channels, Carnegie steel, proper- 
ties of, table, 312-313 

open, velocity of water in, 755 

safe loads, table, 313 

strength of, 352 
Charcoal, 836-837 

absorption of gases and water 
by, 837 

bushel of, 180 

composition of, 836 

pig iron, 440, 452 

results from different methods 
of making, 837 

weights per cubic foot, 180 
Charles's law, 600, 604 
Chatter in tools, 1264 
Chemical elements, table, 173 

symbols, 173 
Chemistry of cast iron, 438-443 
Chezy's formula for flow of water, 

728 
ChiUing cast iron, 441 
Ctiimneys, 944-958 

anchor bolts for, 957 

draught intensity in, 945 

draught, power of, 946 

draught, theory, 944 

draught with oil fuel, 962 

effect of flues on draught. 947 

for ventilating, 712 

height of, 948 

height of water column due to 
imbalanced pressure in, 946 

interior, of Equitable building, 
954 

largest in the world, 952, 954 

lightning protection of, 949 

radial brick, 954 

rate of combustion due to 
height of, 947 

reinforced concrete, 958 

sheet iron, 958 

size of, table, 950 

size of, for oil fuel, 951 

stability of, 954 

steel, 956 

steel, design of, 956 

steel, foundation for, 957, 958 

tall brick, 953 



1486 



chl-cia 



INDEX. 



cla-coe 



Chimneys, velocity of air in, 946 
velocity of gas in, 951 
with forced draught, 952 
Chisels, cold, cutting angle of, 

1261 
Chord of circle, 58 
Chords of trusses, strains in, 545 
Chrome paints, anti-corrosive, 469 
Chrome steel, 496 
Chromium-vanadium steels, 500- 

502 
Cippoleti weir, 764 
Circle, 57-60 
area of, 57 

circumferences in feet, diam- 
eters in inches, table, 1310 
circumferences of, 1 inch to 32 

feet, 120 
diameter of to enclose a num- 
ber of rings, 51 
equation of, 71 

large, to describe an arc of, 51 
length of arc of, 58 
length of arc of, Huyghen's 

approximation, 58 
length of chord of, 58 
problems, 37-44 
properties of, 57, 58 
relation of arc, chord, etc., of, 

58 
relations of, to equal, inscribed 
and circumscribed square, 59 
sectors and segments of, 60 
Circles, area in square feet, diam- 
eter in inches (table of cyl- 
inders), 131, 132 
circumference and area of, 

table, 111-119 
diameter of and sides of equiva- 
lent square, 125 
number inscribed in a larger 
circle, 125 
Circuits, alternating current (see 
Alternating Current) 
electric (see Electric circuits) 
electric, e.m.f. in, 1406 
electric, polyphase, 1445 (see 

Alternating currents) 
electric, power of, 1408 
magnetic, 1430 
Circular arcs, lengths of, 58 

arcs, lengths of, tables, 122-124 
curve, formulae for, 59 
fimctions, Calculus, 81 
inch, 18 
measure, 20 
mil. 18, 29, 30 
mil wire gage, 29, 30 
pitch of gears, 1158 
ring, 60 

segments, areas of, 121, 122 
Circumference of circles, 1 inch 
to 32 feet, table, 120 
of circles, table, 111-119 
Cisterns and tanks, number of 
barrels In, 134 
capacity of, 132-134 
Classification of iron and steel, 436 



Clay, cubic feet per ton, 181 
fire, analysis, 269 
melting point of, 556 
Clearance between journal and 

bearing, 1230 
in steam-engines, 966, 1021 
of rivet heads, 322 
Clutches, friction, 1179, 1239 
Coal, analysis of, 821-830 

analyses and heating values of 

various, tables, 828-830 
and coke, Connellsville, 824 
anthracite, sizes of, 823 
approximate heating value of, 

822 
bituminous, classification of, 

819 
briquets, 831 
burning, lUinois without smoke, 

921 
caking and non-caking, 820 
calorimeter, 826 
calorimetric tests of, 826, 827 
cannel, 821 

classification of, 819-821 
conveyors, 1197 
cost of for steam power, 1010 
cubic feet per ton, 180 
Dulong's formula for heating 

value of, 827 
efiaciencies of, in gas-engine 

tests, 853 
foreign, analysis of, 825 
-gas, composition of, 860 
-gas, manufacture, 858 
heating value of, 821-824, 828- 

830 
products of distillation of, 834 
purchase of, by specification, 830 
Rhode Island graphitic, 821 
sampUng, for analysis, 825, 900 
semi-anthracite, 824 
semi-bitmninous, composition 

of, 819-823, 828 
space occupied by anthracite, 

823 
spontaneous combustion of, 832 
steam, relative value of, 826 
storage bins, 1196 
tests of, 822, 823 
vs. oil as fuel, 842, 843 
washing, 833 
weathering of, 830 
weight of bushel of, 834 
Welsh, analysis of, 825 
Coals, furnaces for different, 827 
Coatings, preservative, 471—474 
Coatings, protective, for pipe, 206 
Coefflcient of elasticity, 274, 374 
expansion, 566 {see Expansion 

by heat) 
fineness, 1369 
friction, definition, 1219 
friction of journals, 1220 
friction, rolling, 1220 
friction, tables, 1220-1223 
performance of ships, 1370 
propellers, 1373 



INDEX. 



com -com 



1487 



CoeflQcient of transverse strength, 
297 
water lines, 1369 
Coils and bends of brass tubes, 
222 
electric, heating of, 1409 
heat radiated from, in blower 
system, 708 
Coiled pipes, 221 
Coke, analyses of, 833 

by-products of manufacture of, 

833, 834 
foundry, quaUty of, 1255 
ovens, generation of steam 

from waste heat of, 834 
weight of, 180, 834 
Coking, experiments in, 833 
Cold-chisels, form of, 1261 

-drawing, effect of, on steel, 361 
-drawn steel, tests of, 361 
effect of, on railroad axles, 465 
effect of, on strength of iron and 

steel, 464 
-roUed steel, tests of, 361 
-roUing, effect of, on steel, 479 
-saw, 1309 
Collapse of corrugated furnaces, 
342 
of tubes, tests of, 341-344 
resistance of hollow cyUnders 
to, 341-345 
Collars for shafting, 1133 • 
Cologarithm, 137 
Color determination of tempera- 
ture, 558 
Color scale for steel tempering, 

493 
Color values of various illumi- 

nants, 1469 
Columns, built steel, tests of, 287 
Carnegie channel, dimensions 

and safe loads, 323-327 
Carnegie plate and angle, 323, 

328—330 
cast-iron, strength of, 289-292 
cast-iron, tests of, 290 
cast-iron, weight of, table, 200 
comparison of formulae for, 286 
eccentric, loading of, 296 
Gordon's formula for, 284 
Hodgkinson's formula for, 283 
made of old boiler tubes, tests 

of, 363 
mill, 1393 

permissible stresses in, 286 
strength of, by New York 

building laws, 1389 
wrought-iron, tests of, 360 
wrought-iron, ultimate strength 
of, table, 285 
Combination, 10 
Combined stresses, 335 
Combustion, analyses of gases of, 
817 
heat of, 560 
of fuels, 816 

of gases, rise of temperature in, 
818 



Combustion, rate of, due to chim- 
neys, 947 

spontaneous,' of coal, 832 

theory of, 816 
Commutating-pole motors, 1437 
Composition of forces, 513 
Compound engines (see Steam- 
engines, compound), 976-983 

interest, 13, 14 

locomotives, 1122, 1124 

proportion, 7 

nimabers, 5 

units of weights and measures, 
27 
Compressed-air, 623, 632-653 

adiabatic and isothermal com- 
pression, 633 

cranes, 1192 

diagrams, curve of, 636 

drills driven by, 645 

engines, adiabatic expansion in, 
638 

engines, efficiency, 641 

flow of, in pipes, 618-624 

for motors, effect of heating, 
639-641 

formulae, 633 

for street railways, 652 

gain due to reheating, 647 

hoisting engines, 646 

horse-power required to com- 
press air, 637 

locomotives, 1128 

loss of energy in, 632 

losses due to heating, 633 

machines, air required to run, 
645, 647 

mean effective pressures, tables. 
636, 637 

mine pumps, 652 

moisture in, 611 

motors, 639-641 

motors with return-air circuit, 
648 

Popp system, 639-641 

practical apphcations of, 647 

pumping with (see also Air-hft), 
645 

reheating of, 641 

table for pumping plants, 645 

tramways, 652 

transmission, efficiencies of, 641 

two-stage compression, 635 

volumes, pressures, tempera- 
tures, table, 636 

work of adiabatic compression, 
634 
Compressed steel, 488 
Compressibihty of liquids, 175 

of water, 721 
Compression, adiabatic, formulae 
for, 633 

and flexure combined, 335 

and shear combined, 335 

and torsion combined, 335 

in steam-engines, 965 

of air, tables, 635-638 
Compressive strength, 281-283 



1488 



com-con 



INDEX. 



con-cop 



Compressive strength of iron bars, 
359 
strength of woods, 366 
tests, specimens for, 282 
Compressor volume in refrigerat- 
ing, 1341 
Compressors, air, effect of intake 
temperature, 647 
air, tables of, 641-643 
Concrete, crushing strength of 
12-in. cubes, 1386 
durabihty of iron in, 466 
reinforced, allowable working 
stresses, 1386 
Condenser, barometric, 1069 
the Leblanc, 1056 
tubes, heat transmission in, 
589 
Condensers, 1069-1079 
air-pump for, 1071, 1073 
calculation of surface of, 939 
choice of, 1078 
circulating pump for, 1075 
continuous use of coohng water 

in, 1076 
contraflow, 1071 
cooling-towers for, 1079 
cooling water required, 1068 
ejector, 1069 

evaporative surface, 1076 
for refrigerating machines, 1353 
heat transference in, 1070 
increase of power due to, 1077 
jet, 1068 
surface, 1069 

tubes and tube plates of, 1072, 
1073 
Condensing apparatus, power 

used by, 1071 
Conductance, electrical, 1401 
Conduction of heat, 580 

of heat, external and internal, 
580 
Conductivity, electrical, of metal, 
1401 
electric, of steel, 477 
Conductors, electrical, heating of, 
1408 
electrical, in series or parallel, 
resistance of, 1407 
Conduit, water, efficiency of, 760 
Cone, measures of, 62 

pulleys, 1136 
Conic sections, 73 
Connecting-rods, steam-engine, 
1025 
tapered, 1026 
Connections, transformer, 1452 
Conoid, parabolic, 65 
Conoidal fans, 666 
Conservation of energy, 531 
Constantan, copper-nickel alloy, 

403 
Constants, steam-engine, 971-974 
Construction of buildings, 1385- 

1395 
Controllers, for electric motors, 
1462 



Convection, Dulong's law of, 
table of factors, for, 597 
loss of heat due to, 596 
of heat, 580 
Conversion tables, metric, 23-26 
Converter, Bessemer, tempera- 
ture in, 555 
Converters, electric, 1453 

synchronous, 1453 
Conveying of coal in mines, 1203 
Conveyors, belt, 1198-1201 
cable-hoist, 1205 
coal, 1197 
horse-power required for, 1198, 

1200 
screw, 1198 
Coohng agents in refrigeration, 
1342 
air for ventilation, 710 
effect, in refrigerating, 1341 
of air, 594 

of air by washing, 687 
Cooling-tower, air per poimd of 
circulating water, table, 1081 
air supply required for, 1080 
for condensers, 1079 
practice in refrigerating plants, 

1354 
water evaporated per poimd of 

air, 1080 
water vapor mixed with air, 
table, 1081 
Co-ordinate axes, 70 
Copper, 178 

and brass-lined iron pipe, 227 

ball pyrometer, 553 

balls, hollow, 345 

cast, strength of, 356, 384 

castings of high conductivity, 

368 
density of, 1406 
drawn, strength of, 356 
effect of on cast-iron, 438 
electric conductivity of, 1402 
-manganese alloys, 401 
-nickel alloys, 402 
plates, strength of, 356 
resistivity of, 1403 
temperature coefficient of, 1403 
tubing, bends and coils, 222 
rods, weight of, table, 230 
steels, 499 

strength of at high tempera- 
tures, 368 
-tin alloys, 384 

-tin alloys, properties and com- 
position of, 384 
-tin-zinc alloys, law of variation 

of strength of, 388 
-tin-zinc alloys, properties and 

composition, 387 
-vanadium alloys, 395 
weight required in different sys- 
tems of transmission, 1459 
Copper- wire and plates, weight of, 
table, 229 
carrying capacity of, Under- 
writer's table, 1410 



cop-era 



INDEX. 



cra-ciir 



1489 



Copper-wire,cross-sectionrequired 
for a given current, 1410 
electrical resistance, table, 1404 
stranded, 253 
table of electrical resistance, 

1404 
weight of for electric circuits, 
1410 
Copper-zinc alloys, strength of, 
386 
-zinc alloys, table of composition 

and properties, 386 
-zinc-iron alloys, 393 
Cord of wood, weight of, 181 
yield of charcoal from, 836 
Cordage, technical terms relating 
to, 411 
weight of, 411, 415, 
Cork, properties of, 377 
Corrosion by stray electric cur- 
rents, 470 
due to overstrain, 470 
electrolytic theory of, 468 
of iron, 467 
of pipe in hot- water heating, 

708 
of steam-boilers, 467, 927-932 
prevention of, 468 
resistance of aluminum aUoys 

to, 401 
resistance to of nickel steel, 498 
Corrosive agents in atmosphere, 

466 
Corrugated arches, 195 
furnaces, 342, 917 
plates, properties of Carnegie 

steel, table, 310 
sheets, sizes and weights, 194 
Cosecant of an angle, table, 170- 

172 
Cosine of an angle, 66 

of an angle, table, 170-172 
Cost of coal for steam-power, 1010 

of steam-power, 1009-1011 
Cotangent of an angle, 66 
Cotangents of angles, table, 170- 

172 
Cotton ropes, strength of, 357 
Coulomb, definition of, 1397 
Counterbalancing of hoisting- 
engines, 1188 
of locomotives, 1126 
of steam-engines, 1008 
Counterpoise system of hoisting, 

1189 
Couples, 515 
Couplings, flange, 1133 

hose, standard sizes, 218 
Coverings for steam-pipe, tests of, 

584-587 
Coversed sine of angles, table, 170- 

172 
Cox's formula for loss of head, 

734 
Crane chains, 264, 265 

installations, notable, 1192 • 
pillar, 150-ton, 1192 
Cranes, 1189-1193 



Cranes and hoists, power required 
for, 1193 
classification of, 1189 
compressed air, 1192 
electric, 1190-1192 
electric, loads and speeds of, 

1191 
guyed, stresses in, 542 
jib, 1190 

power required for, 1191 
quay, 1193 

simple, stresses in, 541 
traveUng, 1190-1193 
Crank angles, steam-engine, table, 
1058 
arm, dimensions of, 1029 
pins, steam-engine, 1027-1029 
pins, steel, specifications for, 

507 
shaft, steam-engine, torsion and 

flexure of, 1038 
shafts, steam-engines, 1030- 
1038 
Cranks, steam-engines, 1029 
Critical point in heat treatment 
of steel, 480 
temperature and pressure of 
gases and liquids, 606 
Cross-head guides, 1025 

pin, 1029 
Cross-sections of materials, for 

draftsmen, 271 
Crucible steel, 475, 490-494 (see 

Steel, crucible) 
Crushing strength of masonry 

materials, 371 
CrystalUzation of iron by fatigue, 

466 
Cubature of voltmies, 77 
Cube root, 9 

roots, table of. 93-108 
Cubes of decimals, table, 108 

of num})ers. tal)le, 93-108 
Cubic feet and gallons, table, 130 

measure, 18 
Cupola fan, power required for, 
1253 
gases, utilization of, 1253 
loss in melting iron in, 1253 
practice, 1247-1257 
practice, improvement of, 1249 
results of increased driving, 
1252 
Cupolas, blast-pipes for, 671 
blast-pressure in, 1247-1251 
blowers for, 661, 662 
charges for, 1247-1250 
charges in stove foimdries, 1250 
dimensions of, 1247 
rotary blowers for, 678 
slag in, 1248 
Current motors, 765 
Currents, electric (see Electric 

currents) 
Curve, railway degree of, 54 
Curve of P V^, construction of, 602 
Curves in pipe-lines, resistance of, 
747 



1490 



cut-dif 



INDEX. 



dif-dyn 



Cut-off for various laps and travel 

of slide valves, 1060 
Cutting metal by oxy-acetylene 

flame, 488 
metal, resistance overcome in, 

1292 
speeds of machine tools, (see also 

Tools, cutting), 1258 
speeds of tools, economical, 

1268 
stone with wire, 1309 
Cycloid, construction of, 50 
differential equations of, 81 
integration of, 81 
measm-es of, 61 
Cycloidal gear-teeth, 1162 
Cylinder condensation in steam- 
engines, 966-968 
lubrication, 1245 
measures of, 62 
Cylinders, hollow, resistance of to 

collapse, 341-345 
hollow, under tension, 339 
hooped, 340 
hydraulic press, thickness of, 

340, 813 
locomotive, 1112 
open-end cast-iron, weight of, 

200 
steam-engine (s^e Steam-engines) 
tables of capacities of, 131 
thick hollow, under tension, 339 
thin hollow, under tension, 340 
Cylindrical ring, 64 

tanks, capacities of, table, 132 

DALTON'S law of gaseous 
pressures, 604 
Dam, stabihty of, 515 
Darcy 's formula, flow of water, 732 
formula, table, of flow of water 
in pipes, 740, 741 
Decimal equivalents of feet and 
inches, 5 
equivalents of fractions, 3 
gage, 32, 
Decimals, 3 

square and cubes of, 108 
Delta connection for alternating 

currents, 1447 
Delta connection transformers, 
1452 
metal wire, 248, 393 
Denominate numbers, 5 
Deoxidized bronze, 395 
Derrick, stresses in, 542 
Detrick and Harvey key, 1330 
Diagonals, formula: for strains in, 

545 
Diametral pitch, 1158 
Diesel oil engine, 1102 
Differential calculus, 73-82 
coefficient, 75 
coefficient, sign of, 78 
gearing, 1169 

of exponential function, 79, 80 
partial, 75 
pulley, 539 



Differential screw, 540, 541 

second, third, etc., 77 

windlass, 540 
Differentials of algebraic func- 
tions, 74 
Differentiation, formulae for, 74 
Discount, 12 

Disk fans (see Fans, disk) 
Displacement of ships, 1369, 1374 
Distillation of coal, 834 
Distiller for marine engines, 1082 
Distilling apparatus, multiple 

system, 570 
Domed heads of boilers, 339 
Domes on steam boilers, 918 
Draught, chimney , intensity of, 945 

chimney, with oil fuel, 952 

forced, chimneys with, 952 

forced for steam boilers, 923 

power of chimneys, 945, 946 

theory of chimneys, 944 
Drawing-press, blanks for, 1322 
Dressings, belt, 1151 
Driers and drying, 574 

performance of, 575 
Drift bolts, resistance of in timber, 

346 
Drill gage, table, 30 
Drills, feeds and speeds for, 1288 

for pipe taps, 201 

high-speed steel, 1285 

performance of, 1289 

rock, air required for, 645 

speed of, 1285 

tap, sizes of, 236, 1320 

twist, experiments with, 1289 
Drilling compounds, 1286 

high-speed, data on, 1289 

holes, speed of, 1287 

steel and cast iron, power re- 
quired for, 1286, 1287 
Drop in electric circuits, 1407 

press, pressures obtainable by, 
1322 
Drums, steam-boiler, 913 
Dry measure, 19 
Drying and evaporation, 569-577 

apparatus, design of, 576 

in a vacuum, 573 

of different materials, 574 
Ductility Of metals, table, 180 
Dulong's formula for heating 
value of coal, 827 

law of convection, table of fac- 
tors for, 597 

law of radiation, table of factors 
for, 596 
Durability of cutting tools, 1268 

of iron, 465-467 
Durand's rule for areas, 56 
Dust explosions, 837 

fuel, 837 
Duty, measure of, 27 

of pumping-engines, 802 

trials of pumping-engines, 802- 
806 
Dynamics, fundamental equations 
of, 525 



dyn-ele 



INDEX. 



ele-ele 



1491 



Dynamo-electric machines, classi- 
fication of, 1437 

e.m.f. of armature circuit, 1436 

moving force of, 1435 

torque of armature, 1435 

strength of field, 1436 
Dynamometers, 1333 

Alden absorption, 1334 

hydraulic absorption, 6000 H.P., 
1335 

Prony brake, 1333 

traction, 1333 

transmission, 1335 
Dynamotors, 1457 
Dyne, definition of, 512 

EARTH, cubic feet per ton, 181 
Eccentric loading of columns, 
296 
Eccentric, steam-engine, 1039 
Economical angle of framed 

structures, 548 
Economics of power-plants, 1011 
Economizers, fuel {see Fuel econ- 
omizers), 924 
Edison wire gage, 29, 30 
Efficiency, definition of, 12 
of a madiine, 532 
of compressed-air engines, 641 
of compressed-air transmission, 

641 
of differential screw, 541 
of electric systems, 1412 
of fans, 656, 657 
of injector, 937 
of pumps, 790 
of riveted joints, 428-434 
of screw, 538 
of screw bolts, 538 
of steam-boilers, 891 
of steam-engines, 964 
Ejector condensers, 1069 
Elastic Limit. 273-278 
apparent, 273 

Bauschinger's definition of, 275 
elevation of, 275 
relation of, to endurance, 275 
Wohler's experiments on, 275 
Elastic resilience, 274 

resistance to torsion, 334 
Elasticity, coefficient of, 274 
moduli of, of various materials, 

374 
modulus of, 274 
Electric brakes. 1240 

circuits (see Circuits, electric) 
conductivity of steel, 477 
current, alternating, 1440-1461 

(see Alternating currents) 
current, cost of fuel for, 796 
current determining the direc- 
tion of, 1432 
current required to fuse wires, 

1409 
currents, direct, 1406 
currents, heating due to, 1408 
currents, short-circuiting of, 
1411 



Electric furnaces, 1422 

heaters, 713, 1420 

heating, 713 

lightmg, 1468-1477 

lighting, cost of, 1475 

lighting, terms used in, 1468 

locomotive, 1416 
Electric Motors {see also Motors), 
1461 

alternating current, variable 
speed, 1463 

changing the number of poles, 
1463 

for the machine-shop, 1294- 
1303, 1466 

for machine tools, 1294-1303, 
1467 

for wood-working tools, 1303- 
1305 

selection of, for different ser- 
vice, 1464 

speed control of, 1462 

types used for various purposes, 
1464 
Electric power, cost of, 1012 

process of treating iron sur- 
faces, 473 
Electric Railways, 1414 

adhesion between wheel and 
rail, 1416 

cars, resistance of, 1110 

efficiency of distributing sys- 
tems, 1417 

safe speed on curves, 1416 

steam railroads electrified, 1418 
Electric resistance of steel rails, 1416 

smelting of pig iron, 1424 

stations, economy of engines 
in, 992 

storage batteries, 1425-1428 

transmission, direct current, 
1410-1413 

transmission, high tension, 
notes on, 1459 

transmission, lines, spacing for 
high voltages, 1460 

transmission, sag of wires, 1461 

vs. steam heating, 1421 

welding, 1419 

wires {see Wires and Copper 
wires) 
Electrical and mechanical units, 

equivalent values of, 1399 
Electrical engineering, 1396-1477 

horse-power, 970, 1408 

machinery, shaft fits, allow- 
ances for. 1326 

resistance, 1400 

resistance of different metals 
and alloys, 1401 

resistance of rail bonds, 1416 

symbols, 1477 

units, relations of. 1397, 1399 
Electricity, analogies to flow of 
water, 1400 

standards of measurements, 1396 

units used in, 1396 
Electro-chemical equivalents, 1429 



1492 



ele-ent 



INDEX. 



ent-eye 



Electro - magnetic measurements, 
1398 
-magnets, 1430-1437 
-magnets, polarity of, 1432 
-magnets, strength of, 1431 
-motive force of armatm-e cir- 
cuit, 1436 
Electrolysis, 1428 
Electrolytic theory of corrosion, 

468 
Elements, chemical, table, 173 

of machines, 535-541 
Elevators, coal, 1196 
gravity discharge, 1197 
perfect discharge, 1197 
ElUpse, construction of, 45-48 
equations of, 71 
measures of, 60 
ElUpsoid, 64 

Elongation, measurement of, 279 
Emery, grades of, 1311 

wheels, safe speeds, 1316, 1317 
wheels, speed and selection of, 

1310-1315 
wheels, stress tn, 1310 
wheels, truing and dressing, 
1317 
E.M.F. of electric circuits, 1407 
Endless screw, 540 
Endurance of materials, relation 

of, to elastic limit, 275 
EneTgy, available, of expanding 
steam, 870 
conservation of, 531 
definition of, 528 
intrinsic or internal, 600 
measure of, 528 
mechanical, of steam expanded 

to various pressures, 963 
of recoil of guns, 531 
of water flowing in a tube, 746, 

765 
sources of, 531 
Engines, alcohol, 1102 

alcohol consumption in, 844 
automobile, capacity of, 1101 
blowing, 680 
compressed air, eflSciency of, 

639-641 
fire, capacities of, 752 
gas, 1095-1108 (see Gas-engines) 
hoisting (see Hoisting engines), 

1186 
hot-air or caloric, 1095 
hydraulic, 815 

internal combustion, 1095-1108 
marine, steam-pipes for, 880 
oil and gasoline, 1101 
petroleum, 1102 
pumping, 802-806 (see Pump- 

ing-engines) 
steam, 959-1095 (see Steam- 
engines) 
solar. 1015 

winding (see Hoisting engines), 
1186 
Entropy, definition of, 599 
of water and steam, 602 



Entropy of water and steam, 
tables, 869, 871-873 

-temperature diagram, 599 
Epicycloid, 50 

Equalization of pipes, 625, 884 
Equation of payments, 14 
Equation of pipes, 884 
Equations, algebraic, 34-36 

of circle, 71 

of elUpse, 71 

of hyberbola, 72 

of parabola, 72 

quadratic, 35 

referred to co-ordinate axes, 70 
Equilibrium of forces, 516 
Equivalent orifice, mine ventila- 
tion, 715 
Equivalents, electro-chemical, 1429 
Erosion of soils by water, 755 
Ether, petrolemn, as fuel, 841 
Euler's formula for long colimins, 

284 
ETaporation, 569-577 

by exhaust steam, 572 

by multiple system, 570 

factors of, 908-912 

in a vacuum, 573 

in salt manufacture, 570 

latent heat of, 569 

of sugar solutions, 572 

of water from reservoirs and 
channels, 569 

total heat of, 569 

unit of, 886 
Evaporator, for marine engines, 

1082 
Evolution, 8 
Exciters, 1449 
Exhauster, steam-jet, 679 
Exhaust-steam, evaporation by, 
572 

for heating, 1009 
Expansion, adiabatic, formulae for, 
638 

by heat, 565 

coefficients of, 566 
Expansion of air, adiabatic, 638 

cast iron, permanent by heat- 
ing, 453 

gases, construction of curve of, 
602 

gases, curve of, 73 

iron and steel by heat, 465 

liquids, 567 

nickel steel, 499 

solids by heat, 566 

steam, 959 

steam, actual ratios of, 965 

timber, 367 

water, 716 
Explosions, dust, 837 

of fuel economizers. 927 
Explosive energy of steam-boilers, 

932 
Exponential function, differential 

of, 79, 80 
Exponents, theory of, 36 
Eye-bars, tests of, 360 



fac-fee 



INDEX. 



fee-fla 



1493 



FACTOR of evaporation, 908- 
912 
of safety, 374-377 
of safety, formulae for, 376 
of safety in steam-boilers, 918 
Factory heating by fan system, 

708, 710 
Fahrenheit-Centigrade conversion 

table, 550, 551 
Failures of stand-pipes, 350 

of steel, 486 
Fairbairn's experiments on ri- 
veted joints, 424 
Falling bodies, graphic represen- 
tation, 522 
height and velocity of tables, 

523, 524 
laws of, 521 
Fan blowers, types of, 654 

tables, caution in regard to, 662 
Fans (see also Blowers) 
and blowers, 653-681 
and chimneys for ventilation, 

712 
and rotary blowers, compara- 
tive efficiencies, 657 
best proportions of, 653 
blast-area of, 655 
centrifugal, 648, 649, 653 
centrifugal, high-pressure, 648 
conoidal, 666 

cupola, power required for, 1253 
design of, 653 
disk, 675-677 
disk, influence of speed on eflQ- 

ciency, 675, 677 
effect of resistance on capacity 

of, 664 
efficiency of, 656, 657, 668 
electric motors for, 1464 
experiments on, 657 
for cupolas, 661 
high-pressure, capacity of, 663 
horse-power of, 668 
influence of spiral casings, 674 
methods of testing, 667 
multiblade, 655, 658 
multiblade, characteristics of, 

656 
pipe lines for, 670 
pressure characteristics of, 655 
pressure due to velocity of, 653 
quantity of air dehvered by, 

655 
relation of speed volume, pres- 
sure and power, 656 
Farad, definition and value of, 

1397 
Fatigue, crystallization of iron by, 
465 
effect of, on iron, 465 
Feed and depth of cut, effect of, 
on speed of tools, 1264 
-pump (see Pumps) 
Feeds and speeds of drills, 1288 
Feed-water, cold, strains caused 
by, 939 
heaters, 938-940 



Feed- water heaters, capacity of, 
939 
heaters: closed vs. open, 940 
heaters, proportions of, 940 
heaters, transmission of heat 

in, 590 
heating, Nordberg system, 1003 
heating, saving due to, 938 
purification of, 723-726 
to boilers by gravity, 938 
Feet and inches, decimal equiva- 
lents of, table, 5 
Fellows stub tooth gear, 1167 
Fence wires, corrosion of, 468 
Ferrite, 439, 480 

Ferro-alloys for foundry use, 1255 
manufacture of, 1424 
silicon, addition of, to cast-iron, 

450 
silicon, dangerous, 1255 
Field, magnetic, 1398 
Fifth roots and fifth powers of 
numbers, 109 
powers, square roots of, 110 
Fineness, coefficient of, 1369 
Finishing temperature, effect of 

in steel rolling, 478 
Fink roof truss, 547 
Fire, temperature of, 817, 818 
Fire-brick arches in locomotives, 
1115 
number required for various 

circles, table, 267 
refractoriness of, 268 
sizes and shapes of, 266 
weight of, 266 
Fire-clay, analysis of, 269 

pyrometer, 553, 556 
Fire-engines, capacities of, 752 
Fire-proof buildings, 1389 
Fire-streams. 749-752 

discharge from nozzles at differ- 
ent pressures, 750, 753 
effect of increased hose length, 

750 
friction loss in hose, 752 
hydrant pressure required for, 
table, 750 
Fireless locomotive, 1127 
Fits, force and shrink, 1324-1327 
force and shrink, pressure re- 
quired to start, 1327 
limits of diameter for, 1325 
press, pressure required for, 

1324-1326 
running, 1325 
stresses due to, 1326 
Fittings (see Pipe-fittings), 206- 

216 
Flagging, strength of. 373 
Flanges, brass, 214, 215 

cast-iron, forms of, 210, 214- 

216 
forged and rolled steel, 211 
forged steel, for riveted pipe, 211 
for riveted pipe, 211 
pipe, extra heavy, tables, 210, 
212 



1494 



fla-flo 



INDEX. 



flo-fou 



Flanges, pipe, tables, 209-213 

reducing, dimensions of, 214 
Flanged fittings, cast-iron, 208- 

210 
Flat plates in steam-boilers, 916 
plates, strength of, 336 
steel ropes, 258, 261 
sm-faces in steam-boilers, 916 
Flattened strand rope, 258, 261 
Flexure and compression com- 
bined, 335 
and tension combined, 335 
and torsion combined, 335 
of beams, formula for, 297, 299 
Flight conveyors, 1197 
Flights, sizes and weights of, 1199 
Floors, maximiun load on, 1390- 
1393 
strength of, 1390-1393 
Flow of air in long pipes, 618-624 
air in pipes, 617-624 
air through orifices, 615-617, 

670 
compressed air, 618-624 
gas in pipes, 864-866 
gas in pipes, tables, 865, 866 
gases, 605 
metals, 1323 
Flow of steam at low pressure, 
699 
capacities of pipes, 877-878 
in long pipes, 877 
in pipes, 877-879 
into atmosphere, 876 
loss of pressure due to friction, 

877 
loss of pressure due to radiation, 

880 
Napier's rule, 876 
resistance of bends, valves, etc., 

879 
tables of, 699, 877-879 
through a nozzle, 876, 1085 
through safety valves, 934 
Flow of water, 726-746 

approximate formulae, 734, 737, 

746 
Chezy's formula, 728 
D'Arcy's formula, 732 
experiments and tables, 737- 

753 
exponential formula, 736 
fall per mile and slope, table, 

729 
formulae for, 726-746 
in cast-iron pipe, 737 
in house service pipes, table, 744 
in pipes at uniform velocity, 

table, 739 
in pipes, table from D'Arcy's 
formula, 740. 741 
table from Hazen & Williams' 

formula, 742, 743 
table from Kutter's formula, 
738, 739 
in riveted steel pipes, 734-736 
in 20-in. pipe, 737 
Kutter's formula, 730 



Flow of water over weirs, 726, 762 
through nozzles, table, 753 
tlirough orifices, 726 
through rectangular orifices, 

760 
values of c, 732, 736 
values of coefiicient of friction, 
734 
Flowing water, horse-power of, 765 
water, measurement of, 757-764 
Flues, collapsing pressure of, 341 
corrugated, 341, 917 (see also 
Tubes and Boilers) 
Flux, magnetic, 1398 
Fly-wheels, arms of, 1050 
centrifugal force in, 1047 
diameters for various speeds, 

1048 
for presses, punches, shears, etc., 

1323 
for steam-engines, 1040, 1044- 

1052 
speed, variation in, 1044-1049 
strains in, 1049 
thickness of rim of, 1052 
weight of, 1045-1048 
weight of, for alternating cur- 
rent units, 1047 
wire wound, for extreme speeds, 

1052 
wooden rim, 1051 
Foaming or priming of steam- 
boilers, 721, 930 
Foot-pound, unit of work, 528 
Force, centrifugal, 521 
definitions of, 512 
graphic representation of, 513 
moment of, 514 
of a blow, 529, 1322 
of acceleration, 526 
units of, 512 
work, power, etc., 528 
Forces, composition of, 513 
equilibrium of, 516 
parallel, 515 
parallelogram of, 513 
parallelopipedon of, 514 
polygon of, 513 
resolution of, 513 
Forced draught, chimneys with. 
952 
draught in steam-boilers, 923 
Forcing and shrinking fits, 1323- 

1327 (see Fits) 
Forging and grinding of tools, 
1263 
heating of steel for, 492 
hydraulic, 814, 815 
of tool steel, 488, 492, 1263 
Forgings, steel, annealing of, 482 

strength of, 353 
Forging-press, hydraulic, 814 
Fottinger transformer or hy- 
draulic pinion, 1095 
Foundation walls, thickness of, 

1386 
Foundations, masonry, allowable 
pressures on, 1386 



fou-fru 



INDEX. 



fru-fur 



1495 



Foundations of buildings, 1386 
Foundry coke, quality of, 1255 
irons (see Pig iron and Cast 

iron) 
ladles, dimensions of, 1257 
molding-sand, 1256 
practice, 1247-1257 
practice, shrinkage of castings, 

1254 
practice, use of softeners, 1253 
use of ferro alloys in, 1255 
Fractions, 2 

product of, in decimals, 4 
Framed structures, stresses in, 

541-548 
Frames, steam-engine, 1043 
Framing, for tanks with flat sides, 

339 
Francis's formulae for weirs, 762 
Freezing point of brine, 1343 

point of water, 719 
French measures and weights, 21- 
26 
thermal unit, 560 
Frequency changers, 1457 
of alternating currents, 1440 
standard, in electric currents, 
1440 
Friction and lubrication, 1219- 
1246 
brakes and friction clutches, 

1239 
brakes, capacity of, 1334 
clutches, 1179 

coefficient of, definition, 1219 
coefficient of, in water-pipes, 

734 
coefficients of, tables, 1219-1221 
drives, power transmitted by, 

1178 
fluid, laws of, 1220 
laws of, of lubricated journals, 

1225 
loss of head by, in water-pipes, 

728, 735, 745 
moment of, 1229 
Morin's laws of, 1223 
of air in mine passages, 714 
of car jouT-nals, 1228 
of hydraulic packing, 813, 1241 
of lubricated journals, 1220- 

1232 
of metals, under steam pressure, 

1223 
of motion, 1219-1222 
of pivot bearings, 1229, 1232 
of rest, 1219 
of solids, 1219 
of steam-engines, 1238 
of steel tires on rails, 1219 
rollers, 1233 
rolling, 1219 

unlubricated. law of, 1219 
work of, 1229 
Frictional gearing, 11 78 

resistance of surfaces moved in 
water, 756 
Frustum of cone, 62 



Frustum of parabolic conoid, 65 
of pyramid, 62 
of spheroid, 64 
of spindle, 65 
Fuel, 816-858 
bagasse, 839 

charcoal, 836-837 (see Char- 
coal) 
coke, 824, 832-834 (see Coke) 
combustion of, 816 
dust, 837 
Fuel, economizers, 924-927 
equation of, 925 
explosions of, 927 
heating surface of, 925 
heat transmission in, 925 
saving due to, 925 
tests of, 926 
Fuel for cupolas, 1248, 1255 
gas, 845 (see Gas) 
gas, for small furnaces, 854 
heat of combustion of, 560, 817 
liquid, 840-844 
peat, 838 
pressed, 831 
sawdust, 838 

soUd, classification of, 818 
straw, 839 

theory of combustion of, 816 
turf, 838 

value of illuminating gas, 863 
weight of, 180 
wet tan bark, 838 
wood, 835, 836 
Fuel-oil, burners for, 842 

California, heating values of, 

842 
chimney draught with, 952 
chimney table for, 951 
specifications for purchaseof, 843 
Functions, tri2:onometric, tables 
of, 170-172 
trigonometric, of half an angle, 

69 
of sum and difference of angles, 

68 
of twice an angle, 69 
Furnace for melting iron for 
malleable castings, 454 
flues, steam-boiler, formulae for, 

917 
heating (see Heating) 
Furnaces, blast, gases of, 855 
blast, temperature in, 555 
corrugated, 342, 917 
down draught, 919 
electric, 1422 
for different coals, 827 
for house heating, 690 
gas, fuel for, 854 
hot-air, heating by, 690 
industrial, temperatures in, 554 
open hearth, temperature in, 

554, 555 
steam-boiler (see Boiler-fur- 
naces) 
steam-boiler, combustion space 
in. 889 



1496 



fus-gas 



INDEX. 



gas-gea 



Fusible alloys, 404 

plugs in boilers, 404, 918 
Fusibility of metals, 180 
Fusing-disk, 1309 

temperatures of substances, 554, 
559 
Fusion, latent heat of, 568 

of electrical wires, 1409 

g, value of, 522, 525 

GAGE, decimal, 32 
lines for steel angles, 321 
sheet metal, 28, 29, 31, 32 
Stub's wire, 28, 
Gages, limit, for iron for screw 

threads, 232 
wire, 28-30 
Gallon, British and American, 27 
Gallons and cubic feet, table, 130 
per minute, cubic feet per 

second, 130 
Galvanic action, corrosion by, 467 
Galvanized sheets, weights of, 192 
wire, test for, 474 
wire rope, 255, 262 
Galvanizing by cementation, 474 
iron surfaces, 473, 474 
of welded pipe 206 
Gas {see also Fuel-gas, Water-gas, 

Producer gas, Illuminating- 
gas) 
ammonia, properties of, 1339 
analyses by volume and weight, 

854 
and electric lighting, 1468 
and oil engines, rules for testing, 

1105 
and vapor mixtures, laws of, 

604 
anthracite, 845 
bituminous, 846 
carbon, 845 
coal, 858 

exhausters, rotary, 679 
fuel (see also Water-gas) 
fuel, cost of. 863 
fuel for small furnaces, 854 
flow of, in pipes, 864-866 (see 

Flow of gas) 
illuminating, 858-866 (see Il- 
luminating-gas) 
lamps, pipe services for, 864 
lights, candle-power of, 860 
lights, Welsbach, standard sizes, 

1474 
meter, Thomas electric, 667, 

669 
natural, 847-848 
perfect, equations of a, 600 
pipe, cast-iron, weights and 

dimensions, 198, 199 
produced from ton of coal, 848 
producer, 848-855 (see also Gas- 

Producers) 
sulphur-dioxide, properties of, 

1338, 1341 
table of factors for equivalent 

volumes of, 865 



Gas, water, 846, 859-864 (see 

Water-gas) 
Gases, absorption of, 605 

Avogadro's law of, 604 

combustion of, rise of tempera- 
ture in, 818 

cupola, utilization of, 1253 

densities of, 604 

expansion of, 601, 603 

expansion of by heat, table, 565 

flow of, 605 

heat of combustion of, 560 

ignition temperature of, 858 

law of Charles, 600, 604 

hquefaction of, 605 

Mariotte's law of, 603 

of combustion, analyses of, 817 

physical properties of, 603-606 

specific heats of, 563, 564 

waste, use of, under boilers, 
898, 899 

weight and specific gravity of, 
table, 176 
Gas-engine, 1095-1108 

calculation of the power of, 1097 

conditions of maximum eflft- 
ciency, 1103 

economical performance of, 1104 

efficiency of, 1103 

four-cycle and two-cycle, 1096 

governing, 1103 

heat losses in, 1104 

horse-power, estimate of, 1101 

ignition in, 1102 

mean effective pressure in, 1098 

pressiu*es developed in, 1097 

pumps, 808 

sizes of, 1100 

temperatures and pressures in, 
1096, 1099 

tests of, 1105-1108 

tests with different coals, 853 
Gas-producers, capacity of, 851 

and scrubbers, proportions of, 
849 

combustion in, 849 

practice, 851 

use of steam in, 854 
Gasoline engines, 1101 

fuel value of, 841 

vapor pressures of, 844 
Gauss, definition and value of, 

1398 
Gear, reduction, for steam tur- 
bines, 1095 

reversing, 1039 

stub-tooth, 1167, 

wheels, calculation of speed of, 
1162 

wheels, formulae for dimensions 
of, 1160 

wheels, milling cutters for, 1162 

wheels, proportions of, 1161 

worm, 540 
Gears, automobile, efficiency of, 
1172 

lathe, for screw cutting, 1259 

of lathes, quick change, 1260 



gea-gor 



INDEX. 



gov-har 



1497 



Gears, spur, machine-cut, 1178 

with short teethe 1160 
Gear-box drive for machine tools, 
1308 
-cutting, speeds and feeds for, 
1284 
Gearing, annular, 1169 
bevel, 1169 
chordal, pitch, 1159 
comparison of formulae, 1174- 

1177 
cycloidal teeth, 1162 
diameters for 1-inch circular 

pitch, 1159 
differential, 1169 
efficiency of, 1170-1172 
forms of teeth, 1162-1167 
frictional. 1178 
involute teeth, 1165 
pitch, pitch-circle, etc., 1157 
proportions of teeth, 1159, 1161 
racks, 1165 
raw-hide, 1177 

relation of diametral and cir- 
cular pitch, 1158 
speed of, 1177 
spiral, 1168 
stepped, 1168 
strength of, 1172-1177 
stub-tooth, 1167 
toothed-wheel, 539, 1157-1180 
twisted, 1168 
worm, 1168 

worm, efficiency of, 1171 
Generator sets, standard dimen- 
sions of, 1007 
Generators, acetylene, 857 

alternating-current, 1448 (see 

Dynamo electric machines) 
electric, 1437, 1448 
Geometrical problems, 37-53 
progression, 11 
propositions, 53 
Geometry, analytical, 70-73 
German silver, 356, 402 
conductivity of, 1401 
Gesner process, treating iron sur- 
faces, 473 
Gib keys, 1332 
Gilbert, unit of magneto-motive 

force, 1398 
Girder beams, Bethlehem steel,'33 1 
Girders, allowed stresses in plate 
and lattice, 289 
and beams, safe load on, 1387 
and beams. New York building 

laws, 1390 
plate, strength of, 353 
Warren, stresses in, 546 
Glass, skylight, sizes and weights, 
196 
strength of, 365 
weight of, 177 
Gold, melting temperature of, 
554, 559 
properties of, 178 
Gordon's formula for colunuis, 
284 



Governor, inertia, 1066 
Governors, steam-engine, 1065- 

1068 
Governing of gas-engines, 1103 
Grade line, hydraulic, 748 
Grain, weight of, 180 
Granite, strength of, 357, 370 
Graphite, Acheson's defloccu- 
lated, 1246 
lubricant, 1246 
paint, 471 
Grate-surface, for house heating, 
boilers and furnaces, 693 
in locomotives, 1115 
of a steam-boiler, 888 
Gravel, cubic feet per ton, 181 
Gravity, acceleration due to, 521, 
525 
boiler-feeders, 938 
center of, 516 

specific (see Specific gravity), 
173-175 
Grease lubricants, 1244 
Greatest common measure or 

divisor, 2 
Greek letters, 1 

Greenhouses, hot-water, heating 
of, 703 
steam-heating of, 702 
Grinding as a substitute for finish 
turning, 1317 
of tools, 1263 
wheel (see Grindstones and 

Emery wheels) 
wheel for high-speed tools, 1263, 
1314 
Grindstones, speed of, 1317 

strains in, 1318 
Guest's formula for combined 

stresses, 335 
Gun-bronze, variation in strength 

of, 386 
Gun-iron, variation in strength 

of, 452 
Gun-metal (bronze), composition 

of, 390 
Guns, energy of recoil of, 531 
Gurley's bronze, composition of, 

390 
Guy ropes for stand-pipes, 349 

ropes, wire, 255 
Gyration, center of, 518 
radius of, 293 
table of radii of, 519 

H- COLUMNS, Bethlehem 
steel, 333 
Halpin heat storage system, 
927, 1014 
Hammering, effect of, on steel, 

488 
Hanger bolts, 243 
Hardening and tempering, change 
of shape due to, 1291 
of soft steel. 479 
Hardness, electro-magnetic tests 
of. 365 
of copper- tin alloys, 385 



1498 



har-hea 



INDEX. 



hea-hea 



Hardness of metals, Brinell's tests, 
364 

of water, 723 

scleroscope tests of, 365 
Harvey process of hardening steel, 

1291 
Harveyizing steel armor-plate, 

1291 
Haulage, wire-rope, 1202-1205 

wire-rope, endless rope system, 
1203 

wire-rope, engine-plane, 1203 

wire-rope, inclined-plane, 1202 

wire-rope, tail-rope system, 1203 

wire-rope tramway, 1204 
HauUng capacity of locomotives, 

1111 
Hawley down-draught furnace, 

919 
Hawsers, steel wire, 262 
Hazen & Williams' formula, table 

of flow of water, 742, 743 
Head, loss of, 728, 735, 745 (see 
Loss of head) 

of air, due to temperature differ- 
ences, 716 

of water, 728 

of water, comparison of, with 
various units, 718 
Heads of boilers, 914 

of boilers, unbraced, wrought 
iron, strength of, 337 
Heat, 549-597 

conducting power of metals, 
580 

conduction by various sub- 
stances, 580-587 

conduction of, 579 

convection of, 579 

effect of on grain of steel, 479 

expansion due to, 565 

generated by electric current, 
1408 

-insulating materials, tests of, 
581 

latent, 568 {see Latent heat) 

loss by convection, 596 

losses in steam-power plants, 
1012 

mechanical equivalent of, 560, 
868 

of combustion, 560 

of combustion of fuels, 560, 817 

produced by human beings, 686 

quantitative measurement of, 
560 

radiating power of substances, 
578 

radiation of, 578 (see also Ra- 
diation) 

reflecting power of substances, 
578 

resistance, coefficients of, 583 

resistance, reciprocal of con- 
ductivity, 582 

specific, 562-565 (see Specific 
heat) 

steam, storing of, 927, 1014 



Heat storage, Halpin system, 927, 

1014 
Heat transmission, Blechynden's 
tests of, 593 
from flame to water, 592 
from gases to water, 592 
from steam to water, 587 
in condenser tubes, 589 
in feed-water heater, 590 
in radiators, 698 
resistance of metals to, 580 
through building walls, etc., 582, 

688 
through plates, 580, 591 
through plates from steam or 
hot water to air, 595 
Heat treatment of a motor-truck 
axle, 479 
treatment of high speed tool 

steel, 1265 
treatment of steel (see Steel) 
unit of, 560, 867 
imits per pound of water, 717 
Heaters and condensers, calcula- 
tion of surface of. 939 
cast iron, for hot-blast heating, 

709 
cast iron, tests of, 709 
electric, 1420 
feed-water, 938-940 
feed- water, open-type, 940 
feed- water, transmission of heat 
in, 590 
Heating and Ventilation, 681-716 
allowance for exposure and 

leakage, 688 
blower system, 708-710 
boiler heating surface, 694 
computation of radiating sur- 
face, 698 
heating surface, indirect, 698 
heating value of radiators, 684, 

697 
quantity of heat required, 690 
steam-heating, 694-703 (see 

Steam-heating) 
transmission of heat through 
building walls, 688 
Heating a building to 70° in zero 
weather, 711 
air, heat absorbed in, 691 
and ventilating by electric cur- 
rent, 1421 
by Jblower system, capacity of 

fans for, 711 
by electricity, 713 
by exhaust steam, 1009 
by hot-air furnaces, 690 
by hot water, 703-708 (see Hot- 
water heating) 
by overhead steam pipes, 702 
by steam (see Steam-heating) 
domestic, by electricity, 1421 
furnace, size of air pipes for, 692 
furnace, with forced air supply, 

690 
guarantees, performance of, 712 
of electrical conductors, 1408 



hea-hol 



INDEX. 



hol-how 



1499 



Heating of factories by blower sys- 
tem, 708, 710 
of greenhouses, 702 
of large buildings, 684 
of steel for forging, 492 
of tool steel, 492 
problems, standard values in, 

687 
steam and electric, 1421 
value of coals, 826-830 
value of wood, 835 
water by steam coils, 591 
Heating-surface of steam-boiler, 

887, 888 
Height, table of, corresponding to 

a given velocity, 523 
Helical steel springs, 418 
Hehx, 61 

Hemp rope, strength of, 357 
rope, table of strength and 
weight of, 410, 415 
Henry, definition and value of, 

1397 
High-speed tool steel {see Steel, 

and Tools) 
Hindley worm gear, 1169 
Hobson's hot-blast pyrometer, 

555 
Hodgkinson's formula for columns 

283 
Hoists, electric motors for, 1464 
Hoisting by hydrauUc pressure, 
813 
counterpoise system, 1189 
cranes, 1189-1193 {see Cranes) 
effect of slack rope, 1186 
endless rope system, 1189 
engines, 1186 

engines, compressed-air, 646 
engines, counterbalancing of, 

1188 
horse-power required for, 1184 
Koepe system, 1189 
loaded wagon system, 1189 
limit of depth for, 1186 
of cargoes, 414 
pneumatic, 1187 
suspension cableways, 1205 
with tapering ropes, 1188 
Hoisting-rope, 410-415 
flexible steel wire, 258, 259 
iron or steel, tables, 255-261 
non-spinning, 258, 261 
stresses in, on inclined planes, 

1204 
tension required to prevent 

slipping. 1206 
wire, sizes and strength of, 410, 
Holding power of bolts in white 
pine, 346 
of expanded boiler tubes, 364 
of lag-screws, 347 
of nails in wood, 347 
of nails, spikes and screws, 346, 

347 
of tubes expanded into sheets, 

364 
of wood screws, 346 



Holes, tube, in steam-boilers, 916 

HoUow cylinders, resistance of to 

collapse, 341-345 

shafts, torsional strength of, 334 

Homogeneity test for fire-box 

steel, 508 
Hooks and shackles, strength of, 
1184 
heavy crane, 1183 
proportions of, 1182 
Horse gin, 534 
work of, 533 
Horse-power {see also Power) 
brake, 970 

brake, definition of, 1017 
computed from torque, 1436 
constants, of steam-engines, 

971-974 
definition of, 27, 528 
electrical, 970, 1408 
electrical, brake and indicated, 

1408 
hours, definition of, 528 
nominal, definition of, 974 
of compound engine, estimat- 
ing, 971 
of fiowing water, 765 
of marine and locomotive boil- 
ers, 888 
of steam-boilers, 885 
of steam-boilers, builders' rat- 
ing, 888 
of steam-engines, 970-976 
water and steam, cost of, 767 
Hose coupUngs, national standard, 
218 
fire, friction losses in, 752 
hydrant pressures required with 

different lengths of, 750 
rubber-lined, friction loss in, 

752 
specifications for, 379 
Hot-air engines, 1095 

heating {see Heating) 
Hot-blast pyrometer, Hobson's, 

555 
Hot-blast system of heating, 708 

{see Heating) 
Hot boxes, 1228' 

Hot-water Heating (see Heating), 
703-708 
arrangement of mains, 703 
computing radiating surface, 

704-706 
corrosion of pipe in, 708 
iudirect, 705 
of greenhouses, 703 
rules for, 703 
size of pipes for, 704 
sizes of flow and return pipes, 

707 
velocity of flow, 703 
with forced circulation, 707 
House-heating {see Heating) 
House-service pipes, flow of water 

in, table, 744 
Howden system of forced draught, 
923 



1500 



How-iU 



INDEX. 



iU-lnt 



Howe truss, stresses in, 546 
Humidity and temperature, com- 
fortable, 685 

relative, table of, 610 
Humphrey gas pvmip, 808 
Hyatt roller bearings, 1235 
Hydraesfer process, treating iron 

surfaces, 473 
Hydrant pressures required with 
different lengths of hose, 750 
Hydraulic air compressor, 650 

apparatus, efficiency of, 812 

cylinders, thickness of, 813 

engine, 815 

forging, 814, 815 

formulae, 726-746 

formulae, approximate, 734, 737, 
746 

grade-Line, 748 

packing, friction of, 813 

pipe, riveted, table, 219 

power in London, 814 

press, thickness of cylinders 
for, 340 

presses in iron works, 813 

ram, 810-812 

riveting machines, 814 
Hydraulics (see Flow of water) 
Hydraulic pressure, hoisting by, 
813 

transmission, 812-816 

transmission, energy of, 812 

transmission, speed of water 
through pipes and valves, 813 

transmission, references, 816 
Hydrometer, 175 
Hygrometer, dry and wet bulb, 

610 
Hyperbola, asymptotes of, 73 

construction of, 49 

equations of, 72 
Hyperbolic curve on indicator 
diagrams, 974 

logarithms, tables of, 164-166 
Hypocycloid, 50 

I-BEAMS (see also Beams) 
Bethlehem steel, 332 
Carnegie, table of, 307-310 
safe loads on, 309 
spacing of, for uniform load, 
311 
Ice-making, absorption evapora- 
tor system, 1367 
machines, 1336-1367 (see Re- 
frigerating machines) 
plant, test of, 1367 
tons of ice per ton of coal, 

1367 
with exhaust steam, 1367 
Ice, manufacture, 1366 
-melting effect, 1343 
properties of, 720 
strength of, 368 
Ignition in gas engines, 1102 
temperature of gases, 858 
Illumuiants, relative color values 
of, 1469 



lUuminants, relative efficiency of, 

1472 
lUumuiating coal-gas, 858 
Illuminatmg-gas, 858-866 

calorific equivalents of constit- 
uents, 860 
fuel value of, 863 
space required for plants, 862 
Illuminating water-gas, 859 
Illumination by arc lamps at 
different distances, 1471 
definition of, 1468 
electric and gas lighting, 1468 
Ulterior, 1473 
of buildings, watts per square 

foot, required for, 1369 
relation of, to vision, 1469 
Impact, 530 
Impedance, 1441 
polygons, 1442 
Impulse water wheels, 779 (see 

Water wheel, tangential) 
Impurities of water, 720 
Incandescent lamps (see Lamps), 

1470 
Inches and fractions as decimals 

of a foot, table, 5 
Inclined-plane, 527, 537 
motion on, 527 
stresses in hoisting ropes on, 

1204 
wire-rope haulage, 1202 
Incrustation and scale, 721, 927- 

932 
India rubber, action imder ten- 
sion, 378 
vulcanized, tests of, 378 
Indicated horse-power, 970-976 
Indicator diagrams, analysis of, 
1017 
diagrams, to draw clearance 

line on, 974 
diagrams, to draw expansion 

curve, 974 
diagrams, tests of locomotives, 

1122 
rig, 969 
Indicators, steam-engine, 968-976 
(see Steam-engines) 
steam-engine, errors of, 969 
Indirect heating radiators, 698 
Inductance, 1440 

of lines and 'circuits, 1445 
Induction, magnetic, 1398 

motors, 1463 
Inertia, definition of, 513 

moment of, 293, 517 
Ingot iron, "Armco," 477 
Injector, 807 

efficiency of, 937 
equation of, 936 
performance of, 937 
Inspection of steam-boilers, 932 
Insulation, underwriters', 1410 
Insulators, electrical value of, 1402 

heat, 581 
Integrals, 75 
table of, 80, 81 



int^Iro 



INDEX. 



Irr-lsm 



1501 



Integration, 76 

Intensity of magnetization, 1398 

Interest, 12 

compound, 13, 14 
Intercoolers for air compressors, 

648 
Interpolation, formula for, 86 
Invar, iron-nickel alloy, 499, 667 
Involute, 52 
gear-teeth, 1165 
gear- teeth, approximation of, 
1166 
Involution, 7 

Iridium, properties oi, 178 
Iron and steel, 178, 436-511 
classification of, 436 
effect of cold on strength of, 

464 
electric furnaces, 1423 
inoxidizable surface for, 472 
preservative coatings for, 471- 

474 
relative corrosion of, 468 
rustless coatings for, 471-474 
sheets, weight of, 183 
tensile strength at high tem- 
peratures, 463 
Iron bars {see Bars) 

bars, weight of square and 

round, 181, 184 
bridges, durability of, 466 
cast, 437-454 {see Cast-iron) 
castings, chemical standards for, 

441 
coated with aluminum, 473 
coated with lead, 474 
coefficients of expansion of, 465 
color of at various tempera- 
tures, 558 
-copper-zinc alloys, 393 
corrosion of, 467 
corrugated, sizes and weights, 

194 
durabiUty of, 465-467 
electrolytic, properties of, 460 
flat-rolled, weight of, 188, 189 
for stay-bolts, 462 
inoxidizable surfaces, produc- 
tion of, 472 
latent heat of fusion of, 568 
maUeable, 454 {see Malleable 

iron) 
pig {see Pig-iron and Cast-iron) 
plates, approximating weight of, 

486 
plates, weight of, table, 187 
properties of, 178 
rivets, shearing resistance of, 

430 
rope, table of strength of, 410 
shearing strength of, 362 
sheets, weights, 31, 32, 183 
-silicon-aluminum alloys, 398 
specific heat of. 562, 563 
tubes, collapsing pressure of, 

341 
wrought, 459-463 {see Wrought 
iron) 



Irregidar figure, area of, 66, 67 

solid, volume of, 66 
Irrigation canals, 755 
Isothermal compression of air, 633 

expansion, 601 

expansion of steam, 959 

JAPANESE alloys, compositioa 
of, 393 
Jarno tapers, 1319 
Jet condensers, 1068 

propulsion of ships, 1384 
reaction of a, 1385 
Jets, steam {see Steam Jets) 

vertical water, 749 
Joints, pipe {see Pipe joints) 
riveted, 424-435 {see Riveted 
joints) 
Joists, contents of, 21 
Joule, definition and value of, 

1396, 1397 
Joule's equivalent, 560 
Journals {see also Shafts and 
Bearings) 
coeflQcients of friction of, 1220 
Journal-bearings, cast-iron, 1223 
friction of, 1220-1232 
of engines, 1034 

KAOLIN, melting point of, 556 
Kelvin's rule for electric 
transmission, 1411 
Kennedy key, 1330 
Kerosene as fuel, 841 

for scale in boilers, 929 
Keys, dimensions of, 1328 
gib, 1332 

holding power of, 1332 
various forms of, 1328 
Key-seats, depth of, 1329 
Keyways for miUing cutters, 1277 
Kinetic energy, 528 
King-post truss, stresses in, 543 
Kirkaldy's tests of strength of 

materials, 352-358 
Knife-edge bearings, 1238 
Koepe's system of hoisting, 1189 
Knot, on nautical mile, 17 
Knots, varieties of, 415, 416 
Krupp steel tires and axles, 354 
Kutter's formula, fiow of water, 730 
formula, tables of flow of water, 
738, 739 

LACING of belts, 1147 
Ladles, foundry, sizes of, 
1257 
Lag screws, holding power of, 347 

screws, sizes and weiglits, 241 
Lamps, arc, 1470 
arc, data of, 1471 
arc, illumination by, at differ- 
ent distances, 1471 
arrangement of, in rooms, 1475 
electric, life of, 1476 
Incandescent, characteristics of, 

1474 
incandescent electric, 1470 



1502 



lam-lin 



INDEX. 



lin-loc 



Lamps, mercury vapor, 1470 

tungsten, 1473 
Land measure, 17 
Lang-lay wire-rope, 254 
Lap and lead in slide valves, 1052- 

1054 
Lap joints, riveted, 426, 427 
Laps and lapping, 1310 
Latent heat of evaporation, 569 

of fusion of iron, 568 

of fusion of various substances, 
568 
Lathe, change-gears for, 1260 

cutting speed of, 1259 

horse-power to run, 1292, 1293 

power required for, 1293 

rules for screw-cutting gears, 
1259 

setting taper in, 1261 

tools, forms of, 1261 
Lattice girders, allowed stresses 

in, 289 
Laws of falling bodies, 521 

of motion, 513 
Lead and tin tubing, 226, 227 

coatings on iron surfaces, 474 

effect of, on copper aUoys, 394 

-lined iron pipes, 227 

paint as a preservative, 471 

pipe, tin-lined, sizes and weights, 
table, 226 

pipe, weights and sizes of, 
table, 226, 227 

properties of, 178 

sheet, weight of, 228 

waste-pipe, weights and sizes 
of, 227 
Leakage of steam in engines, 976 
Least common multiple, 2 
Leather, strength of, 357 
Lea-Deagan two-stage pump, test 

of, 801 
Le Chatelier's pyrometer, 554 
Lentz compound, engine, 997 
Leveling by barometer, 607 

by boiling water, 607 
Lever, 535 

bent, 514, 536 
Lewis's key, 1329 
Lighting, electric and gas, 1468 

electric, cost of, 1475 

of streets, 1471 

quantity of gas and electricity 
required for different rooms, 
1473 

street, recent installations, 1476 
Lightning protection of chimneys, 

949 
Lights (see Lamps) 
Lignites, analysis of, 829 
Lime and cement mortar, strength 
of, 372 

and cement, weight of, 180 
Limestone, strength of, 371 
Limit, elastic, 273-278 

gages for screw-thread iron, 232 
Lines of force, 1430 
Links, steel bridge, strength of, 353 



Link-belting, sizes and weights, 

1199 
Link-motion, locomotive, 1119 

steam-engine, 1062-1065 
Lintels in buildings, 1390 
Liquation of metals in alloys, 388 
Liquefaction of gases, 605 
Liquid air and other gases, 605, 606 

measure, 18 
Liquids, absorption of gases by, 
605 

compressibihty of, 175 

expansion of, 567 

specific gravity of, 175 

specific heats of, 563 
Loading and storage machinery, 

1193 
Lock- joints for pipes, 212 
Locomotive boilers, 1113 

boiler tubes, seamless, 222 

boilers, size of, 1113 

crank-pin, quantity of oil used 
on, 1246 

engine performance, 1122 

forgings, strength of, 353 
Locomotives, 1108-1129 

boiler pressure, 1117 

classification of, 1116 

compounding of, 1125 

compressed-air, 1128 

compressed-air, with compound 
cylinders, 1129 

counterbalancing of, 1126 

dimensions of, 1120-1122 

drivers, sizes of, 1118 

economy of high pressure in, 
1116 

effect of speed on cylinder pres- 
siu-e, 1117 

eflBciency of, 1111 

exhaust-nozzles, 1115 

fire-brick arches in, 1115 

fireless, 1127 

fuel efficiency of, 1119 

fuel waste of, 1125 

grate-surface of, 1115 

hauUng capacity of, 1111 

horse-power of, 1113 

indicator tests of, 1122 

leading types of, 1116 

hght, 1127 

link-motion, 1119 

MaUet compound, 1120 

narrow gage, 1127 

performance of high speed, 1118 

petroleum burning, 1127 

safety valves for, 935 

smoke-stacks, 1115 

speed of, 1118 

steam distribution of, 1117 

steam-ports, size of, 1118 

superheating in, 1126 

testing, 1123 

tractive force of, 1112. 1125 

types of, 1116 

valve travel, 1118 

water consumption of, 1122 

weight of, 1124 



loc-mac 



INDEX. 



mac-man 



1503 



Locomotives, Wootten, 1114 
Logarithmic cm*ve, 73 

ruled paper, 84 

sines, etc., table, 167 
Logarithms, 79 

four-place, table, 168 

hyperboUc, tables of, 164-166 

six-place, table, 137-164 

use of, 135-137 
Logs, area of water required to 
store, 181 

lumber, etc., weight of, 181 

weight of, 181 
Long measure, 17 
Loop, steam, 883 
Loops of force, 1430 
Lord and Haas's tests of coal, 

822, 823 
Loss and profit, 12 

of head. Cox's formula, 734 

of head in cast-iron pipe, tables, 
745 

of head in flow of water, 728, 
735, 745 

of head in riveted steel pipes, 735 
Lowmoor iron bars, strength of, 

352 
Lubricant, water as a, 1246 
Lubricants, examination of, 1242 

grease, 1244 

measurement of durability, 1241 

oil, specifications for, 1242 

qualifications of good, 1242 

relative value of, 1242 

soda mixture, 1246 

solid, 1246 

specifications for petroleum, 
1242 
Lubrication, 1241-1246 

of engines, quantity of oil 
needed -for, 1245 

of steam-engine cylinders, 1245 
Limiber, weight of, 181 
Lumen, definition of, 1469 
"Lusitania," performance of, 
1376, 1381 

turbines and boilers of, 1381 
Lux, definition of, 1469 

MACHINE screws, A. S. M. 
E. standard, table, 234- 

screws, taps for, 1320 

shop, 1258-1333 

shops, electric motors for, 1294- 

1308, 1466 
Machine tools, drives, feeds and 

speeds, 1307 
electric motors for, 1294-1308. 

1466 
gear connections of, to motors, 

1301 
individual motors for driving, 

1308 
methods of driving, 1307 
power required for, 1270, 1278, 

1286. 1293 
sizes of motors for, 1294 



Machine tools, soda mixture for, 
1246 
speed of, 1258 
Machines, dynamo-electric (see 
Dynamo-electric-machines) 
efficiency of, 532 
elements of, 535-541 
in groups, power required for 
driving, 1305 
Machinery, coal-handling, 1196- 
1199 
horse-power required to run, 
1292-1308 
Maclaurin's theorem, 78 
Magnalium, magnesium-alumi- 
num alloy, 399 
Magnesia bricks, 269 
Magnesite, analysis of, 270 
Magnesium, properties of, 179 
Magnet, electro, 1430 
Magnets, lifting, 1193 
Magnetic alloys, 402 

balance, for testing steel, 483 
brakes, 1240 

capacity of iron and steel, ef- 
fect of anneahng on, 483 
circuit, 1430 
circuit, units of, 1398 
. field, 1398 
field, strength of, 1436 
flux, magnetic induction, 1398 
moment, 1398 

pole, imit of, definition, 1398 
Magnetization, intensity of, 1398 
Magneto-motive force, 1398 
Magnolia metal, composition of, 

405 
Mahler's calorimeter, 826 
Malleability of metals, table, 180 
Malleable cast iron, 454 
castings, annealing, 455 
castings, design of, 457 
castings, tests of, 458 
iron, pig iron for, 454 
iron, composition and strength 

of, 454, 458 
iron, improvement in quality, 

458 
iron, physical characteristics,456 
iron, shrinkage of, 455 
iron, specifications, 457 
iron, strength of. 454, 458 
iron test bars, 457 
Mandrels, standard steel, 1318 
Manganese bronze, 401 
-copper alloys, 401 
effect of, on cast iron, 438, 450 
effect of, on steel, 476 
properties of, 179 
steel, 494 

sulphide, dangerous in steel, 486 
Manganin, high resistance alloy, 

404, 1402 
Manhole openings in steam- 
boilers, 914 
Manila rope, 411 

rope, weight and strength of, 
410-415 



1504 



man-mer 



INDEX. 



mer-mod 



Manograph, a high-speed engine- 
indicator, 969 
Manometer, air, 607 

work of, tables, 532, 533 
Man-wheel, 533 
Marble, strength of, 357 
Marine engineering, 1368-1385 
(see Ships and Steam-engines) 

engine, internal combustion, 
1374 

engine practice, advance in, 1380 
Mariotte's law of gases, 603 
Martensite, 439, 480 
Masonry, allowable pressures on, 
1386 

crushing strength of, 371 

materials, weight and specific 
gravity of, 177 
Mass, definition of, 511 
Materials, 173-273 

standard cross-sections, for 
draftsmen, 271 

strength of, 272-379 

strength of, Kirkaldy's tests, 
352-358 

various, weights of, table, 181 
Maxima and minima, 78, 79 
Maxwell, definition and value of, 

1398 
Measures and weights, compoimd 
units, 27 

and weights, metric system, 21- 
26 

apothecaries, 19 

board and timber, 20 

circular, 20 

dry. 19 

liquid, 18 

long, 17 

nautical, 17 

of work, power and duty, 27 

old land, 1 7 

shipping, 19, 1316 

solid or cubic, 18 

square, 18 

surface, 18 

time, 20 
Measurement of air velocity, 624 

of elongation, 279 

of fiowing water, 757-764 

of vessels, 1368 
Measurements, miner's inch, 761 
Mechanics, 511-548 
Mechanical equivalent of heat, 
560, 868 

and electrical units, equivalent 
values of, 1399 

powers, 535 

stokers, 918 
Mekarski compressed-air tram- 
way, 652 
Melting-points of substances, tem- 
peratures, 554, 559 
Mensuration, 54-66 
Mercurial thermometer, 549 
Mercury-arc rectifier, 1456 
Mercury-bath pivot, 1233 

properties of, 179 



Mercury vapor lamp, 1469 
Mesure and Nouel's pyrometric 

telescope, 556 
Metacenter, definition of, 719 
Metals, anti-friction, 1223 

coefiicients of expansion of, 566 

coeflQcients of friction of, 1220 

electrical conductivity of, 1401 

fiow of, 1323 

heat-conducting power of, 580 

life of, imder shocks, 276 

properties of, 177-180 

resistance overcome in cutting 
of, 1292 

specific gravity of, 174 

specific heats of, 562, 563 

table of ductility, infusibihty, 
malleability and tenacity, 180 

tenacity of, at various tempera- 
tures, 463 

weight of, 174 
Metaline lubricant, 1246 
Metallography, 480 
Meter, Thomas electric, for meas- 
uring gas, 667, 669 

Venturi, 758 

water, V-notch recording, 759 
Meters, water deUvered through, 

749 
Methane gas, physical laws of, 604 
Metric conversion tables, meas- 
ures and weights, 21-26 

screw-threads, cutting of, 1261 
Microscopic constituents of cast 

iron and steel, 439, 480 
Mil, circular, 18, 29, 
Mill buildings, columns, 1393 

buildings, approximate cost of, 
1394 

power, 766 
Milling cutters, diameter, clear- 
ance and rake of, 1278 

for gear-wheels, 1162 

inserted teeth, 1276 

key ways in, 1277 

lubricant for, 1281 

number of teeth in, 1276 

side, 1275 

spiral, 1275 
Milhng, high-speed, 1282 

iobs, typical, 1281 

machines, cutting speed of, 
1280, 1284 

machines, high results with, 
1282 

machines, typical jobs on, 1281 

power required for, 1278 

practice, modern, 1279, 1283 

with or against the feed, 1280 
Mine fans, experiments on, 673 

ventilating fans, 673 

ventilation, 714 
Mines, centrifugal fans for, 672 
Miner's inch, 18 

inch measurements, 761 
Modulus of elasticity, 274 

of elasticity of various materials 
374 



mod "Dai 



INDEX. 



nap-ori 



1505 



Modulus of resistance, or section 
modulus, 294 

of rupture, 297 
Moist\u*e in atmosphere, 609-613 

in steam, determination of, 942- 
944 

in steam escaping from boilers, 
944 
Molding-sand, 1266 
Molds, cast-iron, for iron castings, 

analysis of, 1256 
Moment of a couple, 515 

of a force, 514 

of friction, 1229 

of inertia, 293, 295, 517 

statical, 514 
Moments, method of, for deter- 
mining stresses, 545 

of inertia of regular solids, 517 

of inertia of structural shapes, 
295 
Momentum, 527 
Mond gas producer, 852 
Monel metal, copper-nickel alloy, 

403 
Monobar chain conveyor, 1197 
Morin's laws of friction, 1223 
Morse tapers, 1319 
Mortar, strength of, 372 
Motion, accelerated, formulae for, 
527 

friction of, 1219, 1221 

Newton's laws of, 513 

on inchned planes, 527 

perpetual, 532 

retarded, 521 
Motor apphcations, 1464-1468 

boats, power of enginesffor, 1374 

-driven machine tools, 1308 

generators, 1456 

repulsion, induction, 1464 

squirrel-cage, 1463 

temperatures, limits of, 1432 
Motors, alternating-current, 1463 

commutating pole, 1437 

compressed-air, 639-641 

electric {see Electric motors) 

electric, classification of, 1461 

gear connections of, for machine 
tools, 1301 

sizes of, for machine tools, 1294 

water current, 765 
Moving strut, 536 
Mule, work of, 534 
Multiphase electric currents, 1445 
Multiple system of evaporation, 

570 
Multivane fans, 658 
Mimtz metal, composition of, 390 
Mushet steel, 496 

NAILS, cut, table of sizes and 
weights, 244 
cut vs. wire, 347 
holding power of, 346 
wire, table of sizes and weights, 
246, 247 
Nail-holding power of wood, 347 



Naphtha as fuel, 841 

Napier's rule for flow of steam, 

876 
Natural gas, 847, 848 
Nautical measure, 17 

mile, 17 
Newton's laws of motion, 513 
Nickel, effect of on properties of 

steel, 498 
Nickel, properties of, 179, 379 
steel, 497 
steel, tests of, 497 
steel, uses of, 498 
Nickel-copper alloys, 402 

'Vanadimn steels, 499 
Niter process, treating iron sur- 
faces, 473 
Nordberg feed-water heating sys- 
tem, 1003 
key, 1331 

pumping-engine, 805 
Nozzles, flow of steam through, 

876, 1085 
Nozzles, flow of water in, 763 
for measiu'ing discharge of 

pumping-engines, 759 
water, efficiency of, 784 
Nut and bolt heads, thickness of, 
231 

OATS, weight of, 180 
Ocean waves, power of, 786 
Oersted, unit of magnetic 
reluctance, 1398 
Ohm, definition and value of, 1397 
Ohm's law, 1406 

law applied to alternating cur- 
rents, 1442 
law appUed to parallel circuitsf, 

1407 
law apphed to series circuits, 
1407 
OU as fuel (see Fuel Oil), 842, 843 
-engines, 1102 
fire-test of, 1243 
for scale removal in boilers, 930 
for steam turbines, 1244 
fuel, chimney draught with, 952 
fuel, chimney table for, 961 
lubricating, 1242-1245 {see Lub- 
ricants) 
parafflne, 1243 
pressure in a bearing, 1228 
quantity needed for engines, 

12^5 
tempering of steel forgings, 482 
vs. coal as fuel, 842, 843 
well, 1243 

wells, air-lift pump for, 809 
Open-hearth, steel {see Steel, 
open-hearth), 475 
furnace, temperatures in, 554 
Ordinates and abscissas, 70 
Ores, cubic feet per ton, 181 
Orifice, equivalent, In mine ven- 
tilation, 715 
flow of air through, 615-617, 
670 



1506 



orl-pew 



INDEX 



pho-plp 



Orifice, flow of water through, 726 
rectangular, flow of water 
tlirongh, table, 760 
Oscillation, center of, 518 

radius of, 518 
Overhead steam-pipe radiators, 

702 
Ox, work of, 534 
Oxy-acetylene welding, 488 
Oxygen, effect of on strength of 
steel, 477 

TT value and relations of, 57 

PACKING, hydraulic, friction 
of, 1241 
-rings of engines, 1023 
Paddle-wheels, 1383 
Paint, 471 

chrome, preventing corrosion, 
469 

for roofs, 192 

qualities of, 472 

quantity of, for surface, 472 
Paper, logarithmic ruled, 84 
Parabola, area of by calculus, 76 

construction of, 48, 49 

equations of, 72 

path of a projectile, 525 
Parabolic conoid, 65 

spindle, 65 
Parallel forces, 515 

operation of motors, 1439, 1450 
Parallelogram area of, 54 

of forces, 513 

of velocities, 523 
Parallelopipedon of forces, 514 
Parentheses in algebra, 34 
Partial payments, 14 
Parting and threading tools, speed 

of, 1268 
Patterns, weight of, for castings, 

1256 
Payments, equation of, 14 
Pearlite, 439, 480 
Peat, 838 

Pelton water-wheel, 779 
Pendulum, 520 

conical, 520 
Percentage, 12 
Percussion, center of, 518 
Perforated plates, strength of, 425 
Permeability, magnetic, 1400, 

1430 
Permeance, magnetic, 1400 
Permutation, 10 
Perpetual motion, 532 
Petroleum as a metallurgical fuel, 
843 

-burning locomotives, 1127 

cost of as fuel, 842 

engines, 1102 

for scale removal in boilers, 930 

Lima, 841 

products of distillation of, 840 

products, specifications for, 1242 

value of as fuel, 841 
Pewter, composition of, 407 



Phosphor-bronze, composition of, 
390 
specifications for, 395 
springs, 424 
strength of, 395 
Phosphorus, influence on gteel,476 

influence of, on cast iron, 438 
Piano-wire, strength of, 250 
Pictet fluid, for refrigerating, 1337 
Piezometer, 757 
Pig-iron (see also Cast iron) 
analysis of, 439 
charcoal, strength of, 452 
distribution of silicon in, 448 
electric smelting of, 1424 
for maUeable castings, 454 
grading of, 437 

influence of silicon, etc., on, 438 
sampling, 443 
specifications for, 443 
Piles, bearing power of, 1386 
Pillars, strength of, 283 
Pine, strength of, 366 
Pinions, raw-hide, 1177 
Pins, forcing fits of by hydraulic 

pressure, 1324 
Pins, taper, 1321 
Pipe bends, flexibility of, 221 
branches, compound pipes, for- 
mula for, 746 
cast-iron, friction loss in, table, 

747, 748 
cast-iron, speciflcations for 

metal for, 441 
cast-iron, threaded, 199 
corrosion of in hot-water heat- 
ing, 708 
coverings, tests of, 584-587 
dimensions, Briggs standard, 

221 222 
fittings, flanged, 208-214 
flttings, screwed, 207, 216 
fittings, strength of, 216 
fittings, valves, etc., resi.stance 

of, 701 
flanges, extra heavy, tables, 

210 212 
flanges, tables, 209-213 
iron and steel, strength of, 363 
iron, lead-, brass- and copper- 

Imed, 227 
iron, lead-covered, 228 
iron, tin- and lead-lined, 227 
joints, bell and spigot, lead re- 
quired for, 199 
lines for fans and blowers, 670 
lines, long, 743 
specialties, 205 
threading of, force required for, 

363 
welded, weight and bursting 

strength of, 205 
wooden stave, 218, 735 
Pipes, see also Tubes 
air-bound, 748 

air, loss of pressure in, 617-624 
and valves for superheated 
steam, 882 



pip-pip 



INDEX. 



pis-pla 



1507 



Pipes, bent and coiled, 221, 222 
block-tin, weigiits and sizes of 

227 
coiled, table of, 221 
Pipes, cast-iron, bell and spigot 
for gas, 198 
flanged, for gas, 199 
for high-pressure service, 198 
formulae for thickness of, 196 
safe pressures for , tables , 1 96-1 98 
thickness of, for various heads 

196-200 
transverse strength of, 452 
underground, weight of, 197 
weight and dimensions, 196-200 
Pipes, effects of bends in, 624 747 
equaUzation of. table 625 
equation of, 884 
flow of air in, 617-624 
flow of gas in, 864-866 
flow of steam in, 877-879 
flow of water in, 728-746 
for steam heating, 698 
house-service, flow of water in 

table, 744 
iron and steel, corrosion of, 466, 

467 
lead, safe heads for, 226 
lead tin-lined, sizes and weights, 

table, 227 
lead weights and sizes of 

table, 226 
maximum and mean velocities 

m, 758 
proportioning to radiating sur- 
face, 699, 700 
rectangular, flow of air in, 622 
resistance of the inlet, 735 
rifled, for conveying heavy oils, 

746 
riveted, flanges for, table, 211 
riveted hydraulic, weights and 

safe heads, table, 219 
riveted iron, dimensions of 

table. 220 
riveted steel, loss of head in. 

734 
riveted steel, water, 351 
sizes of threads on, 201, 217 
spiral riveted, table of, 220 
steam (see Steam-pipes) 
steam, sizes of in steam heat- 
ing, 699-701 
table of capacities of, 131 
used as columns, 363 
volume of air transmitted in. 

table, 623, 624 
water, loss of head in, 728, 735 

745 (see Loss of head) 
welded, extra strong, 203, 204 
welded, standard, table of di- 
mensions, 202 
Pipe-joint, Converse lock-joint, 

Matheson, 212 
Rockwood, 212 
Piping, power-house, identifica- 
tion of by different colors, 885 



Piston rings, steam-engine, 1023 

rods, steam-engine, 1024 

valves, steam-engine, 1061 
Pistons, steam-engine, 1023 
Pitch, diametral, 1158 

of gearing, 1157 

of rivets, 42/ 

of screw-propeller, 1377 
Pitot-tube, best form of. 667 

gage, 757 

measurements, accuracy of 669 

use in testing fans, 667 
Pivot-bearings, 1229, 1232 

mercury bath, 1233 
Plane incUned, 527, 537 (see In- 
clined Plane) 

surfaces, mensuration of, 54 
Planer, horse-power required to 
run, 1302 

tools, standard. 1271-1274 

work, 1270-1274 
Planers, feeds and speeds of 1270 

power requirements of, 1302 
Planing, time required for 1271 

work that should be planed. 

Planished and Russia iron, 473 
Plank, wooden, maximum spans 

lor, loy^ 
Plate-girder, strength of, 353 

-girders, allowed stresses in, 289 
Plates (see also Sheets) 

acid pickled, heat transmission 

through, 591 
areas of, in square feet, table 

128, 129 
brass, weight of, tables. 228, 229 
Carnegie trough, properties of. 

table, 308 
circular, strength of, 336 
copper, strength of, 356 
copper, weight of, table. 229 
corrugated steel, properties of 

table, 310 
flat, cast-iron, strength of, 336 
flat, for steam-boilers, rules for, 

916 
flat, unstayed, strength of, 337 
for stand-pipes, 349 
iron and steel, approximating 

weight of, 486 
iron, weight of, table, 187, 188 
of different materials, table for 

calculating weights of, 181 
perforated, strength of, 425 
punched, loss of strength in 

424 
stayed, strength of. 338 
steel boiler, specifications for 

507 
ste^el, for cars, specifications for. 

507 
steel, specifications for, 507 
steel, tests of, 353, 355 
transmission of heat through, 

587 
transmission of heat through 
from air to water, 592 



1508 



pla-pre 



INDEX. 



pre-pum 



Plates, transmission of heat 

through, from steam to (air, 

595 

Plating for bulkheads, table, 339 

steel, stresses in, due to water 

pressiu-e, 338 
for tanks, table, 338 
Platinite, 499, 567 
Platinimi, properties of, 179 
pyrometer, 553 
wire, 248 
Plenimi system of heating, 708 
Plow-steel wire, 250 

-steel wire-rope, 257, 259 
Plugs, fusible, in steam boilers, 

918 
Plimger packing, hydraulic, fric- 
tion of, 1239 
Pneumatic conveying, 1201 
hoisting, 1187 
postal transmission, 1201 
Polarity of electro-magnets, 1432 
Poles, tubular, for electric lines, 

206 
Pohshing and buffing, 1310 

wheels, speed of, 1310 
Polyedron, 63 
Polygon, area of, 55 
construction of, 42-45 
of forces, 513 
Polygons, impedance, 1442 

table of, 45, 55 
Polyphase circuits, 1445 
Popp system of compressed-air, 

639-641 
Population of the United States, 

11 
Port opening in steam-engines, 

1057 
Portland cement, strength of, 358 
Postal transmission, pnemnatic, 

1201 
Potential energy, 528 
Pound, British avoirdupois, 26 

-calorie, definition of, 560 
Pounds per square inch, equiva- 
lents of, 27 
Power, animal, 532 

and work, definition of, 528 

electrical, cost of, 1012 

factor of alternating currents, 

1440 
hydraulic, in London, 814 
measures of, 27 
of a waterfall, 765 
of electric circuits, 1408 
of ocean waves, 786 
required for machhie tools, 

1292-1302 
required to drive machines in 

groups, 1305 
unit of. 528 
Powers of numbers, algebraic, 33 
of numbers, tables, 7, 8, 93- 
110 
Power-plant economics, 1011 
Pratt truss, stresses in, 544 
Preservative coatings, 471-474 



Press fits, pressure required for, 
1324-1326 

forging, high-speed, steam hy- 
draulic, 815 

hydrauUc forging, 814 

hydraulic, thickness of cylinders 
for, 340 
Presses, hydraulic, in iron works, 
813 

punches and shears, fly-wheels 
for, 1323 

punches, etc., 1321 
Pressed fuel, 831 
Pressure, collapsing of flues, 342 

collapsing of hollow cylinders, 
341 
Pressures of fluids, conversion 

table for, 607 
Priming, or foaming, of steam 

boilers, 721, 930 
Prism, 62 
Prismoid, 63 

rectangular, 62 
Prismoidal formula, 63 
Problems, geometrical, 37-53 

in circles, 39-44 

in lines and angles, 37-39 

in polygons, 42-45 

in triangles, 41 
Process, the Thermit, 400 
Producer-gas, 848-855 (see Gas) 
Producers, gas (see Gas-producers) 

gas, use of steam in, 854 
Profit and loss, 12 
Progression, arithmetical and geo- 
metrical, 10, 11 
Projectile, parabola path of, 525 
Prony brake, 1333 
Propeller, screw (see Screw-pro- 
peUer) 1377 

shafts, strength of, 354 
Proportion, 6 

compound, 7 
Protective coatings for pipes, 

206 
PuUeys, 1135-1138 

arms of, 1050 

cone, 1136 

cone, on machine tools, 1307 

convexity of, 1136 

differential, 539 

for rope-driving, 1217 

or blocks, 538 

proportions of, 1111 

speed of, 1148, 1162 
Pulsometer, 806 

tests of, 807 
Pumps, air-, for condensers, 1071, 
1073 

air-Uft, 808 

and pumping-engines, 788-812 

boiler-feed, 792 

boiler-feed, efficiency of, 937 

centrifugal, 796-802 

centrifugal, combination single 
stage and two stage, 798 

centrifugal, design of, 797 

centrifugal, multi-stage, 797 



pum-pyr 



INDEX. 



qua-rea 



1509 



Pumps, centrifugal, relation of 
height of hft to velocity, 797 

centrifugal, tests of, 798, 800, 
802 

circulating, for condensers, 1075 

depth of suction of, 788 

direct-acting, eflEiciency of, 790 

direct-acting, proportion of 
steam cyUnder, 790 

electric motors for, 1463 

feed, for marine engines, 1076 

gas-engine, 808 

high-duty, 793 

horse-power of, 788 

jet, 807 

leakage, test of, 803 

lift, water raised by, 790 

mine, operated by compressed 
air, 652 

piston speed of, 791, 792 

rotary, 801 

rotary, tests of, 802 

speed of water in passages of, 
790 

steam, sizes of, tables, 789, 791 

suction of, with hot water, 788 

theoretical capacity of, 788 

underwriters', sizes of, 792 

vacuum, 806 

valves of, 792, 793 
Pump-inspection table, 751 
Pumping by compressed air, 645, 
808 (see also Air-lift) 

by gas-engines, cost of, 795 

by steam pumps, cost of fuel 
for, 795 

cost of electric current for, 794 
Pumping-engine, 72,000,000 gal., 
793 

screw, 794 

the d'Auria, 793 
Pumping-engines, duty trials of, 
802-806 

economy of, 794 

high-duty records, 806 

table of data for duty trials of, 
803-805 

use of nozzles to measure dis- 
charge of, 759 
Punches and dies, clearance of, 1321 

spiral, 1322 
Punched plates, strength of, 425 
Punching and drilUng of steel, 483, 

485 
Purification of water, 723-726 
Pyramid, 62 

frustum of, 62 
Pyrometer, air, Wiborgh's, 555 

copper-ball, 553 

fire-clay, Seger's, 555 

Hobson's hot-blast, 555 

Le Chatelier's, 554 

principles of, 549 

thermo-electric, 553 

Uehling-Steinbart, 557 
Pyrometers, graduation of, 554 
Pyrometric telescope, 556 
Pyrometry, 549 



Q 



UARTER-TWIST belt, 1147 
Queen-post truss, inverted, 

stresses in, 544 
truss, stresses in, 543 
Quenching test for soft steel, 507 

RACK, gearing, 1165 
Radian, definition of, 523 
Radiating power of sub- 
stances, 578 
surface, computation of, for 

hot- water heating, 704 
surface, computation of, for 

steam heating, 698 
surface, proportioning pipes for, 
700 
Radiation, black body, 579 
of heat, 578 

of various substances, 578, 595 
Stefan and Boltzmans law, 579 
table of factors for Dulong's 
laws of, 596 
Radiators, experiments with, 697, 
708 
indirect, 698 

overhead steam-pipe, 702 
steam and hot-water, 697 
steam, removal of air from, 

702 
transmission of heat in, 697 
Radius of gyration, 293, 518 
of gyration, graphical method 

for finding, 294 
of gyration of structural shapes, 

293, 294 
of oscillation, 518 
Rails, steel, electric resistance of, 
1416 
steel, specifications for, 508 
steel, strength of, 353 
Railroad axles, effect of cold on, 
465 
steam, electrifications of, table, 

1418 
track, material required for one 

mile of, 244, 245 
trains, resistance of, 1108-1111 
trains, speed of, 1118 
Railway curve, degree of a, 54 
street, compressed -air, 652 
track bolts and nuts, 244, 245 
Railways, electric (see Electric 
railways), 1414 
narrow-gage, 1127 
Ram, hydraulic, SIO 
Rankine cycle efficiency for differ- 
ent conditions, 1091 
cycle, efficiency of, 906, 1089 
Rankine's formula for columns, 

284 
Ratio, 6 

Raw-hide pinions, 1177 
Reactance of alternating currents, 
1441 
in transformers, 1452 
Reaction of a jet. 1385 
Reamers, taper, 1318 
Reaumur thermometer-scale, 549 



1510 



rec-ref 



INDEX. 



ref-riv 



Recalescence of steel, 480 
Receiver-space in engines, 980 
Receivers on steam pipe lines, 884 
Reciprocals of numbers, tables of, 
87-92 
use of, 92 
Recorder, carbon dioxide, or COo, 
890 
continuous, of water or steam 
consumption, 970 
Rectangle, definition of, 54 

value of diagonal of, 54 
Rectangular prismoid, 62 
Rectifier, in absorption refrigerat- 
ing machine, 1346 
mercury arc, 1456 
Reduction, ascending and de- 
scending, 5 
Reese's fusing disk, 1309 
Reflecting power of substances, 

578 
Refrigerating (see also Ice-mak- 
ing), 1336-1367 
air-macliines, 1343 
direct-expansion method, 1365 
Refrigerating - machines, actual 
and theoretical capacity, 1355 
ammonia absorption, 1346, 1364 
ammonia compression, 1345, 

1356 
condensers for, 1353 
cylinder-heating, 1349 
diagrams of, 1348 
dry, wet, and flooded systems, 

1345 
ether-machines, 1343 
heat-balance, 1359 
ice-melting effect, 1343 
liquids for, pressure and boiling 

points of, 1337 
mean effective pressure and 

horse-power, 1350 
operations of, 1336 
performance of, 1364 
pipe-coils for, 1354 
pounds of ammonia per minute, 

1350 
properties of brine, 1343 
properties of vapor, 1337 
quantity of ammonia required 

for, 1351 
rated capacity of, 1353 
relative efficiency of, 1348 
relative performance of am- 
monia-compression and ab- 
sorption macliines, 1347 
sizes and capacities, 1352 
speed of, 1353 
sulphur-dioxide, 1345 
temperature range, 1360 
test reports of, 1358 
tests of, 1355 
using water vapor, 1345 
volumetric efficiency, 1349 
Voorhoes multiple-effect, 1351 
Refrigerating plants, cooling-tower 
practice in, 1354 
systems, efiQciency of, 1349 



Refrigeration, 1336-1367 
a reversed heat cycle, 600 
coohng effect, compressor vol- 
ume, and power required, 
1341 
cubic feet space per ton of, 1368 
means of applying the cold, 
1365 
Regenerator, heat, 1014 
Regnault's experiments on steam, 

870 
Reinforced concrete, working 

stresses of, 1387 
Reluctance, magnetic, 1398, 1430 
Reluctivity, magnetic, 1400 
Reservoirs, evaporation of water 

in, 569 
Resilience, elastic, 274 

of materials, 274 
Resistance, elastic to torsion, 334 
Resistance, electrical (see also 
Electrical resistance), 1400 
effect of anneahng on, 1402 
effect of temperature on, 1402 
in circuits, 1406 
internal, 1408 
of copper wire, 1402, 1404 
of copper wire, rule for, 1406 
of steel, 477 
of steel rails, 1416 
standard of, 1402 
Resistance, elevation of ultimate, 
275 
frictional, of surfaces moved in 

water, 756 
moment of, and section mod- 
ulus, 294, 295 
of metals to repeated shocks, 276 
of sliips, 1369 
of trains, 1108-1111 
tractive, of an electric car, 1415 
work of, of a material, 274 
Resistivity, definition of, 1403 

of copper, 1403, 1406 
Resolution of forces, 513 
Retarded motion, 521 
Reversing-gear for steam-engines, 

dimensions of, 1039 
Rhomboid, definition and area of, 

54 
Rhombus, definition and area of, 

54 
Rivet-iron and steel, shearing re- 
sistance of, 430 
spacing for structural work, 321, 
322 
Rivets, bearing pressure on, 426 
center distances, of staggered, 

322 
cone-head, 239 
diameters of, for riveted joints. 

table, 429 
in steam-boilers, rules for, 913, 

914 
length required for various 

grips, 241 
minimum spacing and clear- 
ance, 322 



riv-rop 



INDEX. 



rop-sca 



1511 



Rivets, oval head, sizes and 
weights, 238 
pitch of, 426 

pressure required to drive, 435 
round head, weight of, 243 
shearing value, area of rivets, 

and bearing value, 240 
steel, chemical and physical 

tests of, 435 
steel, specifications for, 505 
tinners', table, 239 
Riveted iron pipe, dimensions of, 

table, 220 
Riveted joints, 355, 424-435 
British rules for, 433 
drilled, vs. punched holes, 424 
efficiencies of, 428-434, 914 
notes on, 425 

of maximum efficiency, 431 
proportions of, 427-434 
single riveted lap, 427 
table of proportions, 434 
tests of double-riveted lap and 

butt, 429 
tests of, table, 359 
triple and quadruple, 431 
triple, working pressures on 
steam-boilers with, 917 
Riveted pipe, flow of water in, 
734-736 
pipe, weight of sheet steel for, 
221 
Riveting, cold, pressure required 
for, 435 
efficiency of different methods, 

425 
hand and hydraulic, strength of, 

425 
macliines, hydraulic, 814 
of structural steel, 484 
pressure required for, 435 
Roads, resistance of carriages on, 

534 
Rock-drills, air required for, 645 
requirements of air-driven, 645 
Rods of different materials, tables 
for calculating weights of, 181 
Rollers and balls, steel, carrying 
capacity of, 340 
bearings, 1233 

chain and sprocket drives, 1153 
Rolling of steel, effect of finishing 

temperature, 478 
Roof construction, 191-195 
paints, 192 

-truss, stresses in, 547 
Roofs, snow and wind, [loads on, 
191 
strength of, 1389 
Roofing materials and roof con- 
struction, 191-195 
materials, weight of various, 19€ 
Rope-driving, 1214-1218 
English practice, 1218 
horse-power of, 1215 
pulleys for, 1217 
sag of rope, 1216 
tension of rope, 1214 



Rope-driving, weight of rope, 1218 
Ropes and cables, 410-415 

cotton and hemp, strength of, 

357 
cotton, for transmission, 1218 
for hoisting or transmission, 

410-415 
hemp, iron and steel, table of 

strength and weight of, 410 
hoisting {see Hoisting-rope) 
locked-wire, 262 
manila, 411 

manila, data of, 1214-1218 
manila, hoisting and trans- 
mission, Ufe of, 415 
manila, weight and strength of, 

410-415 
splicing of, 412 
table of strength of iron, steel 

and hemp, 410 
taper, of uniform strength, 1208 
technical terms relating to, 411 
wire, "Lang Lay," 254 
wire (see also Wire-rope) 
wire, track cable for aerial tram- 
ways, 260 
Rotary blowers, 677 

steam engines, 1082 
Rotation, accelerated, work of, 

529 
Rubber belting, 1152 
goods, analysis of, 378 
vulcanized, tests of, 378 
Rule of three, 6, 7 
Running fits, 1325 
Rupture, modulus, of, 297 
Russia and planished iron, 473 

SAFETY, factor of, 374-377 
valves for locomotives, 935 
valves for steam-boilers, 
932-935 
valves, spring-loaded, 933 
Sag of v/ires between poles, 1432 
Salt, solubiUty of, 571 

weight of, 180 
Salt-brine manufacture, evapora- 
tion in, 570 
properties of, 570, 571, 1343 
solution, specific heat of, 564 
Sampling coal for analysis, 825 
Sand, cubic feet per ton, 181 

molding, 1256 
Sand-blast, 1309 
Sand-hme brick, tests of, 371 
Sandstone, strength of, 371 
Saturation point of vapors, 604 
Sawdust as fuel, 838 
Sawing metal, 1309 

-machines for metals, 1291 
metals, speeds and feeds for, 1291 
Scale, boiler, 721, 927-932 
boiler, analyses of, 722 
effect of, on boiler efficiency, 928 
removal of, from steam-boilers, 
930 
Scales, thermometer, comparison 
of, 550, 551 



1512 



sca-sha 



INDEX. 



sha-she 



Scantling, table of contents of, 21 
Schiele pivot bearing, 1233 
Schiele's anti-friction curve, 50 
Scleroscope, for testing hardness, 

365 
Screw, 61 

-bolts, efficiency of, 538 

conveyors, 1198 

differential, 540 

efficiency of a, 538 

(element of machine) , 537 

heads, machine, dimensions of, 
237 

-propeller, 1377 

-propeller, coefficients of, 1378 

-propeller, efficiency of, 1379 

-propeller, slip of, 1379 
Screws and nuts for automobiles, 
table, 233 

cap, table of standard, 238 

lag, holding power of, 347 

lag, table of, 241 

machine, A. S. M. E. standard, 
234 

machine, dimensions of, 234-238 

set, table of standard, 238 

wood, 236 

wood, holding power of, 346 
Screw-threads, 231-238 

Acme, 234 

A. S. M. E. standard, table, 237 

British Association standard, 
232 

English or Whit worth standard, 
table, 232 

International (metric) standard, 
232 

hmit gages for, 232 

metric, cutting of, 1261 

standard sizes for bolts and 
taps, 235, 236 

U. S. or Sellers standard, table 
of, 231 
Scrubbers for gas producers, 849 
Sea-water, freezing-point of, 719 
Secant of an angle, 66 

of an arc, 67 
Secants of angles, table of, 170- 

172 
Section modulus of structural 

shapes, 294, 295 
Sector of circle, 60 
Sediment in steam-boilers, 928 
Seger pyrometer cones, 555 
Segment of circle, 60 
Segments, circular, areas of, 121, 

122 
Segregation in steel ingots, 487 
Self-inductance of lines and cir- 
cuits, 1445 
"Semi-steel," 453 
Separators, steam 941 

steam, efficiency of, 941 
Set-screws, dimensions of, 238 

holding power of, 1332 

standard table of, 238 
Sewers, grade of, 757 
Shackles, strength of, 1184 



Shaft bearings, 1034 

bearings, large, tests of, 1230 

couphngs, flange, 1133 

fit, allowances for electrical ma- 
chinery, 1326 

-governors, 1066 

speeds in geometrical progres- 
sion, 1138 
Shafts and bearings of engines, 
1042-1044 

bearings for, 1034 

bending resistance of, 1032 

dimensions of, 1030-1033 

equivalent twisting moment of, 
1032 

fly-wheel, 1033 

hollow, 1133 

hoUow, torsional strength of, 
334 

steam-engine, 1030-1038 

steel propeller, strength of, 354 

twisting resistance of, 1030 
Shafting, 1130-1134 

collars for, 1133 

deflection of, 1131 

formulae for, 1130 

horse-power transmitted by, 
1130 

keys for, 1328 

laying out, 1134 

power required to drive, ] 305 

torsion tests of, 361 
Shaku-do, Japanese alloy, 393 
Shapers, motors required to run, 

1296 
Shapes of test specimens, 280 

structural steel, dimensions and 
weights, 302-305 
Shear and compression combined, 
335 

and tension combined, 335 

poles, stresses in, 542 
Shearing, effect of on structural 
steel, 483 

resistance of rivets, 430 

strength of iron and steel, 362 

strength of rivets, 240 

strength of woods, table, 367 

strength, relation to tensile 
strength, 362 
Sheaves, diameter of, for wire- 
rope, 1211 

for wire-rope transmission, 1208, 
1211 

size of for manila rope, 414 
Sheet aluminum, weight of, 230 

brass, weight of, table, 228 

copper, weight of, 229 

iron and steel, weight of, 183 

metal gage, 28, 29, 31, 32 

metal, weight of, by decimal 
gage, 32 

metals, strength of various, 356 
Sheets (see Plates) 
Shelby cold-drawn tubing, 223 
Shells for steam-boilers, material 
for, 908 

spherical, strength of, 339 



she-sin 



INDEX. 



sin-spe 



1513 



Sherardizing, 474 

Shibu-ichi, Japanese alloy, 393 

Shingles, weights and areas of, 

196 
Ship " Lusitania," performance of, 

1376, 1381 
Ships, Atlantic steam, perform- 
ance of, 1376, 1383 
coefficient of fineness of, 1369 
coefficient of performance, 1370 
coefficient of water lines, 1369 
displacement of, 1369, 1374 
horse-power for given speeds, 

1373 
horse-power of, from wetted 

surface, 1372 
horse-power of internal com- 
bustion engines for, 1374 
horse-power required for, 1373- 

1375 
jet propulsion of, 1384 
relation of horse-power to speed, 

1373, 1376 
resistance of, 1369 
resistance of, per horse-power, 

1373 
resistance of, Rankine's for- 
mula, 1370 
rules for measuring, 1368 
rules for tonnage, 1369 
small sizes, engine power re- 
quired for, 1374 
wetted surface of, 1371 
wetted surface, empirical equa- 
tions for, 1371 
with reciprocating engine, and 
turbine combined, 1383 
Shipbuilding, steel for, 507 
Shipping measure, 19, 1368 
Shocks, resistance of metals to 
repeated, 276 
stresses produced by, 276 
Short circuits, electric, 1411 
Shrinkage fits {see Fits, 1324) 
of alloys, 409 
of castings, 1254 
of cast-iron, 438, 447 
of maUeable iron castings, 455 
strains reUeved by uniform 
cooling, 448 
Sign of differential coefficients, 78 
of trigonometrical functions, 67 
Signs, arithmetical, 1 
Silicon-aluminum-iron alloys, 398 
-bronze, 395 
-bronze wire, 248, 395 
distribution of in pig iron, 448 
excessive, making cast-iron 

hard, 1254 
influence of, on cast-iron, 438, 

447 
influence of, on steel, 476 
Silundum, 1425 

Silver, melting temperature, 554, 
559 
properties of, 179 
Simpson's riile for areas, 56 
Sine of an angle. 66 



Sines of angles, table, 170-172 

Single-phase circuits, 1445 

Sinking fund, 17 

Siphon, 754 

Sirocco fans, 653, 664-666 

Skin effect in alternating currents, 

1442 
Skylight glass, sizes and weights, 

196 
Slag bricks and slag blocks, 268 
in cupolas, 1248 
in wrought iron, 460 
Slate roofing, sizes, areas, and 

weights, 195 
SHde rule, 82 

Slide-valve, cut-off for various laps 
and travels, table, 1060, 1061 
definitions, 1052 
diagrams, 1053-1055 
effect of lap and lead, 1052- 

1057 
lead. 1057 
port opening, 1057 
ratio of lap to travel, 1058 
relative motion of cross-head 

and crank, 1060 
steam-engine, 1052-1062 
Slope, table of, and faU in feet per 

mile, 729 
Slotters, power required to nm, 

1295 
Smoke-prevention, 920-922 
Smoke-stacks, locomotive, 1115 

sheet-iron, 958 
Snow load on roofs, 191 

weight of, 720 
Soapstone lubricant, 1246 

strength of, 371 
Soda mixture for machine tools, 

1246 
Softeners in foimdry practice, 

1253 
Softening of water, 724 
Soils, bearing power of, 1385 

resistance of, to erosion, 755 
Solar engines, 1015 
Solder, brazing, composition of, 
390 
for aluminum, 382, 383 
Solders, composition of various, 

383, 409 
Soldering aluminum-bronze, 397 
Sohd bodies, mensuration of, 61- 
66 
measiu-e, 18 
of revolution, 64 
Solubility of common salt, 571 

of sulphate of hme, 571 
Soot, effect of on boiler tubes, 931 
Sorbite, 480 
Sources of energy, 531 
Specific gravity, 173-175 

and Baume's hydrometer com- 
pared, table, 175 
and strength of cast iron, 452 
of brine, 571 
of cast-iron, 452 
of copper-tin alloys, 384 



1514 



spe-sph 



INDEX. 



sph-sta 



Specific gravity of copper-zinc al- 
loys, 388 

of gases, 176 

of ice, 720 

of liquids, table, 175 

of metals, table, 174 

of steel, 486 

of stones, brick, etc., 177 
Specific heat, 562-565, 720 

determination of, 562 

of air, 562, 614 

of gases, 563, 564 

of ice, 720 

of iron and steel, 562, 563 

of liquids, 563 

of superheated steam 869 

of metals, 562, 563 

of solids, 562, 563 

of saturated steam, 867 

of water, 564, 720 

of woods, 563 
Specifications for boiler-plate, 507 

castings, 441 

cast iron, 441 

chains, 264 

elliptical steel springs, 423 

foundry pig iron, 443 

fuel oil, 843 

galvanized wire, 250 

helical steel springs, 423 

hose, 379 

malleable iron, 457 

metal for cast-iron pipe, 441 

oils, 1242 

petroleum lubricants, 1242 

phosphor-bronze, 395 

purchase of coal, 830 

spring steel, 507 

steel axles, 507, 509 

steel billets, 507 

steel castings, 489, 510 

steel crank-pins, 507 

steel for automobiles, 510 

steel forgings, 506 

steel for ships, 507 

steel rails, 508 

steel rivets, 505 

steel sphce-bars, 509 

steel tires, 509 

structural steel, 504 

tin and terne-plate, 194 

wrought iron, 461, 462 
Speed of cutting, effect of feed and 
depth of cut on, 1264 

of cutting tools, 1258 

vessels, 1373 
Speeds in geometrical progression, 

1307 
Spelter, (see Zinc) 
Sphere, measures of, 62 
Spheres of different materials, table 
for calculating weight of, 181 

table of volumes and surfaces, 
126, 127 
Spherical polygon, area of, 63 

segment, volume of, 64 

shells and domed boiler heads, 
339 



Spherical polygon shells, strength 
of, 339 

shells, thickness of, to resist a 
given pressure, 339 

triangle, area of, 63 

zone, area and volume of, 64 
Spheroid. 64 
Spikes, holding power of, 346 

railroad and boat, 245, 248 

wrought, 245 
Spindle, surface and volume of, 

64, 65 
Spiral. 51, 61 

conical, 61 

construction of, 51 

gears, 1168 

plane, 61 

-riveted pipe-fittings, table, 220 

-riveted pipe, table of, 220 
Sphce-bars, steel, specifications 

for, 509 
Splices, railroad track, tables, 245 
Splicing of ropes, 412 

of wire rope, 263 
Spontaneous combustion of coal, 

832 
Springs, 417-424 

elliptical, sizes of, 423 

elUptical, specifications for, 423 

for engine-governors, 1066-1068 

hehcal, 418-422 

heUcal, formulae for deflection 
and strength, 418 

helical, specification for, 423 

helical, steel, tables of capacity 
and deflection, 418-422 

laminated steel, 417 

phosphor-bronze, 424 

semi-elliptical, 417 

steel, chromium- vanadium, 424 

steel, strength of, 355 

to resist torsion, 423 
Sprocket wheels, 1154, 1156 
Spruce, strength of, 367 
Square, definition of, 54 

measure, 18 

root, 8 

roots of fifth powers, 110 

roots, tables of, 93-108 

side of, equivalent to circle of 
same area, 125 

value of diagonal of, 54 
Squares of decimals, table, 108 

of numbers, table, 93-108 
Squirrel-cage motor, 1463 
Stabihty, 515 

of chimneys, 954 

of dam, 515 
Stand-pipes, 349-351 

at Yonkers, N. Y., 350 

failures of, 350 

guy-ropes for, 349 

heights of, for various diam- 
eters and plates, table, 351 

thickness of plates of, table, 
351 

thickness of side plates, 349 

wind-strain on, 349 



sta-ste 



INDEX. 



ste-ste 



1515 



Star connection, transformers, 

1452 
Statical moment. 515 
Stay-bolt iron, 462 
Stay-bolts in steam-boilers, 916 
Stays, steam-boiler, loads on, 916 

steam-boiler, material for, 908 
Stayed surfaces, strength of, 338 
Steam, 867-885 

boilers {see Steam-boilers below) 

calorimeters, 942-944 

consumption, continuous re- 
corder for, 970 

consumption in engines, Wil- 
lan's law, 991 

determining moisture in, 942- 
945 

-domes on boilers, 918 

-drums, 913 

dry, definition, 867 

dry, identification of, 944 
. energy of, expanded to various 
pressures, 963 

engines (see Steam-engines, be- 
low) 

entropy of, tables, 871-874 

expanding, available energy of, 
870 

expansion of, 959 

fire-engines, capacity and econ- 
omy of, 993, 994 

flow of, 876-882 (see Flow of 
steam) 

gaseous, 870 

generation of, from waste heat 
of coke-ovens, 834 

heat required to generate 1 
pound of, 867 

heating, 694-703 

heating, diameter of supply 
mains, 699, 701 

heating, indirect, 698 

heating of greenhouses, 702 

heating, pipes for, 699-701 

heating, vacuum systems of, 
702 

jackets on engines, 1004 

-jet blower, 679 

-jet exhauster, 679 

-jet ventilator, 679 

latent heat of, 867 

loop, 883 

loss of pressure in pipes, 880 

maximum eflSciency of, in Car- 
not cycle, 881 

mean pressure of expanded, 960 

-metal (bronze alloy), 390, 392 

moisture in, escaping from 
boilers, 945 

pipe coverings, tests of, 584- 
587 

pipes (see Steam-Pipes below) 

ports, area of. 880 

power, cost of, 1009-1011 

receivers on pipe lines, 884 

Regnault's experiments on, 870 

sampling for moisture, 942 

saturated, definition, 867 



Steam, saturated, density, volume 
and latent heat of, 8()9. 871 

saturat(;d, properties of at high 
temperatures, 868 

saturated, properties of, table, 
869, 871-874 

saturated, specific heat of, 867 

saturated, temperature and 
pressure of, 868 

saturated, total heat of, 867 

separators, 941 

separators, efficiency of, 941 

-ships, Atlantic, performances 
of, 1376, 1383 

superheated (see also Super- 
heated steam) 

superheated, definition. 867 

superheated, economy of steam- 
engines with, 998 

superheated, pipes and valves 
for, 882 

superheated, properties of, 870, 
874, 875 

superheated, specific heat of, 869 

superheated, volume of, 869 

temperature of, 867 

vessels (see Ships) 

weight of, per cubic foot, table, 
871 

wet, definition, 867 
Steam-boilers, 885-944 (see also 
Boilers) 

air-leakage in, 891 

braces in 916 

bumped heads, rules for, 914 

combustion space in furnaces 
of, 889 

compounds, 929 

conditions to secure fuel econ- 
omy in, 890, 893 

construction of, 908-918 

corrosion of, 467, 927-932 

curves of performance of, 894, 
895 

dangerous, 932 

domes on, 918 

down-draught furnace for, 919 

effect of rate of driving, 893 

effect of soot on. 931 
Steam-boiler efficiency, at differ- 
ent rates of driving, 898 

computation of, 687, 891 

effect of excess air supply, 896 

effect of imperfect combustion, 
896 

effect of quality of coal, 895 

maximum, 898 

obtained in practice, 897 

relation of, to rate of driving, 
air-supply, etc.. 893 

straight line formula for, 896 
Steam-boilers, evaporative tests 
of, 898, 899-908 

excess air supply to. 896 

explosive energy of. 932 

factors of evaporation, 908-912 

factors of safety of, 918 

feed-pumps for, eflaciency of, 937 



1516 



ste-ste 



INDEX. 



ste-ste 



Steam-boilers, feed- water heaters 
for, 938-940 {see Feed-water 
heaters) 
feed-water, saving due to heat- 
ing of, 938 
flat plates in, rules for, 916 
flues and gas passages, propor- 
tions of, 889 
foaming or priming of, 721, 930 
for blast-furnaces, 899 
forced combustion in, 923 
fuel economizers, 924 
furnace formulae, 917 
furnaces, height of, 889 
fusible plugs in, 918 
grate-surface, 887, 888 
grate-surface, relation to heat- 
ing surface, 887 
gravity feeders, 938 
heating-surface in, 887, 888 
heating-surface, relation of, to 

grate-surface, 887 
heat losses in, 892 
height of chimney for, 948, 950 
high rates of evaporation, 898 
horse-power of, 885 
hydrostatic test of, 918 
imperfect combustion in, 896 
incrustation of, 927-932 
injectors on, 936-938 {see In- 
jectors) 
man-hole openings in, 914 
marine, corrosion of, 930 
measure of duty of, 886 
mechanical stokers for, 918 
moisture in steam escaping 

from, 944 
performance of, 889 
plates, ductility of, 913 
plates, tensile strength of, 908, 

913 
pressure allowable in, 917, 918 
proportions of, 887-889 
proportions of grate- and heat- 
ing-surface for given horse- 
power, 887, 888 
proportions of grate-spacing, 

889 
quench-bend tests of steel for, 

913 
riveting rules for, 914 
safety-valves, 932-935 
safety-valves, discharge of steam 

through, 934 
safety-valves, formulae for, 932 
safety-valves, spring-loaded, 933 
safe working-pressure, 918 
scale compounds, 029 
scale in, 927-932 
sediment in, 928 
shells, material for, 908 
smoke prevention, 920-923 
stay-bolts in, 916 
stays, loads on, 916 
stays, material for, 908 
steel for, 913 

strain caused by cold feed- 
water, 939 



Steam-boilers, strength of, 908- 

918 
strength of circmnferential 

seams, 913 
strength of rivets, 914 
tests, heat-balance in, 907 
tests, rules for, 899-908 
thickness of plates, 913 
tube holes, 916 
tube-plates, rules for, 914 
tube spacing in, 916 
tubes, holding power of, 916 
tubes, iron and steel, 916, 

917 
tubes, material for, 913 
tubes, size of, 917 
use of kerosene in, 929 
use of zinc in, 931 
using waste gases, 898, 899 
working pressures on with triple 

riveted joints, 917 
Steam-engines, 959-1095 

advantages of compounding, 

976 
advantages of high initial and 

low back pressure, 996 
and turbine, best economy of, 

in 1904, 1005 
bearings, size of, 1034 
bed-plates, dimensions of, 1044 
clearance in, 966 
Steam-engines, compound, 976- 

983 
best cylinder ratios, 982 
calculation of cylinders of, 982 
combined indicator diagram, 

979 
cylinder proportions, 980 
economy of, 997 
estimating horse-power of, 971 
formulae for expansion and 

work in, 981 
high-speed, performance of, 

989, 990 
high-speed, sizes of, 989, 990 
non-condensing, efliciency of, 

1000 
receiver, ideal diagram, 977 
receiver space in, 980 
receiver type, 977 
steam-jacketed, performances 

of, 989 
steam-jacketed, test of, 1005 
Sulzer, water-consumption of, 

998 
test of with and without jackets, 

1005 
two-cylinder vs. three-cylinder, 

997 
velocity of steam in passages of, 

986 
water consumption of. 988 
Woolf, ideal diagram, 977 
Steam-engines, compression, ef- 
fect of, 965 
condensers, 1069-1079 {see Con- 
densers) 
connecting-rod ends, 1026 



ste-ste 



INDEX. 



ste-ste 



1517 



Steam-engines, connecting-rods, 
dimensions of, 1025, 1040, 1041 
cost of power from, 1009-1011 
coimterbalancing of, 1008 
crank-angles, table, 1058 
crank-pins ,|dimensions of, 1027, 

1040, 1041 
crank-pins, pressure on, 1028 
crank-pins, strength of, 1027 
cranks, dimensions of, 1027 
crank-shafts, dimensions of, 

1030-1038, 1040, 1041 
crank-shafts, formulae for torsion 

and flexure, 1038 
crank-shafts for triple-expan- 
sion, 1038 
crank-shafts, three-throw, 1038 
cross-head and crank, relative 

motion of, 1060 
cross-head, dimensions of, 1040, 

1041 
cross-head pin, dimensions of, 

1029, 1040, 1041 
cut-off, most economical point 

of, 1009 
cylinder condensation, experi- 
ments on, 967 
cylinder condensation, loss by, 

966 
cylinder, finding size of, 970 
cylinders, dimensions of, 1021, 

1022, 1039, 1041 
cylinders, ratios of, 980, 982, 986 
cylinder-head bolts, size of, 

1022, 1039, 1041 
cylinder-heads, dimensions of, 

1022, 1039 
design, current practice, 1039- 

1041 
dimensions of parts of, 1007, 

1021-1042 
eccentric-rods, dimensions of, 

1039 
eccentrics, dimensions of, 1039 
economic performance of, 987- 
1007 
Steam-engines, economy at vari- 
ous loads and speeds, 992, 993 
effect on of wet steam, 1001 
of in central stations, 992 
of simple and compound com- 
pared, 997 
tests of high speed, 994 
under variable loads, 992 
with superheated steam, 998 
Steam-engines, effect of leakage 
on indicator diagram, 976 
effect on, of moisture in steam, 

1001 
efficiency in thermal units per 

minute, 964 
estimating I.H.P. of single 
cylinder and compound, 970 
exhaust siteam used for heating, 

1009 
expansions in, table, 965 
fly - wheels {see Fly - wheels) , 
1040, 1041, 1044-1052 



Steam-engines, foundations em- 
bedded in air, 1009 
frames, dimensions of, 1044 
friction of, 1238 
governors, fly-ball, 1066 
governors, fly-wheel, 1066 
governors, shaft, 1066 
governors, springs for, 1066- 

1068 
guides, sizes of. 1024 
highest economy of, 1003 
high piston speed in, 995 
high-speed, British, 995 
high-speed CorUss, 995 
high-speed, economy of, 994 
high-speed, performance of, 

988, 989, 992 
high-speed, sizes of, 988-992 
high-speed throtthng, 996 
horse-power constants, 971-974 
indicated horse-power, 970-976 
indicator diagrams, {see Indi- 
cator), 968-976 
indicator rigs, 909 
indicators, errors of, 969 
influence of vacuum and super- 
heat on economy, 1001 
Lentz compound, 997 
limitations of speed of, 995 
link motions, 1062-1065 
mean and terminal pressures, 960 
mean effective pressure, calcula- 
tions of, 961 
measures of duty of. 963 
non-condensing, 998-990 
oil required for, 1245 
pipes for, 879, 1039, 1040 
piston-rings, .size of, 1023 
piston-rod guides, size of, 1024 
piston-rods, fit of, 1024 
piston-rods, size of, 1024, 1040, 

1041 
pistons, clearance of, 1021 
pistons, dimensions of, 1022, 

1040, 1041 
piston-\'^lves, 1061 
prevention of vibration in. 1008 
proportions, current practice, 

1039-1041 
proportions of, 1021 — 1042 
quadruple-expansion, 986 
quadruple, performance of, 1003 
Rankine cycle efficiencies, 906 
ratio of cylind<T capacity in 

compound marine, 9S0 
ratio of expansion in, 9(i2 
reciprocating parts, weight of, 

1040, 1041 
relative cost of, 1011 
reversing gear, dimensions of, 

1039 
rolling-mill, sizes of, 1008 
rotary, 1082 
rules for tests of, 1015 
setting the valves of, 1061 
shafts and bearings (see Snafts) , 

1030-1033, 1040, 1041 
single-cylinder, economy of, 987 



1518 



ste-ste 



INDEX. 



ste-ste 



Steam - engines , single - cylinder, 
high-speed, sizes and perform- 
ance of, 989 

single-cylinder, water consump- 
tion of, 987-1007 

slide valves (see Slide Valves), 
1053-1055 

small, coal consumption of, 993 

small, water consumption of, 992 

Sulzer compound and triple- 
expansion, 998 

superheated steam in, 998 

steam consumption of differ- 
ent types, 999 

steam-jackets, influence of, 1004 

steam-turbines and gas-engines 
compared, 1013 

Stumpf uniflow, 997 

test of with superheated steam, 
998 

three-cyhnder, 1038 

to change speed of, 1066 

to put on center, 1061 
Steam-engines, triple-expansion, 
983-986 

crank-shafts for, 1038 

cylinder proportions, 983-985 

cylinder ratios, 986 

high-speed, sizes and perform- 
ances of, 990, 991 

non-condensing, 990 

sequence of cranks in, 986 

steam- jacketed, performance of, 
990, 991 

theoretical mean effective pres- 
sures, 984 

types of, 986 

water consumption of, 998 
Steam-engines, using superheated 
steam, 998-1002 

use of reheaters in, 1004 

valve-rods, dimensions of, 1038 

Walschaerts valve-gear, 1064 

water consumption of, 967, 975, 
987-1006 

water consumption from indi- 
cator-cards, 975 

with variable loads, wasteful. 964 

with sulphur-dioxide adden- 
dum, 1007 

wrist-pin, dimensions of, 1029 
Steam-pipes, 882-885 

copper, strength of, 882 

copper, tests of, 882 

failures of, 882 

for engines, 879 

for marine engines, 880 

proportioning for minimum loss 
by radiation and friction, 880 

riveted-steel, 883 

uncovered, loss from, 884 

underground, condensation in, 
884 

valves in, 883 

wire-wound, 882 
Steam turbines, 1083-1095 

and gas-engine, combined plant 
of, 1014 



Steam turbines and steam-engines 

compared, 1005, 1092 
effect of pressure, vacuum and 

superheat, 1090 
effect of vacuum on, 1088 
efficiency of, 1087 
heat consumption of ideal 

engine, 1091 
Impulse and reaction, 1082, 

1087 
low-pressure, 1069 
low - pressure, combined with 

high - pressure reciprocating 

engine, 1383 
most economical vacuum for, 

1075 
Rankine cycle ratio of, 1089 
reduction gear for, 1095 
speed of the blades, 1086 
steam consumption of, 1088, 

1092 
testing oil for, 1244 
tests of, 1088 
theory of, 1084 

using exhaust, from reciprocat- 
ing engines, 1093, 1383 
30,000 K.W., 1092 
Steel, 475-511 

analyses and properties of, 476 
and iron, classification of, 436 
alloy, heat treatment of, 502- 

504 
aluminum, 496 
annealing of, 484, 492 
axle, effect of heat treatment 

on, 479 
axles, specifications for, 507, 

509 
axles, strength of, 354 
bars, effect of nicking, 485 
beams, safe load on, 298 
bending tests of, 478 
Bessemer basic, ultimate 

strength of, 476 
Bessemer, range of strength of, 

478 
blooms, weight of, table, 190 
bridge-links, strength of, 353 
brittleness due to heating, 483 , 
burning carbon out of, 485 t 

burning, overheating, and re- 
storing, 481 
Campbell's formulae for strength 

of, 477 
castings, 489, 510 
castings, specifications for, 489, 

510 
castings, strength of, 355 
cementation or case-hardening 

of, 1291 
chrome, 496 

chromium-vanadium, 500-502 
chromium-vanadium spring, 424 
cold-drawn, tests of, 361 
cold-rolled, tests of, 361 
color-scale for tempering, 493 
comparative tests of large and 

small pieces, 480 



ste-ste 



INDEX. 



ste-ste 



1519 



steel, copper-, 499 
corrosion of, 467, 468 
crank-pins, specifications for, 

507 
critical point in heat treatment 

of, 480 
crucible, 475, 490-494 
crucible, analyses of, 490, 494 
crucible, effect of heat treat- 
ment, 481, 491 
crucible, selection of grades of, 

490 
crucible, specific gravities of, 

490 
dangerous, containing mangan- 
ese sulphide, 486 
effect of annealing, 479 
effect of annealing on grain of, 

479 
effect of annealing on magnetic 

capacity, 483 
effect of cold on strength of, 464 
effect of finishing temperature 

in rolling, 478 
effect of heating, 481 
effect of heat on grain, 479, 491 
effect of oxygen on strength of, 

477 
effect of vibration and load on, 

278 
electric conductivity of, 477 
endurance of, under repeated 

stresses, 487 
expansion of, by heat, 566 
eye-bars, test of, 360 
failures of, 486 
fatigue resistance of, 500 
fire-box, homogeneity test for, 

508 
fluid-compressed, 488 
for bridges, specifications of, 

504, 505 
for car-axles, specifications, 507, 

509 
for different uses, analyses of, 

505-510 
forgings, annealing of, 482 
forgings, oil-tempering of, 482 
forgings, specifications for, 506 
for rails, specifications, 508 
for ships, specifications of, 507 
for steam boilers, 913 
hardening of soft, 479 
Harveyizing, 1291 
heating in a lead bath, 492 
heating in melted salts by an 

electric current, 492 
heating of, for forging, 492 
heat treatment of Cr-Va steel, 

502 
high carbon, resistance of, to 

shock, 277 
high-speed tool, 494 
high-speed tool, emery wheel 

for grinding, 1263, 1314 
high-speed tool, Taylor's experi- 
ments, 1261 
high-speed tool, tests of, 1269 



Steel, high-strength, for shipbuild- 
ing, 507 

ingots, segregation in, 487 

hfe of, under shock, 276 

low strength of, 477 

low strength of, due to insufia- 
cient work, 478 

manganese, 494 

manganese, resistance to abra- 
sion of, 495 

manufacture of, 475 

melting temperature of, 555 

mixture of, with cast iron, 
453 

Mushet, 490 

nickel, 497 

nickel, tests of, 497 

nickel- vanadium, 499 

of different carbons, uses of, 494 

open-hearth, range of strength 
of, 478 

plates (see Plates, steel) 

quench-bend tests of, for boilers, 
913 

rails, electric resistance of, 1416 

rails, specifications for, 508 

rails, strength of, 353 

range of strength in, 478 

recalescence of, 480 

relation between chemical com- 
position and physical char- 
acter of, 476 

rivet, shearing resistance of, 430 

rivets, specifications for, 505 

shearing strength of, 362 

sheets, weight of, 183 

soft, quenching test for, 507 

specific gravity of, 486 

specifications for, 504-511 

splice-bars, specifications for, 
509 

spring, strength of, 355 

springs (see Springs, steel) 

static and dynamic properties 
of, 500 

strength of, Campbell's formulae 
for, 477 

strength of, Kirkaldy's tests, 
353 

strength of, variation in, 478 
Steel, structural, anneaHng of, 484 

effect of punching and shearing, 
483 

punching of, 483 

punching and drilling of, 485 

riveting of, 484 

shapes, properties of, 305-321 

specifications for, 504 

treatment of, 483-485 

upsetting of, 484 

welding of, forbidden, 484 
Steel struts, formulae for, 285 

tempering of, 493 

tensile strength of, at high 
temperatures, 463 

tensile strength of, pure, 477 

tires, specifications for, 509 

tires, strength of, 354 



1520 



ste-str 



INDEX. 



str-str 



Steel tool, composition and heat 
treatment of, 1265 
tool, heating of. 492 
tool, high-speed, 1265 
tmigsten, 496 

used in automobile construc- 
tion, 510 
very pure, low strength of, 477 
water-pipe, 351 
welding of, 484, 498 
wire gage, tables, 30 
w^orking of, at blue heat, 482 
working stresses in bridge 
members, 287 
Stefan and Boltzman law of 

radiation, 579 
Stellite, alloy for cutting tools, 

1269 
Sterro metal, 393 
St. Gothard tunnel, loss of pres- 
sure in air-pipes in, 620 
Stoker, Riley, 919 

Taylor gravity underfeed, 919 
Stokers, mechanical, for steam- 
boilers, 918 
underfeed, 919 
Stone-cutting with wire, 1309 
strength of, 357, 370 
weight and specific gravity of, 
table, 177 
Storage batteries, 1425-1428 
batteries, Edison alkaline, 1428 
batteries, rules for care of, 1427 
of steam heat, 927, 1014 
Storms, pressure of wind in, 627 
Stove foundries, cupola charges 

in, 1250 
Stoves, for heating compressed- 
air, eflaciency of, 641 
Straight-Une formula for columns, 
285 
formula for boiler efficiency, 896 
Strain and stress, 272 
Strand, steel wire, for guys, 255 
Straw as fuel, 839 
Stream, open, measurement of 

flow, 760 
Streams, fire, 749-752 (see Fire 
streams) 
running, horse-power of, 765 
Street-lighting installations, 1476 

kinds of, 1472 
Strength and specific gravity of 
cast iron, 452 
compressive, 281-283 
compressive, of woods, 368 
loss of, in punched plates, 424 
Strength of aluminum, 381 
aluminum-copper alloys, 396 
anchor forgings, 353 
basic Bessemer steel, 476 
belting, 357 

blocks for hoisting, 1181 
boiler-heads, 337, 338 
boiler-plate at high tempera- 
tures, 463 
bolts, 348 
brick, 358 



Strength of brick and stone, 370- 

372 
bridge-links, 353 
bronze, 356, 384 
canvas, 357 
castings, 352 
cast iron, 444-447 
cast-iron beams, 451 
cast-iron columns, 289 
cast-iron cylinders, 452 
cast-iron flanged fittings, 452 
cast iron, relation to size of bar, 

444 
cast-iron water-pipes, 196, 452 
cement mortar, 372 
chain cables, tables, 264, 265 
chains, table, 264, 265 
chalk. 371 

columns, 283-293, 1389 
copper at high temperatures, 

368 
copper plates, 356 
copper-tin alloys, 385 
copper-tin-zinc alloys, graphic 

representation, 388 
copper-zinc alloys, 388 
cordage, table, 410. 415, 1218 
crank-pins, 1027 
electro-magnet, 1431 
flagging, 373 
flat plates, 336 
floors, 1390-1393 * 
German silver, 356 
glass, 365 
granite, 357 
gun-bronze, 386 
hand and hydraulic riveted 

joints, 425 
ice, 368 
iron and steel, effect of cold on, 

464 
iron and steel pipe, 363 
lime-cement mortar, 372 
limestone, 371 
locomotive forgings. 353 
Lowmoor iron bars, 352 
malleable iron, 454, 45S 
marble, 357 
masonry materials, 371 
materials, 272-379 
materials, Kirkaldy's tests, 352- 

358 
perforated plates, 425 
phosphor-bronze, 395 
Portland cement, 358 
riveted joints, 359, 424-435 
roof trusses, 547 
rope. 357, 411, 1218 
sandstone, 371 
silicon-bronze wire, 395 
soapstone, 371 
spring steel, 355 
spruce timber, 367 
stayed surfaces, 338 
steam-boilers, 908-918 
steel axles, 354 
steel castings. 355 
steel, formulae for, 476, 477 



str-sul 



INDEX. 



sul-tay 



1521 



strength of steel propeller-shafts, 
354 
steel rails, 353 
steel tires, 354 
structural shapes, 305-321 
timber, 368 
twisted iron, 280 
unstayed surfaces, 337 
various sheet metals, 356 
welds, 264, 355 
wire, 357, 358 

wire and hemp rope, 356, 357 
wrought-iron columns, 285 
yellow pine, 368 
zinc plates, 370 
Strength, range of, in steel, 478 
shearing, of iron and steel, 

362 
shearing, of woods, table, 367 . 
tensile, 278 
tensile, of iron and steel at high 

temperatures, 463 
tensile, of pure steel, 477 
torsional, 334 
transverse, 297-300 
Stress and strain, 272 

due to temperature, 335 
Stresses allowed in bridge mem- 
bers, 287 
combined, 335 
effect of, 272 

in framed structiu-es, 541-548 
in plating of bulkheads, etc., 

due to water-pressure, 338 
in steel plating due to water 

pressure, 338 
produced by shocks, 276 
Structural materials, permissible 
stresses in, 1387, 1388 
shapes, elements of, 294 
shapes, moment of inertia of, 

295 
shapes, radius of gyration of, 

295 
shapes, steel (see Steel, struc- 
tural, also Beams, angles, 
etc.) 
steel shapes, dimensions and 

weights, 302-305 
steel shapes, properties of, 305- 

321 
work, rivet spacing for, 321, 322 
Structures, framed, stresses in, 

541-548 
Strut, moving, 536 
Struts, steel, formulae for, 285 
strength of, 283 
wrought-iron, formulae for, 285 
Stub gear teeth, 1167 
Stud bolts, 237 
Stumpf uniflow engine, 997 
Suction lift of pumps, 788 
Sugar manufacture, 839 
Sugar solutions, concentration of, 

572 
Sulphate of lime, solubility of, 571 
Sulphur-dioxide refrigerating-ma- 
chine, 1345 



Sulphur - dioxide - addendum to 
steam-engine, 1007 
dioxide, properties of, 1338 
influence of, on cast iron, 438 
influence of, on steel, 476 
Sum and difference of angles, 

functions of, 68 
Sun, heat of, as a source of power, 

1015 
Superheated steam, economy of 
steam-engines with, 998 
steam, effect of on steam con- 
sumption, 998 
steam, practical application of, 
1002 
Superheating, economy due to, 
1006 
in locomotives, 1126 
Surface condensers, 1069 

of sphere, table, 126, 127 
Surfaces of geometrical sohds, 61- 
66 
of revolution, quadrature of, 

77 
unstayed flat, 337 
Suspension cableways, 1205 
Sweet's slide-valve diagram, 1054 
Symbols, chemical, 173 

electrical, 1477 
Synchronous converters, 1453 
generators, 1448, 1453 
-motor, 1463 

T -CONNECTIONS, trans- 

formers, 1452 
T-shapes, properties of Car- 
negie steel, table, 313-315 
T-slots, T-bolts and T-nuts, 1321 
Tackle, hoisting, 1182 
Tackles, rope, efficiency of, 415 
Taggers, tin, 192 

Tail-rope, system of haulage, 1203 
Tanbark as fuel, 838 
Tangent of an angle, 66 
Tangents of angles, table of, 170- 

172 
Tangential or impulse water 

wheels, tables of, 779 
Tanks and cisterns, number of 
barrels in, 134 
capacities of, tables, 132-134 
with flat sides, plating and 
framing for, 339 
Tap-drills, sizes of, 235, 236, 1320 

for pipe taps, 201 
Taper pins, 1321 

to set in a lathe, 1261 
Tapers, Jarno, 1319 

Morse, 1319 
Tapered wire rope, 1208 
Taps, A. S. M. E. standard, 235, 

236 
Tapping and threading, speeds 

for, 1290 
Taylor's experiments on cutting 
tools of high-speed steel, 1261 
Taylor's rules for belting, 1143 
Taylor's theorem, 78 



1522 



tay-thr 



INDEX. 



thr-too 



Taylor -White high-speed tools, 

cutting speeds of, 1266 
Teeth of gears, forms of, 1 162-1 167 
of gears, proportions, 1159, 
1161 
Telegraph poles, tubular, 206 

-wire, tests of, table, 250 
Telpherage, 1196 
Temperature, absolute, 567 

and humidity, comfortable, 685 
coeflScient of resistance of 

copper, 1403 
conversion table, 552 
determination of by color, 558 
determinations of melting- 
points, 554, 559 
effect of on strength, 368, 463- 

465 
-entropy diagram, 600 
-entropy diagram of water and 

steam, 602 
of fire, 817, 818 
rise of, in combustion of gases, 

818 
stress due to, 335 
Temper carbon, in cast-iron, 439 
Tempering, effect of, on steel, 493 
oil, of steel forgings, 482 
steel, change of shape due to, 
1291 
Tenacity of different metals, 180 
of metals at various tempera- 
tures, 368, 463-465 
Tensile strength (see Strength) 
strength, increase of, by twist- " 

ing, 280 
tests, precautions in making, 

279 
tests, specimens for, 280 
Tension and flexure, combined, 335 

and shear, combined, 335 
Terne-plate, or roofing tin, 193 
Terra cotta, weight of, 196 
Tests, compressive (see Compres- 
sive strength) 
of steam-boilers, rules for, 899- 

908 
of steam-engines, rules for, 1015 
of strength of materials (see 

Strength) 
quench-bend, of steel 913 
tensile (see Strength and Ten- 
sile strength) 
Thermal capacity, 562 
storage, 927, 1014 
units, 560 
Thermit process, 401 

welding process, 488 
Thermodynamics, 597-603 

laws of, 598 
Thermometer, air, 557 

centigrade and Fahrenheit com- 
pared, tables, 550 
Threads, pipe, standard, 201, 217 
Threading and parting tools, 
speed of, 1268 
and tapping, speeds for, 1290 
pipe, force required for, 363 



Three-phase circuits, 1445 

transmission, rule for sizes of 
wires, 1459 
Throttle valves, size of, 880 
Thrust bearings, 1232 
Tides, utilization of power of, 787 
Ties, railroad, required per mile 

of track, 245 
Tiles, weight of, 196 
Timber (see also Wood) 

beams, safe loads, 1387, 1393 
beams, strength of, 368 
expansion of, 367 
measure, 20 
preservation of, 368 
strength of, 368-369 
table of contents in feet, 21 
to compute volume of square, 
21 
Time, measures of, 20 
Tin, alloys of (see Alloys) 
lined iron pipe, 227 
plates, 192-194 
properties of, 179 
Tires, locomotive, shrinkage fits, 
1324 
steel, friction of on rails, 1219 
steel, specifications for, 509 
steel, strength of, 354 
Titanium, additions to cast-iron, 
439, 451 
-aluminum alloy, 401 
Tobin bronze, 392 
Toggle-joint, 536 
Tonnage of vessels, 1369 
Tons per mile, equivalent of, in 

lbs. per yard, 27 
Tools, cutting, durabihty of, 1268 
cutting, effect of feed and depth 

of cut on speed of, 1264 
cutting, in small shops, best 

method of treatment, 1268 
cutting, interval between grind- 

ings of, 1264 
cutting, pressure on, 1264 
cutting, use of water on, 1264 
economical cutting speed of, 

1268 
forging and grinding of, 1263 
high speed, table of cutting 

speeds, 1266 
machine (see Machine tools) 
parting and thread -cutting, 

speed of, 1268 
standard planing, 1271 
Tool-steel (see also Steel) 
best quality, 1265 
high-speed, composition and 
heat-treatment of, 1265 
* high-speed, new (1909), tests of, 
1269 
high-speed, Taylor's experi- 
ments, 1265 
in small shops, best treatment 

of, 1268 
of different qualities, 1268 
Toothed- wheel gearing, 539, 1157- 
1180 



tor-tri 



INDEX. 



tro-uni 



1523 



Torque computed from watts and 
revolutions, 1436 
liorse- power and revolutions, 

1436 
of an armature, 1435 
Torsion and compression com- 
bined, 335 
and flexure combined, 335 
elastic resistance to, 334 
of shafts, 1030, 1130 
tests of shafting, 361 
Torsional strength, 334 
Track bolts, 244, 245 

spikes, 245 
Tractive force of locomotive, 1112 
Tractrix, Schiele's anti-friction 

curve, 50 
Train resistance, electric cars, 1415 

loads, average, 1125 
Trains, railroad, resistance of, 
1108 
railroad, speed of, 1187 
Trammels, to describe an ellipse 

with, 45 
Tramways, compressed-air, 652 

wire-rope, 1204 
Transformers, constant current, 
1453 
electrical, 1451 
eflSciency of, 1451 
primary and secondary of, 1451 
Transmission, compressed-air (see 
Compressed-air) 
electric, 1410, 1457 
electric, area of wires, 1410, 1457 
electric, economy of, 1411 
electric, efficiency of, 1411 
electric, weight of copper for, 

1411, 1457 
electric, wire table for, 1413, 1457 
hydraulic-pressure (see Hydrau- 
lic-pressure transmission) 
of heat (see Heat) 
of power by wire-rope (see 

Wire-rope), 1208-1213 
pneumatic postal, 1201 
rope (see Rope-driving) 
rope, iron and steel, 256, 257 
wire-rope (see Wire-rope) 
Transporting power of water, 755 
Transverse strength, 297-300 
Trapezium and Trapezoid, 54 
Trapezoidal rule, 56 
Triangles, mensuration of, 54 
problems in, 41 
solution of, 69 
spherical, 63 
Trigonometrical computations by 
slide rule, 83 
formulae, 68 

functions, logarithmic, 167 
functions, table, 170-172 
Trigonometry, 66-70 
Triple effect evaporators, 570 
Triple-expansion engine (see 

Steam-engines) 
Triple-riveted joints, working 
pressures on boilers with, 917 



Troostite, 480 

Trough plates, properties of, 308 
Troy weight, 19 

Trusses, bridge, stresses in, 543- 
547 

roof, stresses in, 547 
Tubes (see also Pipe) 

aluminum 226 

aluminum bronze, 397 

boiler (see Steam-boiler tubes) 

boiler, table, 204 

boiler, used as columns, 336 

brass, seamless, 224, 225 

collapse of, formula? for, 341-344 

collapse of, tests of, 341-344 

collapsing pressure of, table, 
334 

copper, 225 

expanded, holding power of, 364, 
916 

lead and tin, 227 

of different materials, weight 
of, 181 

seamless, 222-225 

steel, cold-drawn, Shelby, 223 

surface per foot of length, 224 
Tube-plates, steam-boiler, rules 

for, 914 
Tube-spacing in steam-boilers, 

916 
Tungsten and aliuninum alloy, 
399 

electric lamps, 1473 

steel, 496 
Turbines, steam (see Steam- 
turbines) 

fall-increaser for, 778 

of 13,500 H.P., 778 

rating and efficiency of, 774 

wheel tables, 772, 776, 777 

wheels, 768-777 

wheels, proportions of, 768-772 

wheels, tests of, 773 
Turf or peat, as fuel, 838 
Turnbuckles, 243 
Tuyeres for cupolas, 1247 
Twist-drill (see Drills) 

and steel wire gages, 1286 

gage, table, 30 

sizes and speeds, 1285 
Twisted steel bars, strength of, 

280 
Two-phase currents, 1445 
Type-metal, 408 

UEHLING and Stembart 
pyrometer, 557 
Underwriters' rules for elec- 
trical wiring, 1410 
Unequal arms on balances, 20 
Uniflow steam-engines, Stumpf, 

997 
Unions, pipe fittings, 207 
Unit of evaporation, 886 
of force, 512 
of heat, 560 
of power, 528 
of work, 528 



1524 



uni-Ten 



INDEX. 



ven-wat 



Units, electrical and mechanical, 
equivalent values of, 1399 
electrical, relations of, 1397 
of the magnetic circuit, 1399 
United States, population of, 11 

standard sheet metal gage, 29, 
Unstayed surfaces, strength of, 

337 
Upsetting of structural steel, 484 

V -NOTCH recording water 
meter, 759 
Vacuum at different tem- 
peratures, 788 
drying in, 573 
for turbines, most economical, 

1075 
high, advantage of, 1078 
high, influence of on steam-en- 
gine economy, 1001 
inches of mercm-y and absolute 

pressure, 1071 
pmnps, 806 

systems of steam heating, 702 
Valves and elbows, friction of air 
in, 624 
and fittings, loss of pressure due 

to, 747, 748 
and pipe fittings, description 

and sizes, 206-208 
for superheated steam, 882 
in steam pipes, 883 
pump, 792, 793 
straight-way gate, 217, 218 
Valve-gear, Stephenson, 1062 

Walschaerts, 1064 
Valve-stem or rod, design of (see 

Steam-engines), 1038 
Vanadium-chrome steel, 500-502 
-copper alloys, 395 
effect of on cast iron, 439, 450 
-nickel steels, 499 
steel spring, 424 
Vapor and gases, mixtures of, 604 
pressures of various liquids, 844 
saturation point of, 604 
water, and air mixture, weight 
of, 610-613 
Vapors used in refrigerating, 

properties of, 1341 
Varnishes, 471 
Velocity, angular, 522 

due to falling a given height, 

524 
of gas in chimneys, 951 
parallelogram of, 523 
table of height corresponding 
to a given, 523 
Ventilation (see also Heating and 

Ventilation) 
Ventilating ducts, quantity of air 
carried by, 683 
fans, 653-660, 672 
Ventilation by chimneys, 712 
by steam-jet, 679 
cooling air for, 710 
of mines (see Mine- ventilation) 
of mines, equivalent orifice, 715 



w 



Ventilation problems, standard 

values in, 687 
standards of, 686 
Ventilators, centrifugal for mines, 

672 
Venturi meter, 758 
Versed sine of an arc, 67 

sines, table, 170-172 
Verticals, formulae for strains in, 

545 
Vessels (see also Ships) 

framing of, table, 339 
Vibrations in engines, preventing, 

1008 
Vis- viva, 528 
Volumes of revolution, cubature 

of, 77 
Volt, definition of, 1397 
Voltages used in long-distance 

transmission, 1459 
Vulcanized India rubber, 378 

ALLS of buildings, thick- 
ness of, 1388 
of warehouses, factories, 

etc., 1388 
windows, etc., heat loss through, 

688 
Walschaerts valve-gear, 1064 ] 
Warren girder, stresses in, 546 
Washers, cast and wrought, tables 

of, 242, 243 
Washing of coal, 833 
Water, 716-726 

abrading power of, 755 
amount of to develop a given 

horse-power, 784 
analysis of, 722 
as a lubricant, 1246 
boihng-point at various baro- 
metric pressures, 608 
boiling-point of, 719 
comparison of head in feet with 

various units, 718 
compressibility of, 720 
conduits, long, efficiency of, 766 | 
consumption of locomotives, 

1122 
consumption of steam-engines ' 

(see Steam-engines) 
current motors, 765 
drums for boilers, 913 
erosion and abrading by, 755 
flow of (see Flow of water) 
flowing in a tube, power of, 765 
flowing, measurement of, 757- 

764 
freezing-point of, 719 
frictional resistance of surfaces 

moved in. 756 
-gas, 846, 859-864 
-gas analyses of, 860 
-gas, manufacture of, 859 
-gas plant, efficiency of, 861 
-gas plant, space required for, 

862 
hanuner, 749 
hardness of, 723 



wat-wel 



INDEX. 



wel-wif 



1525 



Water, head of, 718 

heating of, by steam coils, 591 
heat-units per pound of, 717 
horse-power required to raise, 

788 
impurities of, 720 
in pipes, loss of energy in, 812 
jets, vertical, 749 
meter, V-notch recording, 759 
meters, capacity of, 749 
pipe, cast-iron, transverse 

strength of, 452 
pipes, compound with branches, 

746 
-power, 765 

-power,plants, high pressure, 785 
-power, value of, 766 
pressure on vertical surfaces, 

719 
pressLire per square uich, equiv- 
alents of, 27, 718 
pressures and heads, table, 718 
prices charged for in cities, 749 
pumping by compressed air, 808 
Durification of, 723-726 
-softening apparatus, 724 
specific heat of, 564, 720 
total heat and entropy of, 869, 

871-873 
tower {see Stand-pipe) 
tower at Yonkers, N. Y., 350 
transporting power of, 755 
under pressure, energy of, 765 
units of pressure and head, 718 
vapor and air mixture, weight of, 

610-613 
velocity of, in open channels, 

755 
weight at different tempera- 
tures, 716, 717 
weight of one cubic foot, 27 
-wheels, 768 

-wheels, jet, power of, 785 
-wheels, Pelton, 779 
-wheels, tangential, 779 
-wheels, tangential, choice of, 

780 
-wheels, tangential, table, 782 
Waterfall, power of a, 765 
Waves, ocean, power of, 786 
Weathering of coal, 830 
Wedge, 537 
Wedge, volmne of, 62 
Weighing on an incorrect balance, 

20 
Weight and specific gravity of 
materials, 174-177 (see also 
Material in question) 
definition of, 511 
measures of, 19 
Weights and measures, 17-27 
Weir dam measurement, 762 
flow of water over, 762 
trapezoidal, 764 
triangular or V-notch, 759 
Welds, strength of, 355 
Welding by oxy-acetylene flame, 
488 



Welding, electric, 1419 
electric arc, 1419 
of steel, 484, 487 
process, the thermit, 488 
Well, artesian, pumping by com- 
pressed air, 810 
Welsbach gas Ughts, standard 

sizes, 1474 
Wheat, weight of, 180 
Wheel and axle, 539 
Wheels, turbine {see Turbine 

wheel) 
Whipple truss, 544 
White-metal alloys, 407 
Whitworth process of compressing 

steel, 488 
Wiborgh air-pyrometer, 555 
Wild wood pumping-engine, high 

economy of, 805 
Willans law of steam consump- 
tion, 991 
Wmd, 626, 627 
force of, 627 
loads on roofs, 191 
pressure of, in storms, 627 
strain on stand-pipes, 349 
Winding engines {see Hoisting 

engines) 1186 
Wmdlass, 539 

differential, 540 
Windows, loss of heat through, 688 
Windmills, 627-632 

capacity and economy, 627-632 
Wire, aluminum, properties of, 
248, 1414 
almniniun-bronze, 248 
brass, properties of, 248 
brass, weight of, table, 229 
copper, hard-drawn, specifica- 
tion for, 251, 252 
copper, rule for resistance of, 

1406 
copper, stranded, 253 
copper, telegraph and tele- 
phone, 251, 252 
copper, weight of bare and in- 
sulated, 252 
gages, tables, 28 
galvanized, for telegraph and 

telephone lines, 250 
galvanized iron, specifications 

for, 250 
galvanized steel strand, 255 
insulated copper, 252 
nails, 246, 247 
of different metals, 248 
phosphor-bronze, 248 
piano, strength of, 250 
platinum, properties of, 248 
plow steel, 250 
silicon-bronze, 248, 395 
steel, properties of, 249 
stranded feed, table, 253 
telegraph, tests af, 250 
weight per mile-ohm, 250 
-wound fly-wheels, 1052 
Wires of various metals, strength 
of, 358 



1526 



wir-woo 



INDEX. 



Wires, sag of between poles, 1432 
Wire-rope, 253-263 

bending curvature of, 1213 

bending of, 254 

breaking strength of, 254, 1209 

exposure to heat, 256 

extra flexible, 258, 259 

flat, 260, 261 

flattened strand, 258, 261 

flexible hoisting, 258, 259 

galvanized, 255, 262 

galvanized steel hawser, 262 

haulage {see Haulage) 

horse-power transmitted by, 
1210 

iron and steel, table of strength 
of, 261, 410 

locked, 262 

notes on use of, 254, 256 

plow steel, 257-259 

protection of, 256 

radius of curvature of, 1213 

sag or deflection of, 1211 

sheaves for, 1208, 1211 

sphcing of, 263 

steel-clad hoisting, 260 

strength of, 356 

table of strength of, 410 

tapered, 1208 

tramways, 1204 

varieties and uses, 254, 256 
Wire-rope transmission, deflec- 
tion of rope, 1207, 1211 

incUned, 1212 

limits of span, 1212 

long distance, 1212 

of power by, 1208 

sheaves for, 1211 
Wiring rules. Underwriters', 1410 

table for direct currents, 1413 

table for three-phase trans- 
mission lines, 1459 
Wohler's experiments on strength 

of materials, 275 
Wood (see also Timber) 

as fuel, 835, 836 

composition of, 835 

drying of, 368 

expansion of, by heat, 368 

expansion of, by water, 368 

heating value of, 835 

holding power of bolts in, 346 

nail-holding power of, 346, 347 

screws, 236 

screws, holding power of, 346 

strength of. 368, 369 



Wood, strength of, Kirkaldy's 
tests, 358 
weight of, 181 
weight and specific gravity of, 

table, 176 
weight and heating values of, 

835 
weight per cord, 181 
Woods, American shearing 
strength of, 367 
tests of, 366 
Wood- working machinery, power 

required for, 1303 
Wooden fly-wheels, 1051 

stave pipe, 218, 735 
Woodruff key, 1331, 1332 
Woolf compound engines, 977 
Wootten locomotive, 1114 
Work, definition of, 27, 528 
energy, power, 528 
of accelerated rotation, 529 
of acceleration, 529 
of a man, horse, etc., 532-534 
of friction, 1229 
Worm gearing, 540, 1168 
Wrist-pins, dimensions of, 1029 
Wrought-iron, chemical compoii= 
tion of, 460 
effect of roUing on strength of, 

460 
manufacture of, 459 
slag in, 460 

specifications, 461, 462 
strength of, 352, 359, 459-463 
strength of, at high tempera- 
tures, 463 
strength of, Kirkaldy's testL, 
352 

YACHT rigging, galvanized 
steel rope, 255 
Yield point, 273 

Z-BARS, Cameje, proper* 
of, 316 
Zero, absolute, 567, 868 
Zeuner's slide-valve diagram, 1055 
Zinc aUoys (see Alloys) 
plates, strength of, 370 
properties of, 179 
sheet, weight of, table, 228 
use of in steam-boilers, 931 
Zirconia, 270 
Zone of spheroid, 64 
of spindle, 65 
spherical, 64 



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